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) \[\frac{2}{3}g\] done clear
B) \[g\] done clear
C) \[\frac{1}{3}g\] done clear
D) Zero done clear
View Answer play_arrowquestion_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 done clear
B) 0.90 kWh done clear
C) 1.11 kWh done clear
D) 0.71 kWh done clear
View Answer play_arrowquestion_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) \[L=R\] done clear
B) \[L=\sqrt{3}R\] done clear
C) \[L=\frac{R}{\sqrt{3}}\] done clear
D) \[L=\sqrt{\frac{3}{2}}R\] done clear
View Answer play_arrowquestion_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) \[3\times {{10}^{12}}N{{m}^{-2}}\] done clear
B) \[2\times {{10}^{12}}N{{m}^{-2}}\] done clear
C) \[{{10}^{12}}N{{m}^{-2}}\] done clear
D) None of these done clear
View Answer play_arrowquestion_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 done clear
B) surface tension of water is very low done clear
C) viscosity of oil is high done clear
D) viscosity of water is high done clear
View Answer play_arrowquestion_answer6) A student attempts to pull himself up by tugging on his hair, the will not succeed
A) as the force exerted is small done clear
B) the frictional force while gripping, is small done clear
C) Newtons law of inertia is not applicable to living beings done clear
D) as the force applied is internal to the system done clear
View Answer play_arrowquestion_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 done clear
B) 1.23 J done clear
C) 0.82 J done clear
D) 2.4 J done clear
View Answer play_arrowquestion_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) \[50\,m{{s}^{-1}}\] done clear
B) \[5\,m{{s}^{-1}}\] done clear
C) \[0.05\,m{{s}^{-1}}\] done clear
D) \[0.5\,m{{s}^{-1}}\] done clear
View Answer play_arrowquestion_answer9) At nodes in stationary waves
A) change in pressure and density are maximum done clear
B) change in pressure and density are minimum done clear
C) strain is zero done clear
D) energy is maximum done clear
View Answer play_arrowquestion_answer10) Eight dipoles of changes of magnitude are placed inside a cube. The total electric flux coming out of the cube will be
A) \[\frac{8e}{{{\varepsilon }_{0}}}\] done clear
B) \[\frac{16e}{{{\varepsilon }_{0}}}\] done clear
C) \[\frac{e}{{{\varepsilon }_{0}}}\] done clear
D) zero done clear
View Answer play_arrowquestion_answer11) The X-ray beam coming from on X-ray tube will be
A) monochromatic done clear
B) having all wavelength smaller than a certain maximum wavelength done clear
C) having all wavelength larger than a certain minimum wavelength done clear
D) having all wavelength lying between a minimum and a maximum wavelength done clear
View Answer play_arrowquestion_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 done clear
B) 6.3 as done clear
C) 40 as done clear
D) 30 as done clear
View Answer play_arrowquestion_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) \[2.8\times {{10}^{-7}}N\] done clear
B) \[3.7\times {{10}^{-7}}N\] done clear
C) \[6.2\times {{10}^{-7}}N\] done clear
D) \[9.1\times {{10}^{-7}}N\] done clear
View Answer play_arrowquestion_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 done clear
B) 250 A done clear
C) 100 A done clear
D) 1000 A done clear
View Answer play_arrowquestion_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) \[{{f}_{o}}t\] done clear
B) \[\frac{1}{2}{{f}_{o}}{{T}^{2}}\] done clear
C) \[{{f}_{o}}{{T}^{2}}\] done clear
D) \[\frac{1}{2}{{f}_{o}}T\] done clear
View Answer play_arrowquestion_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 done clear
B) \[\frac{1}{2}m{{s}^{-2}},N-W\] done clear
C) \[\frac{1}{\sqrt{2}}m{{s}^{-2}},N-E\] done clear
D) \[\frac{1}{\sqrt{2}}m{{s}^{-2}},S-W\] done clear
View Answer play_arrowquestion_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) \[\frac{\rho {{\sigma }^{2}}}{{{p}^{3}}}\] done clear
B) \[\frac{\rho {{\sigma }^{3}}}{\sigma }\] done clear
C) \[\frac{{{\rho }^{3}}\sigma }{\rho }\] done clear
D) \[\frac{\rho }{{{p}^{3}}\sigma }\] done clear
View Answer play_arrowquestion_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 done clear
B) 90 N done clear
C) 30 N done clear
D) 60 N done clear
View Answer play_arrowquestion_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 done clear
B) \[614.4\,\mu \] done clear
C) 64 m done clear
D) None of these done clear
View Answer play_arrowquestion_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) \[2s,3s\] done clear
B) \[1.5s,\text{ }2.5s\] done clear
C) \[1.2s,\text{ }3.2s\] done clear
D) \[3.2s,1.3s\] done clear
View Answer play_arrowquestion_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) \[\frac{{{T}_{1}}}{{{T}_{2}}}={{\left[ \frac{{{H}_{1}}}{{{H}_{2}}} \right]}^{1/2}}\] done clear
B) \[\frac{{{T}_{1}}}{{{T}_{2}}}=\frac{{{H}_{1}}}{{{H}_{2}}}\] done clear
C) \[\frac{{{T}_{1}}}{{{T}_{2}}}={{\left[ \frac{{{M}_{1}}}{{{M}_{2}}} \right]}^{1/2}}\] done clear
D) \[\frac{{{T}_{1}}}{{{T}_{2}}}=\frac{{{M}_{1}}}{{{M}_{2}}}\] done clear
View Answer play_arrowquestion_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) \[-\frac{GMm}{R}\left[ \frac{1}{\sqrt{2}}-\frac{1}{\sqrt{5}} \right]\] done clear
B) \[\frac{GMm}{R}\times \frac{1}{\sqrt{5}}\] done clear
C) \[\frac{GMm}{R}\left[ \frac{1}{\sqrt{2}}-\frac{1}{\sqrt{5}} \right]\] done clear
D) \[\frac{GMm}{R}\left[ \frac{1}{\sqrt{10}} \right]\] done clear
View Answer play_arrowquestion_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 done clear
B) 36 kg done clear
C) 24kg done clear
D) 12kg done clear
View Answer play_arrowquestion_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) \[{{T}_{1}}+{{T}_{2}}\] done clear
B) \[\frac{{{T}_{1}}{{T}_{2}}}{{{T}_{1}}+{{T}_{2}}}\] done clear
C) \[\sqrt{T_{1}^{2}+T_{2}^{2}}\] done clear
D) \[\frac{{{T}_{1}}+{{T}_{2}}}{2}\] done clear
View Answer play_arrowquestion_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 done clear
B) string will vibrate in resonance with the tuning fork done clear
C) string will vibrate with a frequency of 480 Hz, but is not in resonance with the tuning fork done clear
D) string is in resonance with tuning fork, and hence vibrates with a frequency of 240 Hz done clear
View Answer play_arrowquestion_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 done clear
B) 0.4 done clear
C) 0.2 done clear
D) zero done clear
View Answer play_arrowquestion_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 done clear
B) ductility done clear
C) elasticity done clear
D) hardness done clear
View Answer play_arrowquestion_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) \[\frac{Mg}{AK}\] done clear
B) \[\frac{Mg}{3AK}\] done clear
C) \[\frac{3Mg}{AK}\] done clear
D) \[\frac{Mg}{2AK}\] done clear
View Answer play_arrowquestion_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\[2\sqrt{\frac{2hH}{3}}\] done clear
B) The value of\[x\]is\[\sqrt{\frac{4hH}{3}}\] done clear
C) The value of\[x\]cant be computed, from information provided done clear
D) The question is irreverent as no water comes out from the hole done clear
View Answer play_arrowquestion_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) \[W=A(T_{1}^{2}-T_{2}^{2})-B(T_{2}^{2}-T_{1}^{2})\] done clear
B) \[W=A(T_{2}^{2}-T_{1}^{2})-B({{T}_{2}}-{{T}_{1}})\] done clear
C) \[W=A({{T}_{2}}-{{T}_{1}})-B\left( {{T}_{2}}-\frac{1}{2}{{T}_{1}} \right)\] done clear
D) \[W=A({{T}_{2}}-{{T}_{1}})-B\left( T_{2}^{2}-T_{1}^{2} \right)\] done clear
View Answer play_arrowquestion_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) \[9.22\times {{10}^{3}}J{{K}^{-1}}\] done clear
B) \[8.22\times {{10}^{2}}J{{K}^{-1}}\] done clear
C) \[2.31J{{K}^{-1}}\] done clear
D) \[10.00\times {{10}^{3}}J{{K}^{-1}}\] done clear
View Answer play_arrowquestion_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) \[1.96\times {{10}^{6}}V\] done clear
B) \[1.86\times {{10}^{4}}V\] done clear
C) \[1.96\times {{10}^{4}}V\] done clear
D) \[2.96\times {{10}^{4}}V\] done clear
View Answer play_arrowquestion_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) \[4\,\Omega \] done clear
B) \[2\,\Omega \] done clear
C) \[1\,\Omega \] done clear
D) \[0.5\,\Omega \] done clear
View Answer play_arrowquestion_answer34) In the combination of resistance shown in the figure, the potential difference between B and D, is zero, when unknown resistance is
A) \[0.125\,\Omega \] done clear
B) \[2\,\Omega \] done clear
C) \[3\,\Omega \] done clear
D) for finding the value of\[X,\]the emf of cell is required done clear
View Answer play_arrowquestion_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) \[\frac{R}{\sqrt{2}}\] done clear
B) \[\frac{R}{\sqrt{3}}\] done clear
C) \[\sqrt{2}R\] done clear
D) \[\sqrt{3}R\] done clear
View Answer play_arrowquestion_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 done clear
B) 690V done clear
C) 790V done clear
D) 890V done clear
View Answer play_arrowquestion_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) \[\frac{{{\mu }_{0}}I}{2\pi a}\] done clear
B) \[\frac{\sqrt{2}{{\mu }_{0}}I}{2\pi a}\] done clear
C) \[\frac{{{\mu }_{0}}I}{2\sqrt{2}\pi a}\] done clear
D) \[\frac{{{\mu }_{0}}I}{4\sqrt{2}\pi a}\] done clear
View Answer play_arrowquestion_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) \[\frac{{{\mu }_{0}}\pi r_{2}^{2}}{2{{r}_{1}}}\] done clear
B) \[\frac{{{\mu }_{0}}\pi r_{1}^{2}}{2{{r}_{2}}}\] done clear
C) \[\frac{{{\mu }_{0}}\pi ({{r}_{1}}+{{r}_{2}})}{2{{r}_{1}}}\] done clear
D) \[\frac{{{\mu }_{0}}\pi {{({{r}_{1}}+{{r}_{2}})}^{2}}}{2{{r}_{2}}}\] done clear
View Answer play_arrowquestion_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 done clear
B) \[0.5\times {{10}^{-4}}A{{m}^{2}}\] done clear
C) \[1.25\times {{10}^{-4}}A{{m}^{2}}\] done clear
D) magnetic moment is not defined for this case done clear
View Answer play_arrowquestion_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) \[1.45\times {{10}^{-13}}N\] done clear
B) zero done clear
C) \[8.67\times {{10}^{-15}}N\] done clear
D) \[3.87\times {{10}^{-15}}N\] done clear
View Answer play_arrowquestion_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) \[{{10}^{4}}W\] done clear
B) \[10W\] done clear
C) \[2.5\text{ }W\] done clear
D) \[5W\] done clear
View Answer play_arrowquestion_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) \[140\text{ }N{{C}^{-1}}\] done clear
B) \[153\text{ }N{{C}^{-1}}\] done clear
C) \[163\text{ }N{{C}^{-1}}\] done clear
D) \[133\text{ }N{{C}^{-1}}\] done clear
View Answer play_arrowquestion_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 done clear
B) 12 done clear
C) 16 done clear
D) 10 done clear
View Answer play_arrowquestion_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 done clear
B) \[\sqrt{2}\] done clear
C) 4 done clear
D) 2 done clear
View Answer play_arrowquestion_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 done clear
B) 2.4m done clear
C) 2.1m done clear
D) 2.2m done clear
View Answer play_arrowquestion_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) \[3\times {{10}^{10}}m\] done clear
B) \[3.35\times {{10}^{11}}m\] done clear
C) \[1.95\times {{10}^{11}}m\] done clear
D) \[4.32\times {{10}^{10}}m\] done clear
View Answer play_arrowquestion_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 done clear
B) \[1.76\times {{10}^{14}}\]photoelectrons/s done clear
C) \[8.8\times {{10}^{11}}\]photoelectrons/s done clear
D) The value of work function is required to complete the value of emitted photoelectrons/s done clear
View Answer play_arrowquestion_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 done clear
B) 12.1 eV done clear
C) 12.5 eV done clear
D) None of these done clear
View Answer play_arrowquestion_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 \[{{T}_{1}}\] done clear
B) more at \[{{T}_{1}}\] done clear
C) equal in the two cases done clear
D) cannot say done clear
View Answer play_arrowquestion_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) \[\frac{8{{\varepsilon }_{0}}A}{d}\] done clear
B) \[\frac{8{{\varepsilon }_{0}}A}{3d}\] done clear
C) \[\frac{26{{\varepsilon }_{0}}A}{35d}\] done clear
D) \[\frac{12{{\varepsilon }_{0}}A}{35d}\] done clear
View Answer play_arrowquestion_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 done clear
B) The body which has been dropped done clear
C) Both will reach the ground simultaneously done clear
D) Depends on the velocity with which the first bod has been projected horizontally done clear
View Answer play_arrowquestion_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 done clear
B) \[-1.3\,mgH\] done clear
C) 1.3 mgH done clear
D) \[-0.28\,mgH\] done clear
View Answer play_arrowquestion_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) \[50{}^\circ C\] done clear
B) \[60{}^\circ C\] done clear
C) \[70{}^\circ C\] done clear
D) \[80{}^\circ C\] done clear
View Answer play_arrowquestion_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 done clear
B) IV, 1.25V done clear
C) 1.5V, 2.25V done clear
D) 1.5V, 2.56V done clear
View Answer play_arrowquestion_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) \[\frac{m}{h({{\rho }_{s}}+{{\rho }_{w}})}\] done clear
B) \[\frac{m}{h{{\rho }_{w}}}\] done clear
C) \[\frac{m}{h({{\rho }_{s}}-{{\rho }_{w}})}\] done clear
D) \[\frac{m}{h({{\rho }_{w}}-{{\rho }_{s}})}\] done clear
View Answer play_arrowquestion_answer56) Density of a crystal remains unchanged as a result of
A) ionic defect done clear
B) Schottky defect done clear
C) Frenkel defect done clear
D) crystal defect done clear
View Answer play_arrowquestion_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 done clear
B) benzene done clear
C) propyne done clear
D) butyne-1 done clear
View Answer play_arrowquestion_answer58) Which of the following organic compounds exhibits positive Fehling test as well as iodoform test?
A) Methanal done clear
B) Ethanol done clear
C) Ethanal done clear
D) Propanone done clear
View Answer play_arrowquestion_answer59) Oxidation of toluene to benzaldehyde by the use of chromyi chloride is called
A) Wurtz reaction done clear
B) Etards reaction done clear
C) Fittig reaction done clear
D) Rosenmunds reaction done clear
View Answer play_arrowquestion_answer60) The only alcohol that can be prepared by the direct hydration of alkene is
A) ethyl alcohol done clear
B) methyl alcohol done clear
C) propyl alcohol done clear
D) \[iso-\]butyl alcohol done clear
View Answer play_arrowquestion_answer61) The fresh precipitate can be transformed in colloidal state by
A) peptisation done clear
B) coagulation done clear
C) diffusion done clear
D) None of these done clear
View Answer play_arrowquestion_answer62) Which of the following has zero dipole moment?
A) \[CIF\] done clear
B) \[PC{{l}_{3}}\] done clear
C) \[Si{{F}_{4}}\] done clear
D) \[CFC{{l}_{3}}\] done clear
View Answer play_arrowquestion_answer63) The hybrid orbital used by chlorine atom in \[CIO_{2}^{-}\]ion is
A) \[s{{p}^{3}}\] done clear
B) \[s{{p}^{2}}\] done clear
C) \[sp\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer64) The relationship between standard reduction potential of a cell and equilibrium constant is shown by
A) \[E_{cell}^{o}=\frac{n}{0.059}\log {{K}_{c}}\] done clear
B) \[E_{cell}^{o}=\frac{0.059}{n}\log {{K}_{c}}\] done clear
C) \[E_{cell}^{o}=0.059\,n\,\log {{K}_{c}}\] done clear
D) \[E_{cell}^{o}=\frac{\log {{K}_{c}}}{n}\] done clear
View Answer play_arrowquestion_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) \[-76\] done clear
B) \[-322\] done clear
C) \[-161\] done clear
D) \[-152\] done clear
View Answer play_arrowquestion_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 done clear
B) 19.602 done clear
C) 19.402 done clear
D) 19.202 done clear
View Answer play_arrowquestion_answer67) The number of nodal planes in a\[{{p}_{x}}\]orbital is
A) one done clear
B) two done clear
C) three done clear
D) zero done clear
View Answer play_arrowquestion_answer68) 3-phenyl propene on reaction with HBr gives (as a major product)
A) \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}CH(Br)C{{H}_{3}}\] done clear
B) \[{{C}_{6}}{{H}_{5}}CH(Br)C{{H}_{2}}C{{H}_{3}}\] done clear
C) \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}C{{H}_{2}}C{{H}_{2}}Br\] done clear
D) \[{{C}_{6}}{{H}_{5}}CH(Br)CH=C{{H}_{2}}\] done clear
View Answer play_arrowquestion_answer69) Carbolic acid is
A) \[{{C}_{6}}{{H}_{5}}CHO\] done clear
B) \[{{C}_{6}}{{H}_{6}}\] done clear
C) \[{{C}_{6}}{{H}_{5}}COOH\] done clear
D) \[{{C}_{6}}{{H}_{5}}OH\] done clear
View Answer play_arrowquestion_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 done clear
B) salicylic acid done clear
C) tartaric acid done clear
D) oxalic acid done clear
View Answer play_arrowquestion_answer71) Which of the following does give violet colour with neutral ferric chloride?
A) Acetic acid done clear
B) Salicylic acid done clear
C) Formic acid done clear
D) Benzoic acid done clear
View Answer play_arrowquestion_answer72) Cyanohydrin of which of the following forms lactic acid?
A) \[HCHO\] done clear
B) \[C{{H}_{3}}COC{{H}_{3}}\] done clear
C) \[C{{H}_{3}}CHO\] done clear
D) \[C{{H}_{3}}C{{H}_{2}}CHO\] done clear
View Answer play_arrowquestion_answer73) The most basic compound amongst the following is
A) benzyl amine done clear
B) aniline done clear
C) p-nitroaniline done clear
D) ethanamide done clear
View Answer play_arrowquestion_answer74) An aromatic molecule will
A) have\[(4n+2)\pi -\]electrons done clear
B) be planar done clear
C) be cyclic done clear
D) All of the above done clear
View Answer play_arrowquestion_answer75) The IUPAC name of the compound,\[{{(C{{H}_{2}}=CHCHC{{H}_{3}})}_{2}}\]is
A) 1,1-dimethylprop-2-ene done clear
B) 3-methylbut-1-ene done clear
C) 2-vinylpropane done clear
D) 1-iso-propylethylene done clear
View Answer play_arrowquestion_answer76) Which of the following is not a nucleophile?
A) \[{{H}_{2}}O\] done clear
B) \[C{{H}_{3}}OH\] done clear
C) \[{{H}_{2}}\] done clear
D) \[N{{H}_{3}}\] done clear
View Answer play_arrowquestion_answer77) Which of the following is the smallest in size?
A) \[{{N}^{3-}}\] done clear
B) \[{{O}^{2-}}\] done clear
C) \[{{F}^{-}}\] done clear
D) \[N{{a}^{+}}\] done clear
View Answer play_arrowquestion_answer78) Which of the following oxides is amphoteric in character?
A) \[CaO\] done clear
B) \[C{{O}_{2}}\] done clear
C) \[Si{{O}_{2}}\] done clear
D) \[Sn{{O}_{2}}\] done clear
View Answer play_arrowquestion_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\[Ge\] done clear
B) ionisation potential of lead is less than that of\[Ge\] done clear
C) ionic radii of\[P{{b}^{2+}}\]and\[P{{b}^{4+}}\]are larger than those of\[G{{e}^{2+}}\]and\[G{{e}^{4+}}\] done clear
D) more pronounced inert pair effect in lead than in Ge done clear
View Answer play_arrowquestion_answer80) \[P{{H}_{3}},\]the hydride of phosphorus is
A) metallic done clear
B) ionic done clear
C) non-metallic done clear
D) covalent done clear
View Answer play_arrowquestion_answer81) The oxidation number of Cr in\[Cr{{O}_{5}}\]is
A) +2 done clear
B) +4 done clear
C) +6 done clear
D) +8 done clear
View Answer play_arrowquestion_answer82) \[C{{N}^{-}}\]is a strong field ligand. This is due to the fact that
A) it carries a negative charge done clear
B) it is a pseudo halide done clear
C) it can accept electrons from metal species done clear
D) it forms high spin complexes with metal Species done clear
View Answer play_arrowquestion_answer83) Which of the following compounds is square planar and does not have any unpaired electron?
A) \[Ni{{(CO)}_{4}}\] done clear
B) \[{{[Ni{{({{H}_{2}}O)}_{6}}]}^{2+}}\] done clear
C) \[{{[NiC{{l}_{4}}]}^{2-}}\] done clear
D) \[{{[Ni{{(CN)}_{4}}]}^{2-}}\] done clear
View Answer play_arrowquestion_answer84) White anhydrous copper sulphate decomposes to give
A) \[CuS{{O}_{4}}.5{{H}_{2}}O\] done clear
B) \[CuS{{O}_{4}}.{{H}_{2}}O\] done clear
C) \[CuO+S{{O}_{3}}\] done clear
D) \[Cu\] done clear
View Answer play_arrowquestion_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 done clear
B) anionic part done clear
C) both in cationic and anionic part done clear
D) there is no zinc in the solution done clear
View Answer play_arrowquestion_answer86) Chlorine gas is dried over
A) \[CaO\] done clear
B) \[NaOH\] done clear
C) \[KOH\] done clear
D) \[conc.{{H}_{2}}S{{O}_{4}}\] done clear
View Answer play_arrowquestion_answer87) Which of the following halogens does not form its oxyacids?
A) Fluorine done clear
B) Chlorine done clear
C) Bromine done clear
D) Iodine done clear
View Answer play_arrowquestion_answer88) Which of the following hydrides has the lowest boiling point?
A) \[{{H}_{2}}O\] done clear
B) \[{{H}_{2}}S\] done clear
C) \[{{H}_{2}}Se\] done clear
D) \[{{H}_{2}}Te\] done clear
View Answer play_arrowquestion_answer89) Glass is a
A) polymeric mixture done clear
B) microcrystalline solid done clear
C) super cooled liquid done clear
D) gel done clear
View Answer play_arrowquestion_answer90) Thermite is a mixture of iron oxide and
A) zinc powder done clear
B) sodium shavings done clear
C) potassium metal done clear
D) aluminium powder done clear
View Answer play_arrowquestion_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) \[400\,c{{m}^{3}}\] done clear
B) \[500\,c{{m}^{3}}\] done clear
C) \[450\,c{{m}^{3}}\] done clear
D) \[100\,c{{m}^{3}}\] done clear
View Answer play_arrowquestion_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 done clear
B) 0.383 min done clear
C) 23.1 min done clear
D) 8.73 min done clear
View Answer play_arrowquestion_answer93) The hydrolysis of ester in alkaline medium is a
A) first order reaction with molecularity 1 done clear
B) second order reaction with molecularity 2 done clear
C) first order reaction with molecularity 2 done clear
D) second order reaction with molecularity 1 done clear
View Answer play_arrowquestion_answer94) Which is correct statement?
A) Starch is a polymer of a-glucose done clear
B) Amylose is a component of cellulose done clear
C) Proteins are compounds of only one type of amirio acid done clear
D) Incyclic structure of fructose, there are four carbons and one oxygen atom done clear
View Answer play_arrowquestion_answer95) Oleic, stearic and palmitic acids are
A) nucleic acids done clear
B) amino acids done clear
C) fatty acids done clear
D) None of these done clear
View Answer play_arrowquestion_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) \[I>II>III\] done clear
B) \[II>I>III\] done clear
C) \[II>III>I\] done clear
D) \[III>II>I\] done clear
View Answer play_arrowquestion_answer97) Catalyst used in the dimerisation of acetylene to prepare chloroprene is
A) \[HgS{{O}_{4}}+{{H}_{2}}S{{O}_{4}}\] done clear
B) \[C{{u}_{2}}C{{l}_{2}}\] done clear
C) \[C{{u}_{2}}C{{l}_{2}}+N{{H}_{4}}Cl\] done clear
D) \[C{{u}_{2}}C{{l}_{2}}+N{{H}_{4}}OH\] done clear
View Answer play_arrowquestion_answer98) The phenomenon of radioactivity is associated with
A) decay of nucleus done clear
B) fusion of nucleus done clear
C) emission of electrons or protons done clear
D) rearrangement in the extra nuclear electron done clear
View Answer play_arrowquestion_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 done clear
B) \[2Z\] done clear
C) \[\frac{Z}{2}\] done clear
D) \[\frac{Z}{4}\] done clear
View Answer play_arrowquestion_answer100) Conjugate acid of\[SO_{4}^{2-}\]is
A) \[HSO_{4}^{-}\] done clear
B) \[HS{{O}_{4}}\] done clear
C) \[{{H}_{2}}S{{O}_{4}}\] done clear
D) \[SO_{4}^{-}\] done clear
View Answer play_arrowquestion_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 done clear
B) the\[{{K}_{sp}}\]of\[AgI\]is lower than\[{{K}_{sp}}\]of\[AgCl\] done clear
C) the\[{{K}_{sp}}\]of\[AgI\]is higher than\[{{K}_{sp}}\]of\[AgCl\] done clear
D) both\[AgCl\]and\[AgI\]have same solubility product done clear
View Answer play_arrowquestion_answer102) The pH of a solution of hydrochloric acid is 4. The molarity of this solution is
A) 4.0 done clear
B) 0.4 done clear
C) 0.0001 done clear
D) 0.04 done clear
View Answer play_arrowquestion_answer103) Sulphanilic acid is
A) Arrhenius acid done clear
B) Lewis base done clear
C) Neither nor done clear
D) Both (a) and (b) done clear
View Answer play_arrowquestion_answer104) For how many orbitals, the quantum numbers, \[n=3,l=2,\text{ }m=+2\]are possible?
A) 1 done clear
B) 2 done clear
C) 3 done clear
D) 4 done clear
View Answer play_arrowquestion_answer105) The number of gram-molecules of oxygen which are present in\[6.022\times {{10}^{24}}CO\]molecules is
A) 10 g-molecule done clear
B) 5 g-molecule done clear
C) 1 g-molecule done clear
D) 0.5 g-molecule done clear
View Answer play_arrowquestion_answer106) The number of elements present in the fifth period of the Periodic Table is
A) 8 done clear
B) 10 done clear
C) 18 done clear
D) 32 done clear
View Answer play_arrowquestion_answer107) Pyrolusite is
A) an oxide ore done clear
B) a sulphide ore done clear
C) a carbide ore done clear
D) not an ore done clear
View Answer play_arrowquestion_answer108) The reaction,\[{{H}_{2}}S+{{H}_{2}}{{O}_{2}}\xrightarrow{{}}S+2{{H}_{2}}O\]indicates
A) acidic nature of\[{{H}_{2}}{{O}_{2}}\] done clear
B) alkaline nature of\[{{H}_{2}}{{O}_{2}}\] done clear
C) oxidising action of\[{{H}_{2}}{{O}_{2}}\] done clear
D) reducing action of\[{{H}_{2}}{{O}_{2}}\] done clear
View Answer play_arrowquestion_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 done clear
B) 2.303 R done clear
C) 10.0 R done clear
D) 100.0 R done clear
View Answer play_arrowquestion_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 done clear
B) 0.46 done clear
C) 0.57 done clear
D) 0.83 done clear
View Answer play_arrowquestion_answer111) The value of\[\int_{-2}^{3}{|1-{{x}^{2}}|}\,dx\]is
A) \[\frac{7}{3}\] done clear
B) \[\frac{14}{3}\] done clear
C) \[\frac{28}{3}\] done clear
D) \[\frac{1}{3}\] done clear
View Answer play_arrowquestion_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 done clear
B) \[-1\] done clear
C) 1 done clear
D) \[-2\] done clear
View Answer play_arrowquestion_answer113) The domain of the function \[f(x)=\frac{{{\sin }^{-1}}(x-3)}{\sqrt{9-{{x}^{2}}}}\]is
A) [1,2] done clear
B) [2,3] done clear
C) [2,3) done clear
D) [1,2) done clear
View Answer play_arrowquestion_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) \[-\frac{1}{2}\] done clear
B) \[\frac{1}{2}\] done clear
C) \[1\] done clear
D) \[-1\] done clear
View Answer play_arrowquestion_answer115) If\[x={{e}^{y+{{e}^{y+......\infty }}}},x>0,\]then\[\frac{dy}{dx}\]is equal to
A) \[\frac{1-x}{x}\] done clear
B) \[\frac{1}{x}\] done clear
C) \[\frac{x}{1+x}\] done clear
D) \[\frac{1+x}{x}\] done clear
View Answer play_arrowquestion_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) \[{{(y-p)}^{2}}=4qx\] done clear
B) \[{{(y-q)}^{2}}=4py\] done clear
C) \[{{(x-p)}^{2}}=4qy\] done clear
D) \[{{(y-q)}^{2}}=4px\] done clear
View Answer play_arrowquestion_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] done clear
B) \[[-1,1]\] done clear
C) [0, 3] done clear
D) \[[-1,3]\] done clear
View Answer play_arrowquestion_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) done clear
B) (1, 2) done clear
C) (0, 1) done clear
D) (1, 3) done clear
View Answer play_arrowquestion_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) \[\frac{6}{65}\] done clear
B) \[\frac{3}{\sqrt{130}}\] done clear
C) \[-\frac{3}{\sqrt{130}}\] done clear
D) \[-\frac{3}{65}\] done clear
View Answer play_arrowquestion_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) \[{{(x+1)}^{3}}\] done clear
B) \[{{(x-1)}^{3}}\] done clear
C) \[{{(x-1)}^{2}}\] done clear
D) \[{{(x+1)}^{2}}\] done clear
View Answer play_arrowquestion_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) \[-\frac{4}{7},-\frac{11}{7}\] done clear
B) \[-\frac{4}{7},\frac{11}{7}\] done clear
C) \[\frac{4}{7},-\frac{11}{7}\] done clear
D) \[4,\,7\] done clear
View Answer play_arrowquestion_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) \[(3d,\text{ }2a,\text{ }3a),\text{ }(a,\text{ }a,2a)\] done clear
B) \[(3a,\text{ }2a,\text{ }3a),\text{ }(a,\text{ }a,\,a)\] done clear
C) \[(3a,\text{ }3a,\text{ }3a),\text{ (}a,\text{ }a,\text{ }a\text{)}\] done clear
D) \[(2a,\text{ }3a,\text{ }3a),\text{ (2}a,\text{ }a,\text{ }a\text{)}\] done clear
View Answer play_arrowquestion_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) \[x-y+2z=1\] done clear
B) \[x-2y-z=1\] done clear
C) \[x-y-z=1\] done clear
D) \[2x-y-z=1\] done clear
View Answer play_arrowquestion_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) \[\frac{17}{9}km/h\,and\,\frac{13}{9}km/h\] done clear
B) \[\frac{13}{4}km/h\,and\,\frac{17}{4}km/h\] done clear
C) \[\frac{17}{4}km/h\,and\,\frac{13}{4}km/h\] done clear
D) \[\frac{13}{9}km/h\,and\,\frac{17}{9}km/h\] done clear
View Answer play_arrowquestion_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) \[\frac{1}{4}m/s\] done clear
B) \[\frac{1}{4}(\sqrt{3}-1)m/s\] done clear
C) \[\frac{1}{8}m/s\] done clear
D) \[\frac{1}{8}(\sqrt{6}-\sqrt{2})m/s\] done clear
View Answer play_arrowquestion_answer126) Let two numbers have arithmetic mean 9 and geometric mean 4. Then, these numbers are the roots of the quadratic equation
A) \[{{x}^{2}}+18x-16=0\] done clear
B) \[{{x}^{2}}-18x+16=0\] done clear
C) \[{{x}^{2}}+18x+16=0\] done clear
D) \[{{x}^{2}}-18x-16=0\] done clear
View Answer play_arrowquestion_answer127) A point on the parabola\[{{y}^{2}}=18x\]at which the ordinate increases at twice the rate of the abscissa is
A) \[\left( -\frac{9}{8},\frac{9}{2} \right)\] done clear
B) \[(2,-4)\] done clear
C) \[(2,4)\] done clear
D) \[\left( \frac{9}{8},\frac{9}{2} \right)\] done clear
View Answer play_arrowquestion_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\[\lambda \] done clear
B) all except one value of\[\lambda \] done clear
C) all values of\[\lambda \] done clear
D) no value of\[\lambda \] done clear
View Answer play_arrowquestion_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) \[\sqrt{14}\] done clear
B) \[\sqrt{7}\] done clear
C) \[2\] done clear
D) 14 done clear
View Answer play_arrowquestion_answer130) The mean and the variance of a binomial distribution are 4 and 2 respectively. Then, the probability of 2 successes is
A) \[\frac{128}{256}\] done clear
B) \[\frac{219}{256}\] done clear
C) \[\frac{37}{256}\] done clear
D) \[\frac{28}{256}\] done clear
View Answer play_arrowquestion_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 done clear
B) 25, 8 done clear
C) 8,8 done clear
D) 25,25 done clear
View Answer play_arrowquestion_answer132) If A = {1, 2, 3}, B = {3. 2} and C = {2, 3} which one of the following is correct?
A) \[(A\times B)\cap (B\times A)=(A\times C)\cap (B\times C)\] done clear
B) \[(A\times B)\cap (B\times A)=(C\times A)\cap (C\times B)\] done clear
C) \[(A\times B)\cup (B\times A)=(A\times B)\cup (B\times C)\] done clear
D) \[(A\times B)\cup (B\times A)=(A\times B)\cup (A\times C)\] done clear
View Answer play_arrowquestion_answer133) If\[y=\sin ({{x}^{2}}),z={{e}^{{{y}^{2}}}},t=\sqrt{z}\]what is\[\frac{dt}{dx}\]equal to?
A) \[\frac{xyz}{t}\] done clear
B) \[2\frac{xyz}{t}\cos ({{x}^{2}})\] done clear
C) \[\frac{-xyz\,cos({{x}^{2}})}{t}\] done clear
D) \[\frac{xyz\,t}{\cos ({{x}^{2}})}\] done clear
View Answer play_arrowquestion_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 done clear
B) \[f(x)\]is onto done clear
C) Domain of\[f(x)\]is set of renumbers and range of\[f(x)\]is set of integers\[x\] done clear
D) Both domain and range of\[f(x)\]are set of real numbers done clear
View Answer play_arrowquestion_answer135) What is the period of the function\[f(x)=|\sin x+\cos x|\]
A) \[\frac{\pi }{6}\] done clear
B) \[\frac{\pi }{4}\] done clear
C) \[\frac{\pi }{2}\] done clear
D) \[\pi \] done clear
View Answer play_arrowquestion_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 done clear
B) 25 yr done clear
C) 30 yr done clear
D) 35 yr done clear
View Answer play_arrowquestion_answer137) If\[tan\text{ }\theta +sec\text{ }\theta =p,\]then what is the value of \[\sec \theta \]?
A) \[\frac{{{p}^{2}}+1}{{{p}^{2}}}\] done clear
B) \[\frac{{{p}^{2}}+1}{\sqrt{p}}\] done clear
C) \[\frac{{{p}^{2}}+1}{2p}\] done clear
D) \[\frac{p+1}{2p}\] done clear
View Answer play_arrowquestion_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 done clear
B) 40 units done clear
C) 24 units done clear
D) 0 unit done clear
View Answer play_arrowquestion_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 done clear
B) Two done clear
C) Three done clear
D) Four done clear
View Answer play_arrowquestion_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) \[-\frac{4}{9}\] done clear
B) \[-\frac{2}{9}\] done clear
C) \[-\frac{1}{3}\] done clear
D) 1 done clear
View Answer play_arrowquestion_answer141) What is the value of b for which\[f(x)=\sin x-bx+c\] is decreasing in the interval\[(-\infty ,\infty )\]?
A) \[b<1\] done clear
B) \[b\ge 1\] done clear
C) \[b>1\] done clear
D) \[b\le 1\] done clear
View Answer play_arrowquestion_answer142) If\[\int{f(x)}dx=\frac{f(x)}{2}+C,\] then which one of the following is correct?
A) \[f(x)={{e}^{2x}}+C\] done clear
B) \[f(x)=x+C\] done clear
C) \[f(x)=C\] done clear
D) \[f(x)={{e}^{2x}}\] done clear
View Answer play_arrowquestion_answer143) If the sides of a triangle are as\[3:7:8,\]then\[R:r\]is equal to
A) \[2:7\] done clear
B) \[7:2\] done clear
C) \[3:7\] done clear
D) \[7:3\] done clear
View Answer play_arrowquestion_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) \[5-2\sqrt{6}\] done clear
B) \[3\sqrt{3}\] done clear
C) 5 done clear
D) \[5+\sqrt{6}\] done clear
View Answer play_arrowquestion_answer145) The number of solutions of the equation\[\sqrt{1-\cos x}=\sin x,\pi <x<3\pi \] is
A) 0 done clear
B) 1 done clear
C) 2 done clear
D) 3 done clear
View Answer play_arrowquestion_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) \[hm\] done clear
B) \[3\,h\,m\] done clear
C) \[\sqrt{3}\,h\,m\] done clear
D) None of these done clear
View Answer play_arrowquestion_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) \[\frac{2b}{ac}=\frac{{{q}^{2}}}{pr}\] done clear
B) \[\frac{b}{ac}=\frac{q}{pr}\] done clear
C) \[\frac{{{b}^{2}}}{ac}=\frac{{{q}^{2}}}{pr}\] done clear
D) None of these done clear
View Answer play_arrowquestion_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) \[A{{(\theta )}^{-1}}=A(\pi -\theta )\] done clear
B) \[A(\theta )+A(\pi +\theta )\]is a null matrix done clear
C) \[A(\theta )\]is invertible for all\[\theta \in R\] done clear
D) \[A{{(\theta )}^{-1}}=A(-\theta )\] done clear
View Answer play_arrowquestion_answer149) If A is a skew-symmetric matrix and n is odd positive integer, then\[{{A}^{n}}\]is
A) a skew-symmetric matrix done clear
B) a symmetric matrix done clear
C) a diagonal matrix done clear
D) None of the above done clear
View Answer play_arrowquestion_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) \[x\] done clear
B) \[a\] done clear
C) \[2a+3x\] done clear
D) \[d{{x}^{2}}\] done clear
View Answer play_arrowquestion_answer151) If \[^{n}{{C}_{3}}{{+}^{n}}{{C}_{4}}{{>}^{n+1}}{{C}_{3}},\]then
A) \[n>6\] done clear
B) \[n>7\] done clear
C) \[n<6\] done clear
D) None of these done clear
View Answer play_arrowquestion_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 done clear
B) 3 and 2 done clear
C) 2/3 and 9 done clear
D) 3/2 and 6 done clear
View Answer play_arrowquestion_answer153) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin {{x}^{n}}}{{{(\sin x)}^{m}}},(m<n)\]is equal to
A) 1 done clear
B) 0 done clear
C) \[\frac{n}{m}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer154) Let\[f(x)=|x|+|x-1|,\]then
A) \[f(x)\]is continuous at\[x=0\]as well as at\[x=1\] done clear
B) \[f(x)\]is continuous at\[x=0,\]but not at\[x=1\] done clear
C) \[f(x)\]is continuous at\[x=1,\]but not at\[x=0\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer155) On the curve\[{{x}^{3}}=12y,\]the abscissa changes at a faster rate than the ordinate. Then,\[x\]belongs to the interval
A) \[(-2,2)\] done clear
B) \[(-1,1)\] done clear
C) (0, 2) done clear
D) None of these done clear
View Answer play_arrowquestion_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) \[\frac{\pi }{4}\] done clear
B) \[\frac{\pi }{2}\] done clear
C) \[\frac{2\pi }{3}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer157) \[\int{\sin 2x\,d}(\tan x)\]is equal to
A) \[2\log |\cos x|+C\] done clear
B) \[\log |\cos x|+C\] done clear
C) \[2\log |\sec x|+C\] done clear
D) \[\log |\sec x|+C\] done clear
View Answer play_arrowquestion_answer158) The area bounded by the curve\[y=si{{n}^{-1}}x\]and the line \[x=0,|y|=\frac{\pi }{2}\] is
A) 1 done clear
B) 2 done clear
C) \[\pi \] done clear
D) \[2\pi \] done clear
View Answer play_arrowquestion_answer159) The solution of\[y\text{ }dx-x\text{ }dy+3{{x}^{2}}{{y}^{2}}{{e}^{{{x}^{3}}}}\text{ }dx=0\]is.
A) \[\frac{x}{y}+{{e}^{{{x}^{3}}}}=C\] done clear
B) \[\frac{x}{y}-{{e}^{{{x}^{3}}}}=0\] done clear
C) \[-\frac{x}{y}+{{e}^{{{x}^{3}}}}=C\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer160) The point P is equidistant from A (1, 3), B \[(-3,5)\]and\[C(5,-1)\]. Then, PA is equal to
A) \[5\sqrt{5}\] done clear
B) \[5\] done clear
C) \[5\sqrt{10}\] done clear
D) \[25\] done clear
View Answer play_arrowquestion_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) \[\left( \frac{37}{10},-\frac{1}{10} \right)\] done clear
B) \[\left( -\frac{1}{10},\frac{37}{10} \right)\] done clear
C) \[\left( \frac{10}{37},-10 \right)\] done clear
D) \[\left( \frac{2}{3},-\frac{1}{3} \right)\] done clear
View Answer play_arrowquestion_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) \[{{m}^{2}}=1\] done clear
B) \[{{m}^{2}}=3\] done clear
C) \[{{m}^{2}}=7\] done clear
D) \[2{{m}^{2}}=1\] done clear
View Answer play_arrowquestion_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) \[\frac{-20\pm \sqrt{155}}{11}:1\] done clear
B) \[\frac{-2\pm 2\sqrt{155}}{11}:2\] done clear
C) \[-20\pm 2\sqrt{155}:11\] done clear
D) \[-20\pm \sqrt{155}:11\] done clear
View Answer play_arrowquestion_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) \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{25}=1\] done clear
B) \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{16}=1\] done clear
C) \[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{25}=1\] done clear
D) None of these done clear
View Answer play_arrowquestion_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) \[{{m}_{1}}+{{m}_{2}}=-\frac{24}{11}\] done clear
B) \[{{m}_{1}}{{m}_{2}}=\frac{20}{11}\] done clear
C) \[{{m}_{1}}+{{m}_{2}}=\frac{48}{11}\] done clear
D) \[{{m}_{1}}{{m}_{2}}=\frac{11}{20}\] done clear
View Answer play_arrowquestion_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) \[\alpha =1,\text{ }\beta =-1\] done clear
B) \[\alpha =1,\text{ }\beta =\pm 1\] done clear
C) \[\alpha =-1,\text{ }\beta =\pm 1\] done clear
D) \[\alpha =\pm 1,\text{ }\beta =1\] done clear
View Answer play_arrowquestion_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 done clear
B) 78.00 done clear
C) 188.66 done clear
D) 177.33 done clear
View Answer play_arrowquestion_answer168) If the algebraic sum of deviations of 20 observations from 30 is 20, then the mean of observations is
A) 30 done clear
B) 30.1 done clear
C) 29 done clear
D) 31 done clear
View Answer play_arrowquestion_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) \[\frac{41}{161}\] done clear
B) \[\frac{120}{161}\] done clear
C) \[\frac{21}{161}\] done clear
D) None of these done clear
View Answer play_arrowquestion_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) \[\frac{50}{77}\] done clear
B) \[\frac{52}{77}\] done clear
C) \[\frac{25}{88}\] done clear
D) \[\frac{63}{88}\] done clear
View Answer play_arrow
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