Solved papers for JCECE Engineering JCECE Engineering Solved Paper-2013

JCECE Engineering Solved Paper-2013 Total Questions - 150

1) 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
2) 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

View Answer
3) 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)

\[(25.3\pm 0.5)cm\]

View Answer
4) 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
5) 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
6) 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
7) 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
8) 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
9) 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
10) 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
11) 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
12) 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
13) 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)

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

View Answer
14) 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)

\[7/2\]

View Answer
15) 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)

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

View Answer
16) 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
17) 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
18) \[LANDSAT\] 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
19) 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)

\[18\,\,mm\]

View Answer
20) 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)

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

View Answer
21) 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)

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

View Answer
22) 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)

\[20\,\,cm\]

View Answer
23) 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)

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

View Answer
24) 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

View Answer
25) 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)

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

View Answer
26) 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

View Answer
27) 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)

\[16\,\,J\]

View Answer
28) 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
29) 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
30) 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)

\[400\,\,N\]

View Answer
31) 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)

\[2\,\,N\]

View Answer
32) 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)

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

View Answer
33) 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)

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

View Answer
34) 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)

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

View Answer
35) 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)

\[9\,\,eV\]

View Answer
36) 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)

\[-54.4\,\,eV\]

View Answer
37) 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)

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

View Answer
38) 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

View Answer
39) 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

View Answer
40) 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

View Answer
41) 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)

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

View Answer
42) 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)

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

View Answer
43) 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

View Answer
44) 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)

\[100\]

View Answer
45) A deflection magnetometer works on

A)

Coulomb's law

B)

Tangent law

C)

Curie law

D)

The law of vibration of a magnet

View Answer
46) 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

View Answer
47) 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)

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

View Answer
48) 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)

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

View Answer
49) 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

View Answer
50) 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)

\[16\]

View Answer
51) 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

View Answer
52) Which of the following forms acidic halides?

A)

\[HF\]

B)

\[HCl\]

C)

\[HBr\]

D)

\[HI\]

View Answer
53) The maximum covalency of nitrogen is

A)

\[3\]

B)

\[4\]

C)

\[5\]

D)

\[6\]

View Answer
54) 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\[+3\]

View Answer
55) 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)

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

View Answer
56) 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)

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

View Answer
57) 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)

\[27\]

View Answer
58) Spin only magnetic moment value of \[C{{r}^{3+}}\] ion is

A)

\[2.87\,\,BM\]

B)

\[3.87\,\,BM\]

C)

\[3.47\,\,BM\]

D)

\[3.67\,\,BM\]

View Answer
59) 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)

\[Fm\]

View Answer
60) 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

View Answer
61) 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)

View Answer
62) Which of the following is a network solid?

A)

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

B)

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

C)

Diamond

D)

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

View Answer
63) Which kind of defects are introduced by doping?

A)

Dislocation defects

B)

Schottky defects

C)

Electronic defects

D)

Frenkel defects

View Answer
64) 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)

View Answer
65) 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

View Answer
66) \[4L\] 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)

\[0.016\]

View Answer
67) At high concentration of soap in water, soap behave as

A)

molecular solid

B)

associated colloid

C)

macromolecular colloid

D)

lyophilic colloid

View Answer
68) 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

View Answer
69) 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)

View Answer
70) 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

View Answer
71) 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
72) Which of the following is not a target molecule for drug function in body?

A)

Vitamins

B)

Proteins

C)

Lipids

D)

Carbohydrates

View Answer
73) 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
74) 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
75) Methyl \[\alpha -D-\]glucoside and methyl \[\beta -D-\]glucoside are

A)

epimers

B)

anomers

C)

conformational diastereomers

D)

enantiomers

View Answer
76) The number of disulphide linkages present in insulin are

A)

\[1\]

B)

\[2\]

C)

\[3\]

D)

\[4\]

View Answer
77) 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
78) 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
79) \[C{{H}_{3}}-C\equiv CH\xrightarrow[1%HgS{{O}_{4}}]{40%{{H}_{2}}S{{O}_{4}}}a\xrightarrow{Isomerisation}\] 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
80) 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
81) Which of the following species can act as the strongest base?

A)

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

B)

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

C)

D)

View Answer
82) \[IUPAC\]name of w-cresol is

A)

benzene-1, 3-diol

B)

3-chlorophenol

C)

3-methyl phenol

D)

3-methoxyphenol

View Answer
83) 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
84) 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
85) 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
86) Alkynes occur in nature in

A)

free state

B)

partially free state

C)

not in free state

D)

None of these

View Answer
87) 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
88) \[{{C}_{6}}{{H}_{6}}+C{{l}_{2}}(excess)\xrightarrow[dark,\,cold]{Anhy.\,AlC{{l}_{8}}}P\]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
89) 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
90) 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
91) 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
92) 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
93) 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
94) 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
95) 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
96) 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
97) 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
98) 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
99) 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
100) 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
101) 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
102) 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
103) 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
104) 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
105) 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
106) 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
107) 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
108) 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
109) 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
110) 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
111) 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
112) 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
113) 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
114) 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
115) 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
116) \[\int{\frac{1+{{x}^{4}}}{{{(1-{{x}^{4}})}^{3/2}}}}dx\]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
117) 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
118) 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
119) 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
120) 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
121) 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
122) 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
123) 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

View Answer
124) 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
125) 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
126) 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
127) 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

View Answer
128) 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
129) 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
130) 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
131) 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
132) 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
133) 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
134) 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
135) 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
136) 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
137) 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
138) 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

View Answer
139) 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)

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

View Answer
140) \[\mathbf{a}\]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

View Answer
141) 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)

\[0\]

View Answer
142) 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)

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

View Answer
143) 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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144) 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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145) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sqrt{1-\cos x}}{x}\]is equal to

A)

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

B)

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

C)

\[0\]

D)

Does not exist

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146) 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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147) 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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148) 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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149) 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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150) 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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