question_answer1) In ruby laser, the stimulated emission is due to transition from
A) metastable state to any lower state done clear
B) any higher state to lower state done clear
C) metastable state to ground state done clear
D) any higher state to ground state done clear
View Answer play_arrowquestion_answer2) A direct current I flows along the length of an infinitely long straight thin walled pipe, then the magnetic field is
A) uniform throughout the pipe but not zero done clear
B) zero only along the axis of the pipe done clear
C) zero at any point inside the pipe done clear
D) maximum at the centre and minimum at the edge done clear
View Answer play_arrowquestion_answer3) A convex lens made of glass has focal length 0.15 m in air. If the refractive index of glass is \[\frac{3}{2}\] and that of water is \[\frac{4}{3}\], the focal length of lens when immersed in water is
A) 0.45 m done clear
B) 0.15 m done clear
C) 0.30 m done clear
D) 0.6 m done clear
View Answer play_arrowquestion_answer4) Two sources are said to be coherent if they produce waves
A) having a constant phase difference done clear
B) of equal wavelength done clear
C) of equal speed done clear
D) having same shape of wave front done clear
View Answer play_arrowquestion_answer5) Three resistors \[1\,\Omega ,\,2\,\Omega \] and \[3\,\Omega \] are connected to form a triangle. Across \[3\,\Omega \] resistor a \[3\,\Omega \] battery is connected. The current through \[3\,\Omega \] resistor is
A) 0.75 A done clear
B) 1 A done clear
C) 2 A done clear
D) 1.5 A done clear
View Answer play_arrowquestion_answer6) In a common emitter amplifier the input signal is applied across
A) anywhere done clear
B) emitter-collector done clear
C) collector-base done clear
D) base-emitter done clear
View Answer play_arrowquestion_answer7) In a radioactive disintegration, the ratio of initial number of atoms to the number of atoms present at an instant of time equal to its mean life is
A) \[\frac{1}{{{e}^{2}}}\] done clear
B) \[\frac{1}{e}\] done clear
C) e done clear
D) \[{{e}^{2}}\] done clear
View Answer play_arrowquestion_answer8) A ray of light is incident on a surface of glass slab at an angle \[{{45}^{o}}\]. If the lateral shift produced per unit thickness is \[\frac{1}{\sqrt{3}}m\], the angle of refraction produced is
A) \[{{\tan }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\] done clear
B) \[{{\tan }^{-1}}\left( 1-\sqrt{\frac{2}{3}} \right)\] done clear
C) \[{{\sin }^{-1}}\left( 1-\sqrt{\frac{2}{3}} \right)\] done clear
D) \[{{\tan }^{-1}}\left( \frac{2}{\sqrt{3}-1} \right)\] done clear
View Answer play_arrowquestion_answer9) Ferromagnetic materials used in a transformer must have
A) low permeability and high hysterisis loss done clear
B) high permeability and low hysterisis loss done clear
C) high permeability and high hysterisis loss done clear
D) low permeability and low hysterisis loss done clear
View Answer play_arrowquestion_answer10) According to Newton's corpuscular theory, the speed of light is
A) same in all the media done clear
B) lesser in rarer medium done clear
C) lesser in denser medium done clear
D) independent of the medium done clear
View Answer play_arrowquestion_answer11) For the constructive interference the path difference between the two interfering waves must be equal to
A) \[\left( 2n+1 \right)\lambda \] done clear
B) \[2n\pi \] done clear
C) \[n\lambda \] done clear
D) \[\left( 2n+1 \right)\frac{\pi }{2}\] done clear
View Answer play_arrowquestion_answer12) The accurate measurement of emf can be obtained using
A) multimeter done clear
B) voltmeter done clear
C) voltameter done clear
D) potentiometer done clear
View Answer play_arrowquestion_answer13) The kinetic energy of an electron gets tripled, then the de-Broglie wavelength associated with it changes by a factor
A) \[\frac{1}{3}\] done clear
B) \[\sqrt{3}\] done clear
C) \[\frac{1}{\sqrt{3}}\] done clear
D) 3 done clear
View Answer play_arrowquestion_answer14) Which of the following is not a thermodynamic coordinate?
A) Gas constant (R) done clear
B) Pressure (p) done clear
C) Volume (V) done clear
D) Temperature (T) done clear
View Answer play_arrowquestion_answer15) Two solid pieces, one of steel and the other of aluminium when immersed completely in water have equal weights. When the solid pieces are weighed in air
A) the weight of aluminium is half the weight of steel done clear
B) steel piece will weigh more done clear
C) they have the same weight done clear
D) aluminium piece will weigh more done clear
View Answer play_arrowquestion_answer16) The amount of energy released when one microgram of matter is annihilated is
A) 25 kWh done clear
B) \[9\times {{10}^{10}}kWh\] done clear
C) \[3\times {{10}^{10}}kWh\] done clear
D) \[0.5\times {{10}^{5}}kWh\] done clear
View Answer play_arrowquestion_answer17) The number of significant figures in the numbers \[4.8000\times {{10}^{4}}\] and 48000.50 are respectively
A) 5 and 6 done clear
B) 5 and 7 done clear
C) 2 and 7 done clear
D) 2 and 6 done clear
View Answer play_arrowquestion_answer18) \[\beta \]-decay means emission of electron from
A) innermost electron orbit done clear
B) a stable nucleus done clear
C) outermost electron orbit done clear
D) radioactive nucleus done clear
View Answer play_arrowquestion_answer19) An electric heater rated 220 V and 550 W is connected to AC mains. The current drawn by it is
A) 0.8 A done clear
B) 2.5 A done clear
C) 0.4 A done clear
D) 1.25 A done clear
View Answer play_arrowquestion_answer20) A body of mass m moving along a straight line covers half the distance with a speed of \[2\text{ }m{{s}^{-1}}\]. The remaining half of the distance is covered in two equal time intervals with a speed of \[3\text{ }m{{s}^{-1}}\] and \[5\text{ }m{{s}^{-1}}\] respectively. The average speed of the particle for the entire journey is
A) \[\frac{3}{8}m{{s}^{-1}}\] done clear
B) \[\frac{3}{8}m{{s}^{-1}}\] done clear
C) \[\frac{4}{3}m{{s}^{-1}}\] done clear
D) \[\frac{16}{3}m{{s}^{-1}}\] done clear
View Answer play_arrowquestion_answer21) The moment of inertia of a circular ring of radius r and mass M about diameter is
A) \[\frac{2}{5}M{{r}^{2}}\] done clear
B) \[\frac{M{{r}^{2}}}{4}\] done clear
C) \[\frac{M{{r}^{2}}}{2}\] done clear
D) \[\frac{M{{r}^{2}}}{12}\] done clear
View Answer play_arrowquestion_answer22) A body of mass 0.05 kg is observed to fall with an acceleration of \[9.5\text{ }m{{s}^{-2}}\]. The opposing force of air on the body is \[(g=9.8\text{ }m{{s}^{-2}})\]
A) 0.015 N done clear
B) 0.15 N done clear
C) 0.030 N done clear
D) zero done clear
View Answer play_arrowquestion_answer23) The colloidal solution in which both the dispersed phase and dispersion medium are liquids are called
A) emulsions done clear
B) gels done clear
C) foams done clear
D) liquid crystals done clear
View Answer play_arrowquestion_answer24) In fog, photographs of the objects taken with infrared radiations are more clear than those obtained during visible light because
A) \[I-R\] radiation has lesser wavelength than visible radiation done clear
B) scattering of \[I-R\] light is more than visible light done clear
C) the intensity of \[I-R\] light from the object is less done clear
D) scattering of \[I-R\] light is less than visible light done clear
View Answer play_arrowquestion_answer25) Three concurrent co-planar forces 1 N, 2 N and 3 N acting along different directions on a body
A) can keep the body in equilibrium if 2 N and 3 N act at right angle done clear
B) can keep the body in equilibrium if 1 N and 2 N act at right angle done clear
C) cannot keep the body in equilibrium done clear
D) can keep the body in equilibrium in 1 N and 3 N act at an acute angle done clear
View Answer play_arrowquestion_answer26) Sound waves transfer
A) only energy not momentum done clear
B) energy done clear
C) momentum done clear
D) Both (a) and (b) done clear
View Answer play_arrowquestion_answer27) Two rectangular \[0.15\text{ }m{{s}^{-1}}\] blocks A and B of masses 2 kg and 3 kg respectively are connected by a spring of spring constant \[10.8\text{ }N{{m}^{-1}}\] and are placed on a fricrionless horizontal surface. The block A was given an initial velocity of \[0.15\text{ }m{{s}^{-1}}\] in the direction shown in the figure. The maximum compression of the spring during motion is
A) 0.01 m done clear
B) 0.02 m done clear
C) 0.05 m done clear
D) 0.03 m done clear
View Answer play_arrowquestion_answer28) G P Thomson experimentally confirmed the existence of matter waves by the phenomena
A) diffraction done clear
B) refraction done clear
C) polarisation done clear
D) scattering done clear
View Answer play_arrowquestion_answer29) The resistance of a wire at 300 K is found to be \[0.3\,\Omega \]. If the temperature coefficient of resistance of wire is \[1.5\times {{10}^{-3}}{{K}^{-1}}\], the temperature at which the resistance becomes \[0.6\,\,\Omega \] is
A) 720 K done clear
B) 345 K done clear
C) 993 K done clear
D) 690 K done clear
View Answer play_arrowquestion_answer30) The work done by a force acting on a body is as shown in the graph. The total work done in covering an initial distance of 20 m is
A) 225 J done clear
B) 200 J done clear
C) 400 J done clear
D) 175 J done clear
View Answer play_arrowquestion_answer31) Two luminous point sources separated by a certain distance are at 10 km from an observer. If the aperture of his eye is \[2.5\times {{10}^{-3}}m\] and the wavelength of light used is 500 nm, the distance of separation between the point sources just seen to be resolved is
A) 12.2 m done clear
B) 24.2 m done clear
C) 2.44 m done clear
D) 1.22 m done clear
View Answer play_arrowquestion_answer32) A door 1.6 m wide requires a force of 1 N to be applied at the free end to open or close it. The force that is required at a point 0.4 m distance from the hinges for opening or closing the door is
A) 1.2 N done clear
B) 3.6 N done clear
C) 2.4 N done clear
D) 4 N done clear
View Answer play_arrowquestion_answer33) \[0.1\text{ }{{m}^{3}}\] of water at \[{{80}^{o}}C\] is mixed with \[0.3\text{ }{{m}^{3}}\]of water at \[{{60}^{o}}C\]. The final temperature of the mixture is
A) \[{{65}^{o}}C\] done clear
B) \[{{70}^{o}}C\] done clear
C) \[{{60}^{o}}C\] done clear
D) \[{{75}^{o}}C\] done clear
View Answer play_arrowquestion_answer34) The spectral series of the hydrogen atom that lies in the visible region of the electromagnetic spectrum
A) Paschen done clear
B) Balmer done clear
C) Lyman done clear
D) Brackett done clear
View Answer play_arrowquestion_answer35) A graph of pressure versus volume for an ideal gas for different processes is as shown. In the graph curve OC represents
A) isochoric process done clear
B) isothermal process done clear
C) isobaric process done clear
D) adiabatic process done clear
View Answer play_arrowquestion_answer36) Which of the following statement does not hold good for thermal radiation?
A) The wavelength changes when it travels from one medium to another done clear
B) The frequency changes when it travels from one medium to another done clear
C) The speed changes when it travels from one medium to another done clear
D) They travel in straight line in a given medium done clear
View Answer play_arrowquestion_answer37) A planet revolves around the sun in an elliptical orbit. The linear speed of the planet will be maximum at
A) D done clear
B) B done clear
C) A done clear
D) C done clear
View Answer play_arrowquestion_answer38) Horizontal tube of non-uniform cross-section has radii of 0.1 m and 0.05 m respectively at M and N. For a streamline flow of liquid the rate of liquid flow is
A) changing continuously with time done clear
B) greater at M than at N done clear
C) greater at N than at M done clear
D) same at M and N done clear
View Answer play_arrowquestion_answer39) A resistor and a capacitor are connected in series with an AC source. If the potential drop across the capacitor is 5 V and that across resistor is 12 V, then applied voltage is
A) 13 V done clear
B) 17 V done clear
C) 5 V done clear
D) 12 V done clear
View Answer play_arrowquestion_answer40) The amount of heat energy radiated by a metal at temperature T is E. When the temperature is increased to 3T, energy radiated is
A) 81 E done clear
B) 9 E done clear
C) 3 E done clear
D) 27 E done clear
View Answer play_arrowquestion_answer41) The angle of minimum deviation for an incident light ray on an equilateral prism is equal to its refracting angle. The refractive index of its material is
A) \[\frac{1}{\sqrt{2}}\] done clear
B) \[\sqrt{3}\] done clear
C) \[\frac{\sqrt{3}}{2}\] done clear
D) \[\frac{3}{2}\] done clear
View Answer play_arrowquestion_answer42) In the following combinations of logic gates, the outputs of A, B and C are respectively
(a) (b) (c) |
A) 0, 1, 1 done clear
B) 0, 1, 0 done clear
C) 1, 1, 0 done clear
D) 1, 0, 1 done clear
View Answer play_arrowquestion_answer43) A stationary point source of sound emits sound uniformly in all directions in a non-absorbing medium. Two points P and Q are at a distance of 4 m and 9 m respectively from the source. The ratio of amplitudes of the waves at P and Q is
A) \[\frac{3}{2}\] done clear
B) \[\frac{4}{9}\] done clear
C) \[\frac{2}{3}\] done clear
D) \[\frac{9}{4}\] done clear
View Answer play_arrowquestion_answer44) A galvanometer of resistance \[240\text{ }\Omega \] allows only 4% of the main current after connecting a shunt resistance. The value of the shunt resistance is
A) \[10\text{ }\Omega \] done clear
B) \[20\text{ }\Omega \] done clear
C) \[8\text{ }\Omega \] done clear
D) \[5\text{ }\Omega \] done clear
View Answer play_arrowquestion_answer45) The phenomena in which proton flips is
A) nuclear magnetic resonance done clear
B) lasers done clear
C) radioactivity done clear
D) nuclear fusion done clear
View Answer play_arrowquestion_answer46) \[y=3\sin \,\pi \left( \frac{t}{2}-\frac{x}{4} \right)\] represents an equation of a progressive wave, where t is in second and \[x\] is in metre. The distance travelled by the wave in 5 s is
A) 8 m done clear
B) 10 m done clear
C) 5 m done clear
D) 32 m done clear
View Answer play_arrowquestion_answer47) According to the quark model, it is possible to build all the hadrons using
A) 2 quarks and 3 antiquarks done clear
B) 3 quarks and 2 antiquarks done clear
C) 3 quarks and 3 antiquarks done clear
D) 2 quarks and 2 antiquarks done clear
View Answer play_arrowquestion_answer48) An \[\alpha \]-particle of mass \[6.4\times {{10}^{-27}}kg\] and charge \[3.2\times {{10}^{-19}}C\] is situated in a uniform electric field of \[1.6\times 10s\text{ }V{{m}^{-1}}\]. The velocity of the particle at the end of \[2\times {{10}^{-2}}m\] path when it starts from rest is
A) \[2~\sqrt{3}\times {{10}^{5}}m{{s}^{-1}}\] done clear
B) \[8\times {{10}^{5}}m{{s}^{-1}}\] done clear
C) \[16\times {{10}^{5}}m{{s}^{-1}}\] done clear
D) \[4\times {{10}^{5}}m{{s}^{-1}}\] done clear
View Answer play_arrowquestion_answer49) A cylindrical tube open at both the ends has a fundamental frequency of 390 Hz in air. If \[\frac{1}{4}th\] of the tube is immersed vertically in water the fundamental frequency of air column is
A) 260 Hz done clear
B) 130 Hz done clear
C) 390 Hz done clear
D) 520 Hz done clear
View Answer play_arrowquestion_answer50) The surface temperature of the stars is determined using
A) Planck's law done clear
B) Wien's displacement law done clear
C) Rayleigh-Jeans law done clear
D) Kirchhoff?s law done clear
View Answer play_arrowquestion_answer51) The charge deposited on 4\[\mu \]F capacitor in the circuit is
A) \[6\times {{10}^{-6}}C\] done clear
B) \[12\times {{10}^{-6}}C\] done clear
C) \[24\times {{10}^{-6}}C\] done clear
D) \[36\times {{10}^{-6}}C\] done clear
View Answer play_arrowquestion_answer52) A parallel beam of light is incident on a converging lens parallel to its principal axis. As one moves away from the lens on the other side of the principal axis, the intensity of light
A) first decreases and then increases done clear
B) continuously increases done clear
C) continuously decreases done clear
D) first increases and then decreases done clear
View Answer play_arrowquestion_answer53) Continuous emission spectrum is produced by
A) incandescent electric lamp done clear
B) mercury vapour lamp done clear
C) sodium vapour lamp done clear
D) polyatomic substances done clear
View Answer play_arrowquestion_answer54) A coil of n number of turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively. When a current of strength \[I\] is passed through the coil, the magnetic field at its centre is
A) \[\frac{{{\mu }_{0}}nI}{\left( b-a \right)}{{\log }_{e}}\frac{a}{b}\] done clear
B) \[\frac{{{\mu }_{0}}nI}{2\left( b-a \right)}\] done clear
C) \[\frac{2{{\mu }_{0}}nI}{b}\] done clear
D) \[\frac{{{\mu }_{0}}nI}{2\left( b-a \right)}{{\log }_{e}}\frac{b}{a}\] done clear
View Answer play_arrowquestion_answer55) A ray of light is incident on a plane mirror at an angle of \[{{60}^{o}}\]. The angle of deviation produced by the mirror is
A) \[{{120}^{o}}\] done clear
B) \[{{30}^{o}}\] done clear
C) \[{{60}^{o}}\] done clear
D) \[{{90}^{o}}\] done clear
View Answer play_arrowquestion_answer56) The electric potential at any point \[x,y,z\] in metres is given by \[V=3{{x}^{2}}\]. The electric field at a point (2, 0, 1) is
A) \[12\text{ }V{{m}^{-1}}\] done clear
B) \[-6\text{ }V{{m}^{-1}}\] done clear
C) \[6\text{ }V{{m}^{-1}}\] done clear
D) \[-12V{{m}^{-1}}\] done clear
View Answer play_arrowquestion_answer57) Young's double slit experiment gives interference fringes of width 0.3 mm. A thin glass plate made of material of refractive index 1.5 is kept in the path of light from one of the slits, then the fringe width becomes
A) zero done clear
B) 0.3 mm done clear
C) 0.45 mm done clear
D) 0.15 mm done clear
View Answer play_arrowquestion_answer58) Near a circular loop of conducting wire as shown in the figure an electron moves along a straight line. The direction of the induced current if any in the loop is
A) variable done clear
B) clockwise done clear
C) anticlockwise done clear
D) zero done clear
View Answer play_arrowquestion_answer59) Hydrogen atom from excited state comes to the ground stage by emitting a photon of wavelength\[\lambda \]. If R is the Rydberg constant, the principal quantum number n of the excited state is
A) \[\sqrt{\frac{\lambda R}{\lambda R-1}}\] done clear
B) \[\sqrt{\frac{\lambda }{\lambda R-1}}\] done clear
C) \[\sqrt{\frac{\lambda {{R}^{2}}}{\lambda R-1}}\] done clear
D) \[\sqrt{\frac{\lambda R}{\lambda -1}}\] done clear
View Answer play_arrowquestion_answer60) The magnetic dipole moment of a current loop is independent of
A) magnetic field in which it is lying done clear
B) number of turns done clear
C) area of the loop done clear
D) current in the loop done clear
View Answer play_arrowquestion_answer61) The correct statement with regard to \[H_{2}^{+}\] and \[H_{2}^{-}\] is
A) both \[H_{2}^{+}\] and \[H_{2}^{-}\] are equally stable done clear
B) both \[H_{2}^{+}\] and \[H_{2}^{-}\] do not exist done clear
C) Ha is more stable than \[H_{2}^{+}\] done clear
D) \[H_{2}^{+}\] is more stable than \[H_{2}^{-}\] done clear
View Answer play_arrowquestion_answer62) Arrange the following in the increasing order of their bond order \[{{O}_{2}},O_{2}^{+},O_{2}^{-}\] and \[O_{2}^{2-}\]
A) \[O_{2}^{2-},O_{2}^{-},{{O}_{2}},O_{2}^{+}\] done clear
B) \[O_{2}^{2-},O_{2}^{-},O_{2}^{+},{{O}_{2}}\] done clear
C) \[O_{2}^{+},{{O}_{2}},O_{2}^{-},O_{2}^{2-}\] done clear
D) \[{{O}_{2}},O_{2}^{+},O_{2}^{-},O_{2}^{2-}\] done clear
View Answer play_arrowquestion_answer63) 2 g of a radioactive sample having half-life of 15 days was synthesized on 1st Jan 2009. The amount of the sample left behind on 1st March, 2009 (including both the days) is
A) 0 g done clear
B) 0.125 g done clear
C) 1 g done clear
D) 0.5 g done clear
View Answer play_arrowquestion_answer64) For a chemical reaction \[A\to B\], the rate of the reaction is \[2\times {{10}^{-3}}\,mol\,\,d{{m}^{-3}}{{s}^{-1}}\] when the initial concentration is \[0.05\,mol\,d{{m}^{-3}}\]. The rate of the same reaction is \[1.6\times {{10}^{-2}}mol\,d{{m}^{-3}}{{s}^{-1}}\] when the initial concentration is \[0.1\text{ }mol\text{ }d{{m}^{-3}}\]. The order of the reaction is
A) 2 done clear
B) 0 done clear
C) 3 done clear
D) 1 done clear
View Answer play_arrowquestion_answer65) For the decomposition of a compound AB at 600 K, the following data were obtained
[AB] mol \[d{{m}^{-3}}\] | Rate of decomposition of AB in mol \[d{{m}^{-3}}{{s}^{-1}}\] |
0.20 | \[2.75\times {{10}^{-8}}\] |
0.40 | \[11.0\times {{10}^{-8}}\] |
0.60 | \[24.75\times {{10}^{-8}}\] |
A) 1.5 done clear
B) 0 done clear
C) 1 done clear
D) 2 done clear
View Answer play_arrowquestion_answer66) The rate equation for a reaction \[A\to B\] is\[r=k{{[A]}^{0}}\]. If the initial concentration of the reactant is a mol \[d{{m}^{-3}}\], the half-life period of the reaction is
A) \[\frac{a}{2k}\] done clear
B) \[\frac{k}{a}\] done clear
C) \[\frac{a}{k}\] done clear
D) \[\frac{2a}{k}\] done clear
View Answer play_arrowquestion_answer67) 30 cc of \[\frac{M}{3}HCl,\,20\,cc\] of \[\frac{M}{2}HN{{O}_{3}}\] and 40 cc of \[\frac{M}{4}NaOH\] solutions are mixed and the volume was made up to \[1\text{ }d{{m}^{3}}\]. The pH of the resulting solution is
A) 8 done clear
B) 2 done clear
C) 1 done clear
D) 3 done clear
View Answer play_arrowquestion_answer68) An aqueous solution containing 6.5 g of \[NaCl\]of 90% purity was subjected to electrolysis. After the complete electrolysis, the solution was evaporated to get solid \[NaOH\]. The volume of 1 M acetic acid required to neutralise \[NaOH\] obtained above is
A) \[1000\text{ }c{{m}^{3}}\] done clear
B) \[2000\text{ }c{{m}^{3}}\] done clear
C) \[100\text{ }c{{m}^{3}}\] done clear
D) \[200\text{ }c{{m}^{3}}\] done clear
View Answer play_arrowquestion_answer69) The standard electrode potential for the half cell reactions are \[Z{{n}^{2+}}+2{{e}^{-}}\xrightarrow{{}}Zn;\,{{E}^{o}}=-0.76\,V\] \[F{{e}^{2+}}+2{{e}^{-}}\xrightarrow{{}}Fe;\,{{E}^{o}}=-0.44\,V\] The emf of the cell reaction, \[F{{e}^{2+}}+Zn\xrightarrow{{}}Z{{n}^{2+}}+Fe\] is
A) -0.32V done clear
B) -1.20V done clear
C) + 1.20V done clear
D) 4-0.32 V done clear
View Answer play_arrowquestion_answer70) \[{{10}^{-6}}M\,NaOH\] is diluted 100 times. The pH of the diluted base is
A) between 7 and 8 done clear
B) between 5 and 6 done clear
C) between 6 and 7 done clear
D) between 10 and 11 done clear
View Answer play_arrowquestion_answer71) In the electrolysis of acidulated water, it is desired to obtain 1.12 cc of hydrogen per second under STP condition. The current to be passed is
A) 1.93 A done clear
B) 9.65 A done clear
C) 19.3 A done clear
D) 0.965 A done clear
View Answer play_arrowquestion_answer72) The one which decreases with dilution is
A) molar conductance done clear
B) conductance done clear
C) specific conductance done clear
D) equivalent conductance done clear
View Answer play_arrowquestion_answer73) Vapour pressure of pure ?A? is 70 mm of Hg at\[{{25}^{o}}C\]. It forms an ideal solution with ?B? in which mole fraction of A is 0.8. If the vapour pressure of the solution is 84 mm of Hg at\[{{25}^{o}}C\], the vapour pressure of pure ?B? at \[{{25}^{o}}C\] is
A) 28 mm done clear
B) 56 mm done clear
C) 70mm done clear
D) 140mm done clear
View Answer play_arrowquestion_answer74) A 6% solution of urea is isotonic with
A) 1 M solution of glucose done clear
B) 0.05 M solution of glucose done clear
C) 6% solution of glucose done clear
D) 25% solution of glucose done clear
View Answer play_arrowquestion_answer75) In countries nearer to polar region, the roads are sprinkled with \[CaC{{l}_{2}}\]. This is
A) to minimise the wear and tear of the roads done clear
B) to minimise the snow fall done clear
C) to minimise pollution done clear
D) to minimise the accumulation of dust on the road done clear
View Answer play_arrowquestion_answer76) For the reaction \[{{H}_{2}}O(l){{H}_{2}}O(g)\] at 373 K and 1 atm pressure
A) \[\Delta H=0\] done clear
B) \[\Delta E=0\] done clear
C) \[\Delta H=T\Delta S\] done clear
D) \[\Delta H=\Delta E\] done clear
View Answer play_arrowquestion_answer77) A compound of 'A' and 'B' crystallises in a cubic lattice in which 'A' atoms occupy the lattice points at the corners of the cube. The 'B' atoms occupy the centre of each face of the cube. The probable empirical formula of the compound is
A) \[A{{B}_{2}}\] done clear
B) \[{{A}_{3}}B\] done clear
C) \[AB\] done clear
D) \[A{{B}_{3}}\] done clear
View Answer play_arrowquestion_answer78) In electrophilic aromatic substitution reaction, the nitro group is meta directing because it
A) decreases electron density at ortho and para positions done clear
B) decreases electron density at meta position done clear
C) increases electron density at meta position done clear
D) increases electron density at ortho and para positions done clear
View Answer play_arrowquestion_answer79) \[C{{H}_{3}}COOH\xrightarrow{LiAl{{H}_{4}}}X\xrightarrow[{{300}^{o}}C]{Cu}Y\frac{Dilute}{naOH}\]In the above reaction Z is
A) butanol done clear
B) aldol done clear
C) ketol done clear
D) acetal done clear
View Answer play_arrowquestion_answer80) The best method for the conversion of an alcohol into an alkyl chloride is by treating the alcohol with
A) \[PC{{l}_{3}}\] done clear
B) \[PC{{l}_{5}}\] done clear
C) \[SOC{{l}_{2}}\] in presence of pyridine done clear
D) dry \[HCl\] in the presence of anhydrous \[ZnC{{l}_{2}}\] done clear
View Answer play_arrowquestion_answer81) The electrophile involved in the sulphonation of benzene is
A) \[SO_{3}^{+}\] done clear
B) \[SO_{3}^{2-}\] done clear
C) \[H_{3}^{+}O\] done clear
D) \[S{{O}_{3}}\] done clear
View Answer play_arrowquestion_answer82) The carbon-carbon bond length in benzene is
A) in between \[{{C}_{2}}{{H}_{6}}\] and \[{{C}_{2}}{{H}_{4}}\] done clear
B) same as in \[{{C}_{2}}{{H}_{4}}\] done clear
C) in between \[{{C}_{2}}{{H}_{6}}\] and \[{{C}_{2}}{{H}_{2}}\] done clear
D) in between \[{{C}_{2}}{{H}_{4}}\] and \[{{C}_{2}}{{H}_{2}}\] done clear
View Answer play_arrowquestion_answer83) The compound which is not formed during the dry distillation of a mixture of calcium formate and calcium acetate is
A) methanal done clear
B) propanal done clear
C) propanone done clear
D) ethanol done clear
View Answer play_arrowquestion_answer84) An organic compound X is oxidised by using acidified \[{{K}_{2}}C{{r}_{2}}{{O}_{7}}\]. The product obtained reacts with phenyl hydrazine but does not answer silver mirror test. The possible structure of X is
A) \[C{{H}_{3}}C{{H}_{2}}OH\] done clear
B) \[C{{H}_{3}}\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{-C}}\,-C{{H}_{3}}\] done clear
C) \[{{(C{{H}_{3}})}_{2}}CHOH\] done clear
D) \[C{{H}_{3}}CHO\] done clear
View Answer play_arrowquestion_answer85) The reaction involved in the oil of winter green test is salicylic acid \[\xrightarrow[Conc.\,\,{{H}_{2}}S{{O}_{4}}]{\Delta }\] product. The product is treated with \[N{{a}_{2}}C{{O}_{3}}\]solution. The missing reagent in the above reaction is
A) phenol done clear
B) \[NaOH\] done clear
C) ethanol done clear
D) methanol done clear
View Answer play_arrowquestion_answer86) The compound which forms acetaldehyde when heated with dilute \[NaOH\], is
A) 1, 1-dichloroethane done clear
B) 1, 1, 1-trichloroethane done clear
C) 1-chloroethane done clear
D) 1, 2-dichloroethane done clear
View Answer play_arrowquestion_answer87) Arrange the following in the increasing order of their basic strengths\[C{{H}_{3}}N{{H}_{2}},\,{{(C{{H}_{3}})}_{2}}NH\], \[{{(C{{H}_{3}})}_{3}}N,\,N{{H}_{3}}\]
A) \[N{{H}_{3}}<{{(C{{H}_{3}})}_{3}}N<{{(C{{H}_{3}})}_{2}}NH<C{{H}_{3}}N{{H}_{2}}\] done clear
B) \[N{{H}_{3}}<{{(C{{H}_{3}})}_{3}}N<C{{H}_{3}}N{{H}_{2}}<{{(C{{H}_{3}})}_{2}}NH\] done clear
C) \[{{(C{{H}_{3}})}_{3}}N<N{{H}_{3}}<C{{H}_{3}}N{{H}_{2}}<{{(C{{H}_{3}})}_{2}}NH\] done clear
D) \[C{{H}_{3}}N{{H}_{2}}<{{(C{{H}_{3}})}_{2}}NH<{{(C{{H}_{3}})}_{3}}N<N{{H}_{3}}\] done clear
View Answer play_arrowquestion_answer88) The one which has least iodine value is
A) sunflower oil done clear
B) ginger oil done clear
C) ghee done clear
D) groundnut oil done clear
View Answer play_arrowquestion_answer89) A diabetic person carries a packet of glucose with him always, because
A) glucose reduces the blood sugar level slowly done clear
B) glucose increases the blood sugar level slowly done clear
C) glucose reduces the blood sugar level done clear
D) glucose increases the blood sugar level almost instantaneously done clear
View Answer play_arrowquestion_answer90) There are 20 naturally occurring amino acids. The maximum number of tripeptides that can be obtained is
A) 8000 done clear
B) 6470 done clear
C) 7465 done clear
D) 5360 done clear
View Answer play_arrowquestion_answer91) Cooking is fast in a pressure cooker, because
A) food particles are effectively smashed done clear
B) water boils at higher temperature inside the pressure cooker done clear
C) food is cooked at constant volume done clear
D) loss of heat due to radiation is minimum done clear
View Answer play_arrowquestion_answer92) The ore that is concentrated by froth floatation process is
A) zincite done clear
B) cinnabar done clear
C) bauxite done clear
D) malachite done clear
View Answer play_arrowquestion_answer93) The correct set of four quantum numbers for outermost electron of potassium \[(Z=19)\] is
A) \[4,1,0,\frac{1}{2}\] done clear
B) \[3,1,0,\frac{1}{2}\] done clear
C) \[4,0,0,\frac{1}{2}\] done clear
D) \[3,0,0,\frac{1}{2}\] done clear
View Answer play_arrowquestion_answer94) A body of mass \[x\] kg is moving with a velocity of \[100\,\,m{{s}^{-1}}\]. Its de-Broglie wavelength is\[6.62\times {{10}^{-35}}m\]. Hence, \[x\] is \[(h=6.62\times {{10}^{-34}}Js)\]
A) 0.1 kg done clear
B) 0.25 kg done clear
C) 0.15 kg done clear
D) 0.2 kg done clear
View Answer play_arrowquestion_answer95) The correct order of ionisation energy of C, N, O, F is
A) \[F<O<N<C\] done clear
B) \[F<N<C<O\] done clear
C) \[C<N<O<F\] done clear
D) \[C<O<N<F\] done clear
View Answer play_arrowquestion_answer96) The oxide of an element whose electronic configuration is \[1{{s}^{2}},2{{s}^{2}},2{{p}^{6}},3{{s}^{1}}\] is
A) neutral done clear
B) amphoteric done clear
C) basic done clear
D) acidic done clear
View Answer play_arrowquestion_answer97) The characteristic not related to alkali metal is
A) high ionisation energy done clear
B) their ions are isoelectronic with noble gases done clear
C) low melting point done clear
D) low electronegativity done clear
View Answer play_arrowquestion_answer98) Among the following, the compound that contains ionic, covalent and coordinate linkage is
A) \[N{{H}_{3}}\] done clear
B) \[N{{H}_{4}}Cl\] done clear
C) \[NaCl\] done clear
D) \[CaO\] done clear
View Answer play_arrowquestion_answer99) A covalent molecule \[A{{B}_{3}}\] has pyramidal structure. The number of lone pair and bond pair of electrons in the molecule are respectively
A) 2 and 2 done clear
B) 0 and 4 done clear
C) 3 and 1 done clear
D) 1 and 3 done clear
View Answer play_arrowquestion_answer100) Excess of carbon dioxide is passed through 50 mL of 0.5 M calcium hydroxide solution. After the completion of the reaction, the solution was evaporated to dryness. The solid calcium carbonate was completely neutralised with N hydrochloric acid. The volume of hydrochloric acid required is (Atomic mass of calcium = 40)
A) \[300\,\,c{{m}^{3}}\] done clear
B) \[200\,\,c{{m}^{3}}\] done clear
C) \[500\,\,c{{m}^{3}}\] done clear
D) \[400\,\,c{{m}^{3}}\] done clear
View Answer play_arrowquestion_answer101) A bivalent metal has an equivalent mass of 32. The molecular mass of the metal nitrate is
A) 182 done clear
B) 168 done clear
C) 192 done clear
D) 188 done clear
View Answer play_arrowquestion_answer102) The rms velocity of molecules of a gas of density \[4\,kg\,{{m}^{-3}}\] and pressure \[1.2\times {{10}^{5}}N{{m}^{-2}}\] is
A) \[300\,\,m{{s}^{-1}}\] done clear
B) \[900\,\,m{{s}^{-1}}\] done clear
C) \[120\,\,m{{s}^{-1}}\] done clear
D) \[600\,\,m{{s}^{-1}}\] done clear
View Answer play_arrowquestion_answer103) 0.5 mole of each of \[{{H}_{2}},S{{O}_{2}}\] and \[C{{H}_{4}}\] are kept in a container. A hole was made in the container. After 3 h, the order of partial pressures in the container will be
A) \[pS{{O}_{2}}>p{{H}_{2}}>pC{{H}_{4}}\] done clear
B) \[pS{{O}_{2}}>pC{{H}_{4}}>p{{H}_{2}}\] done clear
C) \[p{{H}_{2}}>pS{{O}_{2}}>pC{{H}_{4}}\] done clear
D) \[p{{H}_{2}}>pC{{H}_{4}}>pS{{O}_{2}}\] done clear
View Answer play_arrowquestion_answer104) The enthalpy of formation of \[N{{H}_{3}}\] is\[-46\,\,kJ\,\,mo{{l}^{-1}}\]. The enthalpy change for the reaction \[2N{{H}_{3}}(g)\xrightarrow{{}}{{N}_{2}}(g)+3{{H}_{2}}(g)\] is
A) +184 kJ done clear
B) +23 kJ done clear
C) +92 kJ done clear
D) +46 kJ done clear
View Answer play_arrowquestion_answer105) 5 moles of \[S{{O}_{2}}\] and 5 moles of \[{{O}_{2}}\] are allowed to react. At equilibrium, it was found that 60% of \[S{{O}_{2}}\] is used up. If the partial pressure of the equilibrium mixture is one atmosphere, the partial pressure of \[{{O}_{2}}\] is
A) 0.82 atm done clear
B) 0.52 atm done clear
C) 0.21 atm done clear
D) 0.41 atm done clear
View Answer play_arrowquestion_answer106) \[2HI(g){{H}_{2}}(g)+{{I}_{2}}(g)\] The equilibrium constant of the above reaction is 6.4 at 300 K. If 0.25 mole each of \[{{H}_{2}}\] and \[{{I}_{2}}\] are added to the system, the equilibrium constant will be
A) 6.4 done clear
B) 0.8 done clear
C) 3.2 done clear
D) 1.6 done clear
View Answer play_arrowquestion_answer107) Rate of physical adsorption increases with
A) decrease in surface area done clear
B) decrease in temperature done clear
C) decrease in pressure done clear
D) increase in temperature done clear
View Answer play_arrowquestion_answer108) IUPAC name of \[{{(C{{H}_{3}})}_{2}}CCl\] is
A) n-butyl chloride done clear
B) 3-chloro butane done clear
C) 2-chloro 2-methyl propane done clear
D) t-butyl chloride done clear
View Answer play_arrowquestion_answer109) Lucas test is associated with
A) aldehydes done clear
B) phenols done clear
C) carboxylic acids done clear
D) alcohols done clear
View Answer play_arrowquestion_answer110) An organic compound on heating with CuO produces \[C{{O}_{2}}\] but no water. The organic compound may be
A) carbon tetrachloride done clear
B) chloroform done clear
C) methane done clear
D) ethyl iodide done clear
View Answer play_arrowquestion_answer111) The condensation polymer among the following is
A) rubber done clear
B) protein done clear
C) PVC done clear
D) polyethene done clear
View Answer play_arrowquestion_answer112) The order of stability of metal oxides is
A) \[A{{l}_{2}}{{O}_{3}}<MgO<F{{e}_{2}}{{O}_{3}}<C{{r}_{2}}{{O}_{3}}\] done clear
B) \[C{{r}_{2}}{{O}_{3}}<MgO<A{{l}_{2}}{{O}_{3}}<F{{e}_{2}}{{O}_{3}}\] done clear
C) \[F{{e}_{2}}{{O}_{3}}<C{{r}_{2}}{{O}_{3}}<A{{l}_{2}}{{O}_{3}}<MgO\] done clear
D) \[F{{e}_{2}}{{O}_{3}}<A{{l}_{2}}{{O}_{3}}<C{{r}_{2}}{{O}_{3}}<MgO\] done clear
View Answer play_arrowquestion_answer113) The temperature of the slag zone in the metallurgy of iron using blast furnace is
A) \[1200-{{1500}^{o}}C\] done clear
B) \[1500-{{1600}^{o}}C\] done clear
C) \[400-{{700}^{o}}C\] done clear
D) \[800-{{1000}^{o}}C\] done clear
View Answer play_arrowquestion_answer114) The function of \[Fe{{(OH)}_{3}}\] in the contact process is
A) to remove arsenic impurity done clear
B) to detect colloidal impurity done clear
C) to remove moisture done clear
D) to remove dust particles done clear
View Answer play_arrowquestion_answer115) In which of the following, \[N{{H}_{3}}\] is not used?
A) Tollen's reagent done clear
B) Nessler's reagent done clear
C) Group reagent for the analysis of IV group basic radicals done clear
D) Group reagent for the analysis of III group basic radicals done clear
View Answer play_arrowquestion_answer116) Argon is used
A) in filling airships done clear
B) to obtain low temperature done clear
C) in high temperature welding done clear
D) in radiotherapy for treatment of cancer done clear
View Answer play_arrowquestion_answer117) The incorrect statement in respect of chromyl chloride test is
A) formation of red vapours done clear
B) formation of lead chromate done clear
C) formation of chromyl chloride done clear
D) -liberation of chlorine done clear
View Answer play_arrowquestion_answer118) The magnetic moment of a transition metal ion is \[\sqrt{15}\,BM\]. Therefore, the number of unpaired electrons present in it, is
A) 3 done clear
B) 4 done clear
C) 1 done clear
D) 2 done clear
View Answer play_arrowquestion_answer119) The IUPAC name of \[{{[Co{{(N{{H}_{3}})}_{5}}ONO]}^{2+}}\] ion is
A) penta ammine nitrito cobalt (IV) ion done clear
B) penta ammine nitrito cobalt (III) ion done clear
C) penta ammine nitro cobalt (III) ion done clear
D) penta ammine nitro cobalt (IV) ion done clear
View Answer play_arrowquestion_answer120) The oxidation state of Fe in the brown ring complex: \[[Fe{{({{H}_{2}}O)}_{5}}NO]S{{O}_{4}}\] is
A) +3 done clear
B) 0 done clear
C) +2 done clear
D) +1 done clear
View Answer play_arrowquestion_answer121) The smallest positive integral value of n such that \[{{\left[ \frac{1+\sin \frac{\pi }{8}+i\,\cos \frac{\pi }{8}}{1+\sin \frac{\pi }{8}-i\,\cos \frac{\pi }{8}} \right]}^{n}}\] is purely imaginary is equal to
A) \[4\] done clear
B) \[3\] done clear
C) \[2\] done clear
D) \[8\] done clear
View Answer play_arrowquestion_answer122) Which one of the following is possible?
A) \[\sin \theta =\frac{{{a}^{2}}+{{b}^{2}}}{{{a}^{2}}-{{b}^{2}}},(a\ne b)\] done clear
B) \[\sin \theta =\frac{4}{5}\] done clear
C) \[\sin \theta =45\] done clear
D) \[\cos \theta =\frac{7}{3}\] done clear
View Answer play_arrowquestion_answer123) If one side of a triangle is double the other and the angles opposite to these sides differ by \[{{60}^{o}},\]then the triangle is
A) obtuse angled done clear
B) acute angled done clear
C) isosceles done clear
D) right angled done clear
View Answer play_arrowquestion_answer124) \[3{{(\sin x-\cos x)}^{4}}+6{{(\sin \,x+\operatorname{cosx})}^{2}}\]\[+({{\sin }^{6}}x+{{\cos }^{6}}x)\] is equal to
A) \[12\] done clear
B) \[13\] done clear
C) \[14\] done clear
D) \[11\] done clear
View Answer play_arrowquestion_answer125) A cow is tied to a post by a rope. The cow moves along the circular path always keeping the rope tight. If it describes \[44\text{ }m,\] when it has traced out \[{{72}^{o}}\]at the centre, the length of the rope is
A) \[22\,\,m\] done clear
B) \[56\,\,m\] done clear
C) \[45\,\,m\] done clear
D) \[35\,\,m\] done clear
View Answer play_arrowquestion_answer126) If \[\left| \begin{matrix} 1+{{\sin }^{2}}\theta & {{\cos }^{2}}\theta & 4\,\sin \,2\theta \\ {{\sin }^{2}}\theta & 1+{{\cos }^{2}}\theta & 4\sin 2\theta \\ {{\sin }^{2}}\theta & {{\cos }^{2}}\theta & 4\sin 2\theta -1 \\ \end{matrix} \right|=0\] and \[0<\theta <\frac{\pi }{2},\] then \[\cos \,\,4\theta \] is equal to
A) \[\frac{\sqrt{3}}{2}\] done clear
B) \[0\] done clear
C) \[\frac{-1}{2}\] done clear
D) \[\frac{1}{2}\] done clear
View Answer play_arrowquestion_answer127) The locus of the mid points of the chords of the circle \[{{x}^{2}}+{{y}^{2}}=4\]which subtend a right angle at the origin is
A) \[{{x}^{2}}+{{y}^{2}}=1\] done clear
B) \[{{x}^{2}}+{{y}^{2}}=2\] done clear
C) \[x+y=1\] done clear
D) \[x+y=2\] done clear
View Answer play_arrowquestion_answer128) The length of the chord joining the points\[(4\,\cos \theta ,4sin\theta )\] and \[(4\,\cos (\theta +{{60}^{o}}),\] \[4sin(\theta +{{60}^{o}}))\]of the circle \[{{x}^{2}}+{{y}^{2}}=16\]is
A) \[4\] done clear
B) \[8\] done clear
C) \[16\] done clear
D) \[2\] done clear
View Answer play_arrowquestion_answer129) The number of common tangents to the circles \[{{x}^{2}}+{{y}^{2}}-y=0\] and \[{{x}^{2}}+{{y}^{2}}+y=0\] and \[{{x}^{2}}+{{y}^{2}}+y=0\]is
A) \[2\] done clear
B) \[3\] done clear
C) \[0\] done clear
D) \[1\] done clear
View Answer play_arrowquestion_answer130) The coordinates of the centre of the smallest circle passing through the origin and having \[y=x+1\] as a diameter are
A) \[\left( \frac{1}{2},\frac{-1}{2} \right)\] done clear
B) \[\left( \frac{1}{2},\frac{1}{3} \right)\] done clear
C) \[(-1,0)\] done clear
D) \[\left( -\frac{1}{2},\frac{1}{2} \right)\] done clear
View Answer play_arrowquestion_answer131) The length of the diameter of the circle which cuts three circles \[{{x}^{2}}+{{y}^{2}}-x-y-14=0\] \[{{x}^{2}}+{{y}^{2}}+3x-5y-10=0\] \[{{x}^{2}}+{{y}^{2}}-2x+3y-27=0\] orthogonally, is
A) \[8\] done clear
B) \[6\] done clear
C) \[4\] done clear
D) \[2\] done clear
View Answer play_arrowquestion_answer132) For the parabola \[{{y}^{2}}=4x,\]the point P whose focal distance is 17, is
A) \[(8,8)\] or \[(8,-8)\] done clear
B) \[(4,8)\] or \[(4,-8)\] done clear
C) \[(2,8)\] or \[(2,-8)\] done clear
D) \[(16,8)\] or \[(16,-8)\] done clear
View Answer play_arrowquestion_answer133) The angle between the tangents drawn to the parabola \[{{y}^{2}}=12x\]from the point \[(-3,2)\]is
A) \[{{90}^{o}}\] done clear
B) \[{{60}^{o}}\] done clear
C) \[{{30}^{o}}\] done clear
D) \[{{45}^{o}}\] done clear
View Answer play_arrowquestion_answer134) The number of values of c such that the line \[y=4x+c\]touches the curve \[\frac{{{x}^{2}}}{4}+{{y}^{2}}=1\] is
A) \[1\] done clear
B) \[2\] done clear
C) \[\infty \] done clear
D) \[0\] done clear
View Answer play_arrowquestion_answer135) If the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] intersects the hyperbola \[xy={{c}^{2}}\]four points \[P({{x}_{1}},{{y}_{1}}),\] \[Q({{x}_{2}},{{y}_{2}}),\] \[R({{x}_{3}},{{y}_{3}})\] and \[S({{x}_{4}},{{y}_{4}})\] then,
A) \[{{y}_{1}}+{{y}_{2}}+{{y}_{3}}+{{y}_{4}}=2\] done clear
B) \[{{x}_{1}}{{x}_{2}}{{x}_{3}}{{x}_{4}}=2{{c}^{4}}\] done clear
C) \[{{y}_{1}}{{y}_{2}}{{y}_{3}}{{y}_{4}}=2{{c}^{4}}\] done clear
D) \[{{x}_{1}}+{{x}_{2}}+{{x}_{3}}+{{x}_{4}}=0\] done clear
View Answer play_arrowquestion_answer136) The foot of the perpendicular from the point\[(2,4)\] upon \[x+y=4\]is
A) \[(2,2)\] done clear
B) \[(4,0)\] done clear
C) \[(1,3)\] done clear
D) \[(3,-1)\] done clear
View Answer play_arrowquestion_answer137) The vertices of a triangle are \[(6,0),(0,6)\] and \[(6,6)\]. The distance between its circumventer and centroid is
A) \[2\] done clear
B) \[\sqrt{2}\] done clear
C) \[1\] done clear
D) \[2\sqrt{2}\] done clear
View Answer play_arrowquestion_answer138) The angle between the pair of lines \[{{x}^{2}}+2xy-{{y}^{2}}=0\] is
A) \[\frac{\pi }{6}\] done clear
B) \[\frac{\pi }{2}\] done clear
C) \[0\] done clear
D) \[\frac{\pi }{3}\] done clear
View Answer play_arrowquestion_answer139) \[\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{3.2}^{n+1}}-{{4.5}^{n+1}}}{{{5.2}^{n}}+{{7.5}^{n}}}\] is equal to
A) \[\frac{3}{5}\] done clear
B) \[-\frac{4}{7}\] done clear
C) \[-\frac{20}{7}\] done clear
D) \[0\] done clear
View Answer play_arrowquestion_answer140) The function \[f(x)=\frac{\log (1+ax)-\log (1-bx)}{x}\] is not defined at \[x=0\]. The value which should be assigned to f at \[x=0\] so that it is continuous at \[x=0\] is
A) \[a-b\] done clear
B) \[a+b\] done clear
C) \[\log a+\log b\] done clear
D) \[0\] done clear
View Answer play_arrowquestion_answer141) If \[f(x)=1+nx+\frac{n(n-1)}{2}{{x}^{2}}\]\[+\frac{n(n-1)(n-2)}{6}{{x}^{3}}+.....+{{x}^{n}},\]then \[f''\] (1) is equal to
A) \[n(n-1){{2}^{n-1}}\] done clear
B) \[(n-1){{2}^{n-1}}\] done clear
C) \[n(n-1){{2}^{n-2}}\] done clear
D) \[n(n-1){{2}^{n}}\] done clear
View Answer play_arrowquestion_answer142) If \[f(x)={{\log }_{{{x}^{2}}}}({{\log }_{e}}x),\] then \[f'(x)\] at \[x=e\] is
A) \[1\] done clear
B) \[\frac{1}{e}\] done clear
C) \[\frac{1}{2e}\] done clear
D) \[0\] done clear
View Answer play_arrowquestion_answer143) If \[y={{\sin }^{2}}x\,\cos \,nx,\]then \[\frac{dy}{dx}\] is
A) \[n\,\,{{\sin }^{n-1}}x\,\sin (n+1)x\] done clear
B) \[n\,\,{{\sin }^{n-1}}x\,\cos (n-1)x\] done clear
C) \[n\,\,{{\sin }^{n-1}}\,x\,\cos nx\] done clear
D) \[n{{\sin }^{n-1}}x\,\cos (n+1)x\] done clear
View Answer play_arrowquestion_answer144) If \[f(x)=\frac{g(x)+g(-x)}{2}+\frac{2}{{{[h(x)+h(-x)]}^{-1}}}\]where g and h are differentiable function, then \[f'(0)\]
A) \[1\] done clear
B) \[\frac{1}{2}\] done clear
C) \[\frac{3}{2}\] done clear
D) \[0\] done clear
View Answer play_arrowquestion_answer145) The tangent to a given curve \[y=f(x)\]is perpendicular to the x-axis, if
A) \[\frac{dy}{dx}=1\] done clear
B) \[\frac{dx}{dy}=0\] done clear
C) \[\frac{dx}{dy}=1\] done clear
D) \[\frac{dy}{dx}=0\] done clear
View Answer play_arrowquestion_answer146) The minimum value of s
A) \[-5\] done clear
B) \[\frac{1}{5}\] done clear
C) \[\frac{1}{243}\] done clear
D) \[\frac{1}{27}\] done clear
View Answer play_arrowquestion_answer147) A stone is thrown vertically upwards from the top of a tower \[64\text{ }m\]high according to the law \[s=48t-16{{t}^{2}}.\]The greatest height attained by the stone above ground is
A) \[36\,m\] done clear
B) \[32\,m\] done clear
C) \[100\,\,m\] done clear
D) \[64\,\,m\] done clear
View Answer play_arrowquestion_answer148) The length of the subtangent at t on the curve\[x=a(t+\sin t),\] \[y=a(1-\cos t)\] is
A) \[a\,\,\sin \,t\] done clear
B) \[2a\,\,\sin \,\left( \frac{t}{2} \right)\tan \left( \frac{t}{2} \right)\] done clear
C) \[2a\,\,\sin \,\frac{t}{2}\] done clear
D) \[2a\,\,{{\sin }^{3}}\,\left( \frac{t}{2} \right)\sec \left( \frac{t}{2} \right)\] done clear
View Answer play_arrowquestion_answer149) \[\int{\text{cosec (x-a) cosec x dx}}\] is equal to
A) \[x{{e}^{{{\tan }^{-1}}x}}+c\] done clear
B) \[{{e}^{{{\tan }^{-1}}x}}+c\] done clear
C) \[\frac{1}{2}{{e}^{{{\tan }^{-1}}x}}+c\] done clear
D) \[\frac{1}{2}x{{e}^{{{\tan }^{-1}}x}}+c\] done clear
View Answer play_arrowquestion_answer150) \[\int{\text{cosec (x - a) cosec x dx}}\]is equal to
A) \[\frac{-1}{\sin a}\log |\sin \,x\,\text{cosec(x-a) }\!\!|\!\!\text{ +c}\] done clear
B) \[\frac{-1}{\sin a}\log |\sin \,x\,(x-a)\sin x]+c\] done clear
C) \[\frac{-1}{\sin a}\log |\sin \,x\,(x-a)cosecx]+c\] done clear
D) \[\frac{1}{\sin a}\log |\sin \,(\lambda -a)\sin x]+c\] done clear
View Answer play_arrowquestion_answer151) If \[f(x)=\int_{-1}^{x}{|t|\,\,dt,}\] then for any \[x\ge 0,\] \[f(x)\]equal to
A) \[1-{{x}^{2}}\] done clear
B) \[\frac{1}{2}(1+{{x}^{2}})\] done clear
C) \[1+{{x}^{2}}\] done clear
D) \[\frac{1}{2}(1-{{x}^{2}})\] done clear
View Answer play_arrowquestion_answer152) \[\int_{1}^{3}{\frac{\sqrt{4-x}}{\sqrt{x}+\sqrt{4-x}}}dx\] is equal to
A) \[1\] done clear
B) \[3\] done clear
C) \[2\] done clear
D) \[0\] done clear
View Answer play_arrowquestion_answer153) The area bounded between the parabola\[{{y}^{2}}=4x\]and the line \[y=2x-4\]is equal to
A) \[\frac{17}{3}sq\,unit\] done clear
B) \[\frac{19}{3}sq\,unit\] done clear
C) \[9\,sq\,unit\] done clear
D) \[15\,sq\,unit\] done clear
View Answer play_arrowquestion_answer154) The differential equation of the family of circles passing through the orign and having their centres on the x-axis is
A) \[{{y}^{2}}={{x}^{2}}+2xy\,\frac{dy}{dx}\] done clear
B) \[{{y}^{2}}={{x}^{2}}-2xy\,\frac{dy}{dx}\] done clear
C) \[{{x}^{2}}={{y}^{2}}+xy\,\frac{dy}{dx}\] done clear
D) \[{{x}^{2}}={{y}^{2}}+3xy\,\frac{dy}{dx}\] done clear
View Answer play_arrowquestion_answer155) A population grows at the rate of 10% of the population per year. How long does it take for the population to double?
A) \[20\text{ }log\text{ }2\text{ }yr\] done clear
B) \[10\text{ }log\text{ }2\text{ y}r\] done clear
C) \[5\text{ }log\text{ }2\text{ }yr\] done clear
D) \[2\text{ }log\text{ }10\text{ }yr\] done clear
E) None of these done clear
View Answer play_arrowquestion_answer156) On the set of all natural numbers N, which one of the following * is a binary operation?
A) \[a*b=\sqrt{ab}\] done clear
B) \[a*b=\frac{a-b}{a+b}\] done clear
C) \[a*b=a+3b\] done clear
D) \[a*b=3a-4b\] done clear
View Answer play_arrowquestion_answer157) If \[\int_{0}^{1}{f(x)\,dx=5,}\] then the value of \[....+100\int_{0}^{1}{{{x}^{9}}\,\,f({{x}^{10}})dx}\]is equal to
A) \[125\] done clear
B) \[625\] done clear
C) \[275\] done clear
D) \[55\] done clear
View Answer play_arrowquestion_answer158) If \[ax+by=1,\] where a, b, x and y are integers, then which one of the following is not true?
A) \[(a,y)=1\] done clear
B) \[(x,y)=1\] done clear
C) \[(b,y)=1\] done clear
D) \[(a,b)=1\] done clear
View Answer play_arrowquestion_answer159) The digit in the unit place of the number \[2009!+{{3}^{7886}}\]is
A) \[7\] done clear
B) \[3\] done clear
C) \[1\] done clear
D) \[9\] done clear
View Answer play_arrowquestion_answer160) If \[\left| \begin{matrix} x+1 & x+2 & x+a \\ x+2 & x+3 & x+b \\ x+3 & x+4 & x+c \\ \end{matrix} \right|=0,\] then a, b, c are
A) in GP done clear
B) in HP done clear
C) equal done clear
D) in AP done clear
View Answer play_arrowquestion_answer161) The value of \[\left| \begin{matrix} 1 & {{\log }_{x}}y & {{\log }_{x}}z \\ {{\log }_{y}}x & 1 & {{\log }_{y}}z \\ {{\log }_{z}}x & {{\log }_{e}}y & 1 \\ \end{matrix} \right|\] is equal to
A) \[0\] done clear
B) \[1\] done clear
C) \[xyz\] done clear
D) \[\log \,xyz\] done clear
View Answer play_arrowquestion_answer162) If \[A=\left[ \begin{matrix} 2 & 1 & 0 \\ 0 & 2 & 1 \\ 1 & 0 & 2 \\ \end{matrix} \right],\]then \[|adj\,A|\]is equal to
A) \[0\] done clear
B) \[9\] done clear
C) \[\frac{1}{9}\] done clear
D) \[81\] done clear
View Answer play_arrowquestion_answer163) If A and B are square matrices of the same order such that \[(A+B)\,(A-B)={{A}^{2}}-{{B}^{2}},\] then \[{{(AB{{A}^{-1}})}^{2}}\]is equal to
A) \[{{B}^{2}}\] done clear
B) \[I\] done clear
C) \[{{A}^{2}}{{B}^{2}}\] done clear
D) \[{{A}^{2}}\] done clear
View Answer play_arrowquestion_answer164) If \[\vec{a}.\vec{b}=-|\vec{a}||\vec{b}|,\]then the angle between \[\vec{a}\] and \[\vec{b}\] is
A) \[{{45}^{o}}\] done clear
B) \[{{180}^{o}}\] done clear
C) \[{{90}^{o}}\] done clear
D) \[{{60}^{o}}\] done clear
View Answer play_arrowquestion_answer165) If \[\vec{a}+2\vec{b}+3\vec{c}=\vec{0},\] then \[\vec{a}\times \vec{b}+\vec{b}\times \vec{c}+\vec{c}\times \vec{a}\] is equal to
A) \[2(\vec{b}\times \vec{c})\] done clear
B) \[3(\vec{c}\times \vec{a})\] done clear
C) \[\vec{0}\] done clear
D) \[6(\vec{b}\times \vec{c})\] done clear
View Answer play_arrowquestion_answer166) If the volume of the parallelepiped with \[\vec{a},\] \[\vec{b}\] and \[\vec{c}\]as coterminous edges is \[40\text{ }cu\]unit, then the volume of the parallelepiped having \[\vec{b}+\vec{c},\] \[\vec{c}+\vec{a}\] and \[\vec{a}+\vec{b}\] as coterminous edges in cubic unit is
A) \[80\] done clear
B) \[120\] done clear
C) \[160\] done clear
D) \[40\] done clear
View Answer play_arrowquestion_answer167) In the group \[G\{0,1,2,3,4,5\}\] under addition modulo \[6,{{(2{{+}_{6}}{{3}^{-1}}{{+}_{6}}4)}^{-1}}\] is equal to
A) \[2\] done clear
B) \[3\] done clear
C) \[5\] done clear
D) \[0\] done clear
View Answer play_arrowquestion_answer168) Which one of the following is not true?
A) Inverse of an element in a group is unique. done clear
B) Fourth roots of unity form an additive abelian group. done clear
C) Cancellation laws hold in a group. done clear
D) Identity element in a group is unique. done clear
View Answer play_arrowquestion_answer169) The number of subgroups of the group \[({{Z}_{5}},{{+}_{5}})\] is
A) \[1\] done clear
B) \[3\] done clear
C) \[4\] done clear
D) \[2\] done clear
View Answer play_arrowquestion_answer170) The negation of \[p\wedge (q\to \tilde{\ }r)\] is
A) \[\tilde{\ }p\wedge (q\wedge r)\] done clear
B) \[p\vee (q\vee r)\] done clear
C) \[p\vee (q\wedge r)\] done clear
D) \[\tilde{\ }p\vee (q\wedge r)\] done clear
View Answer play_arrowquestion_answer171) If \[n=(2020)!\]then\[\frac{1}{{{\log }_{2}}n}+\frac{1}{{{\log }_{3}}n}+\frac{1}{{{\log }_{4}}n}+....+\frac{1}{{{\log }_{2020}}n}\]is equal to
A) \[2020\] done clear
B) \[1\] done clear
C) \[(2020)!\] done clear
D) \[0\] done clear
View Answer play_arrowquestion_answer172) If 'n' is a positive integer, then \[{{n}^{3}}+2n\]is divisible by
A) \[2\] done clear
B) \[6\] done clear
C) \[15\] done clear
D) \[3\] done clear
View Answer play_arrowquestion_answer173) On the set of integers Z, define \[f:z\to z\] as \[f(n)=\left\{ \begin{matrix} \frac{n}{2}, & n\,is\,\,even \\ 0, & n\,\,\,is\,\,odd \\ \end{matrix} \right.\], then f is
A) injective but not subjective done clear
B) neither injective nor subjective done clear
C) surjective but not injective done clear
D) objective done clear
View Answer play_arrowquestion_answer174) If \[\alpha \] and \[\beta \] are the roots of then \[{{\alpha }^{16}}+{{\beta }^{16}}\] is equal to
A) \[1\] done clear
B) \[-1\] done clear
C) \[2\] done clear
D) \[0\] done clear
View Answer play_arrowquestion_answer175) The total number of terms in the expansion of \[{{(x+y)}^{100}}+{{(x-y)}^{100}}\] after simplification is
A) \[51\] done clear
B) \[202\] done clear
C) \[100\] done clear
D) \[50\] done clear
View Answer play_arrowquestion_answer176) \[{{\cot }^{-1}}({{2.1}^{2}})+co{{t}^{-1}}({{2.2}^{2}})+{{\cot }^{-1}}({{2.3}^{2}})+...\] upto \[\infty \] is equal to
A) \[\frac{\pi }{4}\] done clear
B) \[\frac{\pi }{3}\] done clear
C) \[\frac{\pi }{2}\] done clear
D) \[\frac{\pi }{5}\] done clear
View Answer play_arrowquestion_answer177) If 'x' takes negative permissible value, then \[{{\sin }^{-1}}x\] is equal to
A) \[-{{\cos }^{-1}}\sqrt{1-{{x}^{2}}}\] done clear
B) \[{{\cos }^{-1}}\sqrt{{{x}^{2}}-1}\] done clear
C) \[\pi -{{\cos }^{-1}}\sqrt{1-{{x}^{2}}}\] done clear
D) \[{{\cos }^{-1}}\sqrt{1-{{x}^{2}}}\] done clear
View Answer play_arrowquestion_answer178) If \[1+\sin +{{\sin }^{2}}x+...\] upto \[\infty =4+2\sqrt{3},\] \[0<x<\pi \]and \[x\ne \frac{\pi }{2},\] then x is equal to
A) \[\frac{\pi }{3},\frac{5\pi }{6}\] done clear
B) \[\frac{2\pi }{3},\frac{\pi }{6}\] done clear
C) \[\frac{\pi }{3},\frac{2\pi }{3}\] done clear
D) \[\frac{\pi }{6},\frac{\pi }{3}\] done clear
View Answer play_arrowquestion_answer179) The complex number \[\frac{1+2i}{1-i}\] lies in
A) second quadrant done clear
B) third quadrant done clear
C) fourth quadrant done clear
D) first quadrant done clear
View Answer play_arrowquestion_answer180) If P is the point in the Agrand diagram corresponding to the complex number \[\sqrt{3}+i\] and if OPQ is an isosceles right angled triangle, right angled at ?O?, then Q represents the complex number
A) \[-1+i\sqrt{3}\] or \[1-i\sqrt{3}\] done clear
B) \[1\pm i\sqrt{3}\] done clear
C) \[\sqrt{3}-i\] or \[1-i\sqrt{3}\] done clear
D) \[-1\pm i\sqrt{3}\] done clear
View Answer play_arrow
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