question_answer1) The only mechanical quantity which has negative dimension of mass is
A) angular momentum
B) torque
C) coefficient of thermal conductivity
D) gravitational constant
View Answer play_arrowquestion_answer2) Two vectors are given by \[\vec{A}=3\hat{i}+\hat{j}+3\hat{k}\]and \[\vec{B}=3\hat{i}+5\hat{j}-2\hat{k}\]. Find the third vector \[\vec{C},\] if \[\vec{A}+3\vec{B}-\vec{C}=\vec{0}\].
A) \[12\hat{i}+14\hat{j}+12\hat{k}\]
B) \[13\hat{i}+17\hat{j}+12\hat{k}\]
C) \[12\hat{i}+16\hat{j}-3\hat{k}\]
D) \[15\hat{i}+13\hat{j}+4\hat{k}\]
View Answer play_arrowquestion_answer3) A particle moves from position \[3\hat{i}+2\hat{j}+6\hat{k}\] to \[14\hat{i}+13\hat{j}+9\hat{k}\] due to a uniform force of\[4\hat{i}+\hat{j}+3k\text{ }N\]. Find the work done, if the displacement is in metre.
A) \[16\text{ }J\]
B) \[64\text{ }J\]
C) \[32\text{ }J\]
D) \[48\text{ }J\]
View Answer play_arrowquestion_answer4) The coordinates of a moving particle at any time t are given by \[x=\alpha {{t}^{3}}\]and \[y=\beta {{t}^{3}}\]. The speed of the particle at time t is given by
A) \[3t\,\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}\]
B) \[3{{t}^{2}}\,\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}\]
C) \[{{t}^{2}}\,\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}\]
D) \[\,\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}\]
View Answer play_arrowquestion_answer5) A body is moving with uniform acceleration. covers \[200\text{ }m\]in the first \[2\text{ }s\]and \[220\text{ }m\]in the next\[4\text{ }s\] . Find the velocity in m/s after\[7\text{ }s\].
A) \[10\]
B) \[15\]
C) \[20\]
D) \[30\]
View Answer play_arrowquestion_answer6) From the top of a tower a body A is projected vertically up, another body B is horizontally thrown and a third body C is thrown vertically down with same velocity. Then
A) B strikes the ground with more velocity
B) C strikes the ground with less velocity
C) A,B,C strike the ground with same velocity
D) A and C strike the ground with more velocity than B
View Answer play_arrowquestion_answer7) A body is released from a great height falls freely towards the earth. Another body is released from the same height exactly a second latter. Then the separation between two bodies, 2 s after the release of the second body is, nearly
A) \[15\,\,m\]
B) \[20\,\,m\]
C) \[25\,\,m\]
D) \[30\,\,m\]
View Answer play_arrowquestion_answer8) A body of mass \[10\text{ }kg\]is acted upon by two forces each of magnitude \[10\,\,N\]making an angle of \[{{60}^{o}}\] with each other. Find the net acceleration of the body.
A) \[2\sqrt{3}m/{{s}^{2}}\]
B) \[\sqrt{3}m/{{s}^{2}}\]
C) \[3\sqrt{3}m/{{s}^{2}}\]
D) \[4\sqrt{3}m/{{s}^{2}}\]
View Answer play_arrowquestion_answer9) A body of mass \[{{m}_{1}}\] collides elastically with another body of mass \[{{m}_{2}}\] at rest. If the velocity of \[{{m}_{1}}\] after collision becomes \[2/3\] times its initial velocity, the ratio of their masses, is
A) \[1:5\]
B) \[5:1\]
C) \[5:2\]
D) \[2:5\]
View Answer play_arrowquestion_answer10) With increase of temperature, the frictional force acting between two surfaces
A) increases
B) remains the same
C) decreases
D) becomes zero
View Answer play_arrowquestion_answer11) The motion of the centre of mass is the result of
A) internal forces
B) external forces
C) attractive forces
D) repulsive forces
View Answer play_arrowquestion_answer12) A stationary bomb explodes into two parts of masses in the ratio of \[1:3\]. If the heavier mass moves with a velocity \[4\text{ }m/s,\] what is the velocity of lighter part?
A) \[12\text{ }m{{s}^{-1}}\]opposite to heavier mass
B) \[12\text{ }m{{s}^{-1}}\] in the direction of heavier mass
C) \[\text{6 }m{{s}^{-1}}\] opposite to heavier mass
D) \[\text{6 }m{{s}^{-1}}\] in the direction of heavier mass
View Answer play_arrowquestion_answer13) A body is tied to one end of the string and whirled in a vertical circle, the physical quantity which remains constant is
A) momentum
B) speed
C) kinetic energy
D) total energy
View Answer play_arrowquestion_answer14) A thin metal disc of radius of \[0.25\text{ }m\]and mass \[2\text{ }kg\]starts from rest and rolls down on an inclined plane. If its rotational kinetic energy is \[4\text{ }J\]at the foot of inclined plane, then the linear velocity at the same point, is in m/s
A) \[2\]
B) \[2\sqrt{2}\]
C) \[2\sqrt{3}\]
D) \[3\sqrt{2}\]
View Answer play_arrowquestion_answer15) A stone tied to one end of rope and rotated in a circular motion. If the string suddenly breaks, then the stone travels
A) in perpendicular direction
B) in direction of centrifugal force
C) towards centripetal force
D) in tangential direction
View Answer play_arrowquestion_answer16) The escape velocity of a body from the earth is \[{{v}_{e}}\]. If the radius of earth contracts to \[\frac{1}{4}th\] of its value, keeping the mass of the earth constant, the escape velocity will be
A) doubled
B) halved
C) tripled
D) unaltered
View Answer play_arrowquestion_answer17) The-radius of the earth is R. The height of a point vertically above the earth's surface at which acceleration due to gravity becomes \[1%\] of its value at the surface is
A) \[8\,\,R\]
B) \[9\,\,R\]
C) \[10\,\,R\]
D) \[20\,\,R\]
View Answer play_arrowquestion_answer18) A heavy uniform rod is hanging vertically from a fixed support. It is stretched by its own weight. The diameter of the rod is
A) smallest at the top and gradually increases down the rod
B) largest at the top and gradually decreases down the rod
C) uniform everywhere
D) maximum in the middle
View Answer play_arrowquestion_answer19) A particular force (F) applied on a wire increases its length by \[2\times {{10}^{-3}}\text{ }m\]. To increase the wire's length by \[4\times {{10}^{-3}}\text{ }m\]the applied force will be
A) \[4\,\,F\]
B) \[3\,\,F\]
C) \[2\,\,F\]
D) \[F\]
View Answer play_arrowquestion_answer20) The meniscus of mercury in a capillary glass tube, is
A) concave
B) plane
C) cylindrical
D) convex
View Answer play_arrowquestion_answer21) Two liquid drops have diameters of \[1\text{ }cm\]and \[1.5\text{ }cm\] The ratio of excess of pressures inside them is
A) \[1:1\]
B) \[5:3\]
C) \[2:3\]
D) \[3:2\]
View Answer play_arrowquestion_answer22) Temperature remaining constant, the pressure of gas is decreased by \[20%\]. The percentage change in volume
A) increases by \[20%\]
B) decreases by \[20%\]
C) increases by \[25%\]
D) decreases by \[25%\]
View Answer play_arrowquestion_answer23) Work done in converting one gram of ice at \[-{{10}^{o}}C\]into steam at \[{{100}^{o}}C\]is
A) \[3045\text{ }J\]
B) \[6056\text{ }J\]
C) \[721\text{ }J\]
D) \[616\text{ }J\]
View Answer play_arrowquestion_answer24) The temperature of the system decreases in the process of
A) free expansion
B) adiabatic expansion
C) isothermal expansion
D) isothermal compression
View Answer play_arrowquestion_answer25) The temperature at which a black body ceases to radiate energy, is
A) \[0\,\,K\]
B) \[273\text{ }K\]
C) \[30\text{ }K\]
D) \[100\text{ }K\]
View Answer play_arrowquestion_answer26) A particle executes SHM with a period of \[8\text{ }s\]and amplitude \[4\text{ }cm\]. Its maximum speed in cm/s, is
A) \[\pi \]
B) \[\frac{\pi }{2}\]
C) \[\frac{\pi }{3}\]
D) \[\frac{\pi }{4}\]
View Answer play_arrowquestion_answer27) The displacement of a particle of mass \[3\text{ }g\] executing simple harmonic motion is given by \[Y=3\text{ }sin\text{ (}0.2\text{ t)}\]in SI units. The KE of the particle at a point which is at a distance equal to \[1/3\] of its amplitude from its mean position is
A) \[12\times {{10}^{-3}}\,J\]
B) \[25\times {{10}^{-3}}\,J\]
C) \[0.48\times {{10}^{-3}}\,J\]
D) \[0.24\times {{10}^{-3}}\,J\]
View Answer play_arrowquestion_answer28) A uniform spring of force constant k is cut into two pieces whose lengths are in the ratio of \[1:2\]. What is the force constant of second piece in terms of k?
A) \[\frac{k}{2}\]
B) \[\frac{2k}{2}\]
C) \[\frac{3k}{2}\]
D) \[\frac{4k}{2}\]
View Answer play_arrowquestion_answer29) A girl swings on cradle in a sitting position. If she stands what happens to the time period of girl and cradle?
A) Time period decreases
B) Time period increases
C) Remains constant
D) First increases and then remains constant
View Answer play_arrowquestion_answer30) The intensity ratio of two waves is \[1:9\]. The ratio of their amplitudes, is
A) \[3:1\]
B) \[1:3\]
C) \[1:9\]
D) \[9:1\]
View Answer play_arrowquestion_answer31) The speed of sound waves in a gas
A) does not depend upon density of the gas
B) 'does not depend upon changes in pressure
C) does not depend upon temperature
D) depends upon density of the gas
View Answer play_arrowquestion_answer32) A segment of wire vibrates with fundamental frequency of \[450\text{ }Hz\]under a tension of\[9\text{ }kg-wt\]. Then tension at which the fundamental frequency of the same wire becomes \[900\text{ }Hz\]is
A) \[36\text{ }kg-wt\]
B) \[27\text{ }kg-wt\]
C) \[18\text{ }kg-wt\]
D) \[72\text{ }kg-wt\]
View Answer play_arrowquestion_answer33) Sound waves in air cannot be polarized because
A) their speed is small
B) they require medium
C) these are longitudinal
D) their speed is temperature dependent
View Answer play_arrowquestion_answer34) Electric potential at the centre of a charged hollow metal sphere is
A) zero
B) twice as that on the surface
C) half of that on the surface
D) same as that on the surface
View Answer play_arrowquestion_answer35) Three charges \[1\mu C,\] \[1\mu C\] and \[2\mu C\] are kept at vertices of A, B and C of an equilateral triangle ABC of \[10\text{ }cm\]side respectively. The resultant force on the charge at C is
A) \[0.9\text{ }N\]
B) \[1.8\text{ }N\]
C) \[2.72\text{ }N\]
D) \[3.12\text{ }N\]
View Answer play_arrowquestion_answer36) A dielectric of dielectric constant K is introduced such that half of its area of a capacitor of capacity C is occupied by it. The new capacity is
A) \[2\,C\]
B) \[C/2\]
C) \[(1+K)C/2\]
D) \[2C(1+K)\]
View Answer play_arrowquestion_answer37) The value equal to the velocity of light in vacuum is
A) \[\frac{\sqrt{{{\mu }_{0}}}}{{{\varepsilon }_{0}}}\]
B) \[\frac{1}{\sqrt{{{\mu }_{0}}{{\varepsilon }_{0}}}}\]
C) \[\sqrt{{{\mu }_{0}}\,{{\varepsilon }_{0}}}\]
D) \[\sqrt{\frac{{{\mu }_{0}}}{\,{{\varepsilon }_{0}}}}\]
View Answer play_arrowquestion_answer38) Two unlike charges of the same magnitude Q are placed at a distance d. The intensity of the electric field at the middle point in the line joining the two charges
A) zero
B) \[\frac{8\,Q}{4\pi {{\varepsilon }_{0}}{{d}^{2}}}\]
C) \[\frac{6\,Q}{4\pi {{\varepsilon }_{0}}{{d}^{2}}}\]
D) \[\frac{4\,Q}{4\pi {{\varepsilon }_{0}}{{d}^{2}}}\]
View Answer play_arrowquestion_answer39) In a meter bridge experiment, the ratio of the left gap resistance to right gap resistance is \[2:3,\] the balance point from left is
A) \[60\text{ }cm\]
B) \[50\text{ }cm\]
C) \[40\text{ }cm\]
D) \[20\text{ }cm\]
View Answer play_arrowquestion_answer40) The physical quantity in electrostatics analogous to temperature in heat is
A) heat energy
B) capacity
C) resistance
D) potential
View Answer play_arrowquestion_answer41) If the electric current through an electric bulb is \[3.2\text{ }A,\] the number of electrons flow through it in one second is
A) \[2\times {{10}^{9}}\]
B) \[2\times {{10}^{19}}\]
C) \[3.2\times {{10}^{19}}\]
D) \[1.6\times {{10}^{18}}\]
View Answer play_arrowquestion_answer42) A wire P has a resistance of \[20\,\Omega \]. Another wire Q of same material but length twice that of P has resistance of \[8\,\,\,\Omega \]. If r is the radius of cross-section of P, the radius of cross-section of Q is
A) \[r\]
B) \[\frac{r}{\sqrt{2}}\]
C) \[\sqrt{5}\,r\]
D) \[2\,r\]
View Answer play_arrowquestion_answer43) When a metal conductor connected to the left gap of a meter bridge is heated, the balancing point
A) shifts towards right
B) shifts towards left
C) remains unchanged
D) remains at zero
View Answer play_arrowquestion_answer44) The thermocouple among the following that can produce maximum thermo emf for the same temperature difference between the junction is
A) \[Fe-Cu\]
B) \[Ag-Au\]
C) \[Sb-Bi\]
D) \[Cu-Pb\]
View Answer play_arrowquestion_answer45) A bar magnet of magnetic moment At and moment of inertia I is freely suspended such that the magnetic axial line is in the direction of magnetic meridian. If the magnet is displaced by a very small angle \[\theta ,\] angular acceleration is (magnetic induction of earth's horizontal field \[={{B}_{H}}\])
A) \[\frac{M{{B}_{H}}\theta }{I}\]
B) \[\frac{I{{B}_{H}}\theta }{M}\]
C) \[\frac{M\theta }{I{{B}_{H}}}\]
D) \[\frac{I\theta }{M{{B}_{H}}}\]
View Answer play_arrowquestion_answer46) A long magnet is cut into two equal parts, such that the length of each half is same as that of original magnet. If the period of original magnet is T, the period of new magnet is
A) \[T\]
B) \[\frac{T}{2}\]
C) \[\frac{T}{4}\]
D) \[2T\]
View Answer play_arrowquestion_answer47) The time period of a freely suspended bar magnet in a field is 2 s. It is cut into two equal parts along its axis, (hen the time period is
A) \[4\,\,s\]
B) \[0.5\,\,s\]
C) \[2\,\,s\]
D) \[0.25\,\,s\]
View Answer play_arrowquestion_answer48) The angle between magnetic meridian and geographical meridian is known as
A) magnetic dip
B) magnetic latitude
C) magnetic declination
D) magnetic longitude
View Answer play_arrowquestion_answer49) The net magnetic flux through any closed surface, kept in a magnetic field is
A) zero
B) \[\frac{{{\mu }_{0}}}{4\pi }\]
C) \[4\,\,\pi {{\mu }_{0}}\]
D) \[\frac{4\,\,{{\mu }_{0}}}{\pi }\]
View Answer play_arrowquestion_answer50) A paramagnetic liquid is taken in a U-tube and arranged so that one of its limbs is kept between pole pieces of the magnet. The liquid level in the limb
A) goes down
B) rises up
C) remains same
D) first goes down and then rises
View Answer play_arrowquestion_answer51) Two wires A and B are of lengths \[40\text{ }cm\]and\[30\text{ }cm\]. A is bent into a circle of radius r and B into an arc of radius r. A current \[{{i}_{1}}\] is passed through A and 13 through B. To have the same magnetic inductions at the centre, the ratio of \[{{i}_{1}}:{{i}_{2}}\] is
A) \[3:4\]
B) \[3:5\]
C) \[2:3\]
D) \[4:3\]
View Answer play_arrowquestion_answer52) An electron and proton having same kinetic energy enter into magnetic field perpendicular to it. Then
A) the path of electron is less curved
B) the path of proton is less curved
C) both have equal curved paths
D) both have straight line paths
View Answer play_arrowquestion_answer53) Two free parallel wires carrying currents in the opposite directions
A) attract each other
B) repel each other
C) do not effect each other
D) get rotated to be perpendicular to each other
View Answer play_arrowquestion_answer54) A circular coil of diameter \[21\text{ }cm\]is placed in a magnetic field of induction\[{{10}^{-4}}\text{ }T\]. The magnitude of flux linked with coil when the plane of coil makes an angle \[{{30}^{o}}\] with the field is
A) \[1.44\times {{10}^{-6}}\,Wb\]
B) \[1.732\times {{10}^{-6}}\,\,Wb\]
C) \[3.1\times {{10}^{-6}}\,\,Wb\]
D) \[4.2\times {{10}^{-6}}\,\,Wb\]
View Answer play_arrowquestion_answer55) The cladding material of optical fibres has refractive index
A) greater than that of core
B) infinity
C) equal to that of core
D) less than that of core
View Answer play_arrowquestion_answer56) Red colour is used for danger signals because
A) it causes fear
B) it undergoes least scattering
C) it undergoes maximum scattering
D) it is in accordance with international convention
View Answer play_arrowquestion_answer57) The least angle of deviation for a glass prism is equal to its refracting angle. The refractive index of glass is \[1.5\]. Then the angle of prism is
A) \[2\,{{\cos }^{-1}}\left( \frac{3}{4} \right)\]
B) \[si{{n}^{-1}}\left( \frac{3}{4} \right)\]
C) \[2\,\,si{{n}^{-1}}\left( \frac{3}{2} \right)\]
D) \[{{\cos }^{-1}}\left( \frac{3}{2} \right)\]
View Answer play_arrowquestion_answer58) In a spectrometer experiment the prisms A, B, C with same angle but different refractive index \[{{\mu }_{A}}=1.33,\,\,{{\mu }_{B}}=1.5,\,\,{{\mu }_{C}}=1.44\]are used. The corresponding angles of minimum deviation \[{{D}_{A}},\,{{D}_{B}},\,{{D}_{C}}\] measured will be such that
A) \[{{D}_{A}}>\,{{D}_{B}}>\,{{D}_{C}}\]
B) \[{{D}_{A}}<\,{{D}_{B}}<\,{{D}_{C}}\]
C) \[{{D}_{A}}<\,{{D}_{C}}<\,{{D}_{B}}\]
D) \[{{D}_{A}}>\,{{D}_{C}}>\,{{D}_{B}}\]
View Answer play_arrowquestion_answer59) Young's double slit experiment arrangement is shifted from air to water medium, the fringe width
A) increases
B) decreases
C) becomes infinite
D) remains the same
View Answer play_arrowquestion_answer60) On introducing a thin film in the path of one of the two interfering beams, the central fringe will shift by one fringe width. If \[\mu =1.5,\] the thickness of the film is (wavelength of monochromatic light is \[\lambda \])
A) \[4\,\lambda \]
B) \[3\,\lambda \]
C) \[2\,\lambda \]
D) \[\lambda \]
View Answer play_arrowquestion_answer61) The critical angle of the medium with respect to vacuum is \[{{30}^{o}}\]. If the velocity of light in vacuum is \[3\times {{10}^{8}}\text{ }m{{s}^{-1}},\] the velocity of light in medium is
A) \[2\times {{10}^{8}}\text{ }m{{s}^{-1}}\]
B) \[1.5\times {{10}^{8}}\text{ }m{{s}^{-1}}\]
C) \[3\times {{10}^{8}}\text{ }m{{s}^{-1}}\]
D) \[\sqrt{2}\times {{10}^{8}}\text{ }m{{s}^{-1}}\]
View Answer play_arrowquestion_answer62) The distance between the first dark and bright band formed in Young's double slit experiment with band width B is
A) \[\frac{B}{4}\]
B) \[B\]
C) \[\frac{B}{2}\]
D) \[\frac{3B}{2}\]
View Answer play_arrowquestion_answer63) The important conclusion given by Millikan's experiment about the charge is
A) charge is never quantized
B) charge has no definite value
C) charge is quantized
D) charge on oil drop always increases
View Answer play_arrowquestion_answer64) An electron is accelerated through a potential difference of V volts. The speed of electrons will be
A) \[\sqrt{\frac{eV}{m}}\]
B) \[\sqrt{\frac{2eV}{m}}\]
C) \[\sqrt{\frac{eV}{2m}}\]
D) \[\sqrt{\frac{m}{2eV}}\]
View Answer play_arrowquestion_answer65) How many photons are emitted by a laser source of \[5\times {{10}^{-3}}W\]operating at \[632.2\text{ }nm\]in \[2s\]?
A) \[3.2\times {{10}^{16}}\]
B) \[1.6\times {{10}^{16}}\]
C) \[4\times {{10}^{16}}\]
D) None of these
View Answer play_arrowquestion_answer66) If a is radius of first Bohr orbit in hydrogen atom, the radius of the third orbit is
A) \[3a\]
B) \[9a\]
C) \[27a\]
D) \[81a\]
View Answer play_arrowquestion_answer67) Nuclear fission can be explained based on
A) Millikan's oil drop method
B) Liquid drop model
C) Shell model
D) Buffs model
View Answer play_arrowquestion_answer68) The radius of a nucleus with atomic mass number 7 is 2 Fermi. Find the radius of nucleus with atomic number 189.
A) 3 Fermi
B) 4 Fermi
C) 5 Fermi
D) 6 Fermi
View Answer play_arrowquestion_answer69) As mass number increases, surface area
A) decreases
B) increases
C) remains the same
D) remains the same and increases
View Answer play_arrowquestion_answer70) All nucleons in an atom are held by
A) nuclear forces
B) van der Waals' forces
C) tensor forces
D) Coulomb forces
View Answer play_arrowquestion_answer71) The temperature of germanium is decreased from room temperature to \[100\text{ }K,\]the resistance of germanium
A) decreases
B) increases
C) unaffected
D) depends on external conditions
View Answer play_arrowquestion_answer72) The potential in depletion layer is due to
A) electrons
B) holes
C) ions
D) forbidden band
View Answer play_arrowquestion_answer73) In breakdown region, a zener diode behaves as a
A) constant current source
B) constant voltage source
C) constant resistance source
D) constant power source
View Answer play_arrowquestion_answer74) When boron is added as an impurity to silicon, the resulting material is
A) n-type semiconductor
B) n-type conductor
C) p -type conductor
D) p -type semiconductor
View Answer play_arrowquestion_answer75) The diode used in the circuit shown in the figure has a constant voltage drop of \[0.5\text{ }V\]at all currents and a maximum power rating of 100 milli-watt. What should be the value of the resistance R, connected in series with the diode, for obtaining maximum current?
A) \[1.5\,\Omega \]
B) \[5\,\Omega \]
C) \[6.67\,\,\Omega \]
D) \[200\]
View Answer play_arrowquestion_answer76) The presence of electric charge on colloidal particles is indicated by the property, called
A) dialysis
B) solubility
C) electrophoresis
D) osmosis
View Answer play_arrowquestion_answer77) The protective action of different lyophilic colloids is expressed in terms of
A) oxidation number
B) atomic number
C) Avogadro number
D) gold number
View Answer play_arrowquestion_answer78) The group of elements in which the differentiating electrons enters in the antipenultimate shell of atoms are called
A) \[f-\]block elements
B) \[p-\]block elements
C) \[s-\]block elements
D) \[d-\]block elements
View Answer play_arrowquestion_answer79) Lanthanides and actinides are also called as
A) short periods
B) inner-transition elements
C) long periods
D) main transition elements
View Answer play_arrowquestion_answer80) The geometrical shape of \[s{{p}^{3}}d\]hybridisation is
A) linear
B) trigonal bipyramid
C) square planar
D) tetrahedral
View Answer play_arrowquestion_answer81) Intermolecular hydrogen bonding exists in
A) \[~o-\] nitrophenol
B) \[~o-\]chlorophenol
C) water
D) ammonium chloride
View Answer play_arrowquestion_answer82) Which one of the following examples exhibit transient existence?
A) H
B) \[H_{2}^{+}\]
C) \[{{H}^{+}}\]
D) He
View Answer play_arrowquestion_answer83) The number of covalent bonds in fluorine molecule is
A) 2
B) 3
C) 1
D) 5
View Answer play_arrowquestion_answer84) Carbon shows the following oxidation state a its hydrides
A) + 1
B) + 4
C) + 2
D) + 3
View Answer play_arrowquestion_answer85) The following is not an example of oxyacids of sulphur
A) \[{{H}_{2}}S{{O}_{3}}\]
B) \[{{H}_{2}}{{S}_{2}}{{O}_{3}}\]
C) \[{{H}_{2}}S{{O}_{4}}\]
D) \[S{{O}_{3}}\]
View Answer play_arrowquestion_answer86) Calcium sulphate is sparingly soluble in
A) water
B) alcohol
C) acetic acid
D) benzene
View Answer play_arrowquestion_answer87) The bleaching action of chlorine is due to the liberation of the following
A) \[HOCl\]
B) \[HCl\]
C) \[[O]\]
D) \[{{O}_{2}}\]
View Answer play_arrowquestion_answer88) The colour of transition metal ions is due to presence of unpaired electron transitions in available empty electron in
A) \[d-\]orbitals
B) \[p-\]orbitals
C) \[s-\]orbitals
D) s and p-orbitals
View Answer play_arrowquestion_answer89) The oxidation state of Cr in chromium trioxide is
A) + 3
B) + 4
C) + 5
D) + 6
View Answer play_arrowquestion_answer90) Monel metal is an alloy of
A) \[Cu,Ni,Fe,Mn\]
B) \[Cu,Sn,Zn\]
C) \[Cu,Sn,P\]
D) \[Cu,Zn\]
View Answer play_arrowquestion_answer91) The catalyst used in the manufacture of \[{{H}_{2}}S{{O}_{4}}\]by contact process is
A) \[{{V}_{2}}{{O}_{3}}\]
B) \[{{V}_{2}}{{O}_{5}}\]
C) \[FeO\]
D) \[Cu\]
View Answer play_arrowquestion_answer92) The tetrahedral complexes have coordination number
A) 3
B) 6
C) 4
D) 8
View Answer play_arrowquestion_answer93) Potassium ferrocyanide is an example of
A) tetrahedral
B) octahedral
C) square planar
D) linear
View Answer play_arrowquestion_answer94) Which one amongst the following, exhibit geometrical isomerism?
A) \[\text{ }\!\![\!\!\text{ C}{{\text{o}}^{\text{III}}}{{\text{(N}{{\text{H}}_{\text{3}}}\text{)}}_{\text{5}}}\text{Br }\!\!]\!\!\text{ S}{{\text{O}}_{\text{4}}}\]
B) \[C{{o}^{\text{III}}}{{[EDTA]}^{-1}}\]
C) \[{{\text{ }\!\![\!\!\text{ C}{{\text{r}}^{\text{III}}}{{(SCN)}_{6}}]}^{3-}}\]
D) \[[P{{t}^{\text{III}}}{{(N{{H}_{3}})}_{2}}C{{l}_{2}}]\]
View Answer play_arrowquestion_answer95) Benzoylacetonato beryllium exhibit isomerism of the type
A) structural
B) geometrical
C) optical
D) conformational
View Answer play_arrowquestion_answer96) The composition of malachite is
A) \[CuFe{{S}_{2}}\]
B) \[CuC{{O}_{3}}\]
C) \[CuCO3.Cu{{(OH)}_{2}}\]
D) \[Cu{{(OH)}_{2}}\]
View Answer play_arrowquestion_answer97) Which one of the following metals, is extracted on smelting of its ore in blast furnace?
A) Iron
B) Sodium
C) Potassium
D) Magnesium
View Answer play_arrowquestion_answer98) Prussian blue is obtained by mixing together aqueous solution of \[\text{F}{{\text{e}}^{\text{3+}}}\]salt with
A) ferricyanide
B) ferrocyanide
C) hydrogen cyanide
D) sodium cyanide
View Answer play_arrowquestion_answer99) The reaction intermediate produced, by homolytic cleavage of a bond is called
A) carbene
B) carbocation
C) carbanion
D) free radical
View Answer play_arrowquestion_answer100) The formation of cyanohydrin from a ketone is an example of
A) electrophilic addition
B) nucleophilic Substitution
C) nucleophilic addition
D) electrophilic substitution
View Answer play_arrowquestion_answer101) According to Huckel?s rule an aromatic compound must possess
A) \[(4n+1)\pi \] electrons
B) \[(4n+2)\pi \] electrons
C) \[4n\,\pi \] electrons
D) \[(4n+3)\pi \] electrons
View Answer play_arrowquestion_answer102) Identify the substitute group, that acts as ortho-para director, during electrophilic substitution in aromatic compounds.
A) \[-N{{H}_{2}}\]
B) \[-N{{O}_{2}}\]
C) \[-S{{O}_{3}}H\]
D) \[{{N}_{2}}\]
View Answer play_arrowquestion_answer103) In a group of isomeric alkyl halides, the order of boiling points is
A) primary < secondary < tertiary
B) primary > secondary < tertiary
C) primary < secondary > tertiary
D) primary > secondary > tertiary
View Answer play_arrowquestion_answer104) On reacting with neutral ferric chloride, phenol gives
A) red colour
B) blue colour
C) violet colour
D) green colour
View Answer play_arrowquestion_answer105) The hybridisation of the ipso-carbon in chlorobenzene is
A) \[sp\]hybridised
B) \[~s{{p}^{2}}\] hybridised
C) \[~s{{p}^{2}}\] hybridised
D) \[~s{{p}^{3}}\] hybridised
View Answer play_arrowquestion_answer106) Which one of the following alcohol is used as an antifreeze reagent for making explosives?
A) Glycerol
B) Glycol
C) Ethanol
D) Phenol
View Answer play_arrowquestion_answer107) \[n-\]pentane, \[iso-\]pentane, and neo-pentane are examples for isomers of the type
A) geometrical
B) optical
C) chain
D) positional
View Answer play_arrowquestion_answer108) One of the following compounds exhibit geometrical isomerism
A) \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{3}}\]
B) \[C{{H}_{3}}-HC(C{{H}_{3}})-H(C)C{{H}_{3}}-C{{H}_{3}}\]
C) \[C{{H}_{3}}-HC(C{{H}_{3}})-C{{H}_{3}}\]
D) \[C{{H}_{3}}CH=CH-C{{H}_{3}}\]
View Answer play_arrowquestion_answer109) Different structures generated due to rotation about, C-C axis, of an organic molecule, are examples of
A) geometrical isomerism
B) conformational isomerism
C) optical isomerism
D) structural isomerism
View Answer play_arrowquestion_answer110) The number of isomeric halopropanes produced, when propane gets halogenated, is
A) 1
B) 2
C) 4
D) 3
View Answer play_arrowquestion_answer111) The acid strength obeys the order. Arrange the following carboxylic acids in the decreasing order of their reactivities
A) \[C{{H}_{3}}COOH\]
B) \[ClC{{H}_{2}}COOH\]
C) \[C{{l}_{2}}CHCOOH\]
D) \[C{{l}_{3}}CCOOH\]
View Answer play_arrowquestion_answer112) Mohocarboxylic acids react with alcohols in the presence of an acid catalyst to form
A) acid chlorides
B) acid amides
C) esters
D) ethers
View Answer play_arrowquestion_answer113) On reaction with hydroxylamine, aldehydes produce
A) ketoxime
B) hydrazone
C) semicarbazone
D) aldoxime
View Answer play_arrowquestion_answer114) Amides are formed by the reaction of acid chloride with
A) \[N{{H}_{2}}N{{H}_{2}}\]
B) \[N{{H}_{3}}\]
C) \[N{{H}_{2}}OH\]
D) \[{{C}_{6}}{{H}_{5}}NHN{{H}_{2}}\]
View Answer play_arrowquestion_answer115) Which one of the following, is more acidic?
A)
B)
C)
D)
View Answer play_arrowquestion_answer116) Aliphatic nitriles are prepared by the treatment of alkyl halides with
A) sodium cyanide
B) sodium isocyanide
C) sodium isocyanate
D) cyanamide
View Answer play_arrowquestion_answer117) Among the following compounds, the most basic is
A) aniline
B) acetanilide
C) \[p-\]nitroaniline
D) benzylamine
View Answer play_arrowquestion_answer118) Reduction of alkyl nitriles, produces
A) secondary amine
B) primary amine
C) tertiary amine
D) amide
View Answer play_arrowquestion_answer119) Polypeptides having, molecular weights, above 10,000 are known as
A) amino acids
B) harmones
C) proteins
D) terminal amino acids
View Answer play_arrowquestion_answer120) Which one of the following is an example of a non-reducing sugar?
A) Sucrose
B) Lactose
C) Maltose
D) Cellobiose
View Answer play_arrowquestion_answer121) The value of Rydberg constant is
A) \[10,9678\,\text{c}{{\text{m}}^{-1}}\]
B) \[10,9876\,\text{c}{{\text{m}}^{-1}}\]
C) \[10,8769\,\text{c}{{\text{m}}^{-1}}\]
D) \[10,8976\,\text{c}{{\text{m}}^{-1}}\]
View Answer play_arrowquestion_answer122) The wavelength of a spectral line in Lyman series, when electron jumps back from 2nd orbit, is
A) \[\text{1162 }\overset{\text{o}}{\mathop{\text{A}}}\,\]
B) \[1216\overset{\text{o}}{\mathop{\text{A}}}\,\]
C) \[1362\overset{\text{o}}{\mathop{\text{A}}}\,\]
D) \[1176\overset{\text{o}}{\mathop{\text{A}}}\,\]
View Answer play_arrowquestion_answer123) The number of electrons accommodated in an orbit with principal quantum number 2, is
A) 2
B) 6
C) 10
D) 8
View Answer play_arrowquestion_answer124) Uranium with a mass number 237 and atomic number 92, changes to a nucleus with atomic number 90 and mass number 233 on emission of
A) \[\beta -\]particle
B) \[\gamma -\]particle
C) \[\alpha -\]particle
D) positron
View Answer play_arrowquestion_answer125) The only, most stable nucleus formed by bombarding, either \[_{\text{13}}\text{A}{{\text{l}}^{\text{27}}}\]by neutrons or \[_{\text{11}}\text{N}{{\text{a}}^{\text{23}}}\]by deuterons, is
A) \[_{15}{{P}^{30}}\]
B) \[_{14}S{{i}^{30}}\]
C) \[_{12}M{{g}^{24}}\]
D) \[_{56}B{{a}^{137}}\]
View Answer play_arrowquestion_answer126) The stable electronic configuration of chromium is
A) \[3{{d}^{6}},4{{s}^{1}}\]
B) \[3{{d}^{5}},4{{s}^{2}}\]
C) \[3{{d}^{5}},4{{s}^{1}}\]
D) \[3{{d}^{6}},4{{s}^{0}}\]
View Answer play_arrowquestion_answer127) The half-life of \[\text{R}{{\text{a}}^{\text{226}}}\]is \[1620\text{ }yr,\] the decay constant (k) is
A) 0.000452
B) 0.0004278
C) 0.04278
D) 0.004278
View Answer play_arrowquestion_answer128) According to Lowry and Bronsted, the strength of an acid depends upon
A) the tendency to gain electrons
B) the tendency to loss protons
C) the tendency to accept protons
D) the tendency to loss electrons
View Answer play_arrowquestion_answer129) By applying law of mass action, the equilibrium constant,\[K\] for the reaction \[HA+{{H}_{2}}O\rightleftharpoons {{H}_{3}}{{O}^{+}}+\bar{A},\]is given as
A) \[K=\frac{[HA][{{H}_{2}}O]}{[{{H}_{3}}{{O}^{+}}][\bar{A}]}\]
B) \[K=\frac{[{{H}_{3}}{{O}^{+}}][\bar{A}]}{[HA][{{H}_{2}}O]}\]
C) \[K=\frac{[{{H}_{3}}{{O}^{+}}][{{H}_{2}}O]}{[\bar{A}][HA]}\]
D) \[K=\frac{[HA][\bar{A}]}{[\bar{A}][HA]}\]
View Answer play_arrowquestion_answer130) The ionisation of strong electrolytes in acetic. acid, compared to in water, is
A) weak, low
B) strong, more
C) medium, the same
D) no ionisation, 100%
View Answer play_arrowquestion_answer131) Calculate the pH of a solution in which hydrogen ion concentration is 0.005 g-equi/L?
A) 2.3
B) 2.8
C) 2.9
D) 2.6
View Answer play_arrowquestion_answer132) Inversion of cane-sugar in dilute acid is a
A) bimolecular reaction
B) Pseudo-unimolecular reaction
C) unimolecular reaction
D) trimolecular reaction
View Answer play_arrowquestion_answer133) The units of the rate constant of a second order reaction are
A) \[mo{{l}^{-1}}L{{\,}^{-1}}{{s}^{-1}}\]
B) \[mo{{l}^{-1}}L\,{{s}^{-1}}\]
C) \[mo{{l}^{-1}}L\,s\]
D) \[mol\,{{L}^{-1}}{{s}^{-1}}\]
View Answer play_arrowquestion_answer134) For the first order reaction half-life is 14 s, the time required for the initial concentration to reduce to 1/8 of its value is
A) \[{{(14)}^{3}}s\]
B) 28 s
C) 42 s
D) \[{{(14)}^{2}}s\]
View Answer play_arrowquestion_answer135) One part of solute in one million parts of solvent is expressed as
A) ppm
B) mg/100 cc
C) g/L
D) g/100cc
View Answer play_arrowquestion_answer136) The molarity of the solution obtained by dissolving 2.5 g of NaCI in 100 mL of water is
A) 0.00428 moles
B) 428 moles
C) 0.428 moles
D) 0.0428 moles
View Answer play_arrowquestion_answer137) The osmotic pressure is expressed in the units of
A) MeV
B) cat
C) cm/s
D) atm
View Answer play_arrowquestion_answer138) Fractional distillation is a process by which the separation of different fractions from mixture of solution is carried by making use of the following property of the fractions.
A) freezing point
B) boiling point.
C) melting point
D) solubility
View Answer play_arrowquestion_answer139) The quantity of heat measured for a reaction in a bomb calorimeter is equal to
A) \[\Delta G\]
B) \[\Delta H\]
C) \[p\Delta V\]
D) \[\Delta E\]
View Answer play_arrowquestion_answer140) All naturally occurring process, proceed in a direction, which leads to
A) increase of enthalpy
B) increase of free energy
C) decrease of free energy
D) decrease of entropy
View Answer play_arrowquestion_answer141) Heat of combustion of carbon monoxide at constant volume and at \[17{{\,}^{o}}C\]is \[-67,710\,\text{cal}\text{.}\]The heat of combustion at constant pressure is
A) \[~-68,000\text{ cal}\]
B) \[~-67,800\text{ cal}\]
C) \[~-67,050\text{ cal}\]
D) \[~+\,68,500\text{ cal}\]
View Answer play_arrowquestion_answer142) The free energy change \[\Delta G=0\] when
A) the reactants are completely consumed
B) a catalyst is added
C) the system is at equilibrium
D) the reactants are initially mixed
View Answer play_arrowquestion_answer143) The units of equivalent conductance, are
A) ohm \[\text{c}{{\text{m}}^{\text{2}}}\text{equivalen}{{\text{t}}^{-1}}\]
B) ohm \[\text{c}{{\text{m}}^{\text{2}}}\,\text{equivalent}\]
C) \[\text{oh}{{\text{m}}^{-1}}\,c{{m}^{2}}\,\text{equivalen}{{\text{t}}^{-1}}\]
D) \[\text{mho c}{{\text{m}}^{\text{2}}}\text{ equivalent}\]
View Answer play_arrowquestion_answer144) The specific conductance \[(\kappa )\] of an electrolyte of 0.1 N concentration is related to equivalent \[(\Lambda )\]by the following formula
A) \[A=\kappa \]
B) \[A=10\,\kappa \]
C) \[A=100\,\kappa \]
D) \[A=10,000\,\kappa \]
View Answer play_arrowquestion_answer145) The standard electrode potential of hydrogen electrode at 1 M concentration and hydrogen gas at 1 atm pressure is
A) \[1\,V\]
B) \[~6\,V\]
C) \[~8\,V\]
D) \[~0\,V\]
View Answer play_arrowquestion_answer146) Pure water does not conduct electricity because it is
A) basic
B) almost not ionized
C) decomposed easily
D) acidic
View Answer play_arrowquestion_answer147) The crystalline structure of \[\text{NaCl}\]is
A) hexagonal close packing
B) face centred cubic
C) square planar
D) body centred cubic
View Answer play_arrowquestion_answer148) Which one, among the following, is the van der Waals' equation, describing the behaviour of one mole of a real gas over wide ranges. temperature and pressure?
A) \[\left( p+\frac{a}{^{{{V}^{2}}}} \right)(V-b)=RT\]
B) \[\left( p-\frac{a}{^{{{V}^{2}}}} \right)(V-b)=RT\]
C) \[\left( p+\frac{a}{^{{{V}^{2}}}} \right)(V-b)=\frac{R}{T}\]
D) \[\left( p+\frac{a}{^{{{V}^{2}}}} \right)(V+b)=RT\]
View Answer play_arrowquestion_answer149) The following is a method to determine surface tension of liquids
A) single capillary method
B) refractometric method
C) polarimetric method
D) boiling point method
View Answer play_arrowquestion_answer150) The colloidal system of a solid dispersed in liquid medium, is called
A) aerosol
B) sol
C) gel
D) foam
View Answer play_arrowquestion_answer151) If \[2\hat{i}+4\hat{j}-5\hat{k}\] and \[\hat{i}+2\hat{j}+3\hat{k}\] are adjacent sides of a parallelogram, then the lengths of its diagonals are
A) \[7,\,\sqrt{69}\]
B) \[6,\,\sqrt{59}\]
C) \[5,\,\sqrt{65}\]
D) \[5,\,\sqrt{55}\]
View Answer play_arrowquestion_answer152) If the points \[\hat{i}-\hat{j}+\hat{k},\,\,\,2\hat{i}+3\hat{j}+4\hat{k}\]and \[3\hat{i}++7\hat{j}+p\hat{k}\]are collinear, then the value of p is
A) \[6\]
B) \[5\]
C) \[4\]
D) \[7\]
View Answer play_arrowquestion_answer153) If \[\hat{i}+2\hat{j}+3\hat{k}\] and \[2\hat{i}-\hat{j}+4\hat{k}\] are the position vectors of the points A and B, then the position vector of the points of trisection of AB are
A) \[\frac{4}{3}\hat{i}+\hat{j}+\frac{10}{3}\hat{k},\,\frac{5}{3}\hat{i}+\frac{11}{3}\hat{k}\]
B) \[-\frac{4}{3}\hat{i}-\hat{j}-\frac{10}{3}\hat{k},-\,\frac{5}{3}\hat{i}-\frac{11}{3}\hat{k}\]
C) \[\frac{4}{3}\hat{i}-\hat{j}-\frac{10}{3}\hat{k},-\,\frac{5}{3}\hat{i}-\frac{11}{3}\hat{k}\]
D) \[-\frac{4}{3}\hat{i}+\hat{j}-\frac{10}{3}\hat{k},\,\frac{5}{3}\hat{i}-\frac{11}{3}\hat{k}\]
View Answer play_arrowquestion_answer154) If \[\vec{a},\,\,\vec{b},\,\,\vec{c}\] are three vectors such that \[|\vec{a}|=3,|\,\,\vec{b}|=4,|\,\,\vec{c}|=5\] and \[\vec{a},\,\,\vec{b},\,\,\vec{c}\] are perpendicular to \[\vec{b}+\vec{c},\,\vec{c}+\vec{a},\,\,\vec{a}+\vec{b}\]respectively, then \[|\vec{a}\,+\,\vec{b}\,+\vec{c}|\] is equal to
A) \[4\sqrt{2}\]
B) \[5\sqrt{2}\]
C) \[6\sqrt{2}\]
D) \[3\sqrt{2}\]
View Answer play_arrowquestion_answer155) The area of a parallelogram having diagonals \[\vec{a}=3\hat{i}+\hat{j}-2\hat{k}\] and \[\vec{b}=\hat{i}-3\hat{j}+4\hat{k}\] is
A) \[10\sqrt{3}\]
B) \[5\sqrt{3}\]
C) \[8\]
D) \[4\]
View Answer play_arrowquestion_answer156) If \[|\vec{a}|=10,\,\,|\vec{b}|=2\] and \[\vec{a}.\vec{b}=12,\]then \[|\vec{a}\times \vec{b}|\] is equal to
A) \[12\]
B) \[14\]
C) \[16\]
D) \[18\]
View Answer play_arrowquestion_answer157) If \[\vec{a}\] and \[\vec{b}\] are unit vectors and a is the angle between them, then \[\vec{a}\,\,.\,\,\vec{b}\] will be a unit vector, if a is equal to
A) \[\frac{\pi }{4}\]
B) \[\frac{\pi }{3}\]
C) \[\frac{2\pi }{3}\]
D) \[\frac{\pi }{2}\]
View Answer play_arrowquestion_answer158) The angle between the lines with direction ratios \[(4,-3,5)\] and \[(3,4,5)\] is
A) \[\frac{\pi }{2}\]
B) \[\frac{\pi }{4}\]
C) \[\frac{\pi }{3}\]
D) \[\frac{\pi }{6}\]
View Answer play_arrowquestion_answer159) If the extremities of a diagonal of a square are \[(1,-2,3)\] and \[(2,-3,5)\] then the length of the side is
A) \[\sqrt{6}\]
B) \[\sqrt{3}\]
C) \[\sqrt{5}\]
D) \[\sqrt{7}\]
View Answer play_arrowquestion_answer160) If the foot of the perpendicular from \[(0,0,0)\]to a plane is \[(1,2,2),\] then the equation of the plane is
A) \[-x+2y+8y-9=0\]
B) \[x+2y+2z-9=0\]
C) \[x+y+z-5=0\]
D) \[x+2y-3z+1=0\]
View Answer play_arrowquestion_answer161) If a line makes angles \[\frac{\pi }{3}\] and \[\frac{\pi }{4}\] with the X and Y-axes respectively, then the angle made by the line and Z-axis is
A) \[\frac{\pi }{2}\]
B) \[\frac{\pi }{3}\]
C) \[\frac{\pi }{4}\]
D) \[\frac{5\pi }{12}\]
View Answer play_arrowquestion_answer162) If \[P=(0,1,2),\,\,Q=(4,-2,1),O=(0,0,0),\] then \[\angle POQ\] is equal to
A) \[\frac{\pi }{6}\]
B) \[\frac{\pi }{4}\]
C) \[\frac{\pi }{3}\]
D) \[\frac{\pi }{2}\]
View Answer play_arrowquestion_answer163) The direction cosines of two rays \[\overrightarrow{AB}\] and \[\overrightarrow{AC}\] are \[\left( \frac{1}{2},\frac{1}{2},-1 \right)\] and \[\left( \frac{2}{7},\frac{-3}{7},\frac{6}{7} \right).\] The direction ratios of one of the bisectors of angle \[\left( \overrightarrow{AB},\overrightarrow{AC} \right)\]are
A) \[(13,\,-5,\,\,4)\]
B) \[(13,\,5,\,\,-5)\]
C) \[(13,\,5,4)\]
D) None of these
View Answer play_arrowquestion_answer164) The equation of the plane passing through the points \[(a,0,0),(0,b,0)\] and \[(0,0,c)\] is
A) \[ax+by+cz=0\]
B) \[ax+by+cz=1\]
C) \[\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1\]
D) \[\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=0\]
View Answer play_arrowquestion_answer165) Through the point \[P(\alpha ,\,\beta ,\,\,\gamma )\] a plane is drawn at right angles to OP to meet the coordinate axes are A, B,. C respectively. If \[OP=p,\]then equation of plane \[\underset{ABC}{\longleftrightarrow}\] is
A) \[\alpha x+\beta y+\gamma z=p\]
B) \[\frac{x}{\alpha }+\frac{x}{\beta }+\frac{z}{\gamma }=p\]
C) \[2\alpha x+2\beta y+2\gamma z={{p}^{2}}\]
D) \[\alpha x+\beta y+\gamma z={{p}^{2}}\]
View Answer play_arrowquestion_answer166) The solution of the equation \[2{{x}^{3}}-{{x}^{2}}-22x-24=0\]when two of the roots are in the ratio \[3:4,\] is
A) \[3,\,4,\frac{1}{2}\]
B) \[-\frac{3}{2},-2,4\]
C) \[-\frac{1}{2},\frac{3}{2},2\]
D) \[\frac{3}{2},2,\frac{5}{2}\]
View Answer play_arrowquestion_answer167) The condition that the roots of the equation \[{{x}^{3}}+3p{{x}^{2}}+3qx+r=0\] satisfied, is
A) \[2{{p}^{3}}-3pq+r=0\]
B) \[2{{p}^{3}}+3pq+r=0\]
C) \[2{{p}^{3}}-3pq-r=0\]
D) \[{{p}^{3}}+3pq-r=0\]
View Answer play_arrowquestion_answer168) If \[\alpha ,\beta ,\gamma \] are the roots of the equation \[{{x}^{3}}-7x+7=0,\] then \[\frac{1}{{{\alpha }^{4}}}+\frac{1}{{{\beta }^{4}}}+\frac{1}{{{\gamma }^{4}}}\] is
A) \[\frac{7}{3}\]
B) \[\frac{3}{7}\]
C) \[\frac{4}{7}\]
D) \[\frac{7}{4}\]
View Answer play_arrowquestion_answer169) At \[x=\frac{3}{2}\] the function \[f(x)=\frac{|2x-3|}{2x-3}\] is
A) continuous
B) discontinuous
C) differentiable
D) non-zero
View Answer play_arrowquestion_answer170) \[\underset{x\to -1}{\mathop{\lim }}\,\frac{1+\sqrt[3]{x}}{1+\sqrt[5]{x}}\]is equal to
A) \[\frac{5}{3}\]
B) \[\frac{3}{7}\]
C) \[\frac{4}{7}\]
D) \[\frac{-3}{5}\]
View Answer play_arrowquestion_answer171) \[\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{2}^{-n}}({{n}^{2}}+5n+6)}{(n+4)\,(n+5)}\] is equal to
A) \[0\]
B) \[1\]
C) \[\infty \]
D) \[-\infty \]
View Answer play_arrowquestion_answer172) \[\underset{x\to \pi /4}{\mathop{\lim }}\,\frac{\sqrt{2}\cos \,x-1}{\cot \,x-1}\] is equal to
A) \[1\]
B) \[-\frac{1}{2}\]
C) \[\frac{1}{2\sqrt{2}}\]
D) \[\frac{1}{2}\]
View Answer play_arrowquestion_answer173) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{1}{x}{{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right)\]is equal to
A) \[-2\]
B) \[0\]
C) \[2\]
D) \[\infty \]
View Answer play_arrowquestion_answer174) If n is an integer, then \[\underset{x\to n}{\mathop{\lim }}\,[x]\]
A) \[n-1\]
B) \[n\]
C) does not exist
D) \[n+1\]
View Answer play_arrowquestion_answer175) If \[f(x)=\frac{{{e}^{1/x}}}{1+{{e}^{1/x}}}\]for \[x\ne 0\] and \[f(0)=0,\] then at \[x=0\] the function \[f(x)\] is
A) continuous
B) discontinuous
C) increasing
D) differentiable
View Answer play_arrowquestion_answer176) Derivative of \[{{\log }_{10}}\,x\] with respect to \[{{x}^{2}}\]is
A) \[2{{x}^{2}}\,{{\log }_{e}}\,10\]
B) \[\frac{{{\log }_{10}}\,e}{2{{x}^{2}}}\]
C) \[\frac{{{\log }_{e}}\,10}{2{{x}^{2}}}\]
D) \[{{x}^{2}}\,{{\log }_{e}}\,10\]
View Answer play_arrowquestion_answer177) The greatest value of \[si{{n}^{3}}x+co{{s}^{3}}x\]is
A) \[1\]
B) \[2\]
C) \[\sqrt{2}\]
D) \[\sqrt{3}\]
View Answer play_arrowquestion_answer178) The function \[f(x)=1-{{x}^{3}}\]
A) increases everywhere
B) decrease in \[(0,\infty )\]
C) increases is \[(0,\infty )\]
D) None of the above
View Answer play_arrowquestion_answer179) The equation of the normal line to the curve \[y=x\,{{\log }_{e}}x\] parallel to\[2x-2y+3=0\] is
A) \[x+y=3{{e}^{-2}}\]
B) \[x-y=6{{e}^{-2}}\]
C) \[x-y=3{{e}^{-2}}\]
D) \[x-y=6{{e}^{2}}\]
View Answer play_arrowquestion_answer180) If \[f(x)=\sin \,x/{{e}^{x}}\] in \[[0,\pi ],\] then \[f(x)\]
A) satisfies Rollers theorem and \[c=\frac{\pi }{4},\] so that \[f'\left( \frac{\pi }{4} \right)=4\]
B) does not satisfy Rolle's theorem but \[f'\left( \frac{\pi }{4} \right)>0\]
C) satisfies Rolle's theorem but \[f'\left( \frac{\pi }{4} \right)=0\]
D) satisfies Lagranges Mean value theorem but \[f'\left( \frac{\pi }{4} \right)\ne 0\]
View Answer play_arrowquestion_answer181) \[\int{\frac{1}{1+\cos \,\,ax}}\,\,dx\] is equal to
A) \[\cot \,\frac{ax}{2}+c\]
B) \[\frac{1}{a}\,\tan \,\frac{ax}{2}+c\]
C) \[\frac{1}{a}(\text{cosec ax - cot ax)+c}\]
D) \[\frac{1}{a}(\text{cosec ax + cot ax)+c}\]
View Answer play_arrowquestion_answer182) \[\int{\frac{{{\log }_{e}}\,(\tan x)}{sin\,x\,\cos \,x}}\,\,dx\] is equal to
A) \[{{[{{\log }_{e}}\,(tan\,x)]}^{2}}+c\]
B) \[\frac{1}{2}{{({{\log }_{e}}\,\tan x)}^{2}}+c\]
C) \[{{\log }_{e}}\,\,({{\log }_{e}}\,\,\tan \,x)+c\]
D) \[{{\log }_{e}}\,\,\tan \,x+c\]
View Answer play_arrowquestion_answer183) \[\int_{0}^{\pi }{{{\cos }^{3}}\,x\,\,dx}\]is equal to
A) \[0\]
B) \[1\]
C) \[-1\]
D) \[\frac{1}{2\sqrt{2}}\]
View Answer play_arrowquestion_answer184) \[\int_{0}^{a}{\sqrt{{{a}^{2}}-{{x}^{2}}}}\,\,\,dx\] is equal to
A) \[\pi {{a}^{2}}\]
B) \[\frac{1}{2}\pi {{a}^{2}}\]
C) \[\frac{1}{3}\pi {{a}^{2}}\]
D) \[\frac{1}{4}\pi {{a}^{2}}\]
View Answer play_arrowquestion_answer185) The area bounded by the curves \[y=3x\]and \[y={{x}^{2}}\]is (in square units)
A) \[10\]
B) \[5\]
C) \[4.5\]
D) \[9\]
View Answer play_arrowquestion_answer186) The order of the differential equation \[{{\left( \frac{dy}{dx} \right)}^{3}}+{{\left( \frac{dy}{dx} \right)}^{2}}+{{y}^{4}}=0\]is
A) \[4\]
B) \[3\]
C) \[1\]
D) \[2\]
View Answer play_arrowquestion_answer187) The solution \[\frac{dy}{dx}+y={{e}^{x}}\]is
A) \[2y={{e}^{2x}}+c\]
B) s\[2y{{e}^{x}}={{e}^{2}}+c\]
C) \[2y{{e}^{x}}={{e}^{2x}}+c\]
D) \[2y{{e}^{2x}}=2{{e}^{x}}+c\]
View Answer play_arrowquestion_answer188) When three dice are thrown the probability of getting a 4 or a 5 on each of the dice simultaneously is
A) \[\frac{1}{72}\]
B) \[\frac{1}{108}\]
C) \[\frac{1}{24}\]
D) None of these
View Answer play_arrowquestion_answer189) The probability of forming a three digit number with the same digits when three digit numbers are formed out of the digits \[0,2,4,6,8\]
A) \[\frac{1}{16}\]
B) \[\frac{1}{12}\]
C) \[\frac{1}{645}\]
D) \[\frac{1}{25}\]
View Answer play_arrowquestion_answer190) \[P(A\cup B)=\frac{1}{2},P(\bar{A})=\frac{2}{3},\] find \[P(\bar{A}\cap B)\]
A) \[\frac{1}{3}\]
B) \[1\]
C) \[\frac{1}{5}\]
D) \[\frac{1}{6}\]
View Answer play_arrowquestion_answer191) A random variable X has the following probability distribution
\[X(={{x}_{i}})\] | \[1\] | \[2\] | \[3\] | \[4\] |
\[P(X={{x}_{i}})\] | \[k\] | \[2k\] | \[3k\] | \[4k\] |
A) \[3\]
B) \[1\]
C) \[4\]
D) \[2\]
View Answer play_arrowquestion_answer192) The mean and variance of a random variable X having a Binomial distribution are 4 and 2 respectively. Then, \[P(X>6)\] is equal to
A) \[\frac{1}{256}\]
B) \[\frac{3}{256}\]
C) \[\frac{9}{256}\]
D) \[\frac{7}{256}\]
View Answer play_arrowquestion_answer193) If A and B are mutually exclusive events with \[P(A)=\frac{1}{2}\times P(B)\] and \[A\cup B=S,\] (total sample space) then \[P(A)\] is equal to
A) \[\frac{2}{3}\]
B) \[\frac{1}{3}\]
C) \[\frac{1}{4}\]
D) \[\frac{3}{4}\]
View Answer play_arrowquestion_answer194) A coin is tossed three times. The probability of getting a head once and a tail twice is
A) \[\frac{1}{8}\]
B) \[\frac{1}{3}\]
C) \[\frac{3}{8}\]
D) \[\frac{1}{2}\]
View Answer play_arrowquestion_answer195) The probability of choosing a number divisible by 6 or 8 from among 1 to 90 is
A) \[\frac{1}{6}\]
B) \[\frac{1}{90}\]
C) \[\frac{1}{30}\]
D) \[\frac{23}{90}\]
View Answer play_arrowquestion_answer196) If the function \[f:R\to R\] denned by \[f(x)=[x]\]where \[[x]\] is the greatest integer not exceeding x, for \[x\in R\] then /is
A) even
B) odd
C) neither even nor odd
D) strictly increasing
View Answer play_arrowquestion_answer197) If \[f:R\to R\] is given by \[f(x)=\left\{ \begin{matrix} -1,\,when\,\,x\,\,is\,\,rational \\ 1,\,when\,\,x\,\,is\,\,irrational \\ \end{matrix} \right.\] then \[(fof)\,(1-\sqrt{3})\] is equal to
A) \[1\]
B) \[-1\]
C) \[\sqrt{3}\]
D) \[0\]
View Answer play_arrowquestion_answer198) If \[\frac{{{(1+i)}^{2}}}{2-i}=x+iy,\] then \[x+y\] is equal to
A) \[-\frac{2}{5}\]
B) \[\frac{6}{5}\]
C) \[\frac{2}{5}\]
D) \[-\frac{6}{5}\]
View Answer play_arrowquestion_answer199) If \[1,\,\omega ,\,{{\omega }^{2}}\] are the cube roots of unity, then \[(1-\omega +{{\omega }^{2}})(1-{{\omega }^{2}}+{{\omega }^{4}})(1-{{\omega }^{4}}+{{\omega }^{8}})\] \[(1-{{\omega }^{8}}+{{\omega }^{16}})....\] upto 2n factors is
A) \[2n\]
B) \[{{2}^{2n}}\]
C) \[1\]
D) \[-{{2}^{2n}}\]
View Answer play_arrowquestion_answer200) If \[\alpha \] and \[\beta \] are the roots of \[{{x}^{2}}+5x+4=0,\]then equation whose roots are \[\frac{\alpha +2}{3},\frac{\beta +2}{3}\]is
A) \[9{{x}^{2}}+3x+2=0\]
B) \[9{{x}^{2}}-3x-2=0\]
C) \[9{{x}^{2}}+3x-2=0\]
D) \[9{{x}^{2}}-3x+2=0\]
View Answer play_arrowquestion_answer201) If the difference between the roots of \[{{x}^{2}}+ax-b=0\]is equal to the difference between the roots of \[{{x}^{2}}-px+q=0,\]then \[{{a}^{2}}-{{p}^{2}}\]in terms of b and q is
A) \[-4(b+q)\]
B) \[4(b+q)\]
C) \[4(b-q)\]
D) \[4(q-b)\]
View Answer play_arrowquestion_answer202) In a geometric progression (GP) the ratio of the sum of the 1st three terms and first six terms is \[125:152\] the common ratio is
A) \[\frac{1}{5}\]
B) \[\frac{2}{5}\]
C) \[\frac{4}{5}\]
D) \[\frac{3}{5}\]
View Answer play_arrowquestion_answer203) The term independent of x in the expansion of \[\left( \frac{2\sqrt{x}}{x}-\frac{1}{2x\sqrt{x}} \right)\] is
A) 5th term
B) 6th term
C) 11 th term
D) no term
View Answer play_arrowquestion_answer204) The mid points of the sides of a triangle are \[D(6,1),\,\,E(3,\,5)\] and \[F(-1,-2),\] then the vertex opposite to D is
A) \[(-4,2)\]
B) \[(-4,5)\]
C) \[(2,\,5)\]
D) \[(10,\,8)\]
View Answer play_arrowquestion_answer205) If the centroid of the triangle formed by the points \[(0,\,0),\,\,(\cos \theta ,\sin \theta )\] and \[(sin\theta ,-\cos \theta )\] lies on the line \[y=2x,\]then \[\theta \] is equal to
A) \[{{\tan }^{-1}}\,\,2\]
B) \[{{\tan }^{-1}}\,\,3\]
C) \[{{\tan }^{-1}}\,\,(-3)\]
D) \[{{\tan }^{-1}}\,\,(-2)\]
View Answer play_arrowquestion_answer206) The point of concurrence of the lines \[ax+by+c=0\]and \[a,b,c\]satisfy the relation \[3a+2b+4c=0\]is
A) \[\left( \frac{3}{2},\frac{1}{4} \right)\]
B) \[\left( \frac{3}{4},\frac{1}{4} \right)\]
C) \[\left( \frac{3}{4},\frac{1}{2} \right)\]
D) \[\left( \frac{3}{2},\frac{1}{2} \right)\]
View Answer play_arrowquestion_answer207) If 3, 4 are intercepts of a line \[L=0,\]then the distance of \[L=0\]from the origin is
A) 5 unit
B) 12 unit
C) \[\frac{5}{12}\]unit
D) \[\frac{12}{5}\]unit
View Answer play_arrowquestion_answer208) The angle between the pair of lines \[({{x}^{2}}+{{y}^{2}}){{\sin }^{2}}\alpha ={{(x\,\cos \theta -y\,\sin \theta )}^{2}}\] is
A) \[\theta \]
B) \[2\,\theta \]
C) \[\alpha \]
D) \[2\,\alpha \]
View Answer play_arrowquestion_answer209) The other end of the diameter through the point \[(-1,1)\] on the circle \[{{x}^{2}}+{{y}^{2}}-6x+4y-12=0\]'
A) \[(-7,5)\]
B) \[(-7,-5)\]
C) \[(7,-5)\]
D) \[(7,5)\]
View Answer play_arrowquestion_answer210) In the parabola \[{{y}^{2}}=4ax,\]the length of the chord passing through the vertex inclined to the axis at\[\frac{\pi }{4}\] is
A) \[4a\sqrt{2}\]
B) \[2a\sqrt{2}\]
C) \[a\sqrt{2}\]
D) \[a\]
View Answer play_arrowquestion_answer211) If \[\frac{1+\cos A}{1-\cos A}=\frac{{{m}^{2}}}{{{n}^{2}}},\] then tan A is equal to
A) \[\pm \frac{2mn}{{{m}^{2}}+{{n}^{2}}}\]
B) \[\pm \frac{2mn}{{{m}^{2}}-{{n}^{2}}}\]
C) \[\frac{{{m}^{2}}+{{n}^{2}}}{{{m}^{2}}-{{n}^{2}}}\]
D) \[\frac{{{m}^{2}}-{{n}^{2}}}{{{m}^{2}}+{{n}^{2}}}\]
View Answer play_arrowquestion_answer212) If \[\alpha +\beta =\frac{\pi }{4},\]then the value of \[(1+\tan \alpha )\] \[(1+\tan \beta )\]is equal to
A) \[1\]
B) \[-1\]
C) \[2\]
D) \[-2\]
View Answer play_arrowquestion_answer213) The value of \[{{\cos }^{2}}\left( \frac{\pi }{4}+\theta \right)-{{\sin }^{2}}\left( \frac{\pi }{4}-\theta \right)\]is
A) \[0\]
B) \[\cos \,\,2\theta \]
C) \[sin\,\,2\theta \]
D) \[\cos \,\theta \]
View Answer play_arrowquestion_answer214) The solutions of \[x+\sin \,5x=\sin 3x\] in \[\left( 0,\frac{\pi }{2} \right)\]
A) \[\frac{\pi }{4},\frac{\pi }{10}\]
B) \[\frac{\pi }{6},\frac{\pi }{3}\]
C) \[\frac{\pi }{4},\frac{\pi }{2}\]
D) \[\frac{\pi }{8},\frac{\pi }{16}\]
View Answer play_arrowquestion_answer215) If \[\cot \,x+\,\text{cosec x = }\sqrt{3},\] the principal value of \[\left( x-\frac{\pi }{6} \right)\]is
A) \[\frac{\pi }{3}\]
B) \[\frac{\pi }{4}\]
C) \[\frac{\pi }{2}\]
D) \[\frac{\pi }{6}\]
View Answer play_arrowquestion_answer216) The value of \[{{\cos }^{-1}}\left( -\frac{1}{2} \right)\] among the following, is
A) \[\frac{9\pi }{3}\]
B) \[\frac{8\pi }{3}\]
C) \[\frac{5\pi }{3}\]
D) \[\frac{11\pi }{3}\]
View Answer play_arrowquestion_answer217) The value of \[{{\cot }^{-1}}\,9+\text{cose}{{\text{c}}^{-1}}\frac{\sqrt{41}}{4}\]is
A) \[\frac{\pi }{2}\]
B) \[\frac{\pi }{4}\]
C) \[\frac{\pi }{3}\]
D) \[\pi \]
View Answer play_arrowquestion_answer218) If \[\left| \begin{matrix} 1 & 1 & 0 \\ 2 & 0 & 3 \\ 5 & -6 & x \\ \end{matrix} \right|=29,\] then x is
A) \[1\]
B) \[2\]
C) \[3\]
D) \[4\]
View Answer play_arrowquestion_answer219) If \[A=\left[ \begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \\ \end{matrix} \right],\] then \[{{A}^{-1}}\]is equal to
A) \[2A\]
B) \[A\]
C) \[-A\]
D) \[I\]
View Answer play_arrowquestion_answer220) If \[x\left[ \begin{matrix} -3 \\ 4 \\ \end{matrix} \right]+y\left[ \begin{matrix} 4 \\ 3 \\ \end{matrix} \right]=\left[ \begin{matrix} 10 \\ -5 \\ \end{matrix} \right],\] then
A) \[x=-2,\,y=1\]
B) \[x=-9,y=10\]
C) \[x=22,y=1\]
D) \[x=2,y=-1\]
View Answer play_arrowquestion_answer221) Let A be a square matrix and \[{{A}^{T}}\] is its transpose, then \[A+{{A}^{T}}\]is
A) a diagonal matrix
B) a symmetric matrix
C) the identity matrix
D) a skew-symmetric matrix
View Answer play_arrowquestion_answer222) If \[\left| \begin{matrix} x & y & z \\ -x & y & z \\ x & -y & z \\ \end{matrix} \right|=kxyz,\] then k is equal to
A) \[1\]
B) \[3\]
C) \[4\]
D) \[2\]
View Answer play_arrowquestion_answer223) The system of equations \[3x-y+4z=3\] \[x+2y-3z=-2\] \[6x+5y+\lambda z=-3\] has at least one solution, if
A) \[\lambda =-5\]
B) \[\lambda =5\]
C) \[\lambda =3\]
D) \[\lambda =-13\]
View Answer play_arrowquestion_answer224) The inverse of \[\left[ \begin{matrix} 5 & 2 \\ 3 & 1 \\ \end{matrix} \right]\]is
A) \[\left[ \begin{matrix} 1 & -2 \\ -3 & 5 \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} -1 & 2 \\ 3 & -5 \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} -1 & -2 \\ -3 & -5 \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} 1 & 2 \\ 3 & 5 \\ \end{matrix} \right]\]
View Answer play_arrowquestion_answer225) \[A=\left[ \begin{matrix} \cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1 \\ \end{matrix} \right],\] then \[{{A}^{-1}}\] is
A) \[A\]
B) \[-A\]
C) \[adj\,(A)\]
D) \[-adj\,(A)\]
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