question_answer1) All capacitors used in the diagram are identical and each is of capacitance C. Then the effective capacitance between the point A and B is
A) 1.5 C
B) 6 C
C) C
D) 3 C
View Answer play_arrowquestion_answer2) Two identical conducting balls A and B have positive charges \[{{q}_{1}}\] and \[{{q}_{2}}\] respectively but \[{{q}_{1}}\ne {{q}_{2}}.\] The balls are brought together so that they touch each other and then kept in their original positions. The force between them is
A) less than that before the balls touched
B) greater than that before the balls touched
C) same as that before the balls touched
D) zero
View Answer play_arrowquestion_answer3) Red light of wavelength 625 nm is incident normally on an optical diffraction grating with \[2\times {{10}^{5}}\] lines/m. Including central principal maxima, how many maxima may be observed on a screen which is far from the grating?
A) 15
B) 17
C) 8
D) 16
View Answer play_arrowquestion_answer4) A battery of emf E has an internal resistance r. A variable resistance R is connected to the terminals of the battery. A current; is drawn from the battery. V is the terminal potential difference. If R alone is gradually reduced to zero, which of the following best describes \[i\]and V?
A) \[i\]approaches zero, V approaches E
B) \[i\] approaches \[\frac{E}{r}\], V approaches zero
C) \[i\] approaches \[\frac{E}{r}\], V approaches E
D) \[i\] approaches infinity, V approaches E
View Answer play_arrowquestion_answer5) Three voltmeters A, B and C having resistances R, 1.5R and 3 R respectively are used in a circuit as shown. When a potential difference is applied between X and Y, the readings of the voltmeters are \[{{V}_{1}},\text{ }{{V}_{2}}\], and \[{{V}_{3}}\]respectively. Then
A) \[{{V}_{1}}={{V}_{2}}={{V}_{3}}\]
B) \[{{V}_{1}}<{{V}_{2}}={{V}_{3}}\]
C) \[{{V}_{1}}>{{V}_{2}}>{{V}_{3}}\]
D) \[{{V}_{1}}>{{V}_{2}}={{V}_{3}}\]
View Answer play_arrowquestion_answer6) A point object O is placed in front of a glass rod having spherical end of radius of curvature 30 cm. The image would be formed at
A) 30 cm left
B) infinity
C) 1 cm to the right
D) 18 cm to the left
View Answer play_arrowquestion_answer7) A, B and C are the parallel sided transparent media of refractive indices \[{{n}_{1}},{{n}_{2}}\] and \[{{n}_{3}}\]respectively. They are arranged as shown in the figure. A ray is incident at an angle \[i\] on the surface of separation of A and B which is as shown in the figure. After the refraction into the medium B, the ray grazes the surface of separation of the madia B and C. Then, \[\sin i\] equals to
A) \[\frac{{{n}_{3}}}{{{n}_{1}}}\]
B) \[\frac{{{n}_{1}}}{{{n}_{3}}}\]
C) \[\frac{{{n}_{2}}}{{{n}_{3}}}\]
D) \[\frac{{{n}_{1}}}{{{n}_{2}}}\]
View Answer play_arrowquestion_answer8) A boat has green light of wavelength \[\lambda =500\,nm\] on the mast. What wavelength would be measured and what colour would be observed for this light as seen by a diver submerged in water by the side of the boat? Given, \[{{n}_{w}}=\frac{4}{3}\].
A) Green of wavelength 376 nm
B) Red of wavelength 665 nm
C) Green of wavelength 500 nm
D) Blue of wavelength 376 nm
View Answer play_arrowquestion_answer9) Two beams of red and violet colours are made to pass separately through a prism of \[A={{60}^{o}}\]. In the minimum deviation position, the angle of refraction inside the prism will be
A) greater for red colour
B) equal but not \[{{30}^{o}}\] for both the colours
C) greater for violet colour
D) \[{{30}^{o}}\] for both the colours
View Answer play_arrowquestion_answer10) A plano-convex lens is made of refractive index of 1.6. The radius of curvature of the curved surface is 60 cm. The focal length of the lens is
A) 400 cm
B) 200 cm
C) 100 cm
D) 50 cm
View Answer play_arrowquestion_answer11) Two simple harmonic motions are represented by \[{{y}_{1}}=5[\sin 2\pi t+\sqrt{3}\cos 2\pi t]\]and \[{{y}_{2}}=5\sin \left( 2\pi t+\frac{\pi }{4} \right)\] The ratio of their amplitudes is
A) \[1:1\]
B) \[2:1\]
C) \[1:3\]
D) \[\sqrt{3}:1\]
View Answer play_arrowquestion_answer12) A bat flies at a steady speed of \[4\text{ }m{{s}^{-1}}\] emitting a sound of \[f=90\times {{10}^{3}}Hz\]. It is flying horizontally towards a vertical wall. The frequency of the reflected sound as detected by the bat will be (take velocity of sound in air is \[330\text{ }m{{s}^{-1}}\])
A) \[88.1\times {{10}^{3}}Hz\]
B) \[87.1\times {{10}^{3}}Hz\]
C) \[92.1\times {{10}^{3}}Hz\]
D) \[89.1\times {{10}^{3}}Hz\]
View Answer play_arrowquestion_answer13) A closed organ pipe and an open organ pipe of same length produce 2 beats/second while vibrating in their fundamental modes. The length of the open organ pipe is halved and that of closed pipe is doubled. Then the number of beats produced per second while vibrating in the fundamental mode is
A) 2
B) 6
C) 8
D) 7
View Answer play_arrowquestion_answer14) A uniform wire of length L, diameter D and density \[\rho \] is stretched under a tension T. The correct relation between, its fundamental frequency \[f\], the length L and the diameter D is
A) \[f\propto \frac{1}{LD}\]
B) \[f\propto \frac{1}{L\sqrt{D}}\]
C) \[f\propto \frac{1}{{{D}^{2}}}\]
D) \[f\propto \frac{1}{L{{D}^{2}}}\]
View Answer play_arrowquestion_answer15) Two small spheres of masses \[{{M}_{1}}\] and \[{{M}_{2}}\]are suspended by weightless insulating threads of lengths \[{{L}_{1}}\] and \[{{L}_{2}}\]. The spheres carry charges \[{{Q}_{1}}\] and \[{{Q}_{2}}\] respectively. The spheres are suspended such that they are in level with one another and the threads are inclined to the vertical at angles of \[{{\theta }_{1}}\] and \[{{\theta }_{2}}\] as shown. Which one of the following conditions is essential, if \[{{\theta }_{1}}={{\theta }_{2}}\]?
A) \[{{M}_{1}}\ne {{M}_{2}},\] but \[{{Q}_{1}}={{Q}_{2}}\]
B) \[{{M}_{1}}={{M}_{2}}\]
C) \[{{Q}_{1}}={{Q}_{2}}\]
D) \[{{L}_{1}}={{L}_{2}}\]
View Answer play_arrowquestion_answer16) The wavelength of the light used in Young's double slit experiment is \[\lambda \]. The intensity at a point on the screen is \[I\], where the path difference is \[\frac{\lambda }{6}\]. If \[{{I}_{0}}\] denotes the maximum intensity, then the ratio of \[I\] and \[{{I}_{0}}\] is
A) 0.866
B) 0.5
C) 0.707
D) 0.75
View Answer play_arrowquestion_answer17) What is the minimum thickness of a thin film required for constructive interference in the reflected light from it? Given, the refractive index of the film = 1.5, wavelength of the light incident on the film = 600 nm.
A) 100 nm
B) 300 nm
C) 50 nm
D) 200 nm
View Answer play_arrowquestion_answer18) There is a uniform electric field of intensity E which is as shown. How many labelled points have the same electric potential as the fully shaded point?
A) 2
B) 3
C) 8
D) 11
View Answer play_arrowquestion_answer19) Critical angle for certain medium is \[si{{n}^{-1}}(0.6)\]. The polarizing angle of that medium is
A) \[ta{{n}^{-1}}[1.5]\]
B) \[{{\sin }^{-1}}[0.8]\]
C) \[{{\tan }^{-1}}[1.6667]\]
D) \[{{\tan }^{-1}}[0.6667]\]
View Answer play_arrowquestion_answer20) The speed of electromagnetic wave in vacuum depends upon the source of radiation
A) increases as we move from \[\gamma \]-rays to radio waves
B) decreases as we move from \[\gamma \]-rays to radio waves
C) is same for all of them
D) None of the above
View Answer play_arrowquestion_answer21) The moment of inertia of a circular disc of radius 2 m and mass 1 kg about an axis passing through the centre of mass but perpendicular to the plane of the disc is\[2\text{ }kg\text{ }{{m}^{2}}\]. Its moment of inertia about an axis parallel to this axis but passing through the edge of the disc is (see the given figure).
A) \[8\text{ }kg\text{ }{{m}^{2}}\]
B) \[4\text{ }kg\text{ }{{m}^{2}}\]
C) \[10\text{ }kg\text{ }{{m}^{2}}\]
D) \[6\text{ }kg\text{ }{{m}^{2}}\]
View Answer play_arrowquestion_answer22) An astronaut on a strange planet finds that acceleration due to gravity is twice as that on the surface of earth. Which of the following could explain this?
A) Both the mass and radius of the planet are half as that of earth
B) Radius of the planet is half as that of earth, but the mass is the same as that of earth
C) Both the mass and radius of the planet are twice as that of earth
D) Mass of the planet is half as that of earth, but radius is same as that of earth
View Answer play_arrowquestion_answer23) Which of the following substances has the highest elasticity?
A) Sponge
B) Steel
C) Rubber
D) Copper
View Answer play_arrowquestion_answer24) Three liquids of equal masses are taken in three identical cubical vessels A, B and C. Their densities are \[{{\rho }_{A}},{{\rho }_{B}}\] and \[{{\rho }_{C}}\]respectively but \[{{\rho }_{A}}<{{\rho }_{B}}<{{\rho }_{C}}.\] The force exerted by the liquid on the base of the cubical vessel is
A) maximum in vessel C
B) minimum in vessel C
C) the same in all the vessels
D) maximum in vessel A
View Answer play_arrowquestion_answer25) Water is in streamline flows along a horizontal pipe with non-uniform cross-section. At a point in the pipe where the area of cross section is \[10\text{ }c{{m}^{2}}\], the velocity of water is \[1\text{ }m{{s}^{-1}}\] and the pressure is 2000 Pa. The pressure at another point where the cross sectional area is \[5\text{ }c{{m}^{2}}\] is
A) 4000 Pa
B) 2000 Pa
C) 1000 Pa
D) 500 Pa
View Answer play_arrowquestion_answer26) In the circuit given here, the points A, B and C are 70 V, zero, 10 V respectively. Then
A) the point D will be at a potential of 60 V
B) the point D will be at a potential of 20 V
C) currents in the paths AD, DB and DC are in the ratio of \[1:2:3\]
D) currents in the paths AB, DB and DC are in the ratio of \[3:2:1\]
View Answer play_arrowquestion_answer27) \[{{B}_{1}},{{B}_{2}}\] and \[{{B}_{3}}\] are the three identical bulbs connected to a battery of steady emf with key K closed. What happens to the brightness of the bulbs \[{{B}_{1}}\] and \[{{B}_{2}}\] when the key is opened?
A) Brightness of the bulb \[{{B}_{1}}\] increases and that of \[{{B}_{2}}\] decreases
B) Brightness of the bulbs \[{{B}_{1}}\] and \[{{B}_{2}}\]increase
C) Brightness of the bulb \[{{B}_{1}}\] decreases and \[{{B}_{2}}\]increases
D) Brightness of the bulbs \[{{B}_{1}}\] and \[{{B}_{2}}\]decrease
View Answer play_arrowquestion_answer28) Magnetic field at the centre of a circular coil of radius R due to \[i\] flowing through it is B. The magnetic field at a point along the axis at distance R from the centre is
A) \[\frac{B}{2}\]
B) \[\frac{B}{4}\]
C) \[\frac{B}{\sqrt{8}}\]
D) \[\sqrt{8}B\]
View Answer play_arrowquestion_answer29) Two thick wires and two thin wires, all of same material and same length, form a square in three different ways P, Q and R as shown in the figure. With correct connections shown, the magnetic field due to the current flow, at the centre of the loop will be zero in case of
A) Q and R
B) P only
C) P and Q
D) P and R
View Answer play_arrowquestion_answer30) There is a uniform magnetic field directed perpendicular and into the plane of the paper. An irregular shaped conducting loop is slowly changing into a circular loop in the plane of the paper. Then
A) current is induced in the loop in the anticlockwise direction
B) current is induced in the loop in the clockwise direction
C) AC is induced in the loop
D) no current is induced in the loop
View Answer play_arrowquestion_answer31) The dimensions of resistance are same as those of..... .where h is the Planck's constant, e is the charge.
A) \[\frac{{{h}^{2}}}{{{e}^{2}}}\]
B) \[\frac{{{h}^{2}}}{e}\]
C) \[\frac{h}{{{e}^{2}}}\]
D) \[\frac{h}{e}\]
View Answer play_arrowquestion_answer32) A train is moving slowly on a straight track with a constant speed of \[2\text{ }m{{s}^{-1}}\]. A passenger in that train starts walking at a steady speed of \[2\text{ }m{{s}^{-1}}\] to the back of the train in the opposite direction of the motion of the train. So to an observer standing on the platform directly in front of that passenger, the velocity of the passenger appears to be
A) \[4\,m{{s}^{-1}}\]
B) \[2\,m{{s}^{-1}}\]
C) \[2\,m{{s}^{-1}}\] in the opposite direction of the train
D) zero
View Answer play_arrowquestion_answer33) A ball rests upon a flat piece of paper on a table top. The paper is pulled horizontally but quickly towards right as shown relative to its initial position with respect to the table, the ball
A) Both (1) and (2)
B) only (3)
C) only (1)
D) only (2)
View Answer play_arrowquestion_answer34) A boy throws a cricket ball from the boundary to the wicket-keeper. If the frictional force due to air cannot be ignored, the forces acting on the ball at the position X are respected by
A)
B)
C)
D)
View Answer play_arrowquestion_answer35) If the linear momentum of a body is increased by 50%, then the kinetic energy of that body increases by
A) 100%
B) 125%
C) 225%
D) 25%
View Answer play_arrowquestion_answer36) The temperature of a gas contained in a closed vessel of constant volume increases by \[{{1}^{o}}C\] when the pressure of the gas is increased by 1%. The initial temperature of the gas is
A) 100 K
B) \[{{273}^{o}}C\]
C) \[{{100}^{o}}C\]
D) 200 K
View Answer play_arrowquestion_answer37) A motorboat covers a given distance in 6 h moving downstream on a river. It covers the same distance in 10 h moving upstream. The time it takes to cover the same distance in still water is
A) 9 h
B) 7.5 h
C) 6.5 h
D) 8 h
View Answer play_arrowquestion_answer38) Two slabs are of the thicknesses \[{{d}_{1}}\] and \[{{d}_{2}}\]. Their thermal conductivities are \[{{K}_{1}}\] and \[{{K}_{2}}\] respectively. They are in series. The free ends of the combination of these two slabs are kept at temperatures \[{{\theta }_{1}}\] and \[{{\theta }_{2}}\]. Assume \[{{\theta }_{1}}>{{\theta }_{2}}\]. The temperature \[\theta \] of their common junction is
A) \[\frac{{{K}_{1}}{{\theta }_{1}}+{{K}_{2}}{{\theta }_{2}}}{{{\theta }_{1}}+{{\theta }_{2}}}\]
B) \[\frac{{{K}_{1}}{{\theta }_{1}}{{d}_{1}}+{{K}_{2}}{{\theta }_{2}}{{d}_{2}}}{{{K}_{1}}{{d}_{2}}+{{K}_{2}}{{d}_{1}}}\]
C) \[\frac{{{K}_{1}}{{\theta }_{1}}{{d}_{2}}+{{K}_{2}}{{\theta }_{2}}{{d}_{1}}}{{{K}_{1}}{{d}_{2}}+{{K}_{2}}{{d}_{1}}}\]
D) \[\frac{{{K}_{1}}{{\theta }_{1}}+{{K}_{2}}{{\theta }_{2}}}{{{K}_{1}}+{{K}_{2}}}\]
View Answer play_arrowquestion_answer39) Hot water cools from \[{{60}^{o}}C\] to \[{{50}^{o}}C\] in the first 10 min and to \[{{42}^{o}}C\] in the next 10 min. Then the temperature of the surroundings is
A) \[{{20}^{o}}C\]
B) \[{{30}^{o}}C\]
C) \[{{15}^{o}}C\]
D) \[{{10}^{o}}C\]
View Answer play_arrowquestion_answer40) The efficiency of Carnot's heat heat engine is 0.5 when the temperature of the source is \[{{T}_{1}}\]that of sink is \[{{T}_{2}}\]. The efficiency of source. Carnot's heat engine is also 0.5. The temperatures of source and second engine are respectively
A) \[2{{T}_{1}},2{{T}_{2}}\]
B) \[2{{T}_{1}},\frac{{{T}_{2}}}{2}\]
C) \[{{T}_{1}}+5,\,{{T}_{2}}-5\]
D) \[{{T}_{1}}+10,\,{{T}_{2}}-10\]
View Answer play_arrowquestion_answer41) A current \[i\] is flowing through the loop. The direction of the current and the shape of the loop are as shown in the figure. The magnetic field at the centre of the loop is \[\frac{{{\mu }_{0}}i}{R}\] times
A) \[\frac{5}{16},\] but out of the plane of the paper
B) \[\frac{5}{16},\] but into the plane of the paper
C) \[\frac{7}{16},\] but out of the plane of the paper
D) \[\frac{7}{16},\] but into the plane of the paper
View Answer play_arrowquestion_answer42) An ideal choke draws a current of 8 A when connected to an AC supply of 100 V, 50 Hz. A pure resistor draws a current of 10 A when connected to the same source. The ideal choke and the resistor are connected in series and then connected to the AC source of 150 V, 40 Hz. The current in the circuit becomes
A) \[\frac{15}{\sqrt{2}}A\]
B) 8 A
C) 18 A
D) 10 A
View Answer play_arrowquestion_answer43) The spectrum of an oil flame is an example for
A) line emission spectrum
B) continuous emission spectrum
C) line absorption spectrum
D) band emission spectrum
View Answer play_arrowquestion_answer44) According to Einstein's photoelectric equation, the graph of KE of the photoelectron emitted from the metal versus the frequency of the incident radiation gives a straight line graph, whose slope
A) depends on the intensity of the incident radiation
B) depends on the nature of the metal and also on the intensity of incident radiation
C) is same for all metals and independent of the intensity of the incident radiation
D) depends on the nature of the metal
View Answer play_arrowquestion_answer45) An electron is moving in an orbit of a hydrogen atom from which there can be a maximum of six transition. An electron is moving in an orbit of another hydrogen atom from which there can be a maximum of three transition. The ratio of the velocities of the electron in these two orbits is
A) \[\frac{1}{2}\]
B) \[\frac{2}{1}\]
C) \[\frac{5}{4}\]
D) \[\frac{3}{4}\]
View Answer play_arrowquestion_answer46) \[{{v}_{1}}\] is the frequency of the series limit of Lyman series, \[{{v}_{2}}\] is the frequency of the first line of Lyman series and \[{{v}_{3}}\] is the frequency of the series limit of the Balmer series. Then
A) \[{{v}_{1}}-{{v}_{2}}={{v}_{3}}\]
B) \[{{v}_{1}}={{v}_{2}}-{{v}_{3}}\]
C) \[\frac{1}{{{v}_{1}}}=\frac{1}{{{v}_{1}}}+\frac{1}{{{v}_{3}}}\]
D) \[\frac{1}{{{v}_{1}}}=\frac{1}{{{v}_{1}}}+\frac{1}{{{v}_{3}}}\]
View Answer play_arrowquestion_answer47) Assume the graph of specific binding energy versus mass number is as shown in the figure. Using this graph, select the correct choice from the following.
A) Fusion of two nuclei of mass number lying in the range of \[100<A<200\] will release energy
B) Fusion of two nuclei of mass number lying in the range of \[51<A<100\] will release energy
C) Fusion of two nuclei of mass number lying in the range of \[1<A<50\] will release energy
D) Fission of the nucleus of mass number lying in the rang of \[100<A<200\] will release energy when broken into two fragments
View Answer play_arrowquestion_answer48) Pick out the correct statement from the following.
A) Energy released per unit mass of the reactant is less in case of fusion reaction
B) Packing fraction may be positive or may be negative
C) \[P{{u}^{239}}\] is not suitable for a fission reaction
D) For stable nucleus, the specific binding energy is low
View Answer play_arrowquestion_answer49) A radioactive sample \[{{S}_{1}}\] having the activity \[{{A}_{1}}\] has twice the number of nuclei as another sample \[{{S}_{2}}\] of activity \[{{A}_{2}}\]. If \[{{A}_{2}}=2{{A}_{1}}\], then the ratio of half-life of \[{{S}_{1}}\] to the half-life of \[{{S}_{2}}\] is
A) 4
B) 2
C) 0.25
D) 0.75
View Answer play_arrowquestion_answer50) When a neutron is disintegrated to give a \[\beta \]-particle,
A) a neutrino alone is emitted
B) a proton and neutrino are emitted
C) a proton alone is emitted
D) a proton and an antineutrino are emitted
View Answer play_arrowquestion_answer51) The forbidden energy gap in Ge is 0.72 eV, Given, \[hc=12400\text{ }eV-\overset{o}{\mathop{A}}\,\]. The maximum wavelength of radiation that will generate electron hole pair is
A) \[172220\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
B) \[172.2\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
C) \[17222\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
D) \[1722\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
View Answer play_arrowquestion_answer52) In a p-n junction diode not connected to any circuit
A) the potential is the same everywhere
B) the p-type side has a higher potential than the n-type side
C) there is an electric field at the junction directed from the n-type side to p-type side
D) there is an electric field at the junction directed from the p-type side to n-type side
View Answer play_arrowquestion_answer53) In a given direction, the intensities of the scattered light by a scattering substance for two beams of light are in the ratio of \[256:81\]. The ratio of the frequency of the first beam to the frequency of the second beam is
A) \[64:127\]
B) \[1:2\]
C) \[64:27\]
D) None of these
View Answer play_arrowquestion_answer54) Identify the logic operation performed by the circuit given here.
A) OR
B) NOR
C) NOT
D) NAND
View Answer play_arrowquestion_answer55) The de-Broglie wavelength of the electron in the ground state of the hydrogen atom is ...... (radius of the first orbit of hydrogen atom\[=0.53\overset{o}{\mathop{A}}\,\]).
A) \[1.67\overset{o}{\mathop{A}}\,\]
B) \[3.33\overset{o}{\mathop{A}}\,\]
C) \[1.06\overset{o}{\mathop{A}}\,\]
D) \[0.53\overset{o}{\mathop{A}}\,\]
View Answer play_arrowquestion_answer56) PQ and RS are long parallel conductors separated by certain distance. M is the midpoint between them (see the figure). The net magnetic field at M is B. Now, the current 2 A is switched off. The field at M now becomes
A) 2 B
B) B
C) \[\frac{B}{2}\]
D) 35
View Answer play_arrowquestion_answer57) An electron enters the space between the plates of a charged capacitor as shown. The charge density on the plate is \[\sigma \]. Electric intensity in the space between the plates is A uniform magnetic field B also exists in the space perpendicular to the direction of E. The electron moves perpendicular to both \[\overrightarrow{E}\] and \[\overrightarrow{B}\] without any change in direction. The time taken by the electron to travel a distance l in the space is
A) \[\frac{\sigma l}{{{\varepsilon }_{0}}B}\]
B) \[\frac{\sigma B}{{{\varepsilon }_{0}}l}\]
C) \[\frac{{{\varepsilon }_{0}}lB}{\sigma B}\]
D) \[\frac{{{\varepsilon }_{0}}l}{\sigma B}\]
View Answer play_arrowquestion_answer58) In a series resonant R-L-C circuit, the voltage across R is 100 V and the value of \[R=1000\,\Omega \]. The capacitance of the capacitor is \[2\times {{10}^{-6}}F\]; angular frequency of AC is \[200\text{ }rad\text{ }{{s}^{-1}}\]. Then the potential difference across the inductance coil is
A) 100 V
B) 40 V
C) 250 V
D) 400 V
View Answer play_arrowquestion_answer59) A capacitor and an inductance coil are connected in separate AC circuits with a bulb glowing in both the circuits. The bulb glows more brightly when
A) an iron rod is introduced into the inductance coil
B) the number of turns in the inductance coil is increased
C) separation between the plates of the capacitor is increased
D) a dielectric is introduced into the gap between the plates of the capacitor
View Answer play_arrowquestion_answer60) A charge +Q is moving upwards vertically. It enters a magnetic field directed to north. The force on the charge will be towards
A) north
B) south
C) east
D) west
View Answer play_arrowquestion_answer61) In the electrolytic refining of zinc
A) graphite is at the anode
B) the impure metal is at the cathode
C) the metal ion get reduced at the anode
D) acidified zinc sulphate is the electrolyte
View Answer play_arrowquestion_answer62) The wave number of the spectral line in the emission spectrum of hydrogen will be equal to \[\frac{8}{9}\] times the Rydberg's constant if the electron jumps from
A) \[n=3\] to \[n=1\]
B) \[n=10\] to \[n=1\]
C) \[n=9\] to \[n=1\]
D) \[n=2\] to \[n=1\]
View Answer play_arrowquestion_answer63) Consider the following gaseous equilibria with equilibrium constants \[{{K}_{1}}\]and \[{{K}_{2}}\] respectively. \[S{{O}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)S{{O}_{3}}(g)\] \[2S{{O}_{3}}(g)2S{{O}_{2}}(g)+{{O}_{2}}(g)\] The equilibrium constants are related as
A) \[K_{1}^{2}=\frac{1}{{{K}_{2}}}\]
B) \[2{{K}_{1}}=K_{2}^{2}\]
C) \[{{K}_{2}}=\frac{2}{K_{1}^{2}}\]
D) \[K_{2}^{2}=\frac{1}{{{K}_{1}}}\]
View Answer play_arrowquestion_answer64) Enthalpy of vaporization of benzene is \[+\,\,35.3\,kJ\,\,mo{{l}^{-1}}\] at its boiling point, \[{{80}^{o}}C\]. The entropy change in the transition of the vapour to liquid at its boiling point in \[[J{{K}^{-1}}mo{{l}^{-1}}]\] is
A) -441
B) -100
C) +441
D) +100
View Answer play_arrowquestion_answer65) Which one of the following conversions involve change in both hybridisation and shape?
A) \[C{{H}_{4}}\xrightarrow{{}}{{C}_{2}}{{H}_{6}}\]
B) \[N{{H}_{3}}\xrightarrow{{}}NH_{4}^{+}\]
C) \[B{{F}_{3}}\xrightarrow{{}}BF_{4}^{-}\]
D) \[{{H}_{2}}O\xrightarrow{{}}{{H}_{3}}{{O}^{+}}\]
View Answer play_arrowquestion_answer66) In chromite ore, the oxidation number of iron, and chromium are respectively
A) + 3, + 2
B) + 3, + 6
C) + 2, + 6
D) + 2, + 3
View Answer play_arrowquestion_answer67) For the reversible reaction. \[A\,(s)+B(g)C\,(g)+D(g);\]\[\Delta {{G}^{o}}=-350\,\,kJ\] Which one of the following statements is true?
A) The entropy change is negative
B) Equilibrium constant is greater than one
C) The reaction should be instantaneous
D) The reaction is thermodynamically not feasible
View Answer play_arrowquestion_answer68) Out of the compounds below the vapour pressure of at a particular temperature is
A) higher than that of
B) lower than that of
C) higher or lower than, depending on the size of the vessel
D) same as that of
View Answer play_arrowquestion_answer69) The amount of heat evolved when \[500\text{ }c{{m}^{3}}\] of \[0.1\text{ }M\,HCl\] is mixed with \[200\text{ }c{{m}^{3}}\] of \[0.2\text{ }NaOH\] is
A) 2.292 kJ
B) 1.292kJ
C) 0.292 kJ
D) 3.392 kJ
View Answer play_arrowquestion_answer70) During the adsorption of krypton on activated charcoal at low temperature
A) \[\Delta H>0\] and \[\Delta S<0\]
B) \[\Delta H<0\] and \[\Delta S<0\]
C) \[\Delta H>0\] and \[\Delta S>0\]
D) \[\Delta H<0\] and \[\Delta S>0\]
View Answer play_arrowquestion_answer71) The set of quantum numbers for the outermost electron for copper in its ground state is
A) \[4,\,\,1,\,\,1,+\frac{1}{2}\]
B) \[3,\,\,2,\,\,2,+\frac{1}{2}\]
C) \[4,\,\,0,\,\,0,+\frac{1}{2}\]
D) \[4,\,\,2,\,\,2,+\frac{1}{2}\]
View Answer play_arrowquestion_answer72) Peroxide ion ......
A) (ii) and (iii)
B) (i), (ii) and (iv)
C) (i), (ii) and (iii)
D) (i) and (iv)
View Answer play_arrowquestion_answer73) Which one of these is not true for benzene?
A) It forms only one type of mono substituted product
B) There are three carbon-carbon single bonds and three carbon-carbon double bonds
C) The heat of hydrogenation of benzene is less than the theoretical value
D) The bond angle between the carbon-carbon bonds is \[{{120}^{o}}\]
View Answer play_arrowquestion_answer74) A mixture of \[CaC{{l}_{2}}\] and \[NaCl\] weighing 4.44 g is treated with sodium carbonate solution to precipitate all the \[C{{a}^{2+}}\] ions as calcium carbonate. The calcium carbonate so obtained is heated strongly to get 0.56 g of CaO. The percentage of \[NaCl\] in the mixture (atomic mass of \[Ca=40\]) is
A) 75
B) 30.6
C) 25
D) 69.4
View Answer play_arrowquestion_answer75) For one mole of an ideal gas, increasing the temperature from \[{{10}^{o}}C\] to \[{{20}^{o}}C\]
A) increases the average kinetic energy by two times
B) increases the rms velocity by \[\sqrt{2}\] times
C) increases the rms velocity by two times
D) increases both the average kinetic energy and rms velocity, but not significantly
View Answer play_arrowquestion_answer76) Generally, the first ionization energy increases along a period. But there are some exceptions. One which is not an exception is
A) N and O
B) Na and Mg
C) Mg and Al
D) Be and B
View Answer play_arrowquestion_answer77) \[50\,\,c{{m}^{3}}\] of \[0.2\text{ }N\,HCl\] is titrated against \[0.1\text{ }N\,NaOH\] solution. The titration is discontinued after adding \[50\,\,c{{m}^{3}}\] of \[NaOH\]. The remaining titration is completed by adding \[0.5\text{ }N\,KOH\]. The volume of \[KOH\]required for completing the titration is
A) \[12\,\,c{{m}^{3}}\]
B) \[10\,\,c{{m}^{3}}\]
C) \[25\,\,c{{m}^{3}}\]
D) \[10.5\,\,c{{m}^{3}}\]
View Answer play_arrowquestion_answer78) In which one of the following, does the given amount of chlorine exert the least pressure in a vessel of capacity \[1\,\,d{{m}^{3}}\] at 273 K?
A) 0.0355 g
B) 0.071 g
C) \[6.023\times {{20}^{21}}\]molecules
D) 0.02 mol
View Answer play_arrowquestion_answer79) Based on the first law of thermodynamics, which one of the following is correct?
A) For an isochoric process \[=\Delta E=-q\]
B) For an adiabatic process \[=\Delta E=-w\]
C) For an isothermal process \[=q=+w\]
D) For a cyclic process \[q=-w\]
View Answer play_arrowquestion_answer80) For alkali metals, which one of the following trends is incorrect?
A) Hydration energy: \[Li>Na>K>Rb\]
B) Ionization energy: \[Li>Na>K>Rb\]
C) Density: \[Li<Na<K<Rb\]
D) Atomic size: \[Li<Na<K<Rb\]
View Answer play_arrowquestion_answer81) 1 g of silver gets distributed between \[10\,\,c{{m}^{3}}\]of molten zinc and \[100\,\,c{{m}^{3}}\] of molten lead at\[{{800}^{o}}C\]. The percentage of silver in the zinc layer is approximately
A) 89
B) 91
C) 97
D) 94
View Answer play_arrowquestion_answer82) One mole of an organic compound A with the formula \[{{C}_{3}}{{H}_{8}}O\] reacts completely with two moles of HI to form X and Y. When Y is boiled with aqueous alkali it forms Z. Z answers the iodoform test. The compound A is
A) propan-2-ol
B) propan-1-ol
C) ethoxyethane
D) methoxyethane
View Answer play_arrowquestion_answer83) The IUPAC name of \[{{K}_{2}}[Ni{{(CN)}_{4}}]\] is
A) potassium tetracyanonickelate (II)
B) potassium tetracyanatonickelate (III)
C) potassium tetracyanatonickelate (II)
D) potassium tetracyanonickelate (III)
View Answer play_arrowquestion_answer84) The spin only magnetic moment of \[M{{n}^{4+}}\] ion is nearly
A) 3 BM
B) 6 BM
C) 4 BM
D) 5 BM
View Answer play_arrowquestion_answer85) In Kjeldahl’s method, ammonia from 5 g of food neutralizes \[30\,c{{m}^{3}}\] of 0.1 N acid. The percentage of nitrogen in the food is
A) 8.4
B) 8.4
C) 16.8
D) 1.68
View Answer play_arrowquestion_answer86) Carbon can reduce ferric oxide to iron at a temperature above 983 K because
A) carbon monoxide formed is thermodynamically less stable than ferric oxide
B) carbon has a higher affinity towards oxidation than iron
C) free energy change for the formation of carbon dioxide is less negative than that for ferric oxide
D) iron has a higher affinity towards oxygen than carbon
View Answer play_arrowquestion_answer87) An oxygen containing organic compound upon oxidation forms a carboxylic acid as the only organic product with its molecular mass higher by 14 units. The organic compound is
A) an aldehyde
B) a primary alcohol
C) a secondary alcohol
D) acetone
View Answer play_arrowquestion_answer88) The compound obtained when acetaldehyde reacts with dilute aqueous sodium hydroxide exhibits
A) geometrical isomerism
B) optical isomerism
C) neither optical nor geometrical isomerism
D) both optical and geometrical isomerism
View Answer play_arrowquestion_answer89) The activation energy for a reaction at the temperature TK was found to be\[2.303\text{ }RT\text{ }J\text{ }mo{{l}^{-1}}\]. The ratio of the rate constant to Arrhenius factor is
A) \[{{10}^{-1}}\]
B) \[{{10}^{-2}}\]
C) \[2\times {{10}^{-3}}\]
D) \[2\times {{10}^{-2}}\]
View Answer play_arrowquestion_answer90) A dibromo derivative of an alkane reacts with sodium metal to form an alicyclic hydrocarbon. The derivative is
A) 1,1-dibromopropane
B) 2, 2-dibromobutane
C) 1, 2-dibromoethane
D) 1, 4-dibromobutane
View Answer play_arrowquestion_answer91) Time required for 100 per cent completion of a zero order reaction is
A) \[\frac{2k}{a}\]
B) \[\frac{a}{2k}\]
C) \[\frac{a}{k}\]
D) \[ak\]
View Answer play_arrowquestion_answer92) 0.023 g of sodium metal is reacted with \[100\text{ }c{{m}^{3}}\] of water. The pH of the resulting solution is
A) 10
B) 11
C) 9
D) 12
View Answer play_arrowquestion_answer93) Which one of the following is wrongly matched?
A) \[{{[Cu{{(N{{H}_{3}})}_{4}}]}^{2+}}\] - Square planar
B) \[[Ni{{(CO)}_{4}}]\] - Neutral ligand
C) \[[Fe{{(C{{N}_{6}})}^{3-}}]\] - \[s{{p}^{3}}{{d}^{2}}\]
D) \[{{[Co{{(en)}_{3}}]}^{3+}}\] - Follows EAN rule
View Answer play_arrowquestion_answer94) Which one of the following conformations of cyclohexane is the least stable?
A) Half-chair
B) Boat
C) Twisted-boat
D) Chair
View Answer play_arrowquestion_answer95) Which one of the following is a molecular crystal?
A) Rock salt
B) Quartz
C) Dry ice
D) Diamond
View Answer play_arrowquestion_answer96) A buffer solution contains 0.1 mole of sodium acetate in \[1000\,\,c{{m}^{3}}\] of 0.1 M acetic acid. To the above buffer solution, 0.1 mole of sodium acetate is further added and dissolved. The pH of the resulting buffer is equal to
A) \[p{{K}_{a}}-\log \,2\]
B) \[p{{K}_{a}}\]
C) \[p{{K}_{a}}+\,2\]
D) \[p{{K}_{a}}+\log \,2\]
View Answer play_arrowquestion_answer97) Which one of the following has the most nucleophilic nitrogen?
A)
B)
C)
D)
View Answer play_arrowquestion_answer98) Chloroacetic acid is a stronger acid than acetic acid. This can be explained using
A) -M effect
B) -I effect
C) + M effect
D) +I effect
View Answer play_arrowquestion_answer99) The correct sequence of reactions to convert p-nitrophenol into quinol involves
A) reduction, diazotization and hydrolysis
B) hydrolysis, diazotization and reduction
C) hydrolysis, reduction and diazotization
D) diazotization, reduction and hydrolysis
View Answer play_arrowquestion_answer100) \[C{{H}_{3}}C{{H}_{2}}Br\xrightarrow[\Delta ]{aq.\,KOH}a=\xrightarrow[\Delta ]{KMn{{O}_{4}}/{{H}^{+}}}\]\[B\xrightarrow[\Delta ]{N{{H}_{3}}}C\xrightarrow[alkali]{B{{r}_{2}}}D,'D'\] is
A) \[C{{H}_{3}}Br\]
B) \[C{{H}_{3}}COON{{H}_{2}}\]
C) \[C{{H}_{3}}N{{H}_{2}}\]
D) \[CHB{{r}_{3}}\]
View Answer play_arrowquestion_answer101) The letter ‘D’ in D-glucose signifies
A) configuration at all chiral carbons
B) dextrorotatory
C) that it is a monosaccharide
D) configuration at a particular chiral carbon
View Answer play_arrowquestion_answer102) Reaction of methyl bromide with aqueous sodium hydroxide involves
A) racemization
B) \[{{S}_{N}}1\] mechanism
C) retention of configuration
D) \[{{S}_{N}}2\] mechanism
View Answer play_arrowquestion_answer103) 9.65 C of electric current is passed through fused anhydrous magnesium chloride. The magnesium metal thus, obtained is completely converted into a Grignard reagent. The number of moles of the Grignard reagent obtained is
A) \[5\times {{10}^{-4}}\]
B) \[1\times {{10}^{-4}}\]
C) \[5\times {{10}^{-5}}\]
D) \[1\times {{10}^{-5}}\]
View Answer play_arrowquestion_answer104) Which one of the following does not involve coagulation?
A) Formation of delta regions
B) Peptization
C) Treatment of drinking water by potash alum
D) Clotting of blood by the use of ferric chloride
View Answer play_arrowquestion_answer105) In alkaline medium, alanine exists predominantly as
A) anion
B) Zwitterion
C) cation
D) covalent form
View Answer play_arrowquestion_answer106) The standard emf of galvanic cell involving 3 moles of electrons in its redox reaction is 0.59 V. The equilibrium constant for the reaction of the cell is
A) \[{{10}^{25}}\]
B) \[{{10}^{20}}\]
C) \[{{10}^{15}}\]
D) \[{{10}^{30}}\]
View Answer play_arrowquestion_answer107) Benzaldehyde and acetone can be best distinguished using
A) Fehling's solution
B) Sodium hydroxide solution
C) 2, 4-DNP
D) Tollen's reagent
View Answer play_arrowquestion_answer108) Which one of the following statements is true?
A) Saponification of oil yields a diol
B) Drying of oil involves hydrolysis
C) Addition of antioxidant to oil minimizes rancidity
D) Refining of oil involves hydrogenation
View Answer play_arrowquestion_answer109) The following data is obtained during the first order thermal decomposition of \[2A(g)\xrightarrow{{}}B(g)+C(s)\]at constant volume and temperature.
S.N. | Time | Total pressure in Pascal |
1. | At the end of 10 min | 300 |
2. | After completion | 200 |
A) 0.0693
B) 6.93
C) 0.00693
D) 69.3
View Answer play_arrowquestion_answer110) Phenol \[\xrightarrow{X}\] forms a tribromo derivative. ‘’X’’ is
A) bromine in benzene
B) bromine in water
C) potassium bromide solution
D) bromine in carbon tetrachloride at \[{{0}^{o}}C\]
View Answer play_arrowquestion_answer111) The correct sequence of steps involved in the mechanism of Cannizaro’s reaction is
A) nucleophilic attack, transfer of \[{{H}^{-}}\]and transfer of \[{{H}^{+}}\]
B) transfer of \[{{H}^{-}}\], transfer of \[{{H}^{+}}\] and nucleophilic attack
C) transfer if \[{{H}^{+}}\] nucleophilic attack and transfer of \[{{H}^{-}}\]
D) electrophilic attack by \[O{{H}^{-}}\], transfer of\[{{H}^{+}}\] and transfer of \[{{H}^{-}}\]
View Answer play_arrowquestion_answer112) Which one of the following is an example for homogeneous catalysis?
A) Manufacture of sulphuric acid by Contact process
B) Manufacture of ammonia by Habeas process
C) Hydrolysis of sucrose in presence of dilute hydrochloric acid
D) Hydrogenation of oil
View Answer play_arrowquestion_answer113) The empirical formula of a non-electrolyte is \[C{{H}_{2}}O\]. A solution containing 6 g of the compound exerts the same osmotic pressure as that of 0.05 M glucose solution at the same temperature. The molecular formula of the compound is
A) \[{{C}_{2}}{{H}_{4}}{{O}_{2}}\]
B) \[{{C}_{3}}{{H}_{6}}{{O}_{3}}\]
C) \[{{C}_{5}}{{H}_{10}}{{O}_{5}}\]
D) \[{{C}_{4}}{{H}_{8}}{{O}_{4}}\]
View Answer play_arrowquestion_answer114) A white crystalline salt A reacts with dilute \[HCl\] to liberate a suffocating gas B and also forms a yellow precipitate. The gas B turns potassium dichromate acidified with dilute \[{{H}_{2}}S{{O}_{4}}\] to a green coloured solution C. A, B and C are respectively
A) \[N{{a}_{2}}S{{O}_{3}},\,S{{O}_{2}}\,\,C{{r}_{2}}{{(S{{O}_{4}})}_{3}}\]
B) \[N{{a}_{2}}{{S}_{2}}{{O}_{3}},\,S{{O}_{2}}\,\,C{{r}_{2}}{{(S{{O}_{4}})}_{3}}\]
C) \[N{{a}_{2}}S,\,\,S{{O}_{2}},\,\,\,C{{r}_{2}}{{(S{{O}_{4}})}_{3}}\]
D) \[N{{a}_{2}}S{{O}_{4}},\,\,S{{O}_{2}},\,C{{r}_{2}}{{(S{{O}_{4}})}_{3}}\]
View Answer play_arrowquestion_answer115) Molecules of a noble gas do not possess vibrational energy because a noble gas
A) is monoatomic
B) is chemically inert
C) has completely filled shells
D) is diamagnetic
View Answer play_arrowquestion_answer116) \[1\,\,d{{m}^{3}}\] solution containing \[{{10}^{-5}}\] moles each of \[C{{l}^{-}}\] ions and \[CrO_{4}^{2-}\] ions is treated with \[{{10}^{-4}}\] moles of silver nitrate. Which one of the following observations is made? \[[{{K}_{sp}}A{{g}_{2}}Cr{{O}_{4}}=4\times {{10}^{-12}}]\]
A) Precipitation does not occur
B) Silver chromate gets precipitated first
C) Silver chloride gets precipitated first
D) Both silver chromate and silver chloride start precipitating simultaneously
View Answer play_arrowquestion_answer117) pH value of which one of the following is not equal to one?
A) \[0.1\text{ }M\text{ }HN{{O}_{3}}\]
B) \[0.05\text{ }M\text{ }{{H}_{2}}S{{O}_{4}}\]
C) \[0.1\text{ }M\text{ }C{{H}_{3}}COOH\]
D) \[50\,\,c{{m}^{3}}\]of \[0.4\,\,M\]\[HCl+50\,\,c{{m}^{3}}\]of \[0.2\,M\,NaOH\]
View Answer play_arrowquestion_answer118) \[{{E}_{1}},\,{{E}_{2}},{{E}_{3}}\] are the emf values of the three galvanic cells respectively.
(i) \[Zn|Zn_{1M}^{2+}||Cu_{0.1M}^{2+}|Cu\] |
(ii) \[Zn|Zn_{1M}^{2+}||Cu_{1M}^{2+}|Cu\] |
(iii) \[Zn|Zn_{0.1\,M}^{2+}||Cu_{1M}^{2+}|Cu\] |
A) \[{{E}_{2}}>{{E}_{3}}>{{E}_{1}}\]
B) \[{{E}_{3}}>{{E}_{2}}>{{E}_{1}}\]
C) \[{{E}_{1}}>{{E}_{2}}>{{E}_{3}}\]
D) \[{{E}_{1}}>{{E}_{3}}>{{E}_{2}}\]
View Answer play_arrowquestion_answer119) The IUPAC name of is
A) 2-methyl-3-bromohexanal
B) - 3-bromo-2-methylbutanal
C) 2-methyl-3-bromobutanal
D) 3-bromo-2-methylpentanal
View Answer play_arrowquestion_answer120) Which one of the following forms propane nitrile as the major product?
A) Ethyl bromide + alcoholic \[KCN\]
B) Propyl bromide + alcoholic \[KCN\]
C) Propyl bromide + alcoholic \[AgCN\]
D) Ethyl bromide + alcoholic \[AgCN\]
View Answer play_arrowquestion_answer121) If then \[{{A}^{2}}+xA+I=0\] for \[(x,y)\] is
A) \[(-4,1)\]
B) \[(-1,3)\]
C) \[(4,-1)\]
D) \[(1,3)\]
View Answer play_arrowquestion_answer122) The constant term of the polynomial is
A) 0
B) 2
C) -1
D) 1
View Answer play_arrowquestion_answer123) If \[\vec{a},\vec{b}\] and \[\vec{c}\] are non-zero coplanar vectors, then \[[2\vec{a}-\vec{b}3\vec{b}-\vec{c}4\vec{c}-\vec{a}]\] is
A) \[25\]
B) \[0\]
C) \[27\]
D) \[9\]
View Answer play_arrowquestion_answer124) A space vector makes the angles \[{{150}^{o}}\] and \[{{60}^{o}}\] with the positive direction of x-and y-axes. The angle made by the vector with the positive direction z-axis is
A) \[{{90}^{o}}\]
B) \[{{60}^{o}}\]
C) \[{{180}^{o}}\]
D) \[{{120}^{o}}\]
View Answer play_arrowquestion_answer125) If \[\vec{a},\vec{b}\]and \[\vec{c}\] are unit vectors, such that \[\vec{a}+\vec{b}+\vec{c}=\vec{0},\]then \[3\vec{a}.\vec{b}+2\,\vec{b}.\vec{c}+\vec{c}.\vec{a}\]
A) -1
B) 1
C) -3
D) 3
View Answer play_arrowquestion_answer126) If \[a>b>c,\] \[{{\sec }^{-1}}\frac{a+b}{a-b}=2{{\sin }^{-1}}x,\] then x is
A) \[-\sqrt{\frac{b}{a+b}}\]
B) \[\sqrt{\frac{b}{a+b}}\]
C) \[-\sqrt{\frac{a}{a+b}}\]
D) \[\sqrt{\frac{a}{a+b}}\]
View Answer play_arrowquestion_answer127) If \[x\ne n\pi ,\] \[x\ne (2n+1)\frac{\pi }{2},\] \[n\in Z,\] then \[\frac{{{\sin }^{-1}}(\cos x)+{{\cos }^{-1}}(\sin x)}{{{\tan }^{-1}}(\cot x)+{{\cot }^{-1}}(\tan x)}\] is
A) \[\frac{\pi }{2}\]
B) \[\frac{\pi }{6}\]
C) \[\frac{\pi }{4}\]
D) \[\frac{\pi }{3}\]
View Answer play_arrowquestion_answer128) The general solution \[1+{{\sin }^{2}}3\sin x.\cos x,\tan x\ne \frac{1}{2},\]is
A) \[2n\pi +\frac{\pi }{4},n\in Z\]
B) \[2n\pi -\frac{\pi }{4},n\in Z\]
C) \[n\pi -\frac{\pi }{4},n\in Z\]
D) \[n\pi +\frac{\pi }{4},n\in Z\]
View Answer play_arrowquestion_answer129) The least positive integer n, for which \[\frac{{{(1+i)}^{n}}}{{{(1-i)}^{n-2}}}\] is positive, is
A) 3
B) 4
C) 1
D) 2
View Answer play_arrowquestion_answer130) If \[x+iy={{(-1+i\sqrt{3})}^{2010}},\] then x is
A) \[-{{2}^{2010}}\]
B) \[{{2}^{2010}}\]
C) \[1\]
D) \[-1\]
View Answer play_arrowquestion_answer131) \[(\sin \theta +\cos \theta )\,(\tan \theta +cot\theta )\] is equal to
A) \[\sin \theta \,\cos \theta \]
B) \[1\]
C) \[\sec \theta +\text{cosec}\theta \]
D) \[\sec \theta \,\,\text{cosec}\theta \]
View Answer play_arrowquestion_answer132) This sides of a triangle are \[6+2\sqrt{3},4\sqrt{3}\] and \[\sqrt{24}.\] the tangent of the smallest angle of the triangle is
A) \[\frac{1}{\sqrt{3}}\]
B) \[\sqrt{2}-1\]
C) \[\sqrt{3}\]
D) \[1\]
View Answer play_arrowquestion_answer133) A simple graph contains 24 edges. Degree of each vertex is 3. The number of vertices is
A) 8
B) 12
C) 21
D) 16
View Answer play_arrowquestion_answer134) \[\underset{x\to \infty }{\mathop{\lim }}\,\,n\,\sin \frac{2\pi }{3n}.\cos \frac{2\pi }{3n}\] is
A) \[\frac{\pi }{6}\]
B) \[\frac{2\pi }{3}\]
C) \[1\]
D) \[\frac{\pi }{3}\]
View Answer play_arrowquestion_answer135) The function \[f(x)=[x],\] where [x] denotes the greatest integer not greater than x, is
A) continuous for all non-integral values of x
B) continuous only at positive integral values of x
C) continuous for all real values of x
D) continuous only at rational values of x
View Answer play_arrowquestion_answer136) The greatest value of x satisfying \[~21=385\](mod x) and \[587=167\] (mod x) is
A) \[156\]
B) \[32\]
C) \[28\]
D) \[56\]
View Answer play_arrowquestion_answer137) The number \[({{49}^{2}}-4)({{49}^{3}}-49)\] is divisible by
A) \[7!\]
B) \[9!\]
C) \[6!\]
D) \[5!\]
View Answer play_arrowquestion_answer138) The least positive integer x satisfying\[{{2}^{2010}}\equiv 3x\](mod 5) is
A) 3
B) 4
C) 1
D) 2
View Answer play_arrowquestion_answer139) If A and B are two square matrices of the same order such that \[AB=B\]and \[BA=A,\] then \[{{A}^{2}}+{{B}^{2}}\]is always equal to
A) \[I\]
B) \[A+B\]
C) \[2AB\]
D) \[2BA\]
View Answer play_arrowquestion_answer140) If A is a \[3\times 3\] non-singular matrix and if \[|A|=3,\]then \[|{{(2A)}^{-1}}|\] is
A) \[24\]
B) \[3\]
C) \[\frac{1}{3}\]
D) \[\frac{1}{24}\]
View Answer play_arrowquestion_answer141) If \[a,-a,\] b are the roots of \[{{x}^{3}}-5{{x}^{2}}-x+5=0,\] then b is a root of
A) \[{{x}^{2}}+3x-20=0\]
B) \[{{x}^{2}}-5x+10=0\]
C) \[{{x}^{2}}-3x-10=0\]
D) \[{{x}^{2}}+5x-30=0\]
View Answer play_arrowquestion_answer142) In the binomial expansion of \[{{(1+x)}^{15}},\] the coefficients of \[{{x}^{r}}\] and \[{{x}^{r+3}}\] are equal. Then, r is
A) \[8\]
B) \[7\]
C) \[4\]
D) \[6\]
View Answer play_arrowquestion_answer143) The nth term of the series \[1+3+7+13+21+.....\] is 9901. The value of n is
A) \[100\]
B) \[90\]
C) \[900\]
D) \[99\]
View Answer play_arrowquestion_answer144) If \[\frac{1}{(3-5x)(2+3x)}=\frac{A}{3-5x}+\frac{B}{2+3x},\] then \[A:B\] is
A) \[2:3\]
B) \[5:3\]
C) \[3:5\]
D) \[3:2\]
View Answer play_arrowquestion_answer145) If \[\hat{i},\hat{j},\hat{k}\] are unit vectors along the positive direction of x, y and z-axes, then a false statement in the following is
A) \[\Sigma \hat{i}\times (\hat{j}+\hat{k})=\vec{0}\]
B) \[\Sigma \hat{i}\times (\hat{j}\times \hat{k})=\vec{0}\]
C) \[\Sigma \,\hat{i}.(\hat{j}\times \hat{k})=\vec{0}\]
D) \[\Sigma \,\hat{i}.(\hat{j}+\hat{k})=\vec{0}\]
View Answer play_arrowquestion_answer146) In P(X), the power set of a non-empty set X, an binary operation * is defined by\[A\,*\,B=A\cup B,\forall A,B\in P(x)\] under *, a true statement is
A) identity law is not satisfied
B) inverse law is not satisfied
C) commutative law is not satisfied
D) associative law is not satisfied
View Answer play_arrowquestion_answer147) The inverse of 2010 in the group \[{{Q}^{+}}\] of all positive rational under the binary operation * defined by \[a*b=\frac{ab}{2010},\forall \,a,b\in {{Q}^{+}},\] is
A) \[2009\]
B) \[2011\]
C) \[1\]
D) \[2010\]
View Answer play_arrowquestion_answer148) If the three function \[f(x),g(x)\] and \[h(x)\] are such that \[h(x)=f(x).g(x)\] and \[f'(x).g'(x)=c\] where c is constant, then
A) \[h'=(x).h''(x)\]
B) \[\frac{h(x)}{h''(x)}\]
C) \[\frac{h''(x)}{h(x)}\]
D) \[\frac{h(x)}{h'(x)}\]
View Answer play_arrowquestion_answer149) The derivative of \[{{e}^{ax}}\,\,\cos \,bx\]with respect x is \[r{{e}^{ax}}\,\,\cos \,bx\,\,{{\tan }^{-1}}\frac{b}{a}.\] When \[a>0,b>0,\]then value of r, is
A) \[\sqrt{{{a}^{2}}+{{b}^{2}}}\]
B) \[\frac{1}{\sqrt{ab}}\]
C) \[ab\]
D) \[a+b\]
View Answer play_arrowquestion_answer150) The chord of the circle \[{{x}^{2}}+{{y}^{2}}-4x=0\] which is bisected at \[(1,0)\] is perpendicular to the line
A) \[y=x\]
B) \[x+y=0\]
C) \[x=1\]
D) \[y=1\]
View Answer play_arrowquestion_answer151) In \[\Delta ABC,\]if \[a=2,b={{\tan }^{-1}}\frac{1}{2}\] and \[C={{\tan }^{-1}}\frac{1}{3},\] then (A, b) equals
A) \[\frac{3\pi }{4},\frac{2}{\sqrt{5}}\]
B) \[\frac{\pi }{4},\frac{2\sqrt{2}}{\sqrt{5}}\]
C) \[\frac{3\pi }{4},\frac{2\sqrt{2}}{\sqrt{5}}\]
D) \[\frac{\pi }{4},\frac{2}{\sqrt{5}}\]
View Answer play_arrowquestion_answer152) The straight line \[2x+3y-k=0,\] \[k>0\] cuts the x and y-axes at A and B. The area of \[\Delta OAB,\], where 0 is the origin, is \[12\text{ }sq\]unit. The equation of the circle having AB as diameter is
A) \[{{x}^{2}}+{{y}^{2}}-6x-4y=0\]
B) \[{{x}^{2}}+{{y}^{2}}+4x-6y=0\]
C) \[{{x}^{2}}+{{y}^{2}}-6x+4y=0\]
D) \[{{x}^{2}}+{{y}^{2}}-4x-6y=0\]
View Answer play_arrowquestion_answer153) Let \[P(x,y)\] be the mid point of the line joining \[(1,0)\] to a point on the curve Then, locus of P is symmetrical about
A) \[y-axis\]
B) \[x-axis\]
C) \[x=1\]
D) \[y=1\]
View Answer play_arrowquestion_answer154) The function \[f(x)=|x-2|+x\] is
A) differentiable at both \[x=2\] and \[x=0\]
B) differentiable at \[x=2\] but not at \[x=0\]
C) continuous at \[x=2\]but not at \[x=0\]
D) continuous at both \[x=2\] and \[x=0\]
View Answer play_arrowquestion_answer155) Let R be an equivalence relation defined on a set containing 6 elements. The minimum number or ordered pairs that R should contain is
A) \[12\]
B) \[6\]
C) \[64\]
D) \[36\]
View Answer play_arrowquestion_answer156) The line joining \[A(2,-7)\] and \[B(6,5)\] is divided into 4 equal parts by the points P, Q and R such that\[AQ=RP=QB\]. The mid-point of PR is
A) \[(4,12)\]
B) \[(-8,1)\]
C) \[(4,-1)\]
D) \[(8,-2)\]
View Answer play_arrowquestion_answer157) Let \[P\equiv (-1,0),\] \[Q\equiv (0,0)\] and \[R=(3,3)\] be three points. The equation of the bisector of the angle PQR is
A) \[x-\sqrt{3}y=0\]
B) \[\sqrt{3}x-y=0\]
C) \[x+\sqrt{3}y=0\]
D) \[\sqrt{3}x+y=0\]
View Answer play_arrowquestion_answer158) If m is the slope of one of the lines represented by \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0,\]then \[{{(h+bm)}^{2}}\] is equal to
A) \[{{(a+b)}^{2}}\]
B) \[{{(a-b)}^{2}}\]
C) \[{{h}^{2}}+ab\]
D) \[{{h}^{2}}-ab\]
View Answer play_arrowquestion_answer159) \[\cos {{12}^{o}}\,\cot {{102}^{o}}+\cot {{102}^{o}}\,\cot {{66}^{o}}\]\[+\cot {{66}^{o}}\,\cot {{12}^{o}}\] is
A) \[-2\]
B) \[1\]
C) \[-1\]
D) \[2\]
View Answer play_arrowquestion_answer160) A wire of length \[20\text{ }cm\]is bent in the form of a sector of a circle. The maximum area that can be enclosed by the wire is
A) \[20\text{ }sq\text{ }cm\]
B) \[25\text{ }sq\text{ }cm\]
C) \[10\,\,sq\,\,cm\]
D) \[30\,\,sq\,\,cm\]
View Answer play_arrowquestion_answer161) Two circles centred at \[(2,3)\] and \[(5,6)\] intersect each other. If the radii are equal, the equation of the common chord is
A) \[x+y+1=0\]
B) \[x-y+1=0\]
C) \[x+y-8=0\]
D) \[x-y-8=0\]
View Answer play_arrowquestion_answer162) Equation of the circle centred at \[(4,3)\] touching the circle \[{{x}^{2}}+{{y}^{2}}=1\]externally, is
A) \[{{x}^{2}}+{{y}^{2}}-8x-6y+9=0\]
B) \[{{x}^{2}}+{{y}^{2}}+8x+6y+9=0\]
C) \[{{x}^{2}}+{{y}^{2}}+8x-6y+9=0\]
D) \[{{x}^{2}}+{{y}^{2}}-8x6y+9=0\]
View Answer play_arrowquestion_answer163) The points \[(1,0),\] \[(0,1),\] \[(0,0)\] and \[(2k,3k),k\ne 0\] are concyclic, if k is
A) \[\frac{1}{5}\]
B) \[-\frac{1}{5}\]
C) \[-\frac{5}{13}\]
D) \[\frac{5}{13}\]
View Answer play_arrowquestion_answer164) The locus of the point of intersection of the tangents drawn at the ends of a focal chord of the parabola \[{{x}^{2}}=-\text{ }8y\] is
A) \[x=2\]
B) \[x=-2\]
C) \[y=2\]
D) \[y=-2\]
View Answer play_arrowquestion_answer165) The condition for the line \[y=mx+c\]to be a normal to the parabola \[{{y}^{2}}=4ax\] is
A) \[c=-2am-a{{m}^{3}}\]
B) \[c=-\frac{a}{m}\]
C) \[c=\frac{a}{m}\]
D) \[c=2am+a{{m}^{3}}\]
View Answer play_arrowquestion_answer166) The eccentric angle of the point \[(2,\sqrt{3})\] lying on \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{4}=1\] is
A) \[\frac{\pi }{4}\]
B) \[\frac{\pi }{2}\]
C) \[\frac{\pi }{3}\]
D) \[\frac{\pi }{6}\]
View Answer play_arrowquestion_answer167) The distance of the focus of \[{{x}^{2}}-{{y}^{2}}=4,\]form the directrix which is nearer to it, is
A) \[4\sqrt{2}\]
B) \[8\sqrt{2}\]
C) \[2\sqrt{2}\]
D) \[\sqrt{2}\]
View Answer play_arrowquestion_answer168) If \[\int{f(x)\,\sin x.\cos x\,dx}\]\[=\frac{1}{2({{b}^{2}}-{{a}^{2}})}\log f(x)+c,\]where c is the constant of integration, then \[f(x)\] is
A) \[\frac{2}{ab\,\,\cos \,\,2x}\]
B) \[\frac{2}{({{b}^{2}}-{{a}^{2}})\,\cos \,2x}\]
C) \[\frac{2}{ab\,\sin \,2x}\]
D) \[\frac{2}{({{b}^{2}}-{{a}^{2}})\,\sin \,2x}\]
View Answer play_arrowquestion_answer169) If \[\int{\frac{\sqrt{x}}{x(x+1)}}\,dx=k\,{{\tan }^{-1}}m,\]then \[(k,m)\] is
A) \[(2,x)\]
B) \[(1,x)\]
C) \[(1,\sqrt{x})\]
D) \[(2,\sqrt{x})\]
View Answer play_arrowquestion_answer170) \[\int_{0}^{\pi /4}{\frac{\sin \,x+\cos x}{3+\sin 2x}}dx\] is
A) \[\frac{1}{4}\log 3\]
B) \[\log 3\]
C) \[\frac{1}{2\log \,3}\]
D) \[2\log 3\]
View Answer play_arrowquestion_answer171) \[\int_{0}^{1}{x{{(1-x)}^{3/2}}}dx\] is
A) \[-\frac{2}{35}\]
B) \[\frac{4}{35}\]
C) \[\frac{24}{35}\]
D) \[-\frac{8}{35}\]
View Answer play_arrowquestion_answer172) The area bounded by the curve \[y=\left\{ \begin{matrix} {{x}^{2}}, & x<0 \\ x, & x\ge 0 \\ \end{matrix} \right.\] and the line \[y=4,\] is
A) \[\frac{32}{3}\]
B) \[\frac{8}{3}\]
C) \[\frac{40}{3}\]
D) \[\frac{16}{3}\]
View Answer play_arrowquestion_answer173) The order and degree of the differential equation \[y=\frac{dp}{dx}x=\sqrt{{{a}^{2}}{{p}^{2}}+{{b}^{2}}},\]where \[p=\frac{dy}{dx}\] (here a and b are arbitrary constants) respectively are
A) \[2,2\]
B) \[1,1\]
C) \[1,2\]
D) \[2,1\]
View Answer play_arrowquestion_answer174) The general solution of the differential equation \[2x\frac{dy}{dx}-y=3\] is a family of
A) hyperbolas
B) parabolas
C) straight lines
D) circles
View Answer play_arrowquestion_answer175) If \[x=a\,{{\cos }^{3}}\theta \]and \[y=a\,{{\sin }^{3}}\,\theta ,\] then \[\frac{dy}{dx}\] is
A) \[\sqrt[3]{\frac{y}{x}}\]
B) \[\sqrt[3]{\frac{x}{y}}\]
C) \[-\sqrt[3]{\frac{x}{y}}\]
D) \[-\sqrt[3]{\frac{y}{x}}\]
View Answer play_arrowquestion_answer176) If \[y={{\tan }^{-1}}\sqrt{{{x}^{2}}-1},\] then the ratio \[\frac{{{d}^{2}}y}{d{{x}^{2}}}:\frac{dy}{dx}\] is
A) \[\frac{x({{x}^{2}}-1)}{1+2{{x}^{2}}}\]
B) \[\frac{1-2{{x}^{2}}}{x({{x}^{2}}-1)}\]
C) \[\frac{1+2{{x}^{2}}}{x({{x}^{2}}+1)}\]
D) \[\frac{x({{x}^{2}}+1)}{1-2{{x}^{2}}}\]
View Answer play_arrowquestion_answer177) P is the point of contact of the tangent form the origin to the curve\[y=lo{{g}_{e}}\text{ }x\]. The length of the perpendicular drawn form the origin to the normal at P is
A) \[\frac{1}{2e}\]
B) \[\frac{1}{e}\]
C) \[2\sqrt{{{e}^{2}}+1}\]
D) \[\sqrt{{{e}^{2}}+1}\]
View Answer play_arrowquestion_answer178) For the curve \[4{{x}^{5}}=5{{y}^{4}},\] the ratio of the cube of the subtangent at a point on the curve the square of the subnormal at the same point is
A) \[\frac{{{4}^{4}}}{5}\]
B) \[\frac{{{5}^{4}}}{4}\]
C) \[\frac{{{4}^{4}}}{{{5}^{4}}}\]
D) \[{{\left( \frac{5}{4} \right)}^{4}}\]
View Answer play_arrowquestion_answer179) The set of real values of x for which \[f(x)=\frac{x}{\log \,x}\]is increasing, is
A) \[\{x:x\ge e\}\]
B) empty
C) \[\{x:x<e\}\]
D) \[\{1\}\]
View Answer play_arrow
You need to login to perform this action.
You will be redirected in
3 sec