question_answer1) All components of the electromagnetic spectrum in vacuum have the same
A) energy
B) velocity
C) wavelength
D) frequency
View Answer play_arrowquestion_answer2) Which one of the following graph represents the variation of maximum kinetic energy \[({{E}_{k}})\] of the emitted electrons with frequency v in photoelectric effect correctly?
A)
B)
C)
D)
View Answer play_arrowquestion_answer3) A and B are two metals with threshold frequencies \[1.8\times {{10}^{14}}Hz\] and \[2.2\times {{10}^{14}}Hz.\]Two identical photons of energy 0.825 eV each are incident on them. Then photoelectrons are emitted by (Take\[h=6.6\times {{10}^{-34}}J-s\])
A) B alone
B) A alone
C) neither A nor B
D) both A and B
View Answer play_arrowquestion_answer4) The ionization energy of \[L{{i}^{2+}}\] is equal to
A) \[9hcR\]
B) \[6hcR\]
C) \[2hcR\]
D) \[hcR\]
View Answer play_arrowquestion_answer5) In the Wheatstone's network given, \[P=10\Omega \], \[Q=20\,\Omega ,\,\,R=15\,\Omega ,\,\,S=30\,\Omega \] the current passing through the battery (of negligible internal resistance) is
A) 0.36 A
B) zero
C) 0.18 A
D) 0.72 A
View Answer play_arrowquestion_answer6) Electrons in a certain energy level \[n={{n}_{1}}\], can emit 3 spectral lines. When they are in another energy level, \[n={{n}_{2}}\], they can emit 6 spectral lines. The orbital speed of the electrons in the orbits are in the ratio
A) \[4:3\]
B) \[3:4\]
C) \[2:1\]
D) \[1:2\]
View Answer play_arrowquestion_answer7) A circular coil carrying a certain current produces a magnetic field \[{{B}_{0}}\] at its centre. The coil is now rewound so as to have 3 turns and the same current is passed through it. The new magnetic field at the centre is
A) \[\frac{{{B}_{0}}}{9}\]
B) \[9\,{{B}_{0}}\]
C) \[\frac{{{B}_{0}}}{3}\]
D) \[3\,{{B}_{0}}\]
View Answer play_arrowquestion_answer8) A proton and a deuteron with the same initial kinetic energy enter a magnetic field in a direction perpendicular to the direction of the field. The ratio of the radii of the circular trajectories described by them is
A) \[1:4\]
B) \[1:\sqrt{2}\]
C) \[1:1\]
D) \[1:2\]
View Answer play_arrowquestion_answer9) Two tangent galvanometers A and B have coils of radii 8 cm and 16 cm respectively and resistance \[8\Omega \] each. They are connected in parallel with a cell of emf 4 V and negligible internal resistance. The deflections produced in the tangent galvanometers A and B are \[{{30}^{o}}\]and \[{{60}^{o}}\] respectively. If A has 2 turns, then B must have
A) 18 turns
B) 12 turns
C) 6 turns
D) 2 turns
View Answer play_arrowquestion_answer10) A charged particle is moving in a magnetic field of strength B perpendicular to the direction of the field. If q and m denote the charge and mass of the particle respectively, then the frequency of rotation of the particle is
A) \[f=\frac{qB}{2\,\pi m}\]
B) \[f=\frac{qB}{2\,\pi {{m}^{2}}}\]
C) \[f=\frac{2\,{{\pi }^{2}}m}{qB}\]
D) \[f=\frac{2\,\pi \,m}{qB}\]
View Answer play_arrowquestion_answer11) Two identical capacitors each of capacitance \[5\mu F\] are charged to potentials 2 kV and 1 kV respectively. Their -ve ends are connected together. When the +ve ends are also connected together, the loss of energy of the system is
A) 160 J
B) zero
C) 5 J
D) 1.25 J
View Answer play_arrowquestion_answer12) A parallel plate capacitor with air as the dielectric has capacitance C. A slab of dielectric constant K and having the same thickness as the separation between the plates is introduced so as to fill one-fourth of the capacitor as shown in the figure. The new capacitance will be
A) \[\left( K+3 \right)\frac{C}{4}\]
B) \[\left( K+2 \right)\frac{C}{4}\]
C) \[\left( K+1 \right)\frac{C}{4}\]
D) \[\frac{KC}{4}\]
View Answer play_arrowquestion_answer13) A current of 5 A is passing through a metallic wire of cross-sectional area \[4\times {{10}^{-6}}{{m}^{2}}\]. If the density of charge carriers of the wire is\[5\times {{10}^{26}}{{m}^{-3}}\], the drift velocity of the electrons will be
A) \[1\times {{10}^{2}}m{{s}^{-1}}\]
B) \[1.56\times {{10}^{-2}}m{{s}^{-1}}\]
C) \[1.56\times {{10}^{-3}}m{{s}^{-1}}\]
D) \[1\times {{10}^{-2}}m{{s}^{-1}}\]
View Answer play_arrowquestion_answer14) Two bulbs rated 25 W-220 V and 100 W-220 V are connected in series to a 440 V supply. The,
A) 100 W bulb fuses
B) 25 W bulb fuses
C) both the bulbs fuse
D) neither of the bulb fuses
View Answer play_arrowquestion_answer15) The current passing through the ideal ammeter in the circuit given below is
A) 1.25 A
B) 1 A
C) 0.75 A
D) 0.5 A
View Answer play_arrowquestion_answer16) A and D are two infinitely long straight parallel conductors. C is another straight conductor of length 1m kept parallel to A and B as shown in the figure. Then the force experienced by C is
A) towards A equal to \[0.6\times {{10}^{-5}}N\]
B) towards B equal to \[5.4\times {{10}^{-5}}N\]
C) towards A equal to \[5.4\times {{10}^{-5}}N\]
D) towards B equal to \[0.6\times {{10}^{-5}}N\]
View Answer play_arrowquestion_answer17) An electric bulb has a rated power of 50 W s: 100 V. If it is used on an AC source 200 V 50 Hz, a choke has to be used in series with is This choke should have an inductance of
A) 0.1 mH
B) 1 mH
C) 0.1 H
D) 1.1 H
View Answer play_arrowquestion_answer18) An inductance of \[\left( \frac{200}{\pi } \right)\,mH\], a capacitance of \[\left( \frac{{{10}^{-3}}}{\pi } \right)F\]and a resistance of \[10\,\Omega \] are connected in series with an AC source 220 V, 50 Hz. The phase angle of the circuit is
A) \[\frac{\pi }{6}\]
B) \[\frac{\pi }{4}\]
C) \[\frac{\pi }{2}\]
D) \[\frac{\pi }{3}\]
View Answer play_arrowquestion_answer19) A step-down transformer reduces the voltage of a transmission line from 2200 V to 220 V. The power delivered by it is 880 W and its efficiency is 88%. The input current is
A) 4.65 A
B) 0.045 A
C) 0.45 A
D) 4.65 A
View Answer play_arrowquestion_answer20) Current in a coil changes from 4 A to zero in 0.1 s and the emf induced is 100 V. The self inductance of the coil is
A) 0.25 H
B) 0.4 H
C) 2.5 H
D) 4 H
View Answer play_arrowquestion_answer21) The electromagnetic theory of light failed to explain
A) photoelectric effect
B) polarization
C) diffraction
D) interference
View Answer play_arrowquestion_answer22) Light from two coherent sources of the same amplitude A and wavelength \[\lambda \] illuminates the screen. The intensity of the central maximum is \[{{I}_{0}}\]. If the sources were incoherent, the intensity at the same point will be
A) \[4{{I}_{0}}\]
B) \[2{{I}_{0}}\]
C) \[{{I}_{0}}\]
D) \[\frac{{{I}_{0}}}{2}\]
View Answer play_arrowquestion_answer23) In Young's double slit experiment with sodium vapour lamp of wavelength 589 nm and the slits 0.589 mm apart, the half angular width of the central maximum is
A) \[{{\sin }^{-1}}\left( 0.01 \right)\]
B) \[{{\sin }^{-1}}\left( 0.0001 \right)\]
C) \[{{\sin }^{-1}}\left( 0.001 \right)\]
D) \[{{\sin }^{-1}}\left( 0.1 \right)\]
View Answer play_arrowquestion_answer24) A single slit Fraunhofer diffraction pattern is formed with white light. For what wavelength of light the third secondary maximum in the diffraction pattern coincides with the second secondary maximum in the pattern for red light of wavelength \[6500\overset{o}{\mathop{A}}\,\]?
A) \[4400\overset{o}{\mathop{A}}\,\]
B) \[4100\overset{o}{\mathop{A}}\,\]
C) \[4642.8\overset{o}{\mathop{A}}\,\]
D) \[9100\overset{o}{\mathop{A}}\,\]
View Answer play_arrowquestion_answer25) The head lights of a jeep are 1.2 m apart. If the pupil of the eye of an observer has a diameter of mm and light of wavelength 5896 \[{{A}^{o}}\]is used, what should be the maximum distance of the jeep from the observer if the two head lights are just separated?
A) 33.9 km
B) 33.9 m
C) 3.34 m
D) 3.39 m
View Answer play_arrowquestion_answer26) The de-Broglie wavelength of a proton (charge \[=1.6\times {{10}^{-19}}C\], mass \[=1.6\times {{10}^{-27}}kg\]) accelerated through a potential difference of 1 kV is
A) \[600\,\overset{o}{\mathop{A}}\,\]
B) \[0.9~{{10}^{-12}}m\]
C) \[7\,\overset{o}{\mathop{A}}\,\]
D) 0.9 nm
View Answer play_arrowquestion_answer27) A radioactive element forms its own isotope after 3 consecutive disintegrations. The particles emitted are
A) \[3\,\beta \]-particles
B) \[2\,\beta \]-particles and \[1\,\alpha \]-particle
C) \[2\,\beta \]-particles and \[1\,\gamma \]-particle
D) \[2\,\alpha \]-particles and \[1\,\beta \]-particle
View Answer play_arrowquestion_answer28) A radioactive substance contains 10000 nuclei and its half-life period is 20 days. The number of nuclei present at the end of 10 days is
A) 7070
B) 9000
C) 8000
D) 7500
View Answer play_arrowquestion_answer29) In Raman effect, Stokes? lines are spectral lines having
A) frequency greater than that of the original line
B) wavelength equal to that of the original line
C) wavelength less than that of the original line
D) wavelength greater than that of the original line
View Answer play_arrowquestion_answer30) The principle of LASER action involves
A) amplification of particular frequency emitted by the system
B) population inversion
C) stimulated emission
D) all of the above
View Answer play_arrowquestion_answer31) A ray of light is travelling from glass to air. (refractive index of glass = 1.5). The angle of incidence is \[{{50}^{o}}\]. The deviation of the ray is
A) \[{{0}^{o}}\]
B) \[{{80}^{o}}\]
C) \[{{50}^{0}}-{{\sin }^{-1}}\left[ \frac{\sin {{50}^{0}}}{1.5} \right]\]
D) \[{{\sin }^{-1}}\left[ \frac{\sin {{50}^{0}}}{1.5} \right]-{{50}^{0}}\]
View Answer play_arrowquestion_answer32) A vessel of height 2d is half-filled with a liquid of refractive index \[\sqrt{2}\] and the other half with a liquid of refractive index n (the given liquids are immiscible). Then the apparent depth of the inner surface of the bottom of the vessel (neglecting the thickness of the bottom of the vessel) will be
A) \[\frac{n}{d(n+\sqrt{2})}\]
B) \[\frac{d\,(n+\sqrt{2})}{n\sqrt{2}}\]
C) \[\frac{\sqrt{2}n}{d\,(n+\sqrt{2})}\]
D) \[\frac{nd}{d+\sqrt{2}n}\]
View Answer play_arrowquestion_answer33) A ray of light is incident normally on one face of a right angled isosceles prism. It then grazes the hypotenuse. The refractive index of the material of the prism is
A) 1.33
B) 1.414
C) 1.5
D) 1.732
View Answer play_arrowquestion_answer34) Two thin equiconvex lenses each of focal length 0.2 m are placed coaxially with their optic centres 0.5 m apart. Then the focal length of the combination is
A) -0.4 m
B) 0.4 m
C) - 0.1 m
D) 0.1 m
View Answer play_arrowquestion_answer35) A prism of a certain angle deviates the red and blue rays by \[{{8}^{o}}\] and \[{{12}^{o}}\] respectively. Another prism of the same angle deviates the red and blue rays by \[{{10}^{o}}\] and \[{{14}^{o}}\] respectively. The prisms are small angled and made of different materials. The dispersive powers of the materials of the prisms are in the ratio
A) \[5:6\]
B) \[9:11\]
C) \[6:5\]
D) \[11:9\]
View Answer play_arrowquestion_answer36) When the angle of incidence is \[{{60}^{o}}\] on the surface of a glass slab, it is found that the reflected ray is completely polarised. The velocity of light in glass is
A) \[\sqrt{2}\times {{10}^{8}}m{{s}^{-1}}\]
B) \[\sqrt{3}\times {{10}^{8}}m{{s}^{-1}}\]
C) \[2\times {{10}^{8}}m{{s}^{-1}}\]
D) \[3\times {{10}^{8}}m{{s}^{-1}}\]
View Answer play_arrowquestion_answer37) A 20 cm length of a certain solution causes right handed rotation of \[{{38}^{o}}\]. A 30 cm length of another solution causes left handed rotation of \[{{24}^{o}}\]. The optical rotation caused by 30 cm length of a mixture of the above solutions in the volume ratio \[1:2\] is
A) left handed rotation of \[{{14}^{o}}\]
B) right handed rotation of \[{{14}^{o}}\]
C) left handed rotation of \[{{3}^{o}}\]
D) right handed rotation of \[{{3}^{o}}\]
View Answer play_arrowquestion_answer38) Two identical charges repel each other with a force equal to 10 mg wt when they are 0.6 m a part in air \[(g=10\text{ }m{{s}^{-2}})\]. The value of each charge is
A) 2 mC
B) \[2\times {{10}^{-7}}C\]
C) 2 nC
D) \[2\,\mu C\]
View Answer play_arrowquestion_answer39) The potential of the electric Held produced by point charge at any point \[(x,y,z)\] is given by\[V=3{{x}^{2}}+5\], where \[x,y\] are in metres and V is m volts. The intensity of the electric Held at \[(-2,1,0)\] is
A) \[+17\text{ }V{{m}^{-1}}\]
B) \[-17\text{ }V{{m}^{-1}}\]
C) \[+12\text{ }V{{m}^{-1}}\]
D) \[-12\text{ }V{{m}^{-1}}\]
View Answer play_arrowquestion_answer40) The potential of a large liquid drop when eight liquid drops are combined is 20 V. Then the potential of each single drop was
A) 10 V
B) 7.5 V
C) 5 V
D) 2.5 V
View Answer play_arrowquestion_answer41) The dimensional formula for impulse is
A) \[[ML{{T}^{-1}}]\]
B) \[[M{{L}^{-1}}T]\]
C) \[[{{M}^{-1}}L{{T}^{-1}}]\]
D) \[[M{{L}^{-1}}{{T}^{-1}}]\]
View Answer play_arrowquestion_answer42) The maximum height attained by a projectile when thrown at an angle \[\theta \] with the horizontal is found to be half the horizontal range. Then 0 is equal to
A) \[{{\tan }^{-1}}\left( 2 \right)\]
B) \[\frac{\pi }{6}\]
C) \[\frac{\pi }{4}\]
D) \[{{\tan }^{-1}}\left( \frac{1}{2} \right)\]
View Answer play_arrowquestion_answer43) A shell of mass 20 kg at rest explodes into two fragments whose masses are in the ratio \[2:3\]. The smaller fragment moves with a velocity of\[6\,\,m{{s}^{-1}}\]. The kinetic energy of the larger fragment is
A) 96 J
B) 216 J
C) 144 J
D) 360 J
View Answer play_arrowquestion_answer44) Water rises in plant fibres due to
A) capillarity
B) viscosity
C) fluid pressure
D) osmosis
View Answer play_arrowquestion_answer45) The acceleration due to gravity becomes \[\left( \frac{g}{2} \right)\] (g = acceleration due to gravity on the surface of the earth) at a height equal to
A) 4 R
B) \[\frac{R}{4}\]
C) 2 R
D) \[\frac{R}{2}\]
View Answer play_arrowquestion_answer46) The cylindrical tube of a spray pump has a cross-section of \[8\text{ }c{{m}^{2}}\], one end of which has 40 fine holes each of area \[{{10}^{-8}}{{m}^{2}}\]. If the liquid flows inside the tube with a speed of\[0.15\text{ }m\text{ }mi{{n}^{-1}}\], the speed with which the liquid is ejected through the holes is
A) \[50\text{ }m{{s}^{-1}}\]
B) \[5\text{ }m{{s}^{-1}}\]
C) \[0.05\text{ }m{{s}^{-1}}\]
D) \[0.5\text{ }m{{s}^{-1}}\]
View Answer play_arrowquestion_answer47) During an adiabatic process, the cube of the pressure is found to be inversely proportional to the fourth power of the volume. Then the ratio of specific heats is
A) 1
B) 1.33
C) 1.67
D) 1.4
View Answer play_arrowquestion_answer48) Two identical rods AC and CB made of two different metals having thermal conductivities in the ratio \[2:3\] are kept in contact with each other at the end C as shown in the figure. A is at \[{{100}^{o}}C\] and B is at \[{{25}^{o}}C\]. Then the junction C is at
A) \[{{55}^{o}}C\]
B) \[{{60}^{o}}C\]
C) \[{{75}^{o}}C\]
D) \[{{50}^{o}}C\]
View Answer play_arrowquestion_answer49) 310 J of heat is required to raise the temperature of 2 moles of an ideal gas at constant pressure from \[{{25}^{o}}C\] to \[{{35}^{o}}C\]. The amount of heat required to raise the temperature of the gas through the same range at constant volume is
A) 384 J
B) 144 J
C) 276 J
D) 452 J
View Answer play_arrowquestion_answer50) A Carnot's engine operates with source at \[{{127}^{o}}C\] and sink at \[{{27}^{o}}C\]. If the source supplies 40 kJ of heat energy, the work done by the engine is
A) 30 kJ
B) 10 kJ
C) 4 kJ
D) 1 kJ
View Answer play_arrowquestion_answer51) The maximum particle velocity in a wave motion is half the wave velocity. Then the amplitude of the wave is equal to
A) \[\frac{\lambda }{4\pi }\]
B) \[\frac{2\lambda }{\pi }\]
C) \[\frac{\lambda }{2\pi }\]
D) \[\lambda \]
View Answer play_arrowquestion_answer52) The ratio of the velocity of sound in hydrogen\[\left( \gamma =7/5 \right)\]to that in helium \[\left( \gamma =\frac{5}{3} \right)\] at the same temperature is
A) \[\sqrt{\frac{5}{42}}\]
B) \[\sqrt{\frac{5}{21}}\]
C) \[\frac{\sqrt{42}}{5}\]
D) \[\frac{\sqrt{21}}{5}\]
View Answer play_arrowquestion_answer53) An engine moving towards a wall with a velocity \[50\text{ }m{{s}^{-1}}\] emits a note of 1.2 kHz. Speed of sound in air is \[350\text{ }m{{s}^{-1}}\]. The frequency of the note after reflection from the wall as heard by the driver of the engine is
A) 2.4 kHz
B) 0.24 kHz
C) 1.6 kHz
D) 1.2 kHz
View Answer play_arrowquestion_answer54) A glass tube is open at both the ends. A tuning fork of frequency \[f\] resonates with the air column inside the tube. Now the tube is placed vertically inside water so that half the length of the tube is filled with water. Now the air column inside the tube is in unison with another fork of frequency \[f'\]. Then
A) \[f'=f\]
B) \[f'=4f\]
C) \[f'=2f\]
D) \[f'=\frac{f}{2}\]
View Answer play_arrowquestion_answer55) The surface temperature of the sun which has maximum energy emission at 500 nm is 6000 K. The temperature of a star which has maximum energy emission at 400 nm will be
A) 8500 K
B) 4500 K
C) 7500 K
D) 6500 K
View Answer play_arrowquestion_answer56) The volume of a nucleus is directly proportional to
A) A
B) \[{{A}^{3}}\]
C) \[\sqrt{A}\]
D) \[{{A}^{1/3}}\] (where A = mass number of the nucleus)
View Answer play_arrowquestion_answer57) An electron is
A) a hadron
B) a baryon
C) a nucleon
D) a lepton
View Answer play_arrowquestion_answer58) Minority carriers in a p-type semiconductor are
A) free electrons
B) holes
C) neither holes nor free electrons
D) both holes and free electrons
View Answer play_arrowquestion_answer59) In a reverse biased diode when the applied voltage changes by 1 V, the current is found to change by \[0.5\,\mu A\] The reverse bias resistance of the diode is
A) \[2\times {{10}^{5}}\Omega \]
B) \[2\times {{10}^{6}}\Omega \]
C) \[200\,\Omega \]
D) \[2\,\Omega \]
View Answer play_arrowquestion_answer60) The truth table given below is for CA and B are the inputs, Y is the output)
A | B | Y |
0 | 0 | 1 |
0 | 1 | 1 |
1 | 0 | 1 |
1 | 1 | 0 |
A) NOR
B) AND
C) XOR
D) NAND
View Answer play_arrowquestion_answer61) The number of unidentate ligands in the complex ion is called
A) oxidation number
B) primary valency
C) coordination number
D) EAN
View Answer play_arrowquestion_answer62) \[2S{{O}_{2}}(g)+{{O}_{2}}(g)\] is an example for
A) neutralisation reaction
B) homogeneous catalysis
C) heterogeneous catalysis
D) irreversible reaction
View Answer play_arrowquestion_answer63) The amino acid which is not optically active is
A) lactic acid
B) serine
C) alanine
D) glycine
View Answer play_arrowquestion_answer64) For a stable molecule, the value of bond order must be
A) there is no relationship between stability and bond order
B) zero
C) positive
D) negative
View Answer play_arrowquestion_answer65) Which one of the following is a second order reaction?
A) \[{{H}_{2}}+B{{r}_{2}}\xrightarrow{{}}2HBr\]
B) \[N{{H}_{4}}N{{O}_{3}}\xrightarrow{{}}{{N}_{2}}+3{{H}_{2}}O\]
C) \[{{H}_{2}}+C{{l}_{2}}\xrightarrow{sunlight}2HCl\]
D) \[C{{H}_{3}}COOCH+NaOH\xrightarrow{{}}C{{H}_{3}}COONa\]\[+{{H}_{2}}0\]
View Answer play_arrowquestion_answer66) Denatured alcohol is
A) ethanol + methahol
B) rectified spirit + methanol + naphtha
C) undistilled ethanol
D) rectified spirit
View Answer play_arrowquestion_answer67) During the formation of a chemical bond
A) electron-electron repulsion becomes more than the nucleus-electron attraction
B) energy of the system does not change
C) energy increases
D) energy decreases
View Answer play_arrowquestion_answer68) One mole of oxygen at 273 K and one mole of sulphur dioxide at 546 K are taken in two separate containers, then,
A) kinetic energy of \[{{O}_{2}}>\] kinetic energy of\[S{{O}_{2}}\]
B) kinetic energy of \[{{O}_{2}}<\] kinetic energy of\[S{{O}_{2}}\]
C) kinetic energy of both are equal
D) None of the above
View Answer play_arrowquestion_answer69) \[+I\] effect is shown by
A) \[-C{{H}_{3}}\]
B) \[-Br\]
C) \[-Cl\]
D) \[-N{{O}_{2}}\]
View Answer play_arrowquestion_answer70) Formation of coloured solution is possible when metal ion in the compound contains
A) paired electrons
B) lone pair of electrons
C) unpaired electrons
D) none of the above
View Answer play_arrowquestion_answer71) Benzene reacts with chlorine in sunlight to give a final product
A) \[CC{{l}_{4}}\]
B) \[{{C}_{6}}{{H}_{6}}C{{l}_{6}}\]
C) \[{{C}_{6}}C{{l}_{6}}\]
D) \[{{C}_{6}}{{H}_{5}}Cl\]
View Answer play_arrowquestion_answer72) In the periodic table metals usually used as catalysts belong to
A) \[f-\]block
B) d-block
C) p-block
D) s-block
View Answer play_arrowquestion_answer73) Dalton's law of partial pressure is applicable to which one of the following systems?
A) \[N{{H}_{3}}+HCl\]
B) \[NO+{{O}_{2}}\]
C) \[{{H}_{2}}+C{{l}_{2}}\]
D) \[CO+{{H}_{2}}\]
View Answer play_arrowquestion_answer74) The general formula of a cycloalkane is
A) \[{{C}_{n}}\,\,{{H}_{n}}\]
B) \[{{C}_{n}}\,\,{{H}_{2n}}\]
C) \[{{C}_{n}}\,\,{{H}_{2n-n}}\]
D) \[{{C}_{n}}\,\,{{H}_{2n\,+\,2}}\]
View Answer play_arrowquestion_answer75) In acetylene molecule, between the carbon atoms there are
A) three pi bonds
B) one sigma and two pi bonds
C) two sigma and one pi bonds
D) three sigma bonds
View Answer play_arrowquestion_answer76) Which of the following is an intensive property?
A) temperature
B) viscosity
C) surface tension
D) all of these
View Answer play_arrowquestion_answer77) Hofmann's bromamide reaction is to convert
A) acid to alcohol
B) alcohol to acid
C) amide to amine
D) amine to amide
View Answer play_arrowquestion_answer78) IUPAC name of \[N{{a}_{3}}[Co{{(N{{O}_{2}})}_{6}}]\] is
A) sodium hexanitrito cobaltate (II)
B) sodium hexanitro cobaltate (III)
C) sodium hexanitrito cobaltate (III)
D) sodium cobaltmitrite
View Answer play_arrowquestion_answer79) In equilibrium state the value of \[\Delta G\] is
A) zero
B) negative
C) positive
D) may be negative or positive
View Answer play_arrowquestion_answer80) How many chiral carbon atoms are present in 2,3, 4-trichloropentane?
A) 4
B) 1
C) 2
D) 3
View Answer play_arrowquestion_answer81) Which one of the following shows functional isomerism?
A) \[{{C}_{2}}{{H}_{4}}\]
B) \[{{C}_{3}}{{H}_{6}}\]
C) \[{{C}_{2}}{{H}_{5}}OH\]
D) \[C{{H}_{2}}C{{l}_{2}}\]
View Answer play_arrowquestion_answer82) In the ionic equation \[-BiO_{3}^{-}+6{{H}^{+}}+x{{e}^{-}}\xrightarrow{{}}\]\[B{{i}^{3+}}+3{{H}_{2}}O\], the values of \[x\] is
A) 6
B) 2
C) 4
D) 3
View Answer play_arrowquestion_answer83) Molarity of a given orthophosphoric acid solution is 3 M. It's normality is
A) 9 N
B) 0.3 N
C) 3 N
D) 1 N
View Answer play_arrowquestion_answer84) Acidified sodium fusion extract on addition of ferric chloride solution gives blood red colouration which confirms the presence of
A) S and \[Cl\]
B) N and S
C) N
D) S
View Answer play_arrowquestion_answer85) A body of mass 10 mg is moving with a velocity of \[100\,\,m{{s}^{-1}}\]. The wavelength of de-Broglie wave associated with it would be \[(h=6.63\times {{10}^{-34}}Js)\]
A) \[6.63\times {{10}^{-35}}m\]
B) \[6.63\times {{10}^{-34}}m\]
C) \[6.63\times {{10}^{-31}}m\]
D) \[6.63\times {{10}^{-37}}m\]
View Answer play_arrowquestion_answer86) Angle strain in cyclopropane is
A) \[{{24}^{o}}44'\]
B) \[{{9}^{o}}44'\]
C) \[44'\]
D) \[-{{5}^{o}}16'\]
View Answer play_arrowquestion_answer87) The number of antibonding electron pairs in \[O_{2}^{2-}\] molecular ion on the basis of molecular orbital theory is (Atomic number of 0 is 18.)
A) 5
B) 4
C) 3
D) 2
View Answer play_arrowquestion_answer88) Hydroxyl ion concentration of \[{{10}^{-2}}M\,HCl\] is
A) \[1\times {{10}^{1}}\,mol\,d{{m}^{-3}}\]
B) \[1\times {{10}^{-12}}\,mol\,d{{m}^{-3}}\]
C) \[1\times {{10}^{-1}}\,mol\,d{{m}^{-3}}\]
D) \[1\times {{10}^{-14}}\,mol\,d{{m}^{-3}}\]
View Answer play_arrowquestion_answer89) Geometrical isomerism is shown by
A) \[-C-C-\]
B) \[\rangle C=C\langle \]
C) \[-C\equiv C-\]
D) None of these
View Answer play_arrowquestion_answer90) The oxidation state of iron in \[{{K}_{4}}[Fe{{(CN)}_{6}}]\]is
A) 1
B) 4
C) 3
D) 2
View Answer play_arrowquestion_answer91) During the extraction of gold the following reactions take place \[Au+C{{N}^{-}}+{{H}_{2}}O\xrightarrow{{{O}_{2}}}[X]\]\[[X]+Zn\xrightarrow{{}}[Y]+Au\]X and Y are respectively
A) \[{{[Au{{(CN)}_{2}}]}^{-}}\] and \[{{[Zn{{(CN)}_{6}}]}^{4-}}\]
B) \[{{[Au{{(CN)}_{4}}]}^{2-}}\] and \[{{[Zn{{(CN)}_{4}}]}^{2-}}\]
C) \[{{[Au{{(CN)}_{4}}]}^{3-}}\] and \[{{[Zn{{(CN)}_{4}}]}^{2-}}\]
D) \[{{[Au{{(CN)}_{2}}]}^{-}}\] and \[{{[Zn{{(CN)}_{4}}]}^{2-}}\]
View Answer play_arrowquestion_answer92) The number of gram molecules of chlorine in \[6.02\times {{10}^{25}}\] hydrogen chloride molecules is
A) 10
B) 100
C) 50
D) 5
View Answer play_arrowquestion_answer93) Graphite is a soft solid lubricant extremely difficult to melt. The reason for this anomalous behaviour is that graphite
A) is an allotropic form of carbon
B) is a non-crystalline substance
C) has carbon atoms arranged in large plates of rings of strongly bond carbon atoms with weak interplate bonds
D) has molecules of variable molecular masses like polymers
View Answer play_arrowquestion_answer94) Paracetamol is a/an
A) antipyretic
B) analgesic
C) both (a) and (b)
D) antimalarial
View Answer play_arrowquestion_answer95) Which one of the following has maximum number of atoms of oxygen?
A) 2 g of carbon monoxide
B) 2 g of carbon dioxide
C) 2 g of sulphur dioxide
D) 2 g of water
View Answer play_arrowquestion_answer96) \[M{{g}^{2+}}\] is isoelectronic with
A) \[C{{u}^{2+}}\]
B) \[Z{{n}^{2+}}\]
C) \[N{{a}^{+}}\]
D) \[C{{a}^{2+}}\]
View Answer play_arrowquestion_answer97) Gram molecular volume of oxygen at STP is
A) \[3200\,c{{m}^{3}}\]
B) \[5600\,c{{m}^{3}}\]
C) \[22400\,c{{m}^{3}}\]
D) \[11200\,c{{m}^{3}}\]
View Answer play_arrowquestion_answer98) Presence of halogen in organic compounds can be detected using
A) Leibigstest
B) Duma's test
C) Kjeldahltest
D) Beilstien?s test
View Answer play_arrowquestion_answer99) The electronic configuration of \[C{{r}^{3+}}\] is
A) \[[Ar]\,3{{d}^{4}}4{{s}^{2}}\]
B) \[[Ar]\,3{{d}^{3}}4{{s}^{0}}\]
C) \[[Ar]\,3{{d}^{2}}4{{s}^{1}}\]
D) \[[Ar]\,3{{d}^{5}}4{{s}^{1}}\]
View Answer play_arrowquestion_answer100) What is the equivalent weight of \[SnC{{l}_{2}}\] in the following reaction\[SnC{{l}_{2}}+C{{l}_{2}}\xrightarrow{{}}SnC{{l}_{4}}?\]
A) 95
B) 45
C) 60
D) 30
View Answer play_arrowquestion_answer101) Which of the following forms a colourless solution in aqueous medium?
A) \[C{{r}^{3+}}\]
B) \[{{V}^{3+}}\]
C) \[S{{c}^{3+}}\]
D) \[T{{i}^{3+}}\]
View Answer play_arrowquestion_answer102) When a sulphur sol is evaporated sulphur is obtained. On mixing with water sulphur sol is not formed. The sol is
A) lyophilic
B) reversible
C) hydrophobic
D) hydrophilic
View Answer play_arrowquestion_answer103) An alkyl halide reacts with alcoholic ammonia in a sealed tube, the product formed will be
A) a primary amine
B) a secondary amine
C) a tertiary amine
D) a mixture of all the three
View Answer play_arrowquestion_answer104) When cone. \[{{H}_{2}}S{{O}_{4}}\] is heated with \[{{P}_{2}}{{O}_{5}}\] the acid is converted into
A) sulphur trioxide
B) sulphur dioxide
C) sulphur
D) a mixture of sulphur dioxide and sulphur trioxide
View Answer play_arrowquestion_answer105) Entropy of the universe is
A) constant
B) zero
C) continuously decreasing
D) continuously increasing
View Answer play_arrowquestion_answer106) Which one of the following salts on being dissolved in water gives \[pH>7\] at \[{{25}^{o}}C\]?
A) \[KCN\]
B) \[KN{{O}_{3}}\]
C) \[N{{H}_{4}}Cl\]
D) \[N{{H}_{4}}CN\]
View Answer play_arrowquestion_answer107) The reagent used in Clemmensen?s reduction is
A) conc.\[{{H}_{2}}S{{O}_{4}}\]
B) Zn?Hg/conc.\[HCl\]
C) \[aqKOH~\]
D) ale. \[KOH\]
View Answer play_arrowquestion_answer108) When \[KBr\] is dissolved in water, \[{{K}^{+}}\] ions are
A) hydrated
B) hydrolysed
C) reduced
D) oxidized
View Answer play_arrowquestion_answer109) The noble gas mixture is cooled in a coconut bulb at 173 K. The gases that are not adsorbed are
A) Ne and Xe
B) He and Xe
C) Ar and Kr
D) He and Ne
View Answer play_arrowquestion_answer110) The volume of 10 N and 4 N \[HCl\] required to make 1 L of 7 N \[HCl\]are
A) 0.50 L of \[10\text{ }N\,HCl\] and 0.50 L of 4 N \[HCl\]
B) 0.60 L of \[10\text{ }N\,HCl\] and 0.40 L of 4 N \[HCl\]
C) 0.80 L of \[10\text{ }N\,HCl\] and 0.20 L of 4 N \[HCl\]
D) 0.75 L of \[10\text{ }N\,HCl\] and 0.25 L of 4 N \[HCl\]
View Answer play_arrowquestion_answer111) A metal present in vitamin \[{{B}_{12}}\] is
A) aluminium
B) zinc
C) iron
D) cobalt
View Answer play_arrowquestion_answer112) An oxide of the element contains 20% \[{{O}_{2}}\] by weight. Calculate the equivalent weight of the element.
A) 8
B) 16
C) 32
D) 12
View Answer play_arrowquestion_answer113) Maximum number of molecules of \[C{{H}_{3}}I\] that can react with a molecule of \[C{{H}_{3}}N{{H}_{2}}\] are
A) 3
B) 4
C) 2
D) 1
View Answer play_arrowquestion_answer114) The relation between \[\Delta \,H\] and \[\Delta \,U\] is
A) \[\Delta \,H=\Delta U+RT\]
B) \[\Delta \,H=\Delta U-\Delta nRT\]
C) \[\Delta \,H=\Delta U+\Delta nRT\]
D) \[\Delta \,U=\Delta H+\Delta nRT\]
View Answer play_arrowquestion_answer115) Identify the ore not cotaining iron.
A) limonite
B) siderite
C) carnallite
D) chalcopyrites
View Answer play_arrowquestion_answer116) In which of the following process, maximum increase in entropy is observed?
A) Melting of ice
B) - Sublimation of naphthalene
C) Condensation of water
D) Dissolution of salt in water
View Answer play_arrowquestion_answer117) Decomposition of benzene diazonium chloride by using \[C{{u}_{2}}C{{l}_{2}}/HCl\] to form chlorobenzene is
A) Raschig's reaction
B) Sandmeyer's reaction
C) Kolbe's reaction
D) Cannizaro's reaction
View Answer play_arrowquestion_answer118) Which complex cannot ionise in solution?
A) \[[CoC{{l}_{3}}{{(N{{H}_{3}})}_{3}}]\]
B) \[{{K}_{4}}[Fe{{(CN)}_{6}}]\]
C) \[{{K}_{2}}[Pt({{F}_{6}})]\]
D) \[[Pt{{(N{{H}_{3}})}_{6}}]C{{l}_{4}}\]
View Answer play_arrowquestion_answer119) Considering the reaction \[C(s)+{{O}_{2}}(g)\] \[\xrightarrow{{}}C{{O}_{2}}(g)+393.5\,kJ\] the signs of \[\Delta H,\,\,\Delta S\] and \[\Delta G\] respectively are
A) \[+,-,-\]
B) \[-,+,+\]
C) \[-,-,-\]
D) \[-,+,-\]
View Answer play_arrowquestion_answer120) The product formed when hydroxylamine condenses with a carbonyl compound is called
A) hydrazide
B) oxime
C) hydrazine
D) hydrazine
View Answer play_arrowquestion_answer121) If \[\vec{a}=2\hat{i}+3\hat{j}-k,\] \[\vec{b}=\hat{i}+2\hat{j}-5\hat{k},\] \[\vec{c}=3\hat{i}+5\hat{j}-\hat{k},\]Then a vector perpendicular to \[\vec{a}\]and in the plane containing \[\overrightarrow{b}\] and \[\overrightarrow{c}\] is
A) \[-17\hat{i}+21\hat{j}-97\hat{k}\]
B) \[17\hat{i}+21\hat{j}-123\hat{k}\]
C) \[-17\hat{i}-21\hat{j}+97\hat{k}\]
D) \[-17\hat{i}-21\hat{j}-97\hat{k}\]
View Answer play_arrowquestion_answer122) \[\overrightarrow{OA}\] and \[\overrightarrow{BO}\] are two vectors of magnitudes 5 and 6 respectively. If Z \[\angle BOA={{60}^{o}},\]then \[\overrightarrow{OA}.\overrightarrow{OB}\]is equal to
A) \[0\]
B) \[15\]
C) \[-15\]
D) \[15\sqrt{3}\]
View Answer play_arrowquestion_answer123) A vector perpendicular to the plane containing the points \[A(1,-1,2),\] \[B(2,0,-1),\] \[C(0,2,1)\] is
A) \[4\hat{i}+8\hat{j}-4\hat{k}\]
B) \[8\hat{i}+4\hat{j}+4\hat{k}\]
C) \[3\hat{i}+\hat{j}+2\hat{k}\]
D) \[\hat{i}+\hat{j}-\hat{k}\]
View Answer play_arrowquestion_answer124) \[\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+....\frac{1}{(3n-1)(3n+2)}\]is equal to
A) \[\frac{n}{6n-4}\]
B) \[\frac{n}{6n+3}\]
C) \[\frac{n}{6n+4}\]
D) \[\frac{n+1}{6n+4}\]
View Answer play_arrowquestion_answer125) The ninth term of the expansion \[{{\left( 3x-\frac{1}{2x} \right)}^{8}}\] is
A) \[\frac{1}{512{{x}^{9}}}\]
B) \[\frac{-1}{512{{x}^{9}}}\]
C) \[\frac{-1}{256.{{x}^{8}}}\]
D) \[\frac{1}{256.{{x}^{8}}}\]
View Answer play_arrowquestion_answer126) The solution of is \[{{\tan }^{-1}}x+2{{\cot }^{-1}}x=\frac{2\pi }{3}\]is
A) \[-\frac{1}{\sqrt{3}}\]
B) \[\frac{1}{\sqrt{3}}\]
C) \[-\sqrt{3}\]
D) \[\sqrt{3}\]
View Answer play_arrowquestion_answer127) \[{{\sin }^{2}}{{17.5}^{o}}+{{\sin }^{2}}{{72.5}^{o}}\] is equal to
A) \[{{\cos }^{2}}{{90}^{o}}\]
B) \[{{\tan }^{2}}{{45}^{o}}\]
C) \[co{{s}^{2}}{{30}^{o}}\]
D) \[{{\sin }^{2}}{{45}^{o}}\]
View Answer play_arrowquestion_answer128) The conjugate of the complex number \[\frac{{{(1+i)}^{2}}}{1-i}\]is
A) \[1-i\]
B) \[1+i\]
C) \[-1+i\]
D) \[-1-i\]
View Answer play_arrowquestion_answer129) ABC is a triangle with \[\angle A={{30}^{o}},\] \[BC=10\text{ }cm\]. The area of the circum circle of the triangle is
A) \[100\pi \,sq\,m\]
B) \[5\,sq\,cm\]
C) \[25\,sq\,cm\]
D) \[\frac{100\pi }{3}\,sq\,cm\]
View Answer play_arrowquestion_answer130) If \[\sin \,3\theta =\sin \theta ,\]how many solutions exist such that \[-2\pi <\theta <2\pi \]?
A) \[8\]
B) \[9\]
C) \[5\]
D) \[7\]
View Answer play_arrowquestion_answer131) A graph G has ?m' vertices of odd degree and ?n' vertices of even degree. Then which of the following statements is necessarily true?
A) \[m+n\]is an odd number
B) \[m+n\] is an even number
C) \[n+1\]is an even number
D) \[m+1\]is an odd number
View Answer play_arrowquestion_answer132) If P is any point on the ellipse \[\frac{{{x}^{2}}}{36}+\frac{{{y}^{2}}}{16}=1,\] and S and S' are the foci, then \[PS+PS'\]is equal to
A) \[4\]
B) \[8\]
C) \[10\]
D) \[12\]
View Answer play_arrowquestion_answer133) The value of \[\sin \left[ 2{{\cos }^{-1}}\frac{\sqrt{5}}{3} \right]\] is
A) \[\frac{\sqrt{5}}{3}\]
B) \[\frac{2\sqrt{5}}{3}\]
C) \[\frac{4\sqrt{5}}{9}\]
D) \[\frac{2\sqrt{5}}{9}\]
View Answer play_arrowquestion_answer134) If \[\frac{{{x}^{2}}}{36}-\frac{{{y}^{2}}}{{{k}^{2}}}=1\] is a hyperbola, then which of the following statements can by true?
A) \[(-3,1)\] lies on the hyperbola
B) \[(3,1)\]lies on the hyperbola
C) \[(10,4)\]lies on the hyperbola
D) \[(5,2)\] lies on the hyperbola
View Answer play_arrowquestion_answer135) The focus of the parabola \[y=2{{x}^{2}}+x\]is
A) \[(0,0)\]
B) \[\left( \frac{1}{2},\frac{1}{4} \right)\]
C) \[\left( -\frac{1}{4},0 \right)\]
D) \[\left( -\frac{1}{4},\frac{1}{8} \right)\]
View Answer play_arrowquestion_answer136) If \[A\left[ \begin{matrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \\ \end{matrix} \right],10B=\left[ \begin{matrix} 4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3 \\ \end{matrix} \right]\] and B is the inverse of A, then the value of \[\alpha \] is
A) \[2\]
B) \[0\]
C) \[5\]
D) \[4\]
View Answer play_arrowquestion_answer137) If \[A=\left[ \begin{matrix} 0 & x & 16 \\ x & 5 & 7 \\ 0 & 9 & x \\ \end{matrix} \right]\] is singular, then the possible values of x are
A) \[0,12,-12\]
B) \[0,1,-1\]
C) \[0,4,-4\]
D) \[0,5,-5\]
View Answer play_arrowquestion_answer138) If \[A=\left[ \begin{matrix} 1 & -2 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \\ \end{matrix} \right]\] then A . adj is equal to
A) \[\left[ \begin{matrix} 5 & 1 & 1 \\ 1 & 5 & 1 \\ 1 & 1 & 5 \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} 8 & 0 & 0 \\ 0 & 8 & 0 \\ 0 & 0 & 8 \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ \end{matrix} \right]\]
View Answer play_arrowquestion_answer139) If \[f:R\to R\] is defined by \[f(x)=|x|,\]then
A) \[{{f}^{-1}}(x)=-x\]
B) \[{{f}^{-1}}(x)=\frac{1}{|x|}\]
C) the function \[{{f}^{-1}}(x)\] does not exist
D) \[{{f}^{-1}}(x)=\frac{1}{x}\]
View Answer play_arrowquestion_answer140) The value of \[\left| \begin{matrix} x & p & q \\ p & x & q \\ p & q & x \\ \end{matrix} \right|\] is
A) \[x(x-p)(x-q)\]
B) \[(x-p)(x-q)(x+p+q)\]
C) \[(p-q)(x-q)(x-p)\]
D) \[pq(x-p)(x-q)\]
View Answer play_arrowquestion_answer141) The imaginary part of \[{{i}^{i}}\]is
A) \[0\]
B) \[1\]
C) \[2\]
D) \[-1\]
View Answer play_arrowquestion_answer142) The amplitude of \[{{(1+i)}^{5}}\] is
A) \[\frac{3\pi }{4}\]
B) \[\frac{-3\pi }{4}\]
C) \[\frac{-5\pi }{4}\]
D) \[\frac{5\pi }{4}\]
View Answer play_arrowquestion_answer143) ABC is triangle. G is the centroid. D is the mid point of BC. If \[A=(2,3)\] and \[G=(7,5),\] then the point D is
A) \[\left( \frac{9}{2},4 \right)\]
B) \[\left( \frac{19}{2},6 \right)\]
C) \[\left( \frac{11}{2},\frac{11}{2} \right)\]
D) \[\left( 8,\frac{13}{2} \right)\]
View Answer play_arrowquestion_answer144) \[\underset{x\to 1}{\mathop{\lim }}\,\,\frac{\tan ({{x}^{2}}-1)}{x-1}\]is equal to
A) \[2\]
B) \[\frac{1}{2}\]
C) \[-2\]
D) \[\frac{-1}{2}\]
View Answer play_arrowquestion_answer145) If \[y={{2}^{\log x}},\] then \[\frac{dy}{dx}\] is
A) \[\frac{{{2}^{\log x}}}{\log 2}\]
B) \[{{2}^{\log x}}.\log 2\]
C) \[\frac{{{2}^{\log x}}}{x}\]
D) \[\frac{{{2}^{\log x}}.\log 2}{x}\]
View Answer play_arrowquestion_answer146) \[{{7}^{2{{\log }_{7}}5}}\]is equal to
A) \[{{\log }_{7}}35\]
B) \[5\]
C) \[25\]
D) \[{{\log }_{7}}25\]
View Answer play_arrowquestion_answer147) In the group \[(G,\,\,{{\otimes }_{15}}),\] where \[G=\{3,6,9,12\},\]\[{{\otimes }_{15}}\]is multiplication modulo 15, the identity element is
A) \[3\]
B) \[6\]
C) \[12\]
D) \[9\]
View Answer play_arrowquestion_answer148) A group \[(G,*)\] has 10 elements. The minimum number of elements of G, which are their own inverses is
A) \[2\]
B) \[1\]
C) \[9\]
D) \[0\]
View Answer play_arrowquestion_answer149) If \[\vec{a}\] and \[\vec{b}\] are vectors such that \[|\vec{a}+\vec{b}|\]\[=|\vec{a}-\vec{b}|,\] then the angle between \[\vec{a}\] and \[\vec{b}\]is
A) \[{{120}^{o}}\]
B) \[{{60}^{o}}\]
C) \[{{90}^{o}}\]
D) \[{{30}^{o}}\]
View Answer play_arrowquestion_answer150) \[\frac{3{{x}^{2}}+1}{{{x}^{2}}-6x+8}\]is equal to
A) \[3+\frac{49}{2(x-4)}-\frac{13}{2(x-2)}\]
B) \[\frac{49}{2(x-4)}-\frac{13}{2(x-2)}\]
C) \[\frac{-49}{2(x-4)}-\frac{13}{2(x-2)}\]
D) \[\frac{49}{2(x-4)}+\frac{13}{2(x-2)}\]
View Answer play_arrowquestion_answer151) The number of common tangents to the circles \[{{x}^{2}}+{{y}^{2}}=4\]and \[{{x}^{2}}+{{y}^{2}}-6x-8y-24=0\]is,
A) \[3\]
B) \[4\]
C) \[2\]
D) \[1\]
View Answer play_arrowquestion_answer152) If \[3x+y+k=0\] is a tangent to the circle \[{{x}^{2}}+{{y}^{2}}=10,\] the values of k are,
A) \[\pm 7\]
B) \[\pm 5\]
C) \[\pm 10\]
D) \[\pm 9\]
View Answer play_arrowquestion_answer153) The negation of the proposition "If 2 is prime, then 3 is odd" is
A) if 2 is not prime, then 3 is not odd
B) 2 is prime and 3 is. not odd
C) 2 is not prime and 3 is odd
D) if 2 is not prime, then 3 is odd
View Answer play_arrowquestion_answer154) The equation of two circles which touch the Y-axis at \[(0,3)\] and make an intercept of 8 unit on X-axis are
A) \[{{x}^{2}}+{{y}^{2}}\pm 10x-6y+9=0\]
B) \[{{x}^{2}}+{{y}^{2}}\pm 6x-10y+9=0\]
C) \[{{x}^{2}}+{{y}^{2}}-8x\pm 10y+9=0\]
D) \[{{x}^{2}}+{{y}^{2}}+10x\pm 6y+9=0\]
View Answer play_arrowquestion_answer155) The orthocenter of the triangle with vertices \[A(0,0),\] \[B\left( 0,\frac{3}{2} \right),\] \[C(-5,0)\]is
A) \[\left( \frac{5}{2},\frac{3}{4} \right)\]
B) \[\left( \frac{-5}{2},\frac{3}{4} \right)\]
C) \[\left( -5,\frac{3}{2} \right)\]
D) \[(0,0)\]
View Answer play_arrowquestion_answer156) \[{{x}^{2}}+{{y}^{2}}-6x-6y+4=0,\] \[{{x}^{2}}+{{y}^{2}}-2x\]\[-4y+3=0,\] \[{{x}^{2}}+{{y}^{2}}+2kx+2y+1=0\]. If the radical centre of the above three circles exists, then which of the following cannot be the value off k?
A) \[2\]
B) \[1\]
C) \[5\]
D) \[4\]
View Answer play_arrowquestion_answer157) If the circles \[{{x}^{2}}+{{y}^{2}}-2x-2y-7=0\]and \[{{x}^{2}}+{{y}^{2}}+4x+2y+k=0\] cut orthogonally, then the length of the common chord of the circles is
A) \[\frac{12}{\sqrt{13}}\]
B) \[2\]
C) \[5\]
D) \[8\]
View Answer play_arrowquestion_answer158) The coordinates of the foot of the perpendicular drawn from the point \[(3,4)\] on the line \[2x+y-7=0\] is
A) \[\left( \frac{9}{5},\frac{17}{5} \right)\]
B) \[(1,5)\]
C) \[(5,1)\]
D) \[(1,-5)\]
View Answer play_arrowquestion_answer159) The area enclosed by the pair of the lines \[xy=0,\] the line \[x-4=0\]and \[y+5=0\] is
A) \[20\,sq\,unit\]
B) \[10\,sq\,unit\]
C) \[\frac{5}{4}\,sq\,unit\]
D) \[0\,sq\,unit\]
View Answer play_arrowquestion_answer160) If the area of the auxiliary circle of the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] \[(a>b)\] is twice the area of the ellipse, then the eccentricity of the ellipse is
A) \[\frac{1}{\sqrt{2}}\]
B) \[\frac{\sqrt{3}}{2}\]
C) \[\frac{1}{\sqrt{3}}\]
D) \[\frac{1}{2}\]
View Answer play_arrowquestion_answer161) The range in which \[y=-{{x}^{2}}+6x-3\] is increasing is
A) \[x<3\]
B) \[x>3\]
C) \[7<x<8\]
D) \[5<x<6\]
View Answer play_arrowquestion_answer162) The value of the integral\[\int_{0}^{\pi /2}{({{\sin }^{100}}x-{{\cos }^{100}}x)dx}\]is
A) \[\frac{1}{100}\]
B) \[\frac{100!}{{{(100)}^{100}}}\]
C) \[\frac{\pi }{100}\]
D) \[0\]
View Answer play_arrowquestion_answer163) OA and OB are two roads enclosing an angle of\[{{120}^{o}}\]. X and y start from ?O' at the same time. X travels along OA with a speed of 4 km/h and Y travels along OB with a speed of 3 km/h. The rate at which the shortest distance between X and V is increasing after \[1\text{ }h\]is
A) \[\sqrt{37}km/h\]
B) \[37m/h\]
C) \[13km/h\]
D) \[\sqrt{13}km/h\]
View Answer play_arrowquestion_answer164) If \[k\int_{0}^{1}{x}.f(3x)dx=\int_{0}^{3}{t.f(t)dt,}\] then the value of k is
A) \[9\]
B) \[3\]
C) \[\frac{1}{9}\]
D) \[\frac{1}{3}\]
View Answer play_arrowquestion_answer165) The value of \[\int{\frac{1}{1+\cos \,8\,x}}dx\]is
A) \[\frac{\tan \,2x}{8}+c\]
B) \[\frac{\tan \,8x}{8}+c\]
C) \[\frac{\tan \,4x}{4}+c\]
D) \[\frac{\tan \,4x}{8}+c\]
View Answer play_arrowquestion_answer166) If \[{{\sec }^{-1}}\left( \frac{1+x}{1-y} \right)=a,\]then \[\frac{dy}{dx}\] is
A) \[\frac{y-1}{x+1}\]
B) \[\frac{y+1}{x-1}\]
C) \[\frac{x-1}{y-1}\]
D) \[\frac{x-1}{y+1}\]
View Answer play_arrowquestion_answer167) If \[y={{\cos }^{2}}\frac{3x}{2}-{{\sin }^{2}}\frac{3x}{2},\] then \[\frac{{{d}^{2}}y}{d{{x}^{2}}}\]is
A) \[-3\sqrt{1-{{y}^{2}}}\]
B) \[9y\]
C) \[-9y\]
D) \[3\sqrt{1-{{y}^{2}}}\]
View Answer play_arrowquestion_answer168) If the function \[f(x)=\left\{ \begin{matrix} \frac{1-\cos \,\,x}{{{x}^{2}}} & for & x\ne 0 \\ k & for & x=0 \\ \end{matrix} \right.\]is continuous at \[x=0,\] then the value of k is
A) \[1\]
B) \[0\]
C) \[\frac{1}{2}\]
D) \[-1\]
View Answer play_arrowquestion_answer169) If \[1,\,\omega ,\,{{\omega }^{2}}\] are the cube roots of unity then \[(1+\omega )(1+{{\omega }^{2}})(1+{{\omega }^{4}})(1+{{\omega }^{8}})\]is equal to
A) \[1\]
B) \[0\]
C) \[{{\omega }^{2}}\]
D) \[\omega \]
View Answer play_arrowquestion_answer170) If \[{{x}^{x}}={{y}^{y}},\]then \[\frac{dy}{dx}\]is
A) \[-\frac{y}{x}\]
B) \[-\frac{x}{y}\]
C) \[1+\log \left( \frac{x}{y} \right)\]
D) \[\frac{1+\log x}{1+\log y}\]
View Answer play_arrowquestion_answer171) The value of \[\int{{{e}^{x}}({{x}^{5}}+5{{x}^{4}}}+1).dx\]is
A) \[{{e}^{x}}.{{x}^{5}}+c\]
B) \[{{e}^{x}}.{{x}^{5}}+{{e}^{x}}+c\]
C) \[{{e}^{x+1}}.{{x}^{5}}+c\]
D) \[5{{x}^{4}}.{{e}^{x}}+c\]
View Answer play_arrowquestion_answer172) The value of \[\int{\frac{{{x}^{2}}+1}{{{x}^{2}}-1}}dx\] is
A) \[\log \left( \frac{x-1}{x+1} \right)+c\]
B) \[\log \left( \frac{x+1}{x-1} \right)+c\]
C) \[x+\log \left( \frac{x-1}{x+1} \right)+c\]
D) \[\log ({{x}^{2}}-1)+c\]
View Answer play_arrowquestion_answer173) The area bounded by the curve \[x=4-{{y}^{2}}\]and the Y-axis is
A) \[16\text{ }sq\text{ }unit\]
B) \[32\text{ }sq\text{ }unit\]
C) \[\frac{32}{3}\text{ }sq\text{ }unit~~\]
D) \[\frac{16}{3}sq\text{ }unit\]
View Answer play_arrowquestion_answer174) The differential equation of the family of straight lines whose slope is equal to y-intercept is
A) \[(x+1)\frac{dy}{dx}-y=0\]
B) \[(x+1)\frac{dy}{dx}+y=0\]
C) \[\frac{dy}{dx}=\frac{x-1}{y-1}\]
D) \[\frac{dy}{dx}=\frac{x+1}{y+1}\]
View Answer play_arrowquestion_answer175) The order and degree of the differential equation \[{{\left[ 1+{{\left( \frac{dy}{dx} \right)}^{5}} \right]}^{\frac{1}{3}}}=\frac{{{d}^{2}}y}{d{{x}^{2}}}\] are respectively
A) \[1,5\]
B) \[2,1\]
C) \[2,5\]
D) \[2,3\]
View Answer play_arrowquestion_answer176) The point on the curve \[{{y}^{2}}=x,\]the tangent at which makes an angle \[{{45}^{o}}\] with -X-axis is
A) \[\left( \frac{1}{4},\frac{1}{2} \right)\]
B) \[\left( \frac{1}{2},\frac{1}{4} \right)\]
C) \[\left( \frac{1}{2},\frac{-1}{2} \right)\]
D) \[\left( \frac{1}{2},\frac{1}{2} \right)\]
View Answer play_arrowquestion_answer177) The length of the sub tangent to the curve \[{{x}^{2}}{{y}^{2}}={{a}^{4}}\] at \[(-a,a)\] is
A) \[\frac{a}{2}\]
B) \[2a\]
C) \[a\]
D) \[\frac{a}{3}\]
View Answer play_arrowquestion_answer178) The number of positive divisors of \[252\] is
A) \[9\]
B) \[5\]
C) \[18\]
D) \[10\]
View Answer play_arrowquestion_answer179) The remainder obtained when \[{{5}^{124}}\]is divided by \[124\] is
A) \[5\]
B) \[0\]
C) \[2\]
D) \[1\]
View Answer play_arrowquestion_answer180) Which of the following is not a group with respect to the given operation?
A) The set of even integers under addition
B) The set, of odd integers under addition
C) \[\{0\}\] under addition
D) \[\{1,-1\}\]under multiplication
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