question_answer 1) The height y and distance x along the horizontal plane of projectile on a certain planet (with no surrounding) are given by: \[y=(8t-5{{t}^{2}})\] metre and x = 6t metre where t is in second. The velocity with which the projectile is projected is:
A)
8 m/s
done
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B)
6 m/s
done
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C)
10 m/s
done
clear
D)
data is not sufficient
done
clear
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question_answer 2) A body of mass a, moving with a velocity b collides with a body of mass c, at rest and sticks to it. They move together with a velocity given by:
A)
\[\frac{ac}{a+b}\]
done
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B)
\[\frac{ab}{a+c}\]
done
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C)
\[\frac{a+b}{ac}\]
done
clear
D)
\[\frac{b+c}{ab}\]
done
clear
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question_answer 3) The refractive index of a material is given by the equation \[n=\frac{A+B}{{{\lambda }^{2}}},\] where A and B are constants. The dimensional formula for B is:
A)
\[\text{ }\!\![\!\!\text{ }{{\text{M}}^{\text{0}}}{{\text{L}}^{\text{2}}}{{\text{T}}^{\text{-1}}}\text{ }\!\!]\!\!\text{ }\]
done
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B)
\[\text{ }\!\![\!\!\text{ }{{\text{M}}^{\text{0}}}{{\text{L}}^{-2}}{{\text{T}}^{0}}\text{ }\!\!]\!\!\text{ }\]
done
clear
C)
\[\text{ }\!\![\!\!\text{ }{{\text{M}}^{\text{0}}}{{\text{L}}^{2}}{{\text{T}}^{-2}}\text{ }\!\!]\!\!\text{ }\]
done
clear
D)
\[\text{ }\!\![\!\!\text{ }{{\text{M}}^{\text{0}}}{{\text{L}}^{2}}{{\text{T}}^{0}}\text{ }\!\!]\!\!\text{ }\]
done
clear
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question_answer 4) A satellite is orbiting around the earth. By what percentage should we increase its velocity, so as to enable it escape away from the earth?
A)
41.4%
done
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B)
50%
done
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C)
82.8%
done
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D)
100%
done
clear
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question_answer 5) At what temperature, the hydrogen molecule will escape from earths surface?
A)
\[{{10}^{1}}K\]
done
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B)
\[{{10}^{2}}K\]
done
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C)
\[{{10}^{3}}K\]
done
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D)
\[{{10}^{4}}K\]
done
clear
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question_answer 6) If the earth is at one-fourth of its present distance from the sun, the duration of the year will be:
A)
half the present year
done
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B)
one-eighth the present year
done
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C)
one-fourth the present year
done
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D)
one-sixth the present year
done
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question_answer 7) An observer moves towards a stationary source of sound with a velocity one-tenth the velocity of sound. The apparent increase in frequency is:
A)
zero
done
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B)
10%
done
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C)
5%
done
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D)
0.1%
done
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question_answer 8) When two conductors of charges and potentials \[{{C}_{1}},\,{{V}_{1}}\] and \[{{C}_{2}},\,{{V}_{2}}\] respectively are joined, the common potential will be:
A)
\[\frac{{{V}_{1}}{{V}_{1}}+{{C}_{2}}{{V}_{2}}}{{{V}_{1}}+{{V}_{2}}}\]
done
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B)
\[\frac{{{C}_{1}}{{V}_{1}}^{2}+{{C}_{2}}{{V}_{2}}^{2}}{{{V}_{1}}^{2}+{{V}_{2}}^{2}}\]
done
clear
C)
\[{{C}_{1}}+{{C}_{2}}\]
done
clear
D)
\[\frac{{{C}_{1}}{{V}_{1}}+{{C}_{2}}{{V}_{2}}^{2}}{{{C}_{1}}+{{C}_{2}}}\]
done
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question_answer 9) A weightless thread can bear tension upto 3.7 kg-wt. A stone of mass 500 g is tied to it and revolved in a circular path of radius 4 m in a vertical plane. If \[g=10\,m/{{s}^{-2}},\] then the maximum angular velocity of the stone will be:
A)
4 rad/s
done
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B)
16 rad/s
done
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C)
\[\sqrt{21}\]rad/s
done
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D)
2 rad/s
done
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question_answer 10) The effective length of a magnet is 31.4 cm and its pole strength is 0.5 Am. If it is bent in the form of semicircle, what will be its magnetic moment then?
A)
\[0.12\,A{{m}^{2}}\]
done
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B)
\[0.1\,A{{m}^{2}}\]
done
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C)
\[0.05\,A{{m}^{2}}\]
done
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D)
\[0.01\,A{{m}^{2}}\]
done
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question_answer 11) Four molecules of a gas have speeds 1, 2, 3 and \[4\,km{{s}^{-1}}\]. The value of ms speed of the gas molecules is:
A)
\[\frac{\text{1}}{\text{2}}\sqrt{\text{15}}\text{km}{{\text{s}}^{\text{-1}}}\]
done
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B)
\[\frac{\text{1}}{\text{2}}\sqrt{\text{10}}\text{km}{{\text{s}}^{\text{-1}}}\]
done
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C)
\[\text{2}\text{.5km}{{\text{s}}^{\text{-1}}}\]
done
clear
D)
\[\sqrt{\frac{15}{2}}\text{km}{{\text{s}}^{\text{-1}}}\]
done
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question_answer 12) If there is change of angular momentum from J to 5 J in 5 s, then the torque is:
A)
\[\frac{\text{3J}}{\text{5}}\]
done
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B)
\[\frac{\text{4J}}{\text{5}}\]
done
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C)
\[\frac{\text{5J}}{4}\]
done
clear
D)
None of these
done
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question_answer 13) Two springs having force constants k each are arranged in parallel and in series. A mass M is attached to two arrangements separately. If time period in first case is \[{{T}_{1}}\] and in second case is \[{{T}_{2}}\] then ratio \[\frac{{{T}_{1}}}{{{T}_{2}}}\] is:
A)
1.5
done
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B)
3.2
done
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C)
0.5
done
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D)
2.1
done
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question_answer 14) If the work done in blowing a bubble of volume V is W, then the work done in blowing a soap bubble of volume 2V will be:
A)
W
done
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B)
2 W
done
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C)
\[\sqrt{2}\]W
done
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D)
\[{{4}^{1/3}}W\]
done
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question_answer 15)
An ideal monoatomic gas is taken round the cycle ABCDA as shown in figure. The work done during the cycle is :
A)
\[PV\]
done
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B)
\[2PV\]
done
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C)
\[\frac{PV}{2}\]
done
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D)
\[\text{zero}\]
done
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question_answer 16) A proton of energy 2 MeV is moving in a circular path in a magnetic field. What should be the energy of a deuteron, so that it also describes circular path of radius equal to that of the proton?
A)
1 MeV
done
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B)
2 MeV
done
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C)
4 MeV
done
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D)
0.5 MeV
done
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question_answer 17) A gas at NTP is suddenly compressed to one-fourth of its original volume. If \[\gamma \] is supposed to be 3/2, then the final pressure is:
A)
4 atm
done
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B)
\[\frac{3}{2}\] atm
done
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C)
8 atm
done
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D)
\[\frac{1}{4}\] atm
done
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question_answer 18) In a series combination\[R=300\,\Omega ,\]\[\text{L=0}\text{.9H,}\]\[\text{C=2}\text{.0}\,\text{F,}\]\[\omega =1000\,\text{rad/s,}\]the impedance of the circuit is :
A)
1300\[\Omega \]
done
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B)
900\[\Omega \]
done
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C)
500\[\Omega \]
done
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D)
400\[\Omega \]
done
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question_answer 19) n identical spherical drops each of radius r are charged to same potential V. They combine to form a bigger drop. The potential of the big drop will be:
A)
\[{{n}^{1/3}}V\]
done
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B)
\[{{n}^{2/3}}V\]
done
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C)
V
done
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D)
\[nV\]
done
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question_answer 20) The wavelength of maximum energy, released during an atomic explosion was \[2.93\,\times {{10}^{-10}}\,m\]. Given that the Wiens constant is \[2.93\,\times {{10}^{-10}}m-K,\] the maximum temperature attained must be of the order of:
A)
\[{{10}^{-7}}K\]
done
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B)
\[{{10}^{7}}K\]
done
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C)
\[{{10}^{-3}}K\]
done
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D)
\[5.86\,\times {{10}^{7}}K\]
done
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question_answer 21) The pressure and density of a diatomic gas \[\left( \gamma =\frac{7}{5} \right)\]change adiabatically from (P, d) to (P, d). If \[\frac{d}{d}=32,\] then\[\frac{P}{P}\] should be:
A)
\[\frac{1}{128}\]
done
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B)
32
done
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C)
128
done
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D)
None of these
done
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question_answer 22) A piece of wax weighs 18.03 g in air. A piece of metal is found to weigh 17.03 g in water. It is tied to the wax and both together weigh 15.23 g in water. Then, the specific gravity of wax is:
A)
\[\frac{18.03}{17.03}\]
done
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B)
\[\frac{17.03}{18.03}\]
done
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C)
\[\frac{18.03}{19.83}\]
done
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D)
\[\frac{15.03}{17.83}\]
done
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question_answer 23) If a mica sheet of thickness t and refractive index \[\mu \] is placed in the path of one of interfering beams in a double slit experiment, then displacement of fringes will be:
A)
\[\frac{D}{d}\mu t\]
done
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B)
\[\frac{D}{d}(\mu -1)t\]
done
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C)
\[\frac{D}{d}(\mu +1)t\]
done
clear
D)
\[\frac{D}{d}({{\mu }^{2}}-1)t\]
done
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question_answer 24) A ray of light propagates from glass (refractive index\[=\frac{3}{2})\] to water (refractive index\[=\frac{4}{3}).\] The value of the critical angle is:
A)
\[{{\sin }^{-1}}\left( \frac{1}{2} \right)\]
done
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B)
\[{{\sin }^{-1}}\left( \sqrt{\frac{9}{8}} \right)\]
done
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C)
\[{{\sin }^{-1}}\left( \frac{8}{9} \right)\]
done
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D)
\[{{\sin }^{-1}}\left( \frac{5}{7} \right)\]
done
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question_answer 25) A ray of light suffers minimum deviation when incident at 60° prism of refractive index \[\sqrt{2.}\] The angle of incidence is:
A)
\[{{\sin }^{-1}}(0.8)\]
done
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B)
\[60{}^\circ \]
done
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C)
\[45{}^\circ \]
done
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D)
\[30{}^\circ \]
done
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question_answer 26) Each of the resistance in the network shown in figure is equal to R. Find the equivalent resistance between two terminals A and B.
A)
\[R\]
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B)
\[5R\]
done
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C)
\[2R\]
done
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D)
\[\frac{2}{3}R\]
done
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question_answer 27) A gas in an air tight container is heated from \[25{}^\circ C\] to \[90{}^\circ C\]. The density of gas will:
A)
increase slightly
done
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B)
remain the same
done
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C)
increase considerably
done
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D)
decrease slightly
done
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question_answer 28) If 2% of the main current is to be passed through the galvanometer of resistance G, the resistance of the shunt required is:
A)
\[\frac{G}{49}\]
done
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B)
\[\frac{G}{50}\]
done
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C)
49 G
done
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D)
50 G
done
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question_answer 29) The current in self-inductance L = 40 mH is increased uniformly from 1 A to 11 A in 4 milliseconds. The induced emf produced in L during this process will be:
A)
100 V
done
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B)
0.2V
done
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C)
440 V
done
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D)
40 V
done
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question_answer 30) \[{{\text{H}}^{\text{+}}}\]\[\text{H}{{\text{e}}^{2+}}\] and \[{{\text{O}}^{\text{2-}}}\] all having the same kinetic energy pass through a region in which there is a uniform magnetic field perpendicular to their velocity. The masses of \[{{\text{H}}^{\text{+}}}\text{,}\] \[\text{H}{{\text{e}}^{\text{2+}}}\] and \[{{\text{O}}^{\text{2-}}}\] are 1 amu, 4 amu and 16 amu, respectively. Then:
A)
\[{{\text{H}}^{\text{+}}}\] will be deflected most
done
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B)
\[{{\text{O}}^{\text{2}}}\] will be deflected most
done
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C)
\[H{{e}^{\text{2+}}}\]and \[{{\text{O}}^{\text{2-}}}\] will be deflected most
done
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D)
all will be deflected most
done
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question_answer 31) The current gain of a transistor in common emitter mode is 49. The change in collector current and emitter current corresponding to the change in base current by \[5.0\,\mu A\] are:
A)
\[\Delta iC=245\,\mu A,\]\[\Delta {{i}_{E}}=250\,\mu A\]
done
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B)
\[\Delta {{i}_{C}}=252\,\mu A,\,\]\[\,\Delta {{i}_{E}}=145\mu A\]
done
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C)
\[\Delta {{i}_{C}}=125\,\mu A,\,\]\[\Delta {{i}_{E}}=250\mu A\]
done
clear
D)
\[\Delta {{i}_{C}}=252\,\mu A,\]\[\Delta {{i}_{E}}=230\mu A\]
done
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question_answer 32) In hydrogen atom when an electron jumps from second to first orbit, the wavelength of line emitted is :
A)
\[0.563\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
done
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B)
\[4861\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
done
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C)
\[4102\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
done
clear
D)
\[1213\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
done
clear
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question_answer 33) How does the magnetic susceptibility \[\chi \] of a paramagnetic material change with absolute temperature T?
A)
\[\chi \propto T\]
done
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B)
\[\chi \propto {{T}^{-1}}\]
done
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C)
\[\chi =\] constant
done
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D)
\[\chi \propto {{e}^{T}}\]
done
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question_answer 34) Two identical heaters of 220 V, 1000 W are placed in parallel with each other across 220 V line, then the combined power is:
A)
1000 W
done
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B)
2000 W
done
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C)
500 W
done
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D)
4000 W
done
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question_answer 35) A bar of magnetic moment M is cut into two pans of equal length. The magnetic moment of either part is;
A)
\[M\]
done
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B)
\[2M\]
done
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C)
\[\frac{M}{2}\]
done
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D)
zero
done
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question_answer 36) A rain drop of radius 0.3 mm has a terminal velocity of 1 m/s and the viscosity of 1 m/s and the viscosity of air is \[18\times {{10}^{-5}}\] poise. The viscous force on the drop is:
A)
\[16.95\times {{10}^{-9}}\,N\]
done
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B)
\[1.695\times {{10}^{-9}}\,N\]
done
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C)
\[10.17\times {{10}^{-9}}\,N\]
done
clear
D)
\[101.17\times {{10}^{-9}}\,N\]
done
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question_answer 37) If magnetic material moves from stronger to weaker parts of magnetic field, then it is known as:
A)
anti-ferromagnetic
done
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B)
ferromagnetic
done
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C)
diamagnetic
done
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D)
paramagnetic
done
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question_answer 38) A charge q is placed at the centre of line joining two equal charges Q. The system of three charges will be in equilibrium, if q is equal to:
A)
\[-\frac{Q}{2}\]
done
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B)
\[-\frac{Q}{4}\]
done
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C)
\[+\frac{Q}{4}\]
done
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D)
\[+\frac{Q}{2}\]
done
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question_answer 39) The temperature of cold, hot junction of a thermocouple are \[0{}^\circ C\] and \[T{}^\circ C\] respectively. The thermo-emf produced is\[E=AT-\frac{1}{2}B{{T}^{2}}.\]If A = 16, B = 0.08, the temperature of inversion will be:
A)
\[100{}^\circ C\]
done
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B)
\[300{}^\circ C\]
done
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C)
\[400{}^\circ C\]
done
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D)
\[500{}^\circ C\]
done
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question_answer 40)
Two light springs of force constants \[{{k}_{1}}\] and \[{{k}_{2}}\] and a block of mass m are in one line AS on a smooth horizontal table, such that one end of each spring is fixed to rigid support and other end is attached to block of mass m kg as shown in figure. The frequency of vibration is:
A)
\[n=\frac{1}{2\pi }\sqrt{\frac{{{k}_{1}}+{{k}_{2}}}{m}}\]
done
clear
B)
\[n=\frac{1}{2\pi }\sqrt{\frac{{{k}_{1}}{{k}_{2}}}{m}}\]
done
clear
C)
\[n=\frac{1}{2\pi }\sqrt{\frac{{{k}_{1}}-{{k}_{2}}}{m}}\]
done
clear
D)
none of these
done
clear
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question_answer 41) Pressure inside two soap bubbles are 1.01 and 1.02 atm. Ratio between their volumes is:
A)
102 : 101
done
clear
B)
\[{{(102)}^{3}}:{{(103)}^{3}}\]
done
clear
C)
8 : 1
done
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D)
2 : 1
done
clear
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question_answer 42)
Two dielectrics of dielectric constants \[{{K}_{1}}\] and \[{{K}_{2}}\]are filled in gap of parallel plate capacitor as shown in figure
The capacitance of capacitor will be:
A)
\[\frac{{{\varepsilon }_{0}}A({{K}_{1}}+{{K}_{2}})}{2d}\]
done
clear
B)
\[\frac{{{\varepsilon }_{0}}A}{2d}\left( \frac{{{K}_{1}}+{{K}_{2}}}{{{K}_{1}}{{K}_{2}}} \right)\]
done
clear
C)
\[\frac{{{\varepsilon }_{0}}}{d}\left( \frac{{{K}_{1}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}} \right)\]
done
clear
D)
\[\frac{{{\varepsilon }_{0}}A}{d}\left( \frac{{{K}_{1}}+{{K}_{2}}}{{{K}_{1}}{{K}_{2}}} \right)\]
done
clear
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question_answer 43) For a series LCR circuit, the phase difference between current and voltage at the condition of resonance will be:
A)
\[\frac{\pi }{2}\]
done
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B)
\[\frac{\pi }{4}\]
done
clear
C)
zero
done
clear
D)
nothing can be said
done
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question_answer 44) A metallic rod of length \[l\] is placed normal to the magnetic field B and revolved in a circular path about one of the ends with angular frequency m. The potential difference across the ends will be:
A)
\[\frac{1}{2}{{B}^{2}}l\omega \]
done
clear
B)
\[\frac{1}{2}B\omega {{l}^{2}}\]
done
clear
C)
\[\frac{1}{8}B\omega {{l}^{3}}\]
done
clear
D)
\[B\omega {{l}^{3}}\]
done
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question_answer 45) A magnetic needle suspended in a vertical plane at \[30{}^\circ \] from the magnetic meridian makes an angle \[45{}^\circ \] with the horizontal. What will be the true angle of dip?
A)
\[{{\tan }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\]
done
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B)
\[{{\tan }^{-1}}(\sqrt{3})\]
done
clear
C)
\[{{45}^{0}}\]
done
clear
D)
\[{{30}^{0}}\]
done
clear
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question_answer 46) A force F is given by \[f=at+b{{t}^{2}},\] where t is rime. What are the dimensions of a and b respectively?
A)
\[\text{ }\!\![\!\!\text{ ML}{{\text{T}}^{\text{-1}}}\text{ }\!\!]\!\!\text{ and}\,\text{ }\!\![\!\!\text{ ML}{{\text{T}}^{\text{-4}}}\text{ }\!\!]\!\!\text{ }\]
done
clear
B)
\[\text{ }\!\![\!\!\text{ ML}{{\text{T}}^{\text{-3}}}\text{ }\!\!]\!\!\text{ and}\,\text{ }\!\![\!\!\text{ ML}{{\text{T}}^{\text{-4}}}\text{ }\!\!]\!\!\text{ }\]
done
clear
C)
\[\text{ }\!\![\!\!\text{ ML}{{\text{T}}^{\text{-4}}}\text{ }\!\!]\!\!\text{ and}\,\text{ }\!\![\!\!\text{ ML}{{\text{T}}^{\text{-2}}}\text{ }\!\!]\!\!\text{ }\]
done
clear
D)
\[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{2}}{{\text{T}}^{3}}\text{ }\!\!]\!\!\text{ and}\,\text{ }\!\![\!\!\text{ }{{\text{M}}^{-1}}{{\text{L}}^{2}}\text{T }\!\!]\!\!\text{ }\]
done
clear
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question_answer 47) In a triode valve, the plate resistance is 10000\[\Omega \] and the anode load resistance is 30000\[\Omega \]. If the amplification factor is 36, then the voltage gain is:
A)
9
done
clear
B)
27
done
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C)
36
done
clear
D)
108
done
clear
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question_answer 48) \[{{g}_{e}}\] and\[{{g}_{p}}\] denote the acceleration due to gravity on the surface of the earth and another planet whose mass and radius are twice to that of the earth, then:
A)
\[{{g}_{p}}=\frac{{{g}_{e}}}{2}\]
done
clear
B)
\[{{g}_{p}}={{g}_{e}}\]
done
clear
C)
\[{{g}_{p}}=2{{g}_{e}}\]
done
clear
D)
\[{{g}_{p}}=\frac{{{g}_{e}}}{\sqrt{2}}\]
done
clear
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question_answer 49) Of the following which relation is true:
A)
\[\beta >\alpha \]
done
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B)
\[\alpha >\beta \]
done
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C)
\[\alpha \,\beta =1\]
done
clear
D)
\[\alpha =\beta \]
done
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question_answer 50) A soap bubble in vacuum has a radius 3 cm and another soap bubble in vacuum has radius 4 cm If two bubbles coalesce under isothermal condition, then the radius of the new bubble will be :
A)
7 cm
done
clear
B)
5 cm
done
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C)
4.5 cm
done
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D)
2.3 cm
done
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question_answer 51) Out of Cu, Al Fe and Zn, metal which can displace all others from their salt solution is:
A)
Al
done
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B)
Cu
done
clear
C)
Zn
done
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D)
Fe
done
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question_answer 52) In which of the following reactions, hydrogen is acting as an oxidizing agent?
A)
With Li to form \[LiH\]
done
clear
B)
With \[{{I}_{2}}\] to give HI
done
clear
C)
With S to give \[{{H}_{2}}S\]
done
clear
D)
None of the above
done
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question_answer 53) Our cells get energy by the conversion of:
A)
ATP \[\xrightarrow{{}}\] Adenine
done
clear
B)
ATP \[\xrightarrow{{}}\]ADP
done
clear
C)
ADP\[\xrightarrow{{}}\]AMP
done
clear
D)
CDP\[\xrightarrow{{}}\] CTP
done
clear
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question_answer 54) The number of optically active isomers of tartaric acid are:
A)
1
done
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B)
3
done
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C)
4
done
clear
D)
2
done
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question_answer 55) The hardness of water is estimated by:
A)
conductivity method
done
clear
B)
titrimetric method
done
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C)
EDTA method
done
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D)
distillation method
done
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question_answer 56) \[N{{a}_{2}}O,\,MgO,\,A{{l}_{2}}{{O}_{3}}\] and \[Si{{O}_{2}}\]have heat of formation equal to \[-416,-602,-1676\] and \[-911\,kJ\,mo{{l}^{-1}}\]respectively. The most stable oxide is:
A)
\[N{{a}_{2}}O\]
done
clear
B)
\[MgO\]
done
clear
C)
\[A{{l}_{2}}{{O}_{3}}\]
done
clear
D)
\[Si{{O}_{2}}\]
done
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question_answer 57) A photon having a wavelength of \[845\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,,\] causes the ionization of N atom. What is the ionization energy of N?
A)
\[1.4\,kJ\]
done
clear
B)
\[1.4\,\times {{10}^{4}}\,kJ\]
done
clear
C)
\[1.4\,\times {{10}^{2}}\,kJ\]
done
clear
D)
\[1.4\,\times {{10}^{3}}\,kJ\]
done
clear
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question_answer 58) The electronic theory of bonding was proposed by:
A)
Pauling
done
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B)
Lewis
done
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C)
Hronsted
done
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D)
Mullikan
done
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question_answer 59) An azeotropic mixture of two liquids has boiling point lower than either of them, when it:
A)
shows a negative deviation from Raoults law
done
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B)
shows no deviation from Raoults law
done
clear
C)
shows positive deviation from Raoults law
done
clear
D)
is saturated
done
clear
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question_answer 60) Troutons rule gives the relation between:
A)
\[{{T}_{b}}\] and\[{{T}_{c}}\]
done
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B)
\[{{T}_{b}}\] and critical pressure
done
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C)
enthalpy of vaporization and boiling point
done
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D)
normal boiling point and boiling point
done
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question_answer 61)
The product X, in the following reaction is:
A)
\[C{{H}_{2}}Br-CH=C{{H}_{2}}\]
done
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B)
\[C{{H}_{3}}-\overset{Br}{\mathop{\overset{|}{\mathop{C}}\,}}\,=C{{H}_{2}}\]
done
clear
C)
\[C{{H}_{3}}CH=CHBr\]
done
clear
D)
none of the above
done
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question_answer 62) What are the products in the following reaction? \[{{C}_{2}}{{H}_{5}}O{{C}_{2}}{{H}_{5}}\xrightarrow[cold]{HI}X+Y\]
A)
\[C{{H}_{3}}COOH,C{{H}_{2}}=C{{H}_{2}}\]
done
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B)
\[C{{H}_{3}}CHO,\,C{{H}_{2}}=C{{H}_{2}}\]
done
clear
C)
\[{{C}_{2}}{{H}_{5}}OH,{{C}_{2}}{{H}_{5}}I\]
done
clear
D)
None of the above
done
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question_answer 63) Which of the following reagent can distinguish between butyne-1 and butyne-2?
A)
Bromine water
done
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B)
Aqueous
done
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C)
Fehlings solution
done
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D)
Ammoniacal\[AgN{{O}_{3}}\]
done
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question_answer 64) Which of the following will have maximum pH?
A)
\[\frac{M}{10}HCl\]
done
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B)
\[\frac{M}{100}HCl\]
done
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C)
\[\frac{M}{10}NaOH\]
done
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D)
\[\frac{M}{100}NaOH\]
done
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question_answer 65) What is AE for system that does 500 cal of work on surrounding and 300 cal of heat is absorbed by the system?
A)
\[-200\]cal
done
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B)
\[-300\]cal
done
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C)
\[+\,200\]cal
done
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D)
\[+\text{ }300\]cal
done
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question_answer 66) The rate of a chemical reaction:
A)
increase as the reaction proceeds
done
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B)
decrease as the reaction proceeds
done
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C)
may increase or decrease during reaction
done
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D)
remain constant as the reaction
done
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question_answer 67) A carbonate ore is:
A)
camallite
done
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B)
limonite
done
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C)
siderite
done
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D)
horn silver
done
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question_answer 68) Cadmium in a nuclear reactor acts as:
A)
nuclear fuel
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B)
neutron absorber
done
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C)
a moderator
done
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D)
neutron liberator to start the chain
done
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question_answer 69) Cement does not contain:
A)
calcium
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B)
aluminium
done
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C)
sulphur
done
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D)
iron
done
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question_answer 70) The simplest way, to check whether a system is a colloid, is by:
A)
Tyndall effect
done
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B)
Brownian movement
done
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C)
Electrodialysis
done
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D)
finding out particle size
done
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question_answer 71)
What is Z in the following reaction?
A)
Benzoic acid
done
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B)
Cyanobenzoic acid
done
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C)
Benzamide
done
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D)
Aniline
done
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question_answer 72) The reaction, \[RCOOH\xrightarrow{Na{{N}_{3}}/conc.{{H}_{2}}S{{O}_{4}}}\] \[RN{{H}_{2}}+{{N}_{2}}+C{{O}_{2}}\] is known as:
A)
Curtius reaction
done
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B)
Lossen reaction
done
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C)
Schmidt reaction
done
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D)
Hofmann reaction
done
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question_answer 73) What is the product in the reaction? \[C{{H}_{3}}MgBr\xrightarrow[(ii)\,{{H}_{2}}O]{(i)\,C{{O}_{2}}}X\]
A)
Acetaldehyde
done
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B)
Acetic acid
done
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C)
Formic acid
done
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D)
Formaldehyde
done
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question_answer 74) What is the value of \[{{E}_{cell}}\] \[Cr|C{{r}^{3+}}(0.1M)||F{{e}^{2+}}(0.01\,M)|Fe\] Given, \[E_{C{{r}^{3+}}/Cr}^{o}=-0.74\,V\] and \[E_{F{{e}^{2+}}/Fe}^{o}=-0.44\,V\]
A)
\[~+\text{ }0.2941\,V\]
done
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B)
\[~+\text{ }0.5212\,V\]
done
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C)
\[+\text{ }0.1308\,V\]
done
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D)
\[-\,0.2606\,V\]
done
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question_answer 75) Elevation in boiling point was \[0.52{{\,}^{o}}C\]when 6g of a compound was dissolved in 100 g of water. Molecular weight of X is (\[{{K}_{b}}\]of water is \[5.2{{\,}^{o}}C\] per 100 g of water):
A)
120
done
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B)
60
done
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C)
600
done
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D)
180
done
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question_answer 76) The solubility of \[PbC{{l}_{2}}\]is:
A)
\[\sqrt{{{K}_{sp}}}\]
done
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B)
\[{{({{K}_{sp}})}^{1/3}}\]
done
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C)
\[{{({{K}_{sp/4}})}^{1/3}}\]
done
clear
D)
\[{{(8{{K}_{sp}})}^{1/2}}\]
done
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question_answer 77) Equilibrium constant K, for the reaction, \[2HI(g){{H}_{2}}(g)+{{I}_{2}}(g)\] at room temperature is 2.85 and that at 698 K is \[1.4\times {{10}^{-2}}.\] This implies that the forward reaction is:
A)
exothermic
done
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B)
endothermic
done
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C)
exergonic
done
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D)
unpredictable
done
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question_answer 78) Which of the following represents hexadentate ligand?
A)
2, 2-bipyridyl
done
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B)
DMG
done
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C)
Ethylenediamine
done
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D)
None of these
done
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question_answer 79) The amount of substance that gives \[3.7\times {{10}^{7}}\] dps, is:
A)
one becquerel
done
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B)
one curie
done
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C)
one millicurie
done
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D)
one Rutherford
done
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question_answer 80) The reaction, \[A{{g}^{2+}}(aq)+Ag(s)2A{{g}^{+}}(aq)\] is an example of:
A)
reduction
done
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B)
oxidation
done
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C)
comproportionation
done
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D)
disproportionation
done
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question_answer 81) DDT is obtained by the reaction, of chlorobenzene with:
A)
chloral
done
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B)
chloroform
done
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C)
dichloromethane
done
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D)
acetaldehyde
done
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question_answer 82) Which of the following is false?
A)
Glycerol has strong hydrogen bonding
done
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B)
Glycol is a poisonous alcohols
done
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C)
Waxes are esters of higher alcohols with higher acids
done
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D)
Alkyl halides have higher b. p. than corresponding alcohols
done
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question_answer 83) Which of the following oxides is most acidic?
A)
\[A{{l}_{2}}{{O}_{3}}\]
done
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B)
\[Si{{O}_{2}}\]
done
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C)
\[{{P}_{2}}{{O}_{5}}\]
done
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D)
\[MgO\]
done
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question_answer 84) Glaubefs salt is:
A)
\[N{{a}_{2}}C{{O}_{3}}.10{{H}_{2}}O\]
done
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B)
\[N{{a}_{2}}S{{O}_{4}}.10{{H}_{2}}O\]
done
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C)
\[MgS{{O}_{4}}.7{{H}_{2}}O\]
done
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D)
\[CaS{{O}_{4}}.5{{H}_{2}}O\]
done
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question_answer 85) Enthalpy change when \[1\,g\]water is frozen at \[(\Delta {{H}_{fus}}=1.435\,\text{kcal}\text{mo}{{\text{l}}^{\text{-1}}})\]
A)
\[0.0797\text{ }kcal~~\]
done
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B)
\[-0.0797\text{ }kcal\]
done
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C)
\[1.435\text{ }kcal\]
done
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D)
\[-1.435\text{ }kcal\]
done
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question_answer 86) Which of the following statement is true?
A)
Some complex metal oxides behave as superconductor
done
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B)
Zinc oxide can act as superconductor
done
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C)
An impurity of tetravalent germanium in trivalent gallium creates electron deficiency
done
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D)
A Frenkel defect is formed when an ion is displaced from its lattice site to an interstitial site
done
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question_answer 87) The correct set of four quantum number for the valence electron of rubidium \[(Z=37)\] is:
A)
\[n=5,\,l=0,\,m=0,\,s=+\,1/2\]
done
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B)
\[n=5,\,l=1,\,m=1,\,s=+\,1/2\]
done
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C)
\[n=5,\,l=1,\,m=1,\,s=+\,1/2\]
done
clear
D)
\[n=6,\,l=0,\,m=0,\,s=+\,1/2\]
done
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question_answer 88) \[s{{p}^{3}}-\]hybridisation is not found in:
A)
\[{{H}_{2}}O\]
done
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B)
\[C{{H}_{4}}\]
done
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C)
\[BC{{l}_{3}}\]
done
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D)
\[N{{H}_{3}}\]
done
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question_answer 89) Chalcopyrites is an ore of:
A)
gallium
done
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B)
copper
done
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C)
calcium
done
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D)
magnesium
done
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question_answer 90) Which of the following statement is correct?
A)
Acidity increases with increase in carbon atoms in carboxylic acids
done
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B)
Solubility of carboxylic adds increases with increase in carbon atoms
done
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C)
Boiling points of acids are higher than corresponding alcohols
done
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D)
None of the above
done
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question_answer 91) Which temperature is most suitable for fermentation?
A)
273 K
done
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B)
298 K
done
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C)
350 K
done
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D)
330 K
done
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question_answer 92) In the reaction, \[HCHO+N{{H}_{3}}\xrightarrow{{}}X,X\]is:
A)
meta-formaldehyde
done
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B)
para-formaldehyde
done
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C)
urotropine
done
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D)
none of the above
done
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question_answer 93) Which of the following have highest melting points?
A)
p-block elements
done
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B)
s-block elements
done
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C)
d-block elements
done
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D)
None of the above
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question_answer 94) An acid has \[pH=5\]and its concentration is 1M. What is the value of \[{{K}_{a}}\]for the acid?
A)
\[{{10}^{-7}}\]
done
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B)
\[{{10}^{-5}}\]
done
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C)
\[{{10}^{-10}}\]
done
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D)
\[{{10}^{-8}}\]
done
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question_answer 95) Fatty acid is to fat as glucose is to:
A)
cellulose
done
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B)
glycogen
done
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C)
starch
done
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D)
all of these
done
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question_answer 96) In aerosol, the dispersion medium is:
A)
solid
done
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B)
liquid
done
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C)
gas
done
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D)
any of these
done
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question_answer 97) Peptisation denotes:
A)
digestion of food
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B)
hydrolysis of protein
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C)
breaking and dispersion into colloidal state
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D)
precipitation of solid from colloidal state
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question_answer 98) Buna-N is a polymer of:
A)
butadiene and isoprene
done
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B)
butadiene and acrylonitrile
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C)
isoprene and ethylene diamine
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D)
isoprene and butyl diamine
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question_answer 99) Which of the following is an engrain dye?
A)
Congo-red
done
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B)
Aniline black
done
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C)
Alizarin
done
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D)
Indigo
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question_answer 100) Which of the following give an explosive, RDX, on nitration?
A)
Toluene
done
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B)
Benzene
done
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C)
Guanidine
done
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D)
Urotropine
done
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question_answer 101) If\[f(x)=\left\{ \begin{matrix} \frac{\sin x}{x}+\cos x, & \text{when}\,\text{x}\ne \text{0} \\ 2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,, & \text{when}\,x=0 \\ \end{matrix} \right.\]
A)
\[\underset{x\to {{0}^{+}}}{\mathop{\lim }}\,f(x)\ne 2\]
done
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B)
\[\underset{x\to {{0}^{-}}}{\mathop{\lim }}\,f(x)=0\]
done
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C)
\[f(x)\]is continuous at \[x=0\]
done
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D)
none of the above
done
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question_answer 102) If \[y=f(x)=\frac{x+2}{x-1},\] then \[x\] is equal to:
A)
\[f(y)\]
done
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B)
\[2f(y)\]
done
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C)
\[\frac{1}{f(y)}\]
done
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D)
none of these
done
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question_answer 103) The value of b and c for which the identity\[f(x+1)-f(x)=8x+3\] is satisfied, where \[f(x)=b{{x}^{2}}+cx+d,\]are:
A)
\[b=2,\,c=1\]
done
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B)
\[b=4,c=-1\]
done
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C)
\[b=-1,c=4\]
done
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D)
\[b=-1,c=1\]
done
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question_answer 104) The range of the function \[f(x)={{x}^{2}}-6x+7\]is:
A)
\[(-\infty ,0)\]
done
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B)
\[[-2,\infty )\]
done
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C)
\[(-\infty ,\infty )\]
done
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D)
\[(-\infty ,-2)\]
done
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question_answer 105) If\[f(x)=x{{\tan }^{-1}}x,\] then \[f(1)\] is equal to:
A)
\[1+\frac{\pi }{4}\]
done
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B)
\[\frac{1}{2}+\frac{\pi }{4}\]
done
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C)
\[\frac{1}{2}-\frac{\pi }{4}\]
done
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D)
2
done
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question_answer 106) \[\frac{d}{dx}\sqrt{\frac{1-\sin 2x}{1+\sin 2x}}\]is equal to:
A)
\[{{\sec }^{2}}x\]
done
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B)
\[-{{\sec }^{2}}\left( \frac{\pi }{4}-x \right)\]
done
clear
C)
\[{{\sec }^{2}}\left( \frac{\pi }{4}+x \right)\]
done
clear
D)
\[{{\sec }^{2}}\left( \frac{\pi }{4}-x \right)\]
done
clear
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question_answer 107) If \[y={{x}^{2}}+\frac{1}{{{x}^{2}}+\frac{1}{{{x}^{2}}+\frac{1}{{{x}^{2}}+...\infty }}}\,\,,\]then \[\frac{dy}{dx}\]is equal to:
A)
\[\frac{2xy}{2y-{{x}^{2}}}\]
done
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B)
\[\frac{xy}{y+{{x}^{2}}}\]
done
clear
C)
\[\frac{xy}{y-{{x}^{2}}}\]
done
clear
D)
\[\frac{2x}{2+\frac{{{x}^{2}}}{y}}\]
done
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question_answer 108) The function \[F(x)=\max [(1-x),(1+x),2],x\in (-\infty ,\infty )\]is:
A)
continuous at all points
done
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B)
differentiable at all points
done
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C)
differentiable at all points except at \[x=1\] and \[x=-1\]
done
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D)
none of the above
done
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question_answer 109) If \[f({{x}_{1}})-f({{x}_{2}})=f\left( \frac{{{x}_{1}}-{{x}_{2}}}{1-{{x}_{2}}{{x}_{2}}} \right)\]for \[{{x}_{1}},{{x}_{2}}\in [-1,1],\]then \[f(x)\]is equal to:
A)
\[{{\tan }^{-1}}\frac{(1+x)}{(1-x)}\]
done
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B)
\[{{\tan }^{-1}}\frac{(1-x)}{(1+x)}\]
done
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C)
\[\log \frac{(1+x)}{(1-x)}\]
done
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D)
none of these
done
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question_answer 110) \[\int_{{}}^{{}}{\frac{dx}{x({{x}^{n}}+1)}}\]is equal to:
A)
\[n\log \frac{{{x}^{n}}}{{{x}^{n}}+1}+c\]
done
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B)
\[n\log \frac{{{x}^{n}}+1}{{{x}^{n}}}+c\]
done
clear
C)
\[\frac{1}{n}\log \frac{{{x}^{n}}}{{{x}^{n}}+1}+c\]
done
clear
D)
\[\frac{1}{n}\log \frac{{{x}^{n}}+1}{{{x}^{n}}}+c\]
done
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question_answer 111) \[\int_{{}}^{{}}{{{\{1+2\tan x(\tan x+\sec x)\}}^{1/2}}dx}\]is equal to:
A)
\[log(sec\text{ }x+tan\text{ }x)+c\]
done
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B)
\[log{{(sec\text{ }x+tan\text{ }x)}^{1/2}}+\text{ }c\]
done
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C)
\[~log\,sec\text{ }x\,(sec\text{ }x+tan\text{ }x)+c\]
done
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D)
none of the above
done
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question_answer 112) The value of \[\int_{0}^{\pi /2}{\frac{\cos \theta }{\sqrt{4-{{\sin }^{2}}\theta }}}d\theta \]is:
A)
\[\frac{\pi }{2}\]
done
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B)
\[\frac{\pi }{6}\]
done
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C)
\[\frac{\pi }{3}\]
done
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D)
\[\frac{\pi }{5}\]
done
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question_answer 113) If the ordinate\[x=a\] divides the area bounded by the curve\[y=\left( 1+\frac{8}{{{x}^{2}}} \right),\]\[x-\]axis and the ordinates \[x=2,\text{ }x=4,\]into two equal parts, then the value of a is:
A)
2a
done
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B)
\[2\sqrt{2}\]
done
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C)
\[\frac{a}{2}\]
done
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D)
none of these
done
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question_answer 114) Area included between the two curves, \[{{y}^{2}}=4ax\]and \[{{x}^{2}}-4ay\]is equal to:
A)
\[\frac{32}{3}{{a}^{2}}\text{sq}\,\text{unit}\]
done
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B)
\[\frac{64}{9}\,\text{sq}\,\text{unit}\]
done
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C)
\[\frac{32}{3}\text{sq}\,\text{unit}\]
done
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D)
\[\frac{16}{3}{{a}^{2}}\text{sq}\,\text{unit}\]
done
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question_answer 115) The differential equation of the family of curves \[y=a\cos (x+b)\]is :
A)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}-y=0\]
done
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B)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}+y=0\]
done
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C)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}+2y=0\]
done
clear
D)
none of these
done
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question_answer 116) The solution of the given differential equation\[\frac{dy}{dx}+2xy=y\]is:
A)
\[y=c{{e}^{x-{{x}^{2}}}}\]
done
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B)
\[y=c{{e}^{{{x}^{2}}-x}}\]
done
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C)
\[y=c{{e}^{x}}\]
done
clear
D)
\[y=c{{e}^{-{{x}^{2}}}}\]
done
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question_answer 117) If the probability of X to fail in the examination is 0.3 and that for Y is 0.2, then the probability that either X or Y fail in examination is:
A)
0.5
done
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B)
0.44
done
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C)
0.6
done
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D)
none of these
done
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question_answer 118) The plane\[\frac{x}{2}+\frac{y}{3}+\frac{z}{4}=1\] cuts the coordinate axes in A, B, C, then the area of the \[\Delta ABC\]is:
A)
\[\sqrt{29}\] sq unit
done
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B)
\[\sqrt{41}\,\text{sq}\,\text{unit}\]
done
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C)
\[\sqrt{61}\,\text{sq}\,\text{unit}\]
done
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D)
none of these
done
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question_answer 119) Let \[~0<P(A)<1,0<P(B)<1~\] and \[P(A\cap B)=P(A)+P(B)-P(A)P(B),\]then:
A)
\[P(B/A)=P(B)-P(A)\]
done
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B)
\[P({{A}^{c}}\cup {{B}^{c}})=P({{A}^{c}})+P({{B}^{c}})\]
done
clear
C)
\[P{{(A\cup B)}^{c}}=P({{A}^{c}})P({{B}^{c}})\]
done
clear
D)
\[P(A/B)=P(A)+P({{B}^{c}})\]
done
clear
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question_answer 120) If the plane \[x+2y+2z-15=0\]cuts the sphere \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-2y-4z-11=0,\]then the radius of the circle is:
A)
\[\sqrt{3}\]
done
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B)
\[\sqrt{5}\]
done
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C)
\[\sqrt{7}\]
done
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D)
\[\sqrt{11}\]
done
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question_answer 121) Forces acting on a particle have a magnitude 5, 3 and 1 unit and act in the direction of the vectors \[6\hat{i}+2\hat{j}+3\hat{k},3\hat{i}-4\hat{j}+6\hat{k}\] and \[2\hat{i}-3\hat{j}-6\hat{k}\]respectively. Then 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
done
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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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View Answer play_arrow
question_answer 122) If \[\vec{a},\vec{b},\vec{c}\]are three non-coplanar vectors, then the vector equation\[\vec{r}=(1-p-q)\vec{a}+p\vec{b}+q\vec{c}\] represents a:
A)
straight line
done
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B)
plane
done
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C)
plane passing through the origin
done
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D)
sphere
done
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question_answer 123) If angle between \[\vec{a}\]and\[\vec{b}\]is\[\frac{2\pi }{3}\] and if\[|\vec{a}|=5,|\vec{b}|=3,\]then\[|\vec{a}-\vec{b}|\]is equal to:
A)
23
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B)
7
done
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C)
17
done
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D)
18
done
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question_answer 124) Let p and q be two statements, then \[(p\ \vee q)\vee \tilde{\ }p\] is:
A)
tautology
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B)
contradiction
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C)
both (a) and (b)
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D)
none of these
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question_answer 125) The values of \[x\] and \[y\]satisfying the equation \[\frac{(1+i)x-2i}{3+i}+\frac{(2-3i)y+i}{3-i}=i\]are:
A)
\[x=-1,y=3\]
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B)
\[x=3,y=-1\]
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C)
\[x=0,y=1\]
done
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D)
\[x=1,y=0\]
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question_answer 126) The points \[{{z}_{1}},{{z}_{2}},{{z}_{3}},{{z}_{4}}\]in the complex plane are the vertices of a parallelogram taken in order, iff:
A)
\[{{z}_{1}}+{{z}_{4}}={{z}_{2}}+{{z}_{3}}\]
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B)
\[{{z}_{1}}+{{z}_{3}}={{z}_{2}}+{{z}_{4}}\]
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C)
\[{{z}_{1}}+{{z}_{2}}={{z}_{3}}+{{z}_{4}}\]
done
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D)
none of these
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question_answer 127) An OR gate is the boolean function defined of:
A)
\[f({{x}_{1}},{{x}_{2}})={{x}_{1}}{{x}_{2}};{{x}_{1}},{{x}_{2}}\in \{0,1\}\]
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B)
\[f({{x}_{1}},{{x}_{2}})={{x}_{1}}+{{x}_{2}};{{x}_{1}},{{x}_{2}}\in \{0,1\}\]
done
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C)
\[f({{x}_{1}},{{x}_{2}})={{x}_{1}};{{x}_{1}},{{x}_{2}}\in \{0,1\}\]
done
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D)
\[f({{x}_{1}},{{x}_{2}})={{x}_{2}};{{x}_{1}},{{x}_{2}}\in \{0,1\}\]
done
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question_answer 128) If the sum of the roots of the equation \[a{{x}^{2}}+bx+c=0\]be equal to the sum of the reciprocal of their squares, then \[b{{c}^{2}},c{{a}^{2}},a{{b}^{2}}\]will be in:
A)
AP
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B)
GP
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C)
HP
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D)
none of these
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question_answer 129) If\[x,y,z\] are in GP and \[{{a}^{x}}={{b}^{y}}={{c}^{z}},\]then:
A)
\[{{\log }_{a}}C={{\log }_{b}}a\]
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B)
\[{{\log }_{b}}a={{\log }_{c}}b\]
done
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C)
\[{{\log }_{c}}b={{\log }_{a}}c\]
done
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D)
none of these
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question_answer 130) The sum of the series \[1+\frac{1}{5}+\frac{1.3}{5.10}+\frac{1.3.5}{5.10.15}+....\]is equal to:
A)
\[\frac{1}{\sqrt{5}}\]
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B)
\[\frac{1}{\sqrt{2}}\]
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C)
\[\sqrt{3}\]
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D)
\[\sqrt{\frac{5}{3}}\]
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question_answer 131) If \[x\]is real, then the value of \[\frac{x+2}{2{{x}^{2}}+3x+6}\]
A)
\[\left( \frac{1}{13},\frac{1}{3} \right)\]
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B)
\[\left[ -\frac{1}{13},\frac{1}{3} \right]\]
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C)
\[\left( -\frac{1}{3},\frac{1}{13} \right)\]
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D)
none of these
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question_answer 132) Let a and P be the roots of the equation \[{{x}^{2}}+x+1=0,\]then the equation whose roots area\[{{\alpha }^{19}},{{\beta }^{7}}\] is:
A)
\[~{{x}^{2}}-x-1=0\]
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B)
\[~{{x}^{2}}-\text{ }x+1=0\]
done
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C)
\[~{{x}^{2}}+x-1=0\]
done
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D)
\[~{{x}^{2}}+\text{ }x+1=0\]
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question_answer 133) For a particle moving in a straight line, if timer be regarded as a function of velocity v, then the rate of change of the acceleration a is given by:
A)
\[{{a}^{2}}\frac{{{d}^{2}}t}{d{{v}^{2}}}\]
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B)
\[{{a}^{3}}\frac{{{d}^{2}}t}{d{{v}^{2}}}\]
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C)
\[-{{a}^{3}}\frac{{{d}^{2}}t}{d{{v}^{2}}}\]
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D)
none of these
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question_answer 134) \[{{\,}^{47}}{{C}_{4}}+\sum\limits_{r=1}^{5}{{{\,}^{52-r}}{{C}_{3}}}\]is equal to:
A)
\[{{\,}^{47}}{{C}_{6}}\]
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B)
\[{{\,}^{52}}{{C}_{5}}\]
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C)
\[{{\,}^{52}}{{C}_{4}}\]
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D)
none of these
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question_answer 135) In how many ways can 21 English and 19 Hindi books be placed in a row so that no two Hindi books are together:
A)
1540
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B)
1450
done
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C)
1504
done
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D)
1405
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question_answer 136) How many words can be made from the letters of the word COMMITTEE:
A)
\[\frac{9!}{{{(2!)}^{2}}}\]
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B)
\[\frac{9!}{{{(2!)}^{3}}}\]
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C)
\[\frac{9!}{2!}\]
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D)
9!
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question_answer 137) Three forces P, Q, and R acting on a particle are in equilibrium. If the angle between P and Q is double the angle between P and R, then P is equal to:
A)
\[\frac{{{Q}^{2}}+{{R}^{2}}}{R}\]
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B)
\[\frac{{{Q}^{2}}-{{R}^{2}}}{Q}\]
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C)
\[\frac{{{Q}^{2}}-{{R}^{2}}}{R}\]
done
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D)
\[\frac{{{Q}^{2}}+{{R}^{2}}}{Q}\]
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question_answer 138) If n is an integer greater than 1, then \[a-{{\,}^{n}}{{C}_{1}}(a-1)+{{\,}^{n}}{{C}_{2}}(a-2)-....+{{(-1)}^{n}}(a-n)\] is equal to:
A)
\[a\]
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B)
\[0\]
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C)
\[{{a}^{2}}\]
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D)
\[{{2}^{n}}\]
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question_answer 139) Forces forming a couple are of magnitude 12N each and the arm of the couple is 8m. The tone of an equivalent couple whose arm is 6 m is of magnitude:
A)
8 N
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B)
16 N
done
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C)
12 N
done
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D)
4 N
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question_answer 140) In the expansion of \[2{{\log }_{e}}x-{{\log }_{e}}(x+1)-{{\log }_{e}}(x-1)\] the coefficient of \[{{x}^{-4}}\]is:
A)
\[\frac{1}{2}\]
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B)
\[-1\]
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C)
1
done
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D)
none of these
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question_answer 141) A tower subtends an angle \[\alpha \]at a point in the plane of its base and the angle of depression of the foot of the tower at a point b ft just above A is \[\beta .\]Then height of the tower is:
A)
\[b\text{ }tan\text{ }\alpha \text{ }cot\beta \]
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B)
\[~b\text{ }cot\text{ }\alpha \text{ }tan\text{ }\beta \]
done
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C)
\[b\text{ }tan\text{ }\alpha \text{ }tan\text{ }\beta \]
done
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D)
\[b\cot \alpha \cot \beta \]
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question_answer 142) The matrix \[\left[ \begin{matrix} 2 & 5 & -7 \\ 0 & 3 & 11 \\ 0 & 0 & 9 \\ \end{matrix} \right]\]is known as:
A)
symmetric matrix
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B)
upper triangular matrix
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C)
diagonal matrix
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D)
skew-symmetric matrix
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question_answer 143) Two bodies of different masses \[{{m}_{1}}\]and \[{{m}_{2}}\]are dropped from different heights \[{{h}_{1}}\]and \[{{h}_{2}}.\]he ratio of the times taken by the two bodies to fall through these distance is:
A)
\[{{h}_{1}}:{{h}_{2}}\]
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B)
\[\sqrt{{{h}_{1}}}:\sqrt{{{h}_{2}}}\]
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C)
\[{{h}_{1}}^{2}:h_{2}^{2}\]
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D)
\[{{h}_{2}}:{{h}_{1}}\]
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question_answer 144) Matrix A is such that \[{{A}^{2}}=2A-I,\]where\[I\]is the identity matrix, then for \[n\ge 2,{{A}^{n}}\]is equal to:
A)
\[nA-(n-1)I\]
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B)
\[nA-I\]
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C)
\[{{2}^{n-1}}A-(n-1)I\]
done
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D)
\[{{2}^{n-1}}A-I\]
done
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question_answer 145) The value of the determinant \[\left| \begin{matrix} x & a & b+c \\ x & b & c+a \\ x & c & a+b \\ \end{matrix} \right|=0\]if:
A)
\[x=a\]
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B)
\[x=b\]
done
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C)
\[x=c\]
done
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D)
\[x\]has any value
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question_answer 146) \[{{12}^{o}}\sin {{48}^{o}}\sin {{54}^{o}}\]is equal to:
A)
1/16
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B)
1/32
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C)
1/8
done
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D)
1/4
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question_answer 147) If\[\tan A=\frac{1-\cos B}{\sin B}.\]then:
A)
\[\tan 2A=\tan B\]
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B)
\[\tan 2A=ta{{n}^{2}}B\]
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C)
\[\tan 2A={{\tan }^{2}}B+2\tan B\]
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D)
none of the above
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question_answer 148) Three points are\[A(6,3),B(-3,5),C(4,-2)\]and \[P(x,y)\]is any point, then the ratio of area of \[\Delta PBC\]and \[\Delta ABC\]is:
A)
\[\frac{x+y-2}{7}\]
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B)
\[\frac{x-y+2}{2}\]
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C)
\[\frac{x-y-2}{7}\]
done
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D)
none of these
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question_answer 149) The circle \[{{x}^{2}}+{{y}^{2}}+4x-4y+4=0\]t touches:
A)
\[x-\]axis
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B)
\[y-\]axis
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C)
\[x-\] axis and \[y-\]axis
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D)
none of the above
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question_answer 150) Three normals to the parabola \[{{y}^{2}}=x\]are drawn a point (c, 0), then:
A)
\[c=\frac{1}{4}\]
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B)
\[c=\frac{1}{2}\]
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C)
\[c>\frac{1}{2}\]
done
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D)
None of these
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