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Solved papers for CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2004

done CEE Kerala Engineering Solved Paper-2004

  • question_answer1) 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

    B) 0.8 g

    C) 1.01 g

    D) 0.9 g

    E) 9 g

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  • question_answer2) 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

    B) 4 Pa

    C) 16 Pa

    D) 10 Pa

    E) 8 Pa

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  • question_answer3) A piece of ice is floating in a jar containing water. When the ice melts, then the level of water......:

    A) rises

    B) falls

    C) remains unchanged

    D) rises or falls

    E) cannot say

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  • question_answer4) 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) \[0.6\text{ }g\text{ }c{{m}^{-3}}\]

    B) \[1.0\text{ }g\text{ }c{{m}^{-3}}\]

    C) \[0.4\text{ }gc{{m}^{-3}}\]

    D) \[0.24\text{ }gc{{m}^{-3}}\]

    E) none of these

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  • question_answer5) 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

    B) increase by 0.75 mL

    C) decrease by 1.50 mL

    D) increase by 1.50 mL

    E) decrease by 0.75 mL

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  • question_answer6) 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) \[\frac{1}{2}(A.L)\left( \frac{Yx}{L} \right)\left( \frac{x}{L} \right)\]

    B) \[(A.L)(YL)\left( \frac{x}{L} \right)\]

    C) \[2(A.L)(YL)\left( \frac{x}{L} \right)\]

    D) \[3(A.L)(YL)\left( \frac{x}{L} \right)\]

    E) \[4(A.L)(YL)\left( \frac{x}{L} \right)\]

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  • question_answer7) Which of the accompanying P-V diagrams best represent; an isothermal process?

    A) A

    B) B

    C) C

    D) D

    E) E

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  • question_answer8) 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) \[\frac{p}{32}\]

    B) \[\left( \frac{24}{5} \right)p\]

    C) \[8P\]

    D) \[\text{32 }P\]

    E) \[16\text{ }P\]

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  • question_answer9) 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

    B) 14

    C) 12

    D) 10

    E) 8

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  • question_answer10) The KE and PE of a particle executing SHM of amplitude a will be equal when displacement is:

    A) \[\frac{a}{2}\]

    B) \[a\sqrt{2}\]

    C) \[2a\]

    D) \[\frac{a\sqrt{2}}{3}\]

    E) \[\frac{a}{\sqrt{2}}\]

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  • question_answer11) 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

    B) period\[T/\lambda \]

    C) speed \[x\lambda \]

    D) velocity in negative\[x-\]direction

    E) speed\[(\lambda /T)\]

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  • question_answer12) 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

    B) a and b

    C) b and m

    D) a, b and m

    E) a, b, m and \[{{v}_{0}}\]

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  • question_answer13) 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) \[\frac{4}{3}\]

    B) \[\frac{3}{4}\]

    C) \[2\]

    D) \[\frac{1}{2}\]

    E) \[\frac{3}{2}\]

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  • question_answer14) 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

    B) 4 kV

    C) 400V

    D) 160V

    E) 16V

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  • question_answer15) 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) \[8:1\]

    B) \[1:8\]

    C) \[2:1\]

    D) \[1:2\]

    E) \[9:8\]

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  • question_answer16) 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) \[{{E}_{A}}=0,{{E}_{B}}=0,{{E}_{C}}=0\]

    B) \[{{E}_{A}}=0,{{E}_{B}}=0,{{E}_{C}}\ne 0\]

    C) \[{{E}_{A}}\ne 0,{{E}_{B}}=0,{{E}_{C}}\ne 0\]

    D) \[{{E}_{A}}\ne 0,{{E}_{B}}\ne 0,{{E}_{C}}\ne 0\]

    E) none of the above

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  • question_answer17) The electric potential due to a small electric dipole at a large distance r from the centre of the dipole is proportional to:

    A) \[r\]

    B) \[\frac{1}{r}\]

    C) \[\frac{1}{{{r}^{5}}}\]

    D) \[\frac{1}{{{r}^{3}}}\]

    E) \[\frac{1}{{{r}^{2}}}\]

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  • question_answer18) In the given circuit the equivalent resistance between the points A and B in ohms is ........:

    A) 9

    B) 11.6

    C) 14.5

    D) 21.2

    E) 23.4

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  • question_answer19) 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

    B) 120

    C) 240

    D) 480

    E) 720

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  • question_answer20) 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

    B) 1.25

    C) 0.4

    D) 1.2

    E) 0.8

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  • question_answer21) 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) \[28{}^\circ C\]

    B) \[48{}^\circ C\]

    C) \[52{}^\circ C\]

    D) \[68{}^\circ C\]

    E) \[72{}^\circ C\]

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  • question_answer22) Heat produced (cals) in a resistance R when a current\[I\]amperes flows through it fort seconds is given by the expression:

    A) \[\frac{{{I}^{2}}Rt}{4.2}\]

    B) \[\frac{I{{R}^{2}}t}{4.2}\]

    C) \[\frac{4.2IR}{{{t}^{2}}}\]

    D) \[\frac{IR{{t}^{2}}}{4.2}\]

    E) \[\frac{4.5}{{{I}^{2}}Rt}\]

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  • question_answer23) Which of the following graphs represent variation of magnetic field B with distance r for a straight long wire carrying current?

    A) P

    B) Q

    C) R

    D) S

    E) T

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  • question_answer24) 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

    B) 1.1 A

    C) 2.1 A

    D) 1.5 A

    E) 2.6 A

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  • question_answer25) 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

    B) 1.0

    C) 1.5

    D) 2.0

    E) 5.5

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  • question_answer26) 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) \[2F\]

    B) \[\frac{F}{2}\]

    C) \[\frac{F}{4}\]

    D) \[F\]

    E) \[4F\]

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  • question_answer27) 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

    B) 3.0

    C) 4.5

    D) 6.0

    E) 1.5

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  • question_answer28) 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) \[2BL\sin \left( \frac{\theta }{2} \right){{(gL)}^{1/2}}\]

    B) \[BL\sin \left( \frac{\theta }{2} \right)(gL)\]

    C) \[BL\sin \left( \frac{\theta }{2} \right){{(gL)}^{3/2}}\]

    D) \[BL\sin \left( \frac{\theta }{2} \right){{(gL)}^{2}}\]

    E) \[BL\sin \left( \frac{\theta }{2} \right){{(gL)}^{5/2}}\]

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  • question_answer29) The maximum value of AC voltage in a circuit is 707 V. Its rms value is:

    A) 70.7V

    B) 100 V

    C) 500V

    D) 707V

    E) 7.07V

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  • question_answer30) 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

    B) 16V

    C) 3V

    D) 4V

    E) 6V

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  • question_answer31) A 50 mH coil carries a current of 2 A, the energy stored in joule is:

    A) 1

    B) 0.05

    C) 10

    D) 0.5

    E) 0.1

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  • question_answer32) Band spectrum is also called:

    A) molecular spectrum

    B) atomic spectrum

    C) flash spectrum

    D) line absorption spectrum

    E) line emission spectrum

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  • question_answer33) Velocity of electromagnetic waves in a medium depends upon:

    A) thermal properties of medium

    B) mechanical and electrical properties of medium

    C) electrical and magnetic properties of the medium

    D) mechanical and magnetic properties of the medium

    E) mechanical properties of the medium

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  • question_answer34) 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

    B) 12 cm

    C) 3.8 cm

    D) 3 cm

    E) 0.75 cm

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  • question_answer35) 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) \[50{}^\circ \]

    B) \[60{}^\circ \]

    C) \[70{}^\circ \]

    D) \[80{}^\circ \]

    E) \[90{}^\circ \]

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  • question_answer36) 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) \[\frac{r}{2}\]

    B) \[\frac{r}{\sqrt{2}}\]

    C) \[\frac{r}{\sqrt{3}}\]

    D) \[\frac{r}{\sqrt{7}}\]

    E) \[\sqrt{3r}\]

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  • question_answer37) The focal length\[(f)\]of a spherical (concave or convex) mirror of radius of curvature R is:

    A) \[\frac{R}{2}\]

    B) \[R\]

    C) \[\left( \frac{3}{2} \right)R\]

    D) \[2R\]

    E) \[\frac{R}{4}\]

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  • question_answer38) In a compound microscope, the intermediate image is:

    A) virtual, erect and magnified

    B) real, erect and magnified

    C) real, inverted and magnified

    D) virtual, erect and reduced

    E) none of the above

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  • question_answer39) 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) \[45{}^\circ \]

    B) \[39{}^\circ \]

    C) \[20{}^\circ \]

    D) \[30{}^\circ \]

    E) \[90{}^\circ \]

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  • question_answer40) 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

    B) 0.08/20 cm

    C) 0.016 cm

    D) 0.16 cm

    E) 1.6cm

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  • question_answer41) 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

    B) 0.2 mm

    C) 0.3 mm

    D) 0.4 mm

    E) 0.5 mm

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  • question_answer42) 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) \[\frac{Ee}{m}\]

    B) \[\frac{-Ee}{m}\]

    C) \[\frac{Ed}{md}\]

    D) \[Ee\frac{d}{m}\]

    E) \[\frac{Em}{ed}\]

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  • question_answer43) The wavelength of a 1 keV photon is 1.24 nm. The frequency of 1 MeV photon is:

    A) \[1.24\times {{10}^{15}}Hz\]

    B) \[2.4\times {{10}^{20}}Hz\]

    C) \[1.24\times {{10}^{18}}Hz\]

    D) \[2.4\times {{10}^{24}}Hz\]

    E) \[2.4\times {{10}^{15}}Hz\text{ },\]

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  • question_answer44) 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

    B) 6

    C) 2

    D) 1.2

    E) 2.6

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  • question_answer45) \[{{C}^{14}}\]has half-life 5700 year. At the end of 11400 years, the actual amount left is:

    A) 0.5 of original amount

    B) 0.25 of original amount

    C) 0.125 of original amount

    D) 0.0625 of original amount

    E) 0.03125 of original amount

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  • question_answer46) 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

    B) 6.8 eV

    C) 13.6 eV

    D) 1.51 eV

    E) \[-3.5eV\]

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  • question_answer47) 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

    B) K four-fold, U two-fold

    C) K four-fold, U also four-fold

    D) K two-fold, U also two-fold

    E) no change in K and U

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  • question_answer48) The depletion layer of a p-n junction:

    A) is of constant width irrespective of the bias

    B) acts like an insulating zone under reverse bias

    C) has a width that increases with an increase in forward bias

    D) is depleted of ions

    E) is n-type material

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  • question_answer49) 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

    B) B and A and C and D

    C) C and A and B and D

    D) C and D and B and A

    E) none of the above

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  • question_answer50) A p-type material is electrically .........:

    A) positive

    B) negative

    C) neutral

    D) depends on the concentration of p impurities

    E) depends on the difference of doping impurities and intrinsic impurities

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  • question_answer51) \[Li\]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

    B) 0.04050 amu

    C) 0.04052 amu

    D) 0.04055 amu

    E) 0.04058 amu

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  • question_answer52) 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) \[{{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{3}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}\]

    B) \[{{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{\frac{3}{2}}}=\frac{{{r}_{1}}}{{{r}_{2}}}\]

    C) \[{{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{4}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{3}}\]

    D) \[\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{\frac{3}{2}}}\]

    E) \[{{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{2}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{3}}\]

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  • question_answer53) The dimensions of kinetic energy is:

    A) \[[{{M}^{2}}{{L}^{2}}{{T}^{-1}}]\]

    B) \[[{{M}^{1}}{{L}^{2}}{{T}^{1}}]\]

    C) \[[{{M}^{1}}{{L}^{2}}{{T}^{-2}}]\]

    D) \[[{{M}^{1}}{{L}^{2}}{{T}^{-1}}]\]

    E) \[[{{M}^{2}}{{L}^{2}}{{T}^{-2}}]\]

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  • question_answer54) 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

    B) 0.98 m

    C) 1.37m

    D) 1.96m

    E) 2.12m

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  • question_answer55) If the figure below represents a parabola, identify the physical quantities representing Y and X for constant acceleration:

    A) \[X=\]time, Y = velocity

    B) \[X=\]velocity,\[Y=\]time

    C) \[X=\]time,\[Y=\]displacement

    D) \[X=\]time,\[Y=\]acceleration

    E) \[X=\]velocity,\[Y=\]displacement

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  • question_answer56) 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

    B) 0.80 h

    C) 0.75 h

    D) 0.64 h

    E) 0.50 h

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  • question_answer57) 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) \[\frac{25}{16}\]

    B) \[\frac{5}{4}\]

    C) \[\frac{4}{5}\]

    D) \[\frac{16}{25}\]

    E) \[\frac{5}{8}\]

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  • question_answer58) 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) \[+3.5\text{ }m{{s}^{-1}}\]

    B) \[-3.5\text{ }m{{s}^{-1}}\]

    C) \[-\sqrt{(3.5)}\text{ }m{{s}^{-1}}\]

    D) \[+\sqrt{(3.5)}\text{ }m{{s}^{-1}}\]

    E) \[\text{+7 }m{{s}^{-1}}\]

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  • question_answer59) 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) \[\frac{hu}{(H-h)}\]

    B) \[\frac{Hu}{(H+h)}\]

    C) \[\frac{(H-h)}{Hu}\]

    D) \[\frac{(H+h)}{Hu}\]

    E) \[\left( \frac{H+h}{H-h} \right)u\]

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  • question_answer60) 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

    B) 8 s

    C) 15 s

    D) 10 s

    E) 5s

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  • question_answer61) In the motion of a rocket, physical quantity which is conserved is:

    A) angular momentum

    B) linear momentum

    C) force

    D) work

    E) energy

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  • question_answer62) 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

    B) 0.33 km

    C) 333.3 km

    D) 33 km

    E) 3.33km

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  • question_answer63) 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) \[4\text{ }m{{s}^{-1}}\]

    B) \[\text{6 }m{{s}^{-1}}\]

    C) \[\text{10 }m{{s}^{-1}}\]

    D) \[\text{12 }m{{s}^{-1}}\]

    E) \[\text{14 }m{{s}^{-1}}\]

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  • question_answer64) When a force is applied on a moving body, its motion is retarded. Then the work done is:

    A) positive

    B) negative

    C) zero

    D) positive and negative

    E) none of the above

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  • question_answer65) Physical independence of force is a consequence of:

    A) third law of motion

    B) second law of motion

    C) first law of motion

    D) all of these laws

    E) none of the above

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  • question_answer66) The kinetic energy of a body becomes four times its initial value. The new momentum will be...............:

    A) same as the initial value

    B) twice the initial value

    C) thrice the initial value

    D) four times the initial value

    E) half of its initial value

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  • question_answer67) 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

    B) 110 N

    C) 209 N

    D) 206 N

    E) 196 N

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  • question_answer68) Moment of a couple is called:

    A) impulse

    B) couple

    C) torque

    D) angular momentum

    E) none of these

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  • question_answer69) 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) \[{{\tan }^{-1}}(4)\]

    B) \[{{\tan }^{-1}}\left( \frac{1}{3} \right)\]

    C) \[{{\tan }^{-1}}\left( \frac{1}{4} \right)\]

    D) \[{{\tan }^{-1}}(2)\]

    E) \[{{\tan }^{-1}}\left( \frac{1}{8} \right)\]

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  • question_answer70) 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

    B) 182

    C) 187

    D) 192

    E) 205

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  • question_answer71) A motor is rotating at a constant angular velocity of 600 rpm. The angular displacement per second is:

    A) \[\frac{3}{50\pi }rad\]

    B) \[\frac{3\pi }{50}rad\]

    C) \[\frac{25\pi }{3}rad\]

    D) \[\frac{3\pi }{25}rad\]

    E) \[\frac{50\pi }{3}rad\]

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  • question_answer72) 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) \[\frac{g}{3}\]

    B) \[\frac{g}{90}\]

    C) \[\frac{g}{10}\]

    D) \[\frac{g}{9}\]

    E) \[\frac{g}{8}\]

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  • question_answer73) The one electron species having ionization energy of 54.4 eV is:

    A) \[H\]

    B) \[H{{e}^{+}}\]

    C) \[{{B}^{4+}}\]

    D) \[L{{i}^{2+}}\]

    E) \[B{{e}^{2+}}\]

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  • question_answer74) The correct set of quantum numbers (n, I and m respectively) for the unpaired electron of chlorine atom is:

    A) \[2,1,0\]

    B) \[2,1,1\]

    C) \[3,1,1\]

    D) \[3,2,1\]

    E) \[3,2,-1\]

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  • question_answer75) Which of the following contains maximum number of molecules?

    A) 100 cc of\[C{{O}_{2}}\]at STP

    B) 150 cc of\[{{N}_{2}}\]at STP

    C) 50 cc of\[S{{O}_{2}}\]at STP

    D) 150 cc of\[{{O}_{2}}\] at STP

    E) 200 cc of\[N{{H}_{3}}\]at STP

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  • question_answer76) Density of a crystal remains unchanged as a result of:

    A) ionic defect

    B) Schottky defect

    C) Frenkel defect

    D) crystal defect

    E) point defect

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  • question_answer77) 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

    B) \[6.02\times {{10}^{23}}\]

    C) 0.0821

    D) \[1.66\times {{10}^{-19}}\]

    E) \[1.62\times {{10}^{-24}}\]

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  • question_answer78) The mass of 11.2 L of ammonia gas at STP is:

    A) 8.5 g

    B) 85 g

    C) 17 g

    D) 1.7 g

    E) 4.25 g

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  • question_answer79) Consider the ion:\[{{K}^{+}},{{S}^{2-}},C{{l}^{-}}\]and\[C{{a}^{2+}}\]. The radii of these ionic species follow the order:

    A) \[C{{a}^{2+}}>{{K}^{+}}>C{{l}^{-}}>{{S}^{2-}}\]

    B) \[C{{l}^{-}}>{{S}^{2-}}>{{K}^{+}}>C{{a}^{2+}}\]

    C) \[C{{a}^{2+}}>C{{l}^{-}}>K>{{S}^{2-}}\]

    D) \[{{K}^{+}}>{{S}^{2-}}>C{{l}^{-}}>C{{a}^{2+}}\]

    E) \[{{S}^{2-}}>C{{l}^{-}}>{{K}^{+}}>C{{a}^{2+}}\]

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  • question_answer80) Identify the correct statement from below, concerning the structure of\[C{{H}_{2}}=C=C{{H}_{2}}:\]

    A) The molecule is planar

    B) One of the three carbon atoms is in an\[-s{{p}^{3}}\]hybridized state

    C) The molecule is non-planar with the two\[C{{H}^{2}}\]groups being in planes perpendicular to each other

    D) All the carbon atoms are sp-hybridized

    E) The molecule is bent with the\[CCC\]angle being 120 degrees.

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  • question_answer81) Which carbon is more electronegative?

    A) \[s{{p}^{3}}-\]hybridized carbon

    B) \[sp-\]hybridized carbon

    C) \[s{{p}^{2}}-\]hybridized carbon

    D) Always same irrespective of its hybrid state

    E) None of the above

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  • question_answer82) 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

    B) the same with 1, 1 and 1 lone pair of electrons respectively

    C) different with 0, 1 and 2 lone pair of electrons respectively

    D) different with 1, 0 arid 2 lone pair of electrons respectively

    E) different with 2, 0, 1 lone pair of electrons respectively.

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  • question_answer83) 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

    B) Daltons law

    C) Raoults law

    D) Charles law

    E) Boyles law

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  • question_answer84) 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

    B) only decrease the freezing point of water

    C) only increase the boiling point of water

    D) be used for cleaning the radiator in a car

    E) prevent corrosion of automobile parts

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  • question_answer85) The enthalpy of a monoatomic gas at T Kelvin is:

    A) \[\frac{7}{2}RT\]

    B) \[\frac{3}{2}RT\]

    C) \[\frac{1}{2}RT\]

    D) \[\frac{1}{2}m{{v}^{2}}\]

    E) \[\frac{5}{2}RT\]

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  • question_answer86) 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

    B) 109.4

    C) \[-109.4\]

    D) \[-209.4\]

    E) 250.4

    View Answer play_arrow
  • question_answer87) 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

    B) 3.6

    C) 4.0

    D) 1.0

    E) 2.0

    View Answer play_arrow
  • question_answer88) 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

    B) 5

    C) 8

    D) 9

    E) 13

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  • question_answer89) 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 \[200{}^\circ C\]

    B) 500 atm and\[500{}^\circ C\]

    C) 1000 atm and \[100{}^\circ C\]

    D) 500 atm and \[100{}^\circ C\]

    E) 1000 atm and\[500{}^\circ C\]

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  • question_answer90) 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) \[1:1:1\]

    B) \[1:2:3\]

    C) \[3:2:1\]

    D) \[6:3:2\]

    E) \[2:3:1\]

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  • question_answer91) \[E_{Cu}^{o}=0.34\,V,\,E_{Zn}^{o}=0.76\,V\]. 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

    B) 1.04V

    C) 1.16V

    D) 1.07V

    E) 1.00V

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  • question_answer92) 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 \[=k{{[B]}^{3}}\]

    B) rate \[=k{{[B]}^{4}}\]

    C) rate \[=k[A]{{[B]}^{3}}\]

    D) rate\[=k{{[A]}^{2}}{{[B]}^{2}}\]

    E) rate \[=k{{[A]}^{3}}[B]\]

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  • question_answer93) 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

    B) 5g

    C) 4g

    D) 2g

    E) 1g

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  • question_answer94) 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

    B) 0.025

    C) 0.25

    D) 2.5

    E) 0.0025

    View Answer play_arrow
  • question_answer95) IUPAC name of acraldehyde is:

    A) but-3-en-l-al

    B) propenyl aldehyde

    C) but-2-ene-l-al

    D) propanal

    E) prop-2-en-l-al

    View Answer play_arrow
  • question_answer96) In Lassaignes test, a blue colour is obtained if the organic compound contains nitrogen. The blue colour is due to:

    A) \[{{K}_{4}}[Fe{{(CN)}_{6}}]\]

    B) \[F{{e}_{4}}{{[Fe{{(CN)}_{6}}]}_{3}}\]

    C) \[N{{a}_{3}}[Fe{{(CN)}_{6}}]\]

    D) \[C{{u}_{2}}[Fe{{(CN)}_{6}}]\]

    E) \[N{{a}_{2}}[Fe{{(CN)}_{2}}NO]\]

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  • question_answer97) A molecule of urea can show:

    A) chain isomerism

    B) position isomerism

    C) geometrical isomerism

    D) optical isomerism

    E) tautomerism

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  • question_answer98) Which of the following compounds will exhibit cis-trans isomerism?

    A) 2-butene

    B) 2-butyne

    C) 2-butanol

    D) Butanone

    E) Butanol

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  • question_answer99) Propyne when passed through a hot iron tube at\[400{}^\circ C\]produces:

    A) benzene

    B) methyl benzene

    C) dimethyl benzene

    D) trimethyl benzene

    E) polypropene

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  • question_answer100) The presence of\[A{{g}^{+}}\]ion increases the solubility of alkenes due to the formation of:

    A) \[d\pi -d\sigma \]bonding

    B) \[p\sigma -p\pi \]bonding

    C) \[p\pi -d\pi \]bonding

    D) \[p\pi -d\sigma \]bonding

    E) none of the above

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  • question_answer101) Glycerine contains:

    A) \[1{}^\circ \]carbon

    B) \[2{}^\circ \]carbon

    C) \[3{}^\circ \]carbon

    D) both\[1{}^\circ \]and\[2{}^\circ \]carbon

    E) both\[2{}^\circ \]and\[3{}^\circ \]carbon

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  • question_answer102) Which of the following reacts fastest with a mixture of anhydrous\[ZnC{{l}_{2}}\]and cone.\[HCl\]?

    A) Trimethyl carbinol

    B) Ethanol

    C) Propanol

    D) Methanol

    E) Isopropanol

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  • question_answer103) Which of the following compounds would have the smallest value for\[p{{K}_{a}}\]?

    A) \[CH{{F}_{2}}C{{H}_{2}}C{{H}_{2}}COOH\]

    B) \[C{{H}_{3}}C{{H}_{2}}C{{F}_{2}}\,COOH\]

    C) \[C{{H}_{2}}FCHFC{{H}_{2}}COOH\]

    D) \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}COOH\]

    E) \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}COOH\]

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  • question_answer104) The reagent with which both acetaldehyde and acetophenone react easily are:

    A) Fehlings solution

    B) Schiffs reagent

    C) Tollens reagent

    D) sodium bisulphite

    E) 2, 4-dinitrophenylhydrazine

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  • question_answer105) 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

    B) p-nitroacetanilide

    C) p-nitroaniline

    D) Aniline

    E) Sulphanilic acid

    View Answer play_arrow
  • question_answer106) 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

    B) a red solution

    C) a green solution

    D) a blue precipitate

    E) a canary yellow precipitate

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  • question_answer107) 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) \[1:1\]

    B) \[2:3\]

    C) \[1:2\]

    D) \[2:1\]

    E) \[3:1\]

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  • question_answer108) Vapour phase refining of nickel is carried out using:

    A) \[{{I}_{2}}\]

    B) \[C{{l}_{2}}\]

    C) \[HCl\]

    D) \[CO\]

    E) \[NO\]

    View Answer play_arrow
  • question_answer109) Thomas slag is referred to as:

    A) calcium silicate

    B) calcium phosphate

    C) barium phosphate

    D) strontium silicate

    E) barium silicate

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  • question_answer110) Commercial 11.2 volume\[{{H}_{2}}{{O}_{2}}\]solution has a molarity of:

    A) 1.0

    B) 0.5

    C) 11.2

    D) 1.12

    E) 0.75

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  • question_answer111) Which one of the following oxides is amphoteric?

    A) \[MgO\]

    B) \[CaO\]

    C) \[N{{a}_{2}}O\]

    D) \[C{{O}_{2}}\]

    E) \[ZnO\]

    View Answer play_arrow
  • question_answer112) The main component of glass which gives heat resistance to laboratory glassware is:

    A) \[PbO\]

    B) \[MgO\]

    C) \[{{B}_{2}}{{O}_{3}}\]

    D) \[A{{l}_{2}}{{O}_{3}}\]

    E) \[{{P}_{2}}{{O}_{5}}\]

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  • question_answer113) Each\[BHB\]bridge in\[{{B}_{2}}{{H}_{6}}\]is formed by the sharing of:

    A) 2 electrons

    B) 4 electrons

    C) 1 electron

    D) 3 electrons

    E) 8 electrons

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  • question_answer114) The characteristic colours given by calcium, strontium and barium in the flame test are respectively:

    A) brick red, apple green, crimson

    B) crimson, apple green, brick red

    C) crimson, brick red, apple green

    D) brick red, crimson, apple green

    E) apple green, brick red, crimson

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  • question_answer115) \[a{{K}_{2}}C{{r}_{2}}{{O}_{7}}+2KCl+c{{H}_{2}}S{{O}_{4}}\xrightarrow{{}}\] \[xCr{{O}_{2}}C{{l}_{2}}+yKHS{{O}_{4}}+z{{H}_{2}}O\]. The above equation balances when:

    A) \[a=2,b=4,c=6\]and \[x=2,y=6,z=3\]

    B) \[a=4,b=2,c=6\]and \[x=6,y=2,z=3\]

    C) \[a=6,b=4,c=2\]and \[x=6,y=3,z=2\]

    D) \[a=1,b=4,c=6\]and \[x=2,y=6,z=3\]

    E) \[a=1,b=6,c=4\]and \[x=6,y=2,z=3\]

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  • question_answer116) Which one of the following pairs of elements is called chemical twins because of their very similar chemical properties?

    A) \[Mn\]and W

    B) \[Mo\]and \[Tc\]

    C) \[Fe\]and\[Re\]

    D) \[Hf\]and\[Zr\]

    E) \[Fe\]and \[Co\]

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  • question_answer117) 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

    B) linkage isomers

    C) co-ordination isomers

    D) hydrate isomers

    E) ionization isomers

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  • question_answer118) Which one of the following is a copolymer?

    A) Polyethylene

    B) Polyvinyl chloride

    C) Polytetrafluoroethylene

    D) Nylon-6, 6

    E) Natural rubber

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  • question_answer119) \[\alpha \]and\[\beta \]glucose differ in the orientation of \[-OH\] group around:

    A) \[{{C}_{1}}\]

    B) \[{{C}_{2}}\]

    C) \[{{C}_{3}}\]

    D) \[{{C}_{4}}\]

    E) \[{{C}_{5}}\]

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  • question_answer120) Barbituric acid is used as:

    A) an antipyretic

    B) an antiseptic

    C) an antibiotic

    D) an analgesic

    E) a tranquilizer

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  • question_answer121) 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

    B) \[\frac{1}{2}\]

    C) \[-2\]

    D) 0

    E) \[-1\]

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  • question_answer122) 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) \[\frac{1}{x}+x\log a\]

    B) \[\frac{\log a}{x}+\frac{x}{\log a}\]

    C) \[\frac{1}{x\log a}+x\log a\]

    D) \[\frac{1}{x\log a}-\frac{\log a}{x{{(\log x)}^{2}}}\]

    E) none of these

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  • question_answer123) If \[y={{e}^{(1/2)\log (1+{{\tan }^{2}}x)}},\]then\[\frac{dy}{dx}\]is equal to:

    A) \[\frac{1}{2}{{\sec }^{2}}x\]

    B) \[{{\sec }^{2}}x\]

    C) \[\sec x\tan x\]

    D) \[{{e}^{1/2\log (1+{{\tan }^{2}}x)}}\]

    E) \[{{e}^{1/2\log (1+{{\tan }^{2}}x)}}.\frac{1}{2}\frac{1}{(1+{{\tan }^{2}}x)}\]

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  • question_answer124) If\[y={{2}^{x}}{{.3}^{2x-1}},\]then\[\frac{{{d}^{2}}y}{d{{x}^{2}}}\]is equal to:

    A) \[(log\text{ }2)\text{ }(log\text{ }3)\]

    B) \[(log\text{ 18})\]

    C) \[(log\text{ 1}{{\text{8}}^{2}}){{y}^{2}}\]

    D) \[(log\text{ 18})y\]

    E) \[{{(log\text{ 18})}^{2}}y\]

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  • question_answer125) 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

    B) proportional to the radius

    C) inversely proportional to the radius

    D) inversely proportional to the surface area

    E) proportional to its surface area

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  • question_answer126) The length of the subtangent to the curve\[{{x}^{2}}+xy+{{y}^{2}}=7\]at\[(1,-3)\]is:

    A) 3

    B) 5

    C) \[\frac{3}{5}\]

    D) 15

    E) 4

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  • question_answer127) If \[y=x+{{x}^{2}}+{{x}^{3}}+...\]to \[\infty \]where \[|x|<1,\]then for \[|y|<1,\frac{dx}{dy}\]is equal to:

    A) \[y+{{y}^{2}}+{{y}^{3}}+...to\,\infty \]

    B) \[1+y+{{y}^{2}}-{{y}^{3}}+....to\,\infty \]

    C) \[1-2y+3{{y}^{2}}-....to\,\infty \]

    D) \[1+2y+3{{y}^{2}}+....to\,\infty \]

    E) \[y+{{y}^{2}}+{{y}^{3}}-....to\,\infty \]

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  • question_answer128) 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

    B) 3 m

    C) 6m

    D) 7m

    E) 5m

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  • question_answer129) If \[y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+........\infty ,}}}\]then\[\frac{dy}{dx}\]is equal to:

    A) \[\frac{\cos x}{2y-1}\]

    B) \[\frac{-\cos x}{2y-1}\]

    C) \[\frac{\sin x}{1-2y}\]

    D) \[\frac{-\sin x}{1-2y}\]

    E) \[\frac{2\cos x}{2y-1}\]

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  • question_answer130) 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\[x=0\]

    B) not continuous at\[x=0\]

    C) both continuous and differentiable at\[x=0\]

    D) not defined at\[x=0\]

    E) continuous but not differentiable at\[x=0\]

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  • question_answer131) \[\underset{x\to 0}{\mathop{\lim }}\,\left[ \frac{{{2}^{x}}-1}{\sqrt{1-x}-1} \right]\]is equal to:

    A) \[{{\log }_{e}}2\]

    B) \[{{\log }_{e}}\sqrt{2}\]

    C) \[{{\log }_{e}}4\]

    D) 2

    E) \[\frac{1}{2}\]

    View Answer play_arrow
  • question_answer132) The value of\[x\]for which the polynomial\[2{{x}^{3}}-9{{x}^{2}}+12x+4\]is a decreasing function of\[x,\] is:

    A) \[-1<x<1\]

    B) \[0<x<2\]

    C) \[x>3\]

    D) \[1<x<2\]

    E) \[1<x<3\]

    View Answer play_arrow
  • question_answer133) \[\int{\frac{({{e}^{x}}+{{e}^{-x}})dx}{({{e}^{x}}+{{e}^{-x}})\log (\cos \,h\,x)}}\]equals to:

    A) \[\log (\tan \,h\,x)+c\]

    B) \[2\log ({{e}^{x}}+{{e}^{-x}})+c\]

    C) \[2\log ({{e}^{x}}-{{e}^{-x}})+c\]

    D) \[2\log [\log ({{e}^{x}}+{{e}^{-x}})]+c\]

    E) \[\log [\log (\cos \,h\,x)]+c\]

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  • question_answer134) 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

    B) \[-1\]

    C) \[-2\]

    D) \[\frac{1}{2}\]

    E) \[-\frac{1}{2}\]

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  • question_answer135) \[\int_{0}^{\pi /2}{\frac{\cos \theta }{\sqrt{4-{{\sin }^{2}}\theta }}}d\theta \]is equal to:

    A) \[\frac{\pi }{2}\]

    B) \[\frac{\pi }{6}\]

    C) \[\frac{\pi }{3}\]

    D) \[\frac{\pi }{5}\]

    E) \[\frac{\pi }{4}\]

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  • question_answer136) 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) \[\tan \frac{x}{2}+c\]

    B) \[x+\tan \frac{x}{2}+c\]

    C) \[x-\frac{1}{2}\tan \frac{x}{2}+c\]

    D) \[\frac{x-\tan \frac{x}{2}}{2}+c\]

    E) \[x-\tan \frac{x}{2}+c\]

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  • question_answer137) \[\int_{0}^{1}{\frac{x\,dx}{[x+\sqrt{1-{{x}^{2}}}\sqrt{1-{{x}^{2}}}]}}\]is equal to:

    A) \[0\]

    B) \[1\]

    C) \[\frac{\pi }{4}\]

    D) \[\frac{{{\pi }^{2}}}{2}\]

    E) \[\frac{\pi }{2}\]

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  • question_answer138) The value of \[\int_{0}^{2a}{\frac{f(x)dx}{f(x)+f(2a-x)}}\]is:

    A) \[f(a)\]

    B) \[f(2a)\]

    C) \[f(0)\]

    D) \[2a\]

    E) \[a\]

    View Answer play_arrow
  • question_answer139) The value of\[\int_{-\pi /4}^{\pi /4}{{{x}^{3}}{{\sin }^{4}}x\,dx}\]is equal to:

    A) \[\frac{\pi }{4}\]

    B) \[\frac{\pi }{2}\]

    C) \[\frac{\pi }{8}\]

    D) \[0\]

    E) \[1\]

    View Answer play_arrow
  • question_answer140) For any positive integer\[n,\int{\frac{dx}{{{x}^{n+1}}+x}}\]is equal to:

    A) \[\frac{1}{n}{{\log }_{e}}({{x}^{n}}+1)+c\]

    B) \[\frac{1}{n}{{\log }_{e}}\left( \frac{1}{{{x}^{n}}+1} \right)+c\]

    C) \[\frac{1}{n}{{\log }_{e}}\left( \frac{x}{{{x}^{n}}+1} \right)+c\]

    D) \[\frac{1}{n+1}{{\log }_{e}}\left( \frac{{{x}^{n}}}{{{x}^{n}}+1} \right)+c\]

    E) \[\frac{1}{n}{{\log }_{e}}\left( \frac{{{x}^{n}}}{{{x}^{n}}+1} \right)+c\]

    View Answer play_arrow
  • question_answer141) \[\int{\cos \left[ 2{{\cot }^{-1}}\sqrt{\frac{1-x}{1+x}} \right]}\,dx\]is equal to:

    A) \[\frac{1}{2}{{x}^{2}}+c\]

    B) \[\frac{1}{2}\sin \left[ 2{{\cot }^{-1}}\sqrt{\frac{1-x}{1+x}} \right]+c\]

    C) \[-\frac{1}{2}{{x}^{2}}+c\]

    D) \[\frac{1}{2}x+c\]

    E) \[-\frac{1}{2}x+c\]

    View Answer play_arrow
  • question_answer142) The area between the curves\[y=x{{e}^{x}}\]and\[y=x{{e}^{-x}}\]and the line\[x=1,\]in sq unit, is:

    A) \[2\left( e+\frac{1}{e} \right)sq\,unit\]

    B) \[0\text{ }sq\text{ }unit\]

    C) \[2e\,sq\text{ }unit\]

    D) \[\frac{2}{e}\,sq\text{ }unit\]

    E) \[2\left( e-\frac{1}{e} \right)\,sq\text{ }unit\]

    View Answer play_arrow
  • question_answer143) 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) \[f(4)f(2)\]

    B) \[f(4)\]

    C) \[f(2)\]

    D) \[0\]

    E) \[1\]

    View Answer play_arrow
  • question_answer144) \[\int_{0}^{\pi /2}{\frac{\cos x}{1+\sin x}dx}\]equals to:

    A) \[log\text{ }2\]

    B) \[2log\text{ }2\]

    C) \[{{(log\text{ }2)}^{2}}\]

    D) \[\frac{1}{2}log\text{ }2\]

    E) \[2\text{ }log\text{ }3\]

    View Answer play_arrow
  • question_answer145) The differential equation of all non-horizontal lines in a plane is:

    A) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=0\]

    B) \[\frac{dx}{dy}=0\]

    C) \[\frac{dy}{dx}=0\]

    D) \[\frac{{{d}^{2}}x}{d{{y}^{2}}}=0\]

    E) \[\frac{dy}{dx}+x=0\]

    View Answer play_arrow
  • question_answer146) 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

    B) 2, 1

    C) 1, 2

    D) 2, 3

    E) 3, 2

    View Answer play_arrow
  • question_answer147) The solution of\[2(y+3)-xy\frac{dy}{dx}=0\]with\[y=-2,\]when\[x=1\]is:

    A) \[(y+3)={{x}^{2}}\]

    B) \[{{x}^{2}}(y+3)=1\]

    C) \[{{x}^{4}}(y+3)=1\]

    D) \[{{x}^{2}}{{(y+3)}^{3}}={{e}^{y+2}}\]

    E) \[{{x}^{2}}{{(y+3)}^{2}}={{e}^{y+2}}\]

    View Answer play_arrow
  • question_answer148) 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

    B) 8

    C) 4

    D) 2

    E) 1

    View Answer play_arrow
  • question_answer149) The solution of\[\frac{dy}{dx}+y\tan x=\sec x\]is:

    A) \[y\text{ }sec\text{ }x=tan\text{ }x+c\]

    B) \[y\text{ }tan\text{ }x=sec\text{ }x+c\]

    C) \[tan\text{ }x=y\text{ }tan\text{ }x+c\]

    D) \[x\text{ }sec\text{ }x=tan\text{ }y+c\]

    E) \[x\text{ }tan\text{ }x=y\text{ }tan\text{ }x+c\]

    View Answer play_arrow
  • question_answer150) The solution of\[\frac{dy}{dx}=\frac{ax+h}{by+k}\]represents a parabola, when:

    A) \[a=0,b=0\]

    B) \[a=1,b=2\]

    C) \[a=0,b\ne 0\]

    D) \[a=2,b=1\]

    E) \[a=-2,b=-1\]

    View Answer play_arrow
  • question_answer151) The range of the function \[\sin ({{\sin }^{-1}}x+co{{s}^{-1}}x),|x|\le 1\] is:

    A) \[[-1,1]\]

    B) \[[1,-1]\]

    C) \[\{0\}\]

    D) \[\{-1\}\]

    E) \[\{1\}\]

    View Answer play_arrow
  • question_answer152) Let\[f:R\to R:f(x)={{x}^{2}}\]and\[g:R\to R:g(x)=x+5,\]then\[gof\]is:

    A) \[(x+5)\]

    B) \[(x+{{5}^{2}})\]

    C) \[({{x}^{2}}+{{5}^{2}})\]

    D) \[{{(x+5)}^{2}}\]

    E) \[({{x}^{2}}+5)\]

    View Answer play_arrow
  • question_answer153) 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) \[{{2}^{99}}\]

    B) \[{{99}^{2}}\]

    C) 100

    D) 18

    E) 9

    View Answer play_arrow
  • question_answer154) 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

    B) 9

    C) 11

    D) 3

    E) 16

    View Answer play_arrow
  • question_answer155) If\[f:R\to R\]is defined by\[f(x)={{x}^{2}}-6x-14,\] then\[{{f}^{-1}}(2)\]equals to:

    A) {2, 8}

    B) \[\{-2,8\}\]

    C) \[\{-2,-8\}\]

    D) \[\{2,-8\}\]

    E) \[\{\phi \}\]

    View Answer play_arrow
  • question_answer156) 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

    B) 6, 3

    C) 6, 4

    D) 7, 4

    E) 3, 7

    View Answer play_arrow
  • question_answer157) \[\tan \left[ i\log \left( \frac{a-ib}{a+ib} \right) \right]\]is equal to:

    A) \[ab\]

    B) \[\frac{2ab}{{{a}^{2}}-{{b}^{2}}}\]

    C) \[\frac{{{a}^{2}}-{{b}^{2}}}{2ab}\]

    D) \[\frac{2ab}{{{a}^{2}}+{{b}^{2}}}\]

    E) \[{{a}^{2}}+{{b}^{2}}\]

    View Answer play_arrow
  • question_answer158) 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

    B) 50

    C) 48

    D) 47

    E) 64

    View Answer play_arrow
  • question_answer159) 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) \[-3\]

    B) \[-2\]

    C) 1

    D) 0

    E) 1

    View Answer play_arrow
  • question_answer160) 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

    B) a circle

    C) an ellipse

    D) a hyperbola

    E) none of these

    View Answer play_arrow
  • question_answer161) The real part of\[{{\left[ 1+\cos \left( \frac{\pi }{5} \right)+i\sin \left( \frac{\pi }{5} \right) \right]}^{-1}}\]is:

    A) \[1\]

    B) \[\frac{1}{2}\]

    C) \[\frac{1}{2}\cos \left( \frac{\pi }{10} \right)\]

    D) \[\frac{1}{2}\cos \left( \frac{\pi }{5} \right)\]

    E) \[\frac{1}{2}\sec \left( \frac{\pi }{10} \right)\]

    View Answer play_arrow
  • question_answer162) 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) \[-1\]

    B) 0

    C) 1

    D) 2

    E) \[-2\]

    View Answer play_arrow
  • question_answer163) 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) \[\frac{2}{3}\]

    B) \[\frac{3}{2}\]

    C) \[\frac{4}{9}\]

    D) \[1\]

    E) \[\frac{9}{4}\]

    View Answer play_arrow
  • question_answer164) 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

    B) Rs. 66000

    C) Rs. 60000

    D) Rs. 66600

    E) Rs. 66666

    View Answer play_arrow
  • question_answer165) 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) \[{{x}^{2}}+20x+16=0\]

    B) \[{{x}^{2}}-10x+16=0\]

    C) \[{{x}^{2}}+10x+16=0\]

    D) \[{{x}^{2}}-10x-16=0\]

    E) \[{{x}^{2}}+20x+32=0\]

    View Answer play_arrow
  • question_answer166) If one of the roots of the equation \[{{x}^{2}}+bx+3=0\]is thrice the other, then b is equal to:

    A) \[\pm 3\]

    B) \[\pm 2\]

    C) 0

    D) \[\pm 4\]

    E) \[\pm 1\]

    View Answer play_arrow
  • question_answer167) 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) \[a,5\]

    B) \[b,5\]

    C) \[a,\alpha \]

    D) \[a,\beta \]

    E) \[a,b\]

    View Answer play_arrow
  • question_answer168) 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) \[\frac{ac}{b}\]

    B) \[1\]

    C) \[\frac{ab}{c}\]

    D) \[\frac{bc}{a}\]

    E) \[\frac{b}{ac}\]

    View Answer play_arrow
  • question_answer169) If the sum of n terms of the series\[{{2}^{3}}+{{4}^{3}}+\]\[{{6}^{3}}\] + ... is 3528, then n equals to:

    A) 10

    B) 7

    C) 8

    D) 9

    E) 6

    View Answer play_arrow
  • question_answer170) 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) \[{{\log }_{2}}\left( \frac{1}{2} \right)\]

    B) \[{{\log }_{2}}\left( \frac{5}{2} \right)\]

    C) \[{{\log }_{2}}\left( \frac{1}{5} \right)\]

    D) \[{{\log }_{2}}\left( \frac{2}{5} \right)\]

    E) \[{{\log }_{2}}(5)\]

    View Answer play_arrow
  • question_answer171) Which term of the GP\[3,3\sqrt{3},9....\]is 2187?

    A) 15

    B) 14

    C) 13

    D) 19

    E) 20

    View Answer play_arrow
  • question_answer172) 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

    B) 240m

    C) 120m

    D) 96m

    E) 320m

    View Answer play_arrow
  • question_answer173) The sum of\[{{15}^{2}}+{{16}^{2}}+{{17}^{2}}+.....+{{30}^{2}}\]is equal to:

    A) 8840

    B) 8440

    C) 8540

    D) 8450

    E) 8000

    View Answer play_arrow
  • question_answer174) 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

    B) 4 and 35

    C) 4 and 34

    D) 4 and 36

    E) 6 and 36

    View Answer play_arrow
  • question_answer175) if\[|x|<1,\]then the coefficient of\[{{x}^{n}}\]in \[{{(1+2x+3{{x}^{2}}+4{{x}^{3}}+....)}^{1/2}},\]is:

    A) n

    B) \[n+1\]

    C) \[-n\]

    D) \[-1\]

    E) 1

    View Answer play_arrow
  • question_answer176) The number of different permutations of the word BANANA is:

    A) 6

    B) 36

    C) 30

    D) 60

    E) 120

    View Answer play_arrow
  • question_answer177) \[^{n}{{p}_{r}}=3024\]and\[^{n}{{C}_{r}}=126\],then r is:

    A) 5

    B) 4

    C) 3

    D) 2

    E) 1

    View Answer play_arrow
  • question_answer178) The rank of the word MOTHER when the letters of the word are arranged alphabetically as in a dictionary, is:

    A) 261

    B) 343

    C) 309

    D) 273

    E) 360

    View Answer play_arrow
  • question_answer179) The sum to n terms of the series\[1+(1+3)+(1+3+9)+(1+3+9+27)+...\]is:

    A) \[\frac{3({{3}^{n}}-1)}{4}-1\]

    B) \[\frac{3({{3}^{n}}-1)-2n}{4}\]

    C) \[\frac{3({{3}^{n}}-1)-n}{4}\]

    D) \[\frac{2n-3({{3}^{n}}-1)}{4}\]

    E) \[\frac{3({{3}^{n}}-1)-n}{2}\]

    View Answer play_arrow
  • question_answer180) 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

    B) 28 ways

    C) 26 ways

    D) 36 ways

    E) 45 ways

    View Answer play_arrow
  • question_answer181) The sum of the rational terms in the expansion of\[{{(\sqrt{2}+{{3}^{1/5}})}^{10}}\]is:

    A) 41

    B) 32

    C) 18

    D) 9

    E) 82

    View Answer play_arrow
  • question_answer182) Let A and B are two square matrices such that \[AB=A\]and\[BA=B,\]then\[{{A}^{2}}\]equals to:

    A) B

    B) A

    C) \[I\]

    D) 0

    E) \[{{A}^{-1}}\]

    View Answer play_arrow
  • question_answer183) \[\left| \begin{matrix} x-2 & 2x-3 & 3x-4 \\ x-4 & 2x-9 & 3x-16 \\ x-8 & 2x-27 & 3x-64 \\ \end{matrix} \right|=0,\]then\[x\]is equal to:

    A) \[-2\]

    B) 3

    C) \[-4\]

    D) 4

    E) 0

    View Answer play_arrow
  • question_answer184) If\[X=\left[ \begin{matrix} 1 & 1 \\ 1 & 1 \\ \end{matrix} \right],\]then\[{{X}^{n}},\]for \[n\in N,\] is equal to:

    A) \[{{2}^{n-1}}X\]

    B) \[{{n}^{2}}X\]

    C) \[nX\]

    D) \[{{2}^{n+1}}X\]

    E) \[{{2}^{n}}X\]

    View Answer play_arrow
  • question_answer185) \[a,b,c\] (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) \[pqr\]

    B) 0

    C) \[p+q+r\]

    D) \[pq+qr+rp\]

    E) \[{{(p+q+r)}^{2}}\]

    View Answer play_arrow
  • question_answer186) 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) \[\left[ \begin{matrix} 1 & 1 \\ 1 & 0 \\ \end{matrix} \right]\]

    B) \[\left[ \begin{matrix} 1 & 1 \\ 0 & 1 \\ \end{matrix} \right]\]

    C) \[\left[ \begin{matrix} 1 & 0 \\ 1 & 1 \\ \end{matrix} \right]\]

    D) \[\left[ \begin{matrix} 0 & 1 \\ 1 & 1 \\ \end{matrix} \right]\]

    E) \[\left[ \begin{matrix} 1 & 1 \\ 1 & 1 \\ \end{matrix} \right]\]

    View Answer play_arrow
  • question_answer187) 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

    B) \[x\] and z

    C) y and z

    D) \[x,y\]and z

    E) independent of\[x,y\]and z

    View Answer play_arrow
  • question_answer188) 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) \[\left[ \begin{matrix} 1 \\ 0 \\ 2 \\ \end{matrix} \right]\]

    B) \[\left[ \begin{matrix} \frac{8}{3} \\ \frac{-1}{3} \\ 0 \\ \end{matrix} \right]\]

    C) \[\left[ \begin{matrix} \frac{-8}{3} \\ 1 \\ 0 \\ \end{matrix} \right]\]

    D) \[\left[ \begin{matrix} \frac{8}{3} \\ \frac{1}{3} \\ -1 \\ \end{matrix} \right]\]

    E) \[\left[ \begin{matrix} \frac{8}{3} \\ \frac{1}{3} \\ 0 \\ \end{matrix} \right]\]

    View Answer play_arrow
  • question_answer189) 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) \[-3{{a}^{2}}\]

    B) \[3{{a}^{2}}\]

    C) \[-4{{a}^{2}}\]

    D) \[4{{a}^{2}}\]

    E) \[2{{a}^{2}}\]

    View Answer play_arrow
  • question_answer190) The centre of the ellipse \[9{{x}^{2}}+25{{y}^{2}}-18x-100y-116=0\]is:

    A) (1, 1)

    B) \[(-1,\text{ }2)\]

    C) \[(-1,\text{ }1)\]

    D) (2, 2)

    E) (1, 2)

    View Answer play_arrow
  • question_answer191) 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

    B) lie on an ellipse

    C) lie on a circle

    D) are the vertices of a triangle

    E) lie on a straight line

    View Answer play_arrow
  • question_answer192) The latus rectum of the ellipse \[9{{x}^{2}}+16{{y}^{2}}=144\]is:

    A) \[4\]

    B) \[\frac{11}{4}\]

    C) \[\frac{7}{2}\]

    D) \[\frac{9}{2}\]

    E) \[\frac{10}{3}\]

    View Answer play_arrow
  • question_answer193) The distance between the pair of parallel lines \[{{x}^{2}}+4xy+4{{y}^{2}}+3x+6y-4=0\]is:

    A) \[\sqrt{5}\]

    B) \[\frac{2}{\sqrt{5}}\]

    C) \[\frac{1}{\sqrt{5}}\]

    D) \[\frac{\sqrt{5}}{2}\]

    E) \[\sqrt{\frac{5}{2}}\]

    View Answer play_arrow
  • question_answer194) 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

    B) for no real value of g

    C) \[g=0\]

    D) \[g<-2,g>2\]

    E) \[g>0\]

    View Answer play_arrow
  • question_answer195) Any point on the hyperbola \[\frac{{{(x+1)}^{2}}}{16}-\frac{{{(y-2)}^{2}}}{4}=1\]is of the form:

    A) \[(4\text{ }sec\theta ,2\text{ }tan\theta )\]

    B) \[(4\text{ }sec\theta +1,\text{ }2\text{ }tan\theta -2)\]

    C) \[(4\text{ }sec\theta -1,2\text{ }tan\theta -2)\]

    D) \[(sec\theta -4,\text{ }tan\theta -2)\]

    E) \[(4\text{ }sec\theta -1,\text{ }2\text{ }tan\theta +2)\]

    View Answer play_arrow
  • question_answer196) 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) \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]

    B) \[{{x}^{2}}+{{y}^{2}}={{b}^{2}}\]

    C) \[{{x}^{2}}+{{y}^{2}}=\frac{{{a}^{2}}{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}\]

    D) \[{{x}^{2}}+{{y}^{2}}=1\]

    E) \[{{x}^{2}}+{{y}^{2}}=\frac{2{{a}^{2}}{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}\]

    View Answer play_arrow
  • question_answer197) The focus of the parabola\[{{y}^{2}}-x-2y+2=0\]is:

    A) \[\left( \frac{1}{4},0 \right)\]

    B) \[(1,2)\]

    C) \[\left( \frac{5}{4},1 \right)\]

    D) \[\left( \frac{3}{4},1 \right)\]

    E) \[\left( \frac{3}{4},2 \right)\]

    View Answer play_arrow
  • question_answer198) 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) \[{{x}^{2}}+{{y}^{2}}-x{{x}_{1}}-y{{y}_{1}}=0\]

    B) \[{{x}^{2}}+{{y}^{2}}=x_{1}^{2}+y_{1}^{2}\]

    C) \[x+y={{x}_{1}}+{{y}_{1}}\]

    D) \[x+y=x_{1}^{2}+y_{1}^{2}\]

    E) \[{{x}^{2}}-{{y}^{2}}-x_{1}^{2}-y_{1}^{2}=0\]

    View Answer play_arrow
  • question_answer199) The condition that\[ax+by+c=0\]is tangent to the parabola\[{{y}^{2}}=4ax,\]is:

    A) \[{{a}^{2}}={{b}^{2}}={{c}^{2}}\]

    B) \[a=b\]

    C) \[{{b}^{2}}=c\]

    D) \[{{b}^{2}}=a\]

    E) \[{{a}^{2}}=b\]

    View Answer play_arrow
  • question_answer200) 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) \[{{x}^{2}}+{{y}^{2}}-x-y=0\]

    B) \[{{x}^{2}}+{{y}^{2}}+x+y=0\]

    C) \[{{x}^{2}}+{{y}^{2}}+2(x-y)=0\]

    D) \[{{x}^{2}}+{{y}^{2}}-2x+y=0\]

    E) \[{{x}^{2}}+{{y}^{2}}+2x-y=0\]

    View Answer play_arrow
  • question_answer201) 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) \[ax=by\]

    B) \[ax+by=0\]

    C) \[bx+ay=0\]

    D) \[bx-ay=0\]

    E) \[\frac{x}{a}+\frac{y}{b}=1\]

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  • question_answer202) 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\[4x+3y+8=0\]

    B) \[4x+3y-9=0\]and\[4x+3y+7=0\]

    C) \[4x+3y+19=0\]and\[4x+3y-31=0\]

    D) \[4x+3y-10=0\]and\[4x+3y+12=0\]

    E) \[4x+3y+3=0\]and\[4x+3y-1=0\]

    View Answer play_arrow
  • question_answer203) The eccentricity of the hyperbola\[{{x}^{2}}-{{y}^{2}}=2004\]is:

    A) \[\sqrt{3}\]

    B) \[2\]

    C) \[2\sqrt{2}\]

    D) \[\sqrt{2}\]

    E) 1.5

    View Answer play_arrow
  • question_answer204) The equation of the directrix of\[{{(x-1)}^{2}}=2(y-2)\]is:

    A) \[2y+3=0\]

    B) \[2x+1=0\]

    C) \[2x-1=0\]

    D) \[2y-1=0\]

    E) \[2y-3=0\]

    View Answer play_arrow
  • question_answer205) On the ellipse\[4{{x}^{2}}+9{{y}^{2}}=1\]the point at which the tangent are parallel to\[8x=9y\]are:

    A) \[\left( \frac{2}{5},\frac{1}{5} \right)or\left( -\frac{2}{5},-\frac{1}{5} \right)\]

    B) \[\left( -\frac{2}{5},\frac{1}{5} \right)or\left( \frac{2}{5},-\frac{1}{5} \right)\]

    C) \[\left( -\frac{2}{5},-\frac{1}{5} \right)\]

    D) \[\left( -\frac{3}{5},-\frac{2}{5} \right)or\left( \frac{3}{5},\frac{2}{5} \right)\]

    E) \[\left( -\frac{3}{5},\frac{2}{5} \right)or\left( \frac{3}{5},-\frac{2}{5} \right)\]

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  • question_answer206) 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) \[{{a}^{2}}co{{s}^{2}}\alpha -{{b}^{2}}si{{n}^{2}}\alpha ={{p}^{2}}\]

    B) \[{{a}^{2}}co{{s}^{2}}\alpha -{{b}^{2}}si{{n}^{2}}\alpha =p\]

    C) \[{{a}^{2}}co{{s}^{2}}\alpha +{{b}^{2}}si{{n}^{2}}\alpha ={{p}^{2}}c\]

    D) \[{{a}^{2}}co{{s}^{2}}\alpha +{{b}^{2}}si{{n}^{2}}\alpha =p\]

    E) \[{{b}^{2}}co{{s}^{2}}\alpha -{{a}^{2}}si{{n}^{2}}\alpha ={{p}^{2}}\]

    View Answer play_arrow
  • question_answer207) 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) \[\frac{\pi }{3}\]

    B) \[\frac{\pi }{2}\]

    C) \[{{\cos }^{-1}}\left( \frac{2}{225} \right)\]

    D) \[\frac{\pi }{4}\]

    E) \[\frac{\pi }{6}\]

    View Answer play_arrow
  • question_answer208) 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) \[\frac{\sqrt{2}}{10}\,knot/h\]

    B) \[\frac{10}{\sqrt{2}}\,knot/h\]

    C) \[10\sqrt{2}\,knot/h\]

    D) \[2\sqrt{10}\,knot/h\]

    E) \[10\,knot/h\]

    View Answer play_arrow
  • question_answer209) 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) \[3\sqrt{2}\]

    B) \[2\sqrt{3}\]

    C) \[2\sqrt{5}\]

    D) \[5\sqrt{2}\]

    E) \[5\sqrt{3}\]

    View Answer play_arrow
  • question_answer210) 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

    B) \[\sqrt{6}\] unit

    C) \[2\sqrt{6}\]unit

    D) 2 unit

    E) \[3\sqrt{2}\]unit

    View Answer play_arrow
  • question_answer211) 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) \[3\overset{\to }{\mathop{QP}}\,\]

    B) \[\overset{\to }{\mathop{QP}}\,\]

    C) \[4\overset{\to }{\mathop{QP}}\,\]

    D) \[\frac{\overset{\to }{\mathop{QP}}\,}{2}\]

    E) \[2\overset{\to }{\mathop{QP}}\,\]

    View Answer play_arrow
  • question_answer212) The equation of the plane which bisects the line joining (2, 3, 4) and (6, 7, 8) is:

    A) \[x-y-z-15=0\]

    B) \[x-y+z-15=0\]

    C) \[x+y+z-15=0\]

    D) \[x+\text{ }y+\text{ }z+15=0\]

    E) \[x-y-z+\text{ }15=0\]

    View Answer play_arrow
  • question_answer213) 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

    B) \[-24\]

    C) 3600

    D) \[-215\]

    E) 360

    View Answer play_arrow
  • question_answer214) 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

    B) \[\frac{\sqrt{3}}{2}\]

    C) 12

    D) 4

    E) 16

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  • question_answer215) 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) \[\frac{25}{9}\]

    B) \[\frac{5}{9}\]

    C) \[\frac{5}{3}\]

    D) \[\frac{2}{3}\]

    E) \[\frac{3}{5}\]

    View Answer play_arrow
  • question_answer216) 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) \[\left( \frac{\hat{j}-\hat{k}}{\sqrt{2}} \right)\]

    B) \[\left( \frac{\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}} \right)\]

    C) \[\left( \frac{\hat{i}+\hat{j}+2\hat{k}}{\sqrt{6}} \right)\]

    D) \[\left( \frac{\hat{i}+2\hat{j}+\hat{k}}{\sqrt{6}} \right)\]

    E) \[\left( \frac{-\hat{j}+2\hat{k}}{\sqrt{5}} \right)\]

    View Answer play_arrow
  • question_answer217) 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

    B) 33 unit

    C) 10 unit

    D) 30 unit

    E) 44 unit

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  • question_answer218) The equation of the plane through the point (1, 2, 3),\[(-1,4,\text{ }2)\]and (3, 1,1) is:

    A) \[5x+y+12z-23=0\]

    B) \[5x+6y+\text{ }2z-23=0\]

    C) \[x+\text{ }6y+\text{ }2z-13=0\]

    D) \[x+y+2-13=0\]

    E) \[5x+y+z-23=0\]

    View Answer play_arrow
  • question_answer219) 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

    B) 1

    C) 0

    D) 3

    E) 4

    View Answer play_arrow
  • question_answer220) \[si{{n}^{2}}5{}^\circ +si{{n}^{2}}10{}^\circ +si{{n}^{2}}15{}^\circ ...+si{{n}^{2}}90{}^\circ \]is equal to:

    A) \[8\frac{1}{2}\]

    B) 9

    C) \[9\frac{1}{2}\]

    D) \[4\frac{1}{2}\]

    E) 0

    View Answer play_arrow
  • question_answer221) 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) \[\frac{\pi }{6}\]

    B) \[\frac{\pi }{4}\]

    C) \[\frac{3\pi }{4}\]

    D) \[\frac{\pi }{3}or\frac{2\pi }{3}\]

    E) \[\frac{5\pi }{6}\]

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  • question_answer222) 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) \[\frac{\pi }{4}\]

    B) \[\frac{\pi }{2}\]

    C) \[\frac{\pi }{3}\]

    D) \[\frac{\pi }{6}\]

    E) \[\pi \]

    View Answer play_arrow
  • question_answer223) 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) \[\frac{\pi }{6}\]

    B) \[\frac{\pi }{3}\]

    C) \[\frac{\pi }{2}\]

    D) \[\frac{2\pi }{3}\]

    E) \[\frac{3\pi }{4}\]

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  • question_answer224) 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) \[b=2h\]

    B) \[b=3h\]

    C) \[b=(1+\sqrt{3})h\]

    D) \[b=(2+\sqrt{3})h\]

    E) \[2b=3h\]

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  • question_answer225) If\[1+cos\text{ }x=k,\]where\[x\]is acute, then\[\sin \frac{x}{2}\]is:

    A) \[\sqrt{\frac{1-k}{2}}\]

    B) \[\sqrt{2-k}\]

    C) \[\sqrt{\frac{2+k}{2}}\]

    D) \[\sqrt{\frac{2-k}{2}}\]

    E) \[\sqrt{\frac{k}{2}}\]

    View Answer play_arrow
  • question_answer226) 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) \[a<b<c\]

    B) \[a=b=c\]

    C) \[{{c}^{2}}\le {{a}^{2}}+{{b}^{2}}\]

    D) \[{{c}^{2}}<{{a}^{2}}-{{b}^{2}}\]

    E) for all real values of a, b and c

    View Answer play_arrow
  • question_answer227) If\[\sin \left( \frac{\pi }{4}\cot \theta \right)=\cos \left( \frac{\pi }{4}\tan \theta \right)\]then\[\theta \]is equal to:

    A) \[2n\pi +\frac{\pi }{4}\]

    B) \[2n\pi \pm \frac{\pi }{4}\]

    C) \[2n\pi -\frac{\pi }{4}\]

    D) \[n\pi -\frac{\pi }{4}\]

    E) \[n\pi +\frac{\pi }{4}\]

    View Answer play_arrow
  • question_answer228) If\[A+B+C=\pi ,\]then\[co{{s}^{2}}A+co{{s}^{2}}B+co{{s}^{2}}C\]is equal to:

    A) \[1-cos\text{ }A\text{ }cos\text{ }B\text{ }cos\text{ }C\]

    B) \[1-2\text{ }cos\text{ }A\text{ }cos\text{ }B\text{ }cos\text{ }C\]

    C) \[2\text{ }cos\text{ }A\text{ }cos\text{ }B\text{ }cos\text{ }C\]

    D) \[1+cos\text{ }A\text{ }cos\text{ }B\text{ }cos\text{ }C\]

    E) \[1+cos\text{ }A\text{ }2\text{ }cos\text{ }C\]

    View Answer play_arrow
  • question_answer229) If\[{{\sin }^{-1}}\left( \frac{5}{x} \right)+{{\sin }^{-1}}\left( \frac{12}{x} \right)=\frac{\pi }{2}\], then\[x\]is equal to:

    A) \[\frac{7}{13}\]

    B) \[\frac{4}{3}\]

    C) \[13\]

    D) \[\frac{13}{7}\]

    E) \[4\]

    View Answer play_arrow
  • question_answer230) 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

    B) \[\sqrt{2}\]

    C) 4

    D) 1

    E) \[\frac{a}{b}\]

    View Answer play_arrow
  • question_answer231) The probability of obtaining sum 8 in a single throw of two dice is:

    A) \[\frac{1}{36}\]

    B) \[\frac{5}{36}\]

    C) \[\frac{4}{36}\]

    D) \[\frac{6}{36}\]

    E) none of these

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  • question_answer232) 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%

    B) 40%

    C) 50%

    D) 45%

    E) 55%

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  • question_answer233) 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) \[\frac{1}{9}\]

    B) \[\frac{2}{9}\]

    C) \[\frac{1}{18}\]

    D) \[\frac{1}{3}\]

    E) \[\frac{8}{9}\]

    View Answer play_arrow
  • question_answer234) The intersecting point of two regression lines is:

    A) \[(\overline{x},0)\]

    B) \[(0,\overline{y})\]

    C) \[({{b}_{xy}},{{b}_{yx}})\]

    D) \[(0,0)\]

    E) \[(\overline{x},\overline{y})\]

    View Answer play_arrow
  • question_answer235) A and B toss a coin alternately till one of them tosses heads and wins the game, their respective probabilities of winning are;

    A) \[\frac{1}{4}and\frac{3}{4}\]

    B) \[\frac{1}{2}and\frac{1}{2}\]

    C) \[\frac{2}{3}and\frac{1}{3}\]

    D) \[\frac{1}{5}and\frac{4}{5}\]

    E) 0 and 1

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  • question_answer236) 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) \[\frac{4}{5}\]

    B) \[\frac{7}{8}\]

    C) \[\frac{8}{7}\]

    D) \[\frac{1}{2}\]

    E) \[1\]

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  • question_answer237) 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)

    B) 5 sin log (6)

    C) 12 sin log (5)

    D) 5 sin log (12)

    E) 12 sin log (6)

    View Answer play_arrow
  • question_answer238) 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

    B) 1

    C) 2

    D) 3

    E) \[-2\]

    View Answer play_arrow
  • question_answer239) 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) \[\sqrt{2}\]

    B) \[2\]

    C) \[\sqrt{3}\]

    D) \[\frac{\sqrt{2}}{3}\]

    E) \[\frac{-2}{\sqrt{3}}\]

    View Answer play_arrow
  • question_answer240) 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

    B) 3

    C) 1

    D) 6

    E) \[\frac{2}{3}\]

    View Answer play_arrow

   



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