Solved papers for JCECE Engineering JCECE Engineering Solved Paper-2014

done JCECE Engineering Solved Paper-2014

  • question_answer1) A mass of \[0.5\,\,kg\] moving with a speed of \[1.5\,\,m{{s}^{-1}}\] on a horizontal smooth surface, collides with a nearly weightless spring of force constant\[k=50\,\,N{{m}^{-1}}\]. The maximum compression of the spring would be

    A) \[0.15\,\,m\]

    B) \[0.23\,\,m\]

    C) \[1.6\,\,m\]

    D) \[0.4\,\,m\]

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  • question_answer2) A particle of mass \[{{m}_{1}}\] moves with velocity \[{{\upsilon }_{1}}\] and collides with another particle at rest of equal mass. The velocity of the second particle after the elastic collision is

    A) \[3{{v}_{1}}\]

    B) \[{{v}_{1}}\]

    C) \[-{{v}_{1}}\]

    D) \[0\]

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  • question_answer3) The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axis is

    A) \[\sqrt{3}:\sqrt{2}\]

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

    C) \[\sqrt{3}:1\]

    D) \[\sqrt{5}:\sqrt{3}\]

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  • question_answer4) A wheel having moment of inertia\[2kg\,\,{{m}^{-2}}\] about its vertical axis, rotates at the rate of \[60\,\,rpm\] about this axis. The torque which can stop the wheel's rotation in one minute would be

    A) \[\frac{2\pi }{13}N-m\]

    B) \[\frac{\pi }{14}N-m\]

    C) \[\frac{\pi }{15}N-m\]

    D) \[\frac{\pi }{20}N-m\]

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  • question_answer5) A sphere of diameter \[0.2\,\,m\] and mass \[2\,\,kg\] is rolling on an inclined plane with velocity\[v=0.5m{{s}^{-1}}\]. The kinetic energy of the sphere is

    A) \[0.4\,\,J\]

    B) \[0.3\,\,J\]

    C) \[0.6\,\,J\]

    D) \[0.42\,\,J\]

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  • question_answer6) If a sphere rolling on an inclined plane with velocity v without slipping, the vertical height of the incline in terms of velocity will be

    A) \[\frac{7v}{10g}\]

    B) \[\frac{7{{v}^{2}}}{10g}\]

    C) \[\frac{2{{v}^{2}}}{5g}\]

    D) \[\frac{3v}{5g}\]

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  • question_answer7) The height vertically above the earth's surface at which the acceleration due to gravity becomes \[1%\] of its value at the surface is (\[R\] is the radius of the earth)

    A) \[8R\]

    B) \[9R\]

    C) \[10R\]

    D) \[20R\]

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  • question_answer8) The motion of a particle executing SHM in one dimension is described by\[x=-0.23\sin \left( t+\frac{\pi }{4} \right)\]where, \[x\] is in metre and t in second. The frequency of oscillation in \[Hz\] is

    A) \[3\]

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

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

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

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  • question_answer9) The change in the gravitational potential energy when a body of mass \[m\] is raised to a height \[nR\] above the surface of the earth is (here, \[R\] is the radius of the earth)

    A) \[\left( \frac{n}{n+1} \right)mgR\]

    B) \[\left( \frac{n}{n-1} \right)mgR\]

    C) \[nmgR\]

    D) \[\frac{mgR}{n}\]

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  • question_answer10) A satellite is rotating around a planet in the orbit of radius \[r\] with time period\[T\]. If gravitational force changes according to\[{{r}^{5/2}}\], the \[{{T}^{2}}\] will be

    A) \[\propto {{r}^{3}}\]

    B) \[\propto {{r}^{7/2}}\]

    C) \[{{\propto }^{9/12}}\]

    D) \[\propto {{r}^{3/2}}\]

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  • question_answer11) A liquid \[X\] of density \[3.36\,\,g/c{{m}^{3}}\] is poured in a U-tube in right arm with height\[10\,\,cm\], which contains\[Hg\]. Another liquid \[Y\] is poured in left arm with height\[8\,\,cm\]. Upper levels of \[X\] and \[Y\] are same. What is the density of\[Y\]?

    A) \[0.8\,\,g/cc\]

    B) \[1.2\,\,g/cc\]

    C) \[1.4\,\,g/cc\]

    D) \[1.6\,\,g/cc\]

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  • question_answer12) Wafer flows along a horizontal pipe whose cross-section is not, constant. The pressure is \[1\,\,cm\] of\[Hg\], where the velocity is\[35\,\,cm{{s}^{-1}}\]. At a point where the velocity is\[65\,\,cm{{s}^{-1}}\], the pressure will be

    A) \[0.89\,\,cm\]of\[Hg\]

    B) \[8.9\,\,cm\]of\[Hg\]

    C) \[0.5\,\,cm\]of\[Hg\]

    D) \[1\,\,cm\]of\[Hg\]

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  • question_answer13) A lead bullet of unknown mass is fired-with a speed of \[180\,\,m{{s}^{-1}}\] into a tree in which it stops. Assuming that in this process two-third of heat produced goes into the bullet and one-third into wood. The temperature of the bullet rises by

    A) \[{{140}^{o}}C\]

    B) \[{{106}^{o}}C\]

    C) \[{{90}^{o}}C\]

    D) \[{{100}^{o}}C\]

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  • question_answer14) The freezer in a refrigerator is located at the top section so that

    A) the entire chamber of the refrigerator is cooled quickly due to convection

    B) the motor is not heated

    C) the heat gained from the environment is high

    D) the heat gained from the environment is low

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  • question_answer15) Two monoatomic ideal gases \[A\] and \[B\] occupying the same volume \[V\] are at the same temperature \[T\] and pressure\[p\]. If they are mixed, the resultant mixture has volume \[V\] and temperature\[T\]. The pressure of the mixture is

    A) \[p\]

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

    C) \[4p\]

    D) \[2p\]

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  • question_answer16) The temperature at which the mean \[KE\] of the molecules of gas is one-third of the mean \[KE\] of its molecules at \[{{180}^{o}}C\] is

    A) \[-{{122}^{o}}C\]

    B) \[-{{90}^{o}}C\]

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

    D) \[{{151}^{o}}C\]

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  • question_answer17) \[U\] is the \[PE\] of an oscillating particle and \[F\] is the force acting on it at a given instant. Which of the following is true?

    A) \[\frac{U}{F}+x=0\]

    B) \[\frac{2U}{F}+x=0\]

    C) \[\frac{F}{U}+x=0\]

    D) \[\frac{F}{2U}+x=0\]

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  • question_answer18) The density of newly discovered planet is twice that of the earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is\[R\], the radius of the plane would be

    A) \[2R\]

    B) \[4R\]

    C) \[\frac{1}{4}R\]

    D) \[\frac{1}{2}R\]

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  • question_answer19) The half-life period of a radioactive substance is\[140\,\,days\]. After, how much time, \[15\,\,g\] will decay from a \[16\,\,g\] sample of the substance?

    A) \[140\,\,days\]

    B) \[280\,\,days\]

    C) \[420\,\,days\]

    D) \[560\,\,days\]

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  • question_answer20) A tuning fork \[A\] produces 4 beats \[{{s}^{-1}}\] with another tuning fork \[B\] of frequency\[320\,\,Hz\]. On filing one of the prongs of\[A\], 4 beats \[{{s}^{-1}}\] are again heard when sounded with the same fork\[B\]. Then, the frequency of 'the fork A before filing is

    A) \[328\,\,Hz\]

    B) \[316\,\,Hz\]

    C) \[324\,\,Hz\]

    D) \[320\,\,Hz\]

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  • question_answer21) Two cars are moving on two perpendicular roads towards a crossing with uniform speeds of\[72\,\,km/h\]\[\text{and}\]\[36\,\,km/h\]. If first car blows horn of frequency\[280\,\,Hz\], then the frequency of horn heard by the driver of second car when line joining the car makes angle of \[{{45}^{o}}\] with the roads, will.be

    A) \[321\,\,Hz\]

    B) \[296\,\,Hz\]

    C) \[289\,\,Hz\]

    D) \[280\,\,Hz\]

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  • question_answer22) A particle moves along a straight line\[OX\]. At a time \[t\] (in second) the distance \[x\] of the particle from \[O\] is given by\[x=40+12t-{{t}^{3}}\]. How long would the particle travel before coming to rest?

    A) \[24\,\,m\]

    B) \[40\,\,m\]

    C) \[56\,\,m\]

    D) \[16\,\,m\]

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  • question_answer23) The capacitance of a spherical conductor with radius \[1\,\,m\] is

    A) \[9\times {{10}^{9}}F\]

    B) \[1\mu F\]

    C) \[1.1\times {{10}^{-10}}F\]

    D) \[1\times {{10}^{-6}}F\]

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  • question_answer24) The electric field due to an electric dipole at a distance \[r\] from its centre in axial position is\[E\]. If the dipole is rotated through an angle of \[{{90}^{o}}\] about its perpendicular axis, the electric field at the same point will be

    A) \[E\]

    B) \[\frac{E}{4}\]

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

    D) \[2E\]

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  • question_answer25) Choose the correct statement.

    A) When we heat a semiconductor its resistance increases

    B) When we heat a semiconductor its resistance decreases

    C) When we cool a semiconductor to\[0\,\,K\], then it be cames superconductor

    D) Resistance of a semiconductor is independent of temperature

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  • question_answer26) A charge \[q\] coulomb makes \[n\] revolutions in one second in a circular orbit of radius r. The magnetic field at the centre of the orbit in\[N{{A}^{-1}}{{m}^{-1}}\]is.

    A) \[\frac{2\pi rn}{q}\times {{10}^{-7}}\]

    B) \[\left( \frac{2\pi q}{r} \right)\times {{10}^{-7}}\]

    C) \[\left( \frac{2\pi q}{nr} \right)\times {{10}^{-7}}\]

    D) \[\left( \frac{2\pi nq}{r} \right)\times {{10}^{-7}}\]

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  • question_answer27) The path of an electron in a uniform magnetic field may be

    A) circular but not helical

    B) helical but not circular

    C) neither helical nor circular

    D) either helical or circular

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  • question_answer28) The couple acting on a magnet of length \[10\,\,cm\] and pole strength\[125\,\,A-m\], kept in a field of \[B=2\times {{10}^{-5}}T\], at an angle of \[{{30}^{o}}\] is

    A) \[1.5\times {{10}^{-5}}N-m\]

    B) \[1.5\times {{10}^{-3}}N-m\]

    C) \[1.5\times {{10}^{-2}}N-m\]

    D) \[1.5\times {{10}^{-6}}N-m\]

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  • question_answer29) \[X\]and\[Y\], two metallic coils are arranged in such a way that, when steady change in current flowing in \[X\] coil is\[4\,\,A\], change in magnetic flux associated with coil \[Y\] is\[0.4\,\,Wb\]. Mutual inductance of the system of these coils is

    A) \[0.2\,\,H\]

    B) \[5\,\,H\]

    C) \[0.8\,\,H\]

    D) \[0.1\,\,H\]

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  • question_answer30) A sinusoidal voltage of peak value \[300\,\,V\] and an angular frequency \[\omega =400\,\,rad/s\] is applied to series \[L-C-R\] circuit, in which \[R=3\Omega ,\,\,L=20\,\,mH\]and\[C=625\mu F\]. The peak current in the circuit is

    A) \[30\sqrt{2}A\]

    B) \[60\,\,A\]

    C) \[100\,\,A\]

    D) \[60\sqrt{2}A\]

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  • question_answer31) A fire screen produces sensation of cooling as

    A) it allows both infrared and visible light but cuts off ultraviolet

    B) it allows infrared and cuts off shorter wavelengths

    C) it cuts off both visible light and infrared

    D) it allows only visible light and cuts off infrared

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  • question_answer32) If the angle of incidence is twice the angle of refraction in a medium of refractive index\[\mu \], then the angle of incidence is

    A) \[2{{\cos }^{-1}}\frac{\mu }{2}\]

    B) \[2{{\sin }^{-1}}\frac{\mu }{2}\]

    C) \[2{{\cos }^{-1}}\mu \]

    D) \[2{{\sin }^{-1}}\mu \]

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  • question_answer33) The magnification produced by an astronomical telescope for normal adjustment is 10 and the length of the telescope.is\[1.1\,\,m\]. The magnification, when the image is formed atleast distance of distinct vision is

    A) \[6\]

    B) \[14\]

    C) \[16\]

    D) \[18\]

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  • question_answer34) In Young's double slit experiment with sodium vapour lamp of wavelength \[589\,\,nm\] and the slits \[0.589\,\,mm\] apart, the half angular width of the central maximum is

    A) \[{{\sin }^{-1}}(0.01)\]

    B) \[{{\sin }^{-1}}(0.0001)\]

    C) \[{{\sin }^{-1}}(0.001)\]

    D) \[{{\sin }^{-1}}(0.1)\]

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  • question_answer35) When the angle of incidence is \[{{60}^{o}}\] on the surface of a glass slab, it is found that the reflected ray is completely polarised. The velocity of light in glass is

    A) \[\sqrt{2}\times {{10}^{8}}m{{s}^{-1}}\]

    B) \[\sqrt{3}\times {{10}^{8}}m{{s}^{-1}}\]

    C) \[2\times {{10}^{8}}m{{s}^{-1}}\]

    D) \[3\times {{10}^{8}}m{{s}^{-1}}\]

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  • question_answer36) Cathode rays of velocity \[{{10}^{6}}m{{s}^{-1}}\] describe an approximate circular path of radius \[1\,\,m\] in an electric field\[300\,\,Vc{{m}^{-1}}\]. If the velocity of the cathode rays are doubled. The value of electric field so that the rays describe the same circular path, will be

    A) \[2400\,\,V\,\,c{{m}^{-1}}\]

    B) \[600\,\,V\,\,c{{m}^{-1}}\]

    C) \[1200\,\,V\,\,c{{m}^{-1}}\]

    D) \[12000\,\,V\,\,c{{m}^{-1}}\]

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  • question_answer37) The de-Broglie wavelength of an electron and the wavelength of a photon are the same. The ratio between the energy of that photon and the momentum of that electron is (\[c=\]velocity of light, \[h=\]Planck's constant)

    A) \[h\]

    B) \[c\]

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

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

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  • question_answer38) When \[1\,\,cm\]thick surface is illuminated with light of wavelength\[\lambda \], the stopping potential is\[V\]. When the same surface is illuminated by light of wavelength\[2\lambda \], the stopping potential is\[\frac{V}{3}\]. Threshold wavelength for metallic surface is

    A) \[\frac{4\lambda }{3}\]

    B) \[4\lambda \]

    C) \[6\lambda \]

    D) \[\frac{8\lambda }{3}\]

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  • question_answer39) For photoelectric emission, tungsten requires light of\[2300\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\]. If light of \[1800\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\] wavelength is incident, then emission

    A) takes place

    B) doesn't take place

    C) may or may not take place

    D) depends on frequency

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  • question_answer40) X-rays are used in determining the molecular structure of crystalline, because

    A) its energy is high

    B) it can penetrate the material

    C) its wavelength is comparable to interatomic distance

    D) its frequency is low

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  • question_answer41) The frequency of vibration of string is given by \[v=\frac{p}{2l}{{\left[ \frac{F}{m} \right]}^{1/2}}\] Here, \[p\] is the number of segments m the string and \[l\] is the length. The dimensional formula for \[m\] will be

    A) \[[{{M}^{0}}L{{T}^{-1}}]\]

    B) \[[M{{L}^{0}}{{T}^{-1}}]\]

    C) \[[M{{L}^{-1}}{{T}^{0}}]\]

    D) \[[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\]

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  • question_answer42) A stone is thrown vertically upwards. When the stone is at a height equal to half of its maximum height its speed will be\[10\,\,m/s\], then the maximum height attained by the stone (Take\[g=10\,\,m/{{s}^{2}})\]

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

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

    C) \[1\,\,m\]

    D) \[10\,\,m\]

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  • question_answer43) A string of length /fixed at one end carries mass \[m\] at the other end. The string makes\[\frac{2}{\pi }\,\,rev/s\] around the horizontal axis through the it fixed end as shown in the figure, the tension in the string is

    A) \[16\,\,ml\]

    B) \[6\,\,ml\]

    C) \[5\,\,ml\]

    D) \[3\,\,ml\]

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  • question_answer44) A gardener pushes a lawn roller through distance\[20\,\,m\]. If he applies a force of \[20\,\,kg-w\] in a direction inclined at \[{{60}^{o}}\] to the ground, the work done by him is

    A) \[1960\,\,J\]

    B) \[196\,\,J\]

    C) \[1.96\,\,J\]

    D) \[196\,\,kJ\]

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  • question_answer45) The breaking stress of a wire depends upon

    A) material of wire

    B) length of wire

    C) radius of wire

    D) shape of cross-section

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  • question_answer46) \[Li\] nucleus has three protons and four neutrons. Mass of lithium nucleus is\[7.016005\,\,amu\]. Mass of proton is \[1.007277\,\,amu\] and mass of neutron is\[1.008665\,\,amu\]. Mass defect for lithium nucleus in \[amu\] is

    A) \[0.04048\]

    B) \[0.04050\]

    C) \[0.04052\]

    D) \[0.04055\]

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  • question_answer47) A voltmeter of range \[2V\] and resistance \[300\Omega \] cannot be converted into ammeter of range

    A) \[1\,\,A\]

    B) \[1\,\,mA\]

    C) \[100\,\,mA\]

    D) \[10\,\,mA\]

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  • question_answer48) The values of two resistors are \[{{R}_{1}}=(6+0.3)k\Omega \] and\[{{R}_{2}}=(10\pm 0.2)k\Omega \]. The percentage error in the equivalent resistance when, they are connected in parallel is

    A) \[5.125%\]

    B) \[2%\]

    C) \[10.125%\]

    D) \[7%\]

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  • question_answer49) A body of mass \[2\,\,kg\] is projected from the ground with a velocity \[20\,\,m{{s}^{-1}}\] at an angle \[{{30}^{o}}\] with the vertical. If \[{{t}_{1}}\] is the time in second at which the body is projected and \[{{t}_{2}}\] is the time in second at which it reaches the ground, the change in momentum in \[kgm{{s}^{-1}}\] during the time \[({{t}_{2}}-{{t}_{1}})\] is

    A) \[40\sqrt{2}\]

    B) \[40\sqrt{3}\]

    C) \[25\sqrt{3}\]

    D) \[45\]

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  • question_answer50) The position vector of a particle is\[r=(a\cos \omega t)\widehat{\mathbf{i}}+(a\sin \omega t)\widehat{\mathbf{j}}\]. The velocity vector of the particle is

    A) parallel to position vector

    B) perpendicular to position vector

    C) directed towards the origin

    D) directed away from the origin

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  • question_answer51) The major product of the reaction between m-dinitrobenzene and \[N{{H}_{4}}HS\]is

    A)

    B)

    C)

    D)

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  • question_answer52) Correct order of nucleophilicity is

    A) \[CH_{3}^{-}<NH_{2}^{-}<O{{H}^{-}}<{{F}^{-}}\]

    B) \[{{F}^{-}}<O{{H}^{-}}<CH_{3}^{-}<NH_{2}^{-}\]

    C) \[O{{H}^{-}}<NH_{2}^{-}<{{F}^{-}}<CH_{3}^{-}\]

    D) \[{{F}^{-}}<O{{H}^{-}}<NH_{2}^{-}<CH_{3}^{-}\]

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  • question_answer53) The main product of the reaction would be 2-butene + chloroform\[\xrightarrow{NaOH}\]?

    A) butanoic acid

    B) 2-methyl butanoic acid

    C) 1, 1, 1-trichloro-2-methyl butane

    D) 1, 4-butane diol

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  • question_answer54) The end product of\[C{{H}_{3}}COOH\xrightarrow{CaC{{O}_{3}}}A\xrightarrow{Heat}B\xrightarrow{N{{H}_{2}}OH}C\]

    A) acetaldehyde

    B) acetoxime

    C) formaldehyde

    D) methyl cyanide

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  • question_answer55) Calorific value is in the order

    A) Fats > Carbohydrates > Proteins

    B) Carbohydrates > Fats > Proteins

    C) Proteins > Carbohydrates > Fats

    D) Fats > Proteins > Carbohydrates

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  • question_answer56) The monomeric unit of orlon molecule is

    A) \[C{{H}_{2}}=CH-Cl\]

    B) \[C{{H}_{3}}COO-CH=C{{H}_{2}}\]

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

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

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  • question_answer57) Which of the following acids possesses oxidising, reducing and complex forming properties?

    A) \[HCl\]

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

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

    D) \[HN{{O}_{3}}\]

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  • question_answer58) Cassiterite is concentrated by

    A) levigation

    B) electromagnetic separation

    C) floatation

    D) liquefaction

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  • question_answer59) The stability of the following alkali metal chlorides follows the order

    A) \[LiCl>KCl>NaCl>CsCl\]

    B) \[CsCl>KCl>NaCl>LiCl\]

    C) \[NaCl>KCl>LiCl>CsCl\]

    D) \[KCl>CsCl>NaCl>LiCl\]

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  • question_answer60) The complex \[{{[Fe{{({{H}_{2}}O)}_{5}}NO]}^{2+}}\] is formed in the brown ring test for nitrates when freshly prepared \[FeS{{O}_{4}}\] solution is added to aqueous solution of \[NO_{3}^{-}\] followed by addition of conc. \[{{H}_{2}}S{{O}_{4}}\]. Select the correct statement about this complex.

    A) Colour change is due to charge transfer

    B) It has iron in \[+1\] oxidation state and nitrosyl as\[N{{O}^{+}}\]

    C) It has, magnetic moment of \[3.87\,\,BM\] confirming three unpaired electrons in\[Fe\]

    D) All the above are correct statements

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  • question_answer61) Consider the following statements. I. Colour of a transition metal complex is dependent on energy difference between two \[d-\]levels. II. Colour of the complex is dependent on the nature of the ligand and the type of complex formed. III. \[ZnS{{O}_{4}}\] and \[Ti{{O}_{2}}\] are white as in both,\[d-d\] spectra are impossible. Select the correct statements.

    A) I, II and III

    B) I and II

    C) II and III

    D) I and III

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  • question_answer62) The outermost electronic configuration of the most electronegative element is

    A) \[n{{s}^{2}}n{{p}^{3}}\]

    B) \[n{{s}^{2}}n{{p}^{4}}\]

    C) \[n{{s}^{2}}n{{p}^{5}}\]

    D) \[n{{s}^{2}}n{{p}^{6}}\]

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  • question_answer63) Standard enthalpy and standard entropy change for the oxidation of \[N{{H}_{3}}\] at \[298\,\,K\] are \[-382.64\,\,kJ\,\,mo{{l}^{-1}}\]and\[-145.6\,\,J\,\,mo{{l}^{-1}}\]respectively. Standard Gibbs energy change for the same reaction at \[298\,\,K\] is

    A) \[+339.3\,\,kJ\,\,mo{{l}^{-1}}\]

    B) \[-439.3\,\,kJ\,\,mo{{l}^{-1}}\]

    C) \[-339.3\,\,kJ\,\,mo{{l}^{-1}}\]

    D) \[-393.3\,\,kJ\,\,mo{{l}^{-1}}\]

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  • question_answer64) According to the Arrhenius equation, a straight line is to be obtained by plotting the logarithm of the rate constant of a chemical reaction \[(\log k)\] against

    A) \[T\]

    B) \[\log T\]

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

    D) \[\log \frac{1}{T}\]

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  • question_answer65) Which of the following is not a reducing agent?

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

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

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

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

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  • question_answer66) For a dilute solution, Raoult's law states that

    A) the lowering of vapour pressure is equal to the mole fraction of the solute

    B) the relative lowering of vapour pressure is equal to the mole fraction of solute

    C) the relative lowering of vapour pressure is equal to the amount of the solution

    D) the vapour pressure of the solution, is equal to the mole fraction of the solvent

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  • question_answer67) The bond dissociation energies of gaseous \[{{H}_{2}},\,\,C{{l}_{2}}\] and \[HCl\] are \[104,\,\,58\] and \[103\,\,kcal\] respectively. The enthalpy of formation of \[HCl\] gas would be

    A) \[-44\,\,kcal\]

    B) \[44\,\,kcal\]

    C) \[-22\,\,kcal\]

    D) \[22\,\,kcal\]

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  • question_answer68) Species acting both as Bronsted acid and base is

    A) \[HSO_{4}^{-}\]

    B) \[N{{a}_{2}}C{{O}_{3}}\]

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

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

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  • question_answer69) The solubility of \[Agl\] in \[Nal\] solution is less than that in pure water because

    A) \[Agl\] forms complex with\[Nal\]

    B) of common ion effect

    C) solubility product of \[Agl\] is less

    D) the temperature of the solution decreases

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  • question_answer70) \[Zn|Z{{n}^{2+}}(a=0.1\,\,M)||F{{e}^{2+}}(a=0.01\,\,M)|Fe.\]The emf of the above cell is\[0.2905\,\,V\]. Equilibrium constant for the cell reaction is

    A) \[{{10}^{0.32/0.0591}}\]

    B) \[{{10}^{0.32/0.0295}}\]

    C) \[{{10}^{0.26/0.0295}}\]

    D) \[{{10}^{0.26/0.0295}}\]

    View Answer play_arrow
  • question_answer71) \[50\,\,mL\] of \[1\,\,M\] oxalic acid (molar mass\[=126\]) is shaken with \[0.5\,\,g\] of wood charcoal. The final concentration of the solution after adsorption is\[0.5\,\,M\]. What is the amount of oxalic acid adsorbed per gram of carbon?

    A) \[3.15\]

    B) \[1.575\]

    C) \[6.30\]

    D) \[12.60\]

    View Answer play_arrow
  • question_answer72) A dust particle has mass equal to\[{{10}^{-11}}g\], diameter \[{{10}^{-4}}cm\] and velocity\[{{10}^{-4}}cm/s\]. The error in measurement of velocity is\[0.1\,\,%\]. What will be the uncertainty in its position?

    A) \[0.527\times {{10}^{10}}cm\]

    B) \[5.27\times {{10}^{9}}cm\]

    C) \[0.527\times {{10}^{-15}}cm\]

    D) \[0.527\times {{10}^{-9}}cm\]

    View Answer play_arrow
  • question_answer73) The value of compression factor, \[Z\] for critical constants is

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

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

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

    D) \[\frac{3}{8}\]

    View Answer play_arrow
  • question_answer74) At what temperature, the \[rms\] velocity of \[S{{O}_{2}}\] be same as that of \[{{O}_{2}}\] at\[303\,\,K\]?

    A) \[273\,\,K\]

    B) \[606\,\,K\]

    C) \[303\,\,K\]

    D) \[403\,\,K\]

    View Answer play_arrow
  • question_answer75) The percentage of water of crystallisation of a sample of blue vitriol is

    A) \[34.07%\]

    B) \[35.07%\]

    C) \[36.07%\]

    D) \[37.07%\]

    View Answer play_arrow
  • question_answer76) Which of the following series of elements have nearly the same atomic radii?

    A) \[F,\,\,Cl,\,\,Br,\,\,I\]

    B) \[Na,\,\,K,\,\,Rb,\,\,Cs\]

    C) \[Li,\,\,Be,\,\,B,\,\,C\]

    D) \[Fe,\,\,Co,\,\,Ni,\,\,Cu\]

    View Answer play_arrow
  • question_answer77) The volume strength of 1 molar solution of\[{{H}_{2}}{{O}_{2}}\]is

    A) \[11.2\]

    B) \[22.4\]

    C) \[5.6\]

    D) \[56\]

    View Answer play_arrow
  • question_answer78) Maximum amount of carbon is present in

    A) wrought iron

    B) cast iron

    C) stainless steel

    D) German silver

    View Answer play_arrow
  • question_answer79) What is the best way to carry out the following transformation? \[1-\text{pentyne}\xrightarrow{{}}\text{pentanal}\]

    A) \[HgS{{O}_{4}}/{{H}_{2}}S{{O}_{4}}\]

    B) \[{{H}_{2}}/Lindlar's\,\,catalyst;\,\,{{O}_{3}};\,\,Zn-{{H}_{2}}O\]

    C) \[Hl{{O}_{4}}/{{H}_{2}}O\]

    D) \[B{{H}_{3}};\,\,{{H}_{2}}{{O}_{2}}/NaOH\]

    View Answer play_arrow
  • question_answer80) Product of this reaction is

    A)

    B)

    C)

    D)

    View Answer play_arrow
  • question_answer81) Etherates are

    A) ethers

    B) solution in ether

    C) complexes of ethers with Lewis acid

    D) complexes of ethers with Lewis base

    View Answer play_arrow
  • question_answer82) Tranquillisers are the substances used for the treatment of

    A) cancer

    B) AIDS

    C) mental diseases

    D) physical disorders

    View Answer play_arrow
  • question_answer83) Which of the following carbonyl compounds on condensation gives an aromatic compound?

    A) \[C{{H}_{3}}CHO\]

    B) \[HCHO\]

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

    D) \[C{{H}_{3}}C{{H}_{2}}CHO\]

    View Answer play_arrow
  • question_answer84) Iron crystallises in a bcc system with a lattice parameter of\[2.861\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\]. Calculate the density of iron in the bcc system (atomic weight of\[Fe=56,\,\,{{N}_{A}}=6.02\times {{10}^{23}}mo{{l}^{-1}})\].

    A) \[7.94\,\,g\,\,m{{L}^{-1}}\]

    B) \[8.96\,\,g\,\,m{{L}^{-1}}\]

    C) \[2.78\,\,g\,\,m{{L}^{-1}}\]

    D) \[6.72\,\,g\,\,m{{L}^{-1}}\]

    View Answer play_arrow
  • question_answer85) Which particle among the following will have the smallest de-Broglie wavelength, assuming that they have the same velocity?

    A) A positron

    B) A photon

    C) An \[\alpha -\]particle

    D) A neutron

    View Answer play_arrow
  • question_answer86) The equilibrium constant for the reaction,\[{{H}_{2}}(g)+{{I}_{2}}(g)2HI(g)\]is 64. If the volume of the container is reduced to half of the original volume, the value of the equilibrium constant will be

    A) \[16\]

    B) \[32\]

    C) \[64\]

    D) \[128\]

    View Answer play_arrow
  • question_answer87) For the reaction,\[Zn(s)+C{{u}^{2+}}(0.1M)\xrightarrow{{}}Z{{n}^{2+}}(1M)+Cu(s)t\]akmg place in a cell;\[E_{cell}^{\text{o}}\]is\[1.10\,\,V\].\[{{E}_{cell}}\] for the cell will be\[\left( 2.303\frac{RT}{F}=0.0591 \right)\]

    A) \[1.80\,\,V\]

    B) \[1.07\,\,V\]

    C) \[0.82\,\,V\]

    D) \[2.14\,\,V\]

    View Answer play_arrow
  • question_answer88) Surface of the eye is protected from bacterial infection by enzyme

    A) carbonic enhydrase

    B) urease

    C) lysozyme

    D) zymase

    View Answer play_arrow
  • question_answer89) The number of \[\sigma \]bonds in \[{{P}_{4}}{{O}_{10}}\] is

    A) \[6\]

    B) \[16\]

    C) \[20\]

    D) \[7\]

    View Answer play_arrow
  • question_answer90) Indicate the wrongly named compound.

    A) \[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,H-C{{H}_{2}}-C{{H}_{2}}-CHO\] (4-methyl-1-pentanal)

    B) \[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,H-C\equiv C-COOH\] (4-methyl-2-pentyn-1-oic acid)

    C) \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,H-COOH\] (2-methyl-1-pentanoic acid)

    D) \[C{{H}_{3}}C{{H}_{2}}-CH=CH-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}\] (3-hexen-5-one)

    View Answer play_arrow
  • question_answer91) Identify the vitamin whose deficiency in our blood decreases reproductive power?

    A) Vitamin E

    B) Vitamin D

    C) Vitamin A

    D) Vitamin C

    View Answer play_arrow
  • question_answer92) Give the major product of the following reaction,

    A)

    B)

    C)

    D) Cannot say

    View Answer play_arrow
  • question_answer93) \[Phenol\xrightarrow[(ii)\,\,C{{O}_{2}}/{{140}^{o}}C]{(i)\,\,NaOH}A\xrightarrow{{{H}^{+}}/{{H}_{2}}O}B\xrightarrow{A{{c}_{2}}O}C\]In this reaction, the end product \['C'\] is

    A) salicylaldehyde

    B) salicylic acid

    C) phenyl acetate

    D) aspirin

    View Answer play_arrow
  • question_answer94) What will be the degree of ionisation of \[0.05\,\,M\] acetic acid if its \[p{{K}_{a}}\] value is\[4.74\]?

    A) \[0.019%\]

    B) \[1.9%\]

    C) \[3.0%\]

    D) \[4.74%\]

    View Answer play_arrow
  • question_answer95) Which of the reactions defines\[\Delta H_{f}^{\text{o}}\]?

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

    B) \[\frac{1}{2}{{H}_{2}}(g)+\frac{1}{2}{{F}_{2}}(g)\xrightarrow{{}}HF(g)\]

    C) \[{{N}_{2}}(l)+3{{H}_{2}}(g)\xrightarrow{{}}2N{{H}_{3}}(g)\]

    D) \[CO(g)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow{{}}C{{O}_{2}}(g)\]

    View Answer play_arrow
  • question_answer96) The equivalent weight of \[N{{a}_{2}}{{S}_{2}}{{O}_{3}}\] in the following reaction is \[2N{{a}_{2}}{{S}_{2}}{{O}_{3}}+{{I}_{2}}\xrightarrow{{}}N{{a}_{2}}{{S}_{4}}{{O}_{6}}+2NaI\]

    A) \[M\]

    B) \[M/8\]

    C) \[M/0.5\]

    D) \[M/2\]

    View Answer play_arrow
  • question_answer97) The half-life period for first order reaction having activation energy \[39.3\,\,kcal\,\,mo{{l}^{-1}}\] at \[{{300}^{o}}C\] and frequency constant \[1.11\times {{10}^{11}}{{s}^{-1}}\] will be

    A) \[1\,\,h\]

    B) \[1.68\,\,h\]

    C) \[1.28\,\,h\]

    D) \[1.11\,\,h\]

    View Answer play_arrow
  • question_answer98) Water is brought to boil under a pressure of\[1.0\,\,atm\]. When an electric current of \[0.50\,\,A\] from a \[12\,\,V\] supply is passed for \[300\,\,s\] through a resistance in thermal contact with it, it is found that \[0.798\,\,g\] of water is vaporised. Calculate the molar internal energy change at boiling point\[(373.15\,\,K)\].

    A) \[375\,\,kJ\,\,mo{{l}^{-1}}\]

    B) \[3.75\,\,kJ\,\,mo{{l}^{-1}}\]

    C) \[42.6\,\,kJ\,\,mo{{l}^{-1}}\]

    D) \[4.26\,\,kJ\,\,mo{{l}^{-1}}\]

    View Answer play_arrow
  • question_answer99) The electrons, identified by quantum numbers\[n\] and\[l\], (i)\[n=4,\,\,l=1\](ii)\[n=4,\,\,l=0\] (iii)\[n=3,\,\,l=2\](iv)\[n=3,\,\,l=1\]can be placed in order of increasing energy, from the lowest to highest, as

    A) (iv) < (ii) < (iii) < (i)

    B) (ii) < (iv) < (i) < (iii)

    C) (i) < (iii) < (ii) < (ii)

    D) (iii) < (i) < (iv) < (ii)

    View Answer play_arrow
  • question_answer100) At certain temperature and a total pressure of\[{{10}^{5}}\,\,Pa\], iodine vapours contains \[40%\] by volume of iodine atoms. \[{{K}_{p}}\] for the equilibrium, \[{{I}_{2}}(g)2I(g)\];will be

    A) \[0.67\]

    B) \[1.5\]

    C) \[2.67\times {{10}^{4}}\]

    D) \[9.0\times {{10}^{4}}\]

    View Answer play_arrow
  • question_answer101) The area of the triangle formed by the lines \[{{x}^{2}}-4{{y}^{2}}=0\] and\[x=a\], is

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

    B) \[\frac{{{a}^{2}}}{2}\]

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

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

    View Answer play_arrow
  • question_answer102) There were two women participating in a chess tournament. Every participant played two games with the other participants. The number of games that the men played between themselves proved to exceed by 66 the number of games that the men played with the women. The number of participants is

    A) 6

    B) 11

    C) 13

    D) None of these

    View Answer play_arrow
  • question_answer103) For which interval, the given function \[f(x)=-2{{x}^{3}}-9{{x}^{2}}-12x+1\]is decreasing?

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

    B) \[(-2,\,\,-1)\]

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

    D) \[(-\infty ,\,\,-2)\]and\[(-1,\,\,\infty )\]

    View Answer play_arrow
  • question_answer104) The value of\[x=\sqrt{2+\sqrt{2+\sqrt{2+...}}}\]is

    A) \[-1\]

    B) \[1\]

    C) \[2\]

    D) \[3\]

    View Answer play_arrow
  • question_answer105) For what value\[k\], will the equation \[{{x}^{2}}-(3k-1)x+2{{k}^{2}}+2k=11\]have equal roots?

    A) \[5\]

    B) \[9\]

    C) Both [a] and [b]

    D) \[0\]

    View Answer play_arrow
  • question_answer106) A student is to answer \[10\] out of \[13\] questions in an examination such that he must choose atleast \[4\] from the first five questions. The number of choices available to him is

    A) \[140\]

    B) \[196\]

    C) \[280\]

    D) \[346\]

    View Answer play_arrow
  • question_answer107) The equations of the tangent and normal at point \[(3,\,\,-2)\] of ellipse \[4{{x}^{2}}+9{{y}^{2}}=36\] are

    A) \[\frac{x}{3}-\frac{y}{2}=1,\,\,\frac{x}{2}+\frac{y}{3}=\frac{5}{6}\]

    B) \[\frac{x}{3}+\frac{y}{2}=1,\,\,\frac{x}{2}-\frac{y}{3}=\frac{5}{6}\]

    C) \[\frac{x}{2}+\frac{y}{3}=1,\,\,\frac{x}{3}-\frac{y}{2}=\frac{5}{6}\]

    D) None of the above

    View Answer play_arrow
  • question_answer108) The angle between the lines whose direction cosines satisfy the equations\[l+m+n=0,\,\,{{l}^{2}}+{{m}^{2}}-{{n}^{2}}=0\], is given by

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

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

    C) \[\frac{5\pi }{3}\]

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

    View Answer play_arrow
  • question_answer109) The equation of the plane containing the line of intersection of the planes \[2x-y=0\] and \[y-3z=0\] and perpendicular to the plane \[4x+5y-3z-8=0\] is

    A) \[28x-17y+9z=0\]

    B) \[28x+17y+9z=0\]

    C) \[28x-17y-9z=0\]

    D) \[7x-3y+z=0\]

    View Answer play_arrow
  • question_answer110) If \[f(x)\] and \[g(x)\] are two functions with \[g(x)=x-\frac{1}{x}\]and \[fog(x)={{x}^{3}}-\frac{1}{{{x}^{3}}}\], then\[f'(x)\] is equal to

    A) \[3{{x}^{2}}+3\]

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

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

    D) \[3{{x}^{2}}+\frac{3}{{{x}^{4}}}\]

    View Answer play_arrow
  • question_answer111) The function \[f:R\to R\] defined as\[f(x)=(x-1)(x-2)(x-3)\]is

    A) one-one but not onto

    B) onto but not one-one

    C) both one-one and onto

    D) neither one-one nor onto

    View Answer play_arrow
  • question_answer112) If\[f(x)=\left\{ \begin{matrix} -{{x}^{2}}, & when\,\,x\le 0 \\ 5x-4, & when\,\,0<x\le 1 \\ 4{{x}^{2}}-3x, & when\,\,1<x<2 \\ 3x+4, & when\,\,x\ge 2 \\ \end{matrix} \right.\]then

    A) \[f(x)\]is continuous at\[x=0\]

    B) \[f(x)\]is continuous at\[x=2\]

    C) \[f(x)\]is discontinuous at\[x=1\]

    D) None of the above

    View Answer play_arrow
  • question_answer113) \[f(x)=\sqrt{ax}+\frac{{{a}^{2}}}{\sqrt{ax}}\], then\[f'(\alpha )\] is equal to

    A) \[-1\]

    B) \[1\]

    C) \[0\]

    D) \[a\]

    View Answer play_arrow
  • question_answer114) If\[y={{t}^{10}}+1\]and\[x={{t}^{8}}\], then \[\frac{{{d}^{2}}y}{d{{x}^{2}}}\] is equal to

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

    B) \[20{{t}^{8}}\]

    C) \[\frac{5}{16{{t}^{6}}}\]

    D) None of these

    View Answer play_arrow
  • question_answer115) The value of \[b\] such that scalar product of the vector \[(\widehat{\mathbf{i}}+\widehat{\mathbf{j}}+\widehat{\mathbf{k}})\] with the unit vector parallel to sum of the vectors \[(2\widehat{\mathbf{i}}+4\widehat{\mathbf{j}}-5\widehat{\mathbf{k}})\] and \[(b\widehat{\mathbf{i}}+2\widehat{\mathbf{j}}+3\widehat{\mathbf{k}})\] is\[1\], is

    A) \[-2\]

    B) \[-1\]

    C) \[0\]

    D) \[1\]

    View Answer play_arrow
  • question_answer116) Angle between the vectors \[\sqrt{3}(\mathbf{a}\times \mathbf{b})\] and\[b-(\mathbf{a}\cdot \mathbf{b})\mathbf{a}\]

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

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

    C) \[0\]

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

    View Answer play_arrow
  • question_answer117) The point of contact of the line \[y=x-1\] with\[3x-4{{y}^{2}}=12\]is

    A) \[(4,\,\,3)\]

    B) \[(3,\,\,4)\]

    C) \[(4,\,\,-3)\]

    D) None of these

    View Answer play_arrow
  • question_answer118) \[\int{\frac{\text{cosec}\,x}{{{\cos }^{2}}\left( 1+\log \tan \frac{x}{2} \right)}dx}\]axis equal to

    A) \[{{\sin }^{2}}\left[ 1+\log \tan \frac{x}{2} \right]+C\]

    B) \[\tan \left[ 1+\log \tan \frac{x}{2} \right]+C\]

    C) \[{{\sec }^{2}}\left[ 1+\log \tan \frac{x}{2} \right]+C\]

    D) \[-\tan \left[ 1+\log \tan \frac{x}{2} \right]+C\]

    View Answer play_arrow
  • question_answer119) \[\int_{2}^{\pi }{\sqrt{\frac{1+\cos 2x}{2}}dx}\]is equal to

    A) \[0\]

    B) \[2\]

    C) \[1\]

    D) \[-1\]

    View Answer play_arrow
  • question_answer120) The distance of the point \[(-1,\,\,5,\,\,-10)\] from the point of intersection of the line \[\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}\] and the plane\[x-y+z=5\], is

    A) \[10\]

    B) \[11\]

    C) \[12\]

    D) \[13\]

    View Answer play_arrow
  • question_answer121) The angle between two diagonals of a cube will be

    A) \[{{\sin }^{-1}}\left( \frac{1}{3} \right)\]

    B) \[{{\cos }^{-1}}\left( \frac{1}{3} \right)\]

    C) variable

    D) None of these

    View Answer play_arrow
  • question_answer122) Domain of function \[f(x)={{\sin }^{-1}}5x\] is

    A) \[\left( -\frac{1}{5},\,\,\frac{1}{5} \right)\]

    B) \[\left[ -\frac{1}{5},\,\,\frac{1}{5} \right]\]

    C) \[R\]

    D) \[\left( 0,\,\,\frac{1}{5} \right)\]

    View Answer play_arrow
  • question_answer123) Range of the function \[f(x)={{\sin }^{2}}({{x}^{4}})+{{\cos }^{2}}({{x}^{4}})\]is

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

    B) \[\{1\}\]

    C) \[(-1,\,\,1)\]

    D) \[(0,\,\,1)\]

    View Answer play_arrow
  • question_answer124) If\[x+y=10\], then the maximum value of \[xy\] is

    A) \[5\]

    B) \[20\]

    C) \[25\]

    D) None of these

    View Answer play_arrow
  • question_answer125) The value of\[\sin \frac{\pi }{14}\sin \frac{3\pi }{14}\sin \frac{5\pi }{14}\sin \frac{7\pi }{14}\sin \frac{9\pi }{14}\sin \frac{11\pi }{14}\sin \frac{13\pi }{14}\]is equal to

    A) \[\frac{1}{8}\]

    B) \[\frac{1}{16}\]

    C) \[\frac{1}{32}\]

    D) \[\frac{1}{64}\]

    View Answer play_arrow
  • question_answer126) \[\cos 2\theta +2\cos \theta \]is always

    A) greater than\[-\frac{3}{2}\]

    B) less than or equal to\[\frac{3}{2}\]

    C) greater than or equal to \[\frac{-3}{2}\] and less than or equal to\[3\]

    D) None of the above

    View Answer play_arrow
  • question_answer127) In the expansion of\[{{(1+3x+2{{x}^{2}})}^{6}}\], the coefficient of \[{{x}^{11}}\] is

    A) \[144\]

    B) \[288\]

    C) \[216\]

    D) \[576\]

    View Answer play_arrow
  • question_answer128) If the second, third and fourth terms in the expansion of \[{{(x+a)}^{n}}\] are \[240,\,\,\,720\] and \[1080\] respectively, then the value of \[n\] is

    A) \[15\]

    B) \[20\]

    C) \[10\]

    D) \[5\]

    View Answer play_arrow
  • question_answer129) The values of \[x\] and \[y\] for which the numbers \[3+i{{x}^{2}}y\]and \[{{x}^{2}}+y+4i\] are conjugate complex, can be

    A) \[(-2,\,\,-1)\]or\[(2,\,\,-1)\]

    B) \[(-1,\,\,2)\]or\[(-2,\,\,1)\]

    C) \[(1,\,\,2)\]or\[(-1,\,\,-2)\]

    D) None of these

    View Answer play_arrow
  • question_answer130) The value of the expression \[1\cdot (2-\omega )(2-{{\omega }^{2}})+2\cdot (3-\omega )(3-{{\omega }^{2}})+...\] \[+(n-1)(n-\omega )(n-{{\omega }^{2}})\], where \[\omega \] is an imaginary cube root of unity, is

    A) \[\frac{1}{2}(n-1)n({{n}^{2}}+3n+4)\]

    B) \[\frac{1}{4}(n-1)n({{n}^{2}}+3n+4)\]

    C) \[\frac{1}{2}(n+1)n({{n}^{2}}+3n+4)\]

    D) \[\frac{1}{4}(n+1)n({{n}^{2}}+3n+4)\]

    View Answer play_arrow
  • question_answer131) If the first term of a \[GP\,\,{{\alpha }_{1}},\,\,{{\alpha }_{2}},\,\,{{\alpha }_{3}},...\]is unity such that \[4{{\alpha }_{2}}+5{{\alpha }_{3}}\] is least, then the common ratio of \[GP\] is

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

    B) \[\frac{-3}{5}\]

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

    D) None of these

    View Answer play_arrow
  • question_answer132) If the \[AM\] of two numbers is greater than \[GM\] of the numbers by \[2\] and the ratio of the numbers is\[4:1\], then the numbers are

    A) \[4,\,\,1\]

    B) \[12,\,\,3\]

    C) \[16,\,\,4\]

    D) None of these

    View Answer play_arrow
  • question_answer133) If \[3x+2y=I\] and \[2x-y=O\], where \[I\] and \[O\] are unit and null matrices of order \[3\] respectively, then

    A) \[x=\frac{1}{7},\,\,y=\frac{2}{7}\]

    B) \[x=\frac{2}{7},\,\,y=\frac{1}{7}\]

    C) \[x=\left( \frac{1}{7} \right)l,\,\,y=\left( \frac{2}{7} \right)l\]

    D) \[x=\left( \frac{2}{7} \right)l,\,\,y=\left( \frac{1}{7} \right)l\]

    View Answer play_arrow
  • question_answer134) Matrix \[A\] is such that\[{{A}^{2}}=2A-I\], where \[I\] is the identity matrix. Then, for \[n\ge 2,\,\,{{A}^{n}}\] is equal to

    A) \[nA-(n-1)l\]

    B) \[nA-l\]

    C) \[{{2}^{n-1}}A-(n-1)l\]

    D) \[{{2}^{n-1}}A-l\]

    View Answer play_arrow
  • question_answer135) If\[3f(x)-2f\left( \frac{1}{x} \right)=x\], then \[f'(x)\] is equal to

    A) \[\frac{2}{7}\]

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

    C) \[2\]

    D) \[\frac{7}{2}\]

    View Answer play_arrow
  • question_answer136) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{2}^{x}}-1}{{{(1+x)}^{1/2}}-1}\]is equal to

    A) \[\log 2\]

    B) \[\log 4\]

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

    D) None of these

    View Answer play_arrow
  • question_answer137) On the parabola\[y={{x}^{2}}\], the point least distant from the straight line \[y=2x-4\] is

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

    B) \[(1,\,\,0)\]

    C) \[(1,\,\,-1)\]

    D) \[(0,\,\,0)\]

    View Answer play_arrow
  • question_answer138) The general value of \[\theta \] in the equation\[2\sqrt{3}\cos \theta =\tan \theta \]

    A) \[2n\pi \pm \frac{\pi }{6}\]

    B) \[2n\pi \pm \frac{\pi }{4}\]

    C) \[n\pi +{{(-1)}^{n}}\frac{\pi }{3}\]

    D) \[n\pi +{{(-1)}^{n}}\frac{\pi }{4}\]

    View Answer play_arrow
  • question_answer139) If\[\sec x\cos 5x+1=0\], where\[0<x<2\pi \], then the value of \[x\] is

    A) \[\frac{\pi }{5},\,\,\frac{\pi }{4}\]

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

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

    D) None of these

    View Answer play_arrow
  • question_answer140) The solution of the differential equation\[({{x}^{2}}-y{{x}^{2}})\frac{dy}{dx}+{{y}^{2}}+x{{y}^{2}}=0\]is

    A) \[\log \left( \frac{x}{y} \right)=\frac{1}{x}+\frac{1}{y}+C\]

    B) \[\log \left( \frac{y}{x} \right)=\frac{1}{x}+\frac{1}{y}+C\]

    C) \[\log (xy)=\frac{1}{x}+\frac{1}{y}+C\]

    D) \[\log (xy)+\frac{1}{x}+\frac{1}{y}=C\]

    View Answer play_arrow
  • question_answer141) The general solution of, the differential equation\[(x+y)dx+xdy=0\]is

    A) \[{{x}^{2}}+{{y}^{2}}=C\]

    B) \[2{{x}^{2}}-{{y}^{2}}=C\]

    C) \[{{x}^{2}}+2xy=C\]

    D) \[{{y}^{2}}+2xy=C\]

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  • question_answer142) The tangent to the curve \[y=a{{x}^{2}}+bx\] at\[(2,\,\,-8)\] is parallel to\[X-axis\]. Then,

    A) \[a=2,\,\,b=-2\]

    B) \[a=2,\,\,b=-4\]

    C) \[a=2,\,\,b=-8\]

    D) \[a=4,\,\,b=-4\]

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  • question_answer143) The mean of a set of observations is\[x\]. If each observation is divided by \[\alpha ,\,\,\alpha \ne 0\] and then is increased by\[10\], then the mean of the new set is

    A) \[\frac{{\bar{x}}}{\alpha }\]

    B) \[\frac{\bar{x}+10}{\alpha }\]

    C) \[\frac{\bar{x}+10\alpha }{\alpha }\]

    D) \[\alpha \bar{x}+10\]

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  • question_answer144) \[\tilde{\ }(p\vee q)\vee (\tilde{\ }p\wedge q)\]is logically equivalent to

    A) \[\tilde{\ }p\]

    B) \[p\]

    C) \[q\]

    D) \[\tilde{\ }q\]

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  • question_answer145) If \[\frac{|z-2|}{|z-3|}=2\] represents a circle, then its radius is equal to

    A) \[1\]

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

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

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

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  • question_answer146) The angle of elevation of the top of a tower from the top of a house is \[{{60}^{o}}\] and the angle of depression of its base is\[{{30}^{o}}\]. If the horizontal distance between the house and the tower be \[12\,\,m\], then the height of the tower is

    A) \[48\sqrt{3}m\]

    B) \[16\sqrt{3}m\]

    C) \[24\sqrt{3}m\]

    D) \[\frac{16}{\sqrt{3}}m\]

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  • question_answer147) Period of\[\frac{\sin \theta +\sin 2\theta }{\cos \theta +\cos 2\theta }\]is

    A) \[2\pi \]

    B) \[\pi \]

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

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

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  • question_answer148) If \[x\] is parallel to \[y\] and\[z\], where\[\mathbf{x}=2\widehat{\mathbf{i}}+\widehat{\mathbf{j}}+\alpha \widehat{\mathbf{k}}\],\[\mathbf{y}=\alpha \widehat{\mathbf{i}}+\widehat{\mathbf{k}}\]and\[\mathbf{z}=5\widehat{\mathbf{i}}-\widehat{\mathbf{j}}\], then a is equal to

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

    B) \[\pm \sqrt{6}\]

    C) \[\pm \sqrt{7}\]

    D) None of these

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  • question_answer149) If\[y={{(x+\sqrt{1+{{x}^{2}}})}^{n}}\], then\[(1+{{x}^{2}})\frac{{{d}^{2}}y}{d{{x}^{2}}}+x\frac{dy}{dx}\]is equal to

    A) \[{{n}^{2}}y\]

    B) \[-{{n}^{2}}y\]

    C) \[-y\]

    D) \[2{{x}^{2}}y\]

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  • question_answer150) The values of a for which\[({{a}^{2}}-1){{x}^{2}}+2(a-1)x+2\] is positive for any\[x\], are

    A) \[a\ge 1\]

    B) \[a\le 1\]

    C) \[a>-3\]

    D) \[a<-3\]or\[a>1\]

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