question_answer 1) Acceleration due to gravity is g on the surface of the earth. Then the value of the acceleration due to gravity at a height of 32 km above earths surface is: (Assume radius of earth to be 6400 km)
A)
0.99 g
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B)
0.8 g
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C)
1.01 g
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D)
0.9 g
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E)
9 g
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question_answer 2) A soap bubble in air (two surfaces) has surface tension\[0.03\text{ }N{{m}^{-1}}\]. Find the gauge pressure inside a bubble of diameter 30 mm.
A)
2 Pa
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B)
4 Pa
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C)
16 Pa
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D)
10 Pa
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E)
8 Pa
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question_answer 3) A piece of ice is floating in a jar containing water. When the ice melts, then the level of water......:
A)
rises
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B)
falls
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C)
remains unchanged
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D)
rises or falls
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E)
cannot say
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question_answer 4) A\[10\text{ }c{{m}^{3}}\]cube floats in water with a height of \[4\text{ }c{{m}^{3}}\]remaining above the surface. The density of the material from which the cube is made is, ......... .
A)
\[0.6\text{ }g\text{ }c{{m}^{-3}}\]
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B)
\[1.0\text{ }g\text{ }c{{m}^{-3}}\]
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C)
\[0.4\text{ }gc{{m}^{-3}}\]
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D)
\[0.24\text{ }gc{{m}^{-3}}\]
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E)
none of these
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question_answer 5) Compressibility of water is\[5\times {{10}^{-10}}{{m}^{2}}/N\]. The change in volume of 100 mL water subjected to\[15\times {{10}^{6}}Pa\]pressure will:
A)
no change
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B)
increase by 0.75 mL
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C)
decrease by 1.50 mL
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D)
increase by 1.50 mL
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E)
decrease by 0.75 mL
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question_answer 6) A wire of length L and area of cross-section A is stretched through a distance x metre by applying a force F along length, then the work done in this process is: (Y is Youngs modulus of the material)
A)
\[\frac{1}{2}(A.L)\left( \frac{Yx}{L} \right)\left( \frac{x}{L} \right)\]
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B)
\[(A.L)(YL)\left( \frac{x}{L} \right)\]
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C)
\[2(A.L)(YL)\left( \frac{x}{L} \right)\]
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D)
\[3(A.L)(YL)\left( \frac{x}{L} \right)\]
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E)
\[4(A.L)(YL)\left( \frac{x}{L} \right)\]
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question_answer 7)
Which of the accompanying P-V diagrams best represent; an isothermal process?
A)
A
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B)
B
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C)
C
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D)
D
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E)
E
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question_answer 8) 800 cc volume of a gas having\[\gamma =\frac{5}{3}\]is suddenly compressed adiabatically to 100 cc. If the initial pressure is P, then the final pressure will
A)
\[\frac{p}{32}\]
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B)
\[\left( \frac{24}{5} \right)p\]
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C)
\[8P\]
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D)
\[\text{32 }P\]
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E)
\[16\text{ }P\]
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question_answer 9) An ice box made of Styrofoam (Thermal conductivity\[=0.01\,J{{m}^{-1}}{{s}^{-1}}{{K}^{-1}})\]is used to keep liquids cool. It has a total wall area including lid of\[0.8\text{ }{{m}^{2}}\]and wall thickness of 2.0 cm. A bottle of water is placed in the box and filled with ice. If the outside temperature is\[30{}^\circ C\] the rate of flow of heat into the box is : (in \[J-{{s}^{-1}}\]):
A)
16
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B)
14
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C)
12
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D)
10
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E)
8
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question_answer 10) The KE and PE of a particle executing SHM of amplitude a will be equal when displacement is:
A)
\[\frac{a}{2}\]
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B)
\[a\sqrt{2}\]
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C)
\[2a\]
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D)
\[\frac{a\sqrt{2}}{3}\]
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E)
\[\frac{a}{\sqrt{2}}\]
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question_answer 11) The equation\[y=A\sin 2\pi \left( \frac{t}{T}-\frac{x}{\lambda } \right),\]where the symbols carry the usual meaning and A, T and \[\lambda \]are positive, represents a wave of:
A)
amplitude 2 A
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B)
period\[T/\lambda \]
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C)
speed \[x\lambda \]
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D)
velocity in negative\[x-\]direction
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E)
speed\[(\lambda /T)\]
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question_answer 12) A particle of mass m moves along x axis with a potential energy represented by\[v(x)=a+b{{x}^{2}}\] where a and b are positive constants. Its initial velocity\[({{v}_{0}})\]is zero when\[x\]is zero. It will execute an SHM with a frequency determined by the value of:
A)
b alone
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B)
a and b
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C)
b and m
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D)
a, b and m
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E)
a, b, m and \[{{v}_{0}}\]
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question_answer 13) A pipe open at both the ends produces a note of fundamental frequency\[{{f}_{1}}\]. When the pipe is kept with\[\frac{3}{4}\]th of its length in water, it produces a note of fundamental frequency\[{{f}_{2}}\]. The ratio of \[\frac{{{f}_{1}}}{{{f}_{2}}}\]is:
A)
\[\frac{4}{3}\]
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B)
\[\frac{3}{4}\]
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C)
\[2\]
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D)
\[\frac{1}{2}\]
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E)
\[\frac{3}{2}\]
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question_answer 14) The potential at a point P which is forming a corner of a square of side 93 mm with charges,\[{{Q}_{1}}=33\text{ }nC,{{Q}_{2}}=-51\text{ }nC,{{Q}_{3}}=47\text{ }nC\] located at the other three comers is nearly:
A)
16 kV
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B)
4 kV
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C)
400V
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D)
160V
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E)
16V
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question_answer 15)
Two equal metal balls are charged to 10 and\[-20\]units of electricity. Then they are brought in contact with each other and then again separated to the original distance. The ratio of magnitudes of the force between the two balls before and after contact is:
A)
\[8:1\]
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B)
\[1:8\]
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C)
\[2:1\]
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D)
\[1:2\]
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E)
\[9:8\]
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question_answer 16) A conductor having a cavity is given a positive charge. Then field strengths\[{{E}_{A}},{{E}_{B}}\]and\[{{E}_{C}}\]at point A (within cavity), at B (within conductor but outside cavity) and C (near conductor) respectively will be:
A)
\[{{E}_{A}}=0,{{E}_{B}}=0,{{E}_{C}}=0\]
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B)
\[{{E}_{A}}=0,{{E}_{B}}=0,{{E}_{C}}\ne 0\]
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C)
\[{{E}_{A}}\ne 0,{{E}_{B}}=0,{{E}_{C}}\ne 0\]
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D)
\[{{E}_{A}}\ne 0,{{E}_{B}}\ne 0,{{E}_{C}}\ne 0\]
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E)
none of the above
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question_answer 17) The electric potential due to a small electric dipole at a large distance r from the centre of the dipole is proportional to:
A)
\[r\]
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B)
\[\frac{1}{r}\]
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C)
\[\frac{1}{{{r}^{5}}}\]
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D)
\[\frac{1}{{{r}^{3}}}\]
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E)
\[\frac{1}{{{r}^{2}}}\]
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question_answer 18)
In the given circuit the equivalent resistance between the points A and B in ohms is ........:
A)
9
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B)
11.6
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C)
14.5
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D)
21.2
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E)
23.4
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question_answer 19) An electric water kettle rated 2.1 kW is filled with 1.5 kg of water at \[20{}^\circ C\]. How many seconds does it take to reach the boiling point of water? Assume that there are no heat losses from the kettle. Specific heat capacity of water is\[4200\,J\,K{{g}^{-1}}{{K}^{-1}}\]:
A)
60
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B)
120
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C)
240
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D)
480
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E)
720
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question_answer 20)
In the electric circuit shown each cell has an emf of, 2V and internal resistance of\[1\,\Omega \]. The external resistance is\[2\,\Omega \]. The value of the current\[I\]is: (in amperes):
A)
2
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B)
1.25
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C)
0.4
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D)
1.2
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E)
0.8
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question_answer 21) An immersion heater with electrical resistance\[7\,\Omega \]. is immersed in 0.1 kg of water at\[20{}^\circ C\]for 3 min. If the flow of current is 4 A, what is the final temperature of the water in ideal conditions? (Specific heat capacity of water\[=4.2\times {{10}^{3}}J\,k{{g}^{-1}}{{K}^{-1}}\]):
A)
\[28{}^\circ C\]
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B)
\[48{}^\circ C\]
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C)
\[52{}^\circ C\]
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D)
\[68{}^\circ C\]
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E)
\[72{}^\circ C\]
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question_answer 22) Heat produced (cals) in a resistance R when a current\[I\]amperes flows through it fort seconds is given by the expression:
A)
\[\frac{{{I}^{2}}Rt}{4.2}\]
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B)
\[\frac{I{{R}^{2}}t}{4.2}\]
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C)
\[\frac{4.2IR}{{{t}^{2}}}\]
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D)
\[\frac{IR{{t}^{2}}}{4.2}\]
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E)
\[\frac{4.5}{{{I}^{2}}Rt}\]
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question_answer 23)
Which of the following graphs represent variation of magnetic field B with distance r for a straight long wire carrying current?
A)
P
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B)
Q
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C)
R
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D)
S
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E)
T
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question_answer 24) The radius of the coil of a TG which has 10 turns is 0.1 m. The current required to produce a deflection of\[60{}^\circ ({{B}_{h}}=4\times {{10}^{-5}}T)\]is:
A)
3 A
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B)
1.1 A
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C)
2.1 A
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D)
1.5 A
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E)
2.6 A
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question_answer 25) If a coil of 40 turns and area\[4.0\text{ }c{{m}^{2}}\]is suddenly removed from a magnetic field, it is observed that a charge of\[2.0\times {{10}^{-4}}C\]flows into the coil. If the resistance of the coil is\[80\,\Omega \], the magnetic flux density in\[Wb/{{m}^{2}}\]is .......
A)
0.5
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B)
1.0
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C)
1.5
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D)
2.0
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E)
5.5
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question_answer 26) The force between two magnetic poles is F. If the distance between the poles and pole strengths of each pole are doubled, then the force experienced is:
A)
\[2F\]
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B)
\[\frac{F}{2}\]
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C)
\[\frac{F}{4}\]
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D)
\[F\]
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E)
\[4F\]
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question_answer 27) A magnet of length 0.1 m and pole strength \[{{10}^{-4}}\]A-m is kept in a magnetic field of \[30\text{ }Wb/{{m}^{2}}\]at an angle\[30{}^\circ \]. The couple acting on it is\[......\times {{10}^{-4}}Nm\] .
A)
7.5
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B)
3.0
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C)
4.5
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D)
6.0
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E)
1.5
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question_answer 28)
A simple pendulum with bob of mass m and conducting wire of length L swings under gravity through an angle\[2\theta \]. The earths magnetic field component in the direction perpendicular to swing is B. Maximum potential difference induced across the pendulum is:
A)
\[2BL\sin \left( \frac{\theta }{2} \right){{(gL)}^{1/2}}\]
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B)
\[BL\sin \left( \frac{\theta }{2} \right)(gL)\]
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C)
\[BL\sin \left( \frac{\theta }{2} \right){{(gL)}^{3/2}}\]
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D)
\[BL\sin \left( \frac{\theta }{2} \right){{(gL)}^{2}}\]
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E)
\[BL\sin \left( \frac{\theta }{2} \right){{(gL)}^{5/2}}\]
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question_answer 29) The maximum value of AC voltage in a circuit is 707 V. Its rms value is:
A)
70.7V
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B)
100 V
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C)
500V
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D)
707V
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E)
7.07V
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question_answer 30) The magnetic flux linked with the coil varies with time as\[\phi =3{{t}^{2}}+4t+9\]. The magnitude of the induced emf at 2 s is:
A)
9V
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B)
16V
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C)
3V
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D)
4V
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E)
6V
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question_answer 31) A 50 mH coil carries a current of 2 A, the energy stored in joule is:
A)
1
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B)
0.05
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C)
10
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D)
0.5
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E)
0.1
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question_answer 32) Band spectrum is also called:
A)
molecular spectrum
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B)
atomic spectrum
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C)
flash spectrum
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D)
line absorption spectrum
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E)
line emission spectrum
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question_answer 33) Velocity of electromagnetic waves in a medium depends upon:
A)
thermal properties of medium
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B)
mechanical and electrical properties of medium
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C)
electrical and magnetic properties of the medium
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D)
mechanical and magnetic properties of the medium
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E)
mechanical properties of the medium
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question_answer 34) A fish at a depth of 12 cm in water is viewed by an observer on the bank of a lake. To what height the image of the fish is raised? (Refractive index of lake water = 4/3)
A)
9 cm
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B)
12 cm
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C)
3.8 cm
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D)
3 cm
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E)
0.75 cm
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question_answer 35) A ray of light is incident at\[50{}^\circ \]on the middle of one of the two mirrors arranged at an angle of\[60{}^\circ \]between them. The ray then touches the second mirror, gets reflected back to the first mirror, making an angle of incidence .....:
A)
\[50{}^\circ \]
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B)
\[60{}^\circ \]
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C)
\[70{}^\circ \]
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D)
\[80{}^\circ \]
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E)
\[90{}^\circ \]
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question_answer 36) A lamp (point source) is hanging along the axis of a circular table of radius r. At what height should the lamp be placed above the table so that the illuminance at the edge of the table is \[\frac{1}{8}\]of that at its centre?
A)
\[\frac{r}{2}\]
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B)
\[\frac{r}{\sqrt{2}}\]
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C)
\[\frac{r}{\sqrt{3}}\]
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D)
\[\frac{r}{\sqrt{7}}\]
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E)
\[\sqrt{3r}\]
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question_answer 37) The focal length\[(f)\]of a spherical (concave or convex) mirror of radius of curvature R is:
A)
\[\frac{R}{2}\]
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B)
\[R\]
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C)
\[\left( \frac{3}{2} \right)R\]
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D)
\[2R\]
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E)
\[\frac{R}{4}\]
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question_answer 38) In a compound microscope, the intermediate image is:
A)
virtual, erect and magnified
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B)
real, erect and magnified
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C)
real, inverted and magnified
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D)
virtual, erect and reduced
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E)
none of the above
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question_answer 39) A ray of light passes through an equilateral prism such that an angle of incidence is equal to the angle of emergence and the latter is equal to\[\frac{3}{4}\]th the angle of prism. The angle of deviation is:
A)
\[45{}^\circ \]
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B)
\[39{}^\circ \]
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C)
\[20{}^\circ \]
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D)
\[30{}^\circ \]
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E)
\[90{}^\circ \]
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question_answer 40) The dispersive power of the material of lens of focal length 20 cm is 0.08. The longitudinal chromatic aberration of the lens is:
A)
0.08 cm
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B)
0.08/20 cm
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C)
0.016 cm
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D)
0.16 cm
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E)
1.6cm
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question_answer 41) A single slit is located effectively at infinity in front of a lens of focal length 1m and it is illuminated normally with light of wavelength 600 nm. The first minima on either side of central maximum are separated by 4 mm. Width of the slit is ......:
A)
0.1 mm
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B)
0.2 mm
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C)
0.3 mm
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D)
0.4 mm
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E)
0.5 mm
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question_answer 42) An electron enters uniform electric field maintained by parallel plates and of value \[EV{{m}^{-1}}\]with a velocity\[v\text{ }m{{s}^{-1}},\]the plates are separated by a distance d metre, then acceleration of the electron in the field is:
A)
\[\frac{Ee}{m}\]
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B)
\[\frac{-Ee}{m}\]
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C)
\[\frac{Ed}{md}\]
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D)
\[Ee\frac{d}{m}\]
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E)
\[\frac{Em}{ed}\]
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question_answer 43) The wavelength of a 1 keV photon is 1.24 nm. The frequency of 1 MeV photon is:
A)
\[1.24\times {{10}^{15}}Hz\]
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B)
\[2.4\times {{10}^{20}}Hz\]
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C)
\[1.24\times {{10}^{18}}Hz\]
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D)
\[2.4\times {{10}^{24}}Hz\]
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E)
\[2.4\times {{10}^{15}}Hz\text{ },\]
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question_answer 44) A photon of energy 8 eV is incident on metal surface of threshold frequency\[1.6\times {{10}^{15}}Hz.\] The kinetic energy of the photoelectrons emitted (in eV): (Take\[h=6\times {{10}^{-34}}J-s\])
A)
1.6
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B)
6
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C)
2
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D)
1.2
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E)
2.6
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question_answer 45) \[{{C}^{14}}\]has half-life 5700 year. At the end of 11400 years, the actual amount left is:
A)
0.5 of original amount
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B)
0.25 of original amount
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C)
0.125 of original amount
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D)
0.0625 of original amount
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E)
0.03125 of original amount
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question_answer 46) The ionization potential of hydrogen is 13.6 V. The energy required to remove an electron from the second orbit of hydrogen is:
A)
3.4 eV
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B)
6.8 eV
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C)
13.6 eV
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D)
1.51 eV
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E)
\[-3.5eV\]
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question_answer 47) As the electron in Bohr orbit of hydrogen atom passes from state\[n=2\]to\[n=1,\]the kinetic energy K and potential energy U change as:
A)
K two-fold, U four-fold
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B)
K four-fold, U two-fold
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C)
K four-fold, U also four-fold
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D)
K two-fold, U also two-fold
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E)
no change in K and U
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question_answer 48) The depletion layer of a p-n junction:
A)
is of constant width irrespective of the bias
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B)
acts like an insulating zone under reverse bias
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C)
has a width that increases with an increase in forward bias
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D)
is depleted of ions
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E)
is n-type material
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question_answer 49)
For the given circuit shown below, to act as full wave rectifier, the AC input should be connected across ...... and ...... and the DC. output would appear across...... and...... .
A)
B and D and A and C
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B)
B and A and C and D
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C)
C and A and B and D
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D)
C and D and B and A
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E)
none of the above
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question_answer 50) A p-type material is electrically .........:
A)
positive
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B)
negative
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C)
neutral
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D)
depends on the concentration of p impurities
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E)
depends on the difference of doping impurities and intrinsic impurities
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question_answer 51) \[Li\]nucleus has three protons and four neutrons. Mass of lithium nucleus is 7.016005 amu. Mass of proton is 1.007277 amu and mass of neutron is 1.008665 amu. Mass defect for lithium nucleus in amu is:
A)
0.04048 amu
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B)
0.04050 amu
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C)
0.04052 amu
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D)
0.04055 amu
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E)
0.04058 amu
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question_answer 52) According to Keplers law of planetary motion if T represents time period and r is orbital radius, then for two planets these are related as:
A)
\[{{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{3}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}\]
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B)
\[{{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{\frac{3}{2}}}=\frac{{{r}_{1}}}{{{r}_{2}}}\]
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C)
\[{{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{4}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{3}}\]
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D)
\[\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{\frac{3}{2}}}\]
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E)
\[{{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{2}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{3}}\]
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question_answer 53) The dimensions of kinetic energy is:
A)
\[[{{M}^{2}}{{L}^{2}}{{T}^{-1}}]\]
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B)
\[[{{M}^{1}}{{L}^{2}}{{T}^{1}}]\]
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C)
\[[{{M}^{1}}{{L}^{2}}{{T}^{-2}}]\]
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D)
\[[{{M}^{1}}{{L}^{2}}{{T}^{-1}}]\]
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E)
\[[{{M}^{2}}{{L}^{2}}{{T}^{-2}}]\]
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question_answer 54) In an experiment to measure the height of a bridge by dropping stone into water underneath if the error in measurement of time is 0.1 s at the end of 2 s, then the error in estimation of height of bridge will be:
A)
0.49 m
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B)
0.98 m
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C)
1.37m
done
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D)
1.96m
done
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E)
2.12m
done
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question_answer 55)
If the figure below represents a parabola, identify the physical quantities representing Y and X for constant acceleration:
A)
\[X=\]time, Y = velocity
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B)
\[X=\]velocity,\[Y=\]time
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C)
\[X=\]time,\[Y=\]displacement
done
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D)
\[X=\]time,\[Y=\]acceleration
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E)
\[X=\]velocity,\[Y=\]displacement
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question_answer 56) A ball which is at rest is dropped from a height h metre. As it bounces off the floor its speed is 80% of what it was just before touching the ground. The ball will then rise to nearly a height:
A)
0.94 h
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B)
0.80 h
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C)
0.75 h
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D)
0.64 h
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E)
0.50 h
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question_answer 57) Two bodies of different masses are dropped from heights of 16 m and 25 m respectively. The ratio of the time taken by them to reach the ground is:
A)
\[\frac{25}{16}\]
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B)
\[\frac{5}{4}\]
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C)
\[\frac{4}{5}\]
done
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D)
\[\frac{16}{25}\]
done
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E)
\[\frac{5}{8}\]
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question_answer 58) The recoil velocity of a 4.0 kg rifle that shoots a 0.050 kg bullet at a speed of\[280\text{ }m{{s}^{-1}}\]is:
A)
\[+3.5\text{ }m{{s}^{-1}}\]
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B)
\[-3.5\text{ }m{{s}^{-1}}\]
done
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C)
\[-\sqrt{(3.5)}\text{ }m{{s}^{-1}}\]
done
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D)
\[+\sqrt{(3.5)}\text{ }m{{s}^{-1}}\]
done
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E)
\[\text{+7 }m{{s}^{-1}}\]
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question_answer 59) A man of height h walks in a straight path towards a lamp post of height H with uniform velocity u. Then the velocity of the edge of the shadow on the ground will be:
A)
\[\frac{hu}{(H-h)}\]
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B)
\[\frac{Hu}{(H+h)}\]
done
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C)
\[\frac{(H-h)}{Hu}\]
done
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D)
\[\frac{(H+h)}{Hu}\]
done
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E)
\[\left( \frac{H+h}{H-h} \right)u\]
done
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question_answer 60) A train of 150 m length is going towards north direction at a speed of\[10\text{ }m{{s}^{-1}}\]. A parrot flies at a speed of \[5\,m{{s}^{-1}}\] towards south direction parallel to the railway track. The time taken by the parrot to cross the train is equal to:
A)
12 s
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B)
8 s
done
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C)
15 s
done
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D)
10 s
done
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E)
5s
done
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question_answer 61) In the motion of a rocket, physical quantity which is conserved is:
A)
angular momentum
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B)
linear momentum
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C)
force
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D)
work
done
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E)
energy
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question_answer 62) An aeroplane is flying horizontally with a velocity of 600 km/h and at a height of 1960 m. When it is vertically above a point A on the ground a bomb is released from it. The bomb strikes the ground at point B. The distance AB is:
A)
1200 m
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B)
0.33 km
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C)
333.3 km
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D)
33 km
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E)
3.33km
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question_answer 63) A 10 kg object collides with stationary 5 kg object and after collision they stick together and move forward with velocity\[4\text{ }m{{s}^{-1}}\]. What is the velocity with which the 10 kg object hit the second one?
A)
\[4\text{ }m{{s}^{-1}}\]
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B)
\[\text{6 }m{{s}^{-1}}\]
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C)
\[\text{10 }m{{s}^{-1}}\]
done
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D)
\[\text{12 }m{{s}^{-1}}\]
done
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E)
\[\text{14 }m{{s}^{-1}}\]
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question_answer 64) When a force is applied on a moving body, its motion is retarded. Then the work done is:
A)
positive
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B)
negative
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C)
zero
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D)
positive and negative
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E)
none of the above
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question_answer 65) Physical independence of force is a consequence of:
A)
third law of motion
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B)
second law of motion
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C)
first law of motion
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D)
all of these laws
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E)
none of the above
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question_answer 66) The kinetic energy of a body becomes four times its initial value. The new momentum will be...............:
A)
same as the initial value
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B)
twice the initial value
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C)
thrice the initial value
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D)
four times the initial value
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E)
half of its initial value
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question_answer 67) An ice cart of mass 60 kg rests on a horizontal snow patch with coefficient of static friction\[\frac{1}{3}\]. Assuming that there is no vertical acceleration, find the magnitude of the maximum horizontal force required to move the ice cart.\[(g=9.8\text{ }m{{s}^{-2}})\]
A)
100 N
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B)
110 N
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C)
209 N
done
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D)
206 N
done
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E)
196 N
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question_answer 68) Moment of a couple is called:
A)
impulse
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B)
couple
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C)
torque
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D)
angular momentum
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E)
none of these
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question_answer 69) A cyclist is moving in a circular track of radius 80 m with a velocity v = 36 km/h. He has to lean from the vertical approximately through an angle: (Take \[g=10\text{ }m{{s}^{-2}})\]
A)
\[{{\tan }^{-1}}(4)\]
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B)
\[{{\tan }^{-1}}\left( \frac{1}{3} \right)\]
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C)
\[{{\tan }^{-1}}\left( \frac{1}{4} \right)\]
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D)
\[{{\tan }^{-1}}(2)\]
done
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E)
\[{{\tan }^{-1}}\left( \frac{1}{8} \right)\]
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question_answer 70) An athlete throws a discus from rest to a final angular velocity of 15 rad/s in 0.270 s before releasing it. During acceleration, discus moves a circular arc of radius 0.810 m. Acceleration of discus before it is released is...... \[m{{s}^{-2}}\].
A)
45
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B)
182
done
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C)
187
done
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D)
192
done
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E)
205
done
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question_answer 71) A motor is rotating at a constant angular velocity of 600 rpm. The angular displacement per second is:
A)
\[\frac{3}{50\pi }rad\]
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B)
\[\frac{3\pi }{50}rad\]
done
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C)
\[\frac{25\pi }{3}rad\]
done
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D)
\[\frac{3\pi }{25}rad\]
done
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E)
\[\frac{50\pi }{3}rad\]
done
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question_answer 72) If the mass of moon is\[\frac{1}{90}\]of earths mass, its radius is\[\frac{1}{3}\]of earths radius and if g is acceleration due to gravity on earth, then the acceleration due to gravity on moon is......:
A)
\[\frac{g}{3}\]
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B)
\[\frac{g}{90}\]
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C)
\[\frac{g}{10}\]
done
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D)
\[\frac{g}{9}\]
done
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E)
\[\frac{g}{8}\]
done
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question_answer 73) The one electron species having ionization energy of 54.4 eV is:
A)
\[H\]
done
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B)
\[H{{e}^{+}}\]
done
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C)
\[{{B}^{4+}}\]
done
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D)
\[L{{i}^{2+}}\]
done
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E)
\[B{{e}^{2+}}\]
done
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question_answer 74) The correct set of quantum numbers (n, I and m respectively) for the unpaired electron of chlorine atom is:
A)
\[2,1,0\]
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B)
\[2,1,1\]
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C)
\[3,1,1\]
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D)
\[3,2,1\]
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E)
\[3,2,-1\]
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question_answer 75) Which of the following contains maximum number of molecules?
A)
100 cc of\[C{{O}_{2}}\]at STP
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B)
150 cc of\[{{N}_{2}}\]at STP
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C)
50 cc of\[S{{O}_{2}}\]at STP
done
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D)
150 cc of\[{{O}_{2}}\] at STP
done
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E)
200 cc of\[N{{H}_{3}}\]at STP
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question_answer 76) Density of a crystal remains unchanged as a result of:
A)
ionic defect
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B)
Schottky defect
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C)
Frenkel defect
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D)
crystal defect
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E)
point defect
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question_answer 77) The numerical value of \[\frac{N}{n}\](where, N is the number of molecules in a given sample of gas and n is the number of moles of the gas) is:
A)
8.314
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B)
\[6.02\times {{10}^{23}}\]
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C)
0.0821
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D)
\[1.66\times {{10}^{-19}}\]
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E)
\[1.62\times {{10}^{-24}}\]
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question_answer 78) The mass of 11.2 L of ammonia gas at STP is:
A)
8.5 g
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B)
85 g
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C)
17 g
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D)
1.7 g
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E)
4.25 g
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question_answer 79) Consider the ion:\[{{K}^{+}},{{S}^{2-}},C{{l}^{-}}\]and\[C{{a}^{2+}}\]. The radii of these ionic species follow the order:
A)
\[C{{a}^{2+}}>{{K}^{+}}>C{{l}^{-}}>{{S}^{2-}}\]
done
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B)
\[C{{l}^{-}}>{{S}^{2-}}>{{K}^{+}}>C{{a}^{2+}}\]
done
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C)
\[C{{a}^{2+}}>C{{l}^{-}}>K>{{S}^{2-}}\]
done
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D)
\[{{K}^{+}}>{{S}^{2-}}>C{{l}^{-}}>C{{a}^{2+}}\]
done
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E)
\[{{S}^{2-}}>C{{l}^{-}}>{{K}^{+}}>C{{a}^{2+}}\]
done
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question_answer 80) Identify the correct statement from below, concerning the structure of\[C{{H}_{2}}=C=C{{H}_{2}}:\]
A)
The molecule is planar
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B)
One of the three carbon atoms is in an\[-s{{p}^{3}}\]hybridized state
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C)
The molecule is non-planar with the two\[C{{H}^{2}}\]groups being in planes perpendicular to each other
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D)
All the carbon atoms are sp-hybridized
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E)
The molecule is bent with the\[CCC\]angle being 120 degrees.
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question_answer 81) Which carbon is more electronegative?
A)
\[s{{p}^{3}}-\]hybridized carbon
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B)
\[sp-\]hybridized carbon
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C)
\[s{{p}^{2}}-\]hybridized carbon
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D)
Always same irrespective of its hybrid state
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E)
None of the above
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question_answer 82) Molecular shapes of\[S{{F}_{4}},C{{F}_{4}},Xe{{F}_{4}}\]are:
A)
the same with 2, 0 and 1 lone pair of electron respectively
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B)
the same with 1, 1 and 1 lone pair of electrons respectively
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C)
different with 0, 1 and 2 lone pair of electrons respectively
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D)
different with 1, 0 arid 2 lone pair of electrons respectively
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E)
different with 2, 0, 1 lone pair of electrons respectively.
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question_answer 83) The statement the relative lowering of the vapour pressure is equal to the ratio of the moles of the solute to the total number of the moles in the solution refers to:
A)
Hesss law
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B)
Daltons law
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C)
Raoults law
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D)
Charles law
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E)
Boyles law
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question_answer 84) Ethylene glycol is added to water as antifreeze. It will:
A)
decrease the freezing point of water in the winter and increase the boiling point of water in the summer
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B)
only decrease the freezing point of water
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C)
only increase the boiling point of water
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D)
be used for cleaning the radiator in a car
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E)
prevent corrosion of automobile parts
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question_answer 85) The enthalpy of a monoatomic gas at T Kelvin is:
A)
\[\frac{7}{2}RT\]
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B)
\[\frac{3}{2}RT\]
done
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C)
\[\frac{1}{2}RT\]
done
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D)
\[\frac{1}{2}m{{v}^{2}}\]
done
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E)
\[\frac{5}{2}RT\]
done
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question_answer 86) The enthalpy change for the transition of liquid water to steam is\[40.8\text{ }kJ\text{ }mo{{l}^{-1}}\]at 373 K. What is the entropy of vaporization of water?
A)
209.4
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B)
109.4
done
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C)
\[-109.4\]
done
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D)
\[-209.4\]
done
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E)
250.4
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question_answer 87) The dissociation constant of acetic acid\[{{K}_{a}}\]is \[1.74\times {{10}^{-5}}\]at 298 K. The pH of a solution of 0.1 M acetic acid is:
A)
2.88
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B)
3.6
done
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C)
4.0
done
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D)
1.0
done
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E)
2.0
done
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question_answer 88) 0.365 g of HCl gas was passed through 100 \[c{{m}^{3}}\]of\[0.2\text{ }M\text{ }NaOH\]solution. The pH of the resulting solution would be:
A)
1
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B)
5
done
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C)
8
done
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D)
9
done
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E)
13
done
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question_answer 89) In the given reaction, \[2X(g)+Y(g)2Z(g)+80\,kcal.,\] Which combination of pressure and temperature will give the highest yield of Z at equilibrium?
A)
1000 arm and \[200{}^\circ C\]
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B)
500 atm and\[500{}^\circ C\]
done
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C)
1000 atm and \[100{}^\circ C\]
done
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D)
500 atm and \[100{}^\circ C\]
done
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E)
1000 atm and\[500{}^\circ C\]
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question_answer 90) If three Faradays of electricity is passed through the solutions of\[AgN{{O}_{3}},CuS{{O}_{4}}\]and \[AuC{{l}_{3}},\]the molar ratio of the cations deposited at the cathodes will be:
A)
\[1:1:1\]
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B)
\[1:2:3\]
done
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C)
\[3:2:1\]
done
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D)
\[6:3:2\]
done
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E)
\[2:3:1\]
done
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question_answer 91) \[E_{Cu}^{o}=0.34\,V,\,E_{Zn}^{o}=0.76\,V\]. A Daniel cell contains\[0.1M\text{ }ZnS{{O}_{4}}\]solution and 0.01M \[CuS{{O}_{4}}\]solution at its electrodes. EMF of the cell is:
A)
1.10V
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B)
1.04V
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C)
1.16V
done
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D)
1.07V
done
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E)
1.00V
done
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question_answer 92)
The data for the reaction\[A+B\to C\] Ex. \[{{\mathbf{[A]}}_{\mathbf{0}}}\] \[{{\mathbf{[B]}}_{\mathbf{0}}}\] Initial rate 1. 0.012 0.035 0.10 2. 0.024 0.070 0.80 3. 0.024 00.035 0.10 4. 0.012 0.070 0.80
The rate law corresponds to the above data is:
A)
rate \[=k{{[B]}^{3}}\]
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B)
rate \[=k{{[B]}^{4}}\]
done
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C)
rate \[=k[A]{{[B]}^{3}}\]
done
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D)
rate\[=k{{[A]}^{2}}{{[B]}^{2}}\]
done
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E)
rate \[=k{{[A]}^{3}}[B]\]
done
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question_answer 93) A radioactive isotope has a half-life of 8 days. If today 125 mg is left over. What was its original weight 32 days earlier?
A)
6g
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B)
5g
done
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C)
4g
done
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D)
2g
done
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E)
1g
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question_answer 94) On addition of 1 mL solution of\[10%\text{ }NaCl\]to 10 mL gold solution in the presence of 0.025 g of starch, the coagulation is prevented because starch has the following gold numbers:
A)
25
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B)
0.025
done
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C)
0.25
done
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D)
2.5
done
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E)
0.0025
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question_answer 95) IUPAC name of acraldehyde is:
A)
but-3-en-l-al
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B)
propenyl aldehyde
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C)
but-2-ene-l-al
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D)
propanal
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E)
prop-2-en-l-al
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question_answer 96) In Lassaignes test, a blue colour is obtained if the organic compound contains nitrogen. The blue colour is due to:
A)
\[{{K}_{4}}[Fe{{(CN)}_{6}}]\]
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B)
\[F{{e}_{4}}{{[Fe{{(CN)}_{6}}]}_{3}}\]
done
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C)
\[N{{a}_{3}}[Fe{{(CN)}_{6}}]\]
done
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D)
\[C{{u}_{2}}[Fe{{(CN)}_{6}}]\]
done
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E)
\[N{{a}_{2}}[Fe{{(CN)}_{2}}NO]\]
done
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question_answer 97) A molecule of urea can show:
A)
chain isomerism
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B)
position isomerism
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C)
geometrical isomerism
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D)
optical isomerism
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E)
tautomerism
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question_answer 98) Which of the following compounds will exhibit cis-trans isomerism?
A)
2-butene
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B)
2-butyne
done
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C)
2-butanol
done
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D)
Butanone
done
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E)
Butanol
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question_answer 99) Propyne when passed through a hot iron tube at\[400{}^\circ C\]produces:
A)
benzene
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B)
methyl benzene
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C)
dimethyl benzene
done
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D)
trimethyl benzene
done
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E)
polypropene
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question_answer 100) The presence of\[A{{g}^{+}}\]ion increases the solubility of alkenes due to the formation of:
A)
\[d\pi -d\sigma \]bonding
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B)
\[p\sigma -p\pi \]bonding
done
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C)
\[p\pi -d\pi \]bonding
done
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D)
\[p\pi -d\sigma \]bonding
done
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E)
none of the above
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question_answer 101) Glycerine contains:
A)
\[1{}^\circ \]carbon
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B)
\[2{}^\circ \]carbon
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C)
\[3{}^\circ \]carbon
done
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D)
both\[1{}^\circ \]and\[2{}^\circ \]carbon
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E)
both\[2{}^\circ \]and\[3{}^\circ \]carbon
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question_answer 102) Which of the following reacts fastest with a mixture of anhydrous\[ZnC{{l}_{2}}\]and cone.\[HCl\]?
A)
Trimethyl carbinol
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B)
Ethanol
done
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C)
Propanol
done
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D)
Methanol
done
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E)
Isopropanol
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question_answer 103) Which of the following compounds would have the smallest value for\[p{{K}_{a}}\]?
A)
\[CH{{F}_{2}}C{{H}_{2}}C{{H}_{2}}COOH\]
done
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B)
\[C{{H}_{3}}C{{H}_{2}}C{{F}_{2}}\,COOH\]
done
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C)
\[C{{H}_{2}}FCHFC{{H}_{2}}COOH\]
done
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D)
\[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}COOH\]
done
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E)
\[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}COOH\]
done
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question_answer 104) The reagent with which both acetaldehyde and acetophenone react easily are:
A)
Fehlings solution
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B)
Schiffs reagent
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C)
Tollens reagent
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D)
sodium bisulphite
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E)
2, 4-dinitrophenylhydrazine
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question_answer 105) Aniline first reacts with acetyl chloride producing compound A. A reacts with nitric acid/sulphuric acid mixture and produces compound B, which hydrolyses to compound C. What is the identity of C?
A)
Acetanilide
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B)
p-nitroacetanilide
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C)
p-nitroaniline
done
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D)
Aniline
done
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E)
Sulphanilic acid
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question_answer 106) Aniline on treatment with\[NaN{{O}_{2}}\]in\[HCl\]at \[0{}^\circ C\]followed by treatment with alkaline \[\beta -\]naphthol gives:
A)
a violet solution
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B)
a red solution
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C)
a green solution
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D)
a blue precipitate
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E)
a canary yellow precipitate
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question_answer 107) 2g of aluminium is treated separately with excess of dil.\[{{H}_{2}}S{{O}_{4}}\]and excess of\[NaOH,\]the ratio of volume of hydrogen evolved is:
A)
\[1:1\]
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B)
\[2:3\]
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C)
\[1:2\]
done
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D)
\[2:1\]
done
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E)
\[3:1\]
done
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question_answer 108) Vapour phase refining of nickel is carried out using:
A)
\[{{I}_{2}}\]
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B)
\[C{{l}_{2}}\]
done
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C)
\[HCl\]
done
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D)
\[CO\]
done
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E)
\[NO\]
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question_answer 109) Thomas slag is referred to as:
A)
calcium silicate
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B)
calcium phosphate
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C)
barium phosphate
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D)
strontium silicate
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E)
barium silicate
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question_answer 110) Commercial 11.2 volume\[{{H}_{2}}{{O}_{2}}\]solution has a molarity of:
A)
1.0
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B)
0.5
done
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C)
11.2
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D)
1.12
done
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E)
0.75
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question_answer 111) Which one of the following oxides is amphoteric?
A)
\[MgO\]
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B)
\[CaO\]
done
clear
C)
\[N{{a}_{2}}O\]
done
clear
D)
\[C{{O}_{2}}\]
done
clear
E)
\[ZnO\]
done
clear
View Answer play_arrow
question_answer 112) The main component of glass which gives heat resistance to laboratory glassware is:
A)
\[PbO\]
done
clear
B)
\[MgO\]
done
clear
C)
\[{{B}_{2}}{{O}_{3}}\]
done
clear
D)
\[A{{l}_{2}}{{O}_{3}}\]
done
clear
E)
\[{{P}_{2}}{{O}_{5}}\]
done
clear
View Answer play_arrow
question_answer 113) Each\[BHB\]bridge in\[{{B}_{2}}{{H}_{6}}\]is formed by the sharing of:
A)
2 electrons
done
clear
B)
4 electrons
done
clear
C)
1 electron
done
clear
D)
3 electrons
done
clear
E)
8 electrons
done
clear
View Answer play_arrow
question_answer 114) The characteristic colours given by calcium, strontium and barium in the flame test are respectively:
A)
brick red, apple green, crimson
done
clear
B)
crimson, apple green, brick red
done
clear
C)
crimson, brick red, apple green
done
clear
D)
brick red, crimson, apple green
done
clear
E)
apple green, brick red, crimson
done
clear
View Answer play_arrow
question_answer 115) \[a{{K}_{2}}C{{r}_{2}}{{O}_{7}}+2KCl+c{{H}_{2}}S{{O}_{4}}\xrightarrow{{}}\] \[xCr{{O}_{2}}C{{l}_{2}}+yKHS{{O}_{4}}+z{{H}_{2}}O\]. The above equation balances when:
A)
\[a=2,b=4,c=6\]and \[x=2,y=6,z=3\]
done
clear
B)
\[a=4,b=2,c=6\]and \[x=6,y=2,z=3\]
done
clear
C)
\[a=6,b=4,c=2\]and \[x=6,y=3,z=2\]
done
clear
D)
\[a=1,b=4,c=6\]and \[x=2,y=6,z=3\]
done
clear
E)
\[a=1,b=6,c=4\]and \[x=6,y=2,z=3\]
done
clear
View Answer play_arrow
question_answer 116) Which one of the following pairs of elements is called chemical twins because of their very similar chemical properties?
A)
\[Mn\]and W
done
clear
B)
\[Mo\]and \[Tc\]
done
clear
C)
\[Fe\]and\[Re\]
done
clear
D)
\[Hf\]and\[Zr\]
done
clear
E)
\[Fe\]and \[Co\]
done
clear
View Answer play_arrow
question_answer 117) The pair of\[[Co(S{{O}_{4}}){{(N{{H}_{3}})}_{5}}]Cl\]and\[[CoCl{{(N{{H}_{3}})}_{5}}]S{{O}_{4}}\]constitutes:
A)
optical isomers
done
clear
B)
linkage isomers
done
clear
C)
co-ordination isomers
done
clear
D)
hydrate isomers
done
clear
E)
ionization isomers
done
clear
View Answer play_arrow
question_answer 118) Which one of the following is a copolymer?
A)
Polyethylene
done
clear
B)
Polyvinyl chloride
done
clear
C)
Polytetrafluoroethylene
done
clear
D)
Nylon-6, 6
done
clear
E)
Natural rubber
done
clear
View Answer play_arrow
question_answer 119) \[\alpha \]and\[\beta \]glucose differ in the orientation of \[-OH\] group around:
A)
\[{{C}_{1}}\]
done
clear
B)
\[{{C}_{2}}\]
done
clear
C)
\[{{C}_{3}}\]
done
clear
D)
\[{{C}_{4}}\]
done
clear
E)
\[{{C}_{5}}\]
done
clear
View Answer play_arrow
question_answer 120) Barbituric acid is used as:
A)
an antipyretic
done
clear
B)
an antiseptic
done
clear
C)
an antibiotic
done
clear
D)
an analgesic
done
clear
E)
a tranquilizer
done
clear
View Answer play_arrow
question_answer 121) If\[f(x)=\cos ({{\log }_{e}}x),\]then \[f(x)f(y)-\frac{1}{2}\left[ f\left( \frac{y}{x} \right)+f(xy) \right]\]has the value:
A)
1
done
clear
B)
\[\frac{1}{2}\]
done
clear
C)
\[-2\]
done
clear
D)
0
done
clear
E)
\[-1\]
done
clear
View Answer play_arrow
question_answer 122) If\[y=lo{{g}_{a}}x+lo{{g}_{x}}a+lo{{g}_{x}}x+lo{{g}_{a}}a,\]then\[\frac{dy}{dx}\]is equal to:
A)
\[\frac{1}{x}+x\log a\]
done
clear
B)
\[\frac{\log a}{x}+\frac{x}{\log a}\]
done
clear
C)
\[\frac{1}{x\log a}+x\log a\]
done
clear
D)
\[\frac{1}{x\log a}-\frac{\log a}{x{{(\log x)}^{2}}}\]
done
clear
E)
none of these
done
clear
View Answer play_arrow
question_answer 123) If \[y={{e}^{(1/2)\log (1+{{\tan }^{2}}x)}},\]then\[\frac{dy}{dx}\]is equal to:
A)
\[\frac{1}{2}{{\sec }^{2}}x\]
done
clear
B)
\[{{\sec }^{2}}x\]
done
clear
C)
\[\sec x\tan x\]
done
clear
D)
\[{{e}^{1/2\log (1+{{\tan }^{2}}x)}}\]
done
clear
E)
\[{{e}^{1/2\log (1+{{\tan }^{2}}x)}}.\frac{1}{2}\frac{1}{(1+{{\tan }^{2}}x)}\]
done
clear
View Answer play_arrow
question_answer 124) If\[y={{2}^{x}}{{.3}^{2x-1}},\]then\[\frac{{{d}^{2}}y}{d{{x}^{2}}}\]is equal to:
A)
\[(log\text{ }2)\text{ }(log\text{ }3)\]
done
clear
B)
\[(log\text{ 18})\]
done
clear
C)
\[(log\text{ 1}{{\text{8}}^{2}}){{y}^{2}}\]
done
clear
D)
\[(log\text{ 18})y\]
done
clear
E)
\[{{(log\text{ 18})}^{2}}y\]
done
clear
View Answer play_arrow
question_answer 125) If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing, is:
A)
a constant
done
clear
B)
proportional to the radius
done
clear
C)
inversely proportional to the radius
done
clear
D)
inversely proportional to the surface area
done
clear
E)
proportional to its surface area
done
clear
View Answer play_arrow
question_answer 126) The length of the subtangent to the curve\[{{x}^{2}}+xy+{{y}^{2}}=7\]at\[(1,-3)\]is:
A)
3
done
clear
B)
5
done
clear
C)
\[\frac{3}{5}\]
done
clear
D)
15
done
clear
E)
4
done
clear
View Answer play_arrow
question_answer 127) If \[y=x+{{x}^{2}}+{{x}^{3}}+...\]to \[\infty \]where \[|x|<1,\]then for \[|y|<1,\frac{dx}{dy}\]is equal to:
A)
\[y+{{y}^{2}}+{{y}^{3}}+...to\,\infty \]
done
clear
B)
\[1+y+{{y}^{2}}-{{y}^{3}}+....to\,\infty \]
done
clear
C)
\[1-2y+3{{y}^{2}}-....to\,\infty \]
done
clear
D)
\[1+2y+3{{y}^{2}}+....to\,\infty \]
done
clear
E)
\[y+{{y}^{2}}+{{y}^{3}}-....to\,\infty \]
done
clear
View Answer play_arrow
question_answer 128) Twenty two metres are available to fence a flower bed in the form of a circular sector. If the flower bed should have the greatest possible surface area, the radius of the circle must be:
A)
4m
done
clear
B)
3 m
done
clear
C)
6m
done
clear
D)
7m
done
clear
E)
5m
done
clear
View Answer play_arrow
question_answer 129) If \[y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+........\infty ,}}}\]then\[\frac{dy}{dx}\]is equal to:
A)
\[\frac{\cos x}{2y-1}\]
done
clear
B)
\[\frac{-\cos x}{2y-1}\]
done
clear
C)
\[\frac{\sin x}{1-2y}\]
done
clear
D)
\[\frac{-\sin x}{1-2y}\]
done
clear
E)
\[\frac{2\cos x}{2y-1}\]
done
clear
View Answer play_arrow
question_answer 130) Given\[f(0)=0\]and\[f(x)=\frac{1}{(1-{{e}^{-1/x}})}\]for\[x\ne 0\]. Then only one of the following statements on\[f(x)\]is true. That is\[f(x),\]is:
A)
continuous at\[x=0\]
done
clear
B)
not continuous at\[x=0\]
done
clear
C)
both continuous and differentiable at\[x=0\]
done
clear
D)
not defined at\[x=0\]
done
clear
E)
continuous but not differentiable at\[x=0\]
done
clear
View Answer play_arrow
question_answer 131) \[\underset{x\to 0}{\mathop{\lim }}\,\left[ \frac{{{2}^{x}}-1}{\sqrt{1-x}-1} \right]\]is equal to:
A)
\[{{\log }_{e}}2\]
done
clear
B)
\[{{\log }_{e}}\sqrt{2}\]
done
clear
C)
\[{{\log }_{e}}4\]
done
clear
D)
2
done
clear
E)
\[\frac{1}{2}\]
done
clear
View Answer play_arrow
question_answer 132) The value of\[x\]for which the polynomial\[2{{x}^{3}}-9{{x}^{2}}+12x+4\]is a decreasing function of\[x,\] is:
A)
\[-1<x<1\]
done
clear
B)
\[0<x<2\]
done
clear
C)
\[x>3\]
done
clear
D)
\[1<x<2\]
done
clear
E)
\[1<x<3\]
done
clear
View Answer play_arrow
question_answer 133) \[\int{\frac{({{e}^{x}}+{{e}^{-x}})dx}{({{e}^{x}}+{{e}^{-x}})\log (\cos \,h\,x)}}\]equals to:
A)
\[\log (\tan \,h\,x)+c\]
done
clear
B)
\[2\log ({{e}^{x}}+{{e}^{-x}})+c\]
done
clear
C)
\[2\log ({{e}^{x}}-{{e}^{-x}})+c\]
done
clear
D)
\[2\log [\log ({{e}^{x}}+{{e}^{-x}})]+c\]
done
clear
E)
\[\log [\log (\cos \,h\,x)]+c\]
done
clear
View Answer play_arrow
question_answer 134) If\[\int_{-1/2}^{1/2}{\cos x\log \left( \frac{1+x}{1-x} \right)}dx=k.\log 2,\]then\[k\]equals to:
A)
0
done
clear
B)
\[-1\]
done
clear
C)
\[-2\]
done
clear
D)
\[\frac{1}{2}\]
done
clear
E)
\[-\frac{1}{2}\]
done
clear
View Answer play_arrow
question_answer 135) \[\int_{0}^{\pi /2}{\frac{\cos \theta }{\sqrt{4-{{\sin }^{2}}\theta }}}d\theta \]is equal to:
A)
\[\frac{\pi }{2}\]
done
clear
B)
\[\frac{\pi }{6}\]
done
clear
C)
\[\frac{\pi }{3}\]
done
clear
D)
\[\frac{\pi }{5}\]
done
clear
E)
\[\frac{\pi }{4}\]
done
clear
View Answer play_arrow
question_answer 136) If\[f(x)=cos\text{ }x-co{{s}^{2}}x+co{{s}^{3}}x-...\text{ }to\text{ }\infty ,\]then\[\int{f(x)}\,dx\]equals to:
A)
\[\tan \frac{x}{2}+c\]
done
clear
B)
\[x+\tan \frac{x}{2}+c\]
done
clear
C)
\[x-\frac{1}{2}\tan \frac{x}{2}+c\]
done
clear
D)
\[\frac{x-\tan \frac{x}{2}}{2}+c\]
done
clear
E)
\[x-\tan \frac{x}{2}+c\]
done
clear
View Answer play_arrow
question_answer 137) \[\int_{0}^{1}{\frac{x\,dx}{[x+\sqrt{1-{{x}^{2}}}\sqrt{1-{{x}^{2}}}]}}\]is equal to:
A)
\[0\]
done
clear
B)
\[1\]
done
clear
C)
\[\frac{\pi }{4}\]
done
clear
D)
\[\frac{{{\pi }^{2}}}{2}\]
done
clear
E)
\[\frac{\pi }{2}\]
done
clear
View Answer play_arrow
question_answer 138) The value of \[\int_{0}^{2a}{\frac{f(x)dx}{f(x)+f(2a-x)}}\]is:
A)
\[f(a)\]
done
clear
B)
\[f(2a)\]
done
clear
C)
\[f(0)\]
done
clear
D)
\[2a\]
done
clear
E)
\[a\]
done
clear
View Answer play_arrow
question_answer 139) The value of\[\int_{-\pi /4}^{\pi /4}{{{x}^{3}}{{\sin }^{4}}x\,dx}\]is equal to:
A)
\[\frac{\pi }{4}\]
done
clear
B)
\[\frac{\pi }{2}\]
done
clear
C)
\[\frac{\pi }{8}\]
done
clear
D)
\[0\]
done
clear
E)
\[1\]
done
clear
View Answer play_arrow
question_answer 140) For any positive integer\[n,\int{\frac{dx}{{{x}^{n+1}}+x}}\]is equal to:
A)
\[\frac{1}{n}{{\log }_{e}}({{x}^{n}}+1)+c\]
done
clear
B)
\[\frac{1}{n}{{\log }_{e}}\left( \frac{1}{{{x}^{n}}+1} \right)+c\]
done
clear
C)
\[\frac{1}{n}{{\log }_{e}}\left( \frac{x}{{{x}^{n}}+1} \right)+c\]
done
clear
D)
\[\frac{1}{n+1}{{\log }_{e}}\left( \frac{{{x}^{n}}}{{{x}^{n}}+1} \right)+c\]
done
clear
E)
\[\frac{1}{n}{{\log }_{e}}\left( \frac{{{x}^{n}}}{{{x}^{n}}+1} \right)+c\]
done
clear
View Answer play_arrow
question_answer 141) \[\int{\cos \left[ 2{{\cot }^{-1}}\sqrt{\frac{1-x}{1+x}} \right]}\,dx\]is equal to:
A)
\[\frac{1}{2}{{x}^{2}}+c\]
done
clear
B)
\[\frac{1}{2}\sin \left[ 2{{\cot }^{-1}}\sqrt{\frac{1-x}{1+x}} \right]+c\]
done
clear
C)
\[-\frac{1}{2}{{x}^{2}}+c\]
done
clear
D)
\[\frac{1}{2}x+c\]
done
clear
E)
\[-\frac{1}{2}x+c\]
done
clear
View Answer play_arrow
question_answer 142) The area between the curves\[y=x{{e}^{x}}\]and\[y=x{{e}^{-x}}\]and the line\[x=1,\]in sq unit, is:
A)
\[2\left( e+\frac{1}{e} \right)sq\,unit\]
done
clear
B)
\[0\text{ }sq\text{ }unit\]
done
clear
C)
\[2e\,sq\text{ }unit\]
done
clear
D)
\[\frac{2}{e}\,sq\text{ }unit\]
done
clear
E)
\[2\left( e-\frac{1}{e} \right)\,sq\text{ }unit\]
done
clear
View Answer play_arrow
question_answer 143) If the tangent to the graph function\[y=f(x)\]makes angles\[\frac{\pi }{4}\]and\[\frac{\pi }{3}\]with the\[x-\]axis is at the point\[x=2\]and\[x=4\]respectively, the value of \[\int_{2}^{4}{f(x)}f\,(x)dx:\]
A)
\[f(4)f(2)\]
done
clear
B)
\[f(4)\]
done
clear
C)
\[f(2)\]
done
clear
D)
\[0\]
done
clear
E)
\[1\]
done
clear
View Answer play_arrow
question_answer 144) \[\int_{0}^{\pi /2}{\frac{\cos x}{1+\sin x}dx}\]equals to:
A)
\[log\text{ }2\]
done
clear
B)
\[2log\text{ }2\]
done
clear
C)
\[{{(log\text{ }2)}^{2}}\]
done
clear
D)
\[\frac{1}{2}log\text{ }2\]
done
clear
E)
\[2\text{ }log\text{ }3\]
done
clear
View Answer play_arrow
question_answer 145) The differential equation of all non-horizontal lines in a plane is:
A)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}=0\]
done
clear
B)
\[\frac{dx}{dy}=0\]
done
clear
C)
\[\frac{dy}{dx}=0\]
done
clear
D)
\[\frac{{{d}^{2}}x}{d{{y}^{2}}}=0\]
done
clear
E)
\[\frac{dy}{dx}+x=0\]
done
clear
View Answer play_arrow
question_answer 146) The order and the degree of the differential equation\[\sqrt{y+\frac{{{d}^{2}}y}{d{{x}^{2}}}}=x+{{\left( \frac{dy}{dx} \right)}^{3/2}}\]are:
A)
2, 2
done
clear
B)
2, 1
done
clear
C)
1, 2
done
clear
D)
2, 3
done
clear
E)
3, 2
done
clear
View Answer play_arrow
question_answer 147) The solution of\[2(y+3)-xy\frac{dy}{dx}=0\]with\[y=-2,\]when\[x=1\]is:
A)
\[(y+3)={{x}^{2}}\]
done
clear
B)
\[{{x}^{2}}(y+3)=1\]
done
clear
C)
\[{{x}^{4}}(y+3)=1\]
done
clear
D)
\[{{x}^{2}}{{(y+3)}^{3}}={{e}^{y+2}}\]
done
clear
E)
\[{{x}^{2}}{{(y+3)}^{2}}={{e}^{y+2}}\]
done
clear
View Answer play_arrow
question_answer 148) Let\[f:R\to R\]be a differentiable function and \[f(1)=4.\]Then the value of\[\underset{x\to 1}{\mathop{\lim }}\,\int_{4}^{f(x)}{\frac{2t}{x-1}}dt,\]if \[f(1)=2\]is:
A)
16
done
clear
B)
8
done
clear
C)
4
done
clear
D)
2
done
clear
E)
1
done
clear
View Answer play_arrow
question_answer 149) The solution of\[\frac{dy}{dx}+y\tan x=\sec x\]is:
A)
\[y\text{ }sec\text{ }x=tan\text{ }x+c\]
done
clear
B)
\[y\text{ }tan\text{ }x=sec\text{ }x+c\]
done
clear
C)
\[tan\text{ }x=y\text{ }tan\text{ }x+c\]
done
clear
D)
\[x\text{ }sec\text{ }x=tan\text{ }y+c\]
done
clear
E)
\[x\text{ }tan\text{ }x=y\text{ }tan\text{ }x+c\]
done
clear
View Answer play_arrow
question_answer 150) The solution of\[\frac{dy}{dx}=\frac{ax+h}{by+k}\]represents a parabola, when:
A)
\[a=0,b=0\]
done
clear
B)
\[a=1,b=2\]
done
clear
C)
\[a=0,b\ne 0\]
done
clear
D)
\[a=2,b=1\]
done
clear
E)
\[a=-2,b=-1\]
done
clear
View Answer play_arrow
question_answer 151) The range of the function \[\sin ({{\sin }^{-1}}x+co{{s}^{-1}}x),|x|\le 1\] is:
A)
\[[-1,1]\]
done
clear
B)
\[[1,-1]\]
done
clear
C)
\[\{0\}\]
done
clear
D)
\[\{-1\}\]
done
clear
E)
\[\{1\}\]
done
clear
View Answer play_arrow
question_answer 152) Let\[f:R\to R:f(x)={{x}^{2}}\]and\[g:R\to R:g(x)=x+5,\]then\[gof\]is:
A)
\[(x+5)\]
done
clear
B)
\[(x+{{5}^{2}})\]
done
clear
C)
\[({{x}^{2}}+{{5}^{2}})\]
done
clear
D)
\[{{(x+5)}^{2}}\]
done
clear
E)
\[({{x}^{2}}+5)\]
done
clear
View Answer play_arrow
question_answer 153) If two sets A and B are having 99 elements in common, then the number of elements common to each of the sets\[A\times B\]and\[B\times A\]are:
A)
\[{{2}^{99}}\]
done
clear
B)
\[{{99}^{2}}\]
done
clear
C)
100
done
clear
D)
18
done
clear
E)
9
done
clear
View Answer play_arrow
question_answer 154) Given\[n(U)=20,n(A)=12,n(B)=9,\]\[n(A\cap B)=4,\]where\[U\]is the universal set, A and B are subsets of\[U\]then\[n[(A\cup {{B}^{c}})]\]equals to:
A)
17
done
clear
B)
9
done
clear
C)
11
done
clear
D)
3
done
clear
E)
16
done
clear
View Answer play_arrow
question_answer 155) If\[f:R\to R\]is defined by\[f(x)={{x}^{2}}-6x-14,\] then\[{{f}^{-1}}(2)\]equals to:
A)
{2, 8}
done
clear
B)
\[\{-2,8\}\]
done
clear
C)
\[\{-2,-8\}\]
done
clear
D)
\[\{2,-8\}\]
done
clear
E)
\[\{\phi \}\]
done
clear
View Answer play_arrow
question_answer 156) Two finite sets have m and n elements. The number of elements in the power set of first set is 48 more than the total number of elements in the power set of the second set. Then the value of m and n are:
A)
7, 6
done
clear
B)
6, 3
done
clear
C)
6, 4
done
clear
D)
7, 4
done
clear
E)
3, 7
done
clear
View Answer play_arrow
question_answer 157) \[\tan \left[ i\log \left( \frac{a-ib}{a+ib} \right) \right]\]is equal to:
A)
\[ab\]
done
clear
B)
\[\frac{2ab}{{{a}^{2}}-{{b}^{2}}}\]
done
clear
C)
\[\frac{{{a}^{2}}-{{b}^{2}}}{2ab}\]
done
clear
D)
\[\frac{2ab}{{{a}^{2}}+{{b}^{2}}}\]
done
clear
E)
\[{{a}^{2}}+{{b}^{2}}\]
done
clear
View Answer play_arrow
question_answer 158) The value of\[(2-\omega )(2-{{\omega }^{2}})(2-{{\omega }^{10}})(2-{{\omega }^{11}})\]where\[\omega \]is the complex cube root of unity, is:
A)
49
done
clear
B)
50
done
clear
C)
48
done
clear
D)
47
done
clear
E)
64
done
clear
View Answer play_arrow
question_answer 159) If\[{{z}_{r}}=\cos \left( \frac{\pi }{{{2}^{r}}} \right)+i\sin \left( \frac{\pi }{{{2}^{r}}} \right),\]then\[{{z}_{1}}.{{z}_{2}}.{{z}_{3}}\]upto \[\infty \]equals:
A)
\[-3\]
done
clear
B)
\[-2\]
done
clear
C)
1
done
clear
D)
0
done
clear
E)
1
done
clear
View Answer play_arrow
question_answer 160) The locus of point z satisfying\[\operatorname{Re}\left( \frac{1}{z} \right)=k,\] where k is a non- zero real number, is:
A)
a straight line
done
clear
B)
a circle
done
clear
C)
an ellipse
done
clear
D)
a hyperbola
done
clear
E)
none of these
done
clear
View Answer play_arrow
question_answer 161) The real part of\[{{\left[ 1+\cos \left( \frac{\pi }{5} \right)+i\sin \left( \frac{\pi }{5} \right) \right]}^{-1}}\]is:
A)
\[1\]
done
clear
B)
\[\frac{1}{2}\]
done
clear
C)
\[\frac{1}{2}\cos \left( \frac{\pi }{10} \right)\]
done
clear
D)
\[\frac{1}{2}\cos \left( \frac{\pi }{5} \right)\]
done
clear
E)
\[\frac{1}{2}\sec \left( \frac{\pi }{10} \right)\]
done
clear
View Answer play_arrow
question_answer 162) For\[a\ne b,\]if the equation\[{{x}^{2}}+ax+b=0\]and \[{{x}^{2}}+bx+a=0\]have a common root, then the value of\[a+b\]equals to:
A)
\[-1\]
done
clear
B)
0
done
clear
C)
1
done
clear
D)
2
done
clear
E)
\[-2\]
done
clear
View Answer play_arrow
question_answer 163) If\[\frac{2{{z}_{1}}}{3{{z}_{2}}}\]is a purely imaginary, then\[\left| \frac{{{z}_{1}}-{{z}_{2}}}{{{z}_{1}}+{{z}_{2}}} \right|\]is:
A)
\[\frac{2}{3}\]
done
clear
B)
\[\frac{3}{2}\]
done
clear
C)
\[\frac{4}{9}\]
done
clear
D)
\[1\]
done
clear
E)
\[\frac{9}{4}\]
done
clear
View Answer play_arrow
question_answer 164) Suppose you are appointed to a post carrying a scale of pay of Rs. 800-50-1200-75-2100. The total pay that you would draw in a span of 6 years is (assume that there is no allowance):
A)
Rs. 66660
done
clear
B)
Rs. 66000
done
clear
C)
Rs. 60000
done
clear
D)
Rs. 66600
done
clear
E)
Rs. 66666
done
clear
View Answer play_arrow
question_answer 165) The quadratic equation in\[x\]such that the arithmetic mean of its roots is 5 and geometric mean of the roots is 4, is given by:
A)
\[{{x}^{2}}+20x+16=0\]
done
clear
B)
\[{{x}^{2}}-10x+16=0\]
done
clear
C)
\[{{x}^{2}}+10x+16=0\]
done
clear
D)
\[{{x}^{2}}-10x-16=0\]
done
clear
E)
\[{{x}^{2}}+20x+32=0\]
done
clear
View Answer play_arrow
question_answer 166) If one of the roots of the equation \[{{x}^{2}}+bx+3=0\]is thrice the other, then b is equal to:
A)
\[\pm 3\]
done
clear
B)
\[\pm 2\]
done
clear
C)
0
done
clear
D)
\[\pm 4\]
done
clear
E)
\[\pm 1\]
done
clear
View Answer play_arrow
question_answer 167) If\[\alpha ,\beta \]are the roots of the equation\[(x-a)(x-b)=5,\]then the roots of the equation\[(x-\alpha )(x-\beta )+5=0,\]are:
A)
\[a,5\]
done
clear
B)
\[b,5\]
done
clear
C)
\[a,\alpha \]
done
clear
D)
\[a,\beta \]
done
clear
E)
\[a,b\]
done
clear
View Answer play_arrow
question_answer 168) If\[\alpha ,\beta \]are the roots of the equation \[a{{x}^{2}}+bx+c=0,\]then the value of \[\frac{1}{a\alpha +b}+\frac{1}{a\beta +b}\]equals to:
A)
\[\frac{ac}{b}\]
done
clear
B)
\[1\]
done
clear
C)
\[\frac{ab}{c}\]
done
clear
D)
\[\frac{bc}{a}\]
done
clear
E)
\[\frac{b}{ac}\]
done
clear
View Answer play_arrow
question_answer 169) If the sum of n terms of the series\[{{2}^{3}}+{{4}^{3}}+\]\[{{6}^{3}}\] + ... is 3528, then n equals to:
A)
10
done
clear
B)
7
done
clear
C)
8
done
clear
D)
9
done
clear
E)
6
done
clear
View Answer play_arrow
question_answer 170) If\[1,log4\text{ }({{2}^{1\text{ }-x}}+1),lo{{g}_{2}}({{5.2}^{x}}+1)\]are in AP, then the value of\[x\]is:
A)
\[{{\log }_{2}}\left( \frac{1}{2} \right)\]
done
clear
B)
\[{{\log }_{2}}\left( \frac{5}{2} \right)\]
done
clear
C)
\[{{\log }_{2}}\left( \frac{1}{5} \right)\]
done
clear
D)
\[{{\log }_{2}}\left( \frac{2}{5} \right)\]
done
clear
E)
\[{{\log }_{2}}(5)\]
done
clear
View Answer play_arrow
question_answer 171) Which term of the GP\[3,3\sqrt{3},9....\]is 2187?
A)
15
done
clear
B)
14
done
clear
C)
13
done
clear
D)
19
done
clear
E)
20
done
clear
View Answer play_arrow
question_answer 172) A ball is dropped from a height of 48 m and rebounds\[\frac{2}{3}\]of the distance it falls. If it continues to fall and rebound in this way, the distance that the ball travels before coming to rest is:
A)
144m
done
clear
B)
240m
done
clear
C)
120m
done
clear
D)
96m
done
clear
E)
320m
done
clear
View Answer play_arrow
question_answer 173) The sum of\[{{15}^{2}}+{{16}^{2}}+{{17}^{2}}+.....+{{30}^{2}}\]is equal to:
A)
8840
done
clear
B)
8440
done
clear
C)
8540
done
clear
D)
8450
done
clear
E)
8000
done
clear
View Answer play_arrow
question_answer 174) If\[{{a}_{1}},{{a}_{2}},{{a}_{3}},{{a}_{4}},{{a}_{5}}\]and\[{{a}_{6}}\]are six arithmetic means between 3 and 31, then\[{{a}_{6}}-{{a}_{5}}\]and\[{{a}_{1}}+{{a}_{6}}\]are respectively equals to:
A)
5 and 34
done
clear
B)
4 and 35
done
clear
C)
4 and 34
done
clear
D)
4 and 36
done
clear
E)
6 and 36
done
clear
View Answer play_arrow
question_answer 175) if\[|x|<1,\]then the coefficient of\[{{x}^{n}}\]in \[{{(1+2x+3{{x}^{2}}+4{{x}^{3}}+....)}^{1/2}},\]is:
A)
n
done
clear
B)
\[n+1\]
done
clear
C)
\[-n\]
done
clear
D)
\[-1\]
done
clear
E)
1
done
clear
View Answer play_arrow
question_answer 176) The number of different permutations of the word BANANA is:
A)
6
done
clear
B)
36
done
clear
C)
30
done
clear
D)
60
done
clear
E)
120
done
clear
View Answer play_arrow
question_answer 177) \[^{n}{{p}_{r}}=3024\]and\[^{n}{{C}_{r}}=126\],then r is:
A)
5
done
clear
B)
4
done
clear
C)
3
done
clear
D)
2
done
clear
E)
1
done
clear
View Answer play_arrow
question_answer 178) The rank of the word MOTHER when the letters of the word are arranged alphabetically as in a dictionary, is:
A)
261
done
clear
B)
343
done
clear
C)
309
done
clear
D)
273
done
clear
E)
360
done
clear
View Answer play_arrow
question_answer 179) The sum to n terms of the series\[1+(1+3)+(1+3+9)+(1+3+9+27)+...\]is:
A)
\[\frac{3({{3}^{n}}-1)}{4}-1\]
done
clear
B)
\[\frac{3({{3}^{n}}-1)-2n}{4}\]
done
clear
C)
\[\frac{3({{3}^{n}}-1)-n}{4}\]
done
clear
D)
\[\frac{2n-3({{3}^{n}}-1)}{4}\]
done
clear
E)
\[\frac{3({{3}^{n}}-1)-n}{2}\]
done
clear
View Answer play_arrow
question_answer 180)
Six\[x\]have to be placed in the squares of the figure below, such that each row contains at least one x, this can be done in:
A)
24 ways
done
clear
B)
28 ways
done
clear
C)
26 ways
done
clear
D)
36 ways
done
clear
E)
45 ways
done
clear
View Answer play_arrow
question_answer 181) The sum of the rational terms in the expansion of\[{{(\sqrt{2}+{{3}^{1/5}})}^{10}}\]is:
A)
41
done
clear
B)
32
done
clear
C)
18
done
clear
D)
9
done
clear
E)
82
done
clear
View Answer play_arrow
question_answer 182) Let A and B are two square matrices such that \[AB=A\]and\[BA=B,\]then\[{{A}^{2}}\]equals to:
A)
B
done
clear
B)
A
done
clear
C)
\[I\]
done
clear
D)
0
done
clear
E)
\[{{A}^{-1}}\]
done
clear
View Answer play_arrow
question_answer 183) \[\left| \begin{matrix} x-2 & 2x-3 & 3x-4 \\ x-4 & 2x-9 & 3x-16 \\ x-8 & 2x-27 & 3x-64 \\ \end{matrix} \right|=0,\]then\[x\]is equal to:
A)
\[-2\]
done
clear
B)
3
done
clear
C)
\[-4\]
done
clear
D)
4
done
clear
E)
0
done
clear
View Answer play_arrow
question_answer 184) If\[X=\left[ \begin{matrix} 1 & 1 \\ 1 & 1 \\ \end{matrix} \right],\]then\[{{X}^{n}},\]for \[n\in N,\] is equal to:
A)
\[{{2}^{n-1}}X\]
done
clear
B)
\[{{n}^{2}}X\]
done
clear
C)
\[nX\]
done
clear
D)
\[{{2}^{n+1}}X\]
done
clear
E)
\[{{2}^{n}}X\]
done
clear
View Answer play_arrow
question_answer 185) \[a,b,c\] (all positive) are the p th, q th and r th terms of a geometric progression, then \[\left| \begin{matrix} {{\log }_{e}}a & p & 1 \\ {{\log }_{e}}b & q & 1 \\ {{\log }_{e}}c & r & 1 \\ \end{matrix} \right|:\]
A)
\[pqr\]
done
clear
B)
0
done
clear
C)
\[p+q+r\]
done
clear
D)
\[pq+qr+rp\]
done
clear
E)
\[{{(p+q+r)}^{2}}\]
done
clear
View Answer play_arrow
question_answer 186) If\[\left[ \begin{matrix} 2 & 1 \\ 3 & 2 \\ \end{matrix} \right]A\left[ \begin{matrix} -3 & 2 \\ 5 & -3 \\ \end{matrix} \right]=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right],\]then the matrix A is equal to:
A)
\[\left[ \begin{matrix} 1 & 1 \\ 1 & 0 \\ \end{matrix} \right]\]
done
clear
B)
\[\left[ \begin{matrix} 1 & 1 \\ 0 & 1 \\ \end{matrix} \right]\]
done
clear
C)
\[\left[ \begin{matrix} 1 & 0 \\ 1 & 1 \\ \end{matrix} \right]\]
done
clear
D)
\[\left[ \begin{matrix} 0 & 1 \\ 1 & 1 \\ \end{matrix} \right]\]
done
clear
E)
\[\left[ \begin{matrix} 1 & 1 \\ 1 & 1 \\ \end{matrix} \right]\]
done
clear
View Answer play_arrow
question_answer 187) If a, b, c, d, e and\[f\]are in GP, then the value of \[\left| \begin{matrix} {{a}^{2}} & {{d}^{2}} & x \\ {{b}^{2}} & {{e}^{2}} & y \\ {{c}^{2}} & {{f}^{2}} & z \\ \end{matrix} \right|\]depends on:
A)
\[x\]and y
done
clear
B)
\[x\] and z
done
clear
C)
y and z
done
clear
D)
\[x,y\]and z
done
clear
E)
independent of\[x,y\]and z
done
clear
View Answer play_arrow
question_answer 188) Let \[X=\left[ \begin{matrix} x \\ y \\ z \\ \end{matrix} \right],D=\left[ \begin{matrix} 3 \\ 5 \\ 11 \\ \end{matrix} \right]\]and \[A=\left[ \begin{matrix} 1 & -1 & -2 \\ 2 & 1 & 1 \\ 4 & -1 & -2 \\ \end{matrix} \right],\] if \[X={{A}^{-1}}D,\]then\[X\]is equal to:
A)
\[\left[ \begin{matrix} 1 \\ 0 \\ 2 \\ \end{matrix} \right]\]
done
clear
B)
\[\left[ \begin{matrix} \frac{8}{3} \\ \frac{-1}{3} \\ 0 \\ \end{matrix} \right]\]
done
clear
C)
\[\left[ \begin{matrix} \frac{-8}{3} \\ 1 \\ 0 \\ \end{matrix} \right]\]
done
clear
D)
\[\left[ \begin{matrix} \frac{8}{3} \\ \frac{1}{3} \\ -1 \\ \end{matrix} \right]\]
done
clear
E)
\[\left[ \begin{matrix} \frac{8}{3} \\ \frac{1}{3} \\ 0 \\ \end{matrix} \right]\]
done
clear
View Answer play_arrow
question_answer 189) If\[({{x}_{1}},{{y}_{1}})\]and\[({{x}_{2}},{{y}_{2}})\]are the ends of a focal chord of\[{{y}^{2}}=4ax,\]then\[{{x}_{1}}{{x}_{2}}+{{y}_{1}}{{y}_{2}}\]to:
A)
\[-3{{a}^{2}}\]
done
clear
B)
\[3{{a}^{2}}\]
done
clear
C)
\[-4{{a}^{2}}\]
done
clear
D)
\[4{{a}^{2}}\]
done
clear
E)
\[2{{a}^{2}}\]
done
clear
View Answer play_arrow
question_answer 190) The centre of the ellipse \[9{{x}^{2}}+25{{y}^{2}}-18x-100y-116=0\]is:
A)
(1, 1)
done
clear
B)
\[(-1,\text{ }2)\]
done
clear
C)
\[(-1,\text{ }1)\]
done
clear
D)
(2, 2)
done
clear
E)
(1, 2)
done
clear
View Answer play_arrow
question_answer 191) If\[{{x}_{1}},{{x}_{2}},{{x}_{3}}\]as well as\[{{y}_{1}},{{y}_{2}},{{y}_{3}}\]are in GP with the same common ratio, then the points\[({{x}_{1}},{{y}_{1}}),({{x}_{2}},{{y}_{2}})\]and\[({{x}_{3}},{{y}_{3}})\]:
A)
lie on a parabola
done
clear
B)
lie on an ellipse
done
clear
C)
lie on a circle
done
clear
D)
are the vertices of a triangle
done
clear
E)
lie on a straight line
done
clear
View Answer play_arrow
question_answer 192) The latus rectum of the ellipse \[9{{x}^{2}}+16{{y}^{2}}=144\]is:
A)
\[4\]
done
clear
B)
\[\frac{11}{4}\]
done
clear
C)
\[\frac{7}{2}\]
done
clear
D)
\[\frac{9}{2}\]
done
clear
E)
\[\frac{10}{3}\]
done
clear
View Answer play_arrow
question_answer 193) The distance between the pair of parallel lines \[{{x}^{2}}+4xy+4{{y}^{2}}+3x+6y-4=0\]is:
A)
\[\sqrt{5}\]
done
clear
B)
\[\frac{2}{\sqrt{5}}\]
done
clear
C)
\[\frac{1}{\sqrt{5}}\]
done
clear
D)
\[\frac{\sqrt{5}}{2}\]
done
clear
E)
\[\sqrt{\frac{5}{2}}\]
done
clear
View Answer play_arrow
question_answer 194) The circle\[{{x}^{2}}+{{y}^{2}}+8y-4=0,\]cuts the real circle\[{{x}^{2}}+{{y}^{2}}+gx+4=0,\]orthogonally, if\[g\]is:
A)
any real number
done
clear
B)
for no real value of g
done
clear
C)
\[g=0\]
done
clear
D)
\[g<-2,g>2\]
done
clear
E)
\[g>0\]
done
clear
View Answer play_arrow
question_answer 195) Any point on the hyperbola \[\frac{{{(x+1)}^{2}}}{16}-\frac{{{(y-2)}^{2}}}{4}=1\]is of the form:
A)
\[(4\text{ }sec\theta ,2\text{ }tan\theta )\]
done
clear
B)
\[(4\text{ }sec\theta +1,\text{ }2\text{ }tan\theta -2)\]
done
clear
C)
\[(4\text{ }sec\theta -1,2\text{ }tan\theta -2)\]
done
clear
D)
\[(sec\theta -4,\text{ }tan\theta -2)\]
done
clear
E)
\[(4\text{ }sec\theta -1,\text{ }2\text{ }tan\theta +2)\]
done
clear
View Answer play_arrow
question_answer 196) Equation of the circle passing through the intersection of ellipses \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]and \[\frac{{{x}^{2}}}{{{b}^{2}}}+\frac{{{y}^{2}}}{{{a}^{2}}}=1\]is:
A)
\[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]
done
clear
B)
\[{{x}^{2}}+{{y}^{2}}={{b}^{2}}\]
done
clear
C)
\[{{x}^{2}}+{{y}^{2}}=\frac{{{a}^{2}}{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}\]
done
clear
D)
\[{{x}^{2}}+{{y}^{2}}=1\]
done
clear
E)
\[{{x}^{2}}+{{y}^{2}}=\frac{2{{a}^{2}}{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}\]
done
clear
View Answer play_arrow
question_answer 197) The focus of the parabola\[{{y}^{2}}-x-2y+2=0\]is:
A)
\[\left( \frac{1}{4},0 \right)\]
done
clear
B)
\[(1,2)\]
done
clear
C)
\[\left( \frac{5}{4},1 \right)\]
done
clear
D)
\[\left( \frac{3}{4},1 \right)\]
done
clear
E)
\[\left( \frac{3}{4},2 \right)\]
done
clear
View Answer play_arrow
question_answer 198) The locus of the middle point of the chords of the circle\[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]such that the chords passes through a given point\[({{x}_{1}},{{y}_{1}}),\]is:
A)
\[{{x}^{2}}+{{y}^{2}}-x{{x}_{1}}-y{{y}_{1}}=0\]
done
clear
B)
\[{{x}^{2}}+{{y}^{2}}=x_{1}^{2}+y_{1}^{2}\]
done
clear
C)
\[x+y={{x}_{1}}+{{y}_{1}}\]
done
clear
D)
\[x+y=x_{1}^{2}+y_{1}^{2}\]
done
clear
E)
\[{{x}^{2}}-{{y}^{2}}-x_{1}^{2}-y_{1}^{2}=0\]
done
clear
View Answer play_arrow
question_answer 199) The condition that\[ax+by+c=0\]is tangent to the parabola\[{{y}^{2}}=4ax,\]is:
A)
\[{{a}^{2}}={{b}^{2}}={{c}^{2}}\]
done
clear
B)
\[a=b\]
done
clear
C)
\[{{b}^{2}}=c\]
done
clear
D)
\[{{b}^{2}}=a\]
done
clear
E)
\[{{a}^{2}}=b\]
done
clear
View Answer play_arrow
question_answer 200) Let AB be the intercept of the line\[y=x\]by the circle\[{{x}^{2}}+{{y}^{2}}-2x=0\]. Then the equation of the circle with AB as its diameter is:
A)
\[{{x}^{2}}+{{y}^{2}}-x-y=0\]
done
clear
B)
\[{{x}^{2}}+{{y}^{2}}+x+y=0\]
done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+2(x-y)=0\]
done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-2x+y=0\]
done
clear
E)
\[{{x}^{2}}+{{y}^{2}}+2x-y=0\]
done
clear
View Answer play_arrow
question_answer 201) The locus of the point\[(x,\text{ }y)\]which is equidistant from the points\[(a+b,b-a)\]and \[(a-b,a+b)\]is:
A)
\[ax=by\]
done
clear
B)
\[ax+by=0\]
done
clear
C)
\[bx+ay=0\]
done
clear
D)
\[bx-ay=0\]
done
clear
E)
\[\frac{x}{a}+\frac{y}{b}=1\]
done
clear
View Answer play_arrow
question_answer 202) The equations of the tangents to the circle \[{{x}^{2}}+{{y}^{2}}-6x+4y-12=0\]which are parallel to the line\[4x+3y+5=0\]are:
A)
\[4x+3y+11=0\]and\[4x+3y+8=0\]
done
clear
B)
\[4x+3y-9=0\]and\[4x+3y+7=0\]
done
clear
C)
\[4x+3y+19=0\]and\[4x+3y-31=0\]
done
clear
D)
\[4x+3y-10=0\]and\[4x+3y+12=0\]
done
clear
E)
\[4x+3y+3=0\]and\[4x+3y-1=0\]
done
clear
View Answer play_arrow
question_answer 203) The eccentricity of the hyperbola\[{{x}^{2}}-{{y}^{2}}=2004\]is:
A)
\[\sqrt{3}\]
done
clear
B)
\[2\]
done
clear
C)
\[2\sqrt{2}\]
done
clear
D)
\[\sqrt{2}\]
done
clear
E)
1.5
done
clear
View Answer play_arrow
question_answer 204) The equation of the directrix of\[{{(x-1)}^{2}}=2(y-2)\]is:
A)
\[2y+3=0\]
done
clear
B)
\[2x+1=0\]
done
clear
C)
\[2x-1=0\]
done
clear
D)
\[2y-1=0\]
done
clear
E)
\[2y-3=0\]
done
clear
View Answer play_arrow
question_answer 205) On the ellipse\[4{{x}^{2}}+9{{y}^{2}}=1\]the point at which the tangent are parallel to\[8x=9y\]are:
A)
\[\left( \frac{2}{5},\frac{1}{5} \right)or\left( -\frac{2}{5},-\frac{1}{5} \right)\]
done
clear
B)
\[\left( -\frac{2}{5},\frac{1}{5} \right)or\left( \frac{2}{5},-\frac{1}{5} \right)\]
done
clear
C)
\[\left( -\frac{2}{5},-\frac{1}{5} \right)\]
done
clear
D)
\[\left( -\frac{3}{5},-\frac{2}{5} \right)or\left( \frac{3}{5},\frac{2}{5} \right)\]
done
clear
E)
\[\left( -\frac{3}{5},\frac{2}{5} \right)or\left( \frac{3}{5},-\frac{2}{5} \right)\]
done
clear
View Answer play_arrow
question_answer 206) The line\[x\text{ }cos\alpha +y\text{ }sin\alpha =p\]touches the hyperbola\[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1,\]if:
A)
\[{{a}^{2}}co{{s}^{2}}\alpha -{{b}^{2}}si{{n}^{2}}\alpha ={{p}^{2}}\]
done
clear
B)
\[{{a}^{2}}co{{s}^{2}}\alpha -{{b}^{2}}si{{n}^{2}}\alpha =p\]
done
clear
C)
\[{{a}^{2}}co{{s}^{2}}\alpha +{{b}^{2}}si{{n}^{2}}\alpha ={{p}^{2}}c\]
done
clear
D)
\[{{a}^{2}}co{{s}^{2}}\alpha +{{b}^{2}}si{{n}^{2}}\alpha =p\]
done
clear
E)
\[{{b}^{2}}co{{s}^{2}}\alpha -{{a}^{2}}si{{n}^{2}}\alpha ={{p}^{2}}\]
done
clear
View Answer play_arrow
question_answer 207) If \[\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0},|\overrightarrow{a}|=3,|\overrightarrow{b}|=5\]and \[|\overrightarrow{c}|=7,\]then the angle between a and b is:
A)
\[\frac{\pi }{3}\]
done
clear
B)
\[\frac{\pi }{2}\]
done
clear
C)
\[{{\cos }^{-1}}\left( \frac{2}{225} \right)\]
done
clear
D)
\[\frac{\pi }{4}\]
done
clear
E)
\[\frac{\pi }{6}\]
done
clear
View Answer play_arrow
question_answer 208) The velocity of a boat\[X\]relative to a boat Y is \[5\hat{i}-2\text{ }\hat{j}\]and that of\[Y\]relative to another boat Z is\[9\hat{i}+4\hat{j}\]where\[\hat{i}\]and\[\hat{j}\] are the velocity of k not per hour, east and north respectively. Then the velocity is:
A)
\[\frac{\sqrt{2}}{10}\,knot/h\]
done
clear
B)
\[\frac{10}{\sqrt{2}}\,knot/h\]
done
clear
C)
\[10\sqrt{2}\,knot/h\]
done
clear
D)
\[2\sqrt{10}\,knot/h\]
done
clear
E)
\[10\,knot/h\]
done
clear
View Answer play_arrow
question_answer 209) Two vectors\[\overrightarrow{a}\]and\[\overrightarrow{b}\]of equal magnitude 5 originating from a point and directs respectively towards north-east and north-west. Then the magnitude of \[\vec{a}-\vec{b}\] is:
A)
\[3\sqrt{2}\]
done
clear
B)
\[2\sqrt{3}\]
done
clear
C)
\[2\sqrt{5}\]
done
clear
D)
\[5\sqrt{2}\]
done
clear
E)
\[5\sqrt{3}\]
done
clear
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question_answer 210) The shortest distance from the point\[(1,2,-1)\] to the surface of the sphere\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=24\] is:
A)
\[3\sqrt{6}\] unit
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B)
\[\sqrt{6}\] unit
done
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C)
\[2\sqrt{6}\]unit
done
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D)
2 unit
done
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E)
\[3\sqrt{2}\]unit
done
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question_answer 211) ABCD is a quadrilateral, P, Q are the mid points of\[\overset{\to }{\mathop{BC}}\,\]and\[\overset{\to }{\mathop{AD}}\,\]then\[\overset{\to }{\mathop{AB}}\,+\overset{\to }{\mathop{DC}}\,\]is equal to:
A)
\[3\overset{\to }{\mathop{QP}}\,\]
done
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B)
\[\overset{\to }{\mathop{QP}}\,\]
done
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C)
\[4\overset{\to }{\mathop{QP}}\,\]
done
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D)
\[\frac{\overset{\to }{\mathop{QP}}\,}{2}\]
done
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E)
\[2\overset{\to }{\mathop{QP}}\,\]
done
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question_answer 212) The equation of the plane which bisects the line joining (2, 3, 4) and (6, 7, 8) is:
A)
\[x-y-z-15=0\]
done
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B)
\[x-y+z-15=0\]
done
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C)
\[x+y+z-15=0\]
done
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D)
\[x+\text{ }y+\text{ }z+15=0\]
done
clear
E)
\[x-y-z+\text{ }15=0\]
done
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question_answer 213) If\[\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}\]are the three vectors mutually perpendicular to each other and \[|\overrightarrow{a}|=1,|\overrightarrow{b}|=3\] and\[|\overrightarrow{c}|=5,\]then \[|\overrightarrow{a}-2\overrightarrow{b},\overrightarrow{b}-3\overrightarrow{c},\overrightarrow{c}-4\overrightarrow{a}|\] is equal to:
A)
0
done
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B)
\[-24\]
done
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C)
3600
done
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D)
\[-215\]
done
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E)
360
done
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question_answer 214) The angle between\[\overrightarrow{a}\]and\[\overrightarrow{b}\]is\[\frac{5\pi }{6}\]and the projection of\[\overrightarrow{a}\]in the direction of\[\overrightarrow{b}\]is\[\frac{-6}{\sqrt{3}},\]then \[|\overrightarrow{a}|\]is equal to:
A)
6
done
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B)
\[\frac{\sqrt{3}}{2}\]
done
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C)
12
done
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D)
4
done
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E)
16
done
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question_answer 215) A line makes acute angles of \[\alpha ,\,\beta \] and \[\gamma \] with the co-ordinate axes such that\[cos\alpha \text{ }cos\beta =\] \[cos\beta \text{ }cos\gamma =\frac{2}{9}\] and\[cos\gamma \text{ }cos\alpha =\frac{4}{9},\] then\[cos\alpha +cos\beta +cos\gamma \]is equal to:
A)
\[\frac{25}{9}\]
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B)
\[\frac{5}{9}\]
done
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C)
\[\frac{5}{3}\]
done
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D)
\[\frac{2}{3}\]
done
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E)
\[\frac{3}{5}\]
done
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question_answer 216) A unit vector coplanar with\[\hat{i}+\text{ }\hat{j}+2\hat{k}\]and \[\hat{i}+2\text{ }\hat{j}+\hat{k},\]and perpendicular to\[\hat{i}+\text{ }\hat{j}+\hat{k},\]is:
A)
\[\left( \frac{\hat{j}-\hat{k}}{\sqrt{2}} \right)\]
done
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B)
\[\left( \frac{\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}} \right)\]
done
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C)
\[\left( \frac{\hat{i}+\hat{j}+2\hat{k}}{\sqrt{6}} \right)\]
done
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D)
\[\left( \frac{\hat{i}+2\hat{j}+\hat{k}}{\sqrt{6}} \right)\]
done
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E)
\[\left( \frac{-\hat{j}+2\hat{k}}{\sqrt{5}} \right)\]
done
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question_answer 217) Forces acting on a particle have magnitude 5, 3 and 1 unit and act in the direction of the vectors\[6\hat{i}+2\hat{j}+3\hat{k},3\hat{i}-2\hat{j}+6\hat{k}\]and \[2\hat{i}-3\hat{j}-6\hat{k}\]respectively. They remain constant while the particle is displaced from the point\[A(2,-1,-3)\]to\[B(5,-1,1)\]. The work done is:
A)
11 unit
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B)
33 unit
done
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C)
10 unit
done
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D)
30 unit
done
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E)
44 unit
done
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question_answer 218) The equation of the plane through the point (1, 2, 3),\[(-1,4,\text{ }2)\]and (3, 1,1) is:
A)
\[5x+y+12z-23=0\]
done
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B)
\[5x+6y+\text{ }2z-23=0\]
done
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C)
\[x+\text{ }6y+\text{ }2z-13=0\]
done
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D)
\[x+y+2-13=0\]
done
clear
E)
\[5x+y+z-23=0\]
done
clear
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question_answer 219) The number of solutions of the equation \[tan\text{ }x+sec\text{ }x=2\text{ }cos\text{ }x\]and\[\cos x\ne 0\]lying in the interval\[(0,2\pi )\]is:
A)
2
done
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B)
1
done
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C)
0
done
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D)
3
done
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E)
4
done
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question_answer 220) \[si{{n}^{2}}5{}^\circ +si{{n}^{2}}10{}^\circ +si{{n}^{2}}15{}^\circ ...+si{{n}^{2}}90{}^\circ \]is equal to:
A)
\[8\frac{1}{2}\]
done
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B)
9
done
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C)
\[9\frac{1}{2}\]
done
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D)
\[4\frac{1}{2}\]
done
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E)
0
done
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question_answer 221) If \[1+sin\,x+si{{n}^{2}}x+si{{n}^{3}}x+...\,to\,\infty \] \[=4+2\sqrt{3},0<x<\pi ,\]then\[x\]is equal to:
A)
\[\frac{\pi }{6}\]
done
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B)
\[\frac{\pi }{4}\]
done
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C)
\[\frac{3\pi }{4}\]
done
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D)
\[\frac{\pi }{3}or\frac{2\pi }{3}\]
done
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E)
\[\frac{5\pi }{6}\]
done
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question_answer 222) The sum of the series \[{{\tan }^{-1}}\frac{1}{1+1+{{1}^{2}}}+{{\tan }^{-1}}\frac{1}{1+2+{{2}^{2}}}+\] \[{{\tan }^{-1}}\frac{1}{1+3+{{3}^{2}}}+.....\infty \] is equal to:
A)
\[\frac{\pi }{4}\]
done
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B)
\[\frac{\pi }{2}\]
done
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C)
\[\frac{\pi }{3}\]
done
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D)
\[\frac{\pi }{6}\]
done
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E)
\[\pi \]
done
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question_answer 223) The perimeter of a triangle ABC is 6 times the arithmetic mean of the sine ratios of its angles. If\[a=1,\]then A is equal to:
A)
\[\frac{\pi }{6}\]
done
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B)
\[\frac{\pi }{3}\]
done
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C)
\[\frac{\pi }{2}\]
done
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D)
\[\frac{2\pi }{3}\]
done
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E)
\[\frac{3\pi }{4}\]
done
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question_answer 224) The base angle of triangle are\[22{{\frac{1}{2}}^{o}}\]and\[122{{\frac{1}{2}}^{o}}\]If b is the base and h is the height of the triangle, then:
A)
\[b=2h\]
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B)
\[b=3h\]
done
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C)
\[b=(1+\sqrt{3})h\]
done
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D)
\[b=(2+\sqrt{3})h\]
done
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E)
\[2b=3h\]
done
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View Answer play_arrow
question_answer 225) If\[1+cos\text{ }x=k,\]where\[x\]is acute, then\[\sin \frac{x}{2}\]is:
A)
\[\sqrt{\frac{1-k}{2}}\]
done
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B)
\[\sqrt{2-k}\]
done
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C)
\[\sqrt{\frac{2+k}{2}}\]
done
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D)
\[\sqrt{\frac{2-k}{2}}\]
done
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E)
\[\sqrt{\frac{k}{2}}\]
done
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question_answer 226) The equation\[a\text{ }cos\theta +b\text{ }sin\theta =c\]has a solution, when a, b and c are real numbers such that:
A)
\[a<b<c\]
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B)
\[a=b=c\]
done
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C)
\[{{c}^{2}}\le {{a}^{2}}+{{b}^{2}}\]
done
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D)
\[{{c}^{2}}<{{a}^{2}}-{{b}^{2}}\]
done
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E)
for all real values of a, b and c
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question_answer 227) If\[\sin \left( \frac{\pi }{4}\cot \theta \right)=\cos \left( \frac{\pi }{4}\tan \theta \right)\]then\[\theta \]is equal to:
A)
\[2n\pi +\frac{\pi }{4}\]
done
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B)
\[2n\pi \pm \frac{\pi }{4}\]
done
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C)
\[2n\pi -\frac{\pi }{4}\]
done
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D)
\[n\pi -\frac{\pi }{4}\]
done
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E)
\[n\pi +\frac{\pi }{4}\]
done
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question_answer 228) If\[A+B+C=\pi ,\]then\[co{{s}^{2}}A+co{{s}^{2}}B+co{{s}^{2}}C\]is equal to:
A)
\[1-cos\text{ }A\text{ }cos\text{ }B\text{ }cos\text{ }C\]
done
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B)
\[1-2\text{ }cos\text{ }A\text{ }cos\text{ }B\text{ }cos\text{ }C\]
done
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C)
\[2\text{ }cos\text{ }A\text{ }cos\text{ }B\text{ }cos\text{ }C\]
done
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D)
\[1+cos\text{ }A\text{ }cos\text{ }B\text{ }cos\text{ }C\]
done
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E)
\[1+cos\text{ }A\text{ }2\text{ }cos\text{ }C\]
done
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question_answer 229) If\[{{\sin }^{-1}}\left( \frac{5}{x} \right)+{{\sin }^{-1}}\left( \frac{12}{x} \right)=\frac{\pi }{2}\], then\[x\]is equal to:
A)
\[\frac{7}{13}\]
done
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B)
\[\frac{4}{3}\]
done
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C)
\[13\]
done
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D)
\[\frac{13}{7}\]
done
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E)
\[4\]
done
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question_answer 230) The value of\[\sec \left[ {{\tan }^{-1}}\left( \frac{b+a}{b-a} \right)-{{\tan }^{-1}}\left( \frac{a}{b} \right) \right]\]is;
A)
2
done
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B)
\[\sqrt{2}\]
done
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C)
4
done
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D)
1
done
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E)
\[\frac{a}{b}\]
done
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question_answer 231) The probability of obtaining sum 8 in a single throw of two dice is:
A)
\[\frac{1}{36}\]
done
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B)
\[\frac{5}{36}\]
done
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C)
\[\frac{4}{36}\]
done
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D)
\[\frac{6}{36}\]
done
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E)
none of these
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question_answer 232) Mean mark scored by the students of a class is 53. The mean mark of the girls is 55 and the mean mark of the boys is 50. What is the percentage of girls in the class?
A)
60%
done
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B)
40%
done
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C)
50%
done
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D)
45%
done
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E)
55%
done
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question_answer 233) The regression coefficient of y on\[x\]is 2/3 and that of\[x\]on y is 4/3. The acute angle between the two regression lines is\[ta{{n}^{-1}}k,\]where k is equal to:
A)
\[\frac{1}{9}\]
done
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B)
\[\frac{2}{9}\]
done
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C)
\[\frac{1}{18}\]
done
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D)
\[\frac{1}{3}\]
done
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E)
\[\frac{8}{9}\]
done
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question_answer 234) The intersecting point of two regression lines is:
A)
\[(\overline{x},0)\]
done
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B)
\[(0,\overline{y})\]
done
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C)
\[({{b}_{xy}},{{b}_{yx}})\]
done
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D)
\[(0,0)\]
done
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E)
\[(\overline{x},\overline{y})\]
done
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question_answer 235) A and B toss a coin alternately till one of them tosses heads and wins the game, their respective probabilities of winning are;
A)
\[\frac{1}{4}and\frac{3}{4}\]
done
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B)
\[\frac{1}{2}and\frac{1}{2}\]
done
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C)
\[\frac{2}{3}and\frac{1}{3}\]
done
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D)
\[\frac{1}{5}and\frac{4}{5}\]
done
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E)
0 and 1
done
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question_answer 236) If birth to a male child and birth to a female child are equal-probable, then what is the probability that at least one of the three children born to a couple is male?
A)
\[\frac{4}{5}\]
done
clear
B)
\[\frac{7}{8}\]
done
clear
C)
\[\frac{8}{7}\]
done
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D)
\[\frac{1}{2}\]
done
clear
E)
\[1\]
done
clear
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question_answer 237) If\[f(x)=\sin (\log x)\]and \[y=f\left( \frac{2x+3}{3-2x} \right),\] then \[\frac{dy}{dx}\]at\[x=1\]is equal to:
A)
6 sin log (5)
done
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B)
5 sin log (6)
done
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C)
12 sin log (5)
done
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D)
5 sin log (12)
done
clear
E)
12 sin log (6)
done
clear
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question_answer 238) The value of a so that the sum of the squares of the roots of the equation\[{{x}^{2}}-(a-2)c-a+1=0\]assumes the least value is:
A)
0
done
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B)
1
done
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C)
2
done
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D)
3
done
clear
E)
\[-2\]
done
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question_answer 239) The length of the longest size rectangle of maximum area that can be inscribed in a semicircle of radius 1, so that 2 vertices lie on the diameter, is:
A)
\[\sqrt{2}\]
done
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B)
\[2\]
done
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C)
\[\sqrt{3}\]
done
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D)
\[\frac{\sqrt{2}}{3}\]
done
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E)
\[\frac{-2}{\sqrt{3}}\]
done
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question_answer 240) If\[f\]be a function such that\[f(9)=9\]and \[f(9)=3,\]then \[\underset{x\to 9}{\mathop{\lim }}\,\frac{\sqrt{f(x)}-3}{\sqrt{x}-3}\]is equal to:
A)
9
done
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B)
3
done
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C)
1
done
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D)
6
done
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E)
\[\frac{2}{3}\]
done
clear
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