question_answer1) A boat carrying a number of large stones is floating in a water tank. What would happen to the water level, if a few stones are unloaded into water?
A) Rises done clear
B) Falls done clear
C) Remains unchanged done clear
D) Rises till half the number of stones are unloaded and then begins to fall done clear
View Answer play_arrowquestion_answer2) A container with square base of side a is filled up to a height H with a liquid. A hole is made at a depth h from the free surface of water. With what acceleration the container must be accelerated, so that the water does not come out?
A) \[g\] done clear
B) \[\frac{g}{2}\] done clear
C) \[\frac{2gH}{2}\] done clear
D) \[\frac{2gh}{2}\] done clear
View Answer play_arrowquestion_answer3) If two soap bubbles of equal radii r coalesce, then the radius of curvature of interface between two bubbles will be
A) r done clear
B) zero done clear
C) infinity done clear
D) \[\frac{1}{2r}\] done clear
View Answer play_arrowquestion_answer4) What is the mass of \[2\text{ }L\]of nitrogen at \[~22.4\text{ }arm\]pressure and \[273\text{ }K\]?
A) \[28\text{ }g\] done clear
B) \[14\times 22.4\text{ }g\] done clear
C) \[56\text{ }g\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer5) \[2\text{ }g\]of water condenses when passed through \[40\text{ }g\]of water initially at\[{{25}^{o}}C\]. The- condensation of steam raises the temperature of water to \[{{54.3}^{o}}C\]. What is the latent heat of steam?
A) \[540\,\,cal/g\] done clear
B) \[536\,\,cal/g\] done clear
C) \[270\,\,cal/g\] done clear
D) \[480\,\,cal/g\] done clear
View Answer play_arrowquestion_answer6) Petrol engine does the work during
A) suction stroke done clear
B) exhaust stroke done clear
C) adiabatic expansion done clear
D) combustion done clear
View Answer play_arrowquestion_answer7) The spectral energy distribution of a star is maximum at twice temperature as that of sun. The total energy radiated by star is
A) twice as that of the sun done clear
B) same as that of the sun done clear
C) sixteen times as that of the sun done clear
D) one-sixteenth of sun done clear
View Answer play_arrowquestion_answer8) Two simple pendulums of lengths \[1.44\text{ }m\]and \[1\text{ }m\] start swinging together. After how many vibrations will they again start swinging together?
A) 5 oscillations of smaller pendulum done clear
B) 6 oscillations of smaller pendulum done clear
C) 4 oscillations of bigger pendulum done clear
D) 6 oscillations of bigger pendulum done clear
View Answer play_arrowquestion_answer9) A wave has velocity u in medium P and velocity \[2u\] in medium Q. If the wave is incident in medium P at an angle \[{{30}^{o}},\]then the angle of refraction will be
A) \[{{30}^{o}}\] done clear
B) \[{{45}^{o}}\] done clear
C) \[{{60}^{o}}\] done clear
D) \[{{90}^{o}}\] done clear
View Answer play_arrowquestion_answer10) In \[1\text{ }m\]long open pipe what is the harmonic of resonance obtained with a tuning fork of frequency \[480\text{ }Hz\]?
A) First done clear
B) Second done clear
C) Third done clear
D) Fourth done clear
View Answer play_arrowquestion_answer11) Three sources of equal intensities with frequencies 400,401 and 402 vib/s are sounded together. The number of beat/s is
A) zero done clear
B) \[1\] done clear
C) \[2\] done clear
D) \[4\] done clear
View Answer play_arrowquestion_answer12) Two pendulums begin to swing simultaneously. If the ratio of the frequency of oscillations of the two is \[7:8,\] then the ratio of lengths of the two pendulums will be
A) \[7:8\] done clear
B) \[8:7\] done clear
C) \[49:64\] done clear
D) \[64:49\] done clear
View Answer play_arrowquestion_answer13) In a resonance pipe the first and second resonances are obtained at depths \[22.7\text{ }cm\]and \[70.2\text{ }cm\]respectively. What will be the end correction?
A) \[1.05\,\,cm\] done clear
B) \[115.5\,\,cm\] done clear
C) \[92.5\,\,cm\] done clear
D) \[113.5\,\,cm\] done clear
View Answer play_arrowquestion_answer14) The intensity level of sound A is 30 dB greater than of B. How many times more intense is the sound A than B?
A) \[10\] done clear
B) \[100\] done clear
C) \[1000\] done clear
D) \[2\] done clear
View Answer play_arrowquestion_answer15) An open tube is in resonance with string. If tube is dipped in water, so that \[75%\]of length of tube is inside water, then the ratio of the frequency \[({{v}_{o}})\] of tube to string is
A) \[{{v}_{o}}\] done clear
B) \[2{{v}_{o}}\] done clear
C) \[\frac{2}{3}{{v}_{o}}\] done clear
D) \[\frac{3}{2}{{v}_{o}}\] done clear
View Answer play_arrowquestion_answer16) Two masses \[{{m}_{1}}\] and \[{{m}_{2}}\] are suspended together by a massless spring of constant k. When the masses are in equilibrium \[{{m}_{1}},\] is removed without disturbing the system. The amplitude of oscillations is
A) \[\frac{{{m}_{1}}g}{k}\] done clear
B) \[\frac{{{m}_{2}}g}{k}\] done clear
C) \[\frac{({{m}_{1}}+{{m}_{2}})g}{k}\] done clear
D) \[\frac{({{m}_{1}}-{{m}_{2}})g}{k}\] done clear
View Answer play_arrowquestion_answer17) If a conducting medium is placed between two charges, then the electric force between will become
A) zero done clear
B) infinity done clear
C) \[1N\] done clear
D) 1 dyne done clear
View Answer play_arrowquestion_answer18) If an electron moves from rest from a point at which potential is \[50\text{ }V\]to another point at which potential is \[70\text{ }V,\] then its kinetic energy in the final state will be
A) \[3.2\times {{10}^{-20}}J~\] done clear
B) \[3.2\times {{10}^{-18}}J\] done clear
C) \[3.2\times {{10}^{-19}}J\] done clear
D) zero done clear
View Answer play_arrowquestion_answer19) In the following diagram the work done in moving a point charge from point P to point A, B and C is respectively as \[{{W}_{A}},\] \[{{W}_{B}}\] and \[{{W}_{C}},\] then
A) \[{{W}_{A}}={{W}_{B}}={{W}_{C}}\] done clear
B) \[{{W}_{A}}={{W}_{B}}={{W}_{C}}=0\] done clear
C) \[{{W}_{A}}>{{W}_{B}}>{{W}_{C}}\] done clear
D) \[{{W}_{A}}<{{W}_{B}}<{{W}_{C}}\] done clear
View Answer play_arrowquestion_answer20) The electric field due to an electric dipole at a distance r from its centre in axial position is E. If the dipole is rotated through an angle of \[{{90}^{o}}\]about its perpendicular axis, the electric field at the same point will be
A) \[E\] done clear
B) \[\frac{E}{4}\] done clear
C) \[\frac{E}{2}\] done clear
D) \[2E\] done clear
View Answer play_arrowquestion_answer21) If eight similar charge drops combine to form a bigger drop, then the ratio of capacitance of bigger drop to that of smaller drop will be
A) \[2:1\] done clear
B) \[8:1\] done clear
C) \[4:1\] done clear
D) \[16:1\] done clear
View Answer play_arrowquestion_answer22) The value of current I in figure is
A) \[4\,A\] done clear
B) \[6\,A\] done clear
C) \[3\,A\] done clear
D) \[5\,A\] done clear
View Answer play_arrowquestion_answer23) The plates of a charged condenser are connected to a voltmeter. If the plates are moved apart, the reading of voltmeter will
A) increase done clear
B) decrease done clear
C) remain unchanged done clear
D) information is insufficient done clear
View Answer play_arrowquestion_answer24) The n rows each containing m cells in series are joined in parallel. Maximum current is taken from this combination across an external resistance of 30 resistance. If the total number of cells used are 24 and internal resistance of each cell is \[0.5\text{ }Q\]then
A) \[m=8,\text{ }n=3\] done clear
B) \[m=6,\text{ }n=4\] done clear
C) \[m=12,\text{ }n=2\] done clear
D) \[m=2,\text{ }n=12\] done clear
View Answer play_arrowquestion_answer25) A railway compartment is lit up by thirteen lamps each taking \[2.1\text{ }A\]at\[15\text{ }V\]. The heat generated per second in each lamp will be m
A) \[4.35\text{ }cal\] done clear
B) \[5.73\text{ }cal\] done clear
C) \[7.5\text{ }cal\] done clear
D) \[2.5\text{ }cal\] done clear
View Answer play_arrowquestion_answer26) The chemical equivalent of copper and zinc are 32 and 108 respectively. When copper and silver voltameter are connected in series and electric current is passed through for sometimes, \[1.6\text{ }g\]of copper is deposited. Then, the mass of silver deposited will be
A) \[3.5\text{ }g\] done clear
B) \[2.8g\] done clear
C) \[5.4\text{ }g\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer27) If the emf of a thermocouple, one junction of which is kept \[0{}^\circ C\]is given by \[e=at+\frac{1}{2}b{{t}^{2}}\] then the neutral temperature will be
A) \[\frac{a}{b}\] done clear
B) \[-\frac{a}{b}\] done clear
C) \[\frac{a}{2b}\] done clear
D) \[-\frac{1}{ab}\] done clear
View Answer play_arrowquestion_answer28) The direction of magnetic lines of force produced by passing a direct current in a conductor is given by
A) Lenz'slaw done clear
B) Fleming's left hand rule done clear
C) Right hand palm rule done clear
D) Maxwell's law done clear
View Answer play_arrowquestion_answer29) A proton, a deuteron and an alpha particle are accelerated through same potential difference and then they enter a normal uniform magnetic field. The ratio of their kinetic energies will be
A) \[2:1:3\] done clear
B) \[1:1:2\] done clear
C) \[1:1:1\] done clear
D) \[1:2:4\] done clear
View Answer play_arrowquestion_answer30) For the magnetic field to be maximum due to a small element of current carrying conductor at a point, the angle between the element and the line joining the element to the given point must be
A) \[{{0}^{o}}\] done clear
B) \[{{90}^{o}}\] done clear
C) \[{{180}^{o}}\] done clear
D) \[{{45}^{o}}\] done clear
View Answer play_arrowquestion_answer31) A circular coil of 20 turns and radius 10 cm is placed in uniform magnetic field of \[0.10\text{ }T\]normal to the plane of the coil. If the current in coil is 5 A, then the torque acting on the coil will be
A) \[31.4\text{ }Nm\] done clear
B) \[3.14\text{ }Nm\] done clear
C) \[0.314\text{ }Nm\] done clear
D) zero done clear
View Answer play_arrowquestion_answer32) The earth's magnetic field inside an iron box as compared to that outside the box is
A) less done clear
B) more done clear
C) zero done clear
D) same done clear
View Answer play_arrowquestion_answer33) The intensity of magnetic field due to an isolated pole of strength m at a point distant r from it will be
A) \[\frac{m}{{{r}^{2}}}\] done clear
B) \[m{{r}^{2}}\] done clear
C) \[\frac{{{r}^{2}}}{m}\] done clear
D) \[\frac{m}{r}\] done clear
View Answer play_arrowquestion_answer34) The dimensions of self-inductance L are
A) \[[M{{L}^{2}}{{T}^{-2}}{{A}^{-2}}]\] done clear
B) \[[M{{L}^{2}}{{T}^{-1}}{{A}^{-2}}]\] done clear
C) \[[M{{L}^{2}}{{T}^{-1}}{{A}^{-1}}]\] done clear
D) \[[M{{L}^{-2}}{{T}^{-2}}{{A}^{-2}}]\] done clear
View Answer play_arrowquestion_answer35) Quantity that remains unchanged in a transformer is
A) voltage done clear
B) current done clear
C) frequency done clear
D) None of these done clear
View Answer play_arrowquestion_answer36) If the capacity of a condenser is 1 F, then its resistance in a DC circuit will be
A) zero done clear
B) infinity done clear
C) \[1\Omega \] done clear
D) \[\frac{1}{2}\,\,\Omega \] done clear
View Answer play_arrowquestion_answer37) The time taken by an alternating current of \[50\text{ }Hz\] in reaching from zero to its maximum value will be
A) \[0.5s\] done clear
B) \[0.005s\] done clear
C) \[0.05\text{ }s\] done clear
D) \[5s\] done clear
View Answer play_arrowquestion_answer38) If the area to be covered for TV telecast is doubled, then height of transmitting antenna (TV tower) will have to be
A) doubled done clear
B) halved done clear
C) quadrupled done clear
D) kept unchanged done clear
View Answer play_arrowquestion_answer39) An electromagnetic radiation has an energy \[14.4\text{ }eV\]. To which region of electromagnetic spectrum does it belong?
A) Ultraviolet region done clear
B) Visible region done clear
C) X-ray region done clear
D) y-ray region done clear
View Answer play_arrowquestion_answer40) When a ray of light is incident normally on a surface, then
A) total internal reflection takes place done clear
B) it passes undeviated done clear
C) it undergoes dispersion done clear
D) it gets absorbed by the surface done clear
View Answer play_arrowquestion_answer41) A ray of light passes through a glass plate of thickness t and refractive index u. If the speed of light in vacuum is c, then the time taken by light in passing through the plate will be
A) \[\mu t\] done clear
B) \[\frac{\mu t}{c}\] done clear
C) \[\frac{tc}{\mu }\] done clear
D) \[\frac{t}{\mu c}\] done clear
View Answer play_arrowquestion_answer42) In Young's double slit experiment with monochromatic light, the central fringe will be
A) coloured done clear
B) white done clear
C) bright done clear
D) black done clear
View Answer play_arrowquestion_answer43) In the phenomenon of interference, energy is
A) destroyed at bright'fringes done clear
B) created at dark fringes done clear
C) conserved but it is redistributed done clear
D) same at all points done clear
View Answer play_arrowquestion_answer44) A very thin film that reflects white light appears
A) coloured done clear
B) white done clear
C) black done clear
D) red done clear
View Answer play_arrowquestion_answer45) The size of an obstacle in order to observe diffraction of light must be
A) of any order done clear
B) of the order of wavelength done clear
C) much larger than wavelength done clear
D) much smaller than wavelength done clear
View Answer play_arrowquestion_answer46) If the binding energies of a deuteron and an alpha-particle are \[1.125\text{ }MeV\]and \[7.2\text{ }MeV,\] respectively, then the more stable of the two is
A) deuteron done clear
B) alpha-particle done clear
C) both [a] and [b] done clear
D) sometimes deuteron and sometimes alpha particle done clear
View Answer play_arrowquestion_answer47) The particle A is converted into C via following reaction, \[A\xrightarrow{{}}B{{+}_{2}}H{{e}^{4}}\] \[B\xrightarrow{{}}C+2{{e}^{-}}\] Then
A) A and C are isobars done clear
B) A and C are isotopes done clear
C) A and B are isobars done clear
D) A and B are isotopes done clear
View Answer play_arrowquestion_answer48) On bombardment of \[{{U}^{235}}\] by slow neutrons, 200 MeV energy is released. If the power output of atomic reactor is \[1.6\text{ }MW,\] then the rate of fission will be
A) \[5\times {{10}^{16}}/s\] done clear
B) \[10\times {{10}^{16}}/s\] done clear
C) \[15\times {{10}^{16}}/s\] done clear
D) \[20\times {{10}^{16}}/s\] done clear
View Answer play_arrowquestion_answer49) The fussion process is possible at high temperatures, because at higher temperatures
A) the nucleus disintegrates done clear
B) the molecules disintegrates done clear
C) atoms become ionized done clear
D) the nucleus get sufficient energy to overcome the strong forces of repulsion done clear
View Answer play_arrowquestion_answer50) For maintaining sustained chain reaction, the following is required
A) protons done clear
B) electrons done clear
C) neutrons done clear
D) positrons done clear
View Answer play_arrowquestion_answer51) Sun maintains its shining because of the
A) fission of helium done clear
B) chemical reaction done clear
C) fusion of hydrogen nuclei done clear
D) burning of carbon done clear
View Answer play_arrowquestion_answer52) Atomic reactor is based on
A) controlled chain reaction done clear
B) uncontrolled chain reaction done clear
C) nuclear fission done clear
D) nuclear fussion done clear
View Answer play_arrowquestion_answer53) If the frequency of light incident on metal surface is doubled, then kinetic energy of emitted electron will become
A) doubled done clear
B) less than double done clear
C) more than double done clear
D) nothing can be said done clear
View Answer play_arrowquestion_answer54) The energy gap of silicon is \[1.14\text{ }eV\]. At what wavelength the silicon will stop to absorb the photon?
A) \[10877\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\] done clear
B) \[\text{9888 }\overset{\text{o}}{\mathop{\text{A}}}\,\] done clear
C) \[1087.7\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\] done clear
D) \[1000\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\] done clear
View Answer play_arrowquestion_answer55) n-p-n transistor are preferred to p-n-p transistor because they have
A) low cost done clear
B) low dissipation energy done clear
C) capability of handling large power done clear
D) electrons having high mobility than holes done clear
View Answer play_arrowquestion_answer56) In a transistor in common-emitter configuration, the ratio of power gain to voltage gain is
A) \[\alpha \] done clear
B) \[\frac{\beta }{\alpha }\] done clear
C) \[\beta \times \beta \] done clear
D) \[\beta \] done clear
View Answer play_arrowquestion_answer57) The ionic bond is absent in
A) \[NaCl\] done clear
B) \[CsCl\] done clear
C) \[LiF\] done clear
D) \[{{H}_{2}}O\] done clear
View Answer play_arrowquestion_answer58) As the temperature rises the resistance offered by metal
A) increases done clear
B) decreases done clear
C) remains same done clear
D) None of these done clear
View Answer play_arrowquestion_answer59) Density of liquid in CGS system is \[0.625\text{ }g/c{{m}^{3}}\] What is its magnitude in SI system?
A) \[0.625\] done clear
B) \[0.0625\] done clear
C) \[0.00625\] done clear
D) \[625\] done clear
View Answer play_arrowquestion_answer60) If the length of rod A is \[3.25\pm 0.01\,cm\]and that of B is \[4.19\pm 0.01\text{ }cm,\] then the rod B is longer than rod A by
A) \[0.94\pm 0.00\text{ }cm\] done clear
B) \[0.94\pm 0.01\text{ }cm\] done clear
C) \[0.94\pm 0.02\text{ }cm\] done clear
D) \[0.94\pm 0.005\text{ }cm\] done clear
View Answer play_arrowquestion_answer61) A man is \[45\text{ }m\]behind the bus, when the bus start accelerating from rest with-acceleration \[2.5m/{{s}^{2}}\]. With what minimum velocity should the man start running to catch the bus?
A) \[12\text{ }m/s\] done clear
B) \[14\text{ }m/s\] done clear
C) \[15\text{ }m/s\] done clear
D) \[16\text{ }m/s\] done clear
View Answer play_arrowquestion_answer62) A particle moves along x-axis as \[x=4\,(t-2)+a{{(t-2)}^{2}}\] Which of the flowing is true?
A) The initial velocity of particle is 4 done clear
B) The acceleration of particle is \[2a\] done clear
C) The particle is at origin at \[t=0\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer63) The momentum of the particle at any instant is given by \[3\,\cos 4t\,\hat{i}+3\,\sin \,4t\,\hat{j}\]. What is the angle between momentum and force-acting on it?
A) \[{{60}^{o}}\] done clear
B) \[{{30}^{o}}\] done clear
C) \[{{45}^{o}}\] done clear
D) \[{{90}^{o}}\] done clear
View Answer play_arrowquestion_answer64) A boat moves with a speed of \[5\text{ }km/h\]relative to water in a river flowing with a speed of \[3\text{ }km/h\]and having a width of\[1\text{ }km\]. The time taken around a round trip is
A) \[5\text{ }min\] done clear
B) \[60\text{ }min\] done clear
C) \[20\text{ }min\] done clear
D) \[30\text{ }min\] done clear
View Answer play_arrowquestion_answer65) A man is standing at the centre of frictionless pond of ice. How can he get himself to the shore?
A) By throwing his shirt in vertically upward direction done clear
B) By spitting horizontally done clear
C) He will wait for the ice to melt in pond done clear
D) Unable to get at the shore done clear
View Answer play_arrowquestion_answer66) If the heart pushes \[1\text{ }cc\]of blood in 1 s under pressure \[20000\text{ }N{{m}^{2}},\]the power of heart is
A) \[0.02\text{ }W\] done clear
B) \[400\text{ }W\] done clear
C) \[5\times {{10}^{-10}}W\] done clear
D) \[0.2\text{ }W\] done clear
View Answer play_arrowquestion_answer67) A body of mass \[4\text{ }kg\]moving with velocity \[12\text{ }m/s\]collides with another body of mass \[\text{6 }kg\] at rest. If two, bodies stick together after collision, then the loss of kinetic energy of system is
A) zero done clear
B) \[288\text{ }J\] done clear
C) \[172.8\text{ }J\] done clear
D) \[144\text{ }J\] done clear
View Answer play_arrowquestion_answer68) A man does a given amount of work in \[10\text{ }s\]. Another man does the' same amount of work in \[20\text{ }s\]. The ratio of the output power of first man to the second man is
A) \[1\] done clear
B) \[1/2\] done clear
C) \[2/1\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer69) Turning effect is produced by
A) tangential component of force done clear
B) radial component of force done clear
C) transverse component of force done clear
D) None of the above done clear
View Answer play_arrowquestion_answer70) For spheres each of mass M and radius R are placed with their centres on the four comers A, B, C and D of a square of side b. The spheres A and B are hollow and C and D are solids. The moment of inertia of the system about side AD of square is
A) \[\frac{8}{3}M{{R}^{2}}+2M{{b}^{2}}\] done clear
B) \[\frac{8}{5}M{{R}^{2}}+2M{{b}^{2}}\] done clear
C) \[\frac{32}{15}M{{R}^{2}}+2M{{b}^{2}}\] done clear
D) \[32M{{R}^{2}}+4M{{b}^{2}}\] done clear
View Answer play_arrowquestion_answer71) A particle describes a horizontal circle in a conical funnel whose inner surface is smooth with speed of \[0.5\text{ }m/s\]. What is the height of the plane of circle from vertex of the funnel?
A) \[0.25\text{ }cm\] done clear
B) \[2\text{ }cm\] done clear
C) \[4\text{ }cm\] done clear
D) \[2.5\text{ }cm\] done clear
View Answer play_arrowquestion_answer72) Two masses \[{{m}_{1}}\] and \[{{m}_{2}}({{m}_{1}}>{{m}_{2}})\]are connected by massless flexible and inextensible string passed over massless and frictionless pulley. The acceleration of centre of mass is
A) \[{{\left( \frac{{{m}_{1}}-{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right)}^{2}}g\] done clear
B) \[\frac{{{m}_{1}}-{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}}g\] done clear
C) \[\frac{{{m}_{1}}+{{m}_{2}}}{{{m}_{1}}-{{m}_{2}}}g\] done clear
D) zero done clear
View Answer play_arrowquestion_answer73) A satellite moves in a circle around the earth. The radius of this circle is equal to one-half of the radius of the moon's orbit. The satellite completes one revolution is
A) \[\frac{1}{2}\] lunar month done clear
B) \[\frac{2}{3}\] lunar month done clear
C) \[{{2}^{-3/2}}\] lunar month done clear
D) \[{{2}^{3/2}}\] lunar month done clear
View Answer play_arrowquestion_answer74) Earth binds the atmosphere because of
A) gravity done clear
B) oxygen between earth and atmosphere done clear
C) both and done clear
D) None of the above done clear
View Answer play_arrowquestion_answer75) A geostationary satellite is revolving around the earth. To make it escape from gravitational field of earth, its velocity must be increased
A) \[100%\] done clear
B) \[41.4%\] done clear
C) \[50%\] done clear
D) \[59.6%\] done clear
View Answer play_arrowquestion_answer76) Who used the quantum theory for the first time to explain the structure of atom?
A) de-Broglie done clear
B) Bohr done clear
C) Heisenberg done clear
D) Einstein done clear
View Answer play_arrowquestion_answer77) The boiling point of water decreases at high altitudes because
A) the atmospheric pressure is low done clear
B) the temperature is low done clear
C) the atmospheric pressure is high done clear
D) the temperature is high done clear
View Answer play_arrowquestion_answer78) In a solid lattice, the cation has left a lattice site and is located at interstitial position, the lattice defect is
A) interstitial defect done clear
B) vacancy defect done clear
C) Frenkel defect done clear
D) Schottky defect done clear
View Answer play_arrowquestion_answer79) The entropy of crystalline substances at absolute zero going by the third law of thermodynamics should be taken as
A) 100 done clear
B) 50 done clear
C) zero done clear
D) different for different substances done clear
View Answer play_arrowquestion_answer80) \[\Delta G\]for a spontaneous reaction is
A) zero done clear
B) negative done clear
C) positive done clear
D) could be positive or negative done clear
View Answer play_arrowquestion_answer81) The IUPAC name for \[C{{H}_{3}}CO-C{{H}_{3}}\]is
A) dimethyl ketone done clear
B) acetone done clear
C) propanal done clear
D) propanone done clear
View Answer play_arrowquestion_answer82) Which of the following is not an endothermic reaction?
A) Dehydrogenation done clear
B) Ethane to ethene done clear
C) Combustion of propane done clear
D) Change of chlorine molecule into chlorine atoms done clear
View Answer play_arrowquestion_answer83) A process in which the system does not exchange heat with the surroundings is known as
A) isothermal done clear
B) isobaric done clear
C) isochoric done clear
D) adiabatic done clear
View Answer play_arrowquestion_answer84) Which of the following is not a non-eletrolyte?
A) Acetic acid done clear
B) Glucose done clear
C) Ethanol done clear
D) Urea done clear
View Answer play_arrowquestion_answer85) The unit \[\text{oh}{{\text{m}}^{-1}}\]is used for
A) molar conductivity done clear
B) equivalent conductivity done clear
C) specific conductivity done clear
D) conductance done clear
View Answer play_arrowquestion_answer86) The tendency of an electrode to lose electrons is known as
A) eletrode potential done clear
B) reduction potential done clear
C) oxidation potential done clear
D) emf done clear
View Answer play_arrowquestion_answer87) For the feasibility of a redox reaction in a cell, the emf should be
A) positive done clear
B) fixed done clear
C) zero done clear
D) negative done clear
View Answer play_arrowquestion_answer88) If the rate reaction\[A\to B\]doubles on increasing the concentration of A by 4 times, the order of the reaction is
A) 2 done clear
B) 1 done clear
C) \[\frac{1}{2}\] done clear
D) 4 done clear
View Answer play_arrowquestion_answer89) Fog is a colloidal solution of
A) solid in gas done clear
B) liquid in gas done clear
C) gas in liquid done clear
D) gas in solid done clear
View Answer play_arrowquestion_answer90) Muddy water can be purified through coagulation by using
A) common salt done clear
B) alums done clear
C) sand done clear
D) lime done clear
View Answer play_arrowquestion_answer91) Formation of ammonia from \[{{\text{H}}_{\text{2}}}\]and \[{{\text{N}}_{2}}\]by Haber's process using Fe is an example of
A) heterogeneous catalysis done clear
B) homogeneous catalysis done clear
C) enzyme catalysis done clear
D) non-catalytic process done clear
View Answer play_arrowquestion_answer92) The reason for almost doubling the rate of reaction on increasing the temperature of the reaction system by \[10{{\,}^{o}}C\]is
A) the value of threshold energy increases done clear
B) collision frequency increases done clear
C) the fraction of the molecule having energy equal to threshold energy increases done clear
D) activation energy decreases done clear
View Answer play_arrowquestion_answer93) The pH of an aqueous solution having hydroxide ion concentration as \[1\times {{10}^{-5}}\] is
A) 5 done clear
B) 9 done clear
C) 4.5 done clear
D) 11 done clear
View Answer play_arrowquestion_answer94) Which of the following is not a Lewis acid?
A) \[B{{F}_{3}}\] done clear
B) \[AlC{{l}_{3}}\] done clear
C) \[S{{O}_{2}}\] done clear
D) \[{{H}_{2}}O\] done clear
View Answer play_arrowquestion_answer95) The precipitation takes place only when the product of concentrations of ions
A) exceeds the solubility product done clear
B) is less than the solubility product done clear
C) is negligible done clear
D) is equal to the solubility products done clear
View Answer play_arrowquestion_answer96) Which of the following has lowest electron affinity?
A) \[Cl\] done clear
B) \[I\] done clear
C) \[F\] done clear
D) \[Br\] done clear
View Answer play_arrowquestion_answer97) In the calcium fluoride structure the coordination number of the cation and anions are respectively
A) 6, 6 done clear
B) 8, 4 done clear
C) 4, 4 done clear
D) 4, 8 done clear
View Answer play_arrowquestion_answer98) The total number of orbitals possible for principal quantum number \[n\] is
A) \[n\] done clear
B) \[{{n}^{2}}\] done clear
C) \[2n\] done clear
D) \[2{{n}^{2}}\] done clear
View Answer play_arrowquestion_answer99) The pair having similar geometry is
A) \[PC{{l}_{3}},N{{H}_{4}}\] done clear
B) \[BeC{{l}_{2}},\,{{H}_{2}}O\] done clear
C) \[C{{H}_{4}},CC{{l}_{4}}\] done clear
D) \[I{{F}_{5}},P{{F}_{5}}\] done clear
View Answer play_arrowquestion_answer100) The \[d-\]orbital invovled in \[s{{p}^{3}}d-\]hybridisation is
A) \[{{d}_{{{x}^{2}}-{{y}^{2}}}}\] done clear
B) \[{{d}_{xy}}\] done clear
C) \[{{d}_{{{z}^{2}}}}\] done clear
D) \[{{d}_{zx}}\] done clear
View Answer play_arrowquestion_answer101) If 8.0 g of a radioactive substance has a half-life of 10 h, the half-life of 2.0 g of the same substance is
A) 2.6 h done clear
B) 5h done clear
C) 10 h done clear
D) 40 h done clear
View Answer play_arrowquestion_answer102) Loss of a beta paticle is equivalent to
A) increase of one neutron only done clear
B) decrease of one neutron only done clear
C) both [a] and [b] done clear
D) none of the above done clear
View Answer play_arrowquestion_answer103) Which of the following is incorrect?
A) Relative lowering of vapour pressure is independent of the nature of the solute and the solvent done clear
B) The ralative lowering of vapour pressure its a colligative property done clear
C) Vapour pressure of a solution is lower than the vapour pressure of the solvent done clear
D) The relative lowering of vapour pressure is directly proportional to the original pressure done clear
View Answer play_arrowquestion_answer104) The presence of the chlorine atom on benzene ring makes the second substituent enter at a position
A) ortho done clear
B) meta done clear
C) para done clear
D) ortho/para done clear
View Answer play_arrowquestion_answer105) Hydrogen is not obtained when zinc reacts with
A) cold water done clear
B) hot \[\text{NaOH}\]solution done clear
C) dil \[{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\] done clear
D) dil \[\text{HCl}\] done clear
View Answer play_arrowquestion_answer106) The oxidation number of xenon in \[\text{XeO}{{\text{F}}_{2}}\]is
A) zero done clear
B) 2 done clear
C) 4 done clear
D) 3 done clear
View Answer play_arrowquestion_answer107) Which of the following is most volatile?
A) \[\text{HF}\] done clear
B) \[\text{HCl}\] done clear
C) \[\text{HBr}\] done clear
D) \[\text{ }\!\!~\!\!\text{ HI}\] done clear
View Answer play_arrowquestion_answer108) The form of iron having the highest carbon content is
A) cast iron done clear
B) wrought ton done clear
C) stainless steel done clear
D) mild steel done clear
View Answer play_arrowquestion_answer109) Which belongs to the actinides series?
A) \[Ce\] done clear
B) \[~Cf\] done clear
C) \[Ca~\] done clear
D) \[~Cs\] done clear
View Answer play_arrowquestion_answer110) Which of the following is planar?
A) \[Xe{{F}_{2}}\] done clear
B) \[Xe{{O}_{3}}F\] done clear
C) \[Xe{{O}_{2}}{{F}_{2}}\] done clear
D) \[Xe{{F}_{4}}\] done clear
View Answer play_arrowquestion_answer111) \[\text{Cr}{{\text{O}}_{\text{3}}}\]dissovles in aqueous \[\text{NaOH}\]to give
A) \[CrO_{4}^{2-}\] done clear
B) \[Cr(OH)_{3}^{-}\] done clear
C) \[C{{r}_{2}}O_{7}^{2-}\] done clear
D) \[Cr{{(OH)}_{2}}\] done clear
View Answer play_arrowquestion_answer112) Which of the following is a tribasic acid?
A) \[~{{H}_{3}}P{{O}_{4}}\] done clear
B) \[~HP{{O}_{3}}\] done clear
C) \[{{H}_{4}}{{P}_{2}}{{O}_{7}}\] done clear
D) \[~{{H}_{4}}{{P}_{2}}{{O}_{6}}\] done clear
View Answer play_arrowquestion_answer113) Ethylene diamine is an example of
A) monodentate ligand done clear
B) bidentate ligand done clear
C) tridentate ligand done clear
D) polydentate ligand done clear
View Answer play_arrowquestion_answer114) The molecule having a pyramidal shape out of the following is
A) \[C{{O}_{2}}\] done clear
B) \[~B{{F}_{3}}\] done clear
C) \[S{{F}_{4}}\] done clear
D) \[~N{{H}_{3}}\] done clear
View Answer play_arrowquestion_answer115) Which of the following doesn't give a ppt. with silver nitrate solution?
A) Ethyl bromide done clear
B) Sodium bromide done clear
C) Calcium chloride done clear
D) Sodium chloride done clear
View Answer play_arrowquestion_answer116) Which is the most stable carbocation?
A) \[iso-\]propyl cation done clear
B) Triphenylmethyl cation done clear
C) Ethyl cation done clear
D) \[n-\]propyl cation done clear
View Answer play_arrowquestion_answer117) Which is most acidic of the following?
A) Methane done clear
B) Acetylene done clear
C) 1-butene done clear
D) Neo-pentane done clear
View Answer play_arrowquestion_answer118) Which is the most reactive of the following?
A) Ethyl acetate done clear
B) Acetic anhydride done clear
C) Acetamide done clear
D) Acetyl chloride done clear
View Answer play_arrowquestion_answer119) Which of the following will be chiral?
A) \[C{{H}_{3}}CHC{{l}_{2}}\] done clear
B) \[C{{H}_{3}}CHBrCl\] done clear
C) \[C{{D}_{2}}C{{l}_{2}}\] done clear
D) \[C{{H}_{2}}ClBr\] done clear
View Answer play_arrowquestion_answer120) Electronic configuration of deuterium atom is
A) \[1{{s}^{1}}\] done clear
B) \[2{{s}^{2}}\] done clear
C) \[2{{s}^{1}}\] done clear
D) \[1{{s}^{2}}\] done clear
View Answer play_arrowquestion_answer121) Which of the following is a phenol?
A) Pentanoic acid done clear
B) Phthalic acid done clear
C) Picric acid done clear
D) Phosphoric acid done clear
View Answer play_arrowquestion_answer122) Which of the following is not an organometallic compound?
A) \[{{C}_{2}}{{H}_{5}}ONa\] done clear
B) \[C{{H}_{3}}MgI\] done clear
C) Tetraethyl done clear
D) \[K{{C}_{4}}{{H}_{9}}\] done clear
View Answer play_arrowquestion_answer123) The correct order of electron affinity is
A) \[B<C<O>N\] done clear
B) \[B>C>N>O\] done clear
C) \[\text{O}>C>B>N\] done clear
D) \[\text{O}<C<B<N\] done clear
View Answer play_arrowquestion_answer124) Ziegler Natta catalyst is an organometallic compound containing
A) iron done clear
B) titanium done clear
C) rhodium done clear
D) zirconium done clear
View Answer play_arrowquestion_answer125) Which of the following cannot undergo nucleophilic substitution under ordinary conditions?
A) Chlorobenzene done clear
B) Tert-butylchloride done clear
C) Isopropyl chloride done clear
D) None of the above done clear
View Answer play_arrowquestion_answer126) The compound which contains all the four\[{{1}^{o}},{{2}^{o}},{{3}^{o}}\]and \[{{4}^{o}}\] carbon atoms is
A) \[2,3-\]dimethyl pentane done clear
B) \[3-\]chloro\[-2,3-\]dimethylpentane done clear
C) \[2,3,4-\]trimethylpentane done clear
D) \[3,3-\]dimethylpentane done clear
View Answer play_arrowquestion_answer127) Brass, bronze and german silver have one common metal. This is
A) Zn done clear
B) Fe done clear
C) Al done clear
D) Cu done clear
View Answer play_arrowquestion_answer128) Which of the following is the green coloured powder produced when ammoniunium dichromate is used in fire works?
A) \[Zn\] done clear
B) \[Fe\] done clear
C) \[Al\] done clear
D) \[Cu\] done clear
View Answer play_arrowquestion_answer129) The \[\pi -\]bonded organometallic compound which has ethene as one of its component is
A) Zeise's salt done clear
B) ferrocene done clear
C) dibenzene chromium done clear
D) tetraethyl tin done clear
View Answer play_arrowquestion_answer130) Malachite is an ore of
A) \[Fe\] done clear
B) \[Ag\] done clear
C) \[Cr\] done clear
D) \[Cu\] done clear
View Answer play_arrowquestion_answer131) The most acidic of the following is
A) \[ClC{{H}_{2}}COOH\] done clear
B) \[{{C}_{6}}{{H}_{5}}COOH\] done clear
C) \[C{{D}_{3}}COOH\] done clear
D) \[C{{H}_{3}}C{{H}_{2}}COOH\] done clear
View Answer play_arrowquestion_answer132) Which of the following is an electrophile?
A) \[{{H}_{2}}O\] done clear
B) \[S{{O}_{3}}\] done clear
C) \[~N{{H}_{3}}\] done clear
D) \[~ROR\] done clear
View Answer play_arrowquestion_answer133) An aromatic compound among other things should have a\[\pi -\]electron cloud containing \[(4n+2)\,\pi \]electrons where \[n\]can't be
A) 1/2 done clear
B) 3 done clear
C) 2 done clear
D) 1 done clear
View Answer play_arrowquestion_answer134) Glycerol is an alcohol which can be classified as
A) trihydric done clear
B) monohydric done clear
C) dihydric done clear
D) hexahydric done clear
View Answer play_arrowquestion_answer135) The oxidation number of cobalt in \[K[Co{{(CO)}_{4}}]\]is
A) \[+\,1\] done clear
B) \[+\,3\] done clear
C) \[~-1\] done clear
D) \[-3\] done clear
View Answer play_arrowquestion_answer136) Bromination of alkanes involves
A) carbanions done clear
B) carbocations done clear
C) carbenes done clear
D) free radicals done clear
View Answer play_arrowquestion_answer137) Methylphenyl ether can be obtained by reacting
A) phenolate ions and methyl iodide done clear
B) methoxide ipns and bromobenzene done clear
C) methanol and phenol done clear
D) bromo benzene and methyl bromide done clear
View Answer play_arrowquestion_answer138) Which is not correct?
A) Phenol is more acidic than acetic acid done clear
B) Ethanol is less acidic than phenol done clear
C) Ethanol has higher boiling point than ethane done clear
D) Ethane is a non-linear molecule done clear
View Answer play_arrowquestion_answer139) Ascorbic acid is also known as
A) vitamin A done clear
B) vitamin B done clear
C) vitamin C done clear
D) vitamin D done clear
View Answer play_arrowquestion_answer140) Reaction of phenol with chloroform/sodium hydroxide to give \[o-\]hydroxy benzaldehyde involves the formation of
A) dichloro carbine done clear
B) trichloro carbene done clear
C) chlorine atoms done clear
D) chlorine molecules done clear
View Answer play_arrowquestion_answer141) One of the following that cannot undergo dehydrohalogenation is
A) \[iso-\]propyl bromide done clear
B) ethariol done clear
C) ethyl bromide done clear
D) none of the above done clear
View Answer play_arrowquestion_answer142) Which requires catalyst?
A) \[S+{{O}_{2}}\to S{{O}_{2}}\] done clear
B) \[2S{{O}_{2}}+\,{{O}_{2}}\to 2S{{O}_{3}}\] done clear
C) \[C+{{O}_{2}}\to C{{O}_{2}}\] done clear
D) All of these done clear
View Answer play_arrowquestion_answer143) Acetic acid will be obtained on oxidation of
A) ethanol done clear
B) propanal done clear
C) methanal done clear
D) glyoxal done clear
View Answer play_arrowquestion_answer144) A carboxylic acid is converted into its anhydride using
A) thionyl chloride done clear
B) sulphur chloride done clear
C) sulphuric acid done clear
D) phosphorus pentoxide done clear
View Answer play_arrowquestion_answer145) Which is false?
A) Glucose is a disaccharide done clear
B) Starch is a polysaccharide done clear
C) Glucose and fructose are not anomers done clear
D) Invert sugar consists of glucose and fructose done clear
View Answer play_arrowquestion_answer146) What kind of isomerism is possible for 1-chloro-2-nitroethene?
A) Functional group isomerism done clear
B) Position isomerism done clear
C) E/Z isomerism done clear
D) Optical isomerism done clear
View Answer play_arrowquestion_answer147) KCN reacts readily to give a cyanide with
A) ethyl alcohol done clear
B) ethyl bromide done clear
C) bromobenzene done clear
D) chlorobenzene done clear
View Answer play_arrowquestion_answer148) Peptides are formed from
A) aliphatic amines done clear
B) carbohydrates done clear
C) a-amino acids done clear
D) aromatic amines done clear
View Answer play_arrowquestion_answer149) Calcium carbide on reaction with water yields
A) methane done clear
B) ethane done clear
C) ethene done clear
D) ethyne done clear
View Answer play_arrowquestion_answer150) The correct set of the four quantum numbers of a \[4d\] electron is
A) \[4,2,1-\frac{1}{2}\] done clear
B) \[4,2,1,0\] done clear
C) \[4,3,2,+\frac{1}{2}\] done clear
D) \[4,3,-2,+\frac{1}{2}\] done clear
View Answer play_arrowquestion_answer151) In a class of 30 pupils. 12 take needls work, 16 take physics and 18 take history. If all the 30 students take at least one subject and no one takes all three, then the number of pupils taking 2 subjects is
A) \[16\] done clear
B) \[6\] done clear
C) \[8\] done clear
D) \[20\] done clear
View Answer play_arrowquestion_answer152) If \[f(2x+3)=\sin x+{{2}^{x}},\] then \[f(4m-2n+3)\] is equal to
A) \[\sin \,(m-2n)+{{2}^{2m-n}}\] done clear
B) \[\sin \,(2m-n)+{{2}^{(m-n)2}}\] done clear
C) \[\sin \,(m-2n)+{{2}^{(m+n)2}}\] done clear
D) \[\sin (2m-n)+{{2}^{2m-n}}\] done clear
View Answer play_arrowquestion_answer153) If \[{{z}_{1}}=1+2i\] and \[{{z}_{2}}=3+5i,\] then \[\operatorname{Re}[{{\bar{z}}_{2}}{{z}_{1}}/{{z}_{2}}]\]is equal to
A) \[-31/17\] done clear
B) \[17/22\] done clear
C) \[-17/31\] done clear
D) \[22/17\] done clear
View Answer play_arrowquestion_answer154) If \[|z+8|+|z-8|=16,\] where z is a complex number, then the point z will lie on
A) circle done clear
B) an ellipse done clear
C) a straight line done clear
D) None of these done clear
View Answer play_arrowquestion_answer155) If twice the 11 th term of an AP is equal to 7times its 21st term, then its 25th term is equal to
A) \[24\] done clear
B) \[120\] done clear
C) \[0\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer156) If one of the roots of equation \[{{x}^{2}}+ax+3=0\] is 3 and one of the roots of the equation \[{{x}^{2}}+ax+b=0\]is three times the other root, then the value of b is equal to
A) \[3\] done clear
B) \[4\] done clear
C) \[2\] done clear
D) \[1\] done clear
View Answer play_arrowquestion_answer157) If S is the sum of an infinite GP, the first term a, then the common ratio r is given by
A) \[\frac{a-S}{S}\] done clear
B) \[\frac{S-a}{S}\] done clear
C) \[\frac{a}{1-S}\] done clear
D) \[\frac{S-a}{a}\] done clear
View Answer play_arrowquestion_answer158) The coefficient of \[{{x}^{4}}\]in the expansion of \[{{\left( \frac{x}{2}-\frac{3}{{{x}^{2}}} \right)}^{10}}\]is.
A) \[405/226\] done clear
B) \[504/289\] done clear
C) \[450/263\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer159) The figure formed by joining the points \[(4,0)\] s\[(3,5)\]and \[(-1,-1)\] in pairs is
A) a right angled triangle done clear
B) an acute angled triangle done clear
C) an obtuse angled triangle done clear
D) None of the above done clear
View Answer play_arrowquestion_answer160) The ortho centre of the triangle with vertices \[(-2,-6),\,\,\,(-2,4)\] and \[(1,3)\] is
A) \[(3,\,1)\] done clear
B) \[(1,\,1/3)\] done clear
C) \[(1,3)\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer161) The in centre of a triangle with vertices \[(7,1),\] \[(-1,5)\] and \[(3+2\sqrt{3},3+4\sqrt{3})\]is
A) \[\left( 3+\frac{2}{\sqrt{3}},\,3+\frac{4}{\sqrt{3}} \right)\] done clear
B) \[\left( 1+\frac{2}{3\sqrt{3}},1+\frac{4}{3\sqrt{3}} \right)\] done clear
C) \[(7,1)\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer162) Let a be the distance between line \[-x+y=2\] and \[x-y=2\]and \[\beta \] be the distance between the lines \[4x-3y=5\] and \[6y-8x=1,\] then
A) \[20\sqrt{2}\beta =11\alpha \] done clear
B) \[20\sqrt{2}\alpha =11\beta \] done clear
C) \[11\sqrt{2}\beta =20\alpha \] done clear
D) None of these done clear
View Answer play_arrowquestion_answer163) The equations of the tangents to circle \[5{{x}^{2}}+5{{y}^{2}}=1,\] parallel to line \[3x+4y=1\] are
A) \[3x+4y=\pm 2\sqrt{5}\] done clear
B) \[6x+8y=\pm \sqrt{5}\] done clear
C) \[3x+4y=\pm \sqrt{5}\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer164) From the point \[(-1,-6)\] two tangents are drawn to the parabola\[{{y}^{2}}=4x\]. Then, the angle between the two tangents is
A) \[{{30}^{o}}\] done clear
B) \[{{45}^{o}}\] done clear
C) \[{{60}^{o}}\] done clear
D) \[{{90}^{o}}\] done clear
View Answer play_arrowquestion_answer165) If the foci of an ellipse are \[(\pm \sqrt{5},0)\] and its eccentricity is \[\sqrt{5}/3,\] then the equation of the ellipse is
A) \[9{{x}^{2}}+4{{y}^{2}}=36\] done clear
B) \[4{{x}^{2}}+9{{y}^{2}}=36\] done clear
C) \[36{{x}^{2}}+9{{y}^{2}}=4\] done clear
D) \[9{{x}^{2}}+36{{y}^{2}}=4\] done clear
View Answer play_arrowquestion_answer166) If \[y=(1+\tan \,A)\,(1-\tan B),\]where \[A-B=\frac{\pi }{4},\]then \[{{(y+1)}^{y+1}}\] is equal to
A) \[9\] done clear
B) \[4\] done clear
C) \[27\] done clear
D) \[81\] done clear
View Answer play_arrowquestion_answer167) If \[x\,\,\sin \theta -y\,\cos \,\theta =0\]and \[x\,{{\sin }^{3}}\theta +y\,{{\cos }^{3}}\theta =\sin \theta \,\,\cos \theta ,\] then \[{{x}^{2}}+{{y}^{2}}\] is equal to
A) \[0\] done clear
B) \[2\] done clear
C) \[4\] done clear
D) \[1\] done clear
View Answer play_arrowquestion_answer168) If \[\tan x=\frac{b}{a},\] then the value of \[a\,\cos \,2x+b\,\sin \,2x\]is
A) \[a\] done clear
B) \[b\] done clear
C) \[a+b\] done clear
D) \[{{a}^{2}}+{{b}^{2}}\] done clear
View Answer play_arrowquestion_answer169) If the expansion in powers of x of the function \[\frac{1}{(1-ax)\,(1-bx)}\]is \[{{a}_{0}}-{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+{{a}_{3}}{{x}^{3}}+.....,\] then \[{{a}_{n}}\] is
A) \[\frac{{{b}^{n+1}}-{{a}^{n+1}}}{b-a}\] done clear
B) \[\frac{{{a}^{n}}-{{b}^{n}}}{b-a}\] done clear
C) \[\frac{{{a}^{n+1}}-{{b}^{n+1}}}{b-a}\] done clear
D) \[\frac{{{b}^{n}}-{{a}^{n}}}{b-a}\] done clear
View Answer play_arrowquestion_answer170) If n is any integer, then the general solution of the equation \[\cos \theta -\sin \theta =\frac{1}{\sqrt{2}}\] is
A) \[\theta =2n\pi -\frac{\pi }{12}\] or\[\theta =2n\pi +\frac{7\pi }{12}\] done clear
B) \[\theta =n\pi +\frac{\pi }{12}\] done clear
C) \[\theta =2n\pi +\frac{\pi }{12}\] or \[\theta =2n\pi -\frac{7\pi }{12}\] done clear
D) \[\theta =2n\pi +\frac{\pi }{12}\] or \[\theta =2n\pi -\frac{7\pi }{12}\] done clear
View Answer play_arrowquestion_answer171) . The value of \[{{\cos }^{-1}}\,(\cos \,12)-{{\sin }^{-1}}\,(\sin 14)\] is
A) \[-2\] done clear
B) \[8\pi -26\] done clear
C) \[4\pi +2\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer172) If a, b and c are the sides of a triangle such that \[{{a}^{4}}+{{b}^{4}}+{{c}^{4}}=2{{c}^{2}}({{a}^{2}}+{{b}^{2}}),\] then the angles opposite to the side C is
A) \[{{45}^{o}}\] or \[{{90}^{o}}\] done clear
B) \[{{30}^{o}}\] or \[{{135}^{o}}\] done clear
C) \[{{45}^{o}}\] or \[{{135}^{o}}\] done clear
D) \[{{60}^{o}}\] or \[{{120}^{o}}\] done clear
View Answer play_arrowquestion_answer173) The value of the determinant \[\left| \begin{matrix} 0 & {{b}^{3}}-{{a}^{3}} & {{c}^{3}}-{{a}^{3}} \\ {{a}^{3}}-{{b}^{3}} & 0 & {{c}^{3}}-{{b}^{3}} \\ {{a}^{3}}-{{c}^{3}} & {{b}^{3}}-{{c}^{3}} & 0 \\ \end{matrix} \right|\]is equal to
A) \[{{a}^{3}}-{{b}^{3}}-{{c}^{3}}\] done clear
B) \[{{a}^{3}}-{{b}^{3}}-{{c}^{3}}\] done clear
C) \[0\] done clear
D) \[-{{a}^{3}}+{{b}^{3}}+{{c}^{3}}\] done clear
View Answer play_arrowquestion_answer174) The integer represented by the determinant \[\left| \begin{matrix} 215 & 342 & 511 \\ 6 & 7 & 8 \\ 36 & 49 & 54 \\ \end{matrix} \right|\] is exactly divisible by
A) \[146\] done clear
B) \[21\] done clear
C) \[20\] done clear
D) \[335\] done clear
View Answer play_arrowquestion_answer175) A root of the equation \[\left| \begin{matrix} 3-x & -6 & 3 \\ -6 & 3-x & 3 \\ 3 & 3 & -6-x \\ \end{matrix} \right|=0\] is given by
A) \[x=0\] done clear
B) \[x=6\] done clear
C) \[x=3\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer176) The determinant \[\left| \begin{matrix} 4+{{x}^{2}} & -6 & -2 \\ -6 & 9+{{x}^{2}} & 3 \\ -2 & 3 & 1+{{x}^{2}} \\ \end{matrix} \right|\] is not divisible by
A) \[x\] done clear
B) \[{{x}^{3}}\] done clear
C) \[14+{{x}^{2}}\] done clear
D) \[{{x}^{5}}\] done clear
View Answer play_arrowquestion_answer177) If X is a square matrix of order \[3\times 3,\lambda \] is a scalar, then adj \[(\lambda x)\]is equal to
A) \[\lambda \,\,adj\,\,(X)\] done clear
B) \[{{\lambda }^{3}}\,\,adj\,\,(X)\] done clear
C) \[{{\lambda }^{2}}\,\,adj\,\,(X)\] done clear
D) \[{{\lambda }^{4}}\,\,adj\,\,(X)\] done clear
View Answer play_arrowquestion_answer178) If \[f(\theta )=\left[ \begin{matrix} \cos \,\theta & -\sin \theta & 0 \\ \sin \,\theta & \cos \,\theta & 0 \\ 0 & 0 & 1 \\ \end{matrix} \right],\]then \[{{\{f(\theta )\}}^{-1}}\]is equal to
A) \[f(-\theta )\] done clear
B) \[f(-\theta )\] done clear
C) \[f(2\theta )\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer179) The minors of \[-4\] and \[9\] and the cofactors of \[-4\]and 9 in matrix \[\left[ \begin{matrix} -1 & -2 & 3 \\ -4 & -5 & -6 \\ -7 & 8 & 9 \\ \end{matrix} \right]\] are respectively
A) \[42,3,-42,3\] done clear
B) \[-42,-3,42\] done clear
C) \[42,3,42,3,-3\] done clear
D) \[42,3,-42,3\] done clear
View Answer play_arrowquestion_answer180) If \[X=\left[ \begin{matrix} -x & -y \\ z & t \\ \end{matrix} \right],\] then transpose of adj (X) is
A) \[\left[ \begin{matrix} t & z \\ -y & -x \\ \end{matrix} \right]\] done clear
B) \[\left[ \begin{matrix} t & y \\ -z & -x \\ \end{matrix} \right]\] done clear
C) \[\left[ \begin{matrix} t & -z \\ y & -x \\ \end{matrix} \right]\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer181) Let PQRS be a parallelogram whose diagonals PR and QS intersect at O?. If O is origin, then \[\overrightarrow{OP}+\overrightarrow{OQ}+\overrightarrow{OR}+\overrightarrow{OS}\]is equal to
A) \[\overrightarrow{OO'}\] done clear
B) \[2\overrightarrow{O}O'\] done clear
C) \[3\overrightarrow{O}Q'\] done clear
D) \[4\overrightarrow{O}O'\] done clear
View Answer play_arrowquestion_answer182) If the vectors \[2\hat{i}+\hat{j}-\hat{k},-\hat{i}+2\hat{j}+\lambda \hat{k}\] and \[-5\,\hat{i}+2\hat{j}-\hat{k}\]are coplanar, then the value of \[\lambda \] is equal to
A) \[-13\] done clear
B) \[13/9\] done clear
C) \[-13/9\] done clear
D) \[-9/13\] done clear
View Answer play_arrowquestion_answer183) If the scalar projection of the vectors \[x\,\hat{i}+\hat{j}+\hat{k}\] on the vector \[2\hat{i}-\hat{j}+5\hat{k}\] is \[\frac{1}{\sqrt{30}},\] then the value of x is
A) \[-3/2\] done clear
B) \[6\] done clear
C) \[-6\] done clear
D) \[3\] done clear
View Answer play_arrowquestion_answer184) If \[\vec{x}+\vec{y}+\vec{z}=\vec{0},\,|\vec{x}|=|\vec{y}|=|\vec{z}|=2\] and \[\theta \] is angle between \[\vec{y}\] and \[\vec{z},\] then the value of \[\text{cose}{{\text{c}}^{2}}\theta +{{\cot }^{2}}\theta \] is equal to
A) \[4/3\] done clear
B) \[5/3\] done clear
C) \[1/3\] done clear
D) \[1\] done clear
View Answer play_arrowquestion_answer185) If the position vectors of two points P and Q are respectively \[9\,\hat{i}-\hat{j}+5\hat{k}\]and \[\hat{i}+3\hat{j}+5\hat{k}\] and the line segment PQ intersects the YOZ plane at a point R, then \[PR:RQ\]is equal to
A) \[9:1\] done clear
B) \[1:9\] done clear
C) \[-1:9\] done clear
D) \[-9:1\] done clear
View Answer play_arrowquestion_answer186) If \[\vec{u},\vec{v}\] and \[\vec{w}\] are three mutually perpendicular unit vectors, then \[|\vec{u}+\vec{v}+\vec{w}|\]is equal to
A) \[\sqrt{3}\] done clear
B) \[1\] done clear
C) \[3\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer187) The angle between the vectors \[\vec{a}+\vec{b}\] and \[\vec{a}-\vec{b}\]when \[\vec{a}=(1,1,4)\] and \[\vec{b}=(1,-1,4)\] is
A) \[{{90}^{o}}\] done clear
B) \[{{45}^{o}}\] done clear
C) \[{{30}^{o}}\] done clear
D) \[{{15}^{o}}\] done clear
View Answer play_arrowquestion_answer188) The line of intersection of the planes \[\vec{r}.(\hat{i}-3\hat{j}+\hat{k})=1\] and \[\vec{r}.(2\hat{i}+5\hat{j}-3\hat{k})=2\] is parallel to the vector
A) \[-4\hat{i}+5\hat{j}+11\hat{k}\] done clear
B) \[4\hat{i}+5\hat{j}+11\hat{k}\] done clear
C) \[-4\hat{i}-5\hat{j}+11\hat{k}\] done clear
D) \[-4\hat{i}+5\hat{j}-11\hat{k}\] done clear
View Answer play_arrowquestion_answer189) A plane meet the coordinate axes at P, Q and R such that the position vector of the centroid of \[\Delta PQR\] is \[2\hat{i}-5\hat{j}+8\hat{k}\]. Then, the equation of the plane is
A) \[\vec{r}.(20\,\hat{i}-8\hat{j}+5\hat{k})=120\] done clear
B) \[\vec{r}.(20\,\hat{i}-8\hat{j}+5\hat{k})=1\] done clear
C) \[\vec{r}.(20\,\hat{i}-8\hat{j}+5\hat{k})=2\] done clear
D) \[\vec{r}.(20\,\hat{i}-8\hat{j}+5\hat{k})=20\] done clear
View Answer play_arrowquestion_answer190) The distance of the point \[(2,3,4)\] from the line \[1-x=\frac{y}{2}=\frac{1}{3}(1+z)\] is
A) \[\frac{1}{7}\sqrt{35}\] done clear
B) \[\frac{4}{7}\sqrt{35}\] done clear
C) \[\frac{2}{7}\sqrt{35}\] done clear
D) \[\frac{3}{7}\sqrt{35}\] done clear
View Answer play_arrowquestion_answer191) The equation of the plane passing through the points \[(0,1,2)\] and \[(-1,\,0,3)\] and perpendicular to the plane \[2x+3y+z=5\] is
A) \[3x-4y+18z+32=0\] done clear
B) \[3x+4y-18x+32=0\] done clear
C) \[4x+3y-17z+31=0\] done clear
D) \[4x-3y+z+1=0\] done clear
View Answer play_arrowquestion_answer192) A line joining the points \[(1,2,0)\] and \[(4,13,5)\] is perpendicular to a plane. Then, the coefficients of x, y and z in the equation of the plane are; respectively
A) \[5,15,5\] done clear
B) \[3,11,5\] done clear
C) \[3,-11,5\] done clear
D) \[-5,-15,5\] done clear
View Answer play_arrowquestion_answer193) The image of the point \[P(1,3,4)\] in the plane \[2x-y+z+3=0\] is
A) \[(3,\,5,-2)\] done clear
B) \[(-3,\,5,2)\] done clear
C) \[(3,-5,2)\] done clear
D) \[(-1,\,4,2)\] done clear
View Answer play_arrowquestion_answer194) The distance between the line \[\vec{r}=2\hat{i}-2\hat{j}+3\hat{k}+\lambda (\hat{i}-\hat{j}+4\hat{k})\] and the plane \[\vec{r}.(\hat{i}+5\hat{j}+\hat{k})=5\] is
A) \[\frac{10}{3}\] done clear
B) \[\frac{3}{10}\] done clear
C) \[\frac{10}{3\sqrt{3}}\] done clear
D) \[\frac{10}{9}\] done clear
View Answer play_arrowquestion_answer195) The distance between the planes \[2x+y+2z=8\]and \[4x+2y+4z+5=0\]
A) \[3/2\] done clear
B) \[7/2\] done clear
C) \[2/5\] done clear
D) \[0\] done clear
View Answer play_arrowquestion_answer196) If \[\alpha ,\beta \] and \[\gamma \] are the roots of equation \[{{x}^{3}}-3{{x}^{2}}+x+5=0,\] then \[y=\Sigma {{\alpha }^{2}}+\alpha \beta \gamma \]satisfies the equation.
A) \[{{y}^{3}}+y+2=0\] done clear
B) \[{{y}^{3}}-{{y}^{2}}-y-2=0\] done clear
C) \[{{y}^{3}}+3{{y}^{2}}-y-3=0\] done clear
D) \[{{y}^{2}}+4{{y}^{2}}+5y+20=0\] done clear
View Answer play_arrowquestion_answer197) If l(x) is the least integer not less than x and g(,x) is the greatest integer not greater than x, then \[\underset{x\to e+\pi }{\mathop{\lim }}\,\{l(x)+g(x)\}\] is equal to
A) \[9\] done clear
B) \[13\] done clear
C) \[1\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer198) The value of \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{27}^{x}}-{{9}^{x}}-{{3}^{x}}+1}{\sqrt{5}-\sqrt{4}+\cos x}\] is
A) \[\sqrt{5}\,{{(\log 3)}^{2}}\] done clear
B) \[8\sqrt{5}\,{{(\log 3)}^{2}}\] done clear
C) \[16\sqrt{5}\,(\log 3)\] done clear
D) \[10\sqrt{5}\,{{(\log 3)}^{2}}\] done clear
View Answer play_arrowquestion_answer199) The value of \[\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{x}^{n}}}{{{x}^{n}}+1},\]where \[x<-1\] is
A) \[1/2\] done clear
B) \[-1/2\] done clear
C) \[1\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer200) The value of \[\underset{x\to \pi /2}{\mathop{\lim }}\,\,\frac{{{2}^{\cot \,x}}-{{2}^{\cos \,x}}}{\cot \,x-\,\cos \,x}\]is
A) \[\log \,2\] done clear
B) \[1\] done clear
C) \[2\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer201) The point of discontinuity of tan x is
A) \[x=n\pi \] done clear
B) \[x=n\pi /6\] done clear
C) \[x=(2n+1)\pi /2\] done clear
D) \[x=n\pi /3\] done clear
View Answer play_arrowquestion_answer202) Let \[f(x)=\left\{ \begin{matrix} (1/2)\,\{g(x)+(x)\}\,\,sin\,(x),\,x\ge 1 \\ \sin \,x/x,\,x<1 \\ \end{matrix} \right.\] where \[g(x)=\left\{ \begin{matrix} 1, & if & x>0 \\ -1, & if & x<0 \\ 0, & if & x=0 \\ \end{matrix} \right.\] Then, \[\underset{x\to 1}{\mathop{\lim }}\,\,\,f(x)\] is equal to
A) \[0\] done clear
B) \[2\] done clear
C) \[sin\text{ }1\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer203) The function \[f(x)=\frac{2{{x}^{2}}+7}{{{x}^{3}}+3{{x}^{2}}-x-3}\]is discontinuous for
A) \[x=1\]only done clear
B) \[x=1\] and \[x=-1\]only done clear
C) \[x=1,\,x=-1,\,x=-3\]only done clear
D) \[x=1,\,x=-1,\,x=-3\] and other values of x done clear
View Answer play_arrowquestion_answer204) If \[f(x)=\left\{ \begin{matrix} x, & for & <x<1 \\ 2-x, & for & 1\le x<2 \\ x-(1/2){{x}^{2}}, & for & x=2 \\ \end{matrix} \right.\] Then, \[f'(1)\]is equal to
A) \[-1\] done clear
B) \[1\] done clear
C) \[0\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer205) If \[y={{\cos }^{-1}}\cos (|x|-f(x)),\] where \[f(x)=\left\{ \begin{matrix} 1, & if & x>0 \\ -1, & if & x<0 \\ 0, & if & x=0 \\ \end{matrix} \right.\] Then, \[{{(dy/dx)}_{x=\frac{5\pi }{4}}}\]is equal to
A) \[-1\] done clear
B) \[1\] done clear
C) \[0\] done clear
D) can't be determined done clear
View Answer play_arrowquestion_answer206) If \[{{x}^{m}}{{y}^{n}}={{(x+y)}^{m+n}},\] then \[{{(dy/dx)}_{x=1,\,y=2}}\] is equal to
A) \[1/2\] done clear
B) \[2\] done clear
C) \[2m/n\] done clear
D) \[~m/2n\] done clear
View Answer play_arrowquestion_answer207) The function \[f(x)=2{{x}^{3}}-3{{x}^{2}}+90x+174\] is increasing in the interval
A) \[1/2<x<1\] done clear
B) \[1/2<x<2\] done clear
C) \[3<x<59/4\] done clear
D) \[-\infty <x<\infty \] done clear
View Answer play_arrowquestion_answer208) The equation of the tangent to the curve \[x=2\,{{\cos }^{3}}\theta \] and \[y=3\,{{\sin }^{3}}\theta \] at the point \[\theta =\pi /4\] is
A) \[2x+3y=3\sqrt{2}\] done clear
B) \[2x-3y=3\sqrt{2}\] done clear
C) \[3x+2y=3\sqrt{2}\] done clear
D) \[3x-2y=3\sqrt{2}\] done clear
View Answer play_arrowquestion_answer209) The minimum value of \[4{{e}^{2x}}+9{{e}^{-2x}}\] is
A) \[11\] done clear
B) \[12\] done clear
C) \[10\] done clear
D) \[14\] done clear
View Answer play_arrowquestion_answer210) The point of parabola \[2y={{x}^{2}},\] which is nearest to the point \[(0,\,\,3)\] is
A) \[(\pm 4,\,8)\] done clear
B) \[(\pm 1,1/2)\] done clear
C) \[(\pm 2,2)\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer211) In the mean value theorem \[f(b)-f(a)=(b-a)\,f'(c),\] if \[a=4,\text{ }b=9\]and \[f(x)=\sqrt{x},\] then the value of c is
A) \[8.00\] done clear
B) \[5.25\] done clear
C) \[4.00\] done clear
D) \[6.25\] done clear
View Answer play_arrowquestion_answer212) If x is any arbitrary constant, then \[\int{{{2}^{{{2}^{{{2}^{x}}}}}}}.\,{{2}^{{{2}^{x}}}}.\,{{2}^{x}}\,\,dx\]is equal to
A) \[\frac{\int{{{2}^{{{2}^{x}}}}}\,dx}{{{(In\,\,2)}^{3}}}+c\] done clear
B) \[\frac{\int{{{2}^{{{2}^{{{2}^{x}}}}}}}\,dx}{{{(In\,\,2)}^{3}}}+c\] done clear
C) \[\int{{{2}^{{{2}^{{{2}^{x}}}}}}}\,\,{{(In\,\,2)}^{3}}+c\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer213) The derivative of function \[f(x)\] is \[{{\tan }^{4}}x\]. If \[f(x)=0,\] then \[\underset{x\to 0}{\mathop{\lim }}\,\frac{f(x)}{x}\]is equal to
A) \[1\] done clear
B) \[0\] done clear
C) \[-1\] done clear
D) none of these done clear
View Answer play_arrowquestion_answer214) The value of \[\int_{1}^{{{e}^{2}}}{\frac{dx}{x{{(1+\log \,x)}^{2}}}}\] is
A) \[2/3\] done clear
B) \[1/3\] done clear
C) \[3/2\] done clear
D) In 2 done clear
View Answer play_arrowquestion_answer215) If \[2f(x)-3f(1/x)=x,\] then \[\int_{1}^{2}{f(x)\,\,dx}\] is equal to
A) \[(3/5)\] In 2 done clear
B) \[(-3/5)\] (\[1+\]In 2) done clear
C) \[(-3/5)\] In 2 done clear
D) None of these done clear
View Answer play_arrowquestion_answer216) If A is the area of the region bounded by the curve \[y=\sqrt{3x+4},\] x-axis and the lines \[x=-1\]and \[x=4\]and B is that area bounded by curve \[{{y}^{2}}=3x+4,\]x axis and the lines \[x=-1\]and \[x=4,\] then \[A:B\]is equal to
A) \[1:1\] done clear
B) \[2:1\] done clear
C) \[1:2\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer217) If c is an arbitrary constant, then the general solution of the differential equation \[ydx-xdy=xy\,\,dx\]is given by
A) \[y=cx{{e}^{-x}}\] done clear
B) \[y=cy{{e}^{-x}}\] done clear
C) \[y+{{e}^{-x}}=cx\] done clear
D) \[y{{e}^{x}}=cx\] done clear
View Answer play_arrowquestion_answer218) The solution of \[dy=\cos \,x(2-y\,\text{cosec x)}\,\text{dx}\]where \[y=\sqrt{2},\] when \[x=\pi /4\] is
A) \[y\sin \,x+\frac{1}{2}\,\text{cosec x}\] done clear
B) \[y=\tan \,(x/2)+\cot (x/2)\] done clear
C) \[y=(1/\sqrt{2})\,\sec \,(x/2)+\sqrt{2}\,\cos \,\,(x/2)\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer219) The probability that at least one of the event A and B occurs is \[0.6\]. If A and B occur simultaneously with probability \[0.2,\] then \[P(\bar{A})+P(\bar{B})\]is equal to
A) \[0.4\] done clear
B) \[0.8\] done clear
C) \[1.2\] done clear
D) \[1.4\] done clear
View Answer play_arrowquestion_answer220) A die is thrown. If it shows a six, we draw a ball from a bag consisting, if 2 black balls and 6 white balls. If it does not show a six, then we toss a coin. Then, the sample spate of this experiment consists of
A) 13 points done clear
B) 18 points done clear
C) 10 points done clear
D) None of the above done clear
View Answer play_arrowquestion_answer221) The probability of getting a total of at least 6 in the simultaneously throw of three dice is
A) \[6/108\] done clear
B) \[5/27\] done clear
C) \[1/24\] done clear
D) \[103/108\] done clear
View Answer play_arrowquestion_answer222) A sample of a 4 items is drawn at a random without replacement from a lot of 10 items containing 3 defectives. If X denotes the number of defective items in the sample, then \[P(0<X<3)\] is equal to
A) \[3/10\] done clear
B) \[4/5\] done clear
C) \[1/2\] done clear
D) \[1/6\] done clear
View Answer play_arrowquestion_answer223) Two cards are drawn successfully with replacement from a well shuffled deck of 52 cards, then the mean of the number of aces is
A) \[1/13\] done clear
B) \[3/13\] done clear
C) \[2/13\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer224) An um contains 4 white and 3 red balls. Three balls are drawn with replacement from this um. Then, the standard deviation of the number of red balls drawn is
A) \[6/7\] done clear
B) \[36/49\] done clear
C) \[5/7\] done clear
D) \[25/49\] done clear
View Answer play_arrowquestion_answer225) A and B are two independent events such that \[P(A)=1/2\] and \[P(A)=1/2\] then P (neither A nor B) is equal to
A) \[2/3\] done clear
B) \[1/6\] done clear
C) \[5/6\] done clear
D) \[1/3\] done clear
View Answer play_arrow
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