Solved papers for JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2006

done Jamia Millia Islamia Solved Paper-2006

  • question_answer1) The v-t graph for a particle is as shown. The distance travelled in the first four seconds is

    A) 12 m

    B) 16 m

    C) 20 m

    D) 24 m

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  • question_answer2) If a convex lens of focal length 75 cm and a concave lens of focal length 50 cm are combined together, what will be their resulting power?

    A) \[-6.6D\]

    B) \[+0.66\text{ }D\]

    C) \[+6.6D\]

    D) \[-0.66D\]

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  • question_answer3) When a ferromagnetic material is heated to temperature above its curie point, the material

    A) is permanently magnetized

    B) remains ferromagnetic

    C) behaves like a diamagnetic material

    D) behaves like a paramagnetic material

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  • question_answer4) Light of energy 2.0 eV falls on a metal of work function 1.4 eV. The stopping potential is

    A) 0.6 V

    B) 2.0 V

    C) 3.4 V

    D) 1.4 V

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  • question_answer5) During an isothermal expansion of an ideal gas

    A) its internal energy decreases

    B) its internal energy does not change

    C) the work done by the gas is equal to the quantity of heat absorbed by it

    D) both (b) and (c) are correct

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  • question_answer6) Find the dimensions of electric permittivity

    A) \[[{{A}^{2}}{{M}^{-1}}{{L}^{-3}}{{T}^{4}}]\]

    B) \[[{{A}^{2}}{{M}^{-1}}{{L}^{3}}{{T}^{0}}]\]

    C) \[[A{{M}^{-1}}{{L}^{-3}}{{T}^{4}}]\]

    D) \[[{{A}^{2}}{{M}^{0}}{{L}^{-3}}{{T}^{4}}]\]

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  • question_answer7) In Youngs double slit experiment, the slits are 3 mm apart. The wavelength of light used is \[5000\text{ }\overset{o}{\mathop{\text{A}}}\,\]and the distance between the slits and the screen is 90 cm. The fringe width in mm is

    A) 1.5

    B) 0.015

    C) 2.0

    D) 0.15

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  • question_answer8) A moving coil galvanometer has a resistance of\[10\text{ }\Omega \]. and full scale deflection of 0.01 A. It can be converted into voltmeter of 10 V full scale by connecting into resistance of

    A) \[\text{9}\text{.90 }\Omega \] in series

    B) \[\text{10 }\Omega \] in series

    C) \[\text{990 }\Omega \] in series

    D) \[\text{0}\text{.10 }\Omega \] in series

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  • question_answer9) A circular disc of radius R rolls without slipping along the horizontal surface with constant velocity vq. We consider a point A on the surface of the disc. Then the acceleration of the point A is

    A) constant in magnitude as well as direction

    B) constant in direction

    C) constant in magnitude

    D) constant

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  • question_answer10) The number of free electrons per 100 mm of ordinary Copper wire is\[2\times {{10}^{21}}\]. Average drift speed of electrons is 0.25 mm/s. The current flowing is

    A) 5 A

    B) 80 A

    C) 8 A

    D) 0.8 A

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  • question_answer11) A Carnot engine whose low temperature reservoir is at\[7{}^\circ C\] has an efficiency of 50%. It is desired to increase the efficiency to 70%. By how many degrees should the temperature of the high temperature reservoir be increased?

    A) 840 K

    B) 280 K

    C) 560 K

    D) 380 K

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  • question_answer12) The current in the\[1\,\Omega \]. resistor shown in the circuit is

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

    B) \[3A\]

    C) \[6\text{ }A\]

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

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  • question_answer13) Water is flowing through a pipe of constant cross-section. At some point the pipe becomes narrow and the cross-section is halved. The speed of water is

    A) reduced to zero

    B) decreased by a factor of 2

    C) increased by a factor of 2

    D) unchanged

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  • question_answer14) In Millikans oil drop experiment, an oil drop of mass\[16\times {{10}^{-6}}kg\]is balanced by an electric field of\[{{10}^{6}}V/m\]. The charge in coulomb on the drop is (assuming\[g=10m/{{s}^{2}}\])

    A) \[6.2\times {{10}^{-11}}\]

    B) \[16\times {{10}^{-9}}\]

    C) \[16\times {{10}^{-11}}\]

    D) \[16\times {{10}^{-13}}\]

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  • question_answer15) The minimum wavelength of X-ray emitted from X-ray machine operating at an accelerating potential of V volts is

    A) \[\frac{hc}{eV}\]

    B) \[\frac{Vc}{eh}\]

    C) \[\frac{eh}{Vc}\]

    D) \[\frac{eV}{hc}\]

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  • question_answer16) Light wave is travelling alongy-direction. If the corresponding E vector at any time is along the \[x-\]axis, the direction of B vector at that time is along

    A) \[y-\]axis

    B) \[x-\]axis

    C) \[+z\]axis

    D) \[-z-\]axis

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  • question_answer17) Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror and parallel to the second is reflected from the second mirror parallel to the first mirror. The angle between the two mirrors is

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

    B) \[45{}^\circ \]

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

    D) \[75{}^\circ \]

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  • question_answer18) A radioactive material has a half-life of 8 yr. The activity of the material will decrease to about 1/8 of its original value in

    A) 256 yr

    B) 128 yr

    C) 64 yr

    D) 24 yr

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  • question_answer19) The number of beats produced per second by two vibrations\[{{x}_{1}}={{x}_{0}}\]and\[{{x}_{2}}={{x}_{0}}\sin 652\pi t\]is

    A) 2

    B) 3

    C) 4

    D) 6

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  • question_answer20) An engine is supposed to operate between two reservoirs at temperature\[727{}^\circ C\]and\[227{}^\circ C\]. The maximum possible efficiency of such an engine is

    A) 1/2

    B) 1/4

    C) 3/4

    D) 1

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  • question_answer21) A string vibrates according to the equation\[y=5\sin \left( \frac{2\pi x}{3} \right)\cos 20\pi t\]where\[x\]and y are in cm and t in second. The distance between two adjacent nodes is

    A) 3 cm

    B) 4.5 cm

    C) 6 cm

    D) 1.5 cm

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  • question_answer22) On Centigrade scale the temperature of a body increases by\[30{}^\circ \]. The increase in temperature on Fahrenheit scale is

    A) \[50{}^\circ \]

    B) \[40{}^\circ \]

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

    D) \[54{}^\circ \]

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  • question_answer23) A particle performs uniform circular motion with an angular momentum L. If the frequency of particles motion is doubled and its KE is halved. the angular momentum becomes

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

    B) \[2L\]

    C) \[4L\]

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

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  • question_answer24) An electron initially at rest is accelerated through a potential difference of\[1V\]. The energy acquired by electron is

    A) \[{{10}^{-19}}J\]

    B) \[1.6\times {{10}^{-19}}erg\]

    C) \[1.6\times {{10}^{-19}}J\]

    D) \[1J\]

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  • question_answer25) A nucleus decays by\[{{\beta }^{+}}-\] emission followed by a\[\gamma -\]emission. If the atomic and mass numbers of the parent nucleus are Z and A respectively, the corresponding numbers for the daughter nucleus are respectively

    A) \[Z-1\]and\[A-1\]

    B) \[Z+1\] and A

    C) \[Z-1\]and A

    D) \[Z+1\]and\[A-1\]

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  • question_answer26) An iron bar of length 10 m is heated from\[0{}^\circ C\] to\[100{}^\circ C\]. If the coefficient of linear thermal expansion of iron is\[10\times {{10}^{-6}}/{}^\circ C,\] the increase in the length of bar is

    A) 0.5 cm

    B) 1.0 cm

    C) 1.5 cm

    D) 2:0 cm

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  • question_answer27) A balloon going upward with a velocity of 12 m/s is at a height of 65 m from the earths surface at any instant. Exactly at this instant a ball drops from it. How much time will the ball take in reaching the surface of earth? \[(g=10m/{{s}^{2}})\]

    A) 5s

    B) 5 s

    C) 10s

    D) None of these

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  • question_answer28) A block moving on a surface with velocity 20 m/s comes to rest because of surface friction over a distance of 40 m. Taking\[(g=10m/{{s}^{2}})\], the coefficient of dynamic friction is

    A) 0.5

    B) 0.3

    C) 0.2

    D) 0.1

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  • question_answer29) A dielectric slab is inserted between the plates of an isolated charged capacitor. Which of the following quantities remain unchanged?

    A) The charge on the capacitor

    B) The stored energy in the capacitor

    C) The potential difference between the plates

    D) The electric field in the capacitor

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  • question_answer30) In a medium of dielectric constant K, the electric field is\[\overrightarrow{E}\]. If\[{{\varepsilon }_{0}}\]is permittivity of the free space, the electric displacement vector is

    A) \[\frac{K\vec{E}}{{{\varepsilon }_{0}}}\]

    B) \[\frac{{\vec{E}}}{K{{\varepsilon }_{0}}}\]

    C) \[\frac{{{\varepsilon }_{0}}\vec{E}}{K}\]

    D) \[K{{\varepsilon }_{0}}\vec{E}\]

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  • question_answer31) The phenomenon of polarization of light indicates that

    A) light is a longitudinal wave

    B) light is a transverse wave

    C) light is not a wave

    D) light travels with the velocity of\[3\times {{10}^{8}}m/s\]

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  • question_answer32) A ray of light passes from vacuum into a medium of refractive index u., the angle of incidence is found to be twice the angle of refraction. Then the angle of incidence is

    A) \[2{{\cos }^{-1}}\left( \frac{\mu }{2} \right)\]

    B) \[{{\sin }^{-1}}\left( \mu \right)\]

    C) \[{{\sin }^{-1}}\left( \frac{\mu }{2} \right)\]

    D) \[{{\cos }^{-1}}\left( \frac{\mu }{2} \right)\]

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  • question_answer33) A body dropped from top of a tower fall through 60 m during the last two seconds of its fall. The height of tower is\[(g=10\text{ }m/{{s}^{2}})\]

    A) 95 m

    B) 60 m

    C) 80 m

    D) 90 m

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  • question_answer34) A compound microscope has an eyepiece of focal length 10 cm and an objective of focal length 4 cm. Calculate the magnification, if an object is kept at a distance of 5 cm from the objective, so that final image is formed at the least distance of distinct vision 20 cm.

    A) 12

    B) 11

    C) 10

    D) 13

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  • question_answer35) The ratio of the velocity of sound in oxygen to that in hydrogen at same temperature and pressure is approximately

    A) \[16:1\]

    B) \[1:16\]

    C) \[4:1\]

    D) \[1:4\]

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  • question_answer36) The ratio\[\frac{g}{{{g}_{h}}},\]where g and\[{{g}_{h}}\]are the accelerations due to gravity at the surface of the earth and at a height h above the earths surface respectively, is

    A) \[{{\left( 1+\frac{h}{R} \right)}^{2}}\]

    B) \[{{\left( 1+\frac{R}{h} \right)}^{2}}\]

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

    D) \[{{\left( \frac{h}{R} \right)}^{2}}\]

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  • question_answer37) In order that the light reflected from the surface of a medium of refractive index a is plane polarized, the angle of incidence should be

    A) \[{{\sin }^{-1}}(\mu )\]

    B) \[{{\tan }^{-1}}(\mu )\]

    C) \[{{\cot }^{-1}}(\mu )\]

    D) \[{{\tan }^{-1}}\left( \frac{1}{\mu } \right)\]

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  • question_answer38) The magnetic field at the centre of a current carrying circular loop is B. If the radius of the loop is doubled, keeping the current same, the magnetic field at the centre of the loop would be

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

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

    C) 2B

    D) 4B

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  • question_answer39) Let V be the electric potential at a given point. Then the electric field\[{{E}_{x}}\]along\[x-\]direction at that point is given by

    A) \[\int_{0}^{\infty }{V}dx\]

    B) \[\frac{dV}{dx}\]

    C) \[-\frac{dV}{dx}\]

    D) \[-V\frac{dV}{dx}\]

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  • question_answer40) Potential at any point inside a charged hollow, sphere

    A) increases with distance

    B) is a constant

    C) decreases with distance from centre

    D) is zero

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  • question_answer41) The length of a simple pendulum is increased by 44 %. What is the percentage increase in its time period?

    A) 10%

    B) 20%

    C) 40 %

    D) 44 %

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  • question_answer42) Four charges\[{{q}_{1}}=2\times {{10}^{-8}}C,{{q}_{2}}=-2\times {{10}^{-8}}C,\]\[{{q}_{3}}=-3\times {{10}^{-8}}C\]and\[{{q}_{4}}=6\times {{10}^{-8}}C\]are placed at four comers of a square of side\[\sqrt{2}m\]. What is the potential at the centre of the square?

    A) 270V

    B) 300V

    C) Zero

    D) 100 V

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  • question_answer43) A point charge + q is placed at the midpoint of a cube of side L. The electric flux emerging from the cube is

    A) \[\frac{q}{{{\varepsilon }_{0}}}\]

    B) \[\frac{q}{6{{L}^{2}}{{\varepsilon }_{0}}}\]

    C) \[\frac{6q{{L}^{2}}}{{{\varepsilon }_{0}}}\]

    D) zero

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  • question_answer44) In which of the following is the interference due to the division of wavefront?

    A) Youngs double slit experiment

    B) Fresnels biprism experiment

    C) Llyods mirror experiment

    D) Demonstration colours of thin film

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  • question_answer45) A source of sound of frequency 500 Hz is moving towards a stationary observer with velocity 30 m/s. The speed of sound is 330 m/s. The frequency heard by the observer will be

    A) 545 Hz

    B) 580 Hz

    C) 458.3 Hz

    D) 550 Hz

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  • question_answer46) A ball is hit at\[45{}^\circ \]to the horizontal with a kinetic energy\[{{E}_{k}}\]. The kinetic energy at the highest point is

    A) \[{{E}_{k}}\]

    B) \[\frac{{{E}_{k}}}{2}\]

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

    D) zero

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  • question_answer47) In stream line flow of liquid, the total energy of liquid is constant at

    A) all points

    B) inner points

    C) outer points

    D) none of these

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  • question_answer48) The magnetic field at the point of intersection of diagonals of a square loop of side L carrying a current\[I\]is

    A) \[\frac{{{\mu }_{0}}I}{\pi L}\]

    B) \[\frac{2{{\mu }_{0}}I}{\pi L}\]

    C) \[\frac{\sqrt{2}{{\mu }_{0}}I}{\pi L}\]

    D) \[\frac{2\sqrt{2}{{\mu }_{0}}I}{\pi L}\]

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  • question_answer49) Two thin lenses of focal lengths\[{{f}_{1}}\]and\[{{f}_{2}}\]are placed in contact with each other. The focal length of the combination is

    A) \[\frac{{{f}_{1}}+{{f}_{2}}}{2}\]

    B) \[\sqrt{{{f}_{1}}}{{f}_{2}}\]

    C) \[\frac{{{f}_{1}}{{f}_{2}}}{{{f}_{1}}+{{f}_{2}}}\]

    D) \[\frac{{{f}_{1}}{{f}_{2}}}{{{f}_{1}}-{{f}_{2}}}\]

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  • question_answer50) For ionising an excited hydrogen atom, the energy required (in eV) will be

    A) a little less than 13.6

    B) 13.6

    C) more than 13.6

    D) 3.4 or less

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  • question_answer51) A hollow sphere of charge does not produce an electric field at any

    A) interior point

    B) outer point

    C) beyond 2 m

    D) beyond 10 m

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  • question_answer52) When a force of 0.1 N is applied, the spring is stretched by 1.5 cm. The spring is cut into three parts and one part is stretched by 3 cm. Find the force required for doing so

    A) 0.2 N

    B) 0.3 N

    C) 0.4 N

    D) 0.6 N

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  • question_answer53) A bomb at rest explodes into 3 parts of the same mass. The momentum of the 2 parts is \[-2p\hat{i}\]and\[p\hat{j}\]. The momentum of the third part will have a magnitude of

    A) \[P\]

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

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

    D) zero

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  • question_answer54) A couple produces a

    A) pure linear motion

    B) pure rotational

    C) no motion

    D) both linear (a) and (b)

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  • question_answer55) If the external forces acting on a system have zero resultant, the centre of mass

    A) may move but not accelerate

    B) may accelerate

    C) must not move

    D) none of the above

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  • question_answer56) In the reaction \[R-C\equiv N+4(H)\xrightarrow[{}]{X}RC{{H}_{2}}N{{H}_{2}}\]\[X\]can be

    A) \[LiAl{{H}_{4}}\]

    B) \[{{H}_{2}}S{{O}_{4}}\]

    C) \[Ni\]

    D) \[2KBr\]

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  • question_answer57) At a given temperature the equilibrium constant for the reaction of\[PC{{l}_{5}}PC{{l}_{3}}+C{{l}_{2}}\]is\[2.4\times {{10}^{-3}}\]. At the same temperature, the equilibrium constant for the reaction\[PC{{l}_{3}}(g)+C{{l}_{2}}(g)PC{{l}_{5}}(g)\]is

    A) \[2.4\times {{10}^{-3}}\]

    B) \[-2.4\times {{10}^{-3}}\]

    C) \[4.2\times {{10}^{2}}\]

    D) \[4.8\times {{10}^{-2}}\]

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  • question_answer58) Which of the following is called polyamide?

    A) Terylene

    B) Rayon

    C) Nylon

    D) Orion

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  • question_answer59) The number of electrons in the valence shell of sulphur in\[S{{F}_{6}}\]is

    A) 12

    B) 10

    C) 8

    D) 11

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  • question_answer60) The minimum energy required for the reacting molecules to undergo reaction is

    A) potential energy

    B) kinetic energy

    C) thermal energy

    D) activation energy

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  • question_answer61) Which of the following is correct for the reaction? \[{{N}_{2}}(g)+3{{H}_{2}}(g)2N{{H}_{3}}(g)\]

    A) \[{{K}_{p}}={{K}_{c}}\]

    B) \[{{K}_{p}}<{{K}_{c}}\]

    C) \[{{K}_{p}}>{{K}_{c}}\]

    D) Pressure is required to predict the correlation

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  • question_answer62) The rate constant of a first order reaction is\[6.9\times {{10}^{-3}}{{s}^{-1}}\]. How much time will it take to reduce the initial concentration to its 1/8th value?

    A) 100s

    B) 200s

    C) 300s

    D) 400s

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  • question_answer63) Which has the minimum freezing point?

    A) One molal\[NaCl\]aqueous solution

    B) One molal\[CaCla\]aqueous solution

    C) One molal\[KCl\]aqueous solution

    D) One molal urea aqueous solution

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  • question_answer64) Among the following, the most acidic is

    A) \[C{{H}_{3}}COOH\]

    B) \[ClC{{H}_{2}}COOH\]

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

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

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  • question_answer65) For a Bohr atom angular momentum M of the electron is: (n = 0, 1, 2, ......)

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

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

    C) \[\frac{\sqrt{n{{h}^{2}}}}{4\pi }\]

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

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  • question_answer66) Which of the following combination will form an electrovalent bond?

    A) P and\[Cl\]

    B) \[N{{H}_{3}}\]and\[B{{F}_{3}}\]

    C) H and \[Ca\]

    D) H and \[S\]

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  • question_answer67) How many moles of\[A{{l}_{2}}{{(S{{O}_{4}})}_{3}}\]would be in 50 g of the substance?

    A) 0.083 mol

    B) 0.952 mol

    C) 0.481 mol

    D) 0.140 mol

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  • question_answer68) The IUPAC name of the compound \[C{{H}_{3}}CONHBr\]is

    A) 1-bromoacetamide

    B) ethanoylbromide

    C) N-bromoethanamide

    D) none of the above

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  • question_answer69) Which of the following is a condensation polymer?

    A) \[-\left[ N{{H}_{2}}-\overset{\begin{smallmatrix} O \\ |\,| \end{smallmatrix}}{\mathop{C}}\,-{{(C{{H}_{2}})}_{5}} \right]{{-}_{n}}\]

    B) Rubber

    C) Polyvinyl chloride

    D) Polyethylene

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  • question_answer70) The solubility of\[Ca{{F}_{2}}\]in pure water is\[2.3\times {{10}^{-4}}mol\text{ }d{{m}^{-3}}\]. Its solubility product will be

    A) \[4.6\times {{10}^{-4}}\]

    B) \[4.6\times {{10}^{-8}}\]

    C) \[6.9\times {{10}^{-12}}\]

    D) \[4.9\times {{10}^{-11}}\]

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  • question_answer71) Copper sulphate solution, when added to an excess of ammonium hydroxide, forms a complex compound due to

    A) \[{{[Cu{{(N{{H}_{3}})}_{2}}]}^{2+}}\]

    B) \[{{[Cu{{(N{{H}_{3}})}_{4}}]}^{2+}}\]

    C) \[{{[Cu{{(N{{H}_{3}})}_{6}}]}^{2+}}\]

    D) \[C{{u}^{2+}}\]

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  • question_answer72) If a solution containing 0.072 g atom of sulphur in 100 g of a solvent\[({{k}_{f}}=7.0)\]gave a freezing point depression of\[0.84{}^\circ C,\]the molecular formula of sulphur in the solutions is

    A) \[{{S}_{6}}\]

    B) \[{{S}_{7}}\]

    C) \[{{S}_{8}}\]

    D) \[{{S}_{9}}\]

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  • question_answer73) Which of the following is a dynamic isomerism?

    A) Metamerism

    B) Geometrical isomerism

    C) Tautomerism

    D) Co-ordinate isomerism

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  • question_answer74) When\[{{K}_{2}}C{{r}_{2}}{{O}_{7}}\]is converted into\[{{K}_{2}}Cr{{O}_{4}},\]the change in oxidation number of chromium is

    A) 0

    B) 5

    C) 7

    D) 9

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  • question_answer75) Which of the following will be the most effective in the coagulation of\[Fe{{(OH)}_{3}}\]Sol?

    A) \[KCN\]

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

    C) \[NaCl\]

    D) \[M{{g}_{3}}{{(P{{O}_{4}})}_{2}}\]

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  • question_answer76) For d-block elements the first ionization potential is of the order

    A) \[Zn>Fe>Cu>Cr\]

    B) \[Sc=Ti<V=Cr\]

    C) \[Zn<Cu<Ni<Co\]

    D) \[V>Cr>Mn>Fe\]

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  • question_answer77) High basicity of IV^NH relative to\[M{{e}_{3}}N\]is attributed to

    A) effect of solvent

    B) inductive effect of Me

    C) shape of \[M{{e}_{2}}NH\]

    D) shape of\[M{{e}_{3}}N\]

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  • question_answer78) In the reaction \[X\]is

    A) \[SiC\]

    B) \[{{H}_{2}}S{{O}_{4}}\]

    C) \[KMn{{O}_{4}}\]

    D) \[Fe/HCl\]

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  • question_answer79) In Grignard reagent the carbon-magnesium bond is

    A) electrovalent

    B) covalent

    C) dative

    D) hydrogen bonding

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  • question_answer80) The radius of hydrogen atom in the ground state is\[0.53\text{ }\overset{o}{\mathop{\text{A}}}\,\]. The radius of\[L{{i}^{2+}}\]ion (atomic number = 3) in a similar state is

    A) \[0.176\text{ }\overset{o}{\mathop{\text{A}}}\,\]

    B) \[\text{0}\text{.30 }\overset{o}{\mathop{\text{A}}}\,\]

    C) \[\text{0}\text{.53 }\overset{o}{\mathop{\text{A}}}\,\]

    D) \[\text{1}\text{.23 }\overset{o}{\mathop{\text{A}}}\,\]

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  • question_answer81) Tyndall effect shown by colloids is due to

    A) scattering of light by the particles

    B) movements of particles

    C) reflection of light by the particles

    D) coagulation of particles

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  • question_answer82) Iodine is a

    A) electrovalent solid

    B) atomic solid

    C) molecular solid

    D) covalent solid

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  • question_answer83) \[F{{e}^{2+}}\]ion is distinguished from\[F{{e}^{3+}}\]ion by

    A) \[BaC{{l}_{2}}\]

    B) \[KCN\]

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

    D) \[N{{H}_{4}}SCN\]

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  • question_answer84) Lattice energy of a solid increases if

    A) size of ions is small

    B) charges of ions are small

    C) ions are neutral

    D) none of the above

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  • question_answer85) Which of the following will not give a positive iodoform test?

    A) \[C{{H}_{3}}C{{H}_{2}}CHOHC{{H}_{3}}\]

    B) \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}COC{{H}_{3}}\]

    C) \[C{{H}_{3}}C{{H}_{2}}COC{{H}_{2}}C{{H}_{3}}\]

    D) \[C{{H}_{3}}CO{{C}_{6}}{{H}_{5}}\]

    View Answer play_arrow
  • question_answer86) The reason for the loss of optical activity of lactic acid when\[-OH\]group is changed by H is that

    A) chiral centre of the molecule is destroyed

    B) molecules acquires asymmetry

    C) due to change in configuration

    D) structural changes occurs

    View Answer play_arrow
  • question_answer87) To distinguish between salicylic acid and phenol one can use

    A) \[NaHC{{O}_{3}}\]solution

    B) \[5%\text{ }NaOH\]solution

    C) neutral\[FeC{{l}_{3}}\]

    D) bromine water

    View Answer play_arrow
  • question_answer88) \[C-H\]bond energy is about 101 kcal/mol for methane, ethane and other alkanes but is only 77 kcal/mol for\[C-H\]bond of\[C{{H}_{3}}\]in toluene. This is because

    A) of inductive effect due to\[-C{{H}_{3}}\]in toluene

    B) of the presence of benzene ring in toluene

    C) of resonance among the structures of benzyl radical in toluene

    D) aromaticity of toluene

    View Answer play_arrow
  • question_answer89) Which of the following ions can be replaced by \[{{H}^{+}}\]ions when\[{{H}_{2}}\]gas is bubbled through the solutions containing these ions?

    A) \[L{{i}^{+}}\]

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

    C) \[C{{u}^{2+}}\]

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

    View Answer play_arrow
  • question_answer90) Alum is added to muddy water because

    A) it acts as disinfectant

    B) it results in coagulation of clay arid sand

    C) clay is soluble in alum, hence removes it

    D) it makes water alkaline which is good for health

    View Answer play_arrow
  • question_answer91) \[N{{H}_{3}}\]gas is dried over

    A) \[CaO\]

    B) \[HN{{O}_{3}}\]

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

    D) \[CuS{{O}_{4}}\]

    View Answer play_arrow
  • question_answer92) Which one of the following is not correct for an ideal solution?

    A) It must obey Raoults law

    B) \[\Delta H=0\]

    C) \[\Delta U=0\]

    D) \[\Delta H=\Delta V\ne 0\]

    View Answer play_arrow
  • question_answer93) Borax bead test of Cr (chromium) is

    A) green

    B) blue

    C) violet

    D) brown

    View Answer play_arrow
  • question_answer94) A catalyst

    A) lowers the activation energy

    B) changes the rate constant

    C) changes the product

    D) itself destroys in the reaction

    View Answer play_arrow
  • question_answer95) Which of the following is cross-linked polymer?

    A) Teflon

    B) Orion

    C) Nylon

    D) Bakelite

    View Answer play_arrow
  • question_answer96) In the reaction sequence\[C{{H}_{3}}CH=C{{H}_{2}}\xrightarrow[(ii){{H}_{2}}O/Zn]{(i){{O}_{3}}}\Pr oducts\]Products will be

    A) \[C{{H}_{3}}COC{{H}_{3}}\]

    B) \[C{{H}_{3}}COC{{H}_{2}}OH\]

    C) \[C{{H}_{3}}COOH+HCOOH\]

    D) \[C{{H}_{3}}CHO+HCHO\]

    View Answer play_arrow
  • question_answer97) The conditions for aromaticity is

    A) molecule must have clouds of delocalized \[\pi -\]electrons

    B) molecule must contain\[(4n+2)\pi -\]electrons

    C) both (a) and (b)

    D) none of the above

    View Answer play_arrow
  • question_answer98) Which of the following increases the octane number?

    A) Branching of chain

    B) Absence of double and triple bond

    C) Non-cyclic alkanes

    D) None of the above

    View Answer play_arrow
  • question_answer99) Chlorobenzene gives aniline with

    A) \[N{{H}_{3}}/C{{u}_{2}}O\]

    B) \[N{{H}_{3}}/{{H}_{2}}S{{O}_{4}}\]

    C) \[NaN{{H}_{2}}\]

    D) none of these

    View Answer play_arrow
  • question_answer100) In\[CsCl\] type structure the co-ordination of\[C{{s}^{+}}\]and\[C{{l}^{-}}\]are

    A) 6, 6

    B) 6, 8

    C) 8, 8

    D) 8, 6

    View Answer play_arrow
  • question_answer101) Hesss law is used to calculate:

    A) enthalpy of reaction

    B) entropy of reaction

    C) work done in reaction

    D) all of the above

    View Answer play_arrow
  • question_answer102) Which of the following is not a Lewis base?

    A) \[N{{H}_{3}}\]

    B) \[{{H}_{2}}O\]

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

    D) None of these

    View Answer play_arrow
  • question_answer103) Active charcoal is a good catalyst because

    A) made up of carbon atoms

    B) is very reactive

    C) has more adsorption power

    D) has inert nature toward reagent

    View Answer play_arrow
  • question_answer104) \[{{H}_{2}}\]cannot be displaced by

    A) \[L{{i}^{+}}\]

    B) \[S{{r}^{2+}}\]

    C) \[A{{l}^{3+}}\]

    D) \[A{{g}^{+}}\]

    View Answer play_arrow
  • question_answer105) Which of the following is amphoteric?

    A) \[{{V}_{2}}{{O}_{3}}\]

    B) \[CuO\]

    C) \[{{V}_{2}}{{O}_{5}}\]

    D) \[NiO\]

    View Answer play_arrow
  • question_answer106) The emf of the cell,\[({{E}_{Z{{n}^{2+}}/Zn}}=-0.76\,V)\]\[Zn/Z{{n}^{2+}}(1M)||C{{u}^{2+}}(1M)Cu\]\[({{E}_{C{{u}^{2+}}/Cu}}=+0.34V)\]will be

    A) \[+1.10\text{ }V\]

    B) \[-1.10\text{ }V\]

    C) \[+\text{ }0.42V\]

    D) \[-0.42V\]

    View Answer play_arrow
  • question_answer107) Which of the following is correct number of carbon atom present as the constituent of kerosene oil?

    A) \[{{C}_{10}}-{{C}_{16}}\]

    B) \[{{C}_{4}}-{{C}_{6}}\]

    C) \[{{C}_{8}}-{{C}_{16}}\]

    D) \[{{C}_{12}}-{{C}_{18}}\]

    View Answer play_arrow
  • question_answer108) Water possesses a high dielectric constant, therefore

    A) it always contains ions

    B) it is a universal solvent

    C) can dissolve covalent compounds

    D) can conduct electricity

    View Answer play_arrow
  • question_answer109) Aldehydes can be oxidised by

    A) Tollens reagent

    B) Fehling solution

    C) Benedict solution

    D) All of these

    View Answer play_arrow
  • question_answer110) The\[\Delta H_{f}^{o}\]for\[C{{O}_{2}}(g),CO(g)\]and\[{{H}_{2}}O(g)\] are \[-393.5,-110.5\] and \[-241.8~kJ/mol\] respectively. The standard enthalpy change (in kJ) for the reaction\[C{{O}_{2}}(g)+{{H}_{2}}(g)\xrightarrow[{}]{{}}CO(g)+{{H}_{2}}O(g)\]is

    A) 524.1

    B) 41.2

    C) \[-262.5\]

    D) \[-41.2\]

    View Answer play_arrow
  • question_answer111) Of a total of 600 bolts, 20% are too large and 10% are too small. The remainder are considered to be suitable. If a bolt is selected at random, the probability that it will be suitable is

    A) \[\frac{1}{5}\]

    B) \[\frac{7}{10}\]

    C) \[\frac{1}{10}\]

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

    View Answer play_arrow
  • question_answer112) The area enclosed within the curve\[|x|+|y|=1\]is

    A) 1 sq unit

    B) \[2\sqrt{2}\]sq unit

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

    D) 2 sq unit

    View Answer play_arrow
  • question_answer113) If\[P(B)=\frac{3}{4},P(A\cap B\cap \overline{C})=\frac{1}{3}\]and\[P(\overline{A}\cap B\cap \overline{C})=\frac{1}{3},\]then\[P(B\cap C)\]is

    A) 1/12

    B) 1/6

    C) 1/15

    D) 1/9

    View Answer play_arrow
  • question_answer114) The value of\[\sin \left( {{\sin }^{-1}}\frac{1}{3}+{{\sec }^{-1}}3 \right)+\]\[\cos \left( {{\tan }^{-1}}\frac{1}{2}+{{\tan }^{-1}}2 \right)\]is

    A) 1

    B) 2

    C) 3

    D) 4

    View Answer play_arrow
  • question_answer115) \[\int_{0}^{\pi /2}{\frac{\sqrt{\cot x}}{\sqrt{\cot x}+\sqrt{\tan x}}}dx\]is equal to

    A) 1

    B) \[-1\]

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

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

    View Answer play_arrow
  • question_answer116) Area bounded by the curve\[y={{\log }_{e}}x,x=0,y\le 0\]and\[x-\]axis is

    A) 1 sq unit

    B) 1/2 sq unit

    C) 2 sq unit

    D) none of these

    View Answer play_arrow
  • question_answer117) If\[|\overrightarrow{a}\times \overrightarrow{b}{{|}^{2}}+|\overrightarrow{a}.\overrightarrow{b}{{|}^{2}}=144\]and\[|\overrightarrow{a}|=4,\]Then\[|\overrightarrow{b}|\]is equal to

    A) 12

    B) 3

    C) 8

    D) 4

    View Answer play_arrow
  • question_answer118) Given that\[|\overrightarrow{a}|=3,|\overrightarrow{b}|=4,|\overrightarrow{a}\times \overrightarrow{b}|=10,\]then\[|\overrightarrow{a}.\overrightarrow{b}{{|}^{2}}\]equals

    A) 88

    B) 44

    C) 22

    D) none of these

    View Answer play_arrow
  • question_answer119) \[\underset{x\to 0}{\mathop{\lim }}\,x\log \sin x\]is equal to

    A) zero

    B) \[\infty \]

    C) 1

    D) cannot be determined

    View Answer play_arrow
  • question_answer120) If\[x=1+a+{{a}^{2}}+......\] to infinity and \[y=1+b+{{b}^{2}}+......\]to infinity, where a, bare proper fractions, then\[1+ab+{{a}^{2}}{{b}^{2}}+...\]to infinity is equal to

    A) \[\frac{xy}{x+y-1}\]

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

    C) \[\frac{xy}{x-y+1}\]

    D) \[\frac{xy}{x+y+1}\]

    View Answer play_arrow
  • question_answer121) \[{{\cos }^{4}}\theta -{{\sin }^{4}}\theta \]is equal to

    A) \[1+2{{\sin }^{2}}\left( \frac{\theta }{2} \right)\]

    B) \[2{{\cos }^{2}}\theta -1\]

    C) \[1-2{{\sin }^{2}}\left( \frac{\theta }{2} \right)\]

    D) \[1+2{{\cos }^{2}}\theta \]

    View Answer play_arrow
  • question_answer122) If\[y=f(x)=\frac{x+2}{x-1},\]then

    A) \[x=f(y)\]

    B) \[f(1)=3\]

    C) \[y\]increases with\[x\]for\[x<1\]

    D) \[f\]is a rational function of\[x\]

    View Answer play_arrow
  • question_answer123) A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is \[60{}^\circ \]. When he retreats 20 ft from the bank, he finds the angle to be\[30{}^\circ \]. The breadth of the river in feet is

    A) 15

    B) \[15\sqrt{3}\]

    C) \[10\sqrt{3}\]

    D) \[10\]

    View Answer play_arrow
  • question_answer124) If\[\tan \alpha =\frac{m}{m+1}\]and\[\tan \beta =\frac{1}{2m+1},\]then\[\alpha +\beta \]is equal to

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

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

    C) zero

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

    View Answer play_arrow
  • question_answer125) If\[f(x)=x[\sqrt{x}-\sqrt{x+1}],\]then

    A) \[f(x)\]is continuous but not differentiable at\[x=0\]

    B) \[f(x)\]is not differentiable at \[x=0\]

    C) \[f(x)\]is differentiable at\[x=0\]

    D) none of the above

    View Answer play_arrow
  • question_answer126) \[tan\alpha +2\text{ }tan\text{ }2\alpha +4\text{ }tan\text{ }4\alpha +8\text{ }cot\text{ }8\alpha \]is equal to

    A) \[tan\text{ }16\alpha \]

    B) 0

    C) \[\cot \alpha \]

    D) none of these

    View Answer play_arrow
  • question_answer127) A book contains 1000 pages numbered consecutively. The probability that the sum of the digits of the number of a page is 9, is

    A) zero

    B) \[\frac{55}{1000}\]

    C) \[\frac{33}{1000}\]

    D) \[\frac{44}{1000}\]

    View Answer play_arrow
  • question_answer128) A number is chosen at random among the first 120 natural numbers. The probability of the number chosen being a multiple of 5 or 15 is

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

    B) \[\frac{1}{5}\]

    C) \[\frac{1}{24}\]

    D) \[\frac{1}{6}\]

    View Answer play_arrow
  • question_answer129) If\[\overrightarrow{a}=2\hat{i}+\hat{j}+\hat{k},\overrightarrow{b}=\hat{i}-2\hat{j}-\hat{k},\]\[\overrightarrow{c}=\hat{i}+\hat{j}+\hat{k},\] then\[\overrightarrow{a}\times (\overrightarrow{b}\times \overrightarrow{c})\]equals

    A) \[5\hat{i}-7\hat{j}-3\hat{k}\]

    B) \[5\hat{i}+7\hat{j}-3\hat{k}\]

    C) \[5\hat{i}-7\hat{j}+3\hat{k}\]

    D) zero

    View Answer play_arrow
  • question_answer130) The coefficient of\[{{x}^{4}}\]in the expansion of\[{{\left( \frac{x}{2}-\frac{3}{{{x}^{2}}} \right)}^{10}}\]is

    A) \[\frac{504}{259}\]

    B) \[\frac{450}{263}\]

    C) \[\frac{405}{256}\]

    D) none of these

    View Answer play_arrow
  • question_answer131) Equation of the ellipse whose foci are (2, 2) and (4, 2) and the major axis is of length 10, is

    A) \[\frac{{{(x+3)}^{2}}}{24}+\frac{{{(y+2)}^{2}}}{25}=1\]

    B) \[\frac{{{(x-3)}^{2}}}{24}+\frac{{{(y-2)}^{2}}}{25}=1\]

    C) \[\frac{{{(x+3)}^{2}}}{24}+\frac{{{(y+2)}^{2}}}{24}=1\]

    D) \[\frac{{{(x-3)}^{2}}}{25}+\frac{{{(y-2)}^{2}}}{24}=1\]

    View Answer play_arrow
  • question_answer132) The volume of the solid generated by the revolution of the curve\[y=\frac{{{a}^{3}}}{{{a}^{2}}+{{x}^{2}}}\]about\[x-\]axis is

    A) \[\frac{1}{2}{{\pi }^{3}}{{a}^{2}}\]

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

    C) \[\frac{1}{2}{{\pi }^{2}}{{a}^{3}}\]

    D) \[{{\pi }^{2}}{{a}^{3}}\]

    View Answer play_arrow
  • question_answer133) The radius of the circle\[\left| \frac{z-i}{z+i} \right|=5\]is given by

    A) \[\frac{13}{12}\]

    B) \[\frac{5}{12}\]

    C) 5

    D) 625

    View Answer play_arrow
  • question_answer134) If\[\overrightarrow{a}=(1,p,1),\overrightarrow{b}=(q,2,2),\overrightarrow{a}.\overrightarrow{b}=r\]and \[\overrightarrow{a}\times \overrightarrow{b}=(0,-3,3)\], then p, q, r are in that order

    A) 1, 5, 9

    B) 9, 5, 1

    C) 5, 1, 9

    D) none of these

    View Answer play_arrow
  • question_answer135) The foci of an ellipse are\[(0,\pm 4)\]and the equations for the directories are\[y=\pm 9\]. The equation for the ellipse is

    A) \[5{{x}^{2}}+9{{y}^{2}}=4\]

    B) \[2{{x}^{2}}-6{{y}^{2}}=28\]

    C) \[6{{x}^{2}}+3{{y}^{2}}=45\]

    D) \[9{{x}^{2}}+5{{y}^{2}}=180\]

    View Answer play_arrow
  • question_answer136) The straight lines \[x+y=0,3x+y-4=0\] and \[x+3y-4=0\]form a triangle which is

    A) right angled

    B) equilateral

    C) isosceles

    D) none of these

    View Answer play_arrow
  • question_answer137) The eccentricity of the hyperbola \[9{{x}^{2}}-16{{y}^{2}}-18x-64y-199=0\]is

    A) \[\frac{16}{9}\]

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

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

    D) zero

    View Answer play_arrow
  • question_answer138) A four-digit number is formed by the digits 1, 2, 3, 4 with no repetition. The probability that the number is odd, is

    A) zero

    B) 1/3

    C) 1/4

    D) none of these

    View Answer play_arrow
  • question_answer139) The coefficient of\[{{x}^{n}}\]in the expansion of\[\frac{(a-bx)}{{{e}^{x}}}\]is

    A) \[\frac{{{(-1)}^{n}}}{n!}(a+bn)\]

    B) \[\frac{{{(-1)}^{n}}}{n!}(b+an)\]

    C) \[\frac{{{(-1)}^{n+1}}}{n!}(a+bn)\]

    D) none of these

    View Answer play_arrow
  • question_answer140) The value of \[{{\cot }^{-1}}9+\cos e{{c}^{-1}}\frac{\sqrt{41}}{4}\]is given by

    A) 0

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

    C) \[{{\tan }^{-1}}2\]

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

    View Answer play_arrow
  • question_answer141) The value of \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{e}^{x}}+\log (1+x)-{{(1-x)}^{-2}}}{{{x}^{2}}}\]is equal to

    A) 0

    B) -3

    C) \[-1\]

    D) infinity

    View Answer play_arrow
  • question_answer142) The values of k for which the equations \[{{x}^{2}}-kx-21=0\]and\[{{x}^{2}}-3kx+35=0\]will have a common roots are

    A) \[k=\pm 4\]

    B) \[k=\pm 1\]

    C) \[k=\pm 3\]

    D) \[k=0\]

    View Answer play_arrow
  • question_answer143) \[\overrightarrow{a}\]and\[\overrightarrow{b}\]are two non-zero vectors, then \[(\overrightarrow{a}+\overrightarrow{b})-(\overrightarrow{a}-\overrightarrow{b})\]is equal to

    A) \[a+b\]

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

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

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

    View Answer play_arrow
  • question_answer144) If\[sin\text{ }x+si{{n}^{2}}x=1,\]then \[co{{s}^{6}}x+co{{s}^{12}}x+3\text{ }co{{s}^{10}}x+3\text{ }co{{s}^{8}}x\] is equal to

    A) 1

    B) \[co{{s}^{3}}x\text{ }si{{n}^{3}}x\]

    C) 0

    D) \[\infty \]

    View Answer play_arrow
  • question_answer145) The integrating factor of the differential equation\[\frac{dy}{dx}+\frac{1}{x}y=3x\]is

    A) \[x\]

    B) In \[x\]

    C) 0

    D) \[\infty \]

    View Answer play_arrow
  • question_answer146) \[\int_{0}^{\pi /2}{x{{\sin }^{2}}x{{\cos }^{2}}x}dx\]is equal to

    A) \[\frac{{{\pi }^{2}}}{32}\]

    B) \[\frac{{{\pi }^{2}}}{16}\]

    C) \[\frac{\pi }{32}\]

    D) none of these

    View Answer play_arrow
  • question_answer147) If H is harmonic mean between P and Q, then the value of\[\frac{H}{P}+\frac{H}{Q}\]is

    A) 2

    B) \[\frac{PQ}{(P+Q)}\]

    C) \[\frac{(P+Q)}{PQ}\]

    D) none of these

    View Answer play_arrow
  • question_answer148) The value of y for which the equation \[{{x}^{2}}+pxy+{{y}^{2}}-5x-7y+6=0\]represents a pair of straight lines is

    A) 5/2

    B) 5

    C) 2

    D) 2/5

    View Answer play_arrow
  • question_answer149) Angle between the vectors\[\sqrt{3}(\overrightarrow{a}\times \overrightarrow{b})\]and\[\overrightarrow{b}-(\overrightarrow{a}.\overrightarrow{b})\overrightarrow{a}\]is

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

    B) 0

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

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

    View Answer play_arrow
  • question_answer150) The equation of the circle passing through (4,5) having the centre (2, 2) is

    A) \[{{x}^{2}}+{{y}^{2}}+4x+4y-5=0\]

    B) \[{{x}^{2}}+{{y}^{2}}-4x-4y-5=0\]

    C) \[{{x}^{2}}+{{y}^{2}}-4x=13\]

    D) \[{{x}^{2}}+{{y}^{2}}-4x-4y+5=0\]

    View Answer play_arrow
  • question_answer151) The smallest positive integer n for which\[{{\left( \frac{1+i}{1-i} \right)}^{n}}=1\]is

    A) \[n=8\]

    B) \[n=12\]

    C) \[n=16\]

    D) none of these

    View Answer play_arrow
  • question_answer152) The equation of tangents drawn from the origin to the circle \[{{x}^{2}}+{{y}^{2}}-2rx-2hy+{{h}^{2}}=0\] are

    A) \[x=0,y=0\]

    B) \[x=1,y=0\]

    C) \[({{h}^{2}}-{{r}^{2}}))x-2rhy=0,y=0\]

    D) \[({{h}^{2}}-{{r}^{2}})x-2rhy=0,x=0\]

    View Answer play_arrow
  • question_answer153) The value of\[{{9}^{1/3}}\times {{9}^{1/9}}\times {{9}^{1/27}}\times ....\infty \]is

    A) 9

    B) 1

    C) 3

    D) none of these

    View Answer play_arrow
  • question_answer154) Let\[0<P(A)<1,0<P(B)<1\]and\[P(A\cup B)=P(A)+P(B)-P(A)\text{ }P(B),\]then

    A) \[P(B/A)=P(B)-P(A)\]

    B) \[P(A\cup B)=P(A)+P(B)\]

    C) \[P(A\cap B)=P(A)P(B)\]

    D) none of the above

    View Answer play_arrow
  • question_answer155) The probability that in the toss of two dice we obtain the sum 7 or 11, is

    A) \[\frac{1}{6}\]

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

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

    D) \[\frac{23}{108}\]

    View Answer play_arrow
  • question_answer156) If\[{{2}^{x}}+{{2}^{y}}={{2}^{x+y}},\]then\[\frac{dy}{dx}\]is equal to

    A) \[\frac{({{2}^{x}}+{{2}^{y}})}{({{2}^{x}}-{{2}^{y}})}\]

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

    C) \[{{2}^{x-y}}\left( \frac{{{2}^{y}}-1}{1-{{2}^{x}}} \right)\]

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

    View Answer play_arrow
  • question_answer157) If the probability of A to fail in an examination is 0.2 and that for B is 0.3, then probability that either A or B is fail, is

    A) 0.5

    B) 0.44

    C) 0.8

    D) 0.25

    View Answer play_arrow
  • question_answer158) If\[f(x)=\cos (\log x),\]then\[f(x)f(y)-\frac{1}{2}\left[ f\left( \frac{x}{y} \right)+f(xy) \right]\]has the value

    A) \[-1\]

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

    C) \[-2\]

    D) zero

    View Answer play_arrow
  • question_answer159) If\[y={{3}^{x-1}}+{{3}^{-x-1}}\] (\[x\]real), then the least value of y is

    A) 2

    B) 6

    C) 2/3

    D) none of these

    View Answer play_arrow
  • question_answer160) The value of\[\theta \]lying between\[\theta =0\]and\[\frac{\pi }{2}\]and satisfying the equation\[\left| \begin{matrix} 1+{{\sin }^{2}}\theta & {{\cos }^{2}}\theta & 4\sin 4\theta \\ {{\sin }^{2}}\theta & 1+{{\cos }^{2}}\theta & 4\sin 4\theta \\ {{\sin }^{2}}\theta & {{\cos }^{2}}\theta & 1+4\sin 4\theta \\ \end{matrix} \right|=0\]is

    A) \[\frac{7\pi }{24}\]

    B) \[\frac{5\pi }{24}\]

    C) \[\frac{11\pi }{2}\]

    D) \[\frac{\pi }{24}\]

    View Answer play_arrow
  • question_answer161) \[{{\left( \frac{-1+\sqrt{-3}}{2} \right)}^{100}}+{{\left( \frac{-1-\sqrt{-3}}{2} \right)}^{100}}\]is equal to

    A) 2

    B) zero

    C) \[-1\]

    D) 1

    View Answer play_arrow
  • question_answer162) If\[\alpha ,\beta \]be the two roots of the equation \[{{x}^{2}}+x+1=0,\]then the equation whose roots are \[\frac{\alpha }{\beta }\]and \[\frac{\beta }{\alpha }\]is

    A) \[{{x}^{2}}+x+1=0\]

    B) \[{{x}^{2}}-x+1=0\]

    C) \[{{x}^{2}}-x-1=0\]

    D) \[{{x}^{2}}+x-1=0\]

    View Answer play_arrow
  • question_answer163) In a binomial distribution, the mean is 4 and variance is 3. Then, its mode is

    A) 5

    B) 6

    C) 4

    D) none of these

    View Answer play_arrow
  • question_answer164) The equation of a line passing through\[(-2,-4)\] and perpendicular to the line\[3x-y+5=0\]is

    A) \[3y+x-8=0\]

    B) \[3x+y+6=0\]

    C) \[x+3y+14=0\]

    D) none of these

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  • question_answer165) \[\underset{x\to 0}{\mathop{\lim }}\,{{(\cos ecx)}^{1/\log x}}\]is equal to

    A) 0

    B) 1

    C) 1/e

    D) none of these

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  • question_answer166) The minimum value of \[f(x)={{\sin }^{4}}x+{{\cos }^{4}}x,0\le x\le \frac{\pi }{2}\]is

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

    B) \[\frac{1}{4}\]

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

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

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  • question_answer167) A vector of magnitude 5 and perpendicular to. \[(\hat{i}-2\hat{j}+\hat{k})\]and\[(2\hat{i}+\hat{j}-3\hat{k})\]is

    A) \[\frac{5\sqrt{3}}{3}(\hat{i}+\hat{j}+\hat{k})\]

    B) \[\frac{5\sqrt{3}}{3}(\hat{i}+\hat{j}-\hat{k})\]

    C) \[\frac{5\sqrt{3}}{3}(\hat{i}-\hat{j}+\hat{k})\]

    D) \[\frac{5\sqrt{3}}{3}(-\hat{i}+\hat{j}+\hat{k})\]

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  • question_answer168) \[\int_{-\pi /3}^{\pi /3}{\frac{x\sin x}{{{\cos }^{2}}x}}dx\]is

    A) \[\frac{1}{3}(4\pi +1)\]

    B) \[\frac{4\pi }{3}-2\log \tan \frac{5\pi }{12}\]

    C) \[\frac{4\pi }{3}+\log \tan \frac{5}{12}\]

    D) none of these

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  • question_answer169) \[\sum\limits_{r=0}^{m}{^{n+r}{{C}_{n}}}\]is equal to

    A) \[^{n+m+1}{{C}_{n+1}}\]

    B) \[^{n+m+2}{{C}_{n}}\]

    C) \[^{n+m+3}{{C}_{n-1}}\]

    D) none of these

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  • question_answer170) The angle between the lines \[2x=3y=-\text{ }z\] and \[6x=-\text{ }y=-4z\]is

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

    B) \[0{}^\circ \]

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

    D) \[45{}^\circ \]

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