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Solved papers for JCECE Engineering JCECE Engineering Solved Paper-2013

done JCECE Engineering Solved Paper-2013

  • question_answer1) A boat can go across a lake and return in time \[{{T}_{0}}\] at a speed\[v\]. On a rough day there is a uniform current at speed \[{{v}_{1}}\] to help the onward journey and impede the return journey. If the time taken to go across and return on the same day be\[T\], then \[T/{{T}_{0}}\] will be

    A) \[\frac{1}{(1-v_{1}^{2}/{{v}^{2}})}\]

    B) \[\frac{1}{(1+v_{1}^{2}/{{v}^{2}})}\]

    C) \[(1-v_{1}^{2}/{{v}^{2}})\]

    D) \[\left( 1+\frac{v_{1}^{2}}{{{v}^{2}}} \right)\]

    View Answer play_arrow
  • question_answer2) If a balloon of mass \[M\] is descending down with an acceleration\[a(<g)\], then what is the value of mass \[m\] (of its contents) that must be removed so that it starts moving up with an acceleration\[a\]?

    A) \[\frac{Ma}{(g+a)}\]

    B) \[\frac{2Ma}{(g+a)}\]

    C) \[\frac{M}{(g+a)}\]

    D) Not Possible

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  • question_answer3) If for a spherical mirror object distance, \[u=(50.1\pm 0.5)\] and image distance\[v=(20.1\pm 0.2)\], then focal length of the spherical mirror will be

    A) \[(14.3\pm 0.1)cm\]

    B) \[(14.3\pm 0.5)cm\]

    C) \[(30.1\pm 0.1)cm\]

    D) \[(25.3\pm 0.5)cm\]

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  • question_answer4) The susceptibility and permeability of a perfectly diamagnetic Substance is

    A) 1 and 0

    B) 0 and 1

    C) -1 and 0

    D) -1 and 1

    View Answer play_arrow
  • question_answer5) If a current carrying circular loop is placed in a \[x-y\] plane as shown in adjoining figure and a magnetic field is applied along\[z-axis\], then the loop will

    A) contract

    B) expand

    C) move towards\[-x-axis\]

    D) move towards\[+x-axis\]

    View Answer play_arrow
  • question_answer6) If the three vectors \[A,\,\,\,B\] and \[C\] satisfy the relation \[\mathbf{A}\bullet \mathbf{B}=0\] and \[\mathbf{A}\bullet \mathbf{C}=0\], then vector A is parallel to

    A) \[\mathbf{A}\]

    B) \[\mathbf{B}\]

    C) \[\mathbf{A}\times \mathbf{B}\]

    D) \[\mathbf{B}\times \mathbf{C}\]

    View Answer play_arrow
  • question_answer7) A car weighing \[2\times {{10}^{3}}kg\] and moving at \[20\,\,m/s\] along a main road collides with a lorry of mass \[8\times {{10}^{3}}kg\] which emerges at \[5\,\,m/s\] from a cross road at right angle to the main road. If the two vehicles lock, what will be then velocity after the collision?

    A) \[4/\sqrt{2}ms,\,\,{{45}^{o}}\]with cross road

    B) \[4/\sqrt{2}ms,\,\,{{45}^{o}}\]with main road

    C) \[4/\sqrt{2}ms,\,\,{{60}^{o}}\]with cross road

    D) \[4/\sqrt{2}ms,\,\,{{60}^{o}}\]with main road

    View Answer play_arrow
  • question_answer8) If a water particle of mass \[10\,\,mg\] and having a charge of \[1.5\times {{10}^{-6}}C\] stays suspended in a room, then the magnitude and direction of electric field in the room is

    A) \[15N/C\], vertically upwards

    B) \[15N/C\], vertically downwards

    C) \[65.3N/C\], vertically upwards

    D) \[65.3N/C\], vertically downwards

    View Answer play_arrow
  • question_answer9) In the adjoining figure,\[E=5\,\,V,\,\,r=1\Omega \]\[,\]\[{{R}_{2}}=4\Omega ,\,\,{{R}_{1}}={{R}_{3}}=1\Omega \] and \[C=3\mu F\]. The numerical value of the charge on each plate of the capacitor is

    A) \[3\mu C\]

    B) \[6\mu C\]

    C) \[12\mu C\]

    D) \[24\mu C\]

    View Answer play_arrow
  • question_answer10) Find out the value of current through \[2\Omega \] resistance for the given circuit

    A) \[zero\]

    B) \[2\,\,A\]

    C) \[4\,\,A\]

    D) \[5\,\,A\]

    View Answer play_arrow
  • question_answer11) A pure resistive circuit element \[X\] when connected to a \[AC\] supply of peak voltage \[200\,\,V\] gives a peak current of\[5\,\,A\]. \[A\] second current element \[Y\] when connected to same \[AC\] supply gives the same value of peak current but the current lags behind by\[{{90}^{o}}\]. If series combination of \[X\] and \[Y\] is connected to the same supply, what is the impedance of the circuit?

    A) \[40\Omega \]

    B) \[80\Omega \]

    C) \[40\sqrt{2}\Omega \]

    D) \[2\sqrt{40}\Omega \]

    View Answer play_arrow
  • question_answer12) Two circular coils \[C\] and \[D\] have equal number of turns and carry equal currents in the same direction in the same sense and subtend same solid angle at point \[O\] as shown in figure. The smaller coil \[C\] is midway between \[O\] and\[D\]. If we represent magnetic field induction due to bigger coil and smaller coil \[C\] as \[{{B}_{D}}\] and \[{{B}_{C}}\] respectively, then By \[{{B}_{D}}/{{B}_{C}}\] is

    A) \[1:4\]

    B) \[1:2\]

    C) \[2:1\]

    D) \[1:1\]

    View Answer play_arrow
  • question_answer13) Equal volume of two immiscible liquids of densities \[p\] and \[2p\] are filled in a vessel as shown in figure. Two small holes are made at depth \[\frac{h}{2}\] and \[\frac{3h}{2}\] from the surface of lighter liquid. If \[{{v}_{1}}\] and \[{{v}_{2}}\] are the velocities of efflux at these two holes, then \[{{v}_{1}}/{{v}_{2}}\] will be.

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

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

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

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

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  • question_answer14) Three conducting rods of same material and cross-section are connected as shown in figure. Temperatures of \[A,\,\,\,D\] and \[C\] are maintained at\[{{20}^{o}}C\], \[{{90}^{o}}C\] and\[{{0}^{o}}C\]. If there is no flow of heat in\[AB\], then ratio of the lengths of \[BC\] and \[BD\] is

    A) \[2/9\]

    B) \[9/2\]

    C) \[2/7\]

    D) \[7/2\]

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  • question_answer15) If two air columns of lengths \[100\,\,cm\] and \[101\,\,cm\] sounding in their fundamental note gave \[17\] beats in \[20\] seconds, then the velocity of sound will be

    A) \[277.8\,\,m/s\]

    B) \[300\,\,m/s\]

    C) \[250\,\,m/s\]

    D) \[343.4\,\,m/s\]

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  • question_answer16) If two springs of spring constants \[{{k}_{1}}\] and \[{{k}_{2}}\] while executing \[SHM\] have equal highest velocities, then the ratio of their amplitudes will be (their masses are in ratio\[1:2)\]

    A) \[\sqrt{2{{k}_{2}}/{{k}_{1}}}\]

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

    C) \[2{{k}_{1}}/{{k}_{2}}\]

    D) \[2{{k}_{2}}/{{k}_{1}}\]

    View Answer play_arrow
  • question_answer17) In the adjoining circuit of logic gate, the output\[Y\]becomes zero if the inputs are

    A) \[A=1,\,\,B=1,\,\,C=0\]

    B) \[A=0,\,\,B=0,\,\,C=0\]

    C) \[A=0,\,\,B=1,\,\,C=1\]

    D) \[A=1,\,\,B=0,\,\,C=0\]

    View Answer play_arrow
  • question_answer18) \[LANDSAT\] series of satellites move in near polar Orbits at an altitude of

    A) \[512\,\,km\]

    B) \[918\,\,km\]

    C) \[3000\,\,km\]

    D) \[3600\,\,km\]

    View Answer play_arrow
  • question_answer19) The intensity of gamma radiation from a given source is\[I\]. If on passing through \[36\,\,mm\] of lead its intensity is reduced to\[\frac{I}{8}\], then what will be the thickness of lead which reduces its intensity to\[\frac{I}{2}\]?

    A) \[6\,\,mm\]

    B) \[9\,\,mm\]

    C) \[12\,\,mm\]

    D) \[18\,\,mm\]

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  • question_answer20) An unpolarized beam of light is incident on a group of four polarizing sheets, which are arranged in such a way that the characteristic direction of each polarizing sheet makes an angle of \[{{30}^{o}}\] with that of the preceding sheet. The fraction of incident unpolarized light transmitted is

    A) \[\frac{27}{128}\]

    B) \[\frac{128}{27}\]

    C) \[\frac{37}{128}\]

    D) \[\frac{128}{37}\]

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  • question_answer21) Two coherent sources of intensity ratio \[\beta \] interfere. Then, the value\[({{I}_{\max }}-{{I}_{\min }})/\]\[({{I}_{\max }}+{{I}_{\min }})\] is

    A) \[\frac{1+\beta }{\sqrt{\beta }}\]

    B) \[\sqrt{\frac{1+\beta }{\beta }}\]

    C) \[\frac{1+\beta }{2\sqrt{\beta }}\]

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

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  • question_answer22) A luminous object is placed at a distance of \[30\,\,cm\] from the convex lens of focal length\[20\,\,cm\]. On the other side of the lens, at what distance from the lens a convex mirror of radius of curvature \[10\,\,cm\] be placed in order to have an upright image of the object coincident with it?

    A) \[60\,\,cm\]

    B) \[50\,\,cm\]

    C) \[30\,\,cm\]

    D) \[20\,\,cm\]

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  • question_answer23) If a charge \[-150\,\,nC\] is given to a concentric spherical shell and a charge \[+50\,\,nC\] is placed at its centre, then the charge on inner and outer surface of the shell is

    A) \[50\,\,nC,\,\,100\,\,nC\]

    B) \[-50\,\,nC,\,\,-100\,\,nC\]

    C) \[50\,\,nC,\,\,200\,\,nC\]

    D) \[-50\,\,nC,\,\,-200\,\,nC\]

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  • question_answer24) Find out the equivalent resistance between \[A\] and \[B\] in the network of resistances shown in adjoining figure

    A) \[25\Omega \]

    B) \[10\Omega \]

    C) \[5\Omega \]

    D) None of these

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  • question_answer25) In the adjoining figure, if \[10\] calorie heat is produced per second in \[5\Omega \] resistor due to the flow of current through it, then the heat produced in \[6\Omega \] resistor is

    A) \[1\,\,cal/s\]

    B) \[2\,\,cal/s\]

    C) \[3\,\,cal/s\]

    D) \[4\,\,cal/s\]

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  • question_answer26) A rod of length \[L\] rotates about an axis passing through one of its ends and perpendicular to its plane. If the linear mass density of the rod varies as\[\rho =(A{{r}^{3}}+B)kg/m\], then the moment of inertia of the rod about the given axis of rotation is

    A) \[\frac{{{L}^{3}}}{3}\left[ \frac{A{{L}^{3}}}{2}+B \right]\]

    B) \[\frac{L}{3}\left[ \frac{A{{L}^{2}}}{2}+B \right]\]

    C) \[\frac{{{L}^{3}}}{3}\left[ \frac{A}{2}+B \right]\]

    D) None of these

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  • question_answer27) If a force of \[4\,\,N\] is applied on a body of mass \[20\,\,kg\], then the work done in 3rd second will be

    A) \[1.2\,\,J\]

    B) \[2\,\,J\]

    C) \[4\,\,J\]

    D) \[16\,\,J\]

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  • question_answer28) A body is projected with velocity \[{{v}_{1}}\] from the point\[A\], another body at the same time is projected vertically upwards from \[B\] with velocity \[{{v}_{2}}\] as shown in adjoining figure. If the point \[B\] lies vertically below the highest point \[C\], then for both bodies to collide the ratio\[\frac{{{v}_{2}}}{{{v}_{1}}}\]should be

    A) \[0.5\]

    B) \[1\]

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

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

    View Answer play_arrow
  • question_answer29) A police van moving on a highway with a speed of \[30\,\,km/h\] fires a bullet at a thief?s car speeding away in the same direction with a speed of\[192\,\,km/h\]. If the muzzle speed of the bullet is\[150\,\,km/h\], with what speed does the bullet hit the thief?s car?

    A) \[105\,\,m/s\]

    B) \[205\,\,m/s\]

    C) \[210\,\,m/s\]

    D) \[250\,\,m/s\]

    View Answer play_arrow
  • question_answer30) A machine gun of mass \[10\,\,kg\] fires \[30\,\,g\] bullets at the rate of \[6\] bullets/s with a speed of\[400\,\,m/s\]. The force required to keep the gun in position will be

    A) \[30\,\,N\]

    B) \[40\,\,N\]

    C) \[72\,\,N\]

    D) \[400\,\,N\]

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  • question_answer31) A body of mass \[0.1\,\,kg\] when rotated in a circular path of diameter \[1.0\,\,m\] on a frictionless horizontal plane by means of string, makes \[10\] revolutions in \[31.4\] seconds. The centripetal force acting on the body will be

    A) \[0.2\,\,N\]

    B) \[0.1\,\,N\]

    C) \[2\,\,N\]

    D) \[2\,\,N\]

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  • question_answer32) A plane electromagnetic wave propagating in \[x\,\,(-)\]direction as a wave function (in \[SI\] units) is given as \[\psi (x,\,\,t)={{10}^{3}}\sin \pi (3\times {{10}^{6}}x-9\times {{10}^{14}}t)\] The speed of the wave is

    A) \[3\times {{10}^{6}}m/s\]

    B) \[3\times {{10}^{7}}m/s\]

    C) \[3\times {{10}^{8}}m/s\]

    D) \[9\times {{10}^{14}}m/s\]

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  • question_answer33) A thin lens of focal length \[f\] and aperture diameter \[d\] forms an image of intensity\[I\]. If the central part of the aperture upto diameter\[d/2\] is blocked by an opaque paper, then the new focal length and intensity of image will be

    A) \[\frac{f}{2},\,\,\frac{l}{2}\]

    B) \[\frac{f}{2},\,\,\frac{3}{4}l\]

    C) \[f,\,\,\frac{l}{2}\]

    D) \[f,\,\,\frac{3}{4}l\]

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  • question_answer34) Light of wavelength \[\lambda \] strikes a photo sensitive surface and electrons are ejected with kinetic energy\[E\]. If the kinetic energy is to be increased to\[2E\], then the wavelength must be changed to\[\lambda '\], where

    A) \[\lambda '>\lambda \]

    B) \[\lambda '=\frac{\lambda }{2}\]

    C) \[\lambda '=2\lambda \]

    D) \[\frac{\lambda }{2}<\lambda '<\lambda \]

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  • question_answer35) In a photo electric effect experiment, the maximum kinetic energy of the emitted electrons is \[1\,\,eV\] for incoming radiation of frequency \[{{v}_{0}}\] and \[3\,\,eV\] for incoming radiation of frequency\[3{{v}_{0}}/2\]. What is the maximum kinetic energy of the electrons emitted for incoming radiations of frequency\[9{{v}_{0}}/4\]?

    A) \[3\,\,eV\]

    B) \[4.5\,\,eV\]

    C) \[6\,\,eV\]

    D) \[9\,\,eV\]

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  • question_answer36) If the energy of hydrogen atom in the ground state is \[-13.6\,\,eV\], then energy of \[H{{e}^{+}}\] ion in first excited state will be

    A) \[6.8\,\,eV\]

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

    C) \[-27.2\,\,eV\]

    D) \[-54.4\,\,eV\]

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  • question_answer37) In a nuclear fission, \[0.1%\] mass is converted into energy. The energy released by the fission of \[1\,\,kg\] mass will be

    A) \[9\times {{10}^{13}}J\]

    B) \[9\times {{10}^{16}}J\]

    C) \[9\times {{10}^{17}}J\]

    D) \[9\times {{10}^{19}}J\]

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  • question_answer38) For a transistor in common base, the current gain is\[~0.95\]. If the load resistance is \[400\,\,k\Omega \] and input resistance is \[200\,\,k\Omega \], then the voltage gain and power gain will be

    A) 1900 and 1800

    B) 1900 and 1805

    C) 5525 and 3591

    D) 1805 and 1900

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  • question_answer39) In the middle of the depletion layer of a reverse biased p-n junction, the

    A) potential is zero

    B) potential is maximum

    C) electric field is maximum

    D) electric field is zero

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  • question_answer40) In amplitude modulation, the total modulation index should not exceed one because

    A) the signal will be distorted

    B) the amplifier will be damaged

    C) the signal will die out quickly

    D) the system will fail

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  • question_answer41) Let a beam of wavelength \[\lambda \] falls on parallel reflecting planes with separation\[d\], then the angle \[\theta \] that the beam should make with the planes so that reflected beams from successive planes may interfere constructively should be (where,\[n=1,\,\,2,\,\,...)\]

    A) \[{{\cos }^{-1}}\left( \frac{n\lambda }{2d} \right)\]

    B) \[{{\sin }^{-1}}\left( \frac{n\lambda }{2d} \right)\]

    C) \[{{\sin }^{-1}}\left( \frac{n\lambda }{d} \right)\]

    D) \[{{\tan }^{-1}}\left( \frac{n\lambda }{d} \right)\]

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  • question_answer42) The dimensions of angular , momentum/ magnetic moment are

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

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

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

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

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  • question_answer43) A weight \[mg\] is suspended from the middle of a rope whose ends are at same level. If the rope is no longer horizontal, the minimum tension required to completely straighten the rope will be

    A) \[mg\]

    B) \[\sqrt{mg}\]

    C) Infinite

    D) zero

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  • question_answer44) Two triodes having amplification factors \[30\] \[\text{and}\] \[21\] and plate resistances \[5k\Omega \] and \[4k\Omega \] respectively are connected in parallel. The composite amplification factor of the system is

    A) \[\text{25}\]

    B) \[\text{50}\]

    C) \[75\]

    D) \[100\]

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  • question_answer45) A deflection magnetometer works on

    A) Coulomb's law

    B) Tangent law

    C) Curie law

    D) The law of vibration of a magnet

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  • question_answer46) If a magnet is dropped along the axial line of a horizontally held copper ring, then the acceleration of the magnet while it passing through the ring will

    A) less than that due to gravity

    B) equal to that due to gravity

    C) more than that due to gravity

    D) depend on the size of the ring and magnet

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  • question_answer47) A clock which keeps correct time at\[{{20}^{o}}C\], is subjected to\[{{40}^{o}}C\]. If coefficient of linear expansion of the pendulum is\[12\times {{10}^{-6}}{{/}^{o}}C\], then how much will it gain or loss in time?

    A) \[5\,\,s/day\]

    B) \[10.3\,\,s/day\]

    C) \[20.6\,\,s/day\]

    D) \[20\,\,\min /day\]

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  • question_answer48) The resistance of a resistance thermometer have values \[2.71\] and \[3.70\] ohms at \[{{10}^{o}}C\] and \[{{100}^{o}}C\] respectively. The temperature at which the resistance is \[3.26\,\,ohm\] is

    A) \[{{40}^{o}}C\]

    B) \[{{50}^{o}}C\]

    C) \[{{60}^{o}}C\]

    D) \[{{70}^{o}}C\]

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  • question_answer49) If the earth were to rotate faster than its present speed, the weight of an object will

    A) increase at the equator but remain unchanged at the poles

    B) decrease at the equator but remain unchanged at the poles

    C) decrease at the poles but remain unchanged at the equator

    D) increase at the pole but remain unchanged at the equator

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  • question_answer50) A coil is wound on a transformer of rectangular cross-section. If all the linear dimensions of the transformer are increased by a factor 2 and the number of turns per unit length of the coil remains the same, the self-inductance increases by a factor of

    A) \[4\]

    B) \[8\]

    C) \[12\]

    D) \[16\]

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  • question_answer51) A drop of water is about\[0.05\,\,mL\]. The density of water at room temperature is about\[1.0\,\,m{{L}^{-1}}\]. The number of water molecules present in a drop of water are

    A) \[1.67\times {{10}^{21}}{{H}_{2}}O\]molecules

    B) \[1.67\times {{10}^{26}}{{H}_{2}}O\]molecules

    C) \[1.806\times {{10}^{23}}{{H}_{2}}O\]molecules

    D) \[1.806\times {{10}^{21}}{{H}_{2}}O\]molecules

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  • question_answer52) Which of the following forms acidic halides?

    A) \[HF\]

    B) \[HCl\]

    C) \[HBr\]

    D) \[HI\]

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  • question_answer53) The maximum covalency of nitrogen is

    A) \[3\]

    B) \[4\]

    C) \[5\]

    D) \[6\]

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  • question_answer54) A black compound of manganese reacts with a halogen acid to give greenish yellow gas. When excess of this gas reacts with \[N{{H}_{3}}\]an unstable trihalide is formed. In this process, the oxidation state of nitrogen changes from

    A) \[0\]to\[-3\]

    B) \[-3\]to\[0\]

    C) \[-3\]to\[+5\]

    D) \[-3\]to\[+3\]

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  • question_answer55) Which of the following is isoelectronic pair?

    A) \[C{{N}^{-}},\,\,{{O}_{3}}\]

    B) \[Cl{{O}_{2}},\,\,Br{{F}_{2}}\]

    C) \[BrO_{2}^{-},\,\,BrF_{2}^{+}\]

    D) \[IC{{I}_{2}},\,\,Cl{{O}_{3}}\]

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  • question_answer56) Bond dissociation enthalpy of \[E-H(E=\] element) bonds is given below. Which of the compounds will act as strongest reducing agent? Compound \[=\]\[N{{H}_{3}}\] \[P{{H}_{3}}\] \[As{{H}_{3}}\] \[Sb{{H}_{3}}\] \[{{\Delta }_{diss(E-H)(kJmo{{l}^{-1}})}}=\]\[389\] \[322\] \[297\] \[255\]

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

    B) \[P{{H}_{3}}\]

    C) \[As{{H}_{3}}\]

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

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  • question_answer57) The electronic configuration of a transition element \['X'\] in \[+3\] oxidation state is\[[Ar]3{{d}^{5}}\]. What is its atomic number?

    A) \[24\]

    B) \[25\]

    C) \[26\]

    D) \[27\]

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  • question_answer58) Spin only magnetic moment value of \[C{{r}^{3+}}\] ion is

    A) \[2.87\,\,BM\]

    B) \[3.87\,\,BM\]

    C) \[3.47\,\,BM\]

    D) \[3.67\,\,BM\]

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  • question_answer59) There are 14 elements in actinoid series. Which of the following elements does not belong to this series?

    A) \[U\]

    B) \[Np\]

    C) \[Tm\]

    D) \[Fm\]

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  • question_answer60) When\[0.1\,\,mol\,\,CoC{{l}_{3}}\], \[{{(N{{H}_{3}})}_{5}}\] is treated with excess of \[AgN{{O}_{3}},\,\,0.2\,\,mole\] of \[AgCl\] are obtained. The conductivity of solution will correspond to

    A) \[1:3\]electrolyte

    B) \[1:2\]electrolyte

    C) \[1:1\]electrolyte

    D) \[3:1\]electrolyte

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  • question_answer61) The correct \[IUPAC\] name of\[[Pt{{(N{{H}_{3}})}_{2}}C{{l}_{2}}]\]is

    A) diammine dichlorido platinum (II)

    B) diammine dichlorido platinum (IV)

    C) diammine dichlorido platinum (0)

    D) dichlorido diammine platinum (IV)

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  • question_answer62) Which of the following is a network solid?

    A) \[S{{O}_{2}}\](solid)

    B) \[{{I}_{2}}\]

    C) Diamond

    D) \[{{H}_{2}}O\](ice)

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  • question_answer63) Which kind of defects are introduced by doping?

    A) Dislocation defects

    B) Schottky defects

    C) Electronic defects

    D) Frenkel defects

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  • question_answer64) The unit of ebullioscopic constant is

    A) \[K\]or\[K{{(molality)}^{-1}}\]

    B) \[mol\,\,kg\,\,{{K}^{-1}}\]or\[{{K}^{-1}}\](molality)

    C) \[kg\,\,mo{{l}^{-1}}{{K}^{-1}}\]or\[{{K}^{-1}}\]\[{{(molality)}^{-1}}\]

    D) \[K\,\,mol\,\,k{{g}^{-1}}\]or\[K\](molality)

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  • question_answer65) A beaker contains a solution of substance\['A'\]. On dissolving substance \['A'\] in small amount in this solution, precipitation of substance \['A'\] takes place. The solution is

    A) concentrated

    B) saturated

    C) unsaturated

    D) super saturated

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  • question_answer66) \[4L\] of \[0.02\,\,M\] aqueous solution of \[NaCl\] was diluted by adding \[1\,\,L\] of water. The molality of the resultant solution is

    A) \[0.004\]

    B) \[0.008\]

    C) \[0.012\]

    D) \[0.016\]

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  • question_answer67) At high concentration of soap in water, soap behave as

    A) molecular solid

    B) associated colloid

    C) macromolecular colloid

    D) lyophilic colloid

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  • question_answer68) Physical adsorption of a gaseous species may change to chemical adsorption with

    A) decrease in temperature

    B) increase in temperature

    C) increase in surface area of adsorbent

    D) decrease in surface area of adsorbent

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  • question_answer69) Consider the reaction \[A\xrightarrow{{}}B\,\,;\]the concentration of both the reactants and the products varies exponentially with time. Which of the following figures correctly describes the change in concentration of reactants and products with time?

    A)

    B)

    C)

    D)

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  • question_answer70) Activation energy of a chemical reaction can be determined by

    A) determining the rate constants at standard temperature

    B) determining the rate constants at two temperatures

    C) determining probability of collision

    D) using catalyst

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  • question_answer71) In the extraction of copper from its sulphide ore, the metal is formed by the reduction of\[C{{u}_{2}}O\]with

    A) \[FeS\]

    B) \[CO\]

    C) \[C{{u}_{2}}S\]

    D) \[S{{O}_{2}}\]

    View Answer play_arrow
  • question_answer72) Which of the following is not a target molecule for drug function in body?

    A) Vitamins

    B) Proteins

    C) Lipids

    D) Carbohydrates

    View Answer play_arrow
  • question_answer73) Which of the following statements is not true about low density polythene?

    A) Tough

    B) Highly branched structure

    C) Poor conductor of electricity

    D) Hard

    View Answer play_arrow
  • question_answer74) Biotin is an organic compound present in yeast. Its deficiency in diet causes dermatitis and paralysis. It is also known as

    A) vitamin\[{{B}_{1}}\]

    B) vitamin\[{{B}_{12}}\]

    C) vitamin\[D\]

    D) vitamin\[H\]

    View Answer play_arrow
  • question_answer75) Methyl \[\alpha -D-\]glucoside and methyl \[\beta -D-\]glucoside are

    A) epimers

    B) anomers

    C) conformational diastereomers

    D) enantiomers

    View Answer play_arrow
  • question_answer76) The number of disulphide linkages present in insulin are

    A) \[1\]

    B) \[2\]

    C) \[3\]

    D) \[4\]

    View Answer play_arrow
  • question_answer77) The source of nitrogen in Gabriel synthesis of amines is

    A) sodium azide\[Na{{N}_{3}}\]

    B) potassium phthalimide\[{{C}_{6}}{{H}_{4}}{{(CO)}_{2}}{{N}^{-}}{{K}^{+}}\]

    C) sodium cyanide

    D) potassium nitrate

    View Answer play_arrow
  • question_answer78) Which is the most suitable reagent for the following conversion? \[C{{H}_{3}}-CH=CH-C{{H}_{2}}-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}\to \]\[C{{H}_{3}}-CH=CH-C{{H}_{2}}-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-OH\]

    A) \[Zn-Hg+HCl\]

    B) \[{{I}_{2}}+NaOH\]

    C) Fehling?s reagent

    D) \[Sn+NaOH\]solution

    View Answer play_arrow
  • question_answer79) \[C{{H}_{3}}-C\equiv CH\xrightarrow[1%HgS{{O}_{4}}]{40%{{H}_{2}}S{{O}_{4}}}a\xrightarrow{Isomerisation}\] Structure of \[A\] and the type of isomerism in the above reaction are respectively.

    A) prop-1-en-2-ol, metamerism

    B) prop-1-en-1-ol, tautomerism

    C) prop-2-en-2-ol, \[cis\] and trans isomerism

    D) prop-2-en-1-ol, tautomerism

    View Answer play_arrow
  • question_answer80) One mole of a symmetrical alkene on ozonolysis gives two moles of an aldehyde having a molecular mass of 44u. The alkene is

    A) ethane

    B) propene

    C) but-1-ene

    D) but-2-ene

    View Answer play_arrow
  • question_answer81) Which of the following species can act as the strongest base?

    A) \[O{{H}^{-}}\]

    B) \[O{{R}^{-}}\]

    C)

    D)

    View Answer play_arrow
  • question_answer82) \[IUPAC\]name of w-cresol is

    A) benzene-1, 3-diol

    B) 3-chlorophenol

    C) 3-methyl phenol

    D) 3-methoxyphenol

    View Answer play_arrow
  • question_answer83) The order of reactivity of following alcohols with halogen acids is \[I.C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}OH\] \[II.C{{H}_{3}}C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,H-C{{H}_{3}}\] \[III.C{{H}_{3}}C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}}\,-OH\]

    A) \[II>I>III\]

    B) \[I>III>II\]

    C) \[III>II>I\]

    D) \[I>II>III\]

    View Answer play_arrow
  • question_answer84) The position of -Br in. the compound in \[C{{H}_{3}}CH=CHC(Br){{(C{{H}_{3}})}_{2}}\]can be classified as

    A) vinyl

    B) secondary

    C) allyl

    D) aryl

    View Answer play_arrow
  • question_answer85) Benzene does not undergo addition reactions easily because

    A) it has a cyclic structure

    B) it has \[6H-\]atoms

    C) double bonds in it are very strong

    D) resonance stabilized system is to be preserved

    View Answer play_arrow
  • question_answer86) Alkynes occur in nature in

    A) free state

    B) partially free state

    C) not in free state

    D) None of these

    View Answer play_arrow
  • question_answer87) Which of the following reagents converts bot acetaldehyde and acetone to alkanes?

    A) \[Ni/{{H}_{2}}\]

    B) \[LiAl{{H}_{4}}\]

    C) \[{{I}_{2}}/NaOH\]

    D) \[Zn-Hg/HCl\]

    View Answer play_arrow
  • question_answer88) \[{{C}_{6}}{{H}_{6}}+C{{l}_{2}}(excess)\xrightarrow[dark,\,cold]{Anhy.\,AlC{{l}_{8}}}P\]Product, \[P\] is

    A) \[{{C}_{6}}{{H}_{5}}Cl\]

    B) \[{{C}_{6}}{{H}_{4}}C{{l}_{2}}\]

    C) \[{{C}_{6}}{{H}_{6}}C{{l}_{6}}\]

    D) \[{{C}_{6}}C{{l}_{6}}\]

    View Answer play_arrow
  • question_answer89) An alkene\['A'\]contains three\[C-C\], eight\[C-H\]\[\sigma -\]bonds and one\[C-C-\pi \]bond.\['A'\]on ozonolysis gives two moles of an aldehyde of molar mass\[44\,\,u\]. \[IUPAC\]name of \[A\]is

    A) but-1-ene

    B) but-2-ene

    C) 2-methylpropane

    D) None of these

    View Answer play_arrow
  • question_answer90) Among the following which one can have a \[meso-\]form?

    A) \[C{{H}_{3}}CH(OH)CH(Cl){{C}_{2}}{{H}_{5}}\]

    B) \[C{{H}_{3}}CH(OH)CH(OH)C{{H}_{3}}\]

    C) \[{{C}_{2}}{{H}_{5}}CH(OH)CH(OH)C{{H}_{3}}\]

    D) \[HOC{{H}_{2}}CH(Cl)C{{H}_{3}}\]

    View Answer play_arrow
  • question_answer91) Calculate \[pH\] of\[1\,\,M\,\,NaHC{{O}_{3}}\]. Given \[{{H}_{2}}C{{O}_{3}}+{{H}_{2}}OHCO_{3}^{-}+{{H}_{3}}{{O}^{+}};\,\,p{{K}_{1}}=6.38\]\[HCO_{3}^{-}+{{H}_{2}}OCO_{3}^{2-}+{{H}_{3}}O;\,\,p{{K}_{2}}=10.26\]

    A) \[8.73\]

    B) \[8.32\]

    C) \[6.73\]

    D) \[6.32\]

    View Answer play_arrow
  • question_answer92) Elements \[Se,\,\,\,Cl\] and \[S\] have been arranged in the order of increasing ionisation energies. Identify the correct order.

    A) \[S<Se<Cl\]

    B) \[Se<S<Cl\]

    C) \[Cl<S<Se\]

    D) \[Se=S<Cl\]

    View Answer play_arrow
  • question_answer93) Which of the following is correct for number of electrons, number of orbitals and type of orbitals respectively in \[N-\]orbit?

    A) 4, 4 and 8

    B) 4, 8 and 16

    C) 32, 16 and 4

    D) 4, 16 and 32

    View Answer play_arrow
  • question_answer94) The de-Broglie wavelength of helium atom at room temperature is

    A) \[6.6\times {{10}^{-34}}m\]

    B) \[4.39\times {{10}^{-10}}m\]

    C) \[7.34\times {{10}^{-11}}m\]

    D) \[2.335\times {{10}^{-20}}m\]

    View Answer play_arrow
  • question_answer95) In which of the following pairs of molecules/ions, the central atoms have \[s{{p}^{2}}\] hydridisation?

    A) \[B{{F}_{3}}\]and\[NH_{2}^{-}\]

    B) \[NO_{2}^{-}\]and\[N{{H}_{3}}\]

    C) \[B{{F}_{3}}\]and\[NO_{2}^{-}\]

    D) \[NH_{2}^{-}\]and\[{{H}_{2}}O\]

    View Answer play_arrow
  • question_answer96) If a gas expands at constant temperature, it indicates that

    A) kinetic energy of molecules decreases

    B) pressure of the gas increases

    C) kinetic energy of molecules remains same

    D) number of the molecules of gas increases

    View Answer play_arrow
  • question_answer97) For the reaction,\[{{C}_{3}}{{H}_{8}}(g)+5{{O}_{2}}(g)\xrightarrow{{}}3C{{O}_{2}}(g)+4{{H}_{2}}O(l)\]at constant temperature, \[\Delta H-\Delta E\] is

    A) \[+3RT\]

    B) \[-RT\]

    C) \[+RT\]

    D) \[-3RT\]

    View Answer play_arrow
  • question_answer98) In which of the following, equilibrium \[{{K}_{c}}\] and \[{{K}_{p}}\] are not equal?

    A) \[2C(s)+{{O}_{2}}(g)2C{{O}_{2}}(g)\]

    B) \[2NO(g){{N}_{2}}(g)+{{O}_{2}}(g)\]

    C) \[S{{O}_{2}}(g)+N{{O}_{2}}(g)S{{O}_{3}}(g)+NO(g)\]

    D) \[{{H}_{2}}(g)+{{I}_{2}}(g)2HI(g)\]

    View Answer play_arrow
  • question_answer99) On adding\[0.1\,\,M\]solution each of\[[A{{g}^{+}}],\,\,[B{{a}^{2+}}],\,\,(C{{a}^{2+}}]\]in \[N{{a}_{2}}S{{O}_{4}}\]solution, species first precipitated is \[[{{K}_{sp}}BaS{{O}_{4}}={{10}^{-11}},\,\,{{K}_{sp}}CaS{{O}_{4}}={{10}^{-6}}\]and\[{{K}_{sp}}A{{g}_{2}}S{{O}_{4}}={{10}^{-5}}]\]

    A) \[A{{g}_{2}}S{{O}_{4}}\]

    B) \[BaS{{O}_{4}}\]

    C) \[CaS{{O}_{4}}\]

    D) All of these

    View Answer play_arrow
  • question_answer100) Heat of neutralisation of \[HF\] (a weak acid) with strong base is\[-16.4\,\,kcal\]. Calculate heat of ionisation of \[HF\] in water.

    A) \[-13.7\,\,kcal\]

    B) \[-\text{ }2.7\,\,kcal\]

    C) \[+30.1\,\,kcal\]

    D) \[+3.01\,\,kcal\]

    View Answer play_arrow
  • question_answer101) If the slope of one of the lines represented by the equation \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] be square of the other, then the value of\[\frac{a+b}{h}+\frac{8{{h}^{2}}}{ab}\]is

    A) \[4\]

    B) \[-6\]

    C) \[6\]

    D) \[-4\]

    View Answer play_arrow
  • question_answer102) If \[\theta \] is real and \[{{z}_{1}},\,\,{{z}_{2}}\] are connected by \[z_{1}^{2}+z_{2}^{2}+2{{z}_{1}}{{z}_{2}}\cos \theta =0\], then triangle with vertices \[0,\,\,{{z}_{1}}\] and \[{{z}_{2}}\] is

    A) equilateral

    B) right angled

    C) isosceles

    D) None of these

    View Answer play_arrow
  • question_answer103) Total number of values of\['a'\], so that \[{{x}^{2}}-x-a=0\] has integral roots, where \[a\in N\] and\[6\le a\le 100\], is equal to

    A) \[2\]

    B) \[4\]

    C) \[8\]

    D) \[6\]

    View Answer play_arrow
  • question_answer104) Total number of \[n-\]digit numbers (where,\[n>1),\] having the property that no two consecutive digits are same, is

    A) \[{{8}^{n}}\]

    B) \[{{9}^{n}}\]

    C) \[9\cdot {{10}^{n-1}}\]

    D) None of these

    View Answer play_arrow
  • question_answer105) If any tangent to the ellipse\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] intercepts equal lengths 'I' on the axes, then\[l\]is equal to

    A) \[{{a}^{2}}+{{b}^{2}}\]

    B) \[\sqrt{{{a}^{2}}+{{b}^{2}}}\]

    C) \[({{a}^{2}}+{{b}^{2}})\]

    D) None of these

    View Answer play_arrow
  • question_answer106) The equation of plane containing the line \[\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}\] and 'the point \[(0,\,\,7,\,\,-7)\] is

    A) \[x+y+z=1\]

    B) \[x+y+z=2\]

    C) \[x+y+z=0\]

    D) None of the above

    View Answer play_arrow
  • question_answer107) lf\[f(x)=\sqrt[n]{{{x}^{m}}},\,\,n\in N\]is an even function, then is

    A) even integer

    B) odd integer

    C) any integer

    D) \[f(x)\] even is not possible

    View Answer play_arrow
  • question_answer108) Period of the function\[\left| {{\sin }^{3}}\frac{x}{2} \right|+\left| {{\cos }^{5}}\frac{x}{2} \right|\]is

    A) \[2\pi \]

    B) \[10\pi \]

    C) \[8\pi \]

    D) \[5\pi \]

    View Answer play_arrow
  • question_answer109) If\[f(x)=\frac{x}{1+x}+\frac{x}{(1+x)(1+2x)}\]\[+\frac{x}{(1+2x)(1+3x)}+...\infty ,\] then

    A) \[f(x)\] is continuous for all x

    B) \[f(x)\]is discontinuous for finite number of points

    C) \[f(x)\]is discontinuous for finite number of points

    D) None of the above

    View Answer play_arrow
  • question_answer110) The value of \['p'\] such that the length of subtangent and subnormal is equal for the curve \[y={{e}^{px}}+px\] at the point \[(0,\,\,1)\] is

    A) \[p=\pm 1\]

    B) \[p=\pm 2\]

    C) \[p=\pm \frac{1}{2}\]

    D) None of these

    View Answer play_arrow
  • question_answer111) If the function \[f(x)=2{{x}^{3}}-9a{{x}^{2}}+12{{a}^{2}}x+1\], where \[a>0\] attains its maximum and minimum at \[p\] and \[q\] respectively, such that \[{{p}^{2}}=q\], then a equals to

    A) \[1\]

    B) \[2\]

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

    D) \[3\]

    View Answer play_arrow
  • question_answer112) If\[\mathbf{a}=x\mathbf{i}+(x-1)\mathbf{j}+\mathbf{k}\]and\[\mathbf{b}=(x+1)\mathbf{i}+\mathbf{j}+a\mathbf{k}\] always make an acute angle with each other for every value of\[x\in R\], then

    A) \[a\in (-\infty ,\,\,2)\]

    B) \[a\in (2,\,\,\infty )\]

    C) \[a\in (-\infty ,\,\,1)\]

    D) \[a\in (1,\,\,\infty )\]

    View Answer play_arrow
  • question_answer113) The number of straight lines that are equally inclined to the three-dimensional coordinate axes, is

    A) \[2\]

    B) \[4\]

    C) \[6\]

    D) \[8\]

    View Answer play_arrow
  • question_answer114) A variable plane passes through the fixed point \[(a,\,\,b,\,\,c)\] and meets the axes at\[A,\,\,B,\,\,C\]. The locus of the point of intersection of the planes through \[A,\,\,B,\,\,C\] and parallel to the coordinates planes is

    A) \[\frac{a}{x}+\frac{b}{y}+\frac{c}{z}=1\]

    B) \[\frac{a}{x}+\frac{b}{y}+\frac{c}{z}=1\]

    C) \[\frac{a}{x}+\frac{b}{y}+\frac{c}{z}=-2\]

    D) \[\frac{a}{x}+\frac{b}{y}+\frac{c}{z}=-1\]

    View Answer play_arrow
  • question_answer115) If \[PQ\] is a double of the .hyperbola\[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] such that \[OPQ\] is an equilateral triangle, \[O\] being the centre of the hyperbola, then the eccentricity \['e'\] of the hyperbola satisfies

    A) \[1<e<\frac{2}{\sqrt{3}}\]

    B) \[e=\frac{2}{\sqrt{3}}\]

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

    D) \[e>\frac{2}{\sqrt{3}}\]

    View Answer play_arrow
  • question_answer116) \[\int{\frac{1+{{x}^{4}}}{{{(1-{{x}^{4}})}^{3/2}}}}dx\]is equal to

    A) \[\frac{1}{\sqrt{{{x}^{2}}-\frac{1}{{{x}^{2}}}}}+C\]

    B) \[\frac{1}{\sqrt{\frac{1}{{{x}^{2}}}-{{x}^{2}}}}+C\]

    C) \[\frac{1}{\sqrt{\frac{1}{{{x}^{2}}}+{{x}^{2}}}}+C\]

    D) None of these

    View Answer play_arrow
  • question_answer117) In a geometric series, the first term \[=a,\] common ratio\[=r\]. If \[{{S}_{n}}\] denotes the sum of the \[n\] terms and\[{{U}_{n}}=\sum\limits_{n=1}^{n}{{{S}_{n}}}\], then\[r{{S}_{n}}+(1-r){{U}_{n}}\] equals to

    A) \[0\]

    B) \[n\]

    C) \[na\]

    D) \[nar\]

    View Answer play_arrow
  • question_answer118) If \[{{x}_{1}}\] and \[{{x}_{2}}\] are two distinct roots of the equation\[a\cos x+b\sin x=c\], then\[\tan \frac{{{x}_{1}}+{{x}_{2}}}{2}\] is equal to

    A) \[\frac{a}{b}\]

    B) \[\frac{b}{a}\]

    C) \[\frac{c}{a}\]

    D) \[\frac{a}{c}\]

    View Answer play_arrow
  • question_answer119) If\[(1+\sqrt{1+x})\tan y=1+\sqrt{1-x}\], then\[\sin 4y\]is equal to

    A) \[4x\]

    B) \[2x\]

    C) \[x\]

    D) None of these

    View Answer play_arrow
  • question_answer120) If\[|\cos \theta \{\sin \theta +\sqrt{{{\sin }^{2}}\theta +{{\sin }^{2}}\alpha }\}|\le K\], the value of \[K\] is

    A) \[\sqrt{1+{{\cos }^{2}}\alpha }\]

    B) \[\sqrt{1+{{\sin }^{2}}\alpha }\]

    C) \[\sqrt{2+{{\sin }^{2}}\alpha }\]

    D) \[\sqrt{2+{{\cos }^{2}}\alpha }\]

    View Answer play_arrow
  • question_answer121) A vertical pole \[PS\] has two marks at \[Q\] and \[R\] such that the portions \[PQ,\,\,\,PR\] and \[PS\] subtend angles \[\alpha ,\,\,\,\beta \] and \[\gamma \] at a point on the ground distance \[x\] from the bottom of pole. If \[PQ=a,\,\,PR=b,\,\,PS=c\]and\[\alpha +\beta +\gamma ={{180}^{o}}\], then \[{{x}^{2}}\] is equal to

    A) \[\frac{{{a}^{3}}}{a+b+c}\]

    B) \[\frac{{{b}^{3}}}{a+b+c}\]

    C) \[\frac{{{c}^{3}}}{a+b+c}\]

    D) \[\frac{abc}{a+b+c}\]

    View Answer play_arrow
  • question_answer122) The term independent of \[x\] in the expansion of\[{{\left( x+\frac{1}{x} \right)}^{2n}}\]is

    A) \[\frac{1\cdot 3\cdot 5...(2n-1)}{n!}\]

    B) \[\frac{1\cdot 3\cdot 5...(2n-1)}{n!}{{2}^{n}}\]

    C) \[\frac{1\cdot 3\cdot 5...(2n+1)}{(n+1)!}\]

    D) None of the above

    View Answer play_arrow
  • question_answer123) The value of\[\int_{0}^{{{\sin }^{2}}x}{{{\sin }^{-1}}\sqrt{t}\,\,dt}+\int_{0}^{{{\cos }^{2}}x}{{{\cos }^{-1}}}\sqrt{t}\,\,dt\]is

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

    B) \[1\]

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

    D) None of these

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  • question_answer124) The degree of the differential equation \[{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{3}}+{{\left( \frac{dy}{dx} \right)}^{2}}+\sin \left( \frac{dy}{dx} \right)+1=0\]is

    A) \[3\]

    B) \[2\]

    C) \[1\]

    D) None of the above

    View Answer play_arrow
  • question_answer125) The solution of the differential equation \[\frac{dy}{dx}={{e}^{x-y}}({{e}^{x}}-{{e}^{y}})\]is

    A) \[{{e}^{y}}=({{e}^{x}}+1)+C{{e}^{-x}}\]

    B) \[{{e}^{y}}=({{e}^{x}}-1)+C\]

    C) \[{{e}^{y}}=({{e}^{x}}-1)+C{{e}^{-x}}\]

    D) None of the above

    View Answer play_arrow
  • question_answer126) The range of\[\alpha \], for which the point \[(\alpha ,\,\,\alpha )\] lies inside the region bounded by the curves \[y=\sqrt{1-{{x}^{2}}}\]and \[x+y=1\] is

    A) \[\frac{1}{2}<\alpha <\frac{1}{\sqrt{2}}\]

    B) \[\frac{1}{2}<\alpha <\frac{1}{3}\]

    C) \[\frac{1}{3}<\alpha <\frac{1}{\sqrt{3}}\]

    D) \[\frac{1}{4}<\alpha <\frac{1}{2}\]

    View Answer play_arrow
  • question_answer127) Find the length of the line segment joining the vertex of the parabola \[{{y}^{2}}=4ax\] and a point on the parabola where the line segment makes an angle \['\theta '\] to the x-axis.

    A) \[\frac{2a\cos \theta }{{{\sin }^{2}}\theta }\]

    B) \[\frac{4a\cos \theta }{{{\sin }^{2}}\theta }\]

    C) \[\frac{4a\cos \theta }{3{{\sin }^{2}}\theta }\]

    D) None of the above

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  • question_answer128) If\[y={{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right)+{{\sec }^{-1}}\left( \frac{1+{{x}^{2}}}{1-{{x}^{2}}} \right)\], then\[\frac{dy}{dx}\] is equal to

    A) \[\frac{7}{1+{{x}^{2}}}\]

    B) \[\frac{4}{1+{{x}^{2}}}\]

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

    D) None of these

    View Answer play_arrow
  • question_answer129) If\[{{a}_{1}},\,\,{{a}_{2}},...,\,\,{{a}_{n-1}}\]are the nth roots of unity, then the value of\[(1-{{a}_{1}})(1-{{a}_{2}})...(1-{{a}_{n-1}})\] is equal to

    A) \[\sqrt{3}\]

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

    C) \[n\]

    D) \[0\]

    View Answer play_arrow
  • question_answer130) If the equation\[{{z}^{2}}+(p+iq)z+r+is=0\], where \[p,\,\,q,\,\,r\] and \[s\] are real and non-zero roots, then

    A) \[pqr={{r}^{2}}+{{p}^{2}}s\]

    B) \[prs={{q}^{2}}+{{r}^{2}}p\]

    C) \[qrs={{p}^{2}}+{{s}^{2}}q\]

    D) \[pqs={{s}^{2}}+{{q}^{2}}r\]

    View Answer play_arrow
  • question_answer131) A person writes a letter to four of his friends. He asks each one of them, to copy the letter and mail to four different persons with instructions that they move the chain similarly. Assuming that the chain is not broken and that it costs \[50\,\,paise\] to mail one letter. When the 8th set of letter is mailed, then the amount on postage will be

    A) \[Rs.\,\,42780\]

    B) \[Rs.\,\,43690\]

    C) \[Rs.\,\,43680\]

    D) None of these

    View Answer play_arrow
  • question_answer132) If \['a'\] be the \[AM\] between \[b\] and \[c\] and \[GM's\]are \[{{G}_{{}}}\] and\[{{G}_{2}}\], then \[G_{1}^{3}+G_{2}^{3}\] is equal to

    A) \[abc\]

    B) \[2abc\]

    C) \[3abc\]

    D) \[4abc\]

    View Answer play_arrow
  • question_answer133) If\[x>0\], then solution of\[\left| x+\frac{1}{x} \right|<4\]is

    A) \[-2-\sqrt{3}<x<-2+\sqrt{3}\]

    B) \[2-\sqrt{3}<x<7+\sqrt{3}\]

    C) \[2-\sqrt{3}<x<2+\sqrt{3}\]

    D) None of the above

    View Answer play_arrow
  • question_answer134) Matrix \[{{M}_{r}}\] is defined as\[{{M}_{r}}=\left[ \begin{matrix} r & r-1 \\ r-1 & r \\ \end{matrix} \right]\],\[r\in N\]value of\[\det ({{M}_{1}})+\det ({{M}_{2}})+\det ({{M}_{3}})\]\[+...+\det ({{M}_{2007}})\]is

    A) \[2007\]

    B) \[2008\]

    C) \[{{(2008)}^{2}}\]

    D) \[{{(2007)}^{2}}\]

    View Answer play_arrow
  • question_answer135) If\[A=\left[ \begin{matrix} \frac{-+i\sqrt{3}}{2i} & \frac{-1-i\sqrt{3}}{2i} \\ \frac{1+i\sqrt{3}}{2i} & \frac{1-i\sqrt{3}}{2i} \\ \end{matrix} \right]i=\sqrt{-1}\]and\[f(x)={{x}^{2}}+2\], then \[f(A)\] is equal to

    A) \[\left( \frac{5-i\sqrt{3}}{2} \right)\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\]

    B) \[\left( \frac{3-i\sqrt{3}}{2} \right)\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\]

    C) \[\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\]

    D) \[(2+i\sqrt{3})\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\]

    View Answer play_arrow
  • question_answer136) If \[{{x}_{1}},\,\,{{x}_{2}},...,\,\,{{x}_{n}}\] be n observations such that \[\Sigma x_{i}^{2}=400\] and\[\Sigma {{x}_{i}}=80\]. Then, a possible value of \[n\] among the following is

    A) \[9\]

    B) \[12\]

    C) \[15\]

    D) \[18\]

    View Answer play_arrow
  • question_answer137) The number of integral values of \[k\] for which the equation \[7\cos x+5\sin x=2k+1\] has a solution is

    A) \[4\]

    B) \[8\]

    C) \[10\]

    D) \[12\]

    View Answer play_arrow
  • question_answer138) If\[a\sin x+b\cos (x+\theta )+b\cos (x-\theta )=d\], then the value of\[|\cos \theta |\]is equal to

    A) \[\frac{1}{2|b|}\sqrt{{{d}^{2}}-{{a}^{2}}}\]

    B) \[\frac{1}{2|a|}\sqrt{{{d}^{2}}-{{a}^{2}}}\]

    C) \[\frac{1}{2|d|}\sqrt{{{d}^{2}}-{{a}^{2}}}\]

    D) None of these

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  • question_answer139) The value of \['a'\] for which the function \[f(x)=(4a-3)(x+\log 5)+2(a-7)\] \[\cot \frac{x}{2}\cdot {{\sin }^{2}}\frac{x}{2}\]does not possess critical points is

    A) \[(-\infty ,\,\,2)\]

    B) \[(-\infty ,\,\,-1)\]

    C) \[[1,\,\,\infty )\]

    D) \[\left( -\infty ,\,\,\frac{-4}{3} \right)\cup (2,\,\,\infty )\]

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  • question_answer140) \[\mathbf{a}\]and \[\mathbf{c}\] are unit vectors and\[|\mathbf{b}|\,\,=4\]. If angle between \[\mathbf{b}\] and \[\mathbf{c}\] is and \[{{\cos }^{-1}}\left( \frac{1}{4} \right)\]\[\text{and}\]\[\mathbf{a}\times \mathbf{b}=2\mathbf{a}\times \mathbf{c}\], then\[\mathbf{b}=\lambda \mathbf{a}+2\mathbf{c}\], where\[\lambda \]is equal to

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

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

    C) \[\pm \,\,1\]

    D) None of the above

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  • question_answer141) If the planes\[x-cy-bz=0\], \[cx-y+az=0\]and\[bx+ay-z=0\] pass through a straight line, then the value of \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}+2abc\]is

    A) \[-1\]

    B) \[2\]

    C) \[1\]

    D) \[0\]

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  • question_answer142) The plane \[ax+by=0\] is rotated through an angle \[\alpha \] about its line of intersection with the plane\[z=0\], then the equation to the plane in new position is

    A) \[ax-by\pm z\sqrt{{{a}^{2}}+{{b}^{2}}}\cdot \cot \alpha =0\]

    B) \[ax-by\pm z\sqrt{{{a}^{2}}+{{b}^{2}}}\cdot \tan \alpha =0\]

    C) \[ax+by\pm z\sqrt{{{a}^{2}}+{{b}^{2}}}\cdot \cot \alpha =0\]

    D) \[ax+by\pm z\sqrt{{{a}^{2}}+{{b}^{2}}}\cdot \tan \alpha =0\]

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  • question_answer143) If\[y=a\cos (\log x)-b\sin (\log x)\], then the value of\[{{x}^{2}}\frac{{{d}^{2}}y}{d{{x}^{2}}}+x\frac{dy}{dx}+y\]is

    A) \[0\]

    B) \[1\]

    C) \[2\]

    D) \[3\]

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  • question_answer144) The inverse of the function\[f(x)=\log ({{x}^{2}}+3x+1),\,\,x\in [1,\,\,3]\], assuming it to be an onto function, is

    A) \[\frac{-3+\sqrt{5+4{{e}^{x}}}}{2}\]

    B) \[\frac{-3\pm \sqrt{5+4{{e}^{x}}}}{2}\]

    C) \[\frac{-3-\sqrt{5+4{{e}^{x}}}}{2}\]

    D) None of the above

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  • question_answer145) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sqrt{1-\cos x}}{x}\]is equal to

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

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

    C) \[0\]

    D) Does not exist

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  • question_answer146) The sum of two numbers is\[z\], the maximum value of the product of the first and the square of second is

    A) \[4\]

    B) \[1\]

    C) \[3\]

    D) \[0\]

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  • question_answer147) If\[{{(1+x-2{{x}^{2}})}^{6}}=1+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+...+{{a}_{12}}{{x}^{12}}\], then the expression\[{{a}_{2}}+{{a}_{4}}+{{a}_{6}}+...+{{a}_{12}}\]has the value

    A) \[32\]

    B) \[63\]

    C) \[64\]

    D) \[31\]

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  • question_answer148) If \[f:\left[ 0,\,\,\frac{\pi }{2} \right]\to [0,\,\,\infty ]\] be a function defined by \[y=\sin \left( \frac{x}{2} \right)\], then \[f\] is

    A) injective

    B) subjective

    C) objective

    D) None of these

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  • question_answer149) If the function \[f(x)\] is defined by \[f(x)=a+bx\] and \[{{f}^{r}}=fff...\] (repeated \[r\] times), then\[\frac{d}{dx}\{{{f}^{r}}(x)\}\]is equal to

    A) \[a+{{b}^{r}}x\]

    B) \[ar+{{b}^{r}}x\]

    C) \[ar\]

    D) \[{{b}^{r}}\]

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  • question_answer150) The statement \[p\to (q\to p)\] is equivalent to

    A) \[p\to (p\leftrightarrow q)\]

    B) \[p\to (p\to q)\]

    C) \[p\to (p\vee q)\]

    D) \[p\to (p\wedge q)\]

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