Solved papers for J & K CET Engineering J and K - CET Engineering Solved Paper-2004

done J and K - CET Engineering Solved Paper-2004

  • question_answer1) The sound wave produced in a gas is always

    A) longitudinal

    B) transverse

    C) stationary

    D) electromagnetic

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  • question_answer2) Source of sound and the observer are mutually at rest. If the speed of sound is changed, then the frequency of sound heard by the observer will appear to be

    A) increased

    B) decreased

    C) unchanged

    D) decreasing exponentially

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  • question_answer3) With what velocity should an observer approach stationary sound source, so that the apparent frequency of sound appear to be double of the initial frequency? (given velocity of sound = v)

    A) \[{{v}_{o}}=\frac{v}{2}\]

    B) \[{{v}_{o}}=3v\]

    C) \[{{v}_{o}}=2v\]

    D) \[{{v}_{o}}=v\]

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  • question_answer4) A charge q is lying at mid-point of the line joining the two similar charges Q. The system will be in equilibrium, if the value of q is

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

    B) \[-\frac{Q}{2}\]

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

    D) \[-\frac{Q}{4}\]

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  • question_answer5) Charges \[2q,\] \[-q\] and \[-q\] lie at the vertices of a triangle. The value of E and Vat the centroid of equilateral triangle will be

    A) \[E\ne 0\]and \[V\ne 0\]

    B) \[E=0\]and \[V=0\]

    C) \[E\ne 0\]and \[V=0\]

    D) \[E=0\] and \[V\ne 0\]

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  • question_answer6) Infinite charges of magnitude q each are lying at \[x=1,2,4,8,...\]metre on X-axis. The value of intensity of electric field at point \[x=0\]due to these charges will be

    A) \[12\times {{10}^{9}}q\,N/C\]

    B) zero

    C) \[6\times {{10}^{9}}q\,N/C\]

    D) \[4\times {{10}^{9}}q\,N/C\]

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  • question_answer7) The capacity of parallel plate capacitor in air and on immersing it into oil is \[50\mu F\] and \[110\mu F\]respectively. The dielectric constant of oil is

    A) \[0.45\]

    B) \[0.55\]

    C) \[1.10\]

    D) \[2.20\]

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  • question_answer8) The energy stored in a condenser is in the form of

    A) kinetic energy

    B) potential energy

    C) elastic energy

    D) magnetic energy

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  • question_answer9) On increasing the plate separation of a charged condenser, the energy

    A) increases

    B) decreases

    C) remains unchanged

    D) becomes zero

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  • question_answer10) The ratio of electric fields on the axis and at equator of an electric dipole will be

    A) \[1:1\]

    B) \[2:1\]

    C) \[4:1\]

    D) \[1:4\]

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  • question_answer11) Some electric bulbs are connected in series across a \[220\text{ }V\]supply in a room. If one bulb is fused, then remaining bulbs are connected again in series across the same supply. The illumination in the room will be

    A) increase

    B) decrease

    C) remain the same

    D) not continuous

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  • question_answer12) If one junction of thermocouple is kept at \[{{0}^{o}}C\]and its emf is given by \[e=at+b{{t}^{2}},\]then the neutral temperature will be

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

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

    C) \[\frac{a}{2b}\]

    D) \[-\frac{a}{2b}\]

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  • question_answer13) A cube is constructed from 12 identical wires. Current enters one comer of the cube and it leaves the opposite comer. If the resistance of each wire is r, then equivalent resistance will be

    A) \[\frac{6\,r}{5}\]

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

    C) \[\frac{5\,r}{12}\]

    D) \[\frac{12\,r}{5}\]

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  • question_answer14) A source of emf \[E=15V\] and having negligible internal resistance, is connected to a variable resistance, so that the current in the circuit increases with time as \[I=1.2t+3\]. Then, the total charge that will flow in first \[5\text{ }s\]will be

    A) \[10\text{ }C\]

    B) \[20\text{ }C\]

    C) \[30\text{ }C\]

    D) \[40\text{ }C\]

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  • question_answer15) The magnetic induction at the centre of a current carrying circular of radius r, is

    A) directly proportional to r

    B) inversely proportional to r

    C) directly proportional to \[{{r}^{2}}\]

    D) inversely proportional to \[{{r}^{2}}\]

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  • question_answer16) A current carrying conductor produces

    A) only electric field

    B) only magnetic field

    C) both electric and magnetic fields

    D) neither electric nor magnetic field

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  • question_answer17) A proton of energy \[8\text{ }eV\]is moving in a circular path in a uniform magnetic field. The energy of an alpha particle moving in the same magnetic field and along the same path will be

    A) \[4\text{ }eV\]

    B) \[2\text{ }eV\]

    C) \[8\,\,eV\]

    D) \[6\,\,eV\]

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  • question_answer18) A \[1\text{ }m\]long wire is lying at right angles to the magnetic field. A force of 1 kg wt. is acting on it in a magnetic field of \[0.98\text{ }T\]. The current flowing in it will be

    A) \[100\text{ }A\]

    B) \[10\text{ }A\]

    C) \[1\text{ }A\]

    D) zero

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  • question_answer19) The resultant magnetic moment of neon atom will be

    A) infinity

    B) \[{{\mu }_{B}}\]

    C) zero

    D) \[\frac{{{\mu }_{B}}}{2}\]

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  • question_answer20) The temperature at which ferromagnetic material becomes paramagnetic is called a

    A) neutral temperature

    B) Curie temperature

    C) inversion temperature

    D) critical temperature

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  • question_answer21) The ultimate individual unit of magnetism in any magnet is called

    A) north pole

    B) south pole

    C) dipole

    D) quadrupole

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  • question_answer22) The power loss in AC circuit will be minimum when

    A) resistance is high, inductance is high

    B) resistance is high, inductance is low

    C) resistance is low, inductance is low

    D) None of the above

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  • question_answer23) At high frequency, the capacitor offer

    A) more reactance

    B) less reactance

    C) zero reactance

    D) infintie reactance

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  • question_answer24) The quantity that. remain unchanged in transformer is

    A) voltage

    B) current

    C) frequency

    D) None of these

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  • question_answer25) A piece of plane glass is placed on a word with letters of different colours. The letters which appear minimum raised are

    A) red

    B) green

    C) yellow

    D) violet

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  • question_answer26) When light waves suffer reflection at the interface between air and glass, the change of phase of the reflected wave is equal to

    A) zero

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

    C) \[\pi \]

    D) \[2\pi \]

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  • question_answer27) If the wavelength of light is \[4000\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,,\] then the number of waves in 1 mm length will be

    A) \[25\]

    B) \[0.25\]

    C) \[0.25\times {{10}^{4}}\]

    D) \[25\times {{10}^{4}}\]

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  • question_answer28) The wave theory of light was given by

    A) Maxwell

    B) Planck

    C) Huygen

    D) Young

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  • question_answer29) In Young's double slit experiment the amplitudes of two sources are \[3a\]and a respectively. The ratio of intensities of bright and dark fringes will be

    A) \[3:1\]

    B) \[4:1\]

    C) \[2:1\]

    D) \[9:1\]

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  • question_answer30) The diffraction effect can be observed in

    A) only sound waves

    B) only light waves

    C) only ultrasonic waves

    D) sound as well as light waves

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  • question_answer31) At what distance from a convex lens of focal length 30 cm, an object should be placed, so that the size of the image be \[\frac{1}{2}th\] of the object?

    A) \[30\,cm\]

    B) \[60\,cm\]

    C) \[15\,cm\]

    D) \[90\,cm\]

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  • question_answer32) Two coherent sources of intensity ratio \[1:4\] produce an interference pattern. The fringe visibility will be

    A) \[1\]

    B) \[0.8\]

    C) \[0.4\]

    D) \[0.6\]

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  • question_answer33) The specific charge of an electron is

    A) \[1.6\times {{10}^{-19}}C\]

    B) \[4.8\times {{10}^{-19}}stat-C\]

    C) \[1.76\times {{10}^{-11}}C/kg\]

    D) \[1.76\times {{10}^{11}}C/kg\]

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  • question_answer34) The colour of the second line of Balmer series is:

    A) blue

    B) yellow

    C) red

    D) violet

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  • question_answer35) If elements with principal quantum number \[n>4\] were not allowed in nature, the number of possible elements would be

    A) \[60\]

    B) \[32\]

    C) \[4\]

    D) \[64\]

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  • question_answer36) The energy of incident photons corresponding to maximum wavelength of visible light is

    A) \[3.2\text{ }eV\]

    B) \[7\,eV\]

    C) \[1.55\text{ }eV\]

    D) \[1\,eV\]

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  • question_answer37) If the work function of potassium is \[2\text{ }eV,\]then its photoelectric threshold wavelength is

    A) \[310\text{ }nm\]

    B) \[620\text{ }nm\]

    C) \[6200\text{ }nm\]

    D) \[3100\text{ }nm\]

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  • question_answer38) Threshold wavelength for a metal\[5200\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]. The photoeletrons will be ejected, if it is irradiated by light from

    A) \[50\text{ }W\]infrared lamp

    B) \[\text{1 }W\] infrared lamp

    C) \[\text{50 }W\] ultraviolet lamp

    D) \[\text{0}\text{.5 }W\] infrared lamp

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  • question_answer39) An electron and a proton are accelerated through the same potential difference. The ratio of their de-Broglie wavelength will be

    A) \[{{\left( \frac{{{m}_{p}}}{{{m}_{e}}} \right)}^{1/2}}\]

    B) \[\frac{{{m}_{e}}}{{{m}_{p}}}\]

    C) \[\frac{{{m}_{p}}}{{{m}_{e}}}\]

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

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  • question_answer40) A particle with rest mass zero is moving with speed c. The de-Broglie wavelength associated with it

    A) zero

    B) infinity

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

    D) \[\frac{{{m}_{0}}c}{h}\]

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  • question_answer41) The nearest distance between two atoms in case of a bcc lattice is equal to

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

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

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

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

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  • question_answer42) Which of the following is an amorphous substance?

    A) Gold

    B) Silver

    C) Copper

    D) Glass

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  • question_answer43) The maximum efficiency of full wave rectifier is

    A) \[100%\]

    B) \[25.20%\]

    C) \[40.6%\]

    D) \[81.2%\]

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  • question_answer44) In a npn-transistor, the collector current is\[10\text{ }mA\]. If \[90%\] of the electrons emitted reach the collector, then the emitter current will be

    A) \[9\,\,mA\]

    B) \[11\,\,mA\]

    C) \[1\,\,mA\]

    D) \[0.1\,\,mA\]

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  • question_answer45) The given truth table is of

    A B X
    0 0 0
    0 1 1
    1 0 1
    1 1 1

    A) OR gate

    B) AND gate

    C) NOT gate

    D) XOR gate

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  • question_answer46) If force (F), length (L) and time (T) are assumed to be the fundamental units, then the dimensional formula of the mass will be

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

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

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

    D) \[[F{{L}^{2}}{{T}^{2}}]\]

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  • question_answer47) The horizontal range of a projectile is \[4\sqrt{3}\] times its maximum height. Its angle of projection will be

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

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

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

    D) \[{{30}^{o}}\]

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  • question_answer48) Two balls of same size but the density of one is greater than that of the other are dropped from the same height, then which ball will reach the earth first (air resistance is negligible)?

    A) Heavy ball

    B) Light ball

    C) Both simultaneously

    D) Will depend upon the density of the balls

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  • question_answer49) A person moves \[30\text{ }m\]north and then \[20\text{ }m\] towards east and finally 30^2 min south-west direction. The displacement of the person from the origin will be

    A) \[10\text{ }m\]along north

    B) \[10\text{ }m\]along south

    C) \[10\text{ }m\] along west

    D) zero

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  • question_answer50) If the velocity of a particle is given by \[v={{(180-16x)}^{1/2}}\,m/s\]. then its acceleration will be

    A) zero

    B) \[8\text{ }m/{{s}^{2}}\]

    C) \[-8\text{ }m/{{s}^{2}}\]

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

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  • question_answer51) Neglecting the air resistance, the time of flight of a projectile is determined by

    A) \[{{U}_{vertical}}\]

    B) \[{{U}_{horizontal}}\]

    C) \[U={{U}_{vertical}}+U_{horizontal}^{2}\]

    D) \[U={{(U_{vertical}^{2}+U_{horizontal}^{2})}^{1/2}}\]

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  • question_answer52) A train is moving towards east and a car is along north, both with same speed. The observed direction of car to the passenger in the train is

    A) east-north direction

    B) west-north direction

    C) south-east direction

    D) None of the above

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  • question_answer53) A body moving with velocity v has momentum and kinetic energy numerically equal. What is the value of v?

    A) \[2\text{ }m/s\]

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

    C) \[1\text{ }m/s\]

    D) \[0.2\text{ }m/s\]

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  • question_answer54) If the kinetic energy of a body becomes four times, then its momentum will be

    A) \[{{P}_{new}}=3{{p}_{initial~}}\]

    B) \[{{P}_{new}}=4{{p}_{initial~}}\]

    C) \[{{P}_{new}}=2{{p}_{initial~}}\]

    D) \[{{P}_{new}}={{p}_{initial~}}\]

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  • question_answer55) A block of mass \[2\text{ }kg\]is lying on an inclined plane, inclined to the horizontal at\[{{30}^{o}}\]. If the coefficient of friction between the block and the plane is \[0.7,\] then magnitude of frictional force acting on the block will be

    A)  \[11.9\text{ }N\]

    B)  \[1.19N\]

    C)  \[0.19\text{ }N\]

    D)  \[11.0\text{ }N\]

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  • question_answer56) A ring of mass m and radius r is melted and then moulded into a sphere. The moment of inertia of the sphere will be

    A) more than that of the ring

    B) less than that of the ring

    C) equal to that of the ring

    D) None of the above

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  • question_answer57) A solid sphere and a hollow sphere of the same material and of a same size can be distinguished without weighing

    A) by determining their moments of inertia about their coaxial axes

    B) by rolling them simultaneously on an inclined plane

    C) by rotating them about a common axis of rotation

    D) by applying equal torque on them

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  • question_answer58) Point masses \[1,\text{ }2,-3\]and \[4\text{ }kg\]are lying at the point \[(0,0,0)\]\[(2,0,0)\]\[(0,3,0)\] and \[(-2,-2,0)\] respectively. The moment of inertia of this system about x-axis will be

    A) \[43\,kg-{{m}^{2}}\]

    B) \[34\,kg-{{m}^{2}}\]

    C) \[27\,kg-{{m}^{2}}\]

    D) \[72\,kg-{{m}^{2}}\]

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  • question_answer59) The radius of gyration of a body about an axis at a distance \[6\text{ }cm\] from its centre of mass is\[10\text{ }cm\]. Then its radius of gyration about a parallel axis through its centre of mass will be

    A) \[80\,\,cm\]

    B) \[8\,\,cm\]

    C) \[0.8\,\,cm\]

    D) \[80\,\,m\]

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  • question_answer60) Two planets of radii in the ratio \[2:3\]are made from the material of density in the ratio\[3:2\]. Then, the ratio of acceleration due to gravity \[\frac{{{g}_{1}}}{{{g}_{2}}}\] at the surface of the two planets will be

    A) \[1\]

    B) \[2.25\]

    C) \[4/9\]

    D) \[0.12\]

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  • question_answer61) If the radius of the earth contracts to half of its present day value without change in mass, then the length of the day will be

    A) \[24\text{ }h\]

    B) \[48\text{ }h\]

    C) \[\text{6 }h\]

    D) \[\text{12 }h\]

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  • question_answer62) A person will get more quantity of matter in kg-wt at

    A) poles

    B) at latitude of \[{{60}^{o}}\]

    C) equator

    D) satellite

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  • question_answer63) The unit of the coefficient of viscosity in SI system is

    A) \[m/kg-s\]

    B) \[~m-s/k{{g}^{2}}\]

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

    D) \[kg/m-s\]

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  • question_answer64) If the excess pressure inside a soap bubble is balanced by oil column of height \[2\text{ }mm,\]then the surface tension of soap solution will be ( \[r=1\text{ }cm\]and density \[d=0.8\text{ }g/\text{ }cc\])

    A) \[3.9\text{ }N/m\]

    B) \[3.9\times {{10}^{-1}}N/m\]

    C) \[3.9\times {{10}^{-2}}N/m\]

    D) \[3.9\,dyne/m\]

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  • question_answer65) A vessel, whose bottom has round holes with diameter of \[1\text{ }mm\]is filled with water. Assuming that surface tension acts only at holes. Then, the maximum height to which the water can be filled in vessel without leakage is (surface tension of water is \[75\times {{10}^{-3}}\text{ }N/m\]and \[g=10\text{ }m/{{s}^{2}}\])

    A) \[3\,cm\]

    B) \[0.3\,cm\]

    C) \[3\text{ }mm\]

    D) \[~3\text{ }m\]

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  • question_answer66) For which of the two pairs, the angle of contact is same?

    A) Water and glass, glass and mercury

    B) Pure water and glass, glass and alcohol

    C) Silver and water, mercury and glass

    D) Silver and chromium, water and chromium

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  • question_answer67) At what temperature the mis velocity of helium molecules will be equal to that of hydrogen moekules at NTP?

    A) \[844\text{ }K\]

    B) \[64\text{ }K\]

    C) \[{{273}^{o}}C\]

    D) \[273\text{ }K\]

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  • question_answer68) Which of the following is unique function of initial and final states?

    A) \[dQ\]

    B) \[dW\]

    C) \[dU\]

    D) \[\Delta Q\,\,and\,\,\Delta W\]

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  • question_answer69) If the initial temperatures of metallic sphere and disc of same radius and nature are equal, then the ratio of their rate of cooling will be

    A) \[1:4\]

    B) \[4:1\]

    C) \[1:2\]

    D) \[2:1\]

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  • question_answer70) What will be the ratio of temperatures of sun and moon, if the wavelengths of their maximum emission radiations rates are \[140\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]and \[4200\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]respectively?

    A) \[1:30\]

    B) \[30:1\]

    C) \[42:14\]

    D) \[14:42\]

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  • question_answer71) A bar magnet is oscillating in the earth's magnetic field with time period T. If its mass is increased four times, then its time period will be

    A) \[4T\]

    B) \[2T\]

    C) \[T\]

    D) \[r\]

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  • question_answer72) The time period of a simple pendulum, when it is made to oscillate on the surface of moon

    A) increases

    B) decreases

    C) remains unchanged

    D) becomes infinite

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  • question_answer73) A condenser of capacity \[20\mu F\] is first charged and then discharged through a \[10\text{ }mH\] inductance. Neglecting the resistance of the coil, the frequency of the resulting vibrations will be

    A) \[356\,cycle/h\]

    B) \[356\,cycle/s\]

    C) \[356\times {{10}^{3}}\,cycle/s\]

    D) \[3.56\,cycle/s\]

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  • question_answer74) Infinite springs with force constants k, 2k, 4k and 8 k... respectively are connected in series. The effective force constant of the spring will be

    A) \[2k\]

    B) \[k\]

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

    D) \[2048\]

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  • question_answer75) The intensity of sound gets reduced by 10% on passing through a slab. The reduction in intensity on passage through three consecutive slabs is

    A) \[30%\]

    B) \[27.1%\]

    C) \[20%\]

    D) \[36%\]

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  • question_answer76) The hydrogen electrode is dipped in a solution of \[pH=3\]at \[25{{\,}^{o}}C.\] The potential of the cell would be (the value of.2.303 RT/F is 0.059 V)

    A) \[~0.177\,V\]

    B) \[~0.087\,V\]

    C) \[~-0.177\,V\]

    D) \[0.059\,V\]

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  • question_answer77) Specific conductivity of a solution

    A) increases with dilution

    B) decreases with dilution

    C) remains unchanged with dilution

    D) depends on mass of electrolyte

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  • question_answer78) \[\text{1 mol}\]of \[{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]is mixed with 2 moles of \[\text{NaOH}\text{.}\]The heat evolved will be

    A) \[57.3\,kJ\]

    B) \[2\times 57.3\,kJ\]

    C) \[57.3/2\,kJ\]

    D) cannot be predicted

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  • question_answer79) In a reversible process, \[\Delta {{S}_{system}}+\Delta {{S}_{\text{surrounding}}}\] is

    A) \[~>0\]

    B) \[<0\]

    C) \[~>0\]

    D) \[=0\]

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  • question_answer80) For the reaction, \[{{N}_{2}}+3{{H}_{2}}2NH;\Delta H=?\]

    A) \[\Delta E=+\,2RT\]

    B) \[\Delta E-\,2RT\]

    C) \[\Delta E+\,RT\]

    D) \[\Delta E-\,RT\]

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  • question_answer81) One mole of a perfect gas expands isothermally to ten times of its original volume. The change in entropy is

    A) 0.1 R

    B) 2.303 R

    C) 10.0 R

    D) 100.0 R

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  • question_answer82) Which of the following solutions will have the highest boiling point?

    A) \[\text{0}\text{.1 M FeC}{{\text{l}}_{\text{3}}}\]

    B) \[\text{0}\text{.1 M BaC}{{\text{l}}_{2}}\]

    C) \[\text{0}\text{.1 M NaCl}\]

    D) \[\text{0}\text{.1}\,\text{M}\,\text{urea}\]

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  • question_answer83) Maximum freezing point falls in

    A) camphor

    B) naphthalene

    C) benzene

    D) water

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  • question_answer84) Azeotropic mixture of \[\text{HCl}\]and water has

    A) \[\text{48 }\!\!%\!\!\text{ HCl}\]

    B) \[\text{ }\!\!~\!\!\text{ 22}\text{.2 }\!\!%\!\!\text{ HCl}\]

    C) \[\text{36 }\!\!%\!\!\text{ HCl}\]

    D) \[\text{ }\!\!~\!\!\text{ 20}\text{.2 }\!\!%\!\!\text{ HCl}\]

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  • question_answer85) Vapour pressure of dilute aqueous solution of glucose is 750 mm of mercury at 373 K. The mole fraction of solute is

    A) \[\frac{1}{76}\]

    B) \[\frac{1}{7.6}\]

    C) \[\frac{1}{38}\]

    D) \[\frac{1}{10}\]

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  • question_answer86) Volume of \[\text{0}\text{.1}\,\text{M}\,{{\text{K}}_{\text{2}}}\text{C}{{\text{r}}_{\text{2}}}{{\text{O}}_{\text{7}}}\] required to oxidize 35 mL of \[\text{0}\text{.5 M FeS}{{\text{O}}_{\text{4}}}\]solution is

    A) 29.2 mL

    B) 17.5 mL

    C) 175 mL

    D) 145 Ml

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  • question_answer87) \[100\,cc\]of \[\text{0}\text{.6}\,\text{N}\,{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]and \[\text{200 cc}\]of \[\text{0}\text{.3}\,\text{N}\,\text{HCl}\]were mixed together. The normality of the solution will be

    A) 0.2 N

    B) 0.4 N

    C) 0.8 N

    D) 0.6 N

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  • question_answer88) The rate of diffusion of a gas is proportional to

    A) \[\frac{p}{\sqrt{d}}\]

    B) \[\sqrt{\frac{p}{d}}\]

    C) \[\frac{p}{d}\]

    D) \[\frac{\sqrt{p}}{d}\]

    View Answer play_arrow
  • question_answer89) Molar volume of \[\text{C}{{\text{O}}_{\text{2}}}\]is maximum at

    A) NTP

    B) \[\text{0}{{\,}^{o}}\text{C}\]and 2.0 atm

    C) \[127{{\,}^{o}}C\] and\[\text{ }\!\!~\!\!\text{ 1 atm}\]

    D) \[~273{{\,}^{o}}C\] and \[2.0\,\text{atm}\]

    View Answer play_arrow
  • question_answer90) Number of atoms of oxygen present in 10.6 g of \[\text{N}{{\text{a}}_{\text{2}}}\text{C}{{\text{O}}_{\text{3}}}\]will be

    A) \[6.02\times {{10}^{23}}\]

    B) \[12.04\times {{10}^{22}}\]

    C) \[1.806\times {{10}^{23}}\]

    D) \[31.80\times {{10}^{2}}\]

    View Answer play_arrow
  • question_answer91) The equilibrium \[{{P}_{4}}(s)+6C{{l}_{2}}(g)\rightleftharpoons 4PC{{l}_{3}}(g)\]is attained by mixing equal moles of\[{{\text{P}}_{\text{4}}}\]and\[\text{C}{{\text{l}}_{\text{2}}}\]in an evacuated vessel. Then, at equilibrium

    A) \[[C{{l}_{2}}]>[PC{{l}_{3}}]\]

    B) \[[C{{l}_{2}}]>[{{P}_{4}}]\]

    C) \[[{{P}_{4}}]>[C{{l}_{2}}]\]

    D) \[[PC{{l}_{3}}]>[{{P}_{4}}]\]

    View Answer play_arrow
  • question_answer92) The activation energy for most of the reactions is approximately \[50\,\text{kJ}\,\text{mo}{{\text{l}}^{-1}}.\] The value of temperature coefficient for such reactions is

    A) \[~>2\]

    B) \[~>3\]

    C) \[~<\,\,1\]

    D) \[~>4\]

    View Answer play_arrow
  • question_answer93) If the mass defect of \[_{\text{4}}^{\text{9}}\text{X}\]is\[\text{0}\text{.090 u,}\] then binding energy per nucleon is \[\text{(1}\,\text{u}\,\text{=}\,\text{931}\text{.5}\,\text{MeV)}\]

    A) \[\text{9}\text{.315 MeV}\]

    B) \[\text{ }\!\!~\!\!\text{ 931}\text{.5 MeV}\]

    C) \[\text{ }\!\!~\!\!\text{ 83}\text{.0 MeV}\]

    D) \[\text{ }\!\!~\!\!\text{ 8}\text{.38 MeV}\]

    View Answer play_arrow
  • question_answer94) \[\text{50 mL}\]of\[\text{0}\text{.1}\,\text{M}\,\text{HCl}\] and 50 mL of 0.2 M \[\text{NaOH}\] are mixed. The pH of the resulting solution is

    A) 1.30

    B) 4.2

    C) 12.70

    D) 11.70

    View Answer play_arrow
  • question_answer95) A substance \[{{A}_{x}}{{B}_{y}}\]crystallises in a face centred cubic lattice in which A atom occupies each comer of cube and atom B occupies the centres of each face of the cube. Identify the correct composition of the substance \[{{A}_{x}}{{B}_{y}}.\]

    A) \[A{{B}_{3}}\]

    B) \[{{A}_{4}}{{B}_{3}}\]

    C) \[{{A}_{3}}B\]

    D) composition cannot be specified

    View Answer play_arrow
  • question_answer96) In coagulating the colloidal solution of \[\text{A}{{\text{s}}_{\text{2}}}{{\text{S}}_{\text{3}}}\]which has the maximum coagulating value?

    A) \[\text{NaCl}\]

    B) \[KCl\]

    C) \[BaC{{l}_{2}}\]

    D) \[AlC{{l}_{3}}\]

    View Answer play_arrow
  • question_answer97) Which of the following is the strongest oxidising agent?

    A) \[HOCl\]

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

    C) \[HCl{{O}_{3}}\]

    D) \[HCl{{O}_{4}}\]

    View Answer play_arrow
  • question_answer98) In the equation \[4M+8C{{N}^{-}}+2{{H}_{2}}O+{{O}_{2}}\xrightarrow{{}}4{{[M{{(CN)}_{2}}]}^{-}}\] \[+\,4\,O{{H}^{-}}\] Identify the metal M.

    A) copper

    B) iron

    C) silver

    D) zinc

    View Answer play_arrow
  • question_answer99) The formula of azurite is

    A) \[CuC{{O}_{3}}.Cu{{(OH)}_{2}}\]

    B) \[2CuC{{O}_{3}}.Cu{{(OH)}_{2}}\]

    C) \[CuC{{O}_{3}}.2Cu{{(OH)}_{2}}\]

    D) \[CuS{{O}_{4}}.Cu{{(OH)}_{2}}\]

    View Answer play_arrow
  • question_answer100) The decreasing order of bond angle is

    A) \[N{{O}_{2}}>NO_{2}^{+}>NO_{2}^{-}\]

    B) \[NO_{2}^{-}>N{{O}_{2}}>NO_{2}^{+}\]

    C) \[NO_{2}^{+}>N{{O}_{2}}>NKO_{2}^{-}\]

    D) \[NO_{2}^{+}>NO_{2}^{-}>N{{O}_{2}}\]

    View Answer play_arrow
  • question_answer101) The fresh precipitate can be transformed in colloidal state by

    A) peptization

    B) coagulation

    C) diffusion

    D) none of these

    View Answer play_arrow
  • question_answer102) Milk is

    A) fat disperse4 in water

    B) fat dispersed in milk

    C) fat dispersed in fat

    D) water dispersed in milk

    View Answer play_arrow
  • question_answer103) Purest form of iron is

    A) cast iron

    B) pig iron

    C) wrought iron

    D) steel

    View Answer play_arrow
  • question_answer104) Most unstable hydride is

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

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

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

    D) \[~Bi{{H}_{3}}\]

    View Answer play_arrow
  • question_answer105) Out of the following metals that cannot be obtained by electrolysis of the aqueous solution of its salts is

    A) Ag

    B) Cr

    C) Cu

    D) Mg

    View Answer play_arrow
  • question_answer106) \[\text{KI}\]and \[\text{CuS}{{\text{O}}_{\text{4}}}\]solution when mixed gives

    A) \[Cu{{l}_{2}}+{{K}_{2}}S{{O}_{4}}\]

    B) \[C{{u}_{2}}{{I}_{2}}+{{K}_{2}}S{{O}_{4}}\]

    C) \[{{K}_{2}}S{{O}_{4}}+C{{u}_{2}}{{I}_{2}}+{{I}_{2}}\]

    D) \[{{K}_{2}}S{{O}_{4}}+Cu{{I}_{2}}+{{I}_{2}}\]

    View Answer play_arrow
  • question_answer107) The strongest reducing agent among the following is

    A) \[{{F}^{-}}\]

    B) \[C{{l}^{-}}\]

    C) \[B{{r}^{-}}\]

    D) \[{{I}^{-}}\]

    View Answer play_arrow
  • question_answer108) \[\text{Xe}{{\text{F}}_{\text{6}}}\]on complete hydrolysis gives

    A) \[\text{Xe}\]

    B) \[\text{ }\!\!~\!\!\text{ Xe}{{\text{O}}_{\text{2}}}\]

    C) \[Xe{{O}_{3}}\]

    D) \[\text{ }\!\!~\!\!\text{ Xe}{{\text{O}}_{\text{4}}}\]

    View Answer play_arrow
  • question_answer109) The correct name of the compound\[[Cu{{(N{{H}_{3}})}_{4}}]{{(N{{O}_{3}})}_{2}},\]according to IUPAC system is

    A) cuprammonium nitrate

    B) tetrammine copper(II) dinitrate

    C) tetrammine copper(II) nitrate

    D) tetrammine copper(II) dinitrite

    View Answer play_arrow
  • question_answer110) Which of the following complex species does not involve inner orbital hybridisation?

    A) \[{{[Co{{F}_{6}}]}^{3-}}\]

    B) \[{{[Co{{(N{{H}_{3}})}_{6}}]}^{3+}}\]

    C) \[{{[Fe{{(CN)}_{6}}]}^{3-}}\]

    D) \[{{[Cr{{(N{{H}_{3}})}_{6}}]}^{3+}}\]

    View Answer play_arrow
  • question_answer111) \[{{\,}_{\text{27}}}\text{C}{{\text{o}}^{\text{60}}}\]is radioactive because

    A) its atomic number is high

    B) it has high \[\frac{p}{n}\]ratio

    C) it has high\[\frac{n}{p}\]ratio

    D) none of the above

    View Answer play_arrow
  • question_answer112) The correct order of solubility of the sulphates of alkaline earth metals in water is

    A) \[~Be>Ca>Mg>Ba>Sr\]

    B) \[~Mg>Be>Ba>Ca>Sr\]

    C) \[Be>Mg>Ca>Sr>Ba\]

    D) \[Mg>Ca>Ba>Be>Sr\]

    View Answer play_arrow
  • question_answer113) Correct order of radii is

    A) \[N<Be<B\]

    B) \[{{F}^{-}}<{{O}^{2-}}<{{N}^{3-}}\]

    C) \[Na<Li<K\]

    D) \[F{{e}^{3+}}<F{{e}^{2+}}<F{{e}^{4+}}\]

    View Answer play_arrow
  • question_answer114) A sudden large jump between the values of first and second ionisation energies of elements would be associated with which of the following electronic configurations?

    A) \[1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},3{{s}^{1}}\]

    B) \[1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},3{{s}^{2}}3{{p}^{1}}\]

    C) \[1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},3{{s}^{1}}3{{p}^{2}}\]

    D) \[1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},3{{s}^{2}}\]

    View Answer play_arrow
  • question_answer115) Which one shows most pronounced inert pair effect?

    A) \[\text{Si}\]

    B) \[Sn\]

    C) \[Pb\]

    D) C

    View Answer play_arrow
  • question_answer116) Which of the following will form a colourless complex?

    A) \[N{{i}^{2+}}\]

    B) \[C{{u}^{+}}\]

    C) \[T{{i}^{2+}}\]

    D) \[F{{e}^{3+}}\]

    View Answer play_arrow
  • question_answer117) Silver containing lead as impurity is purified by

    A) poling

    B) cupellation

    C) lavigation

    D) distillation

    View Answer play_arrow
  • question_answer118) The metal extracted by cyanide process is

    A) silver

    B) copper

    C) iron

    D) sodium

    View Answer play_arrow
  • question_answer119) On the extraction of iron, the slag produced is

    A) \[CO\]

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

    C) \[MgSi{{O}_{3}}\]

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

    View Answer play_arrow
  • question_answer120) Complex forming tendency is more for

    A) \[N{{a}^{+}}\]

    B) \[{{K}^{+}}\]

    C) \[L{{i}^{+}}\]

    D) \[R{{b}^{+}}\]

    View Answer play_arrow
  • question_answer121) In the reaction, The major product A is

    A)

    B)

    C)

    D)

    View Answer play_arrow
  • question_answer122) The IUPAC name of the following compound is

    A) propionic anhydride

    B) dipropanoic anhydride

    C) ethoxy propanoic acid

    D) propanoic anhydride

    View Answer play_arrow
  • question_answer123) Which of the following compounds is not aromatic?

    A)

    B)

    C)

    D)

    View Answer play_arrow
  • question_answer124) Which of the following is the most stable cation?

    A) \[{{F}_{3}}C-CH_{2}^{\oplus }\]

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

    C) \[CH_{3}^{\oplus }\]

    D) \[CF_{3}^{\oplus }\]

    View Answer play_arrow
  • question_answer125) The product A is

    A)

    B)

    C)

    D)

    View Answer play_arrow
  • question_answer126) Tautomerism is not exhibited by

    A)

    B)

    C)

    D)

    View Answer play_arrow
  • question_answer127) In the compound Configuration at \[{{C}_{2}}\]and \[{{C}_{3}}\]atoms are

    A) \[S,S\]

    B) \[R,S\]

    C) \[S,R\]

    D) \[R,R\]

    View Answer play_arrow
  • question_answer128) The product A is

    A)

    B)

    C)

    D)

    View Answer play_arrow
  • question_answer129) Hinsberg reagent is

    A) \[{{C}_{6}}{{H}_{S}}S{{O}_{3}}H\]

    B) \[{{C}_{6}}{{H}_{5}}NO\]

    C) \[{{C}_{6}}{{H}_{5}}S{{O}_{2}}Cl\]

    D) \[{{C}_{6}}{{H}_{5}}{{N}_{2}}Cl\]

    View Answer play_arrow
  • question_answer130) Acetaldehyde cannot show

    A) lodoform test

    B) Lucas test

    C) Benedict's test

    D) Toilers test

    View Answer play_arrow
  • question_answer131) Ethylbenzene with bromine in presence of \[\text{FeB}{{\text{r}}_{\text{3}}}\text{,}\]predominantly gives

    A)

    B)

    C)

    D)

    View Answer play_arrow
  • question_answer132) Which of the following will be most readily dehydrated under acidic conditions?

    A)

    B)

    C)

    D)

    View Answer play_arrow
  • question_answer133) Which of the following cannot reduce Fehling solution?

    A) \[\text{HCOOH}\]

    B) \[\text{ }\!\!~\!\!\text{ }{{\text{H}}_{\text{3}}}\text{CCOOH}\]

    C) \[\text{HCHO}\]

    D) \[~{{H}_{3}}CCHO\]

    View Answer play_arrow
  • question_answer134) Absolute alcohol is prepared by

    A) vacuum distillation

    B) azeotropic distillation

    C) steam distillation

    D) none of the above

    View Answer play_arrow
  • question_answer135) Which of the following compounds is resistant to nucleophilic attack by hydroxyl ion?

    A) Methylacetate

    B) Acetonitrile

    C) Acetamide

    D) Diethyl ether

    View Answer play_arrow
  • question_answer136) Hydrogenation of benzoyl chloride in presence of Pd on\[\text{BaS}{{\text{O}}_{\text{4}}}\]gives

    A) benzyl alcohol

    B) benzaldehyde

    C) benzoicacid

    D) phenol

    View Answer play_arrow
  • question_answer137) \[Ph-C\equiv C-C{{H}_{3}}\xrightarrow{H{{g}^{2+}}/{{H}^{+}}}A\]The product A is

    A)

    B)

    C)

    D)

    View Answer play_arrow
  • question_answer138) Ethyl amine reacts with nitrous acid to form

    A) \[{{C}_{2}}{{H}_{5}}OH\]

    B) \[{{C}_{2}}{{H}_{5}}OH,{{N}_{2}},{{H}_{2}}O\]

    C) \[{{C}_{2}}{{H}_{5}}N_{2}^{+}C{{l}^{-}}\]

    D) \[{{C}_{2}}{{H}_{5}}NHOH,N{{H}_{3}}\]

    View Answer play_arrow
  • question_answer139) Rice is deficient in

    A) lysine

    B) alanine

    C) glycine

    D) leucine

    View Answer play_arrow
  • question_answer140) Mutarotation does not occur in

    A) sucrose

    B) D-glucose

    C) L-glucose

    D) none of these

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  • question_answer141) Aldehyde which is formed during photo synthesis of plants is

    A) methanol

    B) acetaldehyde

    C) propanal

    D) phenylmethanal

    View Answer play_arrow
  • question_answer142) Coupling of diazonium salts of following takes place in the order

    A) \[IV<II<III<I\]

    B) \[IV>III<II<I\]

    C) \[II<IV<I<III\]

    D) \[I<II<III<IV\]

    View Answer play_arrow
  • question_answer143) Which is decreasing order of strength of bases? \[\bar{O}H,\bar{N}{{H}_{2}},HC\equiv {{C}^{-}}\]and \[C{{H}_{3}}CH_{2}^{-}\]

    A) \[{{H}_{3}}CCH_{2}^{-}>NH_{2}^{-}>HC\equiv {{C}^{-}}>O{{H}^{-}}\]

    B) \[HC\equiv {{C}^{-}}>C{{H}_{3}}CH_{2}^{-}>NH_{2}^{-}>O{{H}^{-}}\]

    C) \[O{{H}^{-}}>NH_{2}^{-}>C{{H}^{-}}>{{H}_{3}}CCH_{2}^{-}\]

    D) \[NH_{2}^{-}>HC\equiv {{C}^{-}}>O{{H}^{-}}>{{H}_{3}}CCH_{2}^{-}\]

    View Answer play_arrow
  • question_answer144) The reagent that reacts with nitromethane to form methyl hydroxylamine is

    A) \[Zn/HCl\]

    B) \[Zn/N{{H}_{4}}Cl\]

    C) \[Zn/NaOH\]

    D) \[Sn/HCl\]

    View Answer play_arrow
  • question_answer145) Which is most basic?

    A) \[{{C}_{6}}{{H}_{5}}N{{H}_{2}}\]

    B) \[({{C}_{6}}{{H}_{5}}N{{H}_{2}})\]

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

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

    View Answer play_arrow
  • question_answer146) For d-electron, the orbital angular momentum is

    A) \[\frac{\sqrt{6}h}{2\pi }\]

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

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

    D) \[\frac{2h}{\pi }\]

    View Answer play_arrow
  • question_answer147) Two nodal planes are present in

    A) \[{{\pi }^{*}}2{{p}_{x}}\]

    B) \[\sigma 2{{p}_{z}}\]

    C) \[\pi 2{{p}_{x}}\]

    D) \[\pi 2{{p}_{y}}\]

    View Answer play_arrow
  • question_answer148) One gram mole of a gas at NTP occupies 22.4 L. This fact was derived from

    A) law of gaseous volumes

    B) Avogadro's hypothesis

    C) Berzelius hypothesis

    D) Dalton's atomic theory

    View Answer play_arrow
  • question_answer149) At\[\text{90}{{\,}^{\text{o}}}\text{C,}\] pure water has\[[{{H}_{3}}{{O}^{+}}]={{10}^{-6}}\,mol/L.\] The value of \[{{K}_{w}}\]at \[\text{90}{{\,}^{\text{o}}}\text{C}\]is

    A) \[{{10}^{-6}}\]

    B) \[{{10}^{-8}}\]

    C) \[{{10}^{-12}}\]

    D) \[{{10}^{-14}}\]

    View Answer play_arrow
  • question_answer150) The pH of a buffer solution of \[\text{0}\text{.1}\,\text{M}\,\text{N}{{\text{H}}_{\text{4}}}\text{OH}\]\[\text{ }\!\![\!\!\text{ p}{{\text{K}}_{b}}\text{=5}\text{.0 }\!\!]\!\!\text{ }\]and \[\text{0}\text{.01}\,\text{M}\,\text{N}{{\text{H}}_{\text{4}}}\text{Cl}\]is

    A) 1

    B) 4

    C) 10

    D) 13

    View Answer play_arrow
  • question_answer151) If a point \[(a{{t}^{2}},\,\,2at)\] be the extremity of a focal Chord of parabola \[{{y}^{2}}=4ax,\] then the length of the focal chord is

    A) \[a{{\left( t+\frac{1}{t} \right)}^{2}}\]

    B) \[a{{\left( t+\frac{2}{t} \right)}^{3}}\]

    C) \[a{{\left( t+\frac{1}{t} \right)}^{3}}\]

    D) None of these

    View Answer play_arrow
  • question_answer152) In a test, an examines either guesses or copies or knows the answer to a multiple choice questions with four choices. The probability that he makes a guess; is \[\frac{1}{3}\] and the probability that he copies the answer is \[\frac{1}{6}\].The probability that his answer is correct given that he copied it is\[\frac{1}{8}\]. The probability that his answer is correct, given that he guessed it is\[\frac{1}{4}\]. The probability that they knew the answer to the questions given that he correctly answered is

    A) \[\frac{24}{31}\]

    B) \[\frac{31}{24}\]

    C) \[\frac{24}{29}\]

    D) \[\frac{29}{24}\]

    View Answer play_arrow
  • question_answer153) Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral is equal to

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

    B) \[\frac{1}{5}\]

    C) \[\frac{1}{10}\]

    D) \[\frac{1}{20}\]

    View Answer play_arrow
  • question_answer154) The value of \[\underset{n\to \infty }{\mathop{\lim }}\,\,\cos \left( \frac{x}{2} \right)\cos \left( \frac{x}{4} \right)\,\cos \left( \frac{x}{8} \right).....\,\cos \left( \frac{x}{{{2}^{n}}} \right)\]Is

    A) \[\frac{x}{\sin \,x}\]

    B) \[\frac{x}{\cos \,x}\]

    C) \[\frac{(\sin x)}{x}\]

    D) \[\frac{(cosx)}{x}\]

    View Answer play_arrow
  • question_answer155) The order and degree of the differential equation \[y=\frac{dy}{dx}x+\sqrt{{{a}^{2}}{{\left( \frac{dy}{dx} \right)}^{2}}+{{b}^{2}}}\] is

    A) \[3,1\]

    B) \[1,2\]

    C) \[2,1\]

    D) \[1,3\]

    View Answer play_arrow
  • question_answer156) \[y=a{{e}^{mx}}+b{{e}^{-mx}}\] satisfies which of the following differential equations

    A) \[\frac{dy}{dx}-my=0\]

    B) \[\frac{dy}{dx}+my=0\]

    C) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-{{m}^{2}}y=0\]

    D) None of these

    View Answer play_arrow
  • question_answer157) If \[f(x)={{\left( \frac{x}{1-|x|} \right)}^{1/2002}},\] then \[{{D}_{f}}\] is

    A) \[R-[-1,\,1]\]

    B) \[\{-\infty ,1\}\]

    C) \[\{-\infty ,-1\}\cup (0,1)\]

    D) None of the above

    View Answer play_arrow
  • question_answer158) If \[\vec{a},\vec{b},\vec{c}\] are the unit vectors such that \[\vec{a}\] is perpendicular to the plane \[\vec{b},\vec{c}\] and the angle between \[\vec{b},\vec{c}\] is \[\frac{\pi }{3},\] then \[|\vec{a}+\vec{b}+\vec{c}|\]is equal to

    A) \[0\]

    B) \[\pm 1\]

    C) \[\pm \,2\]

    D) \[\pm \,3\]

    View Answer play_arrow
  • question_answer159) \[\int_{\alpha }^{\beta }{\sqrt{\frac{x-\alpha }{\beta -x}}}\,dx\] is equal to

    A) \[\frac{\pi }{2}(\alpha -\beta )\]

    B) \[\frac{\pi }{2}(\beta -\alpha )\]

    C) \[\pi (\alpha -\beta )\]

    D) \[\pi (\beta -\alpha )\]

    View Answer play_arrow
  • question_answer160) If \[{{a}_{1}},{{a}_{2}}{{a}_{3}},{{a}_{4}},{{a}_{5}},{{a}_{6}}\] are in, AP with common difference \[d\ne 0,\] .then the system of equations \[{{a}_{1}}x+{{a}_{2}}y={{a}_{3}},{{a}_{4}}x+{{a}_{5}}y={{a}_{6}}\]has

    A) infinite number of solutions

    B) unique solution

    C) no solution

    D) cannot say anything

    View Answer play_arrow
  • question_answer161) If the value of \[{{\int_{0}^{\pi }{\left( \frac{x}{1+\sin \,x} \right)}}^{2}}dx=1,\] then the value of the integral \[\int_{0}^{\pi }{\left[ \frac{2{{x}^{2}}\,{{\cos }^{2}}\,x/2}{{{(1+\sin \,x)}^{2}}} \right]}dx\] is equal to

    A) \[1+\pi (2-\pi )\]

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

    C) \[1+\pi (2+\pi )\]

    D) \[1-\pi (2+\pi )\]

    View Answer play_arrow
  • question_answer162) \[\int_{-1}^{1}{(x-[x])\,dx}\] is equal to

    A) \[0\]

    B) \[1\]

    C) \[2\]

    D) \[3\]

    View Answer play_arrow
  • question_answer163) If the normal at ?t? on the parabola \[{{y}^{2}}=4ax\] meets the parabola again at t', then

    A) \[t'=-t-\frac{2}{t}\]

    B) \[t'=-t+\frac{2}{t}\]

    C) \[t'=-t'-\frac{2}{t'}\]

    D) \[t'+t'+2tt'\]

    View Answer play_arrow
  • question_answer164) The complex numbers having positive argument and satisfying \[|2-3i|\,\,<\] is

    A) \[\frac{12}{5}+\frac{16}{5}\,i\]

    B) \[\frac{4}{5}+\frac{6}{5}\,i\]

    C) \[\frac{6}{5}-\frac{5}{2}\,i\]

    D) None of these

    View Answer play_arrow
  • question_answer165) The value of \[\int_{0}^{\pi /2}{\log \,\,\tan \,x\,\,dx}\] is

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

    B) \[\infty \]

    C) \[1\]

    D) \[0\]

    View Answer play_arrow
  • question_answer166) Given that. \[\tan \,\,A\] and \[\tan \,\,B\] are the roots of \[{{x}^{2}}-px+q=0,\] then the value of \[{{\sin }^{2}}(A+B)\]is

    A) \[\frac{{{p}^{2}}}{\{{{p}^{2}}+{{(1-q)}^{2}}\}}\]

    B) \[\frac{{{q}^{2}}}{({{p}^{2}}+{{q}^{2}})}\]

    C) \[\frac{{{q}^{2}}}{\{{{p}^{2}}-(1-{{q}^{2}})\}}\]

    D) \[\frac{{{p}^{2}}}{({{p}^{2}}+{{q}^{2}})}\]

    View Answer play_arrow
  • question_answer167) The least positive non-integral solution of \[\sin \,\,\pi ({{x}^{2}}+x)-\sin \,\pi {{x}^{2}}=0\]is

    A) rational

    B) irrational of the from \[\sqrt{P}\]

    C) irrational of the from \[\frac{\sqrt{P}-1}{4}\]when p is an odd integer

    D) irrational of the from \[\frac{\sqrt{P}+1}{4}\] where p is an even integer

    View Answer play_arrow
  • question_answer168) The general solution of \[\frac{dy}{dx}=\frac{2x-y}{x+2y}\] is

    A) \[{{x}^{2}}-xy+{{y}^{2}}=c\]

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

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

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

    View Answer play_arrow
  • question_answer169) A function \[y=f(x)\] has second order derivative \[f''(x)=6(x-1)\]. If its graph passes through the point \[(2,1)\] and at that point the tangent to the graph is \[y=3x-5,\] then the function is

    A) \[{{(x-1)}^{2}}\]

    B) \[{{(x-1)}^{3}}\]

    C) \[{{(x+1)}^{3}}\]

    D) \[{{(x+1)}^{2}}\]

    View Answer play_arrow
  • question_answer170) If \[f(x)\] is a function satisfying \[f\left( \frac{1}{x} \right)+{{x}^{2}}f(x)=0\]for all non-zero x, then \[\int_{\sin \,\theta }^{\text{cosec }\theta }{f(x)\,\,dx}\]is equal to

    A) \[0\]

    B) \[1\]

    C) \[2\]

    D) \[3\]

    View Answer play_arrow
  • question_answer171) The area bounded by the curves \[{{x}^{2}}+{{y}^{2}}=25,\] \[4y=|4-{{x}^{2}}|\] and \[x=0\] above the x- axis is

    A) \[24\,\,{{\sin }^{-1}}\left( \frac{4}{5} \right)\]

    B) \[25\,\,{{\sin }^{-1}}\left( \frac{4}{5} \right)\]

    C) \[2+\frac{25}{2}{{\sin }^{-1}}\left( \frac{4}{5} \right)\]

    D) None of these

    View Answer play_arrow
  • question_answer172) The curve in which the sub tangent is always bisected at the origin is

    A) A parabola

    B) A circle

    C) A hyperbola

    D) None of these

    View Answer play_arrow
  • question_answer173) The value of \[\int_{0}^{\pi /2}{{{\sin }^{8}}\,x\,\,dx}\] is

    A) \[\frac{105\,\pi }{32(4!)}\]

    B) \[\frac{105\,\pi }{14\,(4!)}\]

    C) \[\frac{105\,}{16\pi \,(4!)}\]

    D) None of these

    View Answer play_arrow
  • question_answer174) A particle is moving in a straight line such that the distance described ?s' and the time taken ?t? are given by \[t=a{{s}^{2}}+bs+c,\,\,\,a>0.\]If v is the velocity of the particle at any time t, then acceleration is

    A) \[-2av\]

    B) \[-2av\]

    C) \[-2av\]

    D) None of these

    View Answer play_arrow
  • question_answer175) If the vectors \[\vec{a}=(c\,\,{{\log }_{2}}\,x)\,\hat{i}-6\hat{j}+3\hat{k}\] and \[\vec{b}=({{\log }_{2}}x)\hat{i}+2\hat{j}+(2c\,{{\log }_{2}}\,x)\hat{k}\] make an obtuse angle for any \[x\,\in \,(0,\infty ),\] then the interval of which 'c? belongs

    A) \[\left( \frac{4}{3},0 \right)\]

    B) \[\left( -\frac{4}{3},0 \right)\]

    C) \[\left( \frac{3}{4},0 \right)\]

    D) \[\left( -\frac{3}{4},0 \right)\]

    View Answer play_arrow
  • question_answer176) Two forces of magnitude 5 and 3 units acting in the directions \[6\hat{i}+2\hat{j}+3\hat{k}\]and \[3\hat{i}-2\hat{j}+6\hat{k}\] respectively act on a particle which is displaced from the point \[(2,2,\,-1)\] to \[(4,3,1)\]. The work done by the forces is

    A) \[\frac{149}{7}\]

    B) \[\frac{148}{6}\]

    C) \[\frac{148}{7}\]

    D) None of these

    View Answer play_arrow
  • question_answer177) The image of the point \[P(1,3,4)\] in the plane \[2x-y+z+3=0\] is

    A) \[(3,\,5,\,-2)\]

    B) \[(-3,\,5,2)\]

    C) \[(3,-\,5,2)\]

    D) \[(3,\,5,2)\]

    View Answer play_arrow
  • question_answer178) If E and F are two events with \[P(E)\le P(F)>0,\]then

    A) occurrence of \[E\Rightarrow \]occurrence of F

    B) Occurrence of \[F\Rightarrow \]occurrence of?

    C) Non-occurrence of \[E\Rightarrow \]non-occurrence of F

    D) None of the above implications hold

    View Answer play_arrow
  • question_answer179) If the normal to the parabola \[{{x}^{2}}=-4ay\] at the points \[({{x}_{1}},\,{{y}_{1}}),\,({{x}_{2}},{{y}_{2}})\] and \[({{x}_{3}},{{y}_{3}})\] are concurrent, then

    A) \[{{y}_{1}}+{{y}_{2}}+{{y}_{3}}=0\]

    B) \[{{x}_{1}}{{x}_{2}}+{{x}_{2}}{{x}_{2}}+{{x}_{3}}{{x}_{1}}=0\]

    C) \[{{x}_{1}}+{{x}_{2}}+{{x}_{3}}=0\]

    D) \[{{x}_{1}}{{y}_{1}}+{{x}_{2}}{{y}_{2}}+{{x}_{3}}{{y}_{3}}=0\]

    View Answer play_arrow
  • question_answer180) If the sum of n terms of the series \[1+\frac{4}{5}+\frac{7}{{{5}^{2}}}+\frac{10}{{{5}^{3}}}+.....\] is \[l+\frac{15}{16}\left( 1-\frac{1}{{{5}^{n-1}}} \right)-\frac{(3n-2)}{4({{5}^{n-1}})},\] then is

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

    B) \[\frac{5}{4}\]

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

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

    View Answer play_arrow
  • question_answer181) It the sides of a triangle are in GP and the largest angle is twice the smallest angle, then the common ratio which is greater than one lies in the interval

    A) \[(1,\,\sqrt{3})\]

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

    C) \[\left( 1,\frac{\sqrt{5}+1}{2} \right)\]

    D) None of these

    View Answer play_arrow
  • question_answer182) If \[f(x)\] is a differentiable function, then \[\underset{x\to a}{\mathop{\lim }}\,\frac{af\,(x)-x\,f(a)}{x-a}\] is equal to

    A) \[af'\,(a)-f(a)\]

    B) \[af\,\,(a)+f'(a)\]

    C) \[af'\,(a)+f(a)\]

    D) \[af\,(a)-f'(a)\]

    View Answer play_arrow
  • question_answer183) The locus represented by the equation \[|z-1|=|z-i|\] is

    A) a circle of radius 1

    B) an ellipse with foci at 1 and \[-i\]

    C) a line through the origin

    D) a circle on the line joining 1 and \[-i\] as diameter

    View Answer play_arrow
  • question_answer184) The rank of the matrix \[\left| \begin{matrix} 4 & 2 & (1-x) \\ 5 & k & 1 \\ 6 & 3 & (1+x) \\ \end{matrix} \right|\] is 2, then

    A) \[k=\frac{5}{2},\,x=\frac{1}{5}\]

    B) \[k=\frac{5}{2},\,x\ne \frac{1}{5}\]

    C) \[k=\frac{1}{5},\,x=\frac{5}{2}\]

    D) None of these

    View Answer play_arrow
  • question_answer185) The largest interval lying in \[\left( -\frac{\pi }{2},\frac{\pi }{2} \right)\] n in which the function \[f(x)={{3}^{-{{x}^{2}}}}+{{\cos }^{-1}}\left( \frac{x}{2}-1 \right)+\log \,\,\cos \,x\]is defined as

    A) \[[0,\pi ]\]

    B) \[\left[ -\frac{\pi }{2},\frac{\pi }{2} \right]\]

    C) \[\left[ 0,\frac{\pi }{2} \right)\]

    D) None of these

    View Answer play_arrow
  • question_answer186) If a and B are two fixed points, then the locus of a point which moves in such a way that the angle APB is a right angle is

    A) a circle

    B) an ellipse

    C) a parabola

    D) None of these

    View Answer play_arrow
  • question_answer187) Equation of the circle which of the mirror image of the circle \[{{x}^{2}}+{{y}^{2}}-2x=0\]in the line \[x+y=2\]is

    A) \[{{x}^{2}}+{{y}^{2}}-2x+4y+3=0\]

    B) \[2({{x}^{2}}+{{y}^{2}})+x+y+1=0\]

    C) \[{{x}^{2}}+{{y}^{2}}-4x-2y+4=0\]

    D) None of the above

    View Answer play_arrow
  • question_answer188) Let \[y=p+q\]where p varies directly as x and q varies inversely as\[{{x}^{2}}\]. If \[y=19\]when \[x=2\] or 3, then y in terms of x is

    A) \[36x+\frac{5}{{{x}^{2}}}\]

    B) \[\frac{5}{x}\,36{{x}^{2}}\]

    C) \[5x+\frac{36}{{{x}^{2}}}\]

    D) None of these

    View Answer play_arrow
  • question_answer189) Seven digits from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 are written in a random order. The probability that these seven digit number is divisible by 9, is

    A) \[\frac{2}{9}\]

    B) \[\frac{1}{5}\]

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

    D) \[\frac{1}{9}\]

    View Answer play_arrow
  • question_answer190) The orthocenter of a triangle formed by the lines \[x+y=1,\,\,2x+3y=6\]and \[4x-y+4=0\] lies in the

    A) Ist quadrant

    B) IInd quadrant

    C) IIIrd quadrant

    D) IVth quadrant

    View Answer play_arrow
  • question_answer191) If a circle and a parabola intersect at four points, then the y am of the ordinates is equal to

    A) AM of radius is of the circle and latusrectum of the par abola

    B) GM of the radius and latusrectum

    C) HM of the radius and latusrectum

    D) Zero

    View Answer play_arrow
  • question_answer192) In \[\Delta \,ABC\] if \[a=3,\,\,b=4,\,c=5,\] then the value of sin 2B s

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

    B) \[\frac{3}{20}\]

    C) \[\frac{24}{25}\]

    D) \[\frac{1}{50}\]

    View Answer play_arrow
  • question_answer193) The equation of the circle of radius 5 in the first quadrant which touches x-axis and the line \[4y=3x\]is

    A) \[{{x}^{2}}+{{y}^{2}}-24x-y-25=0\]

    B) \[{{x}^{2}}+{{y}^{2}}-30x-10y+225=0\]

    C) \[{{x}^{2}}+{{y}^{2}}-16x-18y+64=0\]

    D) \[{{x}^{2}}+{{y}^{2}}-20x-12y+144=0\]

    View Answer play_arrow
  • question_answer194) The line \[lx+my+n=0\] is a normal to the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]

    A) \[\frac{{{a}^{2}}}{{{l}^{2}}}+\frac{{{b}^{2}}}{{{m}^{2}}}=\frac{{{({{a}^{2}}-{{b}^{2}})}^{2}}}{{{n}^{2}}}\]

    B) \[\frac{{{a}^{2}}}{{{m}^{2}}}+\frac{{{b}^{2}}}{{{l}^{2}}}=\frac{{{({{a}^{2}}-{{b}^{2}})}^{2}}}{{{n}^{2}}}\]

    C) \[{{a}^{2}}{{l}^{2}}+{{b}^{2}}{{m}^{2}}={{({{a}^{2}}-{{b}^{2}})}^{2}}{{n}^{2}}\]

    D) None of the above

    View Answer play_arrow
  • question_answer195) The equation \[\left| \sqrt{{{x}^{2}}+{{(y-1)}^{2}}}-\sqrt{{{x}^{2}}+{{(y+1)}^{2}}} \right|=k\]will represent a hyperbola for

    A) \[k\in (0,2)\]

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

    C) \[k\in (1,\infty )\]

    D) \[k\in R'\]

    View Answer play_arrow
  • question_answer196) Two forces \[{{\vec{F}}_{1}}=3\hat{i}-2\hat{j}+\hat{k}\] and \[{{\vec{F}}_{2}}=\hat{i}-3\hat{j}+5\hat{k}\] acting on a particle at A, move to .6. The work done if the position vector of \[\vec{A}\] and \[\vec{B}\]are \[-2\hat{i}+5\hat{k}\]and \[-3\hat{i}-7\hat{j}+2\hat{k}\]is

    A) \[25\]

    B) \[13\]

    C) \[26\]

    D) \[28\]

    View Answer play_arrow
  • question_answer197) If the three angles' of a quadrilateral are \[{{60}^{o}},\] \[{{80}^{o}}\] and \[\frac{5\pi }{6},\]then the fourth angle is

    A) \[{{70}^{o}}\]

    B) \[{{79}^{o}}\]

    C) \[{{80}^{o}}\]

    D) \[{{81}^{o}}\]

    View Answer play_arrow
  • question_answer198) Which one is not periodic

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

    B) \[\cos \,\,\sqrt{x}\,+{{\cos }^{2}}\,x\]

    C) \[\cos \,4x+{{\tan }^{2}}x\]

    D) \[{{\cos }^{2}}x+\sin \,x\]

    View Answer play_arrow
  • question_answer199) Let R be the relation on the set R of all real numbers defined by aRb if \[|a-b|\le 1,\]then R is

    A) Reflexive and symmetric

    B) Symmetric only

    C) Transitive only

    D) Anti symmetric only

    View Answer play_arrow
  • question_answer200) The expression \[(1+\tan \,x+{{\tan }^{2}}x)\,\,(1-\cot \,x+{{\cot }^{2}}x)\] has the positive values for x, given by

    A) \[0\le x\le \frac{\pi }{2}\]

    B) \[0\le x\le \pi \]

    C) For all \[x\in R\]

    D) \[x\ge 0\]

    View Answer play_arrow
  • question_answer201) The equation of a circle with origin as a centre and passing through an equilateral triangle whose median is of length 3a, is

    A) \[{{x}^{2}}+{{y}^{2}}=9{{a}^{2}}\]

    B) \[{{x}^{2}}+{{y}^{2}}=16{{a}^{2}}\]

    C) \[{{x}^{2}}+{{y}^{2}}=4{{a}^{2}}\]

    D) \[{{x}^{2}}+{{y}^{2}}={{d}^{2}}\]

    View Answer play_arrow
  • question_answer202) The point on the curve \[3{{x}^{2}}-4{{y}^{2}}=72\]which is nearest to the line \[3x+2y-1=0,\] is

    A) \[(6,3)\]

    B) \[(6,-3)\]

    C) \[(6,-6)\]

    D) \[(6,5)\]

    View Answer play_arrow
  • question_answer203) A circle is inscribed in a equilateral triangle of side a. The area of the circle is

    A) \[3\pi {{a}^{2}}\] sq unit

    B) \[2{{a}^{2}}\] sq unit

    C) \[{{a}^{2}}\]sq unit

    D) None of these

    View Answer play_arrow
  • question_answer204) If a, b, c are distinct positive real numbers and \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=1,\]then \[3{{({{a}^{2}}{{b}^{2}}{{c}^{2}})}^{1/3}}\] is

    A) Less than 1

    B) Equal to 1

    C) Greater than 1

    D) any real number

    View Answer play_arrow
  • question_answer205) If \[\alpha ,\beta ,\gamma ,\delta \] are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity k, then the value of \[4\,\sin \frac{\alpha }{2}+3\sin \frac{\beta }{2}+2\sin \frac{\gamma }{2}+\sin \frac{\delta }{2}\]is equal to

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

    B) \[2\sqrt{1-k}\]

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

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

    View Answer play_arrow
  • question_answer206) If \[x+9\] is a root of \[\left| \begin{matrix} x & 3 & 7 \\ 2 & x & 2 \\ 7 & 6 & x \\ \end{matrix} \right|=0,\]then other roots are

    A) \[-9,\,2,\,7\]

    B) \[9,\,2,\,7\]

    C) \[9,\,2,-\,7\]

    D) \[9,-\,2,\,7\]

    View Answer play_arrow
  • question_answer207) The value of \[\underset{x\to \pi /2}{\mathop{\lim }}\,\frac{\cot \,x-\cos x}{{{(\pi -2x)}^{3}}}\]

    A) \[1\]

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

    C) \[16\]

    D) None of these

    View Answer play_arrow
  • question_answer208) If the tangent \[P(1,1)\] on \[{{y}^{2}}=x{{(2-x)}^{2}}\] meets the curve again at Q, then Q is

    A) \[(2,2)\]

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

    C) \[\left( \frac{9}{4},\frac{3}{8} \right)\]

    D) None of these

    View Answer play_arrow
  • question_answer209) For the equation \[\frac{1}{x+a}-\frac{1}{x+b}=\frac{1}{x+c},\]if the product of the ratio is zero, then the sum of (he roots is

    A) \[0\]

    B) \[\frac{2ab}{b+c}\]

    C) \[\frac{2ac}{b+c}\]

    D) \[-\frac{2ac}{b+c}\]

    View Answer play_arrow
  • question_answer210) If \[n=2002,\] evaluate \[\frac{1}{{{\log }_{2}}n!}+\frac{1}{{{\log }_{3}}n!}+\frac{1}{{{\log }_{4}}n!}+.....+\frac{1}{{{\log }_{2002}}n!}\]

    A) \[1\]

    B) \[2\]

    C) \[3\]

    D) \[4\]

    View Answer play_arrow
  • question_answer211) A and B are the independent events. The probability that both occur simultaneously is \[\frac{1}{6}\]and the probability that neither occur is \[\frac{1}{3}\]The probability of occurrence of the events A and B

    A) \[\frac{1}{2},\frac{3}{2}\]

    B) \[\frac{1}{2},\frac{1}{3}\]

    C) not possible

    D) None of these

    View Answer play_arrow
  • question_answer212) A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be hearts. The probability of the missing card to be a heart is

    A) \[\frac{50}{11}\]

    B) \[\frac{51}{11}\]

    C) \[\frac{11}{50}\]

    D) None of these

    View Answer play_arrow
  • question_answer213) \[\int_{0}^{\pi /2}{\frac{{{\sin }^{2}}x}{{{\sin }^{2}}x+{{\cos }^{2}}x}}\] is equal to

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

    B) \[2\pi \]

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

    D) \[\frac{1}{2}{{\pi }^{2}}\]

    View Answer play_arrow
  • question_answer214) The centre and the radius of the circle \[z\bar{z}+(2+3i)\,\,\bar{z}-2(2-3i)z+12=0\] is

    A) \[-(2+3i),\,(1)\]

    B) \[(3+2i),(1)\]

    C) \[(3+6i),(3)\]

    D) None of these

    View Answer play_arrow
  • question_answer215) The weight (in Kilogram) of 15 students are as follows 31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36,44, 45, 42, 30. If the weight 44 kg is replaced by 46 kg and \[27\text{ }kg\]is by \[25\text{ }kg,\] then new median is

    A) \[32\]

    B) \[33\]

    C) \[34\]

    D) \[35\]

    View Answer play_arrow
  • question_answer216) If \[1,\,{{\log }_{9}}({{3}^{1-x}}+2),{{\log }_{3}}({{4.3}^{x}}-1)\] are in AP, then x equals

    A) \[{{\log }_{3}}4\]

    B) \[1-{{\log }_{3}}4\]

    C) \[1-{{\log }_{4}}3\]

    D) \[{{\log }_{4}}3\]

    View Answer play_arrow
  • question_answer217) If the roots of the equation \[3{{x}^{2}}-6x+5=0\] are \[\alpha \] and \[\beta ,\] then the equation whose roots are \[\alpha +\beta \]and\[\frac{2}{\alpha +\beta }\]will be

    A) \[{{x}^{2}}+3x-1=0\]

    B) \[{{x}^{2}}+3x-2=0\]

    C) \[{{x}^{2}}+3x+2=0\]

    D) \[{{x}^{2}}-3x+2=0\]

    View Answer play_arrow
  • question_answer218) The equation of the locus of a point equidistant from the points \[({{a}_{1}},\,{{b}_{1}})\] and \[({{a}_{2}},\,{{b}_{2}})\] is \[({{a}_{1}}-{{a}_{2}})x+({{b}_{1}}-{{b}_{2}})y+c=0,\] then the value of c is

    A) \[\sqrt{(a_{1}^{2}+b_{1}^{2}+c_{1}^{2})}\]

    B) \[a_{1}^{2}-b_{1}^{2}-c_{1}^{2}\]

    C) \[\frac{1}{2}(a_{2}^{2}+b_{2}^{2}-a_{1}^{2}-b_{1}^{2})\]

    D) None of these

    View Answer play_arrow
  • question_answer219) The general solution of the equation \[{{2}^{\cos \,2x}}+1={{3.2}^{-\sin \,x}}\]is

    A) \[n\,\pi \]

    B) \[n\,\pi -\pi \]

    C) \[n\,\pi +\pi \]

    D) None of these

    View Answer play_arrow
  • question_answer220) Let \[0<x<\pi \] and \[y(x)\] be given by \[(1+\sin \,x){{y}^{3}}-(\cos \,x){{y}^{2}}+2(1+\sin \,x)y-2cos\,x=0\] The derivative of y with respect to \[\frac{x}{2}\]at \[x=\frac{\pi }{2}\] is

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

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

    C) \[-2\]

    D) \[2\]

    View Answer play_arrow
  • question_answer221) The value of \[\int_{0}^{\pi }{\left( \sum\limits_{r=0}^{3}{{{a}_{r}}\,\,{{\cos }^{3-r\,}}x\,{{\sin }^{r}}x} \right)}dx\]depends upon

    A) \[{{a}_{1}}\] and \[{{a}_{2}}\]

    B) \[{{a}_{0}}\] and \[{{a}_{3}}\]

    C) \[{{a}_{2}}\] and \[{{a}_{3}}\]

    D) \[{{a}_{1}}\] and \[{{a}_{3}}\]

    View Answer play_arrow
  • question_answer222) If the .function \[f:[1,\,\infty )\to [1,\infty )\] is denned by \[f(x)={{2}^{x(x-1)}},\]then \[{{f}^{-1}}(x)\] is

    A) \[{{\left( \frac{1}{2} \right)}^{x(x-1)}}\]

    B) \[\frac{1}{2}(1+\sqrt{1+4{{\log }_{2}}y})\]

    C) \[\frac{1}{2}(1-\sqrt{1+4{{\log }_{2}}y})\]

    D) \[\infty \]

    View Answer play_arrow
  • question_answer223) If the roots of the given equation \[(\cos \,\,p-1){{x}^{2}}+(\cos \,p)x+\sin \,p=0\] are real, then

    A) \[p\in (-\pi ,0)\]

    B) \[p\in \left( -\frac{\pi }{2},\frac{\pi }{2} \right)\]

    C) \[p\in (0,\pi )\]

    D) \[p\in (0,2\pi )\]

    View Answer play_arrow
  • question_answer224) The angle of depression of a boat m in a river is \[{{30}^{o}}\] from the top of a tower, \[87\text{ }m\]high and the speed of the boat is\[5.8\text{ }km/h\]. The time taken by the boat to reach at the base of the tower is

    A) \[9\,\,\min \]

    B) \[\frac{9\sqrt{3}}{10}\,\,\min \]

    C) \[25\,\,\min \]

    D) \[15\,\,\min \]

    View Answer play_arrow
  • question_answer225) If \[\alpha =\frac{3}{5},\,\,(0<\alpha ,\pi )\]and \[\cos \beta =\frac{5}{13},\] then \[(\alpha -\beta )\] lies in the quadrants

    A) I, II, IV

    B) I, III, IV

    C) I, II, III

    D) I,IV

    View Answer play_arrow

   

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