Solved papers for Manipal Engineering Manipal Engineering Solved Paper-2013

done Manipal Engineering Solved Paper-2013

  • question_answer1) The angular velocities of three bodies in simple harmonic motion are\[{{\omega }_{1}},\,\,{{\omega }_{2}},\,\,{{\omega }_{3}}\]with their respective amplitudes as\[{{A}_{1}},\,\,{{A}_{2}},\,\,{{A}_{3}}\]. If all the three bodies have same mass and velocity, then

    A) \[A_{1}^{2}\omega _{1}^{2}=A_{2}^{2}\omega _{2}^{2}=A_{3}^{2}{{\omega }^{2}}\]

    B) \[A_{1}^{2}{{\omega }_{1}}=A_{2}^{2}{{\omega }_{1}}=A_{3}^{2}{{\omega }_{3}}\]

    C) \[{{A}_{1}}\omega _{1}^{2}={{A}_{2}}\omega _{2}^{2},\,\,{{A}_{3}}\omega _{3}^{2}\]

    D) \[{{A}_{1}}{{\omega }_{1}}={{A}_{2}}{{\omega }_{2}}={{A}_{3}}{{\omega }_{3}}\]

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  • question_answer2) If value of surface tension of a liquid is \[70\text{ }dyne/cm\], then its value in \[N/m\] will be

    A) \[7\times {{10}^{3}}N/m\]

    B) \[7\times {{10}^{2}}N/m\]

    C) \[7\times {{10}^{-2}}N/m\]

    D) \[70\,\,N/m\]

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  • question_answer3) A ballon contains\[1500\,\,{{m}^{3}}\]of a helium at\[{{27}^{o}}C\]and 4 atmospheric pressure. The volume of helium at\[-{{3}^{o}}C\]temperature and 2 atmospheric pressure will be

    A) \[2700\,\,{{m}^{3}}\]

    B) \[1900\,\,{{m}^{3}}\]

    C) \[1700\,\,{{m}^{3}}\]

    D) \[1500\,\,{{m}^{3}}\]

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  • question_answer4) A car is moving along a straight horizontal road with a speed\[{{\upsilon }_{0}}\]. If the coefficient of friction between the tyres and the road is\[\mu \], the shortest distance in which the car be stopped is

    A) \[\frac{v_{0}^{2}}{\mu }\]

    B) \[{{\left( \frac{{{v}_{0}}}{{{\mu }_{g}}} \right)}^{2}}\]

    C) \[\frac{v_{0}^{2}}{{{\mu }_{g}}}\]

    D) \[\frac{v_{0}^{2}}{2{{\mu }_{g}}}\]

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  • question_answer5) A car travelling on a straight track moves with uniform velocity of\[{{\upsilon }_{1}}\]for some time and with uniform velocity\[{{\upsilon }_{2}}\]for the next equal time the average velocity on the car is

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

    B) \[\frac{{{v}_{1}}{{v}_{2}}}{4}\]

    C) \[\frac{{{v}_{1}}+{{v}_{2}}}{2}\]

    D) \[\frac{{{v}_{1}}-{{v}_{2}}}{2}\]

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  • question_answer6) Threshold wavelength of a metal is \[4000\overset{\text{o}}{\mathop{\text{A}}}\,\]. If light of wavelength\[3000\overset{\text{o}}{\mathop{\text{A}}}\,\]irradiates the surface, the maximum kinetic energy of photoelectron is

    A) \[1.7\,\,eV\]

    B) \[1.6\,\,eV\]

    C) \[1.5\,\,eV\]

    D) \[1.0\,\,eV\]

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  • question_answer7) Simple pendulum of length\[l\]has a maximum angular displacement\[\theta \]. The maximum kinetic energy of the bob is

    A) \[mgl\,\,(1-\cos \theta )\]

    B) \[0.5\,\,mgl\]

    C) \[mgl\]

    D) \[2\,\,mgl\]

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  • question_answer8) Radius of orbit of satellite of earth is\[R\]. Its kinetic energy is proportional to

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

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

    C) \[R\]

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

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  • question_answer9) The radius\[R\]of the soap bubble is doubled under isothermal condition. If\[T\]be the surface tension of soap bubble, the work done in doing so is given by

    A) \[32\pi {{R}^{2}}T\]

    B) \[24\pi {{R}^{2}}T\]

    C) \[8\pi {{R}^{2}}T\]

    D) \[4\pi {{R}^{2}}T\]

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  • question_answer10) A body of specific heat\[0.2\,\,kcal/k{{g}^{o}}C\]is heated through\[{{100}^{o}}C\]. The percentage increase in its mass is

    A) \[9%\]

    B) \[9.3\times {{10}^{-11}}%\]

    C) \[10%\]

    D) None of these

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  • question_answer11) Two similar coils are kept mutually perpendicular such that their centres coincide. At the centre, find the ratio of the magnetic field due to one coil and the resultant magnetic field through both coils, if the same current is flown

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

    B) \[1:2\]

    C) \[1:3\]

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

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  • question_answer12) A prism of refractive index\[\sqrt{2}\]has refracting angle of\[{{60}^{o}}\]. At what angle a ray must be incident one it so that it suffers a minimum deviation?

    A) \[45{}^\circ \]

    B) \[60{}^\circ \]

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

    D) \[180{}^\circ \]

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  • question_answer13) A elevator car whose floor to distance is\[2.7\,\,m\]starts ascending with a constant acceleration of\[1.2\,\,m/{{s}^{2}}\],\[2s\]after a bolt is begin to fall from the ceiling of the car. The free fall time of the bolt is\[(g=9.8m/{{s}^{e}})\]

    A) \[\sqrt{\frac{2.7}{9.8}}s\]

    B) \[\sqrt{\frac{5.4}{9.8}}s\]

    C) \[\sqrt{\frac{5.4}{8.6}}s\]

    D) \[\sqrt{\frac{5.4}{11}}s\]

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  • question_answer14) A wet open umbrella is held vertical and it whirld about the handle at a uniform rate of 21 revolutions in\[44s\]. If the rim of the umbrella is circle of\[1m\]in diameter and the height of the rim above the flour is\[4.9m\], the locus of the drop is a circle of radius

    A) \[\sqrt{2.5}m\]

    B) \[1\,\,m\]

    C) \[3\,\,m\]

    D) \[1.5\,\,m\]

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  • question_answer15) The moment of inertia of a body about a given axis is\[1.2kg-{{m}^{2}}\]. To produce a rotational kinetic energy of\[1500\,\,J\]an angular acceleration of\[25\text{ }rad/{{s}^{2}}\]must be applied for

    A) \[8.5s\]

    B) \[5s\]

    C) \[2s\]

    D) \[1s\]

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  • question_answer16) A running man has half the kinetic energy of that of a boy of half of his mass. The man speed up 1 m/s, so as the have same kinetic energy as that of a boy. The original speed of the man is

    A) \[(\sqrt{2}-1)m/s\]

    B) \[\sqrt{2}m/s\]

    C) \[\frac{1}{(\sqrt{2}-1)m/s}\]

    D) \[\frac{1}{\sqrt{2}}m/s\]

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  • question_answer17) An earth satellites\[S\]has orbit radius which is 4 times that of communication satellite\[C\]. The period of revolution of\[S\]will be

    A) 32 days

    B) 18 days

    C) 8 days

    D) 9 days

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  • question_answer18) \[n\] small balls, each of mass \[m\] impinge elastically each second on a surface with a velocity \[u\], then the force experienced by the surface in one second, will be

    A) \[4mnu\]

    B) \[2mnu\]

    C) \[1.5mnu\]

    D) \[0.8mnu\]

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  • question_answer19) A circular disc is rotating with angular velocity\[\omega \]. If a man standing at the edge of the disc walks towards its centre then the angular velocity of the disc will

    A) decrease

    B) increase

    C) be halved

    D) not change

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  • question_answer20) The moment of inertia of a disc of mass m and radius\[R\]about an axis, which is tangential to the circumference of the disc and parallel to its diameter is

    A) \[\frac{3}{2}m{{R}^{2}}\]

    B) \[\frac{2}{3}m{{R}^{2}}\]

    C) \[\frac{5}{4}m{{R}^{2}}\]

    D) \[\frac{4}{5}m{{R}^{2}}\]

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  • question_answer21) A body weights \[500N\] on the surface of the earth. How much would it weigh half way below the surface of the earth?

    A) \[1000N\]

    B) \[500N\]

    C) \[250N\]

    D) \[125N\]

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  • question_answer22) Escape velocity at surface of earth is\[11.2\,\,Km/s\]. Escape velocity from a planet whose mass is the same as that of earth and radius\[1/4\]that of earth, is

    A) \[2.8km/s\]

    B) \[15.6km/s\]

    C) \[22.4km/s\]

    D) \[44.8km/s\]

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  • question_answer23) The Bulk Modulus for an incompressible liquid is

    A) zero

    B) unity

    C) infinity

    D) between 0 and 1

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  • question_answer24) In a capillary tube, water rises to 3 mm the height of water that will rise in another capillary tube having one-third radius of the first is

    A) 1 mm

    B) 3 mm

    C) 6 mm

    D) 9 mm

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  • question_answer25) An object is placed at a distance 20 cm from the pole of a convex mirror of focal length 20 cm. The image is produced

    A) 13.3 cm

    B) 20 cm

    C) 25 cm

    D) 10 cm

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  • question_answer26) Angular momentum is conserved

    A) always

    B) never

    C) when external force is absent

    D) when external torque is absent

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  • question_answer27) The plano-convex lens of focal length 20 cm and 30 cm are placed together to form a double convex lens, the final focal length will be

    A) 12 cm

    B) 60cm

    C) 20cm

    D) 30cm

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  • question_answer28) Due to a force of\[(6\widehat{\mathbf{i}}+2\widehat{\mathbf{j}})N\]the displacement of a body is\[(3\widehat{\mathbf{i}}-\widehat{\mathbf{j}})m\], then the work done is

    A) \[16j\]

    B) \[12j\]

    C) \[8j\]

    D) zero

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  • question_answer29) For a body moving with relativistic speed if the velocity is doubled, then

    A) its linear momentum is doubled

    B) its linear momentum will be less than double

    C) its linear momentum will be more than double

    D) its linear momentum remains unchanged

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  • question_answer30) Position of a body with acceleration\[a\]is given by\[x=k{{a}^{m}}{{t}^{n}}\], here\[t\]is time, find the dimension of\[m\]and\[n\]

    A) \[m=1,\,\,n=1\]

    B) \[m=1,\,\,n=2\]

    C) \[m=2,\,\,n=1\]

    D) \[m=2,\,\,n=2\]

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  • question_answer31) The correct relation between\[\alpha \]and\[\beta \]in a transistor is

    A) \[\beta =\frac{\alpha }{1-\alpha }\]

    B) \[\beta =\frac{\alpha }{1+\alpha }\]

    C) \[\beta =\frac{1+\alpha }{\alpha }\]

    D) \[\beta =1-\alpha \]

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  • question_answer32) A man crosses a \[320\,\,m\] wide river perpendicular to the current in 4 min. If in still water he can swim with a speed \[5/3\] times that of the current, then the speed of the current, in\[m{{m}^{-1}}\]in is

    A) 30

    B) 40

    C) 50

    D) 60

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  • question_answer33) Two spheres of equal masses, one of which is a thin spherical shell and the other a solid, have the same moment of inertia about their respective diameters. The ratio of their radii will be

    A) \[5:7\]

    B) \[3:5\]

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

    D) \[\sqrt{3}:\sqrt{7}\]

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  • question_answer34) The speed with which the earth have to rotate on its axis so that a person on the equator would weight\[{{(3/5)}^{th}}\]as much as present. [Radius of earth = 6400 km]

    A) \[4.83\times {{10}^{-3}}rad{{s}^{-1}}\]

    B) \[5.41\times {{10}^{-3}}rad{{s}^{-1}}\]

    C) \[7.82\times {{10}^{-4}}rad{{s}^{-1}}\]

    D) \[8.88\times {{10}^{-14}}rad{{s}^{-1}}\]

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  • question_answer35) The rate of flow of glycerine of density\[1.25\times {{10}^{3}}kg{{m}^{-3}}\]through the conical section of a pipe if the radii of its ends are\[0.1\,\,m\]and\[0.04\text{ }m\]and the pressure drop across its length\[10N{{m}^{-2}}\]is

    A) \[6.93\times {{10}^{-4}}{{m}^{3}}{{s}^{-1}}\]

    B) \[7.8\times {{10}^{-4}}{{m}^{3}}{{s}^{-1}}\]

    C) \[10.4\times {{10}^{-5}}{{m}^{3}}{{s}^{-1}}\]

    D) \[14.5\times {{10}^{-5}}{{m}^{3}}{{s}^{-1}}\]

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  • question_answer36) The temperature of the black body increases from\[T\]to\[2T\]. The factor by which the rate of emission will increases is

    A) 4

    B) 2

    C) 16

    D) 8

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  • question_answer37) A police jeep is chasing with velocity of 45 km/h a thief in another jeep moving with velocity 153 km/h. Police fires a bullet with muzzle velocity of 180 m/s. The velocity it will strike the car of the thief is

    A) 150 m/s

    B) 27 m/s

    C) 450 m/s

    D) 250 m/s

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  • question_answer38) If the energy of a hydrogen atom in\[{{n}^{th}}\]orbit is \[{{E}_{n}}\]then energy in the\[{{n}^{th}}\]orbit of a singly ionized helium atom will be

    A) \[4{{E}_{n}}\]

    B) \[{{E}_{n}}/4\]

    C) \[2{{E}_{n}}\]

    D) \[{{E}_{n}}/2\]

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  • question_answer39) If the work function of a potential is\[6.875\,\,eV\], its threshold wavelength will be (Take \[=c=3\times {{10}^{8}}\,m/s\])

    A) \[3600\overset{\text{o}}{\mathop{\text{A}}}\,\]

    B) \[2400\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

    C) \[1800\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

    D) \[1200\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

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  • question_answer40) Which of the following is unipoler transistor?

    A) \[p-n-p\]transistor

    B) \[n-p-n\]transistor

    C) field effect transistor

    D) point contact transistor

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  • question_answer41) If the length of a pendulum is made 9 times and mass of bob is made 4 times, then the value of time period becomes

    A) \[3\,\,T\]

    B) \[3/2\,\,T\]

    C) \[4\,\,T\]

    D) \[2\,\,T\]

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  • question_answer42) Two weights\[{{w}_{1}}\]and\[{{w}_{2}}\]are suspended to be the two strings on a frictionless pulley. When the pulled up with an acceleration\[g\]then the tension in the string is

    A) \[\frac{4{{w}_{1}}{{w}_{2}}}{{{w}_{1}}+{{w}_{2}}}\]

    B) \[\frac{{{w}_{1}}{{w}_{2}}}{{{w}_{1}}+{{w}_{2}}}\]

    C) \[\frac{2{{w}_{1}}{{w}_{2}}}{{{w}_{1}}+{{w}_{2}}}\]

    D) \[\frac{{{w}_{1}}+{{w}_{2}}}{2}\]

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  • question_answer43) An observer loop at a tree of height 15 m with a telescope of magnifying power 10. To him the tree appears

    A) 10 times taller

    B) 15 times taller

    C) 10 times nearer

    D) 15 times nearer

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  • question_answer44) An inductor is connected to a battery through\[a\]switch induced emf is a when the switch is pressed and\[{{e}_{2}}\]when the switch is opened. Then

    A) \[{{e}_{1}}={{e}_{2}}\]

    B) \[{{e}_{1}}>{{e}_{2}}\]

    C) \[{{e}_{1}}<{{e}_{2}}\]

    D) \[{{e}_{1}}>/<{{e}_{2}}\]

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  • question_answer45) The speed of a wave on a string is\[150\text{ }m/s\]when the tension is\[120N\]. The percentage increase in the tension in order to raise the wave speed by\[20%\] is

    A) \[44%\]

    B) \[40%\]

    C) \[20%\]

    D) \[10%\]

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  • question_answer46) The energy supplied to Kolkata by the state electricity board during an average November week day was\[40GWh\]. If this energy could be obtained by the conservation of matter, how much mass would have to be annihilated?

    A) \[1.6\,\,g\]

    B) \[2.2\,\,g\]

    C) \[4.0\,\,g\]

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

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  • question_answer47) A simple pendulum has time period\[{{T}_{1}}\]. The point of suspension is now moved upward according to the relation \[y=k{{t}^{2}}(k=1m{{s}^{2}})\]where\[y\]is the vertical displacement. The time period now become\[{{T}_{2}}.\] The ratio of\[\frac{T_{1}^{2}}{T_{2}^{2}}\]is\[g=10\,\,m/{{s}^{2}}\]

    A) \[6/5\]

    B) \[5/6\]

    C) \[1\]

    D) \[4/5\]

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  • question_answer48) An electron is moving round the nucleus of a hydrogen atom in a circular orbit of radius\[r\]. The coulomb force F between the two is

    A) \[k\frac{{{e}^{2}}}{{{r}^{3}}}r\]

    B) \[-k\frac{{{e}^{2}}}{{{r}^{3}}}r\]

    C) \[k\frac{{{e}^{2}}}{{{r}^{2}}}r\]

    D) \[-k\frac{{{e}^{2}}}{{{r}^{2}}}r\]

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  • question_answer49) A charge\[q\]is located at the centre of a cube. The electric flux through any face is

    A) \[\frac{\pi \,\,q}{6(4\pi \,\,{{\varepsilon }_{0}})}\]

    B) \[\frac{q}{6(4\pi \,\,{{\varepsilon }_{0}})}\]

    C) \[\frac{2\,\,\pi \,\,q}{6(4\pi \,\,{{\varepsilon }_{0}})}\]

    D) \[\frac{4\,\,\pi \,\,q}{6(4\pi \,\,{{\varepsilon }_{0}})}\]

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  • question_answer50) In the Boolean Algebra\[\mathbf{A}\cdot \mathbf{B}\]is same

    A) \[\mathbf{A+B}\]

    B) \[\mathbf{A}\cdot \mathbf{B}\]

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

    D) \[A+B\]

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  • question_answer51) When a force\[{{F}_{1}}\]acts on a particle, frequency is \[6Hz\]and when a force\[{{F}_{2}}\]acts, frequency is\[8Hz\]. What is the frequency when both the forces act simultaneously in same direction?

    A) \[12Hz\]

    B) \[25Hz\]

    C) \[10Hz\]

    D) \[5Hz\]

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  • question_answer52) For a particle executing simple harmonic motion, the kinetic energy \[k\] is given by\[k={{k}_{0}}{{\cos }^{2}}\omega t\]. The maximum value of potential energy is

    A) \[{{k}_{0}}\]

    B) zero

    C) \[{{k}_{0}}/2\]

    D) not obtainable

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  • question_answer53) A train of \[150m\] length is going towards north direction at a speed of\[10\text{ }m/s\]. A parrot flies at a speed of \[5m/s\] towards south direction parallel to the railway track, the time taken by the parrot to cross the train is equal to

    A) \[12s\]

    B) \[8s\]

    C) \[15s\]

    D) \[10s\]

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  • question_answer54) Ice starts freezing in a lake with water at\[{{0}^{o}}C\] when the atmospheric temperature is\[-{{10}^{o}}C\]. If the time taken for \[1cm\] of ice to be formed is 12 min, the time taken for the thickness of the ice to change from \[1\] to \[2cm\] will be

    A) 12 min

    B) less than 12 min

    C) more than 12 min but less than 24 min

    D) more than 24 min

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  • question_answer55) The wavelength of the\[{{k}_{a}}\]line for an element of atomic number\[43\]is\[\lambda \]. Then the wavelength of the\[{{K}_{a}}\]line for an element of atomic number \[29\]is

    A) \[\left( \frac{43}{29} \right)\lambda \]

    B) \[\left( \frac{42}{28} \right)\lambda \]

    C) \[\left( \frac{9}{4} \right)\lambda \]

    D) \[\left( \frac{4}{9} \right)\lambda \]

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  • question_answer56) The ratio of the speed of an object to the speed of its real image of magnification\[m\]of a convex mirror is

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

    B) \[{{m}^{2}}\]

    C) \[-m\]

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

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  • question_answer57) The maximum current that flow. in the fuse wire before it blows out, varies with the radius\[r\]as

    A) \[{{r}^{3/2}}\]

    B) \[r\]

    C) \[{{r}^{2/3}}\]

    D) \[{{r}^{1/2}}\]

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  • question_answer58) A diatomic gas is heated at certain pressure. What fraction of the heat energy is used to increase the internal energy?

    A) \[3/5\]

    B) \[3/7\]

    C) \[5/7\]

    D) \[5/9\]

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  • question_answer59) In interference pattern, the energy is

    A) created at the minimum

    B) destroyed at the minimum

    C) conserved but redistributed

    D) All of the above

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  • question_answer60) A red flower kept in green light will appear

    A) red

    B) yellow

    C) black

    D) white

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  • question_answer61) \[0.01M\]solution of\[KCl\]and\[CaC{{l}_{2}}\]are prepared in water. The freezing point of\[KCl\]is found to be\[-{{2}^{o}}C\]. What is the freezing point of\[CaC{{l}_{2}}\]to be completely ionised?

    A) \[-{{3}^{o}}C\]

    B) \[+{{3}^{o}}C\]

    C) \[-{{2}^{o}}C\]

    D) \[-{{4}^{o}}C\]

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  • question_answer62) \[1mol\,\,He\]and\[3\,\,mol\,\,{{N}_{2}}\]exert a pressure of\[16\,\,atm\]. Due to a hole in the vessel in which mixture in placed, mixture leaks out. What is the composition of mixture effusing out initially?

    A) \[0.22\]

    B) \[0.44\]

    C) \[~0.66\]

    D) \[0.88\]

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  • question_answer63) What are the four quantum numbers of 19th electron in\[Sc(Z=21)\]?

    A) \[n=4,\,\,l=0,\,\,m=0,\,\,{{m}_{s}}=+\frac{1}{2}\]

    B) \[n=3,\,\,l=1,\,\,m=-1,\,\,{{m}_{s}}=+\frac{1}{2}\]

    C) \[n=4,\,\,l=1,\,\,m=\pm 1,\,\,{{m}_{s}}=-\frac{1}{2}\]

    D) \[n=3,\,\,l=2,\,\,m=\pm 2,\,\,{{m}_{s}}=-\frac{1}{2}\]

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  • question_answer64) \[(A)+\]tap water\[\to \]white turbidity soluble in\[aq.N{{H}_{3}}\] \[(A)\xrightarrow{\Delta }residue(B)+N{{O}_{2}}+{{O}_{2}}\] Aqueous\[(A)\]gives brown ring on adding\[FeS{{O}_{4}}\]and\[Conc.{{H}_{2}}S{{O}_{4}}\].Identify\[(A)\].

    A) \[NaN{{O}_{3}}\]

    B) \[AgN{{O}_{3}}\]

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

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

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  • question_answer65) Each of the following compounds has been dissolved in water to make its\[0.001\,\,M\]solution. Rank them in order of their increasing conductivity in solution (assume\[100%\]ionisation in each case)

    A) \[c<d<a<b\]

    B) \[c<d<b<a\]

    C) \[a<b<c<d\]

    D) \[d<c<a<b\]

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  • question_answer66) Metal carbonyls can have formula\[M{{(CO)}_{x}}\], where\[x=\]number of\[CO\]units coordinated to metal\[M\]. What is the formula of the carbonyl of\[Fe(26)\]if\[EAN\]of Fe in metal carbonyl is 36?

    A) 2

    B) 3

    C) 4

    D) 5

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  • question_answer67) Following method of extracting\[Zn\]is based on thermodynamics \[A:2ZnS+3{{O}_{2}}\xrightarrow{{}}2ZnO+2S{{O}_{2}}\] \[B:ZnO+C\xrightarrow{{}}Zn+CO\] If\[\Delta G_{f}^{\text{o}}\](standard free energies of formation , in\[kJmo{{l}^{-1}}\])of\[ZnS=-205.4\], \[ZnO=-318.0,\,\,S{{O}_{2}}=-300.4\]and of\[CO=-137.3\] Free energy changes of the above reaction\[A\]and\[B\](respectively) will be

    A) \[-826.4\,\,kJ,\,\,+180.9\,\,kJ\]

    B) \[+826.4\,\,kJ,\,\,-180.9\,\,kJ\]

    C) \[-826.4\,\,kJ,\,\,-180.9\,\,kJ\]

    D) \[+826.4\,\,kJ,\,\,+180.9\,\,kJ\]

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  • question_answer68) The final step for the extraction of copper form copper pyrites in Bessemer converter involves the reaction.

    A) \[C{{u}_{2}}S+2FeO\xrightarrow{{}}2Cu+2Fe+S{{O}_{2}}\]

    B) \[C{{u}_{2}}S+2CuO\xrightarrow{{}}6Cu+S{{O}_{2}}\]

    C) \[4C{{u}_{2}}O+FeS\xrightarrow{{}}8Cu+2FeS{{O}_{4}}\]

    D) \[2C{{u}_{2}}O+FeS\xrightarrow{{}}4Cu+Fe+S{{O}_{2}}\]

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  • question_answer69) If\[C{{O}_{2}}(g)\]under pressure is passed into \[N{{a}_{2}}Cr{{O}_{4}}(aq)\], yellow colour solution changes to

    A) blue

    B) green

    C) red

    D) orange-red

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  • question_answer70) Select incorrect statements.

    A) Ionisation energies of Sot-elements are greater than those of 3d and 4of elements.

    B) Cu (I) is diamagnetic while Cu (II) is paramagnetic.

    C) \[{{[Ti{{({{H}_{2}}O)}_{6}}]}^{3+}}\]is coloured while\[{{[Sc{{({{H}_{2}}O)}_{6}}]}^{+}}\]is colourless.

    D) Transition elements cannot form complexes.

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  • question_answer71) \[Cl{{O}_{2}}\], is an/a

    A) anhydride of\[HCl{{O}_{2}}\]

    B) anhydride of\[HCl{{O}_{3}}\]

    C) mixed anhydride of\[HCl{{O}_{2}}\]and\[HCl{{O}_{3}}\]

    D) mixed anhydride of\[HCl{{O}_{3}}\]and\[HCl{{O}_{4}}\]

    View Answer play_arrow
  • question_answer72) Based on the following reaction identify alkene\[A\] \[A\xrightarrow{{{O}_{3}}/({{H}_{2}}O)/Zn}2HCHO+\underset{\begin{smallmatrix} | \\ CHO \end{smallmatrix}}{\mathop{CHO}}\,\]

    A) \[C{{H}_{3}}-\overset{\begin{smallmatrix} C{{H}_{2}} \\ || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}\]

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

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

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

    View Answer play_arrow
  • question_answer73) Which one of the following statements about NO is wrong?

    A) NO is an odd electron molecule

    B) It is a free radical and highly reactive

    C) It readily forms complexes with transition metal ions

    D) It can be prepared by heating\[N{{H}_{4}}N{{O}_{3}}\]at\[{{250}^{o}}C\]

    View Answer play_arrow
  • question_answer74) \[K{{O}_{2}}\]is used in life supports in space crafts, submarines and emergency breathing apparatus since it

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

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

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

    D) absorbs\[C{{O}_{2}}\]and releases\[{{O}_{2}}\]

    View Answer play_arrow
  • question_answer75) Calculate second electron affinity of oxygen for the process, \[{{O}^{-}}(g)+{{e}^{-}}(g)\to {{O}^{2-}}(g)\] by using the following data

    (i) Heat of sublimation of \[Mg(s)=+147.7\,\,kJ\,\,mo{{l}^{-1}}\]
    (ii) lionisation energy of\[Mg(g)\]to form \[M{{g}^{2+}}(g)=2189.0\,\,kJ\,\,mo{{l}^{-1}}\]
    (iii) Bond dissociation energy for \[{{O}_{2}}=498.4\,\,kJ\,\,mo{{l}^{-1}}\]
    (iv) First electron affinity of \[O(g)=-141.0\,\,kJ\,\,mo{{l}^{-1}}\]
    (v) Heat formation of \[MgO=-601.7\,\,kJ\,\,mol-1\]
    (vi) Lattice energy of \[MgO=-3791.0\,\,kJ\,\,mo{{l}^{-1}}\]

    A) \[235.6\,\,kJ\,\,mo{{l}^{-1}}\]

    B) \[468.7\,\,kJ\,\,mo{{l}^{-1}}\]

    C) \[544.4\,\,kJ\,\,mo{{l}^{-1}}\]

    D) \[744.4\,\,kJ\,\,mo{{l}^{-1}}\]

    View Answer play_arrow
  • question_answer76) \[1g\]of fuming\[{{H}_{2}}S{{O}_{4}}\](oleum: It is a mixture of concentrated\[{{H}_{2}}S{{O}_{4}}\]saturated with\[S{{O}_{3}}\]and having formula\[{{H}_{2}}{{S}_{2}}{{O}_{7}}\]) is diluted with\[{{H}_{2}}O\]. This solution is completely neutralised by \[26.7mL\]of\[0.8\text{ }N\text{ }NaOH\]. Find the percentage of free\[S{{O}_{3}}\]in the oleum.

    A) 20.73%

    B) 43.80%

    C) 79.27%

    D) 60.74%

    View Answer play_arrow
  • question_answer77) \[_{7}^{14}N+_{0}^{1}n\to _{6}^{14}C+_{1}^{1}H\]is written as

    A) \[_{7}^{14}N(n,\,\,e)_{1}^{1}H\]

    B) \[_{7}^{14}N(p,\,\,n)_{6}^{14}C\]

    C) \[_{7}^{14}N(n,\,\,p)_{6}^{14}C\]

    D) \[_{6}^{14}C(p,\,\,n)_{7}^{14}N\]

    View Answer play_arrow
  • question_answer78) Photographic paper is developed with alkaline hydroquinone \[2AgBr(s)+2\,OH_{+}^{-}\] \[2\,Ag(s)+2{{H}_{2}}O(l)\,+2B{{r}^{-}}\,(aq)\] Select correct statement.

    A) Hydroquinone is the oxidant

    B) \[A{{g}^{+}}\]is the oxidant

    C) \[B{{r}^{-}}\]is the oxidant

    D) \[A{{g}^{+}}\] is the reductant

    View Answer play_arrow
  • question_answer79) Which has maximum ionisation potential?

    A) \[N\]

    B) \[O\]

    C) \[{{O}^{+}}\]

    D) \[Na\]

    View Answer play_arrow
  • question_answer80) Electronic configuration of\[Gd(64)\]is written as

    A) \[[Xe]4{{f}^{7}}5{{d}^{1}}6{{s}^{2}}\]

    B) \[[Xe]4{{f}^{8}}6{{s}^{2}}\]

    C) \[[Xe]4{{f}^{9}}6{{s}^{1}}\]

    D) \[[Xe]4{{f}^{10}}\]

    View Answer play_arrow
  • question_answer81) Screening effect is not observed in

    A) \[H{{e}^{+}}\]

    B) \[L{{i}^{2+}}\]

    C) \[B{{e}^{3+}}\]

    D) all cases

    View Answer play_arrow
  • question_answer82) Which one of the following isomers of\[PBrC{{l}_{3}}\]have no dipole moment?

    A) Only I

    B) I and II

    C) II and III

    D) Only III

    View Answer play_arrow
  • question_answer83) The type of hybridisation of P atom in\[PC{{l}_{5}}\], \[PCl_{4}^{+}\]and\[PCl_{6}^{-}\]is (respectively)

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

    B) \[s{{p}^{3}}d,\,\,s{{p}^{3}},\,\,s{{p}^{2}}{{d}^{2}}\]

    C) \[s{{p}^{3}},\,\,s{{p}^{3}}{{d}^{2}},\,\,s{{p}^{3}}\]

    D) \[s{{p}^{3}}{{d}^{2}},\,\,s{{p}^{3}},\,\,s{{p}^{3}}d\]

    View Answer play_arrow
  • question_answer84) Which has a maximum repulsive interaction?

    A) \[bp-bp\]

    B) \[lp-lp\]

    C) \[lp-bp\]

    D) Equal

    View Answer play_arrow
  • question_answer85) Calculate the electronegativity of chlorine from bond energy of\[Cl-F\]bond\[(61\,\,kcal\,\,mo{{l}^{-1}})\]\[(38\,\,kcal\,\,mo{{l}^{-1}})\]and\[Cl-Cl\]bond\[(58\,\,kcal\,\,mo{{l}^{-1}})\]and electronegativity of fluorine\[4.0\,\,eV\]

    A) \[1.42\,\,eV\]

    B) \[1.89\,\,eV\]

    C) \[2.67\,\,eV\]

    D) \[3.22\,\,eV\]

    View Answer play_arrow
  • question_answer86) A sample of ammonium phosphate\[{{(N{{H}_{4}})}_{3}}P{{O}_{4}}\]contains\[3.18\,\,moles\]of\[H-\]atom. The number of\[moles\]of\[O-\]atom in the sample is

    A) \[0.265\]

    B) \[0.795\]

    C) \[1.06\]

    D) \[3.18\]

    View Answer play_arrow
  • question_answer87) In the following compound keto group is at position

    A) 1

    B) 2

    C) 3

    D) 4

    View Answer play_arrow
  • question_answer88)

    I. Formation of A has proceeded with racemisation.
    II. Formation of B has proceeded with inversion.
    Select the correct statement.

    A) I and It

    B) Only I

    C) Only III

    D) None of these

    View Answer play_arrow
  • question_answer89) In this reaction, we get types of substituted alcohols (stereoisomers not considered)

    A) one

    B) two

    C) three

    D) four

    View Answer play_arrow
  • question_answer90) Electrophile\[NO_{2}^{\oplus }\]attacks the following In which cases,\[N{{O}_{2}}\]will be at meta position?

    A) II and IV

    B) I, II and III

    C) II and III

    D) Only I

    View Answer play_arrow
  • question_answer91) The reaction of 1- bromo-3- chlorocyclobutane with metallic sodium in dioxane gives

    A)

    B)

    C)

    D)

    View Answer play_arrow
  • question_answer92) \[C{{H}_{3}}CH=C{{H}_{2}}\xrightarrow[{{H}_{2}}{{O}_{2}}/O{{H}^{-}}]{NaB{{D}_{4}}}\]Product\[X\],\[X\]is

    A) \[C{{H}_{3}}\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,HC{{H}_{2}}D\]

    B) \[C{{H}_{3}}\underset{\begin{smallmatrix} | \\ D \end{smallmatrix}}{\mathop{C}}\,HC{{H}_{2}}OH\]

    C) \[C{{H}_{3}}\underset{\begin{smallmatrix} | \\ CO \end{smallmatrix}}{\mathop{C}}\,HC{{H}_{3}}\]

    D) None of these

    View Answer play_arrow
  • question_answer93) End product of following sequence of reaction is

    A)

    B)

    C)

    D)

    View Answer play_arrow
  • question_answer94)

    A)

    B)

    C)

    D)

    View Answer play_arrow
  • question_answer95)

    A)

    B)

    C)

    D)

    View Answer play_arrow
  • question_answer96) A can be

    A) \[C{{H}_{3}}\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,HC{{H}_{3}}\]

    B) \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}OH\]

    C) Both (a) and (b)

    D) None of these

    View Answer play_arrow
  • question_answer97) \[2C{{H}_{3}}\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,O{{C}_{2}}{{H}_{5}}\xrightarrow{{{C}_{2}}{{H}_{5}}ONa}A\], A is formed by Claisen condensation. Which is/are true about A?

    A) A forms oxime

    B) A shows tautomerism

    C) A shows iodoform test

    D) All of the above are true

    View Answer play_arrow
  • question_answer98) When a nucelophile encounters a ketone the site of attack is

    A) the carbon atom of the carbonyl

    B) the oxygen atom of the carbonyl

    C) Both the carbon and oxygen atoms with equal probability

    D) no attack occurs- ketones do not react with nucteophiles

    View Answer play_arrow
  • question_answer99) A is

    A)

    B)

    C)

    D) None of these

    View Answer play_arrow
  • question_answer100) The structure of\[N-\]propyl acetamide is

    A) \[C{{H}_{3}}C{{H}_{2}}CONHC{{H}_{3}}\]

    B) \[C{{H}_{3}}CON{{(C{{H}_{2}}C{{H}_{2}}C{{H}_{3}})}_{2}}\]

    C) \[C{{H}_{3}}CONHC{{H}_{2}}C{{H}_{2}}C{{H}_{3}}\]

    D) \[C{{H}_{3}}CH=NC{{H}_{2}}C{{H}_{2}}C{{H}_{3}}\]

    View Answer play_arrow
  • question_answer101) Which\[A\]gives red colour in the reaction \[A\xrightarrow[(ii)\,\,NaOH]{(i)\,\,HN{{O}_{2}}}red\,\,colour\]

    A) \[C{{H}_{3}}C{{H}_{2}}N{{O}_{2}}\]

    B) \[{{(C{{H}_{3}})}_{2}}-CHN{{O}_{2}}\]

    C) \[{{(C{{H}_{3}})}_{3}}CN{{O}_{2}}\]

    D)

    View Answer play_arrow
  • question_answer102) Alanine forms Zwitter ion which exists as

    A) \[C{{H}_{3}}\overset{\begin{smallmatrix} \oplus N{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}\,HCO{{O}^{-}}\]in acidic medium

    B) \[C{{H}_{3}}\overset{\begin{smallmatrix} \oplus N{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}\,HCOOH\]in a medium of\[pH=4\]

    C) \[C{{H}_{3}}\underset{\begin{smallmatrix} | \\ N{{H}_{2}} \end{smallmatrix}}{\mathop{C}}\,HCO{{O}^{-}}\]in a medium of\[pH=1\]

    D) \[C{{H}_{3}}\underset{\begin{smallmatrix} | \\ N{{H}_{2}} \end{smallmatrix}}{\mathop{C}}\,HCO{{O}^{-}}\]in a medium of\[pH=2\]

    View Answer play_arrow
  • question_answer103) Which gives only glucose by hydrolysis?

    A) Sucrose

    B) Raffinose

    C) Maltose

    D) Galactose

    View Answer play_arrow
  • question_answer104) Which polysaccharide has a-glycoside linkage?

    A) Amylose

    B) Amylopection

    C) Cellulose

    D) All of these

    View Answer play_arrow
  • question_answer105) Product (mixture) Mixture can be of

    A)

    B)

    C) Both (a) and (b)

    D) None of these

    View Answer play_arrow
  • question_answer106) \[p-\]cresol reacts with chloroform in alkaline medium to give the compound\[A\]which adds hydrogen cyanide to form the compound\[B\]. The latter on acidic hydrolysis gives chiral carboxylic acid\[C\]which is

    A)

    B)

    C)

    D)

    View Answer play_arrow
  • question_answer107) Choose the correct statement.

    A) A is more volatile than B

    B) B is more volatile than A

    C) A is formed more rapidly at a higher temperature

    D) A is formed in higher yield at a low temperature

    View Answer play_arrow
  • question_answer108) Sodium extract of thioruea will be ...... colour in Lassaignes test.

    A) blue

    B) red

    C) yellow

    D) green

    View Answer play_arrow
  • question_answer109) Consider the following redox reaction occurring in acidic medium The unknown standard reduction potential is

    A) \[-1.6\,\,V\]

    B) \[1.6\,\,V\]

    C) \[-1.52\,\,V\]

    D) \[1.52\ \,V\]

    View Answer play_arrow
  • question_answer110) The spontaneous reaction that takes place in this cell is

    A) \[Zn+Ni\xrightarrow{{}}Z{{n}^{2+}}+N{{i}^{2+}}\]

    B) \[Zn+N{{i}^{2+}}\xrightarrow{{}}Z{{n}^{2+}}+Ni\]

    C) \[Ni+Z{{n}^{2+}}\xrightarrow{{}}N{{i}^{2+}}+Zn\]

    D) \[N{{i}^{2+}}+2K\xrightarrow{{}}2{{K}^{+}}+Ni\]

    View Answer play_arrow
  • question_answer111) \[A\,\,0.15\]molal solution of\[{{K}_{4}}[Fe{{(CN)}_{6}}]\]in water freezes at\[-{{0.65}^{o}}C\]. What is the apparent percentage of dissociation of this compound in this solution? (\[{{K}_{f}}\]for water\[={{1.86}^{o}}C\,\,mo{{l}^{-1}}\])

    A) 0.33

    B) 0.52

    C) 0.63

    D) 0.79

    View Answer play_arrow
  • question_answer112) \[10g\]of non-volatile solute is dissolved in\[180g\]of\[{{H}_{2}}O\]resulting in lowering of vapour pressure by\[0.5%\]. Determine the boiling point of solution if\[{{K}_{b}}\]of water is\[0.52\,\,K\,\,kg\,\,mo{{l}^{-1}}\].

    A) \[{{100.01}^{o}}C\]

    B) \[{{100.15}^{o}}C\]

    C) \[{{100.23}^{o}}C\]

    D) \[{{100.32}^{o}}C\]

    View Answer play_arrow
  • question_answer113) Which one of the following reaction energy diagrams best represents a reaction in the reverse direction; that it is the most endothermic?

    A)

    B)

    C)

    D)

    View Answer play_arrow
  • question_answer114) A certain reaction rate increases 1000 folds in the presence of a catalyst at\[{{27}^{o}}C\]. The activation energy of the original pathway is\[98\,\,kJ/mol\]. What is the activation energy of the new pathway?

    A) \[80.77\,\,kJ\]

    B) \[56.38\,\,kJ\]

    C) \[24.67\,\,kJ\]

    D) \[90.43\,\,kJ\]

    View Answer play_arrow
  • question_answer115) Consider the following reaction in an aqueous solution \[{{I}^{-}}(aq)+C{{l}^{-}}\to I{{O}^{-}}(aq)+C{{l}^{-}}(aq)\] and the following initial concentration and initial rate data for this reaction.

    Exp. No \[[{{l}^{-}}]M\] \[[O{{C}^{-}}]M\] Initial rate\[M{{s}^{-1}}\]
    1. 2. 3. 4. 0.1000 0.2000 0.3000 0.3000 0.0500 0.0500 0.0100 0.0200 \[3.05\times {{10}^{-4}}\] \[6.10\times {{10}^{-4}}\] \[1.83\times {{10}^{-4}}\] \[3.66\times {{10}^{-4}}\]
    Which of the following is the correct rate law for this reaction?

    A) Rate\[=k{{[{{l}^{-}}]}^{2}}[OC{{l}^{-}}]\]

    B) Rate\[=k[OC{{l}^{-}}]\]

    C) Rate\[=k{{[{{l}^{-}}]}^{2}}\]

    D) Rate\[=k[{{l}^{-}}][OC{{l}^{-}}]\]

    View Answer play_arrow
  • question_answer116) Determine the\[pH\]of\[0.024\,\,M\]hydroxylamine hydrochloride solution. (\[{{k}_{b}}\]of hydroxyl amine is\[{{10}^{-8}}\]).

    A) 8.4

    B) 6.2

    C) 3.8

    D) 5.6

    View Answer play_arrow
  • question_answer117) Determine solubility of\[AgBr\]in a\[0.1\,\,M\,\,KCN\]solution.\[[{{K}_{f}}of{{[Ag{{(CN)}_{2}}]}^{-}}=5.6\times {{10}^{8}}\];\[{{K}_{sp}}\]of\[AgBr=7.7\times {{10}^{-13}}]\]

    A) \[2\times {{10}^{3}}M\]

    B) \[4\times {{10}^{-6}}M\]

    C) \[2\times {{10}^{-6}}M\]

    D) \[4\times {{10}^{-3}}M\]

    View Answer play_arrow
  • question_answer118) Which of the following forms cationic micelles above a certain minimum concentration?

    A) Sodium dodecylsulphate

    B) Sodium acetate

    C) Urea

    D) Cetyl trimethyl ammonium bromide

    View Answer play_arrow
  • question_answer119) Determine the relative size of\[Cs\]atom compared to a\[Li\]atom, if their densities are \[1.87g/cc\] and\[0.53g/cc\] respectively

    A) \[r(Cs)=1.753r(Li)\]

    B) \[r(Cs)=1.936r(Li)\]

    C) \[r(Cs)=2.753r(Li)\]

    D) \[r(Cs)=2.936r(Li)\]

    View Answer play_arrow
  • question_answer120) Nylon threads are made of

    A) polyvinyl polymer

    B) Polyester polymer

    C) polyamide polymer

    D) polyethylene polymer

    View Answer play_arrow
  • question_answer121) The least positive integer\[n\], for which\[n!<{{\left( \frac{n+1}{2} \right)}^{n}}\], is

    A) 1

    B) 2

    C) 3

    D) 4

    View Answer play_arrow
  • question_answer122) The sum to n terms of the series: \[\frac{1}{1+{{1}^{2}}+{{1}^{4}}}+\frac{2}{1+{{2}^{2}}+{{2}^{4}}}+\frac{3}{1+{{3}^{2}}+{{3}^{4}}}+...\]is

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

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

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

    D) None of these

    View Answer play_arrow
  • question_answer123) The sum of\[n\]terms of the series\[+1+\frac{4}{5}+\frac{7}{{{5}^{2}}}\]\[+\frac{10}{{{5}^{3}}}+...\]is

    A) \[\frac{5}{4}+\frac{15}{16}\left( 1-\frac{1}{{{5}^{n-1}}} \right)-\frac{(3n-2)}{4\cdot {{5}^{n-1}}}\]

    B) \[\frac{5}{4}+\frac{1}{16}\left( 1-\frac{1}{{{5}^{n-1}}} \right)-\frac{3n}{4\cdot {{5}^{n-1}}}\]

    C) \[\left( 1-\frac{1}{{{5}^{n-1}}} \right)-\frac{(3n+2)}{4\cdot {{5}^{n-1}}}\]

    D) None of the above

    View Answer play_arrow
  • question_answer124) Sum of the series to \[n\] terms\[5+7+13+31+85+...\]is

    A) \[{{3}^{n}}+8n+1\]

    B) \[\frac{1}{2}[{{3}^{n}}+8n-1]\]

    C) \[\frac{1}{2}({{3}^{n}}+8n+1)\]

    D) None of the above

    View Answer play_arrow
  • question_answer125) If\[b<0\], then the roots\[{{x}_{1}}\]and\[{{x}_{2}}\]of the equation \[2{{x}^{2}}+6x+b=0\], satisfy the condition\[\left( \frac{{{x}_{1}}}{{{x}_{2}}} \right)+\left( \frac{{{x}_{2}}}{{{x}_{1}}} \right)<K\], where\[K\]is equal to

    A) 2

    B) -2

    C) 0

    D) 4

    View Answer play_arrow
  • question_answer126) If the roots of the equation\[(a-1){{({{x}^{2}}+x+1)}^{2}}\]\[=(a+1)({{x}^{4}}+{{x}^{2}}+1)\]are real and distinct then the value of a\[\in \]

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

    B) \[(-\infty ,\,\,-2)\cup (2,\,\,\infty )\]

    C) \[[-2,\,\,2]\]

    D) \[[-3,\,\,\infty )\]

    View Answer play_arrow
  • question_answer127) If the sum of two of the roots of\[{{x}^{3}}+p{{x}^{2}}+qx+r=0\]is zero, then\[pq=\]

    A) \[-r\]

    B) \[2r\]

    C) \[-2r\]

    D) \[r\]

    View Answer play_arrow
  • question_answer128) If\[m\]parallel lines in a plane are intersected by a family of\[n\]parallel lines, then the number of parallelograms that can be formed is

    A) \[\frac{1}{4}mn(m-1)(n-1)\]

    B) \[\frac{1}{2}mn(m-1)(n-1)\]

    C) \[\frac{1}{4}{{m}^{2}}{{n}^{2}}\]

    D) None of these

    View Answer play_arrow
  • question_answer129) A person is permitted to select at least one and at most \[n\] coins from a collection\[(2n+1)\]distinct coins. If the total number of ways in which he can select coins is 255, then \[n\] equals

    A) 4

    B) 8

    C) 16

    D) 32

    View Answer play_arrow
  • question_answer130) The value of \[x\] in the expression\[{{(x+{{x}^{{{\log }_{10}}x}})}^{5}}\], if the third term in the expansion is 1,000,000, is

    A) \[10,\,\,{{10}^{-3/2}}\]

    B) \[100\,\,or\,\,{{10}^{-3/2}}\]

    C) \[10\,\,or\,\,{{10}^{-5/2}}\]

    D) None of these

    View Answer play_arrow
  • question_answer131) \[\sum\limits_{k=0}^{10}{^{20}{{C}_{k}}}\]is equal to

    A) \[{{2}^{19}}+\frac{1}{2}\]\[^{20}{{C}_{10}}\]

    B) \[{{2}^{19}}\]

    C) \[^{20}{{C}_{10}}\]

    D) None of these

    View Answer play_arrow
  • question_answer132) If the point\[(a,\,\,a)\]are placed in between the lines\[|x+y|\,\,=4\]then

    A) \[|a|\,\,=2\]

    B) \[|a|\,\,=3\]

    C) \[|a|\,\,<2\]

    D) \[|a|\,\,<3\]

    View Answer play_arrow
  • question_answer133) The number of rational values of m for which the\[y-\]coordinate of the point of intersection of the lines\[3x+2y=10\]and\[x=my+2\]is an integer is

    A) 2

    B) 4

    C) 6

    D) 8

    View Answer play_arrow
  • question_answer134) A straight line cuts intercepts from the axis of coordinates the sum of the reciprocals of which is a constant\[K\]. Then it always passes through a fixed point

    A) \[(K,\,\,K)\]

    B) \[\left( \frac{1}{K},\,\,\frac{1}{K} \right)\]

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

    D) \[(K-1,\,\,K-1)\]

    View Answer play_arrow
  • question_answer135) If the line\[\frac{x}{a}+\frac{y}{b}=1\]moves in such a way that \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{1}{{{c}^{2}}}\]where,\[c\]is a constant, then the locus of the foot of perpendicular from the origin on the straight line is

    A) Straight line

    B) Parabola

    C) Ellipse

    D) Circle

    View Answer play_arrow
  • question_answer136) The pair of lines\[\sqrt{3}{{x}^{2}}-4xy+\sqrt{3}{{y}^{2}}=0\]are rotated about the origin by\[\frac{\pi }{6}\]in the anticlockwise sense. The equation of the pair in the new position is

    A) \[{{x}^{2}}-\sqrt{3}xy=0\]

    B) \[xy-\sqrt{3}{{y}^{2}}=0\]

    C) \[\sqrt{3}{{x}^{2}}-xy=0\]

    D) None of the above

    View Answer play_arrow
  • question_answer137) The value of\[\underset{x\to 1}{\mathop{\lim }}\,\frac{\left[ \sum\limits_{K=1}^{100}{-{{x}^{K}}} \right]-100}{x-1}\]is

    A) \[-5050\]

    B) \[0\]

    C) \[5050\]

    D) None of these

    View Answer play_arrow
  • question_answer138) . The value of\[\underset{x\to \infty }{\mathop{\lim }}\,\left\{ \frac{x}{x+\frac{\sqrt[3]{x}}{x+\frac{\sqrt[3]{x}}{x+\sqrt[3]{x}}}...} \right\}\]is

    A) 0

    B) 1

    C) 2

    D) 1/2

    View Answer play_arrow
  • question_answer139) lf\[f(x)\]defined by\[f(x)=\left\{ \begin{matrix} \frac{|{{x}^{2}}-x|}{{{x}^{2}}-x}, & x\ne 0,\,\,1 \\ 1, & x=0 \\ -1, & x=1 \\ \end{matrix} \right.\]then\[f(x)\]is continuous for all

    A) \[x\]

    B) \[x\]except at\[x=0\]

    C) \[x\]except at\[x=1\]

    D) \[x\]except at\[x=0\]and\[x=1\]

    View Answer play_arrow
  • question_answer140) Function\[f(x)\]is defined as follows \[f(x)=\left\{ \begin{matrix} ax-b, & x\le 1 \\ 3x, & 1<x<2 \\ b{{x}^{2}}-a, & x\ge 2 \\ \end{matrix} \right.\] lf\[f(x)\] is continuous at\[x=1\], but discontinuous at\[x=2\]then the locus of the point\[(a,\,\,b)\] is a straight line excluding the point where it cuts the line

    A) \[y=3\]

    B) \[y=2\]

    C) \[y=0\]

    D) \[y=1\]

    View Answer play_arrow
  • question_answer141) The maximum value of\[(\cos {{\alpha }_{1}})\cdot (\cos {{\alpha }_{2}})...(cos{{\alpha }_{n}})\]. Under the restrictions\[0\le {{\alpha }_{1}},\,\,{{\alpha }_{2}},...{{\alpha }_{n}}\le \frac{\pi }{2}\]and\[(\cot {{\alpha }_{1}})\cdot (cot{{\alpha }_{2}})...(\cot {{\alpha }_{n}})=1\]is

    A) \[\frac{1}{{{2}^{n/2}}}\]

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

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

    D) \[1\]

    View Answer play_arrow
  • question_answer142) The minimum value of the expression\[\sin \alpha +\sin \beta +\sin \gamma \], where\[\alpha ,\,\,\beta ,\,\,\gamma \]are real numbers satisfying\[\alpha +\beta +\gamma =\pi \]is

    A) positive

    B) zero

    C) negative

    D) -3

    View Answer play_arrow
  • question_answer143) If\[\theta \]the angle between the unit vectors\[\mathbf{a}\]and\[\mathbf{b}\], then\[\cos \frac{\theta }{2}\]is equal to

    A) \[\frac{1}{2}|\mathbf{a}-\mathbf{b}|\]

    B) \[\frac{1}{2}|\mathbf{a}+\mathbf{b}|\]

    C) \[\frac{|\mathbf{a}-\mathbf{b}|}{|\mathbf{a}+\mathbf{b}|}\]

    D) \[\frac{|\mathbf{a}+\mathbf{b}|}{|\mathbf{a}-\mathbf{b}|}\]

    View Answer play_arrow
  • question_answer144) If\[\mathbf{a}\cdot \mathbf{i}=\mathbf{a}\cdot (\mathbf{j}+\mathbf{i})=\mathbf{a}\cdot (\mathbf{i}+\mathbf{j}+\mathbf{k})\], then\[\mathbf{a}\]is equal to

    A) \[\mathbf{i}\]

    B) \[\mathbf{k}\]

    C) \[\mathbf{j}\]

    D) \[(\mathbf{i}+\mathbf{j}+\mathbf{k})\]

    View Answer play_arrow
  • question_answer145) If the scalar projection of the vector\[x\mathbf{i}-\mathbf{j}+\mathbf{k}\]on the vector\[2\mathbf{i}-\mathbf{j}+5\mathbf{k}\]is\[\frac{1}{\sqrt{30}}\]then value of re is equal to

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

    B) \[6\]

    C) \[-6\]

    D) \[3\]

    View Answer play_arrow
  • question_answer146) If\[\mathbf{a}\times \mathbf{b}=\mathbf{c},\,\,\mathbf{b}\times \mathbf{c}=\mathbf{a}\]and\[\mathbf{a},\,\,\mathbf{b},\,\,\mathbf{c}\]be the moduli of the vectors\[\mathbf{a},\,\,\mathbf{b},\,\,\mathbf{c}\]respectively, then

    A) \[a=1,\,\,b=1\]

    B) \[c=1,\,\,a=1\]

    C) \[\mathbf{a}\cdot (\mathbf{b}\times \mathbf{c})=1\]

    D) \[b=1,\,\,c=a\]

    View Answer play_arrow
  • question_answer147) A unit vectors coplanar with\[\mathbf{i}+\mathbf{j}+2\mathbf{k}\]and\[\mathbf{i}+2\mathbf{j}+\mathbf{k}\]and perpendicular to\[\mathbf{i}+\mathbf{j}+\mathbf{k}\]is

    A) \[\frac{\mathbf{j}-\mathbf{k}}{\sqrt{2}}\]

    B) \[\frac{\mathbf{i}+\mathbf{j}+\mathbf{k}}{\sqrt{2}}\]

    C) \[\frac{\mathbf{i}+\mathbf{j}+2\mathbf{k}}{\sqrt{6}}\]

    D) \[\frac{-\mathbf{j}+2\mathbf{k}}{\sqrt{5}}\]

    View Answer play_arrow
  • question_answer148) Let\[A=\left[ \begin{matrix} 0 & \alpha \\ 0 & 0 \\ \end{matrix} \right]\]and\[{{(A+I)}^{50}}-50A=\left[ \begin{matrix} a & b \\ c & d \\ \end{matrix} \right]\]then the value of\[a+b+c+d\]is

    A) 2

    B) 1

    C) 4

    D) None of these

    View Answer play_arrow
  • question_answer149) For two unimodular complex numbers\[{{z}_{1}}\]and\[{{z}_{2}},\,\,{{\left[ \begin{matrix} {{{\bar{z}}}_{1}} & {{z}_{2}} \\ {{{\bar{z}}}_{2}} & {{z}_{1}} \\ \end{matrix} \right]}^{-1}}{{\left[ \begin{matrix} {{z}_{1}} & {{z}_{2}} \\ -{{{\bar{z}}}_{2}} & {{{\bar{z}}}_{1}} \\ \end{matrix} \right]}^{-1}}\]is equal to

    A) \[\left[ \begin{matrix} {{z}_{1}} & {{z}_{2}} \\ {{{\bar{z}}}_{1}} & {{{\bar{z}}}_{2}} \\ \end{matrix} \right]\]

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

    C) \[\left[ \begin{matrix} 1/2 & 0 \\ 0 & 1/2 \\ \end{matrix} \right]\]

    D) None of these

    View Answer play_arrow
  • question_answer150) If\[A\]is a square matrix of order n such that\[|adj(adj\,\,A)|\,\,=\,\,|A{{|}^{9}}\], then the value of n can be

    A) 4

    B) 2

    C) either 4 or 2

    D) None of these

    View Answer play_arrow
  • question_answer151) Coefficient of\[x\]in \[f(x)=\left| \begin{matrix} x & {{(1+\sin x)}^{3}} & \cos x \\ 1 & \log (1+x) & 2 \\ {{x}^{2}} & {{(1+x)}^{2}} & 0 \\ \end{matrix} \right|\] is

    A) 0

    B) 1

    C) - 2

    D) Cannot be determined

    View Answer play_arrow
  • question_answer152) Let\[{{\alpha }_{1}},\,\,{{\alpha }_{2}}\]and\[{{\beta }_{1}},\,\,{{\beta }_{2}}\]be the roots of\[a{{x}^{2}}+bx+c=0\]and\[p{{x}^{2}}+qx+r=0\]respectively. If the system of equations\[{{\alpha }_{1}}y+{{\alpha }_{2}}z=0\]and\[{{\beta }_{1}}y+{{\beta }_{2}}z=0\]has a non-trivial solution, then

    A) \[{{b}^{2}}pr={{q}^{2}}ac\]

    B) \[bp{{r}^{2}}=qa{{c}^{2}}\]

    C) \[b{{p}^{2}}r=q{{a}^{2}}c\]

    D) None of these

    View Answer play_arrow
  • question_answer153) The values of\[\alpha \]for which the point\[(\alpha -1,\,\,\alpha +1)\]lies in the larger segment of the circle\[{{x}^{2}}+{{y}^{2}}-x-y-6=0\]made by the chord whose equation is\[x+y-2=0\]is

    A) \[-1<\alpha <1\]

    B) \[1<\alpha <\infty \]

    C) \[-\infty <\alpha <-1\]

    D) \[\alpha \le 0\]

    View Answer play_arrow
  • question_answer154) The circles whose equations are\[{{x}^{2}}+{{y}^{2}}+{{c}^{2}}=2ax\]and\[{{x}^{2}}+{{y}^{2}}+{{c}^{2}}-2by=0\]will touch each other externally if

    A) \[\frac{1}{{{b}^{2}}}+\frac{1}{{{c}^{2}}}=\frac{1}{{{a}^{2}}}\]

    B) \[\frac{1}{{{c}^{2}}}+\frac{1}{{{a}^{2}}}=\frac{1}{{{b}^{2}}}\]

    C) \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{1}{{{c}^{2}}}\]

    D) None of these

    View Answer play_arrow
  • question_answer155) The tangents to\[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]having inclinations\[\alpha \]and\[\beta \]intersect at\[P\]. If\[\cot \alpha +\cot \beta =0\], then the locus of\[P\]is

    A) \[x+y=0\]

    B) \[x-y=0\]

    C) \[xy=0\]

    D) None of these

    View Answer play_arrow
  • question_answer156) An equilateral triangle\[SAB\]is inscribed in the parabola\[{{y}^{2}}=4ax\]having its focus at\[S\]. If chord\[AB\]lies towards the lefit of\[S\], then side length of this triangle is

    A) \[2a(2-\sqrt{3})\]

    B) \[4a(2-\sqrt{3})\]

    C) \[a(2-\sqrt{3})\]

    D) \[8a(2-\sqrt{3})\]

    View Answer play_arrow
  • question_answer157) Minimum distance between the curves\[{{y}^{2}}=4ax\]and\[{{x}^{2}}+{{y}^{2}}-12x+31=0\]is

    A) \[\sqrt{5}\]

    B) \[\sqrt{21}\]

    C) \[\sqrt{28}-\sqrt{5}\]

    D) \[\sqrt{21}-\sqrt{5}\]

    View Answer play_arrow
  • question_answer158) If the line\[lx+my+n=0\]cuts the ellipse\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{25}=1\]in points whose eccentoric angles differ by\[\frac{\pi }{2}\], then\[\frac{{{a}^{2}}{{l}^{2}}+{{b}^{2}}{{m}^{2}}}{{{n}^{2}}}\]is equal to

    A) 1

    B) 2

    C) 4

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

    View Answer play_arrow
  • question_answer159) If the tangent to ellipse\[{{x}^{2}}+2y=1\]at point \[P\left( \frac{1}{\sqrt{2}},\,\,\frac{1}{2} \right)\] meets the auxiliary circle at the points\[R\]and\[Q\], then tangents to circle at\[Q\]and\[R\]intersect at

    A) \[\left( \frac{1}{\sqrt{2}},\,\,1 \right)\]

    B) \[\left( 1,\,\,\frac{1}{\sqrt{2}} \right)\]

    C) \[\left( \frac{1}{2},\,\,\frac{1}{2} \right)\]

    D) \[\left( \frac{1}{2},\,\,\frac{1}{\sqrt{2}} \right)\]

    View Answer play_arrow
  • question_answer160) Which one of the following is independent of a in the hyperbola\[(0<\alpha <\pi /2)\]\[\frac{{{x}^{2}}}{{{\cos }^{2}}\alpha }-\frac{{{y}^{2}}}{{{\sin }^{2}}\alpha }=1\]

    A) Eccentricity

    B) Abscissa of foci

    C) Directrix

    D) Vertex

    View Answer play_arrow
  • question_answer161) If\[PQ\]is a double ordinate 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_answer162) If\[i{{z}^{4}}+1=0\], then\[z\]can take the value

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

    B) \[\cos \frac{\pi }{8}+\mathbf{i}\sin \frac{\pi }{8}\]

    C) \[\frac{1}{4\mathbf{i}}\]

    D) \[\mathbf{i}\]

    View Answer play_arrow
  • question_answer163) If\[\cos \alpha +\cos \beta +\cos \gamma =\sin \alpha +\sin \beta +\sin \gamma =0\], then the value of\[\cos 3\alpha +\cos 3\beta +\cos 3\gamma \]

    A) \[0\]

    B) \[\cos (\alpha +\beta +\gamma )\]

    C) \[3\cos (\alpha +\beta +\gamma )\]

    D) \[3\sin (\alpha +\beta +\gamma )\]

    View Answer play_arrow
  • question_answer164) If\[Q\]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_answer165) Let\[f(xy)=f(x)\cdot f(y)\]for all\[x,\,\,y\in R\]. If\[f(1)=2\]and\[f(4)=4\], then\[f(4)\]equal to

    A) \[4\]

    B) \[1\]

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

    D) \[8\]

    View Answer play_arrow
  • question_answer166) If\[y=\sqrt{(a-x)(x-b)}-(a-b){{\tan }^{-1}}\sqrt{\frac{a-x}{x-b}}\], then\[\frac{dy}{dx}\]is equal to

    A) \[1\]

    B) \[\sqrt{\frac{a-x}{x-b}}\]

    C) \[\sqrt{(a-x)(x-b)}\]

    D) \[\frac{1}{\sqrt{(a-x)(b-x)}}\]

    View Answer play_arrow
  • question_answer167) If\[{{\sin }^{-1}}\left( \frac{{{x}^{2}}-{{y}^{2}}}{{{x}^{2}}+{{y}^{2}}} \right)=\log a\], then\[\frac{{{d}^{2}}y}{d{{x}^{2}}}\]equals

    A) \[\frac{x}{y}\]

    B) \[\frac{y}{{{x}^{2}}}\]

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

    D) \[0\]

    View Answer play_arrow
  • question_answer168) A man 1.6 m high walks at the rate of\[30\text{m}/\min \] away from a lamp which is\[4m\]above ground. How fast is the mans shadow lengthening?

    A) \[22\text{m/min}\]

    B) \[20\text{m/min}\]

    C) \[15\text{m/min}\]

    D) \[25\text{m/min}\]

    View Answer play_arrow
  • question_answer169) The value\[P\]such that the length of subtangent and subnormal is equal for the curve\[{{y}^{2}}={{e}^{Px}}+Px\]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_answer170) \[AB\]is a diameter of a circle and\[C\]is any point on the circumference of the circle, then

    A) The area of \[\Delta ABC\] is maximum when it is isosceles

    B) The area of \[\Delta ABC\] is minimum when it is isosceles

    C) The perimeter of \[\Delta ABC\] is minimum when it is isosceles

    D) None of these

    View Answer play_arrow
  • question_answer171) The value of\[\left\{ \frac{1}{2}{{\cos }^{-1}}\left( \frac{\sqrt{5}}{3} \right) \right\}\]is

    A) \[\frac{3+\sqrt{5}}{2}\]

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

    C) \[\frac{1}{2}(3-\sqrt{5})\]

    D) None of these

    View Answer play_arrow
  • question_answer172) The interval for which\[2{{\tan }^{-1}}+{{\sin }^{-1}}\frac{2x}{1+{{x}^{2}}}\]is independent of\[x\]is

    A) \[|x|\,\,<1\]

    B) \[|x|\,\,>1\]

    C) \[|x|\,\,=1\]

    D) \[\phi \]

    View Answer play_arrow
  • question_answer173) The number of solutions of the equation\[1+\sin x\cdot {{\sin }^{2}}\frac{x}{2}=0\]in\[[-\pi ,\,\,\pi ]\]is

    A) zero

    B) 1

    C) 2

    D) 3

    View Answer play_arrow
  • question_answer174) If\[x,\,\,y\in [0,\,\,2\pi ]\]then the total number of ordered pairs\[(x,\,\,y)\]satisfying\[x\cdot \cos y=1\]is equal to

    A) 1

    B) 3

    C) 5

    D) 7

    View Answer play_arrow
  • question_answer175) \[\int{{{x}^{x}}\log (ex)}\]is equal to

    A) \[{{x}^{x}}+c\]

    B) \[x\cdot \log x+c\]

    C) \[{{(\log x)}^{x}}+c\]

    D) \[{{x}^{\log x}}+c\]

    View Answer play_arrow
  • question_answer176) \[\int{\sqrt{1+\cos ecx}\,\,dx}\]is equal to

    A) \[\pm {{\sin }^{-1}}(\tan x-\sec x)+c\]

    B) \[2{{\sin }^{-1}}(\cos x)+c\]

    C) \[{{\sin }^{-1}}\left( \cos \frac{x}{2}-\sin \frac{x}{2} \right)+c\]

    D) \[\pm 2{{\sin }^{-1}}\left( \sin \frac{x}{2}-\cos \frac{x}{2} \right)+c\]

    View Answer play_arrow
  • question_answer177) If\[\int{\frac{dx}{{{x}^{2}}{{({{x}^{n}}+1)}^{\frac{(n-1)}{n}}}}={{[f(x)]}^{1/n}}+c}\]then\[f(x)\]is

    A) \[1+{{x}^{n}}\]

    B) \[1+{{x}^{-n}}\]

    C) \[{{x}^{n}}+{{x}^{-n}}\]

    D) None of these

    View Answer play_arrow
  • question_answer178) The value of\[\underset{n\to \infty }{\mathop{\lim }}\,\left\{ \frac{1}{na}+\frac{1}{na+1}+\frac{1}{na+2}+...+\frac{1}{{{n}_{b}}} \right\}\]is

    A) \[\log (ab)\]

    B) \[\log (a/b)\]

    C) \[\log (b/a)\]

    D) \[-\log (a/b)\]

    View Answer play_arrow
  • question_answer179) The value of\[\int_{a}^{b}{\frac{|x|}{x}dx}\]is

    A) \[|b|-|a|\]

    B) \[|a|-|b|\]

    C) \[|b|+|a|\]

    D) \[-|b|-|a|\]

    View Answer play_arrow
  • question_answer180) \[y=\int_{1/8}^{{{\sin }^{2}}x}{{{\sin }^{-1}}\sqrt{t}dt+\int_{1/8}^{{{\cos }^{2}}x}{{{\cos }^{-1}}\sqrt{t}dt}}\],\[0\le x\le x/2\]

    A) Is the equation of a straight line parallel to the x-axis

    B) Is the equation of a straight line which is the bisector of first quadrant

    C) Is the equation of a straight line which is the bisector of second quadrant

    D) None of the above

    View Answer play_arrow
  • question_answer181) The area of the region \[[(x,\,\,y):{{x}^{2}}+{{y}^{2}}\le 1\le x+y]\]is;

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

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

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

    D) \[\frac{\pi }{4}-\frac{1}{2}\]

    View Answer play_arrow
  • question_answer182) The area of the figure bounded by the parabola\[{{(y-2)}^{2}}=x-1\], the tangent to it at the point with the ordinate 3 and the x-axis is

    A) 3

    B) 6

    C) 9

    D) None of these

    View Answer play_arrow
  • question_answer183) The degree of the differential equation\[{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{2}}+{{\left( \frac{dy}{dx} \right)}^{2}}=x\sin \left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)\]

    A) 1

    B) 2

    C) 3

    D) None of these

    View Answer play_arrow
  • question_answer184) The slope of the tangent at\[(x,\,\,y)\]to a curve passing through\[\left( 1,\,\,\frac{\pi }{4} \right)\]is given by\[\frac{y}{x}-{{\cos }^{2}}\left( \frac{y}{x} \right)\]the equation of the curve is

    A) \[y={{\tan }^{-1}}\left( \log \frac{c}{x} \right)\]

    B) \[y=x{{\tan }^{-1}}\left( \log \frac{x}{c} \right)\]

    C) \[y=x{{\tan }^{-1}}\left( \log \frac{c}{x} \right)\]

    D) None of these

    View Answer play_arrow
  • question_answer185) The solution of the equation \[\frac{dy}{dx}=\frac{x(2\log x+1)}{\sin y+y\cos y}\]

    A) \[y\sin y={{x}^{2}}\log x+\frac{{{x}^{2}}}{y}+c\]

    B) \[y\cos y={{x}^{2}}(\log x+1)+c\]

    C) \[y\cos y={{x}^{2}}\log x+\frac{{{x}^{2}}}{2}+c\]

    D) \[y\sin y={{x}^{2}}\log x+c\]

    View Answer play_arrow
  • question_answer186) The curve for which the length of the normal is equal to the length of the radius vector, are

    A) only circles

    B) only rectangular hyperbolas

    C) either circles or rectangular hyperbolas

    D) None of the above

    View Answer play_arrow
  • question_answer187) If\[\frac{1}{x(x+1)(x+2)...(x+n)}=\frac{{{A}_{0}}}{x}+\frac{{{A}_{1}}}{x+1}\]\[+\frac{{{A}_{2}}}{x+2}+...+\frac{{{A}_{n}}}{x+n}\] then \[{{A}_{r}}\] is equal to

    A) \[\frac{r!{{(1)}^{r}}}{(n-r)!}\]

    B) \[\frac{{{(-1)}^{r}}}{r!(n-r)!}\]

    C) \[\frac{1}{r!(n-r)!}\]

    D) None of these

    View Answer play_arrow
  • question_answer188) \[{{\log }_{2}}(9-{{2}^{x}})={{10}^{\log (3-x)}}\], solve for\[x\].

    A) 0

    B) 3

    C) both (a) and (b)

    D) 0 and 6

    View Answer play_arrow
  • question_answer189) 3 numbers are in GP therefore, their logarithms are in

    A) GP

    B) HP

    C) AP

    D) None of these

    View Answer play_arrow
  • question_answer190) In an equilateral triangle, the in-radius, circum-radius and one of the ex-radii are in the ratio

    A) \[2:3:5\]

    B) \[1:2:3\]

    C) \[1:3:7\]

    D) \[3:7:9\]

    View Answer play_arrow
  • question_answer191) In a triangle, the length of the two larger sides are 24 and 22, respectively. If the angles are in \[AP\], then the third side is

    A) \[12+2\sqrt{3}\]

    B) \[12-2\sqrt{3}\]

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

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

    View Answer play_arrow
  • question_answer192) \[G\]is a set of all rational numbers except\[-1\]and\[*\]is defined by\[a*b=a+b+ab\]for all\[a,\,\,b\in G\], in the group\[(G,\,\,*)\], the solution of \[{{2}^{-1}}*\,x*\,{{3}^{-1}}=5\] is

    A) \[71\]

    B) \[68\]

    C) \[63/5\]

    D) \[72/5\]

    View Answer play_arrow
  • question_answer193) If\[G\]is an abelian group then for all\[a,\,\,b\in G\] \[{{b}^{-1}}*\,{{a}^{-1}}\,*b*\,a\]is equal to

    A) \[a*b\]

    B) \[{{a}^{-1}}*{{b}^{-1}}\]

    C) \[e\]

    D) None of these

    View Answer play_arrow
  • question_answer194) If\[(G,\,\,*)\]is a group such that\[{{(a*b)}^{2}}=(a*a)\]\[*(b*b)\] for all\[a,\,\,b*G\], then\[G\]is

    A) abelian

    B) finite

    C) infinite

    D) None of these

    View Answer play_arrow
  • question_answer195) A graph which has no edges or node is known as

    A) Digraph

    B) Mixed graph

    C) Nullgraph

    D) Multigraph

    View Answer play_arrow
  • question_answer196) If all edges are directed in a graph then it is called as

    A) Null graph

    B) Digraph

    C) Mixed graph

    D) None of these

    View Answer play_arrow
  • question_answer197) Find the greatest value of xyz for positive values of\[x,\,\,y,\,\,z\]subject to the condition\[xy+yz+zx=12\].

    A) 64

    B) 8

    C) 16

    D) 32

    View Answer play_arrow
  • question_answer198) \[a,\,\,b,\,\,c\]are prime numbers,\[x\]is an even number,\[y\]is an odd number. Which of the following is/are never true? I.\[a+x=b\] II.\[b+y=c\] III.\[ab=c\] IV.\[a+b=c\]

    A) I and II

    B) II and III

    C) Only III

    D) III and IV

    View Answer play_arrow
  • question_answer199) \[(p\wedge \tilde{\ }q)\wedge (\tilde{\ }p\wedge q)\]

    A) A tautology

    B) A contradiction

    C) Both a tautology and a contradiction

    D) Neither a tautology nor a contradiction

    View Answer play_arrow
  • question_answer200) \[(\tilde{\ }p\wedge q)\]is logically equivalent to

    A) \[p\to q\]

    B) \[q\to p\]

    C) \[\tilde{\ }(p\to q)\]

    D) \[\tilde{\ }(q\to p)\]

    View Answer play_arrow
  • question_answer201) No sooner he reached home than all the villagers gathered at his home to listen to his story.

    A) would he reach

    B) did he reach

    C) had he reached

    D) No improvement

    View Answer play_arrow
  • question_answer202) Because of his mastery in this field, his suggestions are wide accepted.

    A) are widely accepted

    B) are wide acceptance

    C) have widely accepted

    D) No improvement

    View Answer play_arrow
  • question_answer203) You are warned against committing the same mistake again.

    A) for committing

    B) against to commit

    C) to commit

    D) No improvement

    View Answer play_arrow
  • question_answer204) The teacher gave the students some advice.

    A) advise

    B) advises

    C) advices

    D) No improvement

    View Answer play_arrow
  • question_answer205) I shall ring him tomorrow in the afternoon.

    A) ring to him

    B) ring up to him

    C) ring him up

    D) No improvement

    View Answer play_arrow
  • question_answer206) Directions: In the following questions, out of the four alternatives, choose the one, which best expresses the meaning of the given word. RADIANT

    A) Bright

    B) Beautiful

    C) Plight

    D) Influential

    View Answer play_arrow
  • question_answer207) Directions: In the following questions, out of the four alternatives, choose the one, which best expresses the meaning of the given word. PRUNE

    A) Lend

    B) Reduce

    C) Expand

    D) Prolong

    View Answer play_arrow
  • question_answer208) Directions: In the following questions, out of the four alternatives, choose the one, which best expresses the meaning of the given word. DILETTANTE

    A) Opponent

    B) Specialist

    C) Amateur

    D) Expert

    View Answer play_arrow
  • question_answer209) Directions: In the following questions, out of the four alternatives, choose the one, which best expresses the meaning of the given word. FOSTER

    A) Encourage

    B) Fabricate

    C) Forment

    D) Nurture

    View Answer play_arrow
  • question_answer210) Directions: In the following questions, out of the four alternatives, choose the one, which best expresses the meaning of the given word. ENIGMA

    A) Elusive

    B) Clear

    C) Puzzle

    D) Praise

    View Answer play_arrow
  • question_answer211) Directions: In the following questions, choose the word opposite in meaning to the given word. CONFORM

    A) Disappoint

    B) Reform

    C) Deform

    D) Dissent

    View Answer play_arrow
  • question_answer212) Directions: In the following questions, choose the word opposite in meaning to the given word. ABORIGINAL

    A) Modern

    B) -Popular

    C) Current

    D) Contemporary

    View Answer play_arrow
  • question_answer213) Directions: In the following questions, choose the word opposite in meaning to the given word. AMENABLE

    A) Stubborn

    B) Docile

    C) Obedient

    D) Offensive

    View Answer play_arrow
  • question_answer214) Directions: In the following questions, choose the word opposite in meaning to the given word. ACQUIT

    A) Confirm

    B) Blame

    C) Punish

    D) Indict

    View Answer play_arrow
  • question_answer215) Directions: In the following questions, choose the word opposite in meaning to the given word. FORBIDDEN

    A) Allowed

    B) Prohibited

    C) Agreed

    D) Foresaken

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  • question_answer216) Rahul fought tooth and nail to save his company.

    A) with weapons

    B) as best as he could

    C) using unfair means

    D) with strength and fury

    View Answer play_arrow
  • question_answer217) Mr Roy is known as a shop-lifter in the city commercial centre.

    A) daily visitor

    B) buyer of all new things

    C) smuggler

    D) a thief in guise of customer

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  • question_answer218) We should guard against our green-eyed friends.

    A) rich

    B) jealous

    C) handsome

    D) enthusiastic

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  • question_answer219) This place affords a birds eye view of the green valley below.

    A) beautiful view

    B) general view

    C) narrow view

    D) ugly view

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  • question_answer220) I wont mind even if he goes to dogs.

    A) goes mad

    B) is insulted

    C) is ruined

    D) becomes brutal

    View Answer play_arrow
  • question_answer221) Directions: In the following questions out of the four alternatives, choose the one, which can be substituted for the given words/sentence. A person who lives alone and avoids other people.

    A) Ascetic

    B) Recluse

    C) Unsocial

    D) Agnostic

    View Answer play_arrow
  • question_answer222) Directions: In the following questions out of the four alternatives, choose the one, which can be substituted for the given words/sentence. Explicit undertaking to do something.

    A) Agreement

    B) Decision

    C) Settlement

    D) Promise

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  • question_answer223) Directions: In the following questions out of the four alternatives, choose the one, which can be substituted for the given words/sentence. Murder of a king.

    A) Matricide

    B) Genocide

    C) Regicide

    D) Homicide

    View Answer play_arrow
  • question_answer224) Directions: In the following questions out of the four alternatives, choose the one, which can be substituted for the given words/sentence. A person interested in reading books and nothing else.

    A) Student

    B) Book worn

    C) Scholar

    D) Book-keeper

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  • question_answer225) Directions: In the following questions out of the four alternatives, choose the one, which can be substituted for the given words/sentence. A book or picture produced merely to bring in money.

    A) Money-spinner

    B) Pot-hook

    C) Pot-boiler

    D) Blue-bird

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  • question_answer226) Directions: In the following questions, you have to rearrange the parts P, Q, R and S to produce a proper sentence.

    (P) took place
    (Q) when militants opened fire on BSF men
    (R) the encounter lasting over two hours
    (S) in the town around 8.30 am

    A) QPRS

    B) QSRP

    C) RPQS

    D) RPSQ

    View Answer play_arrow
  • question_answer227) Directions: In the following questions, you have to rearrange the parts P, Q, R and S to produce a proper sentence.

    They are plant eaters
    (P) and various kinds of vegetation
    (Q) browsing on grass
    (R) and consume
    (S) vast quantities of pasture

    A) QPRS

    B) QSRP

    C) RSPQ

    D) RSQP

    View Answer play_arrow
  • question_answer228) Directions: In the following questions, you have to rearrange the parts P, Q, R and S to produce a proper sentence.

    (P) is becomes difficult
    (Q) satisfying our desire
    (R) but once we set about
    (S) if not impossible to restrain them

    A) POPS

    B) QRPS

    C) RQPS

    D) RQSP

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  • question_answer229) Directions: In the following questions, you have to rearrange the parts P, Q, R and S to produce a proper sentence. The captain

    (P) when engaged against the enemy
    (Q) who was himself a brave man
    (R) never to lose heart
    (S) advised the soldiers

    A) PQSR

    B) QPSR

    C) QSRP

    D) SQRP

    View Answer play_arrow
  • question_answer230) Directions: In the following questions, you have to rearrange the parts P, Q, R and S to produce a proper sentence.

    Some remarks
    (P) put the police on the right scent
    (Q) by a woman
    (R) and they discoverd
    (S) casually dropped
    (6) the whole gang of brigands

    A) QSPR

    B) RPSQ

    C) RQSP

    D) SQPR

    View Answer play_arrow
  • question_answer231) Directions: In the following questions, some of the sentences have errors and some have none. Find out which part of a sentence has an error. The letter of that part is your answer. If there is no error, your answer is (d) i.e., No error.

    A) Unless you do not listen to his advice

    B) I am not going

    C) to help you.

    D) No error

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  • question_answer232) Directions: In the following questions, some of the sentences have errors and some have none. Find out which part of a sentence has an error. The letter of that part is your answer. If there is no error, your answer is (d) i.e., No error.

    A) The teacher called Ravi

    B) and asked him

    C) to describe about the incident.

    D) No error

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  • question_answer233) Directions: In the following questions, some of the sentences have errors and some have none. Find out which part of a sentence has an error. The letter of that part is your answer. If there is no error, your answer is (d) i.e., No error.

    A) Be smart

    B) not only in dress

    C) and also inaction.

    D) No error

    View Answer play_arrow
  • question_answer234) Directions: In the following questions, some of the sentences have errors and some have none. Find out which part of a sentence has an error. The letter of that part is your answer. If there is no error, your answer is (d) i.e., No error.

    A) The reason for

    B) his failure is because

    C) he did not work hard.

    D) No error

    View Answer play_arrow
  • question_answer235) Directions: In the following questions, some of the sentences have errors and some have none. Find out which part of a sentence has an error. The letter of that part is your answer. If there is no error, your answer is (d) i.e., No error.

    A) If I was you

    B) I would have

    C) terminated his services them and there.

    D) No error

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  • question_answer236) Directions: In the following questions, groups of four words are given. In each group, one word is wrong spelt. Find the missplet word.

    A) Laudable

    B) Honourable

    C) Lovable

    D) Honourary

    View Answer play_arrow
  • question_answer237) Directions: In the following questions, groups of four words are given. In each group, one word is wrong spelt. Find the missplet word.

    A) Behaviour

    B) Commend

    C) Mentenance

    D) Appraise

    View Answer play_arrow
  • question_answer238) Directions: In the following questions, groups of four words are given. In each group, one word is wrong spelt. Find the missplet word.

    A) Focal

    B) Vocal

    C) Vehical

    D) Mystical

    View Answer play_arrow
  • question_answer239) Directions: In the following questions, groups of four words are given. In each group, one word is wrong spelt. Find the missplet word.

    A) Dairy

    B) Dafodil

    C) Dainty

    D) Damage

    View Answer play_arrow
  • question_answer240) Directions: In the following questions, groups of four words are given. In each group, one word is wrong spelt. Find the missplet word.

    A) Cureable

    B) Currency

    C) Campaign

    D) Chronicle

    View Answer play_arrow

   

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