Solved papers for JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2011

done Jamia Millia Islamia Solved Paper-2011

  • question_answer1) With what minimum acceleration can a fireman slides down a rope while breaking strength of the rope is\[\frac{2}{3}\]of his weight?

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

    B) \[g\]

    C) \[\frac{1}{3}g\]

    D) Zero

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  • question_answer2) An ice cream has a marked value of 700 kcal. How many kilowatt-hour of energy will it deliver to the body as it if digested?

    A) 0.81 kWh

    B) 0.90 kWh

    C) 1.11 kWh

    D) 0.71 kWh

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  • question_answer3) A Uniform cylinder has a radius R and length L. If the moment of inertia of this cylinder about an axis passing through its centre and normal to its circular face is equal to the moment of inertia of the same cylinder about an axis passing through its centre and perpendicular to it length then

    A) \[L=R\]

    B) \[L=\sqrt{3}R\]

    C) \[L=\frac{R}{\sqrt{3}}\]

    D) \[L=\sqrt{\frac{3}{2}}R\]

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  • question_answer4) The Youngs modulus of the material of a wire is\[6\times {{10}^{12}}N/{{m}^{2}}\]and there is no transverse Strain in it, then its modulus of rigidity will be

    A) \[3\times {{10}^{12}}N{{m}^{-2}}\]

    B) \[2\times {{10}^{12}}N{{m}^{-2}}\]

    C) \[{{10}^{12}}N{{m}^{-2}}\]

    D) None of these

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  • question_answer5) Oil spreads over the surface of water whereas water does not spread over the surface of the oil, due to

    A) surface tension of water is very high

    B) surface tension of water is very low

    C) viscosity of oil is high

    D) viscosity of water is high

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  • question_answer6) A student attempts to pull himself up by tugging on his hair, the will not succeed

    A) as the force exerted is small

    B) the frictional force while gripping, is small

    C) Newtons law of inertia is not applicable to living beings

    D) as the force applied is internal to the system

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  • question_answer7) A circular disc of mass 0.41 kg and radius 10 m rolls without slippling with a velocity of 2 m/s. The total kinetic energy of disc is

    A) 0.41 J

    B) 1.23 J

    C) 0.82 J

    D) 2.4 J

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  • question_answer8) The cylindrical tube of a spray pump has a cross-section of\[8\text{ }c{{m}^{2}},\] are end of which has 45 fine holes each of area\[{{10}^{-8}}{{m}^{2}}\]. If the liquid flows inside the tube with a speed of 0.15 m \[mi{{n}^{-1}},\]the speed with which the liquid is ejected through the holes is

    A) \[50\,m{{s}^{-1}}\]

    B) \[5\,m{{s}^{-1}}\]

    C) \[0.05\,m{{s}^{-1}}\]

    D) \[0.5\,m{{s}^{-1}}\]

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  • question_answer9) At nodes in stationary waves

    A) change in pressure and density are maximum

    B) change in pressure and density are minimum

    C) strain is zero

    D) energy is maximum

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  • question_answer10) Eight dipoles of changes of magnitude are placed inside a cube. The total electric flux coming out of the cube will be

    A) \[\frac{8e}{{{\varepsilon }_{0}}}\]

    B) \[\frac{16e}{{{\varepsilon }_{0}}}\]

    C) \[\frac{e}{{{\varepsilon }_{0}}}\]

    D) zero

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  • question_answer11) The X-ray beam coming from on X-ray tube will be

    A) monochromatic

    B) having all wavelength smaller than a certain maximum wavelength

    C) having all wavelength larger than a certain minimum wavelength

    D) having all wavelength lying between a minimum and a maximum wavelength

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  • question_answer12) The half of\[^{215}At\]is 100 as. The time taken for the radioactivity of a sample of 215 At to decay to 1/ 16th of its initial value is

    A) 400 as

    B) 6.3 as

    C) 40 as

    D) 30 as

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  • question_answer13) In a hydrogen atom, the distance between the electron and proton is\[2.5\times {{10}^{-11}}m\]. The electrical force of attraction between them will be

    A) \[2.8\times {{10}^{-7}}N\]

    B) \[3.7\times {{10}^{-7}}N\]

    C) \[6.2\times {{10}^{-7}}N\]

    D) \[9.1\times {{10}^{-7}}N\]

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  • question_answer14) A cable of resistance\[10\,\Omega \] arrives electric power from a generator producing 250 kW at 10000 V. The current in the cable is

    A) 25 A

    B) 250 A

    C) 100 A

    D) 1000 A

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  • question_answer15) A particle moving along x-axis has acceleration \[f,\]at time t, given by\[f={{f}_{0}}\left( 1-\frac{t}{T} \right),\] where\[{{f}_{0}}\] and T are constants. The particle at\[t=0,\]has zero velocity. In the time interval between\[t=0,\]and the instant when\[f=0,\]the particles velocity\[({{v}_{s}})\]is

    A) \[{{f}_{o}}t\]

    B) \[\frac{1}{2}{{f}_{o}}{{T}^{2}}\]

    C) \[{{f}_{o}}{{T}^{2}}\]

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

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  • question_answer16) A particle moves towards east with velocity 5 \[m{{s}^{-1}}\]. After 10 s its direction changes towards north with same velocity. The average acceleration of the particle is

    A) zero

    B) \[\frac{1}{2}m{{s}^{-2}},N-W\]

    C) \[\frac{1}{\sqrt{2}}m{{s}^{-2}},N-E\]

    D) \[\frac{1}{\sqrt{2}}m{{s}^{-2}},S-W\]

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  • question_answer17) A soap bubble oscillates with time period T, which in turn depends on the pressure p, density\[\rho \]and surface tension o. Which of the following correctly represents the expression for\[{{T}^{2}}\]?

    A) \[\frac{\rho {{\sigma }^{2}}}{{{p}^{3}}}\]

    B) \[\frac{\rho {{\sigma }^{3}}}{\sigma }\]

    C) \[\frac{{{\rho }^{3}}\sigma }{\rho }\]

    D) \[\frac{\rho }{{{p}^{3}}\sigma }\]

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  • question_answer18) If an object weigh 270 N at the earths surface, what will be the weight of the object at an altitude equal to twice the radius of earth?

    A) 270 N

    B) 90 N

    C) 30 N

    D) 60 N

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  • question_answer19) A fixed mortar fires a bomb at an angle of\[53{}^\circ \]above the horizontal with a muzzle velocity of\[80\text{ }m{{s}^{-1}}\]. A tank is advancing directly towards the mortar on level ground at a constant speed of\[\text{5 }m{{s}^{-1}}\]. The initial separation (at the instant mortar is fired) between the mortar and tank so that the tank would be hit is [Take\[g=10\text{ }m{{s}^{-2}}\]]

    A) 678.4m

    B) \[614.4\,\mu \]

    C) 64 m

    D) None of these

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  • question_answer20) A rock is dropped from a 100 m high cliff. How long does it take to fall first 50 m and the second 50m?

    A) \[2s,3s\]

    B) \[1.5s,\text{ }2.5s\]

    C) \[1.2s,\text{ }3.2s\]

    D) \[3.2s,1.3s\]

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  • question_answer21) Two bodies of masses\[{{M}_{1}}\]and\[{{M}_{2}}\]are dropped from heights\[{{H}_{1}}\]and\[{{H}_{2}}\]respectively. They reach the ground after time\[{{T}_{1}}\]and\[{{T}_{2}}\] respectively. Which of the following relation is correct?

    A) \[\frac{{{T}_{1}}}{{{T}_{2}}}={{\left[ \frac{{{H}_{1}}}{{{H}_{2}}} \right]}^{1/2}}\]

    B) \[\frac{{{T}_{1}}}{{{T}_{2}}}=\frac{{{H}_{1}}}{{{H}_{2}}}\]

    C) \[\frac{{{T}_{1}}}{{{T}_{2}}}={{\left[ \frac{{{M}_{1}}}{{{M}_{2}}} \right]}^{1/2}}\]

    D) \[\frac{{{T}_{1}}}{{{T}_{2}}}=\frac{{{M}_{1}}}{{{M}_{2}}}\]

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  • question_answer22) A circular ring having uniformly distributed mass m and radius r is as shown in the figure. If a point mass m is taken slowly from A to B, then work done by the external agent will be

    A) \[-\frac{GMm}{R}\left[ \frac{1}{\sqrt{2}}-\frac{1}{\sqrt{5}} \right]\]

    B) \[\frac{GMm}{R}\times \frac{1}{\sqrt{5}}\]

    C) \[\frac{GMm}{R}\left[ \frac{1}{\sqrt{2}}-\frac{1}{\sqrt{5}} \right]\]

    D) \[\frac{GMm}{R}\left[ \frac{1}{\sqrt{10}} \right]\]

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  • question_answer23) A plank of mass 12 kg is supported by two identical springs as shown in figure. The plank always remains horizontal. When the plank is pressed down and released, it performs SHM with time period 3 s. When a block of mass m is attached to plank the time period changes to 6 s. The mass of the block is

    A) 48 kg

    B) 36 kg

    C) 24kg

    D) 12kg

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  • question_answer24) Two springs are made to oscillate simple harmonically due to the same mass individually. The time periods obtained are\[{{T}_{1}}\]and\[{{T}_{2}}\]. If both the springs are connected in series and then made to oscillate by the same mass, the resulting time will be

    A) \[{{T}_{1}}+{{T}_{2}}\]

    B) \[\frac{{{T}_{1}}{{T}_{2}}}{{{T}_{1}}+{{T}_{2}}}\]

    C) \[\sqrt{T_{1}^{2}+T_{2}^{2}}\]

    D) \[\frac{{{T}_{1}}+{{T}_{2}}}{2}\]

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  • question_answer25) A string fixed at both ends whose fundamental frequency is 240 Hz is vibrated with the help of tuning fork having frequency 480 Hz, then

    A) string will vibrate with a frequency of 240 Hz

    B) string will vibrate in resonance with the tuning fork

    C) string will vibrate with a frequency of 480 Hz, but is not in resonance with the tuning fork

    D) string is in resonance with tuning fork, and hence vibrates with a frequency of 240 Hz

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  • question_answer26) A material has Poissons ratio 0.50. If a uniform rod of it suffers a longitudinal strain of \[2\times {{10}^{-3}},\]then the percentage change in volume is

    A) 0.6

    B) 0.4

    C) 0.2

    D) zero

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  • question_answer27) The property of metals which allows them to be drawn readily into thin wires beyond the elastic limit without rupturing is known as

    A) malleability

    B) ductility

    C) elasticity

    D) hardness

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  • question_answer28) A solid sphere of radius fi made up of a material of bulk modulus K is surrounded by a liquid in cylindrical container. A massless piston of area A floats on the surface of the liquid. When a mass M is placed on the piston to compress the liquid, the fractional change in the radius of the sphere

    A) \[\frac{Mg}{AK}\]

    B) \[\frac{Mg}{3AK}\]

    C) \[\frac{3Mg}{AK}\]

    D) \[\frac{Mg}{2AK}\]

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  • question_answer29) An open vessel full of water is falling freely under gravity. There is a small hole in one face of the vessel, as shown in the figure. The water which comes out from the hole at the instant when hole is at height H above the ground, strikes the ground at distance of\[x\]from P. Which of the following is correct for the situation described?

    A) The value of\[x\]is\[2\sqrt{\frac{2hH}{3}}\]

    B) The value of\[x\]is\[\sqrt{\frac{4hH}{3}}\]

    C) The value of\[x\]cant be computed, from information provided

    D) The question is irreverent as no water comes out from the hole

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  • question_answer30) Pressure p, volume V, and temperature T certain material are related by \[p=\frac{AT-B{{T}^{2}}}{V}\]where A and B are constants. Find an expression for the work done by the material if the temperature changes from\[{{T}_{1}}\]to\[{{T}_{2}}\]while the pressure remains constant.

    A) \[W=A(T_{1}^{2}-T_{2}^{2})-B(T_{2}^{2}-T_{1}^{2})\]

    B) \[W=A(T_{2}^{2}-T_{1}^{2})-B({{T}_{2}}-{{T}_{1}})\]

    C) \[W=A({{T}_{2}}-{{T}_{1}})-B\left( {{T}_{2}}-\frac{1}{2}{{T}_{1}} \right)\]

    D) \[W=A({{T}_{2}}-{{T}_{1}})-B\left( T_{2}^{2}-T_{1}^{2} \right)\]

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  • question_answer31) Four moles of an ideal gas undergo a reversible isothermal expansion from volume \[{{V}_{1}}\] to volume\[{{V}_{2}}=2{{V}_{1}}\]at temperature T = 400 K. Find the entropy change of the gas.

    A) \[9.22\times {{10}^{3}}J{{K}^{-1}}\]

    B) \[8.22\times {{10}^{2}}J{{K}^{-1}}\]

    C) \[2.31J{{K}^{-1}}\]

    D) \[10.00\times {{10}^{3}}J{{K}^{-1}}\]

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  • question_answer32) A drop, having a mass of\[4.8\times {{10}^{-10}}g\]and a charge of\[2.4\times {{10}^{-8}}C\] is suspended between two charged horizontal plates at a distance 1.0 cm apart. Find the potential difference between the plates.

    A) \[1.96\times {{10}^{6}}V\]

    B) \[1.86\times {{10}^{4}}V\]

    C) \[1.96\times {{10}^{4}}V\]

    D) \[2.96\times {{10}^{4}}V\]

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  • question_answer33) In a potentiometer experiment the balancing with a cell is at length 240 cm. On shunting the cell with a resistance of\[2\,\Omega \] the balancing length becomes 120 cm. The internal resistance of the cell is

    A) \[4\,\Omega \]

    B) \[2\,\Omega \]

    C) \[1\,\Omega \]

    D) \[0.5\,\Omega \]

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  • question_answer34) In the combination of resistance shown in the figure, the potential difference between B and D, is zero, when unknown resistance is

    A) \[0.125\,\Omega \]

    B) \[2\,\Omega \]

    C) \[3\,\Omega \]

    D) for finding the value of\[X,\]the emf of cell is required

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  • question_answer35) At what distance along the central axis of a uniformly charged plastic disk of radius R is the magnitude of the electric field equal to one-half the. magnitude of the field at the centre of the surface of the disk?

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

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

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

    D) \[\sqrt{3}R\]

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  • question_answer36) potential of 500 V is observed near the surface with\[V=0\]at infinity). If two such drops of the same charge and radius combine to form a single spherical drop, the potential at the surface at the new drop?

    A) 590V

    B) 690V

    C) 790V

    D) 890V

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  • question_answer37) Two infinite long current carrying wires A and B are placed as shown in figure. Each wire carries same current\[I\]. The resultant magnetic field intensity at point P is

    A) \[\frac{{{\mu }_{0}}I}{2\pi a}\]

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

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

    D) \[\frac{{{\mu }_{0}}I}{4\sqrt{2}\pi a}\]

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  • question_answer38) The mutual inductance between two planar concentric rings of radii\[{{r}_{1}}\]and\[{{r}_{2}}\](with\[{{r}_{1}}>{{r}_{2}}\]) placed in air is given by

    A) \[\frac{{{\mu }_{0}}\pi r_{2}^{2}}{2{{r}_{1}}}\]

    B) \[\frac{{{\mu }_{0}}\pi r_{1}^{2}}{2{{r}_{2}}}\]

    C) \[\frac{{{\mu }_{0}}\pi ({{r}_{1}}+{{r}_{2}})}{2{{r}_{1}}}\]

    D) \[\frac{{{\mu }_{0}}\pi {{({{r}_{1}}+{{r}_{2}})}^{2}}}{2{{r}_{2}}}\]

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  • question_answer39) A charge\[4\mu C\]is placed on a small conducting sphere that is located at the end of thin insulating rod of length 0.5 m. The rod rotates in horizontal plane with a constant angular velocity of\[100\text{ }rad{{s}^{-1}}\]about a vertical axis that passes through its other end. The magnetic moment of the rotating charge is

    A) zero

    B) \[0.5\times {{10}^{-4}}A{{m}^{2}}\]

    C) \[1.25\times {{10}^{-4}}A{{m}^{2}}\]

    D) magnetic moment is not defined for this case

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  • question_answer40) A parallel plate capacitor is moving with a velocity of\[25\text{ }m{{s}^{-1}}\]through a uniform magnetic field of 1.5 T as shown in figure. If the electric field within the capacitor plates is\[175\text{ }N{{C}^{-1}}\] and plate area is\[25\times {{10}^{-7}}{{m}^{2}},\]then the magnetic force experienced by positive charge plate is

    A) \[1.45\times {{10}^{-13}}N\]

    B) zero

    C) \[8.67\times {{10}^{-15}}N\]

    D) \[3.87\times {{10}^{-15}}N\]

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  • question_answer41) In an AC circuit the potential difference V and current I are given respectively by \[V=100\sin (100t)volt\] and \[I=100\sin \left( 100t+\frac{\pi }{3} \right)mA\] The power dissipated in the circuit will be

    A) \[{{10}^{4}}W\]

    B) \[10W\]

    C) \[2.5\text{ }W\]

    D) \[5W\]

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  • question_answer42) The amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is\[{{B}_{0}}=510\,nT\]. What is the amplitude of the electric field part of the wave?

    A) \[140\text{ }N{{C}^{-1}}\]

    B) \[153\text{ }N{{C}^{-1}}\]

    C) \[163\text{ }N{{C}^{-1}}\]

    D) \[133\text{ }N{{C}^{-1}}\]

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  • question_answer43) Monochromatic light of wavelength 800 nm is used in double slit experiment. One of the slit is covered with a transparent slab of thickness\[2.4\times {{10}^{-5}}m\]. The refractive index of the material of slab is 1.4. What is the number of fringes that will shift due to introduction of the sheet?

    A) 14

    B) 12

    C) 16

    D) 10

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  • question_answer44) A simple pendulum has a time period\[{{T}_{1}}\]when on the earths surface and\[{{T}_{2}}\]when taken to a height R above the earths surface where R is the radius of the earth. The value of\[\frac{{{T}_{2}}}{{{T}_{1}}}\]is

    A) 1

    B) \[\sqrt{2}\]

    C) 4

    D) 2

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  • question_answer45) A cube of side 3 m is placed in front of a concave mirror of focal length 2 m with its face P at a distance 4 m and face Q at a distance 7 m from the mirror. What is distance between the images of face P and Q?

    A) 1.2m

    B) 2.4m

    C) 2.1m

    D) 2.2m

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  • question_answer46) Two stars are situated at distance of 8 light years from the earth. These are to be just resolved by a telescope of diameter 0.25 m. If the wavelength of light used is\[5000\,\overset{o}{\mathop{\text{A}}}\,\]then the distance between the stars must be

    A) \[3\times {{10}^{10}}m\]

    B) \[3.35\times {{10}^{11}}m\]

    C) \[1.95\times {{10}^{11}}m\]

    D) \[4.32\times {{10}^{10}}m\]

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  • question_answer47) Ultraviolet light of wavelength 350 nm and intensity\[1.00\text{ }W{{m}^{-2}}\]is incident on a potassium surface. If 0.5% of the photons participate in ejecting the photoelectrons, how many photo electrons, are emitted per second, if the potassium surface has an area of\[1\text{ }c{{m}^{2}}\]?

    A) \[1.76\times {{10}^{18}}\]photoelectrons/s

    B) \[1.76\times {{10}^{14}}\]photoelectrons/s

    C) \[8.8\times {{10}^{11}}\]photoelectrons/s

    D) The value of work function is required to complete the value of emitted photoelectrons/s

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  • question_answer48) An electron collides with a hydrogen atom in its ground state and excites it to\[n=3\]. The energy given to hydrogen atom in this inelastic collision is [Neglect the recoiling of hydrogen atom]

    A) 10.2 eV

    B) 12.1 eV

    C) 12.5 eV

    D) None of these

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  • question_answer49) A black body radiates at two temperatures\[{{T}_{1}}\]and\[{{T}_{2}}\]. Such that\[{{T}_{1}}<{{T}_{2}}\]. The frequency corresponding to maximum intensity is

    A) less at \[{{T}_{1}}\]

    B) more at \[{{T}_{1}}\]

    C) equal in the two cases

    D) cannot say

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  • question_answer50) Three dielectric slabs of thickness\[\frac{d}{4},\frac{d}{7}\]and \[\frac{d}{2}\] having dielectric constants 2, 8/7 and 4 respectively are inserted between the plates of a parallel plate capacitor having plate separation d and plate area A. The remaining space is filled with a conducting medium. Find the capacitance of the System.

    A) \[\frac{8{{\varepsilon }_{0}}A}{d}\]

    B) \[\frac{8{{\varepsilon }_{0}}A}{3d}\]

    C) \[\frac{26{{\varepsilon }_{0}}A}{35d}\]

    D) \[\frac{12{{\varepsilon }_{0}}A}{35d}\]

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  • question_answer51) Two bodies of different masses has been released from the top of tower. One is thrown in horizontal direction while other is dropped, then which will reach the ground first?

    A) The body which has been thrown horizontally

    B) The body which has been dropped

    C) Both will reach the ground simultaneously

    D) Depends on the velocity with which the first bod has been projected horizontally

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  • question_answer52) A body dropped from a height H reaches the ground with a speed of\[1.2\sqrt{gH}\]. Calculate the work done by air-friction.

    A) 2.8 mgH

    B) \[-1.3\,mgH\]

    C) 1.3 mgH

    D) \[-0.28\,mgH\]

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  • question_answer53) The resistance of a wire at\[20{}^\circ C\]is\[20\,\Omega \] and at \[500{}^\circ C\] is \[60\,\Omega \]. At which temperature its resistance will be\[25\,\Omega \]?

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

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

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

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

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  • question_answer54) Two cells connected in series have electromotive force of 1.5 V each. Their internal resistance are\[0.5\,\Omega \]. and\[0.25\,\Omega \] respectively. This combination is connected to a resistance of\[2.25\,\Omega \]. Potential difference across the terminals of each cell

    A) IV, 0.25V

    B) IV, 1.25V

    C) 1.5V, 2.25V

    D) 1.5V, 2.56V

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  • question_answer55) A swimmer of mass m rests on top of a Styrofoam slab, which has thickness h and density\[{{\rho }_{s}}\]. The area of the slab if it floats in water with its upper surface just awash is [Take density of water to be\[{{\rho }_{w}}\]].

    A) \[\frac{m}{h({{\rho }_{s}}+{{\rho }_{w}})}\]

    B) \[\frac{m}{h{{\rho }_{w}}}\]

    C) \[\frac{m}{h({{\rho }_{s}}-{{\rho }_{w}})}\]

    D) \[\frac{m}{h({{\rho }_{w}}-{{\rho }_{s}})}\]

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  • question_answer56) Density of a crystal remains unchanged as a result of

    A) ionic defect

    B) Schottky defect

    C) Frenkel defect

    D) crystal defect

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  • question_answer57) The hydrocarbon which does not decolourise alkaline\[KMn{{O}_{4}}\]solution and also does not give any precipitate with ammonia Cal silver nitrate is

    A) acetylene

    B) benzene

    C) propyne

    D) butyne-1

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  • question_answer58) Which of the following organic compounds exhibits positive Fehling test as well as iodoform test?

    A) Methanal

    B) Ethanol

    C) Ethanal

    D) Propanone

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  • question_answer59) Oxidation of toluene to benzaldehyde by the use of chromyi chloride is called

    A) Wurtz reaction

    B) Etards reaction

    C) Fittig reaction

    D) Rosenmunds reaction

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  • question_answer60) The only alcohol that can be prepared by the direct hydration of alkene is

    A) ethyl alcohol

    B) methyl alcohol

    C) propyl alcohol

    D) \[iso-\]butyl alcohol

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  • question_answer61) The fresh precipitate can be transformed in colloidal state by

    A) peptisation

    B) coagulation

    C) diffusion

    D) None of these

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  • question_answer62) Which of the following has zero dipole moment?

    A) \[CIF\]

    B) \[PC{{l}_{3}}\]

    C) \[Si{{F}_{4}}\]

    D) \[CFC{{l}_{3}}\]

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  • question_answer63) The hybrid orbital used by chlorine atom in \[CIO_{2}^{-}\]ion is

    A) \[s{{p}^{3}}\]

    B) \[s{{p}^{2}}\]

    C) \[sp\]

    D) None of the above

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  • question_answer64) The relationship between standard reduction potential of a cell and equilibrium constant is shown by

    A) \[E_{cell}^{o}=\frac{n}{0.059}\log {{K}_{c}}\]

    B) \[E_{cell}^{o}=\frac{0.059}{n}\log {{K}_{c}}\]

    C) \[E_{cell}^{o}=0.059\,n\,\log {{K}_{c}}\]

    D) \[E_{cell}^{o}=\frac{\log {{K}_{c}}}{n}\]

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  • question_answer65) The half-cell reactions for the corrosion are \[2{{H}^{+}}+\frac{1}{2}{{O}_{2}}+2{{e}^{-}}\xrightarrow[{}]{{}}{{H}_{2}}O;\] \[E{}^\circ =1.23\,V\] \[F{{e}^{2+}}+2{{e}^{-}}\xrightarrow[{}]{{}}Fe(s);\] \[E{}^\circ =-0.44\,V\] Find the\[\Delta G{}^\circ \](in kJ) for the overall reaction.

    A) \[-76\]

    B) \[-322\]

    C) \[-161\]

    D) \[-152\]

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  • question_answer66) The vapour pressure of water at\[23{}^\circ C\]is i9.8 mm of Hg.0.1 mol of glucose is dissolved in 178.2 g of water. What is the vapour pressure (in mm Hg) of the resultant solution?

    A) 19.0

    B) 19.602

    C) 19.402

    D) 19.202

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  • question_answer67) The number of nodal planes in a\[{{p}_{x}}\]orbital is

    A) one

    B) two

    C) three

    D) zero

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  • question_answer68) 3-phenyl propene on reaction with HBr gives (as a major product)

    A) \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}CH(Br)C{{H}_{3}}\]

    B) \[{{C}_{6}}{{H}_{5}}CH(Br)C{{H}_{2}}C{{H}_{3}}\]

    C) \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}C{{H}_{2}}C{{H}_{2}}Br\]

    D) \[{{C}_{6}}{{H}_{5}}CH(Br)CH=C{{H}_{2}}\]

    View Answer play_arrow
  • question_answer69) Carbolic acid is

    A) \[{{C}_{6}}{{H}_{5}}CHO\]

    B) \[{{C}_{6}}{{H}_{6}}\]

    C) \[{{C}_{6}}{{H}_{5}}COOH\]

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

    View Answer play_arrow
  • question_answer70) A compound A when treated with methyl alcohol and few drops of\[{{H}_{2}}S{{O}_{4}},\], gave smell of winter green. The compound A is

    A) succinic acid

    B) salicylic acid

    C) tartaric acid

    D) oxalic acid

    View Answer play_arrow
  • question_answer71) Which of the following does give violet colour with neutral ferric chloride?

    A) Acetic acid

    B) Salicylic acid

    C) Formic acid

    D) Benzoic acid

    View Answer play_arrow
  • question_answer72) Cyanohydrin of which of the following forms lactic acid?

    A) \[HCHO\]

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

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

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

    View Answer play_arrow
  • question_answer73) The most basic compound amongst the following is

    A) benzyl amine

    B) aniline

    C) p-nitroaniline

    D) ethanamide

    View Answer play_arrow
  • question_answer74) An aromatic molecule will

    A) have\[(4n+2)\pi -\]electrons

    B) be planar

    C) be cyclic

    D) All of the above

    View Answer play_arrow
  • question_answer75) The IUPAC name of the compound,\[{{(C{{H}_{2}}=CHCHC{{H}_{3}})}_{2}}\]is

    A) 1,1-dimethylprop-2-ene

    B) 3-methylbut-1-ene

    C) 2-vinylpropane

    D) 1-iso-propylethylene

    View Answer play_arrow
  • question_answer76) Which of the following is not a nucleophile?

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

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

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

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

    View Answer play_arrow
  • question_answer77) Which of the following is the smallest in size?

    A) \[{{N}^{3-}}\]

    B) \[{{O}^{2-}}\]

    C) \[{{F}^{-}}\]

    D) \[N{{a}^{+}}\]

    View Answer play_arrow
  • question_answer78) Which of the following oxides is amphoteric in character?

    A) \[CaO\]

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

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

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

    View Answer play_arrow
  • question_answer79) \[Ge(II)\]compounds are more powerful reducing agents whereas\[Pb(IV)\]compounds are strong oxidants. It can be due to

    A) \[Pb\]is more electropositive than\[Ge\]

    B) ionisation potential of lead is less than that of\[Ge\]

    C) ionic radii of\[P{{b}^{2+}}\]and\[P{{b}^{4+}}\]are larger than those of\[G{{e}^{2+}}\]and\[G{{e}^{4+}}\]

    D) more pronounced inert pair effect in lead than in Ge

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  • question_answer80) \[P{{H}_{3}},\]the hydride of phosphorus is

    A) metallic

    B) ionic

    C) non-metallic

    D) covalent

    View Answer play_arrow
  • question_answer81) The oxidation number of Cr in\[Cr{{O}_{5}}\]is

    A) +2

    B) +4

    C) +6

    D) +8

    View Answer play_arrow
  • question_answer82) \[C{{N}^{-}}\]is a strong field ligand. This is due to the fact that

    A) it carries a negative charge

    B) it is a pseudo halide

    C) it can accept electrons from metal species

    D) it forms high spin complexes with metal Species

    View Answer play_arrow
  • question_answer83) Which of the following compounds is square planar and does not have any unpaired electron?

    A) \[Ni{{(CO)}_{4}}\]

    B) \[{{[Ni{{({{H}_{2}}O)}_{6}}]}^{2+}}\]

    C) \[{{[NiC{{l}_{4}}]}^{2-}}\]

    D) \[{{[Ni{{(CN)}_{4}}]}^{2-}}\]

    View Answer play_arrow
  • question_answer84) White anhydrous copper sulphate decomposes to give

    A) \[CuS{{O}_{4}}.5{{H}_{2}}O\]

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

    C) \[CuO+S{{O}_{3}}\]

    D) \[Cu\]

    View Answer play_arrow
  • question_answer85) If\[NaOH\]is added to an aqueous solution of zinc ions, a white precipitate appears and on adding excess of\[NaOH\], the precipitate dissolves. In this solution zinc exist in the

    A) cationic part

    B) anionic part

    C) both in cationic and anionic part

    D) there is no zinc in the solution

    View Answer play_arrow
  • question_answer86) Chlorine gas is dried over

    A) \[CaO\]

    B) \[NaOH\]

    C) \[KOH\]

    D) \[conc.{{H}_{2}}S{{O}_{4}}\]

    View Answer play_arrow
  • question_answer87) Which of the following halogens does not form its oxyacids?

    A) Fluorine

    B) Chlorine

    C) Bromine

    D) Iodine

    View Answer play_arrow
  • question_answer88) Which of the following hydrides has the lowest boiling point?

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

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

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

    D) \[{{H}_{2}}Te\]

    View Answer play_arrow
  • question_answer89) Glass is a

    A) polymeric mixture

    B) microcrystalline solid

    C) super cooled liquid

    D) gel

    View Answer play_arrow
  • question_answer90) Thermite is a mixture of iron oxide and

    A) zinc powder

    B) sodium shavings

    C) potassium metal

    D) aluminium powder

    View Answer play_arrow
  • question_answer91) The volume of water to be added to\[100\text{ }c{{m}^{3}}\]of \[0.5\text{ }N\text{ }{{H}_{2}}S{{O}_{4}}\]to get decinormal concentration is

    A) \[400\,c{{m}^{3}}\]

    B) \[500\,c{{m}^{3}}\]

    C) \[450\,c{{m}^{3}}\]

    D) \[100\,c{{m}^{3}}\]

    View Answer play_arrow
  • question_answer92) The rate of a first order reaction is\[1.5\times {{10}^{-2}}\] \[mol\text{ }{{L}^{-1}}mi{{n}^{-1}}\]at 0.5 M concentration of the reactant. The half-life of the reaction is

    A) 7.53 min

    B) 0.383 min

    C) 23.1 min

    D) 8.73 min

    View Answer play_arrow
  • question_answer93) The hydrolysis of ester in alkaline medium is a

    A) first order reaction with molecularity 1

    B) second order reaction with molecularity 2

    C) first order reaction with molecularity 2

    D) second order reaction with molecularity 1

    View Answer play_arrow
  • question_answer94) Which is correct statement?

    A) Starch is a polymer of a-glucose

    B) Amylose is a component of cellulose

    C) Proteins are compounds of only one type of amirio acid

    D) Incyclic structure of fructose, there are four carbons and one oxygen atom

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  • question_answer95) Oleic, stearic and palmitic acids are

    A) nucleic acids

    B) amino acids

    C) fatty acids

    D) None of these

    View Answer play_arrow
  • question_answer96) Arrange the following halides in the decreasing order of\[{{S}_{N}}1\]reactivity. \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}Cl,\] \[C{{H}_{2}}=CHCH(Cl)C{{H}_{3}},\] \[(I)\] \[(II)\] \[C{{H}_{3}}c{{H}_{2}}CH(Cl)C{{H}_{3}}\] \[(III)\]

    A) \[I>II>III\]

    B) \[II>I>III\]

    C) \[II>III>I\]

    D) \[III>II>I\]

    View Answer play_arrow
  • question_answer97) Catalyst used in the dimerisation of acetylene to prepare chloroprene is

    A) \[HgS{{O}_{4}}+{{H}_{2}}S{{O}_{4}}\]

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

    C) \[C{{u}_{2}}C{{l}_{2}}+N{{H}_{4}}Cl\]

    D) \[C{{u}_{2}}C{{l}_{2}}+N{{H}_{4}}OH\]

    View Answer play_arrow
  • question_answer98) The phenomenon of radioactivity is associated with

    A) decay of nucleus

    B) fusion of nucleus

    C) emission of electrons or protons

    D) rearrangement in the extra nuclear electron

    View Answer play_arrow
  • question_answer99) If Z is the number of atoms in the unit cell that represents the closest packing sequence\[-ABC,\]\[ABC-,\] the number of tetrahedral voids in the unit cell is equal to

    A) Z

    B) \[2Z\]

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

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

    View Answer play_arrow
  • question_answer100) Conjugate acid of\[SO_{4}^{2-}\]is

    A) \[HSO_{4}^{-}\]

    B) \[HS{{O}_{4}}\]

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

    D) \[SO_{4}^{-}\]

    View Answer play_arrow
  • question_answer101) \[AgCl+KIKCl+AgI\]In the above reaction as KI is added, the equilibrium is shifted towards right giving more.\[AgI\]precipitate, because

    A) both\[AgCl\]and\[AgI\]are sparingly soluble

    B) the\[{{K}_{sp}}\]of\[AgI\]is lower than\[{{K}_{sp}}\]of\[AgCl\]

    C) the\[{{K}_{sp}}\]of\[AgI\]is higher than\[{{K}_{sp}}\]of\[AgCl\]

    D) both\[AgCl\]and\[AgI\]have same solubility product

    View Answer play_arrow
  • question_answer102) The pH of a solution of hydrochloric acid is 4. The molarity of this solution is

    A) 4.0

    B) 0.4

    C) 0.0001

    D) 0.04

    View Answer play_arrow
  • question_answer103) Sulphanilic acid is

    A) Arrhenius acid

    B) Lewis base

    C) Neither nor

    D) Both (a) and (b)

    View Answer play_arrow
  • question_answer104) For how many orbitals, the quantum numbers, \[n=3,l=2,\text{ }m=+2\]are possible?

    A) 1

    B) 2

    C) 3

    D) 4

    View Answer play_arrow
  • question_answer105) The number of gram-molecules of oxygen which are present in\[6.022\times {{10}^{24}}CO\]molecules is

    A) 10 g-molecule

    B) 5 g-molecule

    C) 1 g-molecule

    D) 0.5 g-molecule

    View Answer play_arrow
  • question_answer106) The number of elements present in the fifth period of the Periodic Table is

    A) 8

    B) 10

    C) 18

    D) 32

    View Answer play_arrow
  • question_answer107) Pyrolusite is

    A) an oxide ore

    B) a sulphide ore

    C) a carbide ore

    D) not an ore

    View Answer play_arrow
  • question_answer108) The reaction,\[{{H}_{2}}S+{{H}_{2}}{{O}_{2}}\xrightarrow{{}}S+2{{H}_{2}}O\]indicates

    A) acidic nature of\[{{H}_{2}}{{O}_{2}}\]

    B) alkaline nature of\[{{H}_{2}}{{O}_{2}}\]

    C) oxidising action of\[{{H}_{2}}{{O}_{2}}\]

    D) reducing action of\[{{H}_{2}}{{O}_{2}}\]

    View Answer play_arrow
  • question_answer109) One mole of a perfect gas expands isothermally to ten times of its original volume. The change in entropy is

    A) 0.1 R

    B) 2.303 R

    C) 10.0 R

    D) 100.0 R

    View Answer play_arrow
  • question_answer110) For the reaction,\[PC{{l}_{3}}(g)+C{{l}_{2}}(g)PC{{l}_{5}}(g)\]the value of\[{{K}_{c}}\]at\[250{}^\circ C\]is 26. The value of\[{{K}_{p}}\] at this temperature will be

    A) 0.0006

    B) 0.46

    C) 0.57

    D) 0.83

    View Answer play_arrow
  • question_answer111) The value of\[\int_{-2}^{3}{|1-{{x}^{2}}|}\,dx\]is

    A) \[\frac{7}{3}\]

    B) \[\frac{14}{3}\]

    C) \[\frac{28}{3}\]

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

    View Answer play_arrow
  • question_answer112) If the sum of the slopes of the lines given by \[{{x}^{2}}-2cxy-7{{y}^{2}}=0\]is four times their product, then c has the value

    A) 2

    B) \[-1\]

    C) 1

    D) \[-2\]

    View Answer play_arrow
  • question_answer113) The domain of the function \[f(x)=\frac{{{\sin }^{-1}}(x-3)}{\sqrt{9-{{x}^{2}}}}\]is

    A) [1,2]

    B) [2,3]

    C) [2,3)

    D) [1,2)

    View Answer play_arrow
  • question_answer114) Let\[f(x)=\frac{1-\tan x}{4x-\pi },x\ne \frac{\pi }{4},x\in \left[ 0,\frac{\pi }{2} \right].F(x)\]is continuous in\[\left[ 0,\frac{\pi }{2} \right],\]then\[\frac{dy}{dx}\]is

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

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

    C) \[1\]

    D) \[-1\]

    View Answer play_arrow
  • question_answer115) If\[x={{e}^{y+{{e}^{y+......\infty }}}},x>0,\]then\[\frac{dy}{dx}\]is equal to

    A) \[\frac{1-x}{x}\]

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

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

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

    View Answer play_arrow
  • question_answer116) A variable circle passes through fixed point A (p, q) and touches x-axis. The locus of the other end of the diameter through A is

    A) \[{{(y-p)}^{2}}=4qx\]

    B) \[{{(y-q)}^{2}}=4py\]

    C) \[{{(x-p)}^{2}}=4qy\]

    D) \[{{(y-q)}^{2}}=4px\]

    View Answer play_arrow
  • question_answer117) If\[f:R\to S\] defined by \[f(x)=\sin x-\sqrt{3}\cos x+1,\]is onto, then the interval of S is

    A) [0, 1]

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

    C) [0, 3]

    D) \[[-1,3]\]

    View Answer play_arrow
  • question_answer118) If\[2a+3b+6c=0,\] then at least one root of the equation\[a{{x}^{2}}+bx+c=0\]lies in the interval

    A) (2, 3)

    B) (1, 2)

    C) (0, 1)

    D) (1, 3)

    View Answer play_arrow
  • question_answer119) Let\[\alpha ,\beta \]be such that\[\pi <\alpha -\beta <3\pi \].If \[\sin \alpha +\sin \beta =\frac{21}{65}\]and\[\cos \alpha +\cos \beta =-\frac{27}{65},\] then the value of\[\cos \left( \frac{\alpha -\beta }{2} \right)\]is

    A) \[\frac{6}{65}\]

    B) \[\frac{3}{\sqrt{130}}\]

    C) \[-\frac{3}{\sqrt{130}}\]

    D) \[-\frac{3}{65}\]

    View Answer play_arrow
  • question_answer120) A function\[y=f(x)\]has a second order derivative\[f\,(x)=6(x-1).\]. If its graph passes through the point (2, 1) and at that point the tangent to the graph is\[y=3x-5,\]then the function is

    A) \[{{(x+1)}^{3}}\]

    B) \[{{(x-1)}^{3}}\]

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

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

    View Answer play_arrow
  • question_answer121) If the two lines of regression are \[4x+3y+7=0\]and\[3x+4y+8=0,\]then the means of\[x\]and y are

    A) \[-\frac{4}{7},-\frac{11}{7}\]

    B) \[-\frac{4}{7},\frac{11}{7}\]

    C) \[\frac{4}{7},-\frac{11}{7}\]

    D) \[4,\,7\]

    View Answer play_arrow
  • question_answer122) A line with direction cosines proportional to 2, 1,2 meets each of the lines\[x=y+a=z\]and \[x+a=2y=2z\]. The coordinates of each of the points of intersection are given by

    A) \[(3d,\text{ }2a,\text{ }3a),\text{ }(a,\text{ }a,2a)\]

    B) \[(3a,\text{ }2a,\text{ }3a),\text{ }(a,\text{ }a,\,a)\]

    C) \[(3a,\text{ }3a,\text{ }3a),\text{ (}a,\text{ }a,\text{ }a\text{)}\]

    D) \[(2a,\text{ }3a,\text{ }3a),\text{ (2}a,\text{ }a,\text{ }a\text{)}\]

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  • question_answer123) The intersection of the spheres\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+7x-2y-z=13\]and \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-3x+3y+4z=8\]is the same as the intersection of one of the sphere and the plane

    A) \[x-y+2z=1\]

    B) \[x-2y-z=1\]

    C) \[x-y-z=1\]

    D) \[2x-y-z=1\]

    View Answer play_arrow
  • question_answer124) A particle moves towards East from a point A to a point B at the rate of 4 km/h and then towards North from B to C at the rate of 5 km/h. If\[AB=12\]km and\[BC=5\text{ }km,\]there its average speed for its journey from A to C are respectively

    A) \[\frac{17}{9}km/h\,and\,\frac{13}{9}km/h\]

    B) \[\frac{13}{4}km/h\,and\,\frac{17}{4}km/h\]

    C) \[\frac{17}{4}km/h\,and\,\frac{13}{4}km/h\]

    D) \[\frac{13}{9}km/h\,and\,\frac{17}{9}km/h\]

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  • question_answer125) A velocity\[\frac{1}{4}\]m/s is resolved into two components along OA and OB making angles \[30{}^\circ \]and\[45{}^\circ ,\]respectively with the given velocity. Then, the component along OB is

    A) \[\frac{1}{4}m/s\]

    B) \[\frac{1}{4}(\sqrt{3}-1)m/s\]

    C) \[\frac{1}{8}m/s\]

    D) \[\frac{1}{8}(\sqrt{6}-\sqrt{2})m/s\]

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  • question_answer126) Let two numbers have arithmetic mean 9 and geometric mean 4. Then, these numbers are the roots of the quadratic equation

    A) \[{{x}^{2}}+18x-16=0\]

    B) \[{{x}^{2}}-18x+16=0\]

    C) \[{{x}^{2}}+18x+16=0\]

    D) \[{{x}^{2}}-18x-16=0\]

    View Answer play_arrow
  • question_answer127) A point on the parabola\[{{y}^{2}}=18x\]at which the ordinate increases at twice the rate of the abscissa is

    A) \[\left( -\frac{9}{8},\frac{9}{2} \right)\]

    B) \[(2,-4)\]

    C) \[(2,4)\]

    D) \[\left( \frac{9}{8},\frac{9}{2} \right)\]

    View Answer play_arrow
  • question_answer128) If a, b and c are non-coplanar vectors and\[\lambda \]is a real number, then the vectors\[2a+2b+3c,\]\[\lambda b+4c\]and\[(\lambda -1)c\]are non-coplanar for

    A) all except two values of\[\lambda \]

    B) all except one value of\[\lambda \]

    C) all values of\[\lambda \]

    D) no value of\[\lambda \]

    View Answer play_arrow
  • question_answer129) Let\[u,\text{ }v,\text{ }w\]be such that\[|u|=1,|v|=2,|w|=3\]If the projection v along u is equal to that of w along\[u\]and\[v,\text{ }w\]are perpendicular to each other, then\[|u-v+w|\]equals to

    A) \[\sqrt{14}\]

    B) \[\sqrt{7}\]

    C) \[2\]

    D) 14

    View Answer play_arrow
  • question_answer130) The mean and the variance of a binomial distribution are 4 and 2 respectively. Then, the probability of 2 successes is

    A) \[\frac{128}{256}\]

    B) \[\frac{219}{256}\]

    C) \[\frac{37}{256}\]

    D) \[\frac{28}{256}\]

    View Answer play_arrow
  • question_answer131) If\[\frac{\log x}{\log 5}=\frac{\log 36}{\log 6}=\frac{\log \,64}{\log y},\]what are the values of\[x\]and y respectively?

    A) 8, 25

    B) 25, 8

    C) 8,8

    D) 25,25

    View Answer play_arrow
  • question_answer132) If A = {1, 2, 3}, B = {3. 2} and C = {2, 3} which one of the following is correct?

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

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

    C) \[(A\times B)\cup (B\times A)=(A\times B)\cup (B\times C)\]

    D) \[(A\times B)\cup (B\times A)=(A\times B)\cup (A\times C)\]

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  • question_answer133) If\[y=\sin ({{x}^{2}}),z={{e}^{{{y}^{2}}}},t=\sqrt{z}\]what is\[\frac{dt}{dx}\]equal to?

    A) \[\frac{xyz}{t}\]

    B) \[2\frac{xyz}{t}\cos ({{x}^{2}})\]

    C) \[\frac{-xyz\,cos({{x}^{2}})}{t}\]

    D) \[\frac{xyz\,t}{\cos ({{x}^{2}})}\]

    View Answer play_arrow
  • question_answer134) Let\[f(x)=[x],\]where\[[x]\]denotes the greatest integer contained in\[x\]. Which one of the following is correct?

    A) \[f(x)\]is one-to-one

    B) \[f(x)\]is onto

    C) Domain of\[f(x)\]is set of renumbers and range of\[f(x)\]is set of integers\[x\]

    D) Both domain and range of\[f(x)\]are set of real numbers

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  • question_answer135) What is the period of the function\[f(x)=|\sin x+\cos x|\]

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

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

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

    D) \[\pi \]

    View Answer play_arrow
  • question_answer136) A man saves ` 135 in the first year, ` 150 in the second year and in this way he increases his savings by ` 15 every, year. In what time will his total saving be ` 5550?

    A) 20 yr

    B) 25 yr

    C) 30 yr

    D) 35 yr

    View Answer play_arrow
  • question_answer137) If\[tan\text{ }\theta +sec\text{ }\theta =p,\]then what is the value of \[\sec \theta \]?

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

    B) \[\frac{{{p}^{2}}+1}{\sqrt{p}}\]

    C) \[\frac{{{p}^{2}}+1}{2p}\]

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

    View Answer play_arrow
  • question_answer138) If a particle is acted on by constant forces \[4i+j-3k\]and\[3i+j-k\]it displace from a point\[(i+2j+3k)\]to the point\[5i+4j+k,\] what is the total work done by the forces?

    A) 50 units

    B) 40 units

    C) 24 units

    D) 0 unit

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  • question_answer139) What is the number of common tangents to the circles\[{{x}^{2}}+{{y}^{2}}=1\]and\[{{x}^{2}}+{{y}^{2}}-4x+3=0\]?

    A) One

    B) Two

    C) Three

    D) Four

    View Answer play_arrow
  • question_answer140) If tangent to the curve\[{{y}^{2}}={{x}^{3}}\]at its point \[({{m}^{2}},{{m}^{3}})\]is also normal to the curve at \[({{M}^{2}},\text{ }{{M}^{3}}),\]then what is the value of\[mM\]?

    A) \[-\frac{4}{9}\]

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

    C) \[-\frac{1}{3}\]

    D) 1

    View Answer play_arrow
  • question_answer141) What is the value of b for which\[f(x)=\sin x-bx+c\] is decreasing in the interval\[(-\infty ,\infty )\]?

    A) \[b<1\]

    B) \[b\ge 1\]

    C) \[b>1\]

    D) \[b\le 1\]

    View Answer play_arrow
  • question_answer142) If\[\int{f(x)}dx=\frac{f(x)}{2}+C,\] then which one of the following is correct?

    A) \[f(x)={{e}^{2x}}+C\]

    B) \[f(x)=x+C\]

    C) \[f(x)=C\]

    D) \[f(x)={{e}^{2x}}\]

    View Answer play_arrow
  • question_answer143) If the sides of a triangle are as\[3:7:8,\]then\[R:r\]is equal to

    A) \[2:7\]

    B) \[7:2\]

    C) \[3:7\]

    D) \[7:3\]

    View Answer play_arrow
  • question_answer144) In a triangle, the lengths of the two larger sides are 10 and 9, respectively. If the angles are in AP, then the length of the third side can be

    A) \[5-2\sqrt{6}\]

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

    C) 5

    D) \[5+\sqrt{6}\]

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  • question_answer145) The number of solutions of the equation\[\sqrt{1-\cos x}=\sin x,\pi <x<3\pi \] is

    A) 0

    B) 1

    C) 2

    D) 3

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  • question_answer146) A tower subtends an angle of\[30{}^\circ \]at a point on the same level as the foot of the tower and at a second point, h metre above the first, the depression of the foot of the tower is\[60{}^\circ \]. The height of the tower is

    A) \[hm\]

    B) \[3\,h\,m\]

    C) \[\sqrt{3}\,h\,m\]

    D) None of these

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  • question_answer147) If the ratio of the roots of\[a{{x}^{2}}+2bx+c=0\]is same as the ratio of the\[p{{x}^{2}}+2qx+r=0,\]then

    A) \[\frac{2b}{ac}=\frac{{{q}^{2}}}{pr}\]

    B) \[\frac{b}{ac}=\frac{q}{pr}\]

    C) \[\frac{{{b}^{2}}}{ac}=\frac{{{q}^{2}}}{pr}\]

    D) None of these

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  • question_answer148) If\[A(\theta )=\left[ \begin{matrix} \sin \theta & i\cos \theta \\ i\cos \theta & \sin \theta \\ \end{matrix} \right],\]then which of the following is not true?

    A) \[A{{(\theta )}^{-1}}=A(\pi -\theta )\]

    B) \[A(\theta )+A(\pi +\theta )\]is a null matrix

    C) \[A(\theta )\]is invertible for all\[\theta \in R\]

    D) \[A{{(\theta )}^{-1}}=A(-\theta )\]

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  • question_answer149) If A is a skew-symmetric matrix and n is odd positive integer, then\[{{A}^{n}}\]is

    A) a skew-symmetric matrix

    B) a symmetric matrix

    C) a diagonal matrix

    D) None of the above

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  • question_answer150) If\[f(x)=\left| \begin{matrix} a & -1 & 0 \\ ax & a & -1 \\ a{{x}^{2}} & ax & a \\ \end{matrix} \right|,\]then\[f(2x)-f(x)\]is not divisible by

    A) \[x\]

    B) \[a\]

    C) \[2a+3x\]

    D) \[d{{x}^{2}}\]

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  • question_answer151) If \[^{n}{{C}_{3}}{{+}^{n}}{{C}_{4}}{{>}^{n+1}}{{C}_{3}},\]then

    A) \[n>6\]

    B) \[n>7\]

    C) \[n<6\]

    D) None of these

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  • question_answer152) The first three terms in the expansion of \[{{(1+ax)}^{n}}(n\ne 0)\]are\[1,6x\]and\[16{{x}^{2}}\]. Then, the value of a and n are respectively

    A) 2 and 9

    B) 3 and 2

    C) 2/3 and 9

    D) 3/2 and 6

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  • question_answer153) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin {{x}^{n}}}{{{(\sin x)}^{m}}},(m<n)\]is equal to

    A) 1

    B) 0

    C) \[\frac{n}{m}\]

    D) None of these

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  • question_answer154) Let\[f(x)=|x|+|x-1|,\]then

    A) \[f(x)\]is continuous at\[x=0\]as well as at\[x=1\]

    B) \[f(x)\]is continuous at\[x=0,\]but not at\[x=1\]

    C) \[f(x)\]is continuous at\[x=1,\]but not at\[x=0\]

    D) None of the above

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  • question_answer155) On the curve\[{{x}^{3}}=12y,\]the abscissa changes at a faster rate than the ordinate. Then,\[x\]belongs to the interval

    A) \[(-2,2)\]

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

    C) (0, 2)

    D) None of these

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  • question_answer156) The value of C in Lagranges theorem for the function\[f(x)=log\text{ }sin\text{ }x\]in the interval\[\left[ \frac{\pi }{6},\frac{5\pi }{6} \right]\]is

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

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

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

    D) None of these

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  • question_answer157) \[\int{\sin 2x\,d}(\tan x)\]is equal to

    A) \[2\log |\cos x|+C\]

    B) \[\log |\cos x|+C\]

    C) \[2\log |\sec x|+C\]

    D) \[\log |\sec x|+C\]

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  • question_answer158) The area bounded by the curve\[y=si{{n}^{-1}}x\]and the line \[x=0,|y|=\frac{\pi }{2}\] is

    A) 1

    B) 2

    C) \[\pi \]

    D) \[2\pi \]

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  • question_answer159) The solution of\[y\text{ }dx-x\text{ }dy+3{{x}^{2}}{{y}^{2}}{{e}^{{{x}^{3}}}}\text{ }dx=0\]is.

    A) \[\frac{x}{y}+{{e}^{{{x}^{3}}}}=C\]

    B) \[\frac{x}{y}-{{e}^{{{x}^{3}}}}=0\]

    C) \[-\frac{x}{y}+{{e}^{{{x}^{3}}}}=C\]

    D) None of these

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  • question_answer160) The point P is equidistant from A (1, 3), B \[(-3,5)\]and\[C(5,-1)\]. Then, PA is equal to

    A) \[5\sqrt{5}\]

    B) \[5\]

    C) \[5\sqrt{10}\]

    D) \[25\]

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  • question_answer161) The coordinates of the foot of the perpendicular from the point (2, 3) on the line\[-y+3x+4=0\]are given by

    A) \[\left( \frac{37}{10},-\frac{1}{10} \right)\]

    B) \[\left( -\frac{1}{10},\frac{37}{10} \right)\]

    C) \[\left( \frac{10}{37},-10 \right)\]

    D) \[\left( \frac{2}{3},-\frac{1}{3} \right)\]

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  • question_answer162) If the lines joining the origin to the intersection of the line\[y=mx+2\]and the curve\[{{x}^{2}}+{{y}^{2}}=1\] are at right angles, then

    A) \[{{m}^{2}}=1\]

    B) \[{{m}^{2}}=3\]

    C) \[{{m}^{2}}=7\]

    D) \[2{{m}^{2}}=1\]

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  • question_answer163) The ratio in which the line segment joining the points\[(4,-6)\]and (3, 1) is divided by the parabola\[{{y}^{2}}=4x\]is

    A) \[\frac{-20\pm \sqrt{155}}{11}:1\]

    B) \[\frac{-2\pm 2\sqrt{155}}{11}:2\]

    C) \[-20\pm 2\sqrt{155}:11\]

    D) \[-20\pm \sqrt{155}:11\]

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  • question_answer164) If the centre, one of the foci and semi-major axis of an ellipse be (0, 0), (0, 3) and 5, then its equation is

    A) \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{25}=1\]

    B) \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{16}=1\]

    C) \[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{25}=1\]

    D) None of these

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  • question_answer165) If\[{{m}_{1}}\]and\[{{m}_{2}}\]are the slopes of the tangents to the hyperbola\[\frac{{{x}^{2}}}{25}-\frac{{{y}^{2}}}{16}=1\]which pass through the point (6, 2), then

    A) \[{{m}_{1}}+{{m}_{2}}=-\frac{24}{11}\]

    B) \[{{m}_{1}}{{m}_{2}}=\frac{20}{11}\]

    C) \[{{m}_{1}}+{{m}_{2}}=\frac{48}{11}\]

    D) \[{{m}_{1}}{{m}_{2}}=\frac{11}{20}\]

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  • question_answer166) If\[a=i+j+k,~~b=4i+3j+4k\]and \[c=i+\alpha j+\beta k\]are linearly dependent vectors and\[|c|=\sqrt{3},\] then

    A) \[\alpha =1,\text{ }\beta =-1\]

    B) \[\alpha =1,\text{ }\beta =\pm 1\]

    C) \[\alpha =-1,\text{ }\beta =\pm 1\]

    D) \[\alpha =\pm 1,\text{ }\beta =1\]

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  • question_answer167) In an experiment with 15 observations on\[x,\]the following results were available \[\Sigma {{x}^{2}}=2830,\]\[\Sigma x=170\]. One observation that was 20 was found to be wrong and was replaced by the correct value 30. Then, the corrected variance is

    A) 80.33

    B) 78.00

    C) 188.66

    D) 177.33

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  • question_answer168) If the algebraic sum of deviations of 20 observations from 30 is 20, then the mean of observations is

    A) 30

    B) 30.1

    C) 29

    D) 31

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  • question_answer169) A bag contains 12 pairs of socks, 4 socks are picked up at random. Then, the probability that there is at least one pair is

    A) \[\frac{41}{161}\]

    B) \[\frac{120}{161}\]

    C) \[\frac{21}{161}\]

    D) None of these

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  • question_answer170) The odds against a certain event is\[5:2\]and the odds in favour of another event is\[6:5\]. If both the events are independent, then the probability that at least one of the events will happens is

    A) \[\frac{50}{77}\]

    B) \[\frac{52}{77}\]

    C) \[\frac{25}{88}\]

    D) \[\frac{63}{88}\]

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