question_answer1) In ruby laser, the stimulated emission is due to transition from
A) metastable state to any lower state
B) any higher state to lower state
C) metastable state to ground state
D) any higher state to ground state
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
B) zero only along the axis of the pipe
C) zero at any point inside the pipe
D) maximum at the centre and minimum at the edge
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
B) 0.15 m
C) 0.30 m
D) 0.6 m
View Answer play_arrowquestion_answer4) Two sources are said to be coherent if they produce waves
A) having a constant phase difference
B) of equal wavelength
C) of equal speed
D) having same shape of wave front
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
B) 1 A
C) 2 A
D) 1.5 A
View Answer play_arrowquestion_answer6) In a common emitter amplifier the input signal is applied across
A) anywhere
B) emitter-collector
C) collector-base
D) base-emitter
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) \[\frac{1}{{{e}^{2}}}\]
B) \[\frac{1}{e}\]
C) e
D) \[{{e}^{2}}\]
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) \[{{\tan }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\]
B) \[{{\tan }^{-1}}\left( 1-\sqrt{\frac{2}{3}} \right)\]
C) \[{{\sin }^{-1}}\left( 1-\sqrt{\frac{2}{3}} \right)\]
D) \[{{\tan }^{-1}}\left( \frac{2}{\sqrt{3}-1} \right)\]
View Answer play_arrowquestion_answer9) Ferromagnetic materials used in a transformer must have
A) low permeability and high hysterisis loss
B) high permeability and low hysterisis loss
C) high permeability and high hysterisis loss
D) low permeability and low hysterisis loss
View Answer play_arrowquestion_answer10) According to Newton's corpuscular theory, the speed of light is
A) same in all the media
B) lesser in rarer medium
C) lesser in denser medium
D) independent of the medium
View Answer play_arrowquestion_answer11) For the constructive interference the path difference between the two interfering waves must be equal to
A) \[\left( 2n+1 \right)\lambda \]
B) \[2n\pi \]
C) \[n\lambda \]
D) \[\left( 2n+1 \right)\frac{\pi }{2}\]
View Answer play_arrowquestion_answer12) The accurate measurement of emf can be obtained using
A) multimeter
B) voltmeter
C) voltameter
D) potentiometer
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) \[\frac{1}{3}\]
B) \[\sqrt{3}\]
C) \[\frac{1}{\sqrt{3}}\]
D) 3
View Answer play_arrowquestion_answer14) Which of the following is not a thermodynamic coordinate?
A) Gas constant (R)
B) Pressure (p)
C) Volume (V)
D) Temperature (T)
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
B) steel piece will weigh more
C) they have the same weight
D) aluminium piece will weigh more
View Answer play_arrowquestion_answer16) The amount of energy released when one microgram of matter is annihilated is
A) 25 kWh
B) \[9\times {{10}^{10}}kWh\]
C) \[3\times {{10}^{10}}kWh\]
D) \[0.5\times {{10}^{5}}kWh\]
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
B) 5 and 7
C) 2 and 7
D) 2 and 6
View Answer play_arrowquestion_answer18) \[\beta \]-decay means emission of electron from
A) innermost electron orbit
B) a stable nucleus
C) outermost electron orbit
D) radioactive nucleus
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
B) 2.5 A
C) 0.4 A
D) 1.25 A
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) \[\frac{3}{8}m{{s}^{-1}}\]
B) \[\frac{3}{8}m{{s}^{-1}}\]
C) \[\frac{4}{3}m{{s}^{-1}}\]
D) \[\frac{16}{3}m{{s}^{-1}}\]
View Answer play_arrowquestion_answer21) The moment of inertia of a circular ring of radius r and mass M about diameter is
A) \[\frac{2}{5}M{{r}^{2}}\]
B) \[\frac{M{{r}^{2}}}{4}\]
C) \[\frac{M{{r}^{2}}}{2}\]
D) \[\frac{M{{r}^{2}}}{12}\]
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
B) 0.15 N
C) 0.030 N
D) zero
View Answer play_arrowquestion_answer23) The colloidal solution in which both the dispersed phase and dispersion medium are liquids are called
A) emulsions
B) gels
C) foams
D) liquid crystals
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
B) scattering of \[I-R\] light is more than visible light
C) the intensity of \[I-R\] light from the object is less
D) scattering of \[I-R\] light is less than visible light
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
B) can keep the body in equilibrium if 1 N and 2 N act at right angle
C) cannot keep the body in equilibrium
D) can keep the body in equilibrium in 1 N and 3 N act at an acute angle
View Answer play_arrowquestion_answer26) Sound waves transfer
A) only energy not momentum
B) energy
C) momentum
D) Both (a) and (b)
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
B) 0.02 m
C) 0.05 m
D) 0.03 m
View Answer play_arrowquestion_answer28) G P Thomson experimentally confirmed the existence of matter waves by the phenomena
A) diffraction
B) refraction
C) polarisation
D) scattering
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
B) 345 K
C) 993 K
D) 690 K
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
B) 200 J
C) 400 J
D) 175 J
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
B) 24.2 m
C) 2.44 m
D) 1.22 m
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
B) 3.6 N
C) 2.4 N
D) 4 N
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) \[{{65}^{o}}C\]
B) \[{{70}^{o}}C\]
C) \[{{60}^{o}}C\]
D) \[{{75}^{o}}C\]
View Answer play_arrowquestion_answer34) The spectral series of the hydrogen atom that lies in the visible region of the electromagnetic spectrum
A) Paschen
B) Balmer
C) Lyman
D) Brackett
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
B) isothermal process
C) isobaric process
D) adiabatic process
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
B) The frequency changes when it travels from one medium to another
C) The speed changes when it travels from one medium to another
D) They travel in straight line in a given medium
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
B) B
C) A
D) C
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
B) greater at M than at N
C) greater at N than at M
D) same at M and N
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
B) 17 V
C) 5 V
D) 12 V
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
B) 9 E
C) 3 E
D) 27 E
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) \[\frac{1}{\sqrt{2}}\]
B) \[\sqrt{3}\]
C) \[\frac{\sqrt{3}}{2}\]
D) \[\frac{3}{2}\]
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
B) 0, 1, 0
C) 1, 1, 0
D) 1, 0, 1
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) \[\frac{3}{2}\]
B) \[\frac{4}{9}\]
C) \[\frac{2}{3}\]
D) \[\frac{9}{4}\]
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) \[10\text{ }\Omega \]
B) \[20\text{ }\Omega \]
C) \[8\text{ }\Omega \]
D) \[5\text{ }\Omega \]
View Answer play_arrowquestion_answer45) The phenomena in which proton flips is
A) nuclear magnetic resonance
B) lasers
C) radioactivity
D) nuclear fusion
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
B) 10 m
C) 5 m
D) 32 m
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
B) 3 quarks and 2 antiquarks
C) 3 quarks and 3 antiquarks
D) 2 quarks and 2 antiquarks
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) \[2~\sqrt{3}\times {{10}^{5}}m{{s}^{-1}}\]
B) \[8\times {{10}^{5}}m{{s}^{-1}}\]
C) \[16\times {{10}^{5}}m{{s}^{-1}}\]
D) \[4\times {{10}^{5}}m{{s}^{-1}}\]
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
B) 130 Hz
C) 390 Hz
D) 520 Hz
View Answer play_arrowquestion_answer50) The surface temperature of the stars is determined using
A) Planck's law
B) Wien's displacement law
C) Rayleigh-Jeans law
D) Kirchhoff?s law
View Answer play_arrowquestion_answer51) The charge deposited on 4\[\mu \]F capacitor in the circuit is
A) \[6\times {{10}^{-6}}C\]
B) \[12\times {{10}^{-6}}C\]
C) \[24\times {{10}^{-6}}C\]
D) \[36\times {{10}^{-6}}C\]
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
B) continuously increases
C) continuously decreases
D) first increases and then decreases
View Answer play_arrowquestion_answer53) Continuous emission spectrum is produced by
A) incandescent electric lamp
B) mercury vapour lamp
C) sodium vapour lamp
D) polyatomic substances
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) \[\frac{{{\mu }_{0}}nI}{\left( b-a \right)}{{\log }_{e}}\frac{a}{b}\]
B) \[\frac{{{\mu }_{0}}nI}{2\left( b-a \right)}\]
C) \[\frac{2{{\mu }_{0}}nI}{b}\]
D) \[\frac{{{\mu }_{0}}nI}{2\left( b-a \right)}{{\log }_{e}}\frac{b}{a}\]
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) \[{{120}^{o}}\]
B) \[{{30}^{o}}\]
C) \[{{60}^{o}}\]
D) \[{{90}^{o}}\]
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) \[12\text{ }V{{m}^{-1}}\]
B) \[-6\text{ }V{{m}^{-1}}\]
C) \[6\text{ }V{{m}^{-1}}\]
D) \[-12V{{m}^{-1}}\]
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
B) 0.3 mm
C) 0.45 mm
D) 0.15 mm
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
B) clockwise
C) anticlockwise
D) zero
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) \[\sqrt{\frac{\lambda R}{\lambda R-1}}\]
B) \[\sqrt{\frac{\lambda }{\lambda R-1}}\]
C) \[\sqrt{\frac{\lambda {{R}^{2}}}{\lambda R-1}}\]
D) \[\sqrt{\frac{\lambda R}{\lambda -1}}\]
View Answer play_arrowquestion_answer60) The magnetic dipole moment of a current loop is independent of
A) magnetic field in which it is lying
B) number of turns
C) area of the loop
D) current in the loop
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
B) both \[H_{2}^{+}\] and \[H_{2}^{-}\] do not exist
C) Ha is more stable than \[H_{2}^{+}\]
D) \[H_{2}^{+}\] is more stable than \[H_{2}^{-}\]
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) \[O_{2}^{2-},O_{2}^{-},{{O}_{2}},O_{2}^{+}\]
B) \[O_{2}^{2-},O_{2}^{-},O_{2}^{+},{{O}_{2}}\]
C) \[O_{2}^{+},{{O}_{2}},O_{2}^{-},O_{2}^{2-}\]
D) \[{{O}_{2}},O_{2}^{+},O_{2}^{-},O_{2}^{2-}\]
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
B) 0.125 g
C) 1 g
D) 0.5 g
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
B) 0
C) 3
D) 1
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
B) 0
C) 1
D) 2
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) \[\frac{a}{2k}\]
B) \[\frac{k}{a}\]
C) \[\frac{a}{k}\]
D) \[\frac{2a}{k}\]
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
B) 2
C) 1
D) 3
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) \[1000\text{ }c{{m}^{3}}\]
B) \[2000\text{ }c{{m}^{3}}\]
C) \[100\text{ }c{{m}^{3}}\]
D) \[200\text{ }c{{m}^{3}}\]
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
B) -1.20V
C) + 1.20V
D) 4-0.32 V
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
B) between 5 and 6
C) between 6 and 7
D) between 10 and 11
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
B) 9.65 A
C) 19.3 A
D) 0.965 A
View Answer play_arrowquestion_answer72) The one which decreases with dilution is
A) molar conductance
B) conductance
C) specific conductance
D) equivalent conductance
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
B) 56 mm
C) 70mm
D) 140mm
View Answer play_arrowquestion_answer74) A 6% solution of urea is isotonic with
A) 1 M solution of glucose
B) 0.05 M solution of glucose
C) 6% solution of glucose
D) 25% solution of glucose
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
B) to minimise the snow fall
C) to minimise pollution
D) to minimise the accumulation of dust on the road
View Answer play_arrowquestion_answer76) For the reaction \[{{H}_{2}}O(l){{H}_{2}}O(g)\] at 373 K and 1 atm pressure
A) \[\Delta H=0\]
B) \[\Delta E=0\]
C) \[\Delta H=T\Delta S\]
D) \[\Delta H=\Delta E\]
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) \[A{{B}_{2}}\]
B) \[{{A}_{3}}B\]
C) \[AB\]
D) \[A{{B}_{3}}\]
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
B) decreases electron density at meta position
C) increases electron density at meta position
D) increases electron density at ortho and para positions
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
B) aldol
C) ketol
D) acetal
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) \[PC{{l}_{3}}\]
B) \[PC{{l}_{5}}\]
C) \[SOC{{l}_{2}}\] in presence of pyridine
D) dry \[HCl\] in the presence of anhydrous \[ZnC{{l}_{2}}\]
View Answer play_arrowquestion_answer81) The electrophile involved in the sulphonation of benzene is
A) \[SO_{3}^{+}\]
B) \[SO_{3}^{2-}\]
C) \[H_{3}^{+}O\]
D) \[S{{O}_{3}}\]
View Answer play_arrowquestion_answer82) The carbon-carbon bond length in benzene is
A) in between \[{{C}_{2}}{{H}_{6}}\] and \[{{C}_{2}}{{H}_{4}}\]
B) same as in \[{{C}_{2}}{{H}_{4}}\]
C) in between \[{{C}_{2}}{{H}_{6}}\] and \[{{C}_{2}}{{H}_{2}}\]
D) in between \[{{C}_{2}}{{H}_{4}}\] and \[{{C}_{2}}{{H}_{2}}\]
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
B) propanal
C) propanone
D) ethanol
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) \[C{{H}_{3}}C{{H}_{2}}OH\]
B) \[C{{H}_{3}}\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{-C}}\,-C{{H}_{3}}\]
C) \[{{(C{{H}_{3}})}_{2}}CHOH\]
D) \[C{{H}_{3}}CHO\]
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
B) \[NaOH\]
C) ethanol
D) methanol
View Answer play_arrowquestion_answer86) The compound which forms acetaldehyde when heated with dilute \[NaOH\], is
A) 1, 1-dichloroethane
B) 1, 1, 1-trichloroethane
C) 1-chloroethane
D) 1, 2-dichloroethane
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) \[N{{H}_{3}}<{{(C{{H}_{3}})}_{3}}N<{{(C{{H}_{3}})}_{2}}NH<C{{H}_{3}}N{{H}_{2}}\]
B) \[N{{H}_{3}}<{{(C{{H}_{3}})}_{3}}N<C{{H}_{3}}N{{H}_{2}}<{{(C{{H}_{3}})}_{2}}NH\]
C) \[{{(C{{H}_{3}})}_{3}}N<N{{H}_{3}}<C{{H}_{3}}N{{H}_{2}}<{{(C{{H}_{3}})}_{2}}NH\]
D) \[C{{H}_{3}}N{{H}_{2}}<{{(C{{H}_{3}})}_{2}}NH<{{(C{{H}_{3}})}_{3}}N<N{{H}_{3}}\]
View Answer play_arrowquestion_answer88) The one which has least iodine value is
A) sunflower oil
B) ginger oil
C) ghee
D) groundnut oil
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
B) glucose increases the blood sugar level slowly
C) glucose reduces the blood sugar level
D) glucose increases the blood sugar level almost instantaneously
View Answer play_arrowquestion_answer90) There are 20 naturally occurring amino acids. The maximum number of tripeptides that can be obtained is
A) 8000
B) 6470
C) 7465
D) 5360
View Answer play_arrowquestion_answer91) Cooking is fast in a pressure cooker, because
A) food particles are effectively smashed
B) water boils at higher temperature inside the pressure cooker
C) food is cooked at constant volume
D) loss of heat due to radiation is minimum
View Answer play_arrowquestion_answer92) The ore that is concentrated by froth floatation process is
A) zincite
B) cinnabar
C) bauxite
D) malachite
View Answer play_arrowquestion_answer93) The correct set of four quantum numbers for outermost electron of potassium \[(Z=19)\] is
A) \[4,1,0,\frac{1}{2}\]
B) \[3,1,0,\frac{1}{2}\]
C) \[4,0,0,\frac{1}{2}\]
D) \[3,0,0,\frac{1}{2}\]
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
B) 0.25 kg
C) 0.15 kg
D) 0.2 kg
View Answer play_arrowquestion_answer95) The correct order of ionisation energy of C, N, O, F is
A) \[F<O<N<C\]
B) \[F<N<C<O\]
C) \[C<N<O<F\]
D) \[C<O<N<F\]
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
B) amphoteric
C) basic
D) acidic
View Answer play_arrowquestion_answer97) The characteristic not related to alkali metal is
A) high ionisation energy
B) their ions are isoelectronic with noble gases
C) low melting point
D) low electronegativity
View Answer play_arrowquestion_answer98) Among the following, the compound that contains ionic, covalent and coordinate linkage is
A) \[N{{H}_{3}}\]
B) \[N{{H}_{4}}Cl\]
C) \[NaCl\]
D) \[CaO\]
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
B) 0 and 4
C) 3 and 1
D) 1 and 3
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) \[300\,\,c{{m}^{3}}\]
B) \[200\,\,c{{m}^{3}}\]
C) \[500\,\,c{{m}^{3}}\]
D) \[400\,\,c{{m}^{3}}\]
View Answer play_arrowquestion_answer101) A bivalent metal has an equivalent mass of 32. The molecular mass of the metal nitrate is
A) 182
B) 168
C) 192
D) 188
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) \[300\,\,m{{s}^{-1}}\]
B) \[900\,\,m{{s}^{-1}}\]
C) \[120\,\,m{{s}^{-1}}\]
D) \[600\,\,m{{s}^{-1}}\]
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) \[pS{{O}_{2}}>p{{H}_{2}}>pC{{H}_{4}}\]
B) \[pS{{O}_{2}}>pC{{H}_{4}}>p{{H}_{2}}\]
C) \[p{{H}_{2}}>pS{{O}_{2}}>pC{{H}_{4}}\]
D) \[p{{H}_{2}}>pC{{H}_{4}}>pS{{O}_{2}}\]
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
B) +23 kJ
C) +92 kJ
D) +46 kJ
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
B) 0.52 atm
C) 0.21 atm
D) 0.41 atm
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
B) 0.8
C) 3.2
D) 1.6
View Answer play_arrowquestion_answer107) Rate of physical adsorption increases with
A) decrease in surface area
B) decrease in temperature
C) decrease in pressure
D) increase in temperature
View Answer play_arrowquestion_answer108) IUPAC name of \[{{(C{{H}_{3}})}_{2}}CCl\] is
A) n-butyl chloride
B) 3-chloro butane
C) 2-chloro 2-methyl propane
D) t-butyl chloride
View Answer play_arrowquestion_answer109) Lucas test is associated with
A) aldehydes
B) phenols
C) carboxylic acids
D) alcohols
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
B) chloroform
C) methane
D) ethyl iodide
View Answer play_arrowquestion_answer111) The condensation polymer among the following is
A) rubber
B) protein
C) PVC
D) polyethene
View Answer play_arrowquestion_answer112) The order of stability of metal oxides is
A) \[A{{l}_{2}}{{O}_{3}}<MgO<F{{e}_{2}}{{O}_{3}}<C{{r}_{2}}{{O}_{3}}\]
B) \[C{{r}_{2}}{{O}_{3}}<MgO<A{{l}_{2}}{{O}_{3}}<F{{e}_{2}}{{O}_{3}}\]
C) \[F{{e}_{2}}{{O}_{3}}<C{{r}_{2}}{{O}_{3}}<A{{l}_{2}}{{O}_{3}}<MgO\]
D) \[F{{e}_{2}}{{O}_{3}}<A{{l}_{2}}{{O}_{3}}<C{{r}_{2}}{{O}_{3}}<MgO\]
View Answer play_arrowquestion_answer113) The temperature of the slag zone in the metallurgy of iron using blast furnace is
A) \[1200-{{1500}^{o}}C\]
B) \[1500-{{1600}^{o}}C\]
C) \[400-{{700}^{o}}C\]
D) \[800-{{1000}^{o}}C\]
View Answer play_arrowquestion_answer114) The function of \[Fe{{(OH)}_{3}}\] in the contact process is
A) to remove arsenic impurity
B) to detect colloidal impurity
C) to remove moisture
D) to remove dust particles
View Answer play_arrowquestion_answer115) In which of the following, \[N{{H}_{3}}\] is not used?
A) Tollen's reagent
B) Nessler's reagent
C) Group reagent for the analysis of IV group basic radicals
D) Group reagent for the analysis of III group basic radicals
View Answer play_arrowquestion_answer116) Argon is used
A) in filling airships
B) to obtain low temperature
C) in high temperature welding
D) in radiotherapy for treatment of cancer
View Answer play_arrowquestion_answer117) The incorrect statement in respect of chromyl chloride test is
A) formation of red vapours
B) formation of lead chromate
C) formation of chromyl chloride
D) -liberation of chlorine
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
B) 4
C) 1
D) 2
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
B) penta ammine nitrito cobalt (III) ion
C) penta ammine nitro cobalt (III) ion
D) penta ammine nitro cobalt (IV) ion
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
B) 0
C) +2
D) +1
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) \[4\]
B) \[3\]
C) \[2\]
D) \[8\]
View Answer play_arrowquestion_answer122) Which one of the following is possible?
A) \[\sin \theta =\frac{{{a}^{2}}+{{b}^{2}}}{{{a}^{2}}-{{b}^{2}}},(a\ne b)\]
B) \[\sin \theta =\frac{4}{5}\]
C) \[\sin \theta =45\]
D) \[\cos \theta =\frac{7}{3}\]
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
B) acute angled
C) isosceles
D) right angled
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) \[12\]
B) \[13\]
C) \[14\]
D) \[11\]
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) \[22\,\,m\]
B) \[56\,\,m\]
C) \[45\,\,m\]
D) \[35\,\,m\]
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) \[\frac{\sqrt{3}}{2}\]
B) \[0\]
C) \[\frac{-1}{2}\]
D) \[\frac{1}{2}\]
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) \[{{x}^{2}}+{{y}^{2}}=1\]
B) \[{{x}^{2}}+{{y}^{2}}=2\]
C) \[x+y=1\]
D) \[x+y=2\]
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) \[4\]
B) \[8\]
C) \[16\]
D) \[2\]
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) \[2\]
B) \[3\]
C) \[0\]
D) \[1\]
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) \[\left( \frac{1}{2},\frac{-1}{2} \right)\]
B) \[\left( \frac{1}{2},\frac{1}{3} \right)\]
C) \[(-1,0)\]
D) \[\left( -\frac{1}{2},\frac{1}{2} \right)\]
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) \[8\]
B) \[6\]
C) \[4\]
D) \[2\]
View Answer play_arrowquestion_answer132) For the parabola \[{{y}^{2}}=4x,\]the point P whose focal distance is 17, is
A) \[(8,8)\] or \[(8,-8)\]
B) \[(4,8)\] or \[(4,-8)\]
C) \[(2,8)\] or \[(2,-8)\]
D) \[(16,8)\] or \[(16,-8)\]
View Answer play_arrowquestion_answer133) The angle between the tangents drawn to the parabola \[{{y}^{2}}=12x\]from the point \[(-3,2)\]is
A) \[{{90}^{o}}\]
B) \[{{60}^{o}}\]
C) \[{{30}^{o}}\]
D) \[{{45}^{o}}\]
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) \[1\]
B) \[2\]
C) \[\infty \]
D) \[0\]
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) \[{{y}_{1}}+{{y}_{2}}+{{y}_{3}}+{{y}_{4}}=2\]
B) \[{{x}_{1}}{{x}_{2}}{{x}_{3}}{{x}_{4}}=2{{c}^{4}}\]
C) \[{{y}_{1}}{{y}_{2}}{{y}_{3}}{{y}_{4}}=2{{c}^{4}}\]
D) \[{{x}_{1}}+{{x}_{2}}+{{x}_{3}}+{{x}_{4}}=0\]
View Answer play_arrowquestion_answer136) The foot of the perpendicular from the point\[(2,4)\] upon \[x+y=4\]is
A) \[(2,2)\]
B) \[(4,0)\]
C) \[(1,3)\]
D) \[(3,-1)\]
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) \[2\]
B) \[\sqrt{2}\]
C) \[1\]
D) \[2\sqrt{2}\]
View Answer play_arrowquestion_answer138) The angle between the pair of lines \[{{x}^{2}}+2xy-{{y}^{2}}=0\] is
A) \[\frac{\pi }{6}\]
B) \[\frac{\pi }{2}\]
C) \[0\]
D) \[\frac{\pi }{3}\]
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) \[\frac{3}{5}\]
B) \[-\frac{4}{7}\]
C) \[-\frac{20}{7}\]
D) \[0\]
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) \[a-b\]
B) \[a+b\]
C) \[\log a+\log b\]
D) \[0\]
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) \[n(n-1){{2}^{n-1}}\]
B) \[(n-1){{2}^{n-1}}\]
C) \[n(n-1){{2}^{n-2}}\]
D) \[n(n-1){{2}^{n}}\]
View Answer play_arrowquestion_answer142) If \[f(x)={{\log }_{{{x}^{2}}}}({{\log }_{e}}x),\] then \[f'(x)\] at \[x=e\] is
A) \[1\]
B) \[\frac{1}{e}\]
C) \[\frac{1}{2e}\]
D) \[0\]
View Answer play_arrowquestion_answer143) If \[y={{\sin }^{2}}x\,\cos \,nx,\]then \[\frac{dy}{dx}\] is
A) \[n\,\,{{\sin }^{n-1}}x\,\sin (n+1)x\]
B) \[n\,\,{{\sin }^{n-1}}x\,\cos (n-1)x\]
C) \[n\,\,{{\sin }^{n-1}}\,x\,\cos nx\]
D) \[n{{\sin }^{n-1}}x\,\cos (n+1)x\]
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) \[1\]
B) \[\frac{1}{2}\]
C) \[\frac{3}{2}\]
D) \[0\]
View Answer play_arrowquestion_answer145) The tangent to a given curve \[y=f(x)\]is perpendicular to the x-axis, if
A) \[\frac{dy}{dx}=1\]
B) \[\frac{dx}{dy}=0\]
C) \[\frac{dx}{dy}=1\]
D) \[\frac{dy}{dx}=0\]
View Answer play_arrowquestion_answer146) The minimum value of s
A) \[-5\]
B) \[\frac{1}{5}\]
C) \[\frac{1}{243}\]
D) \[\frac{1}{27}\]
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) \[36\,m\]
B) \[32\,m\]
C) \[100\,\,m\]
D) \[64\,\,m\]
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) \[a\,\,\sin \,t\]
B) \[2a\,\,\sin \,\left( \frac{t}{2} \right)\tan \left( \frac{t}{2} \right)\]
C) \[2a\,\,\sin \,\frac{t}{2}\]
D) \[2a\,\,{{\sin }^{3}}\,\left( \frac{t}{2} \right)\sec \left( \frac{t}{2} \right)\]
View Answer play_arrowquestion_answer149) \[\int{\text{cosec (x-a) cosec x dx}}\] is equal to
A) \[x{{e}^{{{\tan }^{-1}}x}}+c\]
B) \[{{e}^{{{\tan }^{-1}}x}}+c\]
C) \[\frac{1}{2}{{e}^{{{\tan }^{-1}}x}}+c\]
D) \[\frac{1}{2}x{{e}^{{{\tan }^{-1}}x}}+c\]
View Answer play_arrowquestion_answer150) \[\int{\text{cosec (x - a) cosec x dx}}\]is equal to
A) \[\frac{-1}{\sin a}\log |\sin \,x\,\text{cosec(x-a) }\!\!|\!\!\text{ +c}\]
B) \[\frac{-1}{\sin a}\log |\sin \,x\,(x-a)\sin x]+c\]
C) \[\frac{-1}{\sin a}\log |\sin \,x\,(x-a)cosecx]+c\]
D) \[\frac{1}{\sin a}\log |\sin \,(\lambda -a)\sin x]+c\]
View Answer play_arrowquestion_answer151) If \[f(x)=\int_{-1}^{x}{|t|\,\,dt,}\] then for any \[x\ge 0,\] \[f(x)\]equal to
A) \[1-{{x}^{2}}\]
B) \[\frac{1}{2}(1+{{x}^{2}})\]
C) \[1+{{x}^{2}}\]
D) \[\frac{1}{2}(1-{{x}^{2}})\]
View Answer play_arrowquestion_answer152) \[\int_{1}^{3}{\frac{\sqrt{4-x}}{\sqrt{x}+\sqrt{4-x}}}dx\] is equal to
A) \[1\]
B) \[3\]
C) \[2\]
D) \[0\]
View Answer play_arrowquestion_answer153) The area bounded between the parabola\[{{y}^{2}}=4x\]and the line \[y=2x-4\]is equal to
A) \[\frac{17}{3}sq\,unit\]
B) \[\frac{19}{3}sq\,unit\]
C) \[9\,sq\,unit\]
D) \[15\,sq\,unit\]
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) \[{{y}^{2}}={{x}^{2}}+2xy\,\frac{dy}{dx}\]
B) \[{{y}^{2}}={{x}^{2}}-2xy\,\frac{dy}{dx}\]
C) \[{{x}^{2}}={{y}^{2}}+xy\,\frac{dy}{dx}\]
D) \[{{x}^{2}}={{y}^{2}}+3xy\,\frac{dy}{dx}\]
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) \[20\text{ }log\text{ }2\text{ }yr\]
B) \[10\text{ }log\text{ }2\text{ y}r\]
C) \[5\text{ }log\text{ }2\text{ }yr\]
D) \[2\text{ }log\text{ }10\text{ }yr\]
E) None of these
View Answer play_arrowquestion_answer156) On the set of all natural numbers N, which one of the following * is a binary operation?
A) \[a*b=\sqrt{ab}\]
B) \[a*b=\frac{a-b}{a+b}\]
C) \[a*b=a+3b\]
D) \[a*b=3a-4b\]
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) \[125\]
B) \[625\]
C) \[275\]
D) \[55\]
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) \[(a,y)=1\]
B) \[(x,y)=1\]
C) \[(b,y)=1\]
D) \[(a,b)=1\]
View Answer play_arrowquestion_answer159) The digit in the unit place of the number \[2009!+{{3}^{7886}}\]is
A) \[7\]
B) \[3\]
C) \[1\]
D) \[9\]
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
B) in HP
C) equal
D) in AP
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) \[0\]
B) \[1\]
C) \[xyz\]
D) \[\log \,xyz\]
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) \[0\]
B) \[9\]
C) \[\frac{1}{9}\]
D) \[81\]
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) \[{{B}^{2}}\]
B) \[I\]
C) \[{{A}^{2}}{{B}^{2}}\]
D) \[{{A}^{2}}\]
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) \[{{45}^{o}}\]
B) \[{{180}^{o}}\]
C) \[{{90}^{o}}\]
D) \[{{60}^{o}}\]
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) \[2(\vec{b}\times \vec{c})\]
B) \[3(\vec{c}\times \vec{a})\]
C) \[\vec{0}\]
D) \[6(\vec{b}\times \vec{c})\]
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) \[80\]
B) \[120\]
C) \[160\]
D) \[40\]
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) \[2\]
B) \[3\]
C) \[5\]
D) \[0\]
View Answer play_arrowquestion_answer168) Which one of the following is not true?
A) Inverse of an element in a group is unique.
B) Fourth roots of unity form an additive abelian group.
C) Cancellation laws hold in a group.
D) Identity element in a group is unique.
View Answer play_arrowquestion_answer169) The number of subgroups of the group \[({{Z}_{5}},{{+}_{5}})\] is
A) \[1\]
B) \[3\]
C) \[4\]
D) \[2\]
View Answer play_arrowquestion_answer170) The negation of \[p\wedge (q\to \tilde{\ }r)\] is
A) \[\tilde{\ }p\wedge (q\wedge r)\]
B) \[p\vee (q\vee r)\]
C) \[p\vee (q\wedge r)\]
D) \[\tilde{\ }p\vee (q\wedge r)\]
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) \[2020\]
B) \[1\]
C) \[(2020)!\]
D) \[0\]
View Answer play_arrowquestion_answer172) If 'n' is a positive integer, then \[{{n}^{3}}+2n\]is divisible by
A) \[2\]
B) \[6\]
C) \[15\]
D) \[3\]
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
B) neither injective nor subjective
C) surjective but not injective
D) objective
View Answer play_arrowquestion_answer174) If \[\alpha \] and \[\beta \] are the roots of then \[{{\alpha }^{16}}+{{\beta }^{16}}\] is equal to
A) \[1\]
B) \[-1\]
C) \[2\]
D) \[0\]
View Answer play_arrowquestion_answer175) The total number of terms in the expansion of \[{{(x+y)}^{100}}+{{(x-y)}^{100}}\] after simplification is
A) \[51\]
B) \[202\]
C) \[100\]
D) \[50\]
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) \[\frac{\pi }{4}\]
B) \[\frac{\pi }{3}\]
C) \[\frac{\pi }{2}\]
D) \[\frac{\pi }{5}\]
View Answer play_arrowquestion_answer177) If 'x' takes negative permissible value, then \[{{\sin }^{-1}}x\] is equal to
A) \[-{{\cos }^{-1}}\sqrt{1-{{x}^{2}}}\]
B) \[{{\cos }^{-1}}\sqrt{{{x}^{2}}-1}\]
C) \[\pi -{{\cos }^{-1}}\sqrt{1-{{x}^{2}}}\]
D) \[{{\cos }^{-1}}\sqrt{1-{{x}^{2}}}\]
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) \[\frac{\pi }{3},\frac{5\pi }{6}\]
B) \[\frac{2\pi }{3},\frac{\pi }{6}\]
C) \[\frac{\pi }{3},\frac{2\pi }{3}\]
D) \[\frac{\pi }{6},\frac{\pi }{3}\]
View Answer play_arrowquestion_answer179) The complex number \[\frac{1+2i}{1-i}\] lies in
A) second quadrant
B) third quadrant
C) fourth quadrant
D) first quadrant
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 \[1-i\sqrt{3}\]
B) \[1\pm i\sqrt{3}\]
C) \[\sqrt{3}-i\] or \[1-i\sqrt{3}\]
D) \[-1\pm i\sqrt{3}\]
View Answer play_arrow
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