Solved papers for J & K CET Engineering J and K - CET Engineering Solved Paper-2015

done J and K - CET Engineering Solved Paper-2015

  • question_answer1) Conductivity of semiconductors

    A) is maximum at 0 K

    B) Decreases with increase in temperature

    C) Increases with increase in temperature

    D) is maximum at 300 K

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  • question_answer2) Two copper spheres having same radii, one solid and other hollow, are charged to the same potential. Which of the following statements is correct?

    A) Hollow sphere will hold more charge

    B) Solid sphere will hold more charge

    C) Solid sphere will have uniform volume charge density

    D) Both spheres will hold same charge-

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  • question_answer3) Two pendula oscillate with a constant phase difference of \[{{45}^{o}}\] and same amplitude. If the maximum velocity of one of them is v and that of other is \['v+x',\] then the value of Y will be

    A) \[0\]

    B) \[v/2\]

    C) \[v/\sqrt{2}\]

    D) \[(\sqrt{2})v\]

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  • question_answer4) An observer standing near the sea-coast counts 48 waves per min. If the wavelength of the wave is \[10\text{ }m,\] the velocity of the waves will be

    A) \[8\,\,m/s\]

    B) \[12\,\,m/s\]

    C) \[16\,\,m/s\]

    D) \[20\,\,m/s\]

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  • question_answer5) The carbon resistor has the color band sequence of green, orange, blue and silver. The value of resistance will be

    A) \[64\times {{10}^{7}}\pm 20%\,\,\Omega \]

    B) \[53\times {{10}^{6}}\pm 20%\,\,\Omega \]

    C) \[64\times {{10}^{7}}\pm 10%\,\,\Omega \]

    D) \[53\times {{10}^{6}}\pm 10%\,\,\Omega \]

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  • question_answer6) A parallel narrow-beam of light is falling normally on a glass sphere. It will come to a focus

    A) Inside the sphere (except at its centre)

    B) On the surface of the sphere

    C) Outside the sphere

    D) Exactly at the centre of the sphere

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  • question_answer7) Which of the following is NOT an electromagnetic wave?

    A) Sound wave

    B) Thermal radiation

    C) Microwave

    D) Gamma ray

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  • question_answer8) The ratio of mass defect of the nucleus to its mass number is maximum for

    A) \[{{U}^{238}}\]

    B) \[{{N}^{14}}\]

    C) \[S{{i}^{28}}\]

    D) \[F{{e}^{56}}\]

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  • question_answer9) Assuming density d of a planet to be uniform, we can say that the time period of its artificial satellite is proportional to

    A) \[d\]

    B) \[\sqrt{d}\]

    C) \[1/\sqrt{d}\]

    D) \[1/d\]

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  • question_answer10) An ideal gas is heated at constant volume until its pressure doubles. Which one of the following statements is correct?

    A) The mean speed of the molecules doubles

    B) Root mean square speed of the molecules doubles

    C) Mean square speed of the molecules doubles

    D) Mean square speed of the molecules remains unchanged

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  • question_answer11) In a cyclic process, the change in the internal energy of a system over one complete cycle

    A) Depends on the path

    B) is always negative

    C) Is always zero

    D) is always positive

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  • question_answer12) In a transformer the number of primary turns is four times that of the secondary turns. Its primary is connected to an AC source of voltage V. Then,

    A) Current through its secondary is about four times that of the current through its primary

    B) Voltage across its secondary is about four times that of the voltage across its primary

    C) Voltage across its secondary is about two times that of the voltage across its primary

    D) Voltage across its secondary is about times that of the voltage across its primary

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  • question_answer13) The path of a charge particle after it enters a region of a uniform electrostatic field with velocity perpendicular to the field will be

    A) Straight line

    B) Circular

    C) Helical

    D) Parabolic

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  • question_answer14) The dimension of magnetic flux is

    A) \[[ML{{T}^{-1}}{{A}^{-1}}]\]

    B) \[[M{{L}^{-1}}T{{A}^{-2}}]\]

    C) \[[M{{L}^{-2}}{{T}^{2}}{{A}^{-2}}]\]

    D) \[[M{{L}^{2}}{{T}^{-2}}{{A}^{-1}}]\]

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  • question_answer15) A ball is dropped from the top of \[80\text{ }m\]high tower. If after 2 s of fall the gravity \[(g=10\,m/{{s}^{2}})\] disappears, then time taken to reach the ground since the gravity disappeared is

    A) \[2\,s\]

    B) \[3\,s\]

    C) \[4\,s\]

    D) \[5\,s\]

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  • question_answer16) Which of the following is correct statement about the magnitude of the acceleration 'a' of the particle executing simple harmonic motion?

    A) A will be maximum at the equilibrium position

    B) A will be maximum at the extreme position

    C) A will be always constant

    D) A will always be zero

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  • question_answer17) A concave mirror has focal length f. A convergent beam of light is made incident on it. Then the image distance v is

    A) Zero

    B) less than T

    C) Equal to T

    D) more than T

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  • question_answer18) In an n-p-n transistor, 'p' is

    A) Intrinsic semiconductor

    B) Emitter

    C) Collector

    D) Base

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  • question_answer19) In the fringe pattern of a Young's double slit experiment the ratio of intensities of maxima and minima is\[25:9\]. Then, the ratio of the amplitudes of interfering waves is

    A) \[4:1\]

    B) \[5:3\]

    C) \[4:3\]

    D) \[25:9\]

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  • question_answer20) Consider a ray of light travelling from a denser to a rarer medium. If it is incident at the critical angle then

    A) it will emerge out into the rarer medium

    B) it will undergo total internal reflection

    C) it will travel along the interface separating the two media

    D) it will retrace its path

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  • question_answer21) Radius of Earth is \[6400\text{ }km\]and that of Mars is \[3200\text{ }km\]. Mass of Mars is \[0.1\] that of Earth's mass. Then, the acceleration due to gravity on Mars is nearly

    A) \[1m/{{s}^{2}}\]

    B) \[2.5\text{ }m/{{s}^{2}}\]

    C) \[4m/{{s}^{2}}\]

    D) \[5\,m/{{s}^{2}}\]

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  • question_answer22) Consider boiling water converting into steam. Under this condition, the specific heat of water is

    A) less than zero

    B) zero

    C) slightly greater than zero

    D) infinite

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  • question_answer23) Smallest division on the main scale of given vernier calipers is \[0.5\text{ }mm\]. Vernier scale has 25 divisions and these coincide with 24 main scale divisions. The least count of vernier calipers is

    A) \[0.001\text{ }cm\]

    B) \[0.002\,\,cm\]

    C) \[~0.01\text{ }cm\]

    D) \[0.02\,\,cm\]

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  • question_answer24) If R is Rydberg's constant, the series limit of the wavelength of Balmer series for hydrogen atom is given by

    A) \[1/R\]

    B) \[4/R\]

    C) \[9/R\]

    D) \[16/R\]

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  • question_answer25) In which of the following both transverse and longitudinal waves propagate?

    A) Heat transfer

    B) Elastic wave motion in a solid

    C) Microwave communication

    D) X-ray motion

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  • question_answer26) The combination of gates as shown in the figure forms the

    A) AND gate

    B) OR gale

    C) NOR gate

    D) NOT gate

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  • question_answer27) A magnet makes a single pass through a coil. Then, across the ends of the coil it produces

    A) DC voltage

    B) Sinusoidal voltage

    C) Single voltage pulse

    D) Two voltage pulses

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  • question_answer28) The energy per mole per degree of freedom of an ideal gas is

    A) \[(3/2){{k}_{B}}T\]

    B) \[(1/2){{k}_{B}}T\]

    C) \[(3/2)RT\]

    D) \[(1/2)RT\]

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  • question_answer29) Metal alloys are used for making standard resistance coils because

    A) They have high thermal conductivity

    B) Their resistance depends weakly on temperature

    C) They have low thermal conductivity

    D) Their resistance depends strongly on temperature

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  • question_answer30) The dielectric constant of a perfect conductor is

    A) \[+1\]

    B) \[0\]

    C) Infinite

    D) \[-1\]

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  • question_answer31) The \[220\text{ }V\]AC line voltage that we receive in our homes is

    A) Rms value

    B) peak value

    C) Average value

    D) none of these

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  • question_answer32) A person is standing on a weighing-scale and observes that the reading is\[60\text{ }kg\]. He then suddenly jumps up and observes that reading goes to\[70\text{ }kg\]. Then his maximum upward acceleration is

    A) zero

    B) \[1.4\text{ }m/{{s}^{2}}\]

    C) \[1.63\text{ }m/{{s}^{2}}\]

    D) \[9.8\text{ }m/{{s}^{2}}\]

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  • question_answer33) A solid sphere is rolling down an inclined plane. Then, the ratio of its translational kinetic energy to its rotational kinetic energy is

    A) \[2.5\]

    B) \[1.5\]

    C) \[1\]

    D) \[0.4\]

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  • question_answer34) A block of mass 3 kg starts from rest and slides down a curved path in the shape of a quarter-circle of radius \[2\text{ }m\]and reaches the bottom of path with a speed \[1\text{ }m/s\]. If ?g' is \[10\text{ }m/{{s}^{2}},\] the amount of work done against friction is

    A) \[60\,\,J\]

    B) \[36\,\,J\]

    C) \[24\,\,J\]

    D) \[12\,\,J\]

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  • question_answer35) Values for Brewster's angle can be

    A) only less than \[{{45}^{o}}\]

    B) only greater than \[{{45}^{o}}\]

    C) any value in the range \[{{0}^{o}}\] to \[{{90}^{o}}\] except \[{{45}^{o}}\]

    D) any value in the range \[{{0}^{o}}\] to \[{{90}^{o}}\] including \[{{45}^{o}}\]

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  • question_answer36) Consider a bi-convex lens and a plano-convex lens, with radii of curvature of all the curved surfaces being same. If 'f is the focal length of bi-convex lens then, the focal length of the plano-convex lens is

    A) \[4\,f\]

    B) \[2\,f\]

    C) \[f\]

    D) \[0.5\,\,f\,\]

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  • question_answer37) A body is travelling towards East with a speed of \[9\text{ }m/s\]and with an acceleration of \[2\text{ }m/{{s}^{2}}\]acting along West on it. The displacement of the body during the 5th second of its motion is

    A) \[0.25\text{ }m\]

    B) \[0.5\text{ }m\]

    C) \[0.75\text{ }m\]

    D) zero

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  • question_answer38) Bulk modulus is defined by

    A) increase in length per unit length per unit applied stress

    B) increase in volume per unit volume per unit applied stress

    C) lateral displacement per unit length per unit applied stress

    D) change in cross-sectional area per unit area per unit applied stress

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  • question_answer39) A bullet fired from a rifle loses \[20%\]of its speed while passing through a wooden plank. Then, minimum number of wooden planks required to completely stop the bullet is

    A) \[3\]

    B) \[5\]

    C) \[15\]

    D) \[25\]

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  • question_answer40) If the forward bias voltage in a p-n junction diode is decreased, the length of depletion region will

    A) Increase

    B) Decrease

    C) Not change

    D) Initially increase and then decrease

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  • question_answer41) A particle is undergoing uniform circular motion with angular momentum L. While moving on the same path if its kinetic energy becomes four times, then its angular momentum will be

    A) \[L/4\]

    B) \[L/2\]

    C) \[L\]

    D) \[2L\]

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  • question_answer42) A \[1m\] long solenoid containing 1000 turns produces a flux density of \[3.14\times {{10}^{-3}}\text{ }T\]. The current in the solenoid will be

    A) \[2.0\text{ }A\]

    B) \[2.5\,\,A\]

    C) \[3.0\,\,A\]

    D) \[3.5\,\,A\]

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  • question_answer43) Which of the following is incorrect about sky waves?

    A) Sky waves are not used in long distance communication

    B) Their propagation takes place by total internal reflection

    C) Sky waves support the so-called AM band

    D) The frequency of sky waves ranges typically from \[3\text{ }MHz\]to \[30\text{ }MHz\]

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  • question_answer44) The wave nature of electrons is demonstrated by the

    A) Photoelectric effect

    B) Rutherford's experiment

    C) Doppler's effect

    D) Davisson and Germer experiment

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  • question_answer45) A person carrying a whistle emitting continuously a note of \[272\text{ }Hz\]is running towards a reflecting surface with a speed of\[18\text{ }km/h\]. If the speed of sound is \[345\text{ }m/s,\]the number of beats heard by him are

    A) \[4\]

    B) \[6\]

    C) \[8\]

    D) \[10\]

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  • question_answer46) Consider the two cells having emf \[{{E}_{1}}\] and \[{{E}_{2}}\] \[({{E}_{1}}>{{E}_{2}})\] connected as shown in the figure. A potentiometer is used to measure potential difference between P and Q and the balancing length of the potentiometer wire is\[0.8m\]. Same potentiometer is then used to measure potential difference between P and R and the balancing length is \[0.2\text{ }m\]. Then, the ratio \[{{E}_{1}}/{{E}_{2}}\] is

    A) \[4/3\]

    B) \[5/4\]

    C) \[5/3\]

    D) \[4/1\]

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  • question_answer47) Which of the following is NOT an example of primary cell?

    A) Voltaic cell

    B) Lead-acid cell

    C) Daniel ceil

    D) Leclanche cell

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  • question_answer48) Red, blue, green and violet colour lights are one by one made incident on a photocathode. It is observed that only one color light produces photo-electrons.

    A) Red

    B) Blue

    C) Green

    D) Violet

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  • question_answer49) What amount of original radioactive material is left?

    A) \[6.5%\]

    B) \[12.5%\]

    C) \[25.5%\]

    D) \[33.3%\]

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  • question_answer50) Consider a region of uniform magnetic field directed along positive X-axis. Now a positive test charge Q, located at origin O \[(0,0)\] inside the field, is released from rest position. The particle will

    A) Remain stationary at origin O

    B) Move along positive X-axis

    C) Move along negative X-axis

    D) Undergo a circular motion in the X-Y plane

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  • question_answer51) A charge particle having charge \[1\times {{10}^{-19}}\,C\] revolves in an orbit of radius 1 A such that the frequency of revolution is\[1016\text{ }Hz\]. The resulting magnetic moment in SI units will be

    A) \[1.57\times {{10}^{-21}}\]

    B) \[3.14\times {{10}^{-21}}\]

    C) \[1.57\times {{10}^{-23}}\]

    D) \[3.14\times {{10}^{-23}}\]

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  • question_answer52) The length of antenna to transmit waves of \[1\text{ }MHz\]will be

    A) \[3\,\,m\]

    B) \[15\,\,m\]

    C) \[30\,\,m\]

    D) \[300\,\,m\]

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  • question_answer53) A series LCR circuit is connected to an AC source and is showing resonance. Then

    A) \[{{V}_{R}}=0\]

    B) \[{{V}_{L}}={{V}_{R}}\]

    C) \[{{V}_{C}}={{V}_{R}}\]

    D) \[{{V}_{L}}={{V}_{C}}\]

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  • question_answer54) Dimensions of Planck's constant are

    A) \[[M{{L}^{2}}{{T}^{-1}}]\]

    B) \[[M{{L}^{2}}{{T}^{-3}}]\]

    C) \[[ML{{T}^{-1}}]\]

    D) \[[M{{L}^{3}}{{T}^{-3}}]\]

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  • question_answer55) Consider an electric dipole placed in a region of non-uniform electric field. Choose the correct statement out of the following options:

    A) The dipole will experience only a force

    B) The dipole will experience only a torque

    C) The dipole will experience both the force and torque

    D) The dipole will neither experience a force nor a torque

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  • question_answer56) A block of mass 'm' is placed on an inclined plane having coefficient of friction 'm?. The plane is making an angle \[\theta \] with the horizontal. The minimum value of upward force acting along the inclined plane that can just move the block up is

    A) \[mg\,\,\cos \,\theta \]

    B) \[mmg\,\,\cos \,\theta \]

    C) \[mg\,\,sin\,\theta \]

    D) \[mmg\,\,sin\,\theta \]

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  • question_answer57) A ball is projected up at an angle 9 with horizontal from the top of a tower with speed V. It hits the ground at point A after time \[{{t}_{A}}\] with speed \[{{v}_{A}}\]. Now, this ball is projected at ' same angle and speed from the base of the tower (located at point P) and it hits ground at point B after time \[{{t}_{B}}\] with speed \[{{v}_{B}}\]. Then

    A) \[PA=PB\]

    B) \[{{t}_{A}}<{{t}_{B}}\]

    C) \[{{v}_{A}}<{{v}_{B}}\]

    D) Ball A hits the ground at an angle \[(-\theta )\] with horizontal

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  • question_answer58) The electric field of an electric dipole at a point on its axis at a distance 'd? from the centre of the dipole varies as

    A) \[1/d\]

    B) \[1/{{d}^{2}}\]

    C) \[1/{{d}^{3}}\]

    D) \[1/{{d}^{3/2}}\]

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  • question_answer59) Un-polarised light is travelling from a medium of refractive index 2 to a medium of refractive index 3. The angle of incidence is\[{{60}^{o}}\]. Then

    A) Reflected light will be partially polarized

    B) Reflected light will be plane polarised in a plane perpendicular to plane of incidence

    C) Refracted light will be plane polarised in a plane perpendicular to plane of incidence

    D) Refracted light will be plane polarised in a plane parallel to plane of incidence

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  • question_answer60) Newton's law of cooling applies when a body is losing heat to its surroundings by

    A) Conduction

    B) Convection

    C) Radiation

    D) Conduction as well as radiation

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  • question_answer61) If a homogeneous colloid placed in dark is observed in the direction of light, it appears clear and if it is observed from a direction at right angles to the direction of light beam, it appears perfectly dark. This is known as

    A) Brownian effect

    B) Hardy Schuize effect

    C) Einstein effect

    D) Tyndall effect

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  • question_answer62) When powdered plaster of Paris is mixed with correct amount of water, it sets into a solid mass of

    A) \[CaS{{O}_{4}}.5{{H}_{2}}O\]

    B) \[CaS{{O}_{4}}.3{{H}_{2}}O\]

    C) \[CaS{{O}_{4}}.2{{H}_{2}}O\]

    D) \[CaS{{O}_{4}}.1/2{{H}_{2}}O\]

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  • question_answer63) pV value decreases with increases in p at constant temperature when

    A) there is no attractive or repulsive forces between molecules

    B) attractive and repulsive forces between molecules are equal

    C) attractive forces between molecules are predominant

    D) repulsive forces between molecules are predominant

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  • question_answer64) For a reaction, \[C(s)+C{{O}_{2}}(g)\xrightarrow{{}}2CO(g);\]the partial pressure of \[C{{O}_{2}}\]and CO are 4 and 8 atm, respectively. \[{{K}_{p}}\]for the reaction is

    A) 0.5

    B) 2

    C) 16

    D) 4

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  • question_answer65) HA is a weak acid. At\[\text{25}{{\,}^{\text{o}}}\text{C,}\]the molar conductivity of 0.02 M HA is \[150\,{{\Omega }^{-1}}c{{m}^{2}}mo{{l}^{-1}}.\]If its\[\text{ }\!\!\Lambda\!\!\text{ }_{\text{m}}^{\text{o}}\] is \[300\,{{\Omega }^{-1}}\,c{{m}^{2}}mo{{l}^{-1}},\]then equilibrium constant of HA dissociation is

    A) 0.001

    B) 0.005

    C) 0.01

    D) 0.02

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  • question_answer66) The product of the following reaction is

    A)

    B)

    C)

    D)

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  • question_answer67) Identify the major product for the reaction given below:

    A)

    B)

    C)

    D)

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  • question_answer68) 30 mL of 0.02 M ammonium hydroxide is mixed with 15 mL of 0.02 M HCl. What will be the pH of the solution \[(p{{K}_{b}}=4.0)\]?

    A) 4

    B) 8

    C) 4

    D) 10

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  • question_answer69) In an acidified aqueous solution of\[\text{M}{{\text{n}}^{\text{2+}}}\text{,N}{{\text{i}}^{\text{2+}}}\text{,C}{{\text{u}}^{\text{2+}}}\]and \[\text{H}{{\text{g}}^{\text{2+}}}\,\text{ions,}\,{{\text{H}}_{\text{2}}}\text{S}\]gas was passed. Precipitates are

    A) MnS and CuS

    B) NiS and HgS

    C) MnS and NiS

    D) CuS and HgS

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  • question_answer70) Shape of \[\text{S}{{\text{F}}_{\text{4}}}\]is

    A) tetrahedral

    B) square planar

    C) trigonal pyramid

    D) see-saw

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  • question_answer71) The following tripeptide can be synthesized from the following ammo acid

    A) Glycine, Leucine and Alanine

    B) Alanine, Isoleucine and Glycine

    C) Valine, Afanine and Glycine

    D) Alanine, Serine and Glycine

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  • question_answer72) The species which cannot serve as an initiator for the free radical polymerisation, is

    A)

    B)

    C)

    D)

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  • question_answer73) Nylon is a

    A) polyamide

    B) carbonate

    C) ester

    D) polycarboxylic acid

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  • question_answer74) A gas at high temperature is cooled. The highest temperature at which liquefaction of gas first occurs is called

    A) Boyle temperature

    B) critical temperature

    C) boiling temperature

    D) freezing temperature

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  • question_answer75) Buna-N synthetic rubber is obtained by copolymerisation of

    A) \[C{{H}_{2}}=CH-CH=C{{H}_{2}}\]and \[{{H}_{5}}{{C}_{6}}-CH=C{{H}_{2}}\]

    B) \[C{{H}_{2}}=CH-CN\]and \[{{H}_{2}}C=CH-CH=C{{H}_{2}}\]

    C) \[{{H}_{2}}C=CH-CN\]and \[C{{H}_{2}}=CH-C(C{{H}_{3}})=C{{H}_{2}}\]

    D) \[{{H}_{2}}C=CH-C(Cl)=C{{H}_{2}}\]and \[{{H}_{2}}C=CH-CH=C{{H}_{2}}\]

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  • question_answer76) When the following amide is treated with \[B{{r}_{2}}/KOH,\]it gives

    A)

    B)

    C)

    D)

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  • question_answer77) The IUPAC name of the coordination compound\[[Co{{({{H}_{2}}O)}_{2}}{{(N{{H}_{3}})}_{4}}]C{{l}_{3}}\] is

    A) tetraamminediaquacobalt (III) chloride

    B) cobalt (III) tetraamminediaqua chloride

    C) diaquatetraammine cobalt (III) chloride

    D) tetraamminediaquacobalt (II) chloride

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  • question_answer78) Siderite is mainly ore of

    A) Zn

    B) Fe

    C) Cd

    D) Ru

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  • question_answer79) Among P, S, Cl, F, the elements with most negative and least negative electron gain enthalpy respectively, are

    A) CI, S

    B) F, S

    C) CI, P

    D) F, P

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  • question_answer80) For a reaction \[\text{2A}\xrightarrow{\text{3B}}\text{3B;}\]if the rate of formation of B is\[x\,\text{mol/L,}\]the rate of consumption of A is

    A) \[x\]

    B) \[\frac{3x}{2}\]

    C) \[\frac{2x}{3}\]

    D) \[3x\]

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  • question_answer81) The following alcohol after treatment with acid gives compound A. Ozonolsis of A gives nonane-2, 8-dione. The compound A is

    A)

    B)

    C)

    D)

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  • question_answer82) In \[\text{H}{{\text{e}}_{\text{2}}}\text{,}\]the electrons in bonding and anti-bonding orbitals are

    A) 2, 2

    B) 4, 2

    C) 4, 0

    D) 2, 4

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  • question_answer83) 0.5 molal solution of a solute in benzene shows a depression in freezing point equal to 2 K. Molal depression constant for benzene is \[\text{5}\,\text{K}\,\text{kg}\,\text{mo}{{\text{l}}^{-1}}.\]If the solute forms dimer in benzene, what is the % association?

    A) 40

    B) 50

    C) 60

    D) 80

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  • question_answer84) The major product of the following transformation is

    A)

    B)

    C)

    D)

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  • question_answer85) A highly stable conformation for the following compound is

    A)

    B)

    C)

    D)

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  • question_answer86) Molar enthalpy change for melting of ice is 6 kJ/mol. Then the internal energy change (in kJ/mol) when 1 mole of water is converted into ice at 1 atm at \[0{{\,}^{o}}C\]is

    A) \[RT/1000\]

    B) 6

    C) \[6-(RT/1000)\]

    D) \[6+(RT/1000)\]

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  • question_answer87) Identify the correct product of the following reaction

    A)

    B)

    C)

    D)

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  • question_answer88) Among second period elements/the correct order for first ionisation enthalpy is

    A) \[Li<Be<B<C<N<O<F<Ne\]

    B) \[Li<B<Be<C<O<N<F<Ne\]

    C) \[Li>Be>B>C>N>O>F>Ne\]

    D) .\[Li>B>C>Be>O>N>F>Ne\]

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  • question_answer89) For the reaction \[A(s)+2{{B}^{+}}(aq)\to {{A}^{2+}}(aq)+2B(s);\]the \[{{E}^{o}}\]is 1.18 V. Then the equilibrium constant for the reaction is

    A) \[{{10}^{10}}\]

    B) \[{{10}^{20}}\]

    C) \[{{10}^{40}}\]

    D) \[{{10}^{60}}\]

    View Answer play_arrow
  • question_answer90) Identify the correct statement about the following pairs of compounds.

    A) A and B diastereomer; C and D diastereomer

    B) A and B enantiomer; C and D diastereomer

    C) A and B diastereomer; C and D enantiomer

    D) A and B enantiomer; C and D enantiomer

    View Answer play_arrow
  • question_answer91) One of the following complexes shows geometrical isomerism. The complex is

    A) \[PtC{{l}_{4}}\]

    B) \[Pt{{(N{{H}_{3}})}_{2}}C{{l}_{2}}\]

    C) \[Pt{{(N{{H}_{3}})}_{3}}Cl\]

    D) \[Ni{{(N{{H}_{3}})}_{3}}Cl\]

    View Answer play_arrow
  • question_answer92) The ionisation potential of hydrogen atom is 13.6 eV. The energy required to remove an electron from \[n=2\]state of hydrogen atom is

    A) \[27.2\,eV\]

    B) \[13.6\,\,eV\]

    C) \[6.8\,eV\]

    D) \[3.4\,eV\]

    View Answer play_arrow
  • question_answer93) Among the following pair, which one has both variables as intensive variable?

    A) \[T,V\]

    B) \[m,p\]

    C) \[d,V\]

    D) \[\rho ,T\]

    View Answer play_arrow
  • question_answer94) Which one of the following will quickly react with \[\text{AgN}{{\text{O}}_{\text{3}}}\]?

    A)

    B)

    C)

    D)

    View Answer play_arrow
  • question_answer95) The number of tetrahedral and octahedral void per unit cell of cubic closed packed structure is

    A) 4, 8

    B) 4.4

    C) 8,4

    D) 8,8

    View Answer play_arrow
  • question_answer96) In the following disaccharide,

    A) Ring [A] ispyranonewith\[\alpha -\]glycosidiclink

    B) Ring [A] is furanone with \[\alpha -\]glycosidic link

    C) Ring [S] is pyranone with \[\beta -\]glycosidic link

    D) Ring [B] is furanone with \[\alpha -\]glycosidic link

    View Answer play_arrow
  • question_answer97) When a dilute solution of ammonia is saturated with \[{{\text{H}}_{\text{2}}}\text{S}\]it gives

    A) \[{{(N{{H}_{4}})}_{2}}S\]

    B) \[N{{H}_{4}}HS\]

    C) \[{{(N{{H}_{3}})}_{2}}{{H}_{2}}S\]

    D) \[N{{H}_{3}}.{{H}_{2}}S\]

    View Answer play_arrow
  • question_answer98) If \[{{E}^{o}}_{{{M}^{+}}/M}=-1.2V,{{E}^{o}}_{{{x}_{2}}/{{x}^{-}}}=-1.1\,V\]and \[{{E}^{o}}_{{{o}_{2}}/{{H}_{2}}O}=1.23\,V,\]then on electrolysis of aqueous solution of salt MX, the products obtained are

    A) \[M,{{X}_{2}}\]

    B) \[{{H}_{2}},{{X}_{2}}\]

    C) \[{{H}_{2}},{{O}_{2}}\]

    D) \[M,{{O}_{2}}\]

    View Answer play_arrow
  • question_answer99) For the process to occur under adiabatic condition, the correct condition is

    A) \[\Delta T=0\]

    B) \[\Delta U=0\]

    C) \[\Delta p=0\]

    D) \[\Delta q=0\]

    View Answer play_arrow
  • question_answer100) Which of the element is available in carbonic anhydrase?

    A) Pd

    B) Fe

    C) Zn

    D) Pt

    View Answer play_arrow
  • question_answer101) Identify reactant for the following reaction

    A)

    B)

    C)

    D)

    View Answer play_arrow
  • question_answer102) Identify the product of the following reaction.

    A)

    B)

    C)

    D)

    View Answer play_arrow
  • question_answer103) The absolute configuration of the following compound is

    A) \[R,R,R\]

    B) \[R,R,S\]

    C) \[R,S,R\]

    D) \[S,R,R\]

    View Answer play_arrow
  • question_answer104) The wrong statement among the following is

    A) acid rain is mostly because of oxides of nitrogen and sulphur

    B) green house effect is responsible for global warming

    C) ozone layer does not permit infrared infrared radiation from the sun to reach earth

    D) chlorofluorocarbons are responsible for ozone layer depletion

    View Answer play_arrow
  • question_answer105) The vapour pressure of pure benzene at certain temperature is 1 bar. A non-volatile, non-electrolyte solid weighing 2 g when added to 39 g of benzene (molar mass\[78\,g\,mo{{l}^{-1}}\]) yields solution of vapour pressure of 0.8 bar. The molar mass of solid substance is

    A) 32

    B) 16

    C) 64

    D) 48

    View Answer play_arrow
  • question_answer106) \[\text{HCl}{{\text{O}}_{\text{4}}}\text{.2}{{\text{H}}_{\text{2}}}\text{O}\]after reaction with fuming sulphuric acid generates.

    A) \[Cl{{O}_{2}}+{{H}_{2}}S{{O}_{4}}\]

    B) \[C{{l}_{2}}{{O}_{7}}+{{H}_{2}}S{{O}_{4}}\]

    C) \[HCl{{O}_{4}}+{{H}_{2}}S{{O}_{4}}\]

    D) \[C{{l}_{2}}{{O}_{6}}+{{H}_{2}}S{{O}_{4}}\]

    View Answer play_arrow
  • question_answer107) The compound formed upon combustion of potassium metal in excess air is

    A) \[{{K}_{2}}{{O}_{2}}\]

    B) \[K{{O}_{2}}\]

    C) \[{{K}_{2}}O\]

    D) \[KOH\]

    View Answer play_arrow
  • question_answer108) Energy of activation of forward reaction for an endothermic process is 90 kJ. If enthalpy change for the reaction is 50 kJ then activation energy for backward reaction will be

    A) 40 kJ

    B) 140 kJ

    C) 90 kJ

    D) 50 kJ

    View Answer play_arrow
  • question_answer109) For ion \[{{O}_{2}}^{-},\]the bond order is

    A) 2

    B) 1.5

    C) 2.5

    D) 0

    View Answer play_arrow
  • question_answer110) Extraction of mercury from cinnabar is achieved by

    A) heating it in air

    B) electrolytic reduction

    C) roasting followed by reduction with carbon

    D) roasting followed by reduction with another metal

    View Answer play_arrow
  • question_answer111) The correct order of the ligands,\[O{{H}^{-}},NO_{3}^{-},PP{{h}_{3}},\] pyridine, according to their increasing field strength is

    A) \[NO_{3}^{-}<O{{H}^{-}}<pyridine<PP{{h}_{3}}\]

    B) \[O{{H}^{-}}<NO_{3}^{-}<PP{{h}_{3}}<\text{pyridine}\]

    C) \[O{{H}^{-}}<NO_{3}^{-}<\text{pyridine}<PP{{h}_{3}}\]

    D) \[NO_{3}^{-}<O{{H}^{-}}<PP{{h}_{3}}<Pyridine\]

    View Answer play_arrow
  • question_answer112) When \[{{\text{(C}{{\text{H}}_{\text{3}}}\text{)}}_{\text{3}}}\text{CC}{{\text{H}}_{\text{2}}}\text{Cl}\]is heated at \[\text{300}{{\,}^{o}}\text{C,}\] it gives

    A)

    B)

    C)

    D)

    View Answer play_arrow
  • question_answer113) If the density of methanol is \[0.8\,\text{kg}\,{{\text{L}}^{-1}},\] what is its volume needed for making 4 L of its 0.25 M solution?

    A) 4mL

    B) 8 mL

    C) 40 mL

    D) 80 mL

    View Answer play_arrow
  • question_answer114) The number of Na atom in 46 g Na (atomic weight of Na= 2 3) is

    A) \[6.023\times {{10}^{23}}\]

    B) 2

    C) 1

    D) \[12.046\times {{10}^{23}}\]

    View Answer play_arrow
  • question_answer115) If the solubility of a sparingly soluble salt\[\text{A}{{\text{X}}_{\text{2}}}\] is s mol/L, the solubility product is

    A) \[4{{s}^{3}}\]

    B) \[8{{s}^{3}}\]

    C) \[4{{s}^{2}}\]

    D) \[{{s}^{2}}\]

    View Answer play_arrow
  • question_answer116) Which one of the following does not have \[\text{s}{{\text{p}}^{\text{3}}}\]hybridisation?

    A) \[C{{H}_{4}}\]

    B) \[Xe{{F}_{4}}\]

    C) \[{{H}_{2}}O\]

    D) \[N{{H}_{3}}\]

    View Answer play_arrow
  • question_answer117) Milk is an example of

    A) emulsion

    B) sol

    C) gel

    D) foam

    View Answer play_arrow
  • question_answer118) \[\frac{{{K}_{p}}}{{{K}_{C}}}\]for the reaction \[A(g)+2{{B}_{2}}(g)\xrightarrow{{}}A{{B}_{2}}(g)\]is

    A) \[RT\]

    B) \[{{(RT)}^{2}}\]

    C) \[\frac{1}{RT}\]

    D) \[\frac{1}{{{(RT)}^{2}}}\]

    View Answer play_arrow
  • question_answer119) One mole of an ideal gas expands isothermally and reversibly from 2 L to 20 L at 300 K. If the final pressure of the gas is 1 bar, the work done by the gas is

    A) \[-300\,R\,\ln \,10\]

    B) \[300\,R\,\ln \,10\]

    C) \[18\]

    D) \[-18\]

    View Answer play_arrow
  • question_answer120) A unit cell with edge length \[a\ne b\ne c\]and axial angles \[\alpha =\beta =\gamma ={{90}^{o}}\]is called

    A) cubic

    B) tetragonal

    C) orthorhombic

    D) hexagonal

    View Answer play_arrow
  • question_answer121) The number of values of \[\alpha \in \,[-\pi ,\pi ]\] for which \[{{\sin }^{2}}\left( \frac{\pi }{8}+\alpha \right)-{{\sin }^{2}}\left( \frac{\pi }{8}-\alpha \right)=\frac{1}{2\sqrt{2}}\], is

    A) \[1\]

    B) \[2\]

    C) \[3\]

    D) \[4\]

    View Answer play_arrow
  • question_answer122) The area of the parallelogram with co-terminal edges \[a=3\hat{i}-3\hat{j}+k\] and \[b=4\hat{i}+9\hat{j}+2\hat{k}\]is

    A) \[5\sqrt{70}\]

    B) \[50\,\sqrt{7}\]

    C) \[\,\sqrt{70}\]

    D) \[5\,\sqrt{7}\]

    View Answer play_arrow
  • question_answer123) The number of values of \[\theta \,\,\in \,(-\pi ,\pi ),\] satisfying \[\sin 5\theta \,\cos 3\theta =\sin \,6\theta \,\cos 2\theta ,\] is

    A) \[1\]

    B) \[2\]

    C) \[3\]

    D) \[4\]

    E) None of these

    View Answer play_arrow
  • question_answer124) Let \[X=\{a,b,c,d,e\}\] and \[R=\{(a,a),\,(b,b),\]\[(c,c),\,\,(a,b),\,\,(b,a)\}.\] Then, the relation R on X is

    A) reflexive and symmetric

    B) not reflexive, but symmetric

    C) symmetric and transitive, but not reflexive

    D) reflexive, but not transitive

    View Answer play_arrow
  • question_answer125) If \[\sin \theta +\cos \theta =\sqrt{2},\] is \[{{\cos }^{6}}\theta +{{\sin }^{6}}\theta \]equal to

    A) \[\frac{1}{4}\]

    B) \[\frac{1}{2}\]

    C) \[\frac{3}{4}\]

    D) \[2\sqrt{2}\]

    View Answer play_arrow
  • question_answer126) The shortest distance between the lines \[\frac{x}{-1}=\frac{y}{1}=\frac{z}{1}\] and \[\frac{x-3}{0}=\frac{y+3}{1}=\frac{z-3}{-1}\] is

    A) \[\sqrt{6}\]

    B) \[6\]

    C) \[2\sqrt{3}\]

    D) \[3\sqrt{2}\]

    View Answer play_arrow
  • question_answer127) The last digit in the integer \[{{3}^{101}}+1\] is

    A) \[1\]

    B) \[2\]

    C) \[3\]

    D) \[4\]

    View Answer play_arrow
  • question_answer128) If \[^{32}{{P}_{6}}=k\,{{(}^{32}}{{C}_{6}}),\] then k is equal to

    A) \[6\]

    B) \[24\]

    C) \[120\]

    D) \[720\]

    View Answer play_arrow
  • question_answer129) The integer \[\int_{0}^{\pi }{\frac{x}{2\,\text{cosec}\,\text{x-sin}\,\text{x}}\,\,dx}\] is equal to

    A) \[\frac{\pi }{4}\]

    B) \[\frac{\pi }{2}\]

    C) \[\frac{{{\pi }^{2}}}{2}\]

    D) \[\frac{{{\pi }^{2}}}{4}\]

    View Answer play_arrow
  • question_answer130) Let P be the set of real numbers and let \[G\subseteq {{R}^{2}}\] be a relation defined by \[G=\{(a,b),\,(c,d)|\,b-a=d-c\}.\]. Then, G is

    A) reflexive only

    B) symmetric only

    C) transitive only

    D) an equivalence relation

    View Answer play_arrow
  • question_answer131) \[\underset{x\to 0}{\mathop{\lim }}\,\,\frac{\sin {{x}^{2}}}{1-\cos x}\] is

    A) \[\frac{1}{2}\]

    B) \[0\]

    C) \[1\]

    D) \[2\]

    View Answer play_arrow
  • question_answer132) The sum of lengths of major and minor axes- of an ellipse whose eccentricity is \[\frac{4}{5}\] and length of latuserectum is \[14.4\], is

    A) \[24\]

    B) \[32\]

    C) \[64\]

    D) \[48\]

    View Answer play_arrow
  • question_answer133) If \[|a|=7\] and \[|b|=11,\] then the angle between the vectors \[a+b\]and \[a-b\] is equal to

    A) \[\pi \]

    B) \[\frac{5\pi }{6}\]

    C) \[\frac{2\pi }{3}\]

    D) \[\frac{3\pi }{4}\]

    View Answer play_arrow
  • question_answer134) The number of integer value(s) of A: for which the expression \[{{x}^{2}}-2(4k-1)x+15{{k}^{2}}\] \[-2k-7>0\] for every real number x, is/are

    A) None

    B) one

    C) finitely many, but greater than 1

    D) infinitely many

    View Answer play_arrow
  • question_answer135) At present, a firm manufactures 1099 items. It is estimated that the rate of change of production P with respect to additional number of workers x is given by \[\frac{dP}{dx}=100-12\sqrt{x}.\]. If the firm empower 25 more workers, then the new level of production of items is

    A) \[2000\]

    B) \[2500\]

    C) \[3000\]

    D) \[3500\]

    View Answer play_arrow
  • question_answer136) The function is \[f(x)=\frac{1}{2-\cos \,3x},\,x\,\in \left[ 0,\frac{\pi }{3} \right],\]is

    A) one-one, but not onto

    B) onto, but not one-one

    C) one-one as well as onto

    D) neither one-one nor onto

    View Answer play_arrow
  • question_answer137) Let function \[f(x)={{(x-1)}^{2}}{{(x+1)}^{3}}.\]Then, which of the following is false?

    A) There exists a point where \[f(x)\] has a maximum value

    B) There exists a point where \[f(x)\] has a minimum value

    C) There exists a point where \[f(x)\] has neither maximum nor minimum value

    D) All of the above

    View Answer play_arrow
  • question_answer138) Consider the curve given by \[{{({{x}^{2}}+{{y}^{2}})}^{2}}=4({{x}^{2}}-{{y}^{2}})\]. Which of the following is not true?

    A) The curve has two tangents parallel to X-axis

    B) The curve has two tangents parallel to Y-axis

    C) The area of the region bounded by this curve is less than 8

    D) All of the above

    View Answer play_arrow
  • question_answer139) Let A and B be points \[(8,\,\,10)\] and \[(18,\,20),\] respectively. If the point Q divides AB externally in the ratio \[2:3\] and M is the S mid-point of AB, then the length MQ is equal to

    A) \[25\]

    B) \[5\sqrt{34}\]

    C) \[25\sqrt{2}\]

    D) \[5\sqrt{26}\]

    View Answer play_arrow
  • question_answer140) The number of the solutions of the equation \[{{5}^{2x-1}}+{{5}^{x+1}}=250,\] is/are

    A) \[0\]

    B) \[1\]

    C) \[2\]

    D) infinitely many

    View Answer play_arrow
  • question_answer141) A crime is committed by one of two suspects, A and B. Initially, there is equal evidence against both of them. In further investigation at the crime scene, it is found that the guilty party had a blood type found in 20% of the population. If the suspect A does match this blood type, whereas the blood type of suspect B is unknown, then the probability that A is the guilty party, is

    A) \[\frac{3}{5}\]

    B) \[\frac{5}{6}\]

    C) \[\frac{1}{3}\]

    D) \[\frac{2}{3}\]

    View Answer play_arrow
  • question_answer142) Let \[A=\left( \begin{matrix} 1 & 2 \\ 2 & 1 \\ \end{matrix} \right)\] Then, determinant of \[\frac{1}{3}A[adj\,(adj\,A)]\] is

    A) \[1\]

    B) \[-1\]

    C) \[\frac{1}{3}\]

    D) \[3\]

    View Answer play_arrow
  • question_answer143) Let X be a random variable with its expectation \[E(X)=3\]and its variance \[V(X)=2\]. If V is another random variable defined by \[Y=10X,\]then the ordered pair \[(E(Y),\,V(Y))\] is equal to

    A) \[(10,\,200)\]

    B) \[(30,\,20)\]

    C) \[(10,\,20)\]

    D) \[(30,\,200)\]

    View Answer play_arrow
  • question_answer144) The number of values of k for which the following system of equations has at least three solutions \[8x+16y\,\,\,+8z=25,\] \[x+y+z=k\]and \[3x+y+3z={{k}^{2}},\] is

    A) \[0\]

    B) \[1\]

    C) \[2\]

    D) \[3\]

    View Answer play_arrow
  • question_answer145) If the plane \[2x-3y+6z-11=0\]makes an angle \[\theta \] with the X-axis, then the value of \[\tan \theta \]is equal to

    A) \[\frac{2}{3}\]

    B) \[\frac{2}{15}\]

    C) \[\frac{\sqrt{2}}{3}\]

    D) \[\frac{2\sqrt{5}}{15}\]

    View Answer play_arrow
  • question_answer146) Let the general term of a series be \[(2k-1)\,\,(2k)\]\[(2k+1),\,\,k=1,2,3...,n.\]If the sum of first. N terms is. \[24090,\]then n is equal to

    A) \[8\]

    B) \[9\]

    C) \[10\]

    D) \[11\]

    View Answer play_arrow
  • question_answer147) In an isosceles right angled triangle ABC, a value of \[\tan \left( \frac{A}{2} \right)+\tan \left( \frac{B}{2} \right)+\tan \left( \frac{C}{2} \right)\] is

    A) \[\sqrt{2}-1\]

    B) \[2\sqrt{2}\]

    C) \[2\sqrt{2}-1\]

    D) \[2\sqrt{2}+1\]

    View Answer play_arrow
  • question_answer148) Suppose, 70% of all voters in a city support ,a candidate A. If 40 voters in the city are randomly selected, then the expected number of voters that will support candidate A in this group, is

    A) \[12\]

    B) \[20\]

    C) \[28\]

    D) \[32\]

    View Answer play_arrow
  • question_answer149) The radius of the largest circle, having centre \[(1,0),\] that can be inscribed in the ellipse \[{{x}^{2}}+4{{y}^{2}}=16,\]is

    A) \[\sqrt{11}\]

    B) \[\sqrt{\frac{11}{3}}\]

    C) \[\sqrt{\frac{22}{3}}\]

    D) \[\sqrt{22}\]

    View Answer play_arrow
  • question_answer150) The area bounded by the curves \[y=\sqrt{|x|}\] and \[y=\pm x,\] is

    A) \[0\]

    B) \[\frac{1}{6}\]

    C) \[\frac{1}{3}\]

    D) \[\frac{2}{3}\]

    View Answer play_arrow
  • question_answer151) Let \[M=\left[ \begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ \end{matrix} \right],\]Then, \[\frac{1}{3}\,\det \,(3\,(M+{{M}^{T}}))\] is equal to

    A) \[-18\]

    B) \[54\]

    C) \[-72\]

    D) \[72\]

    View Answer play_arrow
  • question_answer152) If there are 6 red and 30 white beads, then the probability of drawing red beads in 2 successive trials, with replacement, is

    A) \[\frac{1}{18}\]

    B) \[\frac{1}{6}\]

    C) \[\frac{5}{216}\]

    D) \[\frac{1}{36}\]

    View Answer play_arrow
  • question_answer153) The sum of the common roots of the equations , \[{{x}^{3}}+2{{x}^{2}}-5x+2=0~\] and\[{{x}^{3}}+\text{ }{{x}^{2}}-8x+4=0,\]is

    A) \[-3\]

    B) \[\frac{3}{2}\]

    C) \[-\frac{\sqrt{17}}{2}\]

    D) \[\frac{\sqrt{17}}{2}\]

    View Answer play_arrow
  • question_answer154) Which of the following is a tangent to the curve given by \[{{x}^{3}}+{{y}^{3}}=2xy?\]

    A) \[y=x\]

    B) \[y=x+2\]

    C) \[y=-x+2\]

    D) \[y=-x+3\]

    View Answer play_arrow
  • question_answer155) If a tangent to the hyperbola \[4{{x}^{2}}-9{{y}^{2}}=1\] cuts the ellipse \[4\text{ }{{x}^{2}}+9{{y}^{2}}=1\] in points L and R, then the locus of the mid-point of segment LR is

    A) \[{{(4{{x}^{2}}+9{{y}^{2}})}^{2}}=4{{x}^{2}}-9{{y}^{2}}\]

    B) \[{{(4{{x}^{2}}-9{{y}^{2}})}^{2}}=4{{x}^{2}}+9{{y}^{2}}\]

    C) \[{{(2{{x}^{2}}+3{{y}^{2}})}^{2}}=2{{x}^{2}}-3{{y}^{2}}\]

    D) \[{{(2{{x}^{2}}-3{{y}^{2}})}^{2}}=2{{x}^{2}}+3{{y}^{2}}\]

    View Answer play_arrow
  • question_answer156) Let an odd number of terms n of an AP be such that the sum and product of its first and last terms are 10 and 0, respectively. If the common difference is \[\frac{1}{10}\], then the number of terms n is

    A) \[99\]

    B) \[101\]

    C) \[103\]

    D) \[191\]

    View Answer play_arrow
  • question_answer157) If \[^{n}{{C}_{r}}\]denotes the binomial coefficient, then which of the following formula is correct?

    A) \[^{n+1}{{C}_{r}}{{-}^{n}}{{C}_{r-1}}{{=}^{n}}{{C}_{r}}\]

    B) \[^{n+1}{{C}_{r}}{{-}^{n-1}}{{C}_{r}}{{=}^{n}}{{C}_{r}}\]

    C) \[^{n}{{C}_{r+1}}{{-}^{n}}{{C}_{r-1}}{{=}^{n}}{{C}_{r}}\]

    D) \[^{n=1}{{C}_{r}}{{+}^{n}}{{C}_{r}}{{=}^{n+1}}{{C}_{r}}\]

    View Answer play_arrow
  • question_answer158) Let \[G=\{(b,b),\,(b,c),\,(c,c),\,(c,d)\}\] and \[H=\{(b,a),\,(c,b),\,(d,c)\}\] Then, the number of elements in the set \[(G\cup H)\oplus {{(G\cup H)}^{-1}}\] where \[\oplus \] denotes the symmetric difference, is

    A) \[0\]

    B) \[2\]

    C) \[7\]

    D) \[14\]

    View Answer play_arrow
  • question_answer159) Let the nth term of a sequence be \[{{t}_{n}}=\frac{1}{2}\{{{(1+\sqrt{3})}^{n}}+{{(1-\sqrt{3})}^{n}}\},\]\[n=3,4,5,.....\]Then, form \[=100\] which of the following is true?

    A) \[\frac{1}{4}{{t}_{m}}\] is the arithmetic mean of \[{{t}_{m-1}}\] and \[{{t}_{m-2}}\]

    B) \[\frac{1}{4}{{t}_{m-1}}\] is the arithmetic mean of \[{{t}_{m}}\] and \[{{t}_{m-2}}\]

    C) \[\frac{1}{4}{{t}_{m}}\] is the geometric mean of \[{{t}_{m-1}}\] and \[{{t}_{m-2}}\]

    D) \[\frac{1}{4}{{t}_{m-1}}\] is the geometric mean of \[{{t}_{m}}\] and \[{{t}_{m-2}}\]

    View Answer play_arrow
  • question_answer160) The roots of the equation \[6\,{{\sin }^{-1}}\left( {{x}^{3}}-6{{x}^{2}}+8x+\frac{1}{2} \right)=\pi ,\]are

    A) in AP

    B) in GP

    C) in AP and GP both

    D) neither in AP nor in

    View Answer play_arrow
  • question_answer161) Sum of the first 100 terms of the series \[1+3+7+15+31+....,\] is

    A) \[{{2}^{100}}-102\]

    B) \[{{2}^{101}}-102\]

    C) \[{{2}^{102}}-103\]

    D) \[{{2}^{102}}\text{ }-104\]

    View Answer play_arrow
  • question_answer162) The points \[(1,3,4),\,(-1,6,10),\,(-7,4,7)\] and \[(-5,1,1)\]

    A) form a rectangle which is not a square

    B) form a rhombus which is not a square

    C) form a parallelogram which is not a rhombus

    D) are collinear

    View Answer play_arrow
  • question_answer163) A bag contains one marble which is either green or blue, with equal probability. A green marble is put in the bag (so there are 2 marbles now) and then a marble is picked at random from the bag. If the marble taken out is green, then the probability that the remaining marble is also green, is

    A) \[\frac{1}{2}\]

    B) \[1\]

    C) \[\frac{2}{3}\]

    D) \[\frac{1}{3}\]

    View Answer play_arrow
  • question_answer164) If the image of the point \[(1,\,-2,3)\] in the plane \[2x+3y-z=7\]is the point \[(\alpha ,\beta ,\gamma )\] then \[\alpha +\beta +\gamma \] is equal to

    A) \[-6\]

    B) \[10\]

    C) \[8\]

    D) \[-4\]

    View Answer play_arrow
  • question_answer165) Equation of the circle having the diameter as the line segment joining the complex numbers \[-1-i\]and \[1+i\] is

    A) \[|z+1+i{{|}^{2}}+|z-1-i{{|}^{2}}=8\]

    B) \[|z{{|}^{2}}=|1+i{{|}^{2}}+|-1-i{{|}^{2}}\]

    C) \[|z-1+i{{|}^{2}}-|z+1-i{{|}^{2}}=4\]

    D) \[|z+1+i{{|}^{2}}=|z-1-i{{|}^{2}}\]

    E) None of these

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  • question_answer166) The range of the function \[y(x)=4\,\sin \,x-3\,\cos x\]is

    A) \[(-5,5)\]

    B) \[(-5,5]\]

    C) \[[-5,5)\]

    D) \[[-5,5]\]

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  • question_answer167) An equation of the plane, parallel to the plane passing through the points \[(1,1,1),\,\,(2,3,5)\] and \[(-1,0,2)\] and at a distance 3 from it, is

    A) \[2x-3y+z+3\sqrt{14}=0\]

    B) \[2x-3y+z+2\sqrt{14}=0\]

    C) \[2x-3y+z+\sqrt{14}=0\]

    D) \[2x-3y+z-2\sqrt{14}=0\]

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  • question_answer168) In which of the following interval, the function \[y(x)={{x}^{3}}-3{{x}^{2}}-9x+5\] is always decreasing?

    A) \[(-1,3)\]

    B) \[(-3,3)\]

    C) \[(-4,4)\]

    D) \[(-2,2)\]

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  • question_answer169) If getting a number greater than 4 is a success in a throw of a fair die, then the probability of at least 2 successes in six throws of a fair die is

    A) \[0.649\]

    B) \[0.351\]

    C) \[0.267\]

    D) \[0.667\]

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  • question_answer170) Let \[f(x)={{x}^{2}},\,g(x)={{\log }_{e}}x\]. The number of values of for which \[(fog)\,(x)=(gof)\,(x),\] is

    A) 1

    B) 2

    C) finite but greater than 2

    D) infinitely many

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  • question_answer171) If \[{{z}_{1}}=\cos \alpha +i\,\sin \alpha \]since and \[{{z}_{2}}=\cos \beta +i\,\sin \beta ,\] then \[\frac{({{z}_{1}}-{{z}_{2}})\,({{z}_{1}}{{z}_{2}}+1)}{({{z}_{1}}+{{z}_{2}})({{z}_{1}}{{z}_{2}}-1)}\]is equal to

    A) \[\tan \left( \frac{\alpha +\beta }{2} \right)\,\,\tan \left( \frac{\alpha -\beta }{2} \right)\]

    B) \[\cot \left( \frac{\alpha +\beta }{2} \right)\,\,\cot \left( \frac{\alpha +\beta }{2} \right)\]

    C) \[\cot \left( \frac{\alpha -\beta }{2} \right)\,\,\cot \left( \frac{\alpha +\beta }{2} \right)\]

    D) \[\cot \left( \frac{\alpha +\beta }{2} \right)\,\,\cot \left( \frac{\alpha +\beta }{2} \right)\]

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  • question_answer172) \[\underset{x\to \infty }{\mathop{\lim }}\,\,\frac{0+2+4+6+....+2n}{1+3+5+7+....+(2n-1)}\] is equal to

    A) \[0\]

    B) \[1\]

    C) \[2\]

    D) Does not exist

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  • question_answer173) In a \[\Delta ABC,\] if \[\sin (A)=\frac{5}{13}\] and \[\sin (B)=\frac{99}{101},\] then the value of \[(1313\,\cos \,(C))\] is

    A) \[255\]

    B) \[265\]

    C) \[275\]

    D) \[770\]

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  • question_answer174) Out of 64 students in a class, the number of students taking Mathematics is 55 and the number of students taking both Mathematics and Physics is 10. If all the students take either Mathematics or Physics or both, then the number of students taking only Physics is

    A) \[19\]

    B) \[20\]

    C) \[15\]

    D) \[25\]

    E) None of these

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  • question_answer175) The derivative of sin x with respect to \[cos\text{ }x\]is

    A) \[sin\,\,x\]

    B) \[-cos\,x\]

    C) \[tan\,\,x\]

    D) \[-cot\,x\]

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  • question_answer176) In how many ways, you can choose one or more identical balls out of six identical balls?

    A) \[31\]

    B) \[32\]

    C) \[63\]

    D) \[64\]

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  • question_answer177) If M is a \[3\times 3\]skew symmetric matrix, then det (M)is

    A) \[-1\]

    B) \[0\]

    C) \[4\]

    D) \[1\]

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  • question_answer178) Length of the segment of the normal at the point \[(1,1)\] to the curve given by \[{{y}^{2}}(2-x)={{x}^{3}}\] between X-axis and the point is

    A) \[\frac{\sqrt{5}}{2}\]

    B) \[\sqrt{5}\]

    C) \[2\sqrt{5}\]

    D) \[\sqrt{2}\]

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  • question_answer179) If the direction ratios of a line are \[(\lambda +1,\,1-\lambda ,2)\]and the line makes an angle 60? with the Y-axis, then a value of \[\lambda \] is

    A) \[1+\sqrt{3}\]

    B) \[2-\sqrt{3}\]

    C) \[3+\sqrt{5}\]

    D) \[2-\sqrt{5}\]

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  • question_answer180) Value of \[\cos \,\left( {{\sin }^{-1}}\left( \frac{2}{5} \right) \right)\] is

    A) \[\frac{17}{25}\]

    B) \[-\frac{51}{135}\]

    C) \[\frac{-2\sqrt{18}}{120}\]

    D) \[\frac{9\sqrt{21}}{125}\]

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