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Solved papers for CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2002

done CEE Kerala Engineering Solved Paper-2002

  • question_answer1) A body of mass 2 kg makes an elastic collision with another body at rest and continues to move in the original direction with one-fourth its original speed. The mass of the second body which collides with the first body is:

    A) 2 kg

    B) 1.2 kg

    C) 3 kg

    D) 1.5 kg

    E) 1 kg

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  • question_answer2) In the stable equilibrium position, a body has:

    A) maximum potential energy

    B) minimum potential energy

    C) minimum kinetic energy

    D) neither maximum nor minimum potential energy

    E) none of the above

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  • question_answer3) A particle of mass m at rest is acted upon by a force P for a time t. Its kinetic energy after an interval t is:

    A) \[\frac{{{p}^{2}}{{t}^{2}}}{m}\]

    B) \[\frac{{{p}^{2}}{{t}^{2}}}{2m}\]

    C) \[\frac{{{p}^{2}}{{t}^{2}}}{3m}\]

    D) \[\frac{pt}{2m}\]

    E) \[\frac{p{{t}^{2}}}{2m}\]

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  • question_answer4) A car of mass 1000 kg accelerates uniformly from rest to a velocity of 54 km/h in 5 s. The average power of the engine during this period in watts is (neglect friction):

    A) 2000 W

    B) 22500 W

    C) 5000 W

    D) 2250 W

    E) 1000 W

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  • question_answer5) A quarter horse power motor runs at a speed of 600 rpm. Assuming 40% efficiency the work done by the motor in one rotation will be:

    A) 7.46 J

    B) 7400 J

    C) 7.46 erg

    D) 74.6 J

    E) 746 J

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  • question_answer6) In the\[HCl\]molecule, the separation between the nuclei of the two atoms is about \[1.27\overset{\text{o}}{\mathop{\text{A}}}\,\] \[(1\overset{\text{o}}{\mathop{\text{A}}}\,={{10}^{-10}})\]. The approximate location of the centre of mass of the molecule, assuming the chlorine atom to be about 35.5 times as massive as hydrogen is:

    A) \[1\overset{\text{o}}{\mathop{\text{A}}}\,\]

    B) \[2.5\overset{\text{o}}{\mathop{\text{A}}}\,\]

    C) \[1.24\overset{\text{o}}{\mathop{\text{A}}}\,\]

    D) \[1.5\overset{\text{o}}{\mathop{\text{A}}}\,\]

    E) \[0.9\overset{\text{o}}{\mathop{\text{A}}}\,\]

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  • question_answer7) A sphere of mass 10 kg and radius 0.5 m rotates about a tangent. The moment of inertia of the sphere is:

    A) \[5kg-{{m}^{2}}\]

    B) \[2.7kg-{{m}^{2}}\]

    C) \[3.5kg-{{m}^{2}}\]

    D) \[4.5\text{ }kg-{{m}^{2}}\]

    E) \[4kg-{{m}^{2}}\]

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  • question_answer8) A solid sphere (mass 2 m) and a thin spherical shell (mass M) both of the same size, roll down an inclined plane, then:

    A) solid sphere will reach the bottom first

    B) hollow spherical shell will reach the bottom first

    C) both will reach at the same time

    D) cannot be predicted as the data is insufficient

    E) none of the above

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  • question_answer9) If the earth were to suddenly contract to half the present radius (without any external torque acting on it), by how much would the day be decreased? (Assume earth to be a perfect solid sphere of moment of inertia\[\frac{2}{5}M{{R}^{2}}\])

    A) \[8\,h\]

    B) \[6\,h\]

    C) \[4\,h\]

    D) \[2\,h\]

    E) \[1\,h\]

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  • question_answer10) A research satellite of mass 200 kg circles the earth in an orbit of average radius 3R/2, where R is the radius of the earth. Assuming the gravitational pull on a mass of 1 kg on the earths surface to be 10 N, the pull on the satellite will be:

    A) 880 N

    B) 889 N

    C) 890 N

    D) 892 N

    E) 885 N

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  • question_answer11) If M = Mass, L = Length, T= Time and\[I=\]Electric current, then the dimensional formula for electrical resistance R is given by:

    A) \[[R]=[{{M}^{1}}{{L}^{2}}{{T}^{-3}}{{I}^{-2}}]\]

    B) \[[R]=[{{M}^{1}}{{L}^{2}}{{T}^{-3}}{{I}^{2}}]\]

    C) \[[R]=[{{M}^{1}}{{L}^{2}}{{T}^{3}}{{I}^{-2}}]\]

    D) \[[R]=[{{M}^{1}}{{L}^{2}}{{T}^{3}}{{I}^{2}}]\]

    E) \[[R]=[{{M}^{-1}}{{L}^{2}}{{T}^{-3}}{{I}^{-2}}]\]

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  • question_answer12) A body is moving at a speed near\[0.3\text{ }m{{s}^{-1}}\]. To measure its speed with an accuracy about 1%, using a sampling distance 3 mm, the measuring clock should have a least count of the order of:

    A) 0.1 s

    B) 0.01 s

    C) 0.001 s

    D) 0.0001 s

    E) 0.015 s

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  • question_answer13) A train moves from one station to another in 2 hours time. Its speed-time graph during this motion is shown below. The maximum acceleration during the journey is:

    A) \[140\,km{{h}^{-2}}\]

    B) \[160\,km{{h}^{-2}}\]

    C) \[100\,km{{h}^{-2}}\]

    D) \[120\,km{{h}^{-2}}\]

    E) \[150\,km{{h}^{-2}}\]

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  • question_answer14) A body dropped from a height h with an initial speed zero reaches the ground with a velocity of 3 km/h. Another body of the same mass was dropped from the same height h with an initial speed 4 km/h will reach the ground with a velocity of:

    A) 3 km/h

    B) 4 km/h

    C) 5 km/h

    D) 12 km/h

    E) 8 km/h

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  • question_answer15) If the acceleration due to gravity is\[10\text{ }m{{s}^{-2}}\]and the units of length and time are changed to kilometre and hour respectively, the numerical value of the acceleration due to gravity is:

    A) 360000

    B) 72000

    C) 36000

    D) 129600

    E) 73000

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  • question_answer16) A boat man can row with a speed of 10 km/h in still water. If the river flows at 5 km/h, the direction in which the boat man should row to reach a point on the other bank directly opposite to the point from where he started is (width of the river is 2 km):

    A) in a direction inclined at\[120{}^\circ \]to the direction of river flow

    B) in a direction inclined at\[90{}^\circ \]to the direction of river flow

    C) \[60{}^\circ \]in the north-west direction

    D) should row directly along the river flow

    E) none of the above

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  • question_answer17) The maximum and minimum magnitudes of the resultant of two given vectors are 17 units and 7 units respectively. If these two vectors are at right angles to each other, the magnitude of their resultant is:

    A) 14

    B) 16

    C) 18

    D) 13

    E) 12

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  • question_answer18) A cricketer can throw a ball to a maximum horizontal distance of 100 m. The speed with which he throws the ball is (to the nearest integer):

    A) \[30\text{ }m{{s}^{-1}}\]

    B) \[\text{42 }m{{s}^{-1}}\]

    C) \[32\text{ }m{{s}^{-1}}\]

    D) \[\text{35 }m{{s}^{-1}}\]

    E) \[\text{40 }m{{s}^{-1}}\]

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  • question_answer19) A box whose mass is 5 kg lies on a spring balance inside a lift. The lift starts to ascend with an acceleration of\[2\text{ }m{{s}^{-2}}\]. The reading of the machine or balance is\[(g=10\,m{{s}^{-2}})\]:

    A) 50 kg

    B) zero

    C) 49 kg

    D) 60 kg

    E) 45 kg

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  • question_answer20) A ball of mass 0.5 kg moving with a velocity of \[2\text{ }m{{s}^{-1}}\]strikes a wall normally and bounces back with the same speed. If the time of contact between the ball and wall is\[{{10}^{-3}}s,\] the average force exerted by the wall on the ball is:

    A) 1125N

    B) 1000 N

    C) 500 N

    D) 2000 N

    E) 5000 N

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  • question_answer21) A telescope has an objective of focal length 50 cm and an eye-piece of focal length 5 cm. The least distance of distinct vision is 25 cm. The telescope is focussed for distinct vision on a scale 200 cm away. The separation between the objective and the eye-piece is:

    A) 75 cm

    B) 60 cm

    C) 71 cm

    D) 74 cm

    E) 65 cm

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  • question_answer22) The colour of the +ve column in a gas discharge tube depends on:

    A) the type of glass used to construct the tube

    B) the gas in the tube

    C) the applied voltage

    D) the material of the cathode

    E) none of the above

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  • question_answer23) Cathode rays are produced when the pressure is of the order of:

    A) 2 cm of Hg

    B) 0.1 cm of Hg

    C) 0.01 mm of Hg

    D) 1 u m of Hg

    E) 0.001 mm of Hg

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  • question_answer24) A radio transmitter radiates 1 kW power at a wavelength 198.6 m. How many photons does it emit per second?

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

    B) \[{{10}^{20}}\]

    C) \[{{10}^{30}}\]

    D) \[{{10}^{40}}\]

    E) \[{{10}^{50}}\]

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  • question_answer25) Consider the spectral line resulting from the transition from\[n=2\]to\[n=1,\]in atoms and ions given below. The shortest wavelength is produced by:

    A) hydrogen atom

    B) deuterium atom

    C) singly ionized helium

    D) doubly ionized helium

    E) doubly ionized lithium

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  • question_answer26) The energy of an electron in excited hydrogen atom is\[-\,3.4\text{ }eV\]. Then according to Bohrs theory, the angular momentum of the electron is:

    A) \[2.1\times {{10}^{-34}}J-s\]

    B) \[3\times {{10}^{-34}}J-s\]

    C) \[2\times {{10}^{-34}}J-s\]

    D) \[0.5\times {{10}^{-34}}J-s\]

    E) \[1\times {{10}^{-34}}J-s\]

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  • question_answer27) If the speed of light were 2/3 of its present value, the energy released in a given atomic explosion would:

    A) decrease by a factor 2/3

    B) decrease by a factor 4/9

    C) decrease by a factor 5/9

    D) decrease by a factor\[\sqrt{5}/9\]

    E) increase by a factor 2/3

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  • question_answer28) A semiconductor has an electron concentration of\[8\times {{10}^{13}}/{{m}^{3}}\]and hole concentration of\[5.5\times {{10}^{12}}/{{m}^{3}}\]. The semiconductor is:

    A) n-type

    B) p-type

    C) intrinsic semiconductor

    D) p-n junction

    E) none of the above

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  • question_answer29) In the figure shown below, which of the diodes are forward biased?

    A) 1, 2, 3

    B) 2, 4, 5

    C) 1, 3, 4

    D) 2, 3, 4

    E) 1, 4, 5

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  • question_answer30) Given below are four logic gate symbols. Those for OR, NOR and NAND are respectively:

    A) 1, 4, 3

    B) 4, 1, 2

    C) 1, 3, 4

    D) 4, 2, 1

    E) 3, 2, 1

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  • question_answer31) The albedo of a planet is indicative of its:

    A) transmission coefficient

    B) reflection coefficient

    C) absorption coefficient

    D) adsorption coefficient

    E) none of the above

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  • question_answer32) Mass of the earth has been determined through:

    A) use of Keplers\[{{T}^{2}}/{{R}^{3}}\]constancy law

    B) sampling the density of earths crust and using R

    C) Cavendishs determination of G and using R and g at surface

    D) use of periods of satellites at different heights above earths surface

    E) it is impossible to determine

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  • question_answer33) If 96500 C of electricity liberates\[1\,g\]equivalent of any substance, the time taken for a current of 0.15A to deposit 20 mg of copper from a solution of copper sulphate is (chemical equivalent of copper = 32):

    A) 5 min 20 s

    B) 6 min 42 s

    C) 4 min 40 s

    D) 5 min 50 s

    E) 6 min

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  • question_answer34) An electric motor operates on a 50 V supply and a current of 12 A. If the efficiency of the motor is 30%, what is the resistance of the winding of the motor?

    A) \[6\,\Omega \]

    B) \[4\,\Omega \]

    C) \[2.9\,\Omega \]

    D) \[3.1\,\Omega \]

    E) \[2.5\,\Omega \]

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  • question_answer35) Two long straight wires are set parallel to each other. Each carries a current in the same direction and the separation between them is 2 r. The intensity of the magnetic field mid-way between them is:

    A) \[\frac{{{\mu }_{0}}i}{r}\]

    B) \[\frac{4{{\mu }_{0}}i}{r}\]

    C) zero

    D) \[\frac{{{\mu }_{0}}i}{4r}\]

    E) \[\frac{{{\mu }_{0}}i}{2r}\]

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  • question_answer36) A galvanometer of resistance \[20\,\Omega \] is to be converted into an ammeter of range 1A. If a current of 1 mA produces full scale deflection, the shunt required for the purpose is:

    A) \[0.01\,\Omega \]

    B) \[0.05\,\Omega \]

    C) \[0.02\,\Omega \]

    D) \[0.04\Omega \]

    E) \[0.03\Omega \]

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  • question_answer37) There are three voltmeters of the same range but of resistance\[10000\text{ }\Omega ,\text{ }8000\text{ }\Omega \]and\[40000\text{ }\Omega \]respectively. The best voltmeter among these is the one whose resistance is:

    A) \[10000\text{ }\Omega \]

    B) \[8000\text{ }\Omega \]

    C) \[4000\text{ }\Omega \]

    D) all are equally good

    E) none of the above

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  • question_answer38) A magnetic needle is kept in a non-uniform magnetic field. It experiences:

    A) force and torque

    B) a force but not a torque

    C) a torque but not a force

    D) neither a force nor a torque

    E) none of the above

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  • question_answer39) A small rod of bismuth is suspended freely between the poles of a strong electromagnet. It is found to arrange itself at right angles to the magnetic field. This observation establishes that bismuth is:

    A) diamagnetic

    B) paramagnetic

    C) ferro-magnetic

    D) anti ferro-magnetic

    E) ferri-magnetic

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  • question_answer40) Alternating current is transmitted to distant places:

    A) at high voltage and low current

    B) at high voltage and high current

    C) at low voltage and low current

    D) at low voltage and high current

    E) none of the above

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  • question_answer41) In a step-up transformer the voltage in the primary is 220 V and the current is 5 A. The secondary voltage is found to be 22000 V. The current in the secondary (neglect losses) is:

    A) 5 A

    B) 50 A

    C) 500 A

    D) 0.05 A

    E) 0.5 A

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  • question_answer42) In a pure inductive circuit, current:

    A) lags behind emf by\[\pi /2\]

    B) leads the emf by\[\pi /2\]

    C) lags behind by \[\pi \]

    D) leads the emf by\[\pi \]

    E) lags behind the emf by \[\pi /4\]

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  • question_answer43) Two circuits have mutual inductance of 0.1 H. What average emf is induced in one circuit when the current in the other circuit changes from 0 to 20 A in 0.02 s?

    A) 240 V

    B) 230 V

    C) 100 V

    D) 300 V

    E) 200 V

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  • question_answer44) A micro-wave and an ultrasonic sound wave have the same wavelength. Their frequencies are in the ratio (approximately):

    A) \[{{10}^{6}}:1\]

    B) \[{{10}^{4}}:1\]

    C) \[{{10}^{2}}:1\]

    D) \[10:1\]

    E) \[1:1\]

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  • question_answer45) The ozone layer absorbs:

    A) infrared radiations

    B) ultraviolet radiations

    C) X-rays

    D) \[\gamma \]-rays

    E) visible light

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  • question_answer46) Huygens principle of secondary wavelets may be used to:

    A) find the velocity of light in vacuum

    B) explain the particle behaviour of light

    C) find the new position of a wavefront

    D) explain photoelectric effect

    E) explain scattering of light

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  • question_answer47) In Youngs double slit experiment, the intensity of light coming from one of the slits is double the intensity from the other slit. The ratio of the maximum intensity to the minimum intensity in the interference fringe pattern observed is:

    A) 34

    B) 40

    C) 25

    D) 38

    E) 30

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  • question_answer48) Three observers A, B, C measure the speed of light coming from a source to be\[{{v}_{A}},{{v}_{B}}\]and\[{{v}_{C}}\]. The observer A moves away from the source at the same speed. The observer B stays stationary. The surrounding space is vacuum everywhere. Then:

    A) \[{{v}_{A}}>{{v}_{B}}>{{v}_{C}}\]

    B) \[{{v}_{A}}<{{v}_{B}}<{{v}_{C}}\]

    C) \[{{v}_{A}}={{v}_{B}}={{v}_{C}}\]

    D) \[{{v}_{A}}={{v}_{B}}>{{v}_{C}}\]

    E) \[{{v}_{B}}={{v}_{C}}>{{v}_{A}}\]

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  • question_answer49) Lumen is the unit of:

    A) luminous flux

    B) luminosity

    C) illuminance

    D) quantity of light

    E) illumination

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  • question_answer50) A man runs towards a mirror at a speed 15 m/s. The speed of the image relative to the man is:

    A) \[15\,m{{s}^{-1}}\]

    B) \[30\text{ }m{{s}^{-1}}\]

    C) \[35\text{ }m{{s}^{-1}}\]

    D) \[20\text{ }m{{s}^{-1}}\]

    E) \[25\,m{{s}^{-1}}\]

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  • question_answer51) The refractive index of water is 1.33. The direction in which a man under water should look to see the setting sun is:

    A) \[49{}^\circ \]to the horizontal

    B) \[90{}^\circ \]with the vertical

    C) \[49{}^\circ \]to the vertical

    D) along the horizontal

    E) in any direction

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  • question_answer52) The solar spectrum during a complete solar eclipse is:

    A) continuous

    B) emission line

    C) dark line

    D) dark band

    E) absorption

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  • question_answer53) When the displacement is one-half the amplitude in SHM, the fraction of the total enersy that is potential is:

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

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

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

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

    E) \[\frac{1}{6}\]

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  • question_answer54) When a stationary wave is formed then its frequency is:

    A) same as that of the individual waves

    B) twice that of the individual waves

    C) half that of the individual waves

    D) \[\sqrt{2}\]that of the individual waves

    E) none of the above

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  • question_answer55) A person carrying a whistle emitting continuously a note of 272 Hz is running towards a reflecting surface with a speed of 18 km/h. The speed of sound in air is 345\[m{{s}^{-1}}\]. The number of beats heard by him is:

    A) 4

    B) 6

    C) 8

    D) 3

    E) zero

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  • question_answer56) The distance between charges \[5\times {{10}^{-11}}C\]and \[-2.7\times {{10}^{-11}}C\]is 0.2 m. The distance at which a third charge should be placed from 4e in order that it will not experience any force along the line joining the two charges is:

    A) 0.44 m

    B) 0.65 m

    C) 0.556 m

    D) 0.350 m

    E) 0.5 m

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  • question_answer57) Small rain drops of the same size are charged to .potential V volts each. If n such drops coalesce to form a single drop, then the potential of the bigger drop is:

    A) \[{{n}^{1/3}}V\]

    B) \[{{n}^{2/3}}V\]

    C) \[nV\]

    D) \[{{n}^{3/2}}V\]

    E) \[{{n}^{1/2}}V\]

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  • question_answer58) A parallel plate capacitor has plate of area A and separation d. It is charged to a potential difference\[{{V}_{0}}\]. charging battery is disconnected and the plates are pulled apart to three times the initial separation. The work required to separate the plates is:

    A) \[\frac{{{\varepsilon }_{0}}AV_{0}^{2}}{3d}\]

    B) \[\frac{{{\varepsilon }_{0}}AV_{0}^{2}}{2d}\]

    C) \[\frac{{{\varepsilon }_{0}}AV_{0}^{2}}{4d}\]

    D) \[\frac{{{\varepsilon }_{0}}AV_{0}^{2}}{d}\]

    E) \[\frac{{{\varepsilon }_{0}}AV_{0}^{2}}{4d}\]

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  • question_answer59) A small sphere is charged to a potential of 50 V and a big hollow sphere is charged to potential of 100 V. Charge will flow from the smaller sphere to the bigger one when:

    A) the smaller one is placed inside the bigger one and connected by a wire

    B) the bigger one is placed inside the smaller one and connected by means of a wire

    C) bigger one placed by the side of the smaller one and connected by a wire

    D) smaller one placed by the side of the bigger one

    E) None of the above

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  • question_answer60) In the circuit, the potential difference across PQ will be nearest to:

    A) 9.6 V

    B) 6.6 V

    C) 4.8 V

    D) 3.2 V

    E) 2.8 V

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  • question_answer61) A wire of length 100 cm is connected to a cell of emf 2V and negligible internal resistance. The resistance of the wire is\[3\,\Omega ,\]the additional resistance required to produce a PD of 1 mV/cm is:

    A) \[60\,\,\Omega \]

    B) \[47\,\,\Omega \]

    C) \[57\,\,\Omega \]

    D) \[35\,\,\Omega \]

    E) \[55\,\,\Omega \]

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  • question_answer62) In the figure a carbon resistor has bands of different colours on its body as mentioned in the figure. The value of the resistance is:

    A) \[2.2\,\,\Omega \]

    B) \[3.3\,\,\Omega \]

    C) \[5.6\,\,\Omega \]

    D) \[9.1\,\,\Omega \]

    E) \[4.7\,\,\Omega \]

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  • question_answer63) The period of moons rotation around the earth is nearly 29 days. If moons mass were 2 fold its present value and all other things remained unchanged, the period of moons rotation would be nearly:

    A) \[29\sqrt{2}\,days\]

    B) \[\frac{29}{\sqrt{2}}\,days\]

    C) \[29\times 2\,\,days\]

    D) \[29\,\,days\]

    E) \[\frac{29}{2}\,\,days\]

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  • question_answer64) A uniform plank of Youngs modulus Y is moved over a smooth horizontal surface by a constant horizontal force F. The area of cross-section of the plank is A. The compressive strain on the plank in the direction of the force is:

    A) \[\frac{F}{AY}\]

    B) \[\frac{2F}{AY}\]

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

    D) \[\frac{3F}{AY}\]

    E) \[\frac{F}{3AY}\]

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  • question_answer65) Observers on 10th, 5th and ground floor of a tall building measure the velocity of certain rain drop by some accurate method. Surprisingly the velocity of rain drop measured by the three observers is found to be same. This is because:

    A) there is no gravitational force acting on the drop

    B) gravitational force on the rain drop is balanced by force produced by surrounding air

    C) gravitational force on the rain drop is balanced by upward force of attraction produced by the cloud

    D) data is insufficient to predict

    E) none of the above

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  • question_answer66) The rms speed of the molecules of a gas in a vessel is\[400\text{ }m{{s}^{-1}}\]. If half of the gas leaks out, at constant temperature, the rms speed of the remaining molecules will be:

    A) \[800\,m{{s}^{-1}}\]

    B) \[400\sqrt{2}\,m{{s}^{-1}}\]

    C) \[400\,m{{s}^{-1}}\]

    D) \[200\,m{{s}^{-1}}\]

    E) \[200\sqrt{2}\,m{{s}^{-1}}\]

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  • question_answer67) An electron tube was sealed off during manufacture at a pressure of\[1.2\times {{10}^{-7}}mm\]of mercury at\[27{}^\circ C\]. Its volume is 100 cm3. The number of molecules that remain in the tube is:

    A) \[2\times {{10}^{16}}\]

    B) \[3\times {{10}^{15}}\]

    C) \[3.86\times {{10}^{11}}\]

    D) \[5\times {{10}^{11}}\]

    E) \[2.5\times {{10}^{12}}\]

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  • question_answer68) A liquid wets a solid completely. The meniscus of the liquid in a sufficiently long tube is:

    A) flat

    B) concave

    C) convex

    D) cylindrical

    E) none of the above

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  • question_answer69) A steel scale is to be prepared such that the millimetre intervals are to be accurate within\[6\times {{10}^{-5}}mm\]. The maximum temperature variation during the ruling of the millimeter marks is\[(a=12\times {{10}^{-6}}/{}^\circ C)\]:

    A) \[4.0{}^\circ C\]

    B) \[4.5{}^\circ C\]

    C) \[5.0{}^\circ C\]

    D) \[3{}^\circ C\]

    E) \[5.5{}^\circ C\]

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  • question_answer70) A constant volume gas thermometer works on:

    A) Archimedes principle

    B) Pascals law

    C) Boyles law

    D) Charles law

    E) Newtons law

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  • question_answer71) The rate of emission of a black body at\[0{}^\circ C\]is R, its rate of emission at\[273{}^\circ C\]is:

    A) 4R

    B) 8R

    C) 16 R

    D) 32 R

    E) 10 R

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  • question_answer72) The equation of a simple harmonic motion is \[X=0.34\cos (3000t+0.74),\]where X and t are in mm and sec respectively. The frequency of the motion in Hz is:

    A) \[3000\]

    B) \[\frac{3000}{2\pi }\]

    C) \[\frac{0.74}{2\pi }\]

    D) \[\frac{3000}{\pi }\]

    E) \[\frac{3000}{t}\]

    View Answer play_arrow
  • question_answer73) The unit of specific conductivity is:

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

    B) \[\Omega \,c{{m}^{-2}}\]

    C) \[{{\Omega }^{-1}}\,cm\]

    D) \[\Omega \,c{{m}^{-3}}\]

    E) \[{{\Omega }^{-1}}\,c{{m}^{-1}}\]

    View Answer play_arrow
  • question_answer74) The rate of a reaction is doubled for every\[10{}^\circ \]rise in temperature. The increase in reaction rate as a result of temperature rise from\[10{}^\circ \]to\[100{}^\circ \]is:

    A) 112

    B) 512

    C) 400

    D) 614

    E) 100

    View Answer play_arrow
  • question_answer75) The first artificial disintegration of an atomic nucleus was achieved by:

    A) Geiger

    B) Wilson

    C) Madam Curie

    D) Rutherford

    E) Soddy

    View Answer play_arrow
  • question_answer76) When a beam of light is passed through a colloidal solution it:

    A) is reflected

    B) is scattered

    C) transmitted

    D) absorbed

    E) refracted

    View Answer play_arrow
  • question_answer77) An important industrial solvent, also a laboratory reagent called 2-butanone is nothing but:

    A) methyl ethyl ketone

    B) dimethyl ketone

    C) diethyl ketone

    D) propyi ketone

    E) methyl propyi ketone

    View Answer play_arrow
  • question_answer78) Lassaignes test is used to detect:

    A) nitrogen and halogens

    B) sodium and halogens

    C) halogens and sulphur

    D) nitrogen and sulphur

    E) nitrogen, sulphur and halogens

    View Answer play_arrow
  • question_answer79) The number of possible structural isomers of butene are:

    A) 3

    B) 2

    C) 4

    D) 5

    E) 1

    View Answer play_arrow
  • question_answer80) Disymmetric object is one which is:

    A) superimposable on its mirror image

    B) non-superimposable on its mirror image

    C) optically inactive

    D) achiral

    View Answer play_arrow
  • question_answer81) Cycloalkane has the formula:

    A) \[{{C}_{n}}{{H}_{2n+2}}\]

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

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

    D) \[{{C}_{2n}}{{H}_{2}}\]

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

    View Answer play_arrow
  • question_answer82) Three fused benzene rings are found in:

    A) naphthalene

    B) anthracene

    C) phenanthroline

    D) triphenyl methane

    E) none of these

    View Answer play_arrow
  • question_answer83) To differentiate between carbon-12, carbon-13 and carbon-14, the instrument that you would use is:

    A) infra-red spectrometer

    B) atomic absorption spectrometer

    C) mass spectrometer

    D) ultraviolet spectrometer

    E) calorimeter

    View Answer play_arrow
  • question_answer84) Irrespective of the source, pure sample of water always yields 88.89% mass of oxygen and 11.11% mass of hydrogen. This is explained by the law of:

    A) conservation of mass

    B) constant composition

    C) multiple proportion

    D) constant volume

    E) Gay-Lussac

    View Answer play_arrow
  • question_answer85) A mixture of sand and iodine can be separated by:

    A) crystallisation

    B) sublimation

    C) distillation

    D) fractionation

    E) filtration

    View Answer play_arrow
  • question_answer86) When the product of pressure and volume is plotted against pressure for a given amount of gas, the line obtained is:

    A) parallel to X-axis

    B) parallel to Y-axis

    C) linear with positive slope

    D) linear with negative slope

    E) either (a) or (c)

    View Answer play_arrow
  • question_answer87) 32 g of\[{{O}_{2}}\], 2g of\[{{H}_{2}}\]and 28g of\[{{N}_{3}}\]at STP, occupy separately a volume of:

    A) 1 L

    B) 2 L

    C) 22.4 L

    D) 2.24 L

    E) 0.224 L

    View Answer play_arrow
  • question_answer88) Air at sea level is dense. This is a practical implimentation of:

    A) Boyles law

    B) Charles law

    C) Avogadros law

    D) Daltons law

    E) Gay-Lussac law

    View Answer play_arrow
  • question_answer89) The electron affinity values for the halogens show the following trend:

    A) \[F<Cl>Br>I\]

    B) \[F<Cl<Br<I\]

    C) \[F>Cl>Br>I\]

    D) \[F<Cl>Br<I\]

    E) \[F>Cl<Br>I\]

    View Answer play_arrow
  • question_answer90) Acetylene molecule has carbon in:

    A) sp -hybridization

    B) \[s{{p}^{2}}-\]hybridization

    C) \[s{{p}^{3}}-\]hybridization

    D) \[s{{p}^{3}}d-\]hybridization

    E) \[s{{p}^{3}}{{d}^{2}}-\]hybridization

    View Answer play_arrow
  • question_answer91) When \[{{H}_{2}}S\] gas is passed through nitric acid, the product is:

    A) rhombic S

    B) prismatic S (colloidal)

    C) amorphous S

    D) monoclinic S

    E) plastic S

    View Answer play_arrow
  • question_answer92) Pyrosilicate ion is:

    A) \[SiO_{2}^{2-}\]

    B) \[SiO_{4}^{2-}\]

    C) \[S{{i}_{2}}O_{4}^{6-}\]

    D) \[SiO_{3}^{-}\]

    E) \[S{{i}_{2}}O_{7}^{6-}\]

    View Answer play_arrow
  • question_answer93) Atoms in a\[{{P}_{4}}\]molecule of white phosphorus are arranged regularly in space in which of the following way?

    A) At the corners of tetrahedron

    B) At the corners of a cube

    C) At the corners of a four membered ring

    D) At the centre and corners of a equivalent triangle

    E) At the centre and corners of a tetrahedron

    View Answer play_arrow
  • question_answer94) The effective component of bleaching powder is the ............. of calcium:

    A) \[OCl_{2}^{2-}\]

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

    C) \[{{O}_{2}}C{{l}^{-}}\]

    D) \[{{O}^{2-}}\]

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

    View Answer play_arrow
  • question_answer95) The catalytic activity of the transition metals and their compounds is ascribed to:

    A) their chemical reactivity

    B) their magnetic behaviour

    C) their unfilled d-orbitals

    D) their ability to adopt multiple oxidation states and their complexing ability

    E) none of the above

    View Answer play_arrow
  • question_answer96) The compound\[ZnF{{e}_{2}}{{O}_{4}}\]is:

    A) a normal spinel compound

    B) a inverse spinel compound

    C) interstitial compound

    D) covalent compound

    E) co-ordination compound

    View Answer play_arrow
  • question_answer97) The catalyst used for the polymerization of olefins is:

    A) Ziegler-Natta catalyst

    B) Wilkinsons catalyst

    C) Pd-catalyst

    D) Zeises salt catalyst

    E) Zeolite

    View Answer play_arrow
  • question_answer98) Bakelite is a:

    A) urea-formaldehyde resin

    B) phenol formaldehyde resin

    C) polyethylene

    D) artificial rubber

    E) polyvinyl chloride

    View Answer play_arrow
  • question_answer99) \[\alpha -\]helix is found in:

    A) DNA

    B) RNA

    C) lipid

    D) carbohydrates

    E) protein

    View Answer play_arrow
  • question_answer100) Aspirin is:

    A) acetyl salicylic acid

    B) 2-methoxy benzoic acid

    C) acetyl oxalic acid

    D) methyl benzoic acid

    E) ethoxy benzoic acid

    View Answer play_arrow
  • question_answer101) \[{{N}^{+}}\equiv NBF_{4}^{-}\]

    A) fluorobenzene

    B) benzene

    C) 1, 2-difluoro benzene

    D) 1, 3-difluoro benzene

    E) 1, 4-difluoro benzene

    View Answer play_arrow
  • question_answer102) Oxidation of aldehydes gives:

    A) esters

    B) acids

    C) ethers

    D) alcohols

    E) esters and acids

    View Answer play_arrow
  • question_answer103) The common acid used in the manufacture of rayon and plastic is:

    A) methanoic acid

    B) ethanoic acid

    C) propanoic acid

    D) butanoic acid

    E) malonic acid

    View Answer play_arrow
  • question_answer104) The compound used as an explosive is:

    A) 2, 4, 6-tribromoaniline

    B) 1, 3, 5-trinkrobenzene

    C) 2, 4, 6-trichlorotoluene

    D) 1, 3, 5-trichlorobenzene

    E) 2, 4, 6-trinitrotoluene (TNT)

    View Answer play_arrow
  • question_answer105) The indicator that is obtained by coupling the diazonium salt of sulphanilic acid with\[N,N-\]dimethylaniline is:

    A) phenanthroline

    B) methyl orange

    C) methyl red

    D) phenolphthalein

    E) indigo

    View Answer play_arrow
  • question_answer106) High purity Si and Ge for semiconductor properties can be obtained by:

    A) calcination

    B) roasting

    C) zone refining

    D) thermic process

    E) electrolytic reduction

    View Answer play_arrow
  • question_answer107) Name of the alloy of aluminium which is used in aeroplane is:

    A) duralumin

    B) bell metal

    C) \[\gamma \]-alloy (gamma alloy)

    D) aluminium bronze

    E) alumina

    View Answer play_arrow
  • question_answer108) Invar, an alloy of Fe and Ni is used in watches and meter scale. Its characteristic property is:

    A) small coefficient of expansion

    B) resistance of corrosion

    C) hardness and elasticity

    D) resistance to wear

    E) magnetic nature

    View Answer play_arrow
  • question_answer109) An alloy of Pb and Sn in equal proportion is called:

    A) pewter

    B) type metal

    C) solder

    D) constantan

    E) gun metal

    View Answer play_arrow
  • question_answer110) Aqua-regia is obtained by mixing two different acids in the ratio:

    A) \[1\text{ }HN{{O}_{3}}:2\text{ }HCl\]

    B) \[\text{3 }HN{{O}_{3}}:1\,HCl\]

    C) \[\text{2 }HN{{O}_{3}}:2\text{ }HCl\]

    D) \[\text{2 }HN{{O}_{3}}:3\,HCl\]

    E) \[\text{1 }HN{{O}_{3}}:3\,HCl\]

    View Answer play_arrow
  • question_answer111) A compound with cubic structure is made of elements A and B. A atoms are at the comers of the cube and B atoms are at the face centres. The simplest formula of the compound is:

    A) \[{{A}_{5}}B\]

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

    C) \[AB\]

    D) \[A{{B}_{6}}\]

    E) \[A{{B}_{8}}\]

    View Answer play_arrow
  • question_answer112) Oxygen molecule contains:

    A) no unpaired electron

    B) one unpaired electron

    C) two unpaired electrons

    D) three unpaired electrons

    E) four unpaired electrons

    View Answer play_arrow
  • question_answer113) Colligative properties are used for the determination of:

    A) molar mass

    B) equivalent weight

    C) arrangement of molecules

    D) melting point and boiling point

    E) both (a) and (b)

    View Answer play_arrow
  • question_answer114) Identify the mixture that shows positive deviation from Raoults law:

    A) \[CHC{{l}_{3}}+{{(C{{H}_{3}})}_{2}}CO\]

    B) \[{{(C{{H}_{3}})}_{2}}CO+{{C}_{6}}{{H}_{5}}NH\]

    C) \[CHC{{l}_{3}}+{{C}_{6}}{{H}_{6}}\]

    D) \[{{(C{{H}_{3}})}_{2}}CO+C{{S}_{2}}\]

    E) \[{{C}_{6}}{{H}_{5}}N+C{{H}_{3}}COOH\]

    View Answer play_arrow
  • question_answer115) If\[\Delta G\]for a reaction is negative, you infer that the change is:

    A) spontaneous

    B) non-spontaneous

    C) reversible

    D) irreversible

    E) equilibrium

    View Answer play_arrow
  • question_answer116) The law of thermodynamics formulated by Dr. N. Nemst is:

    A) first law of thermodynamics

    B) second law of thermodynamics

    C) third law of thermodynamics

    D) both (a) and (b)

    E) both (b) and (c)

    View Answer play_arrow
  • question_answer117) Which of the following will favour the reverse reaction in a chemical equilibrium?

    A) Increasing the concentration of the Reactants

    B) Removal of at least one of the products at regular intervals

    C) Increasing the concentration of one or more of the products

    D) Increasing the pressure

    E) None of the above

    View Answer play_arrow
  • question_answer118) In the lime kiln, the reaction \[CaC{{O}_{3}}(s)\xrightarrow[{}]{{}}CaO(s)+C{{O}_{2}}(g)\] goes to completion because:

    A) of high temperature

    B) \[CaO\]is more stable than\[CaC{{O}_{3}}\]

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

    D) \[CaO\]is not dissociated

    E) \[C{{O}_{2}}\]is a gaseous product

    View Answer play_arrow
  • question_answer119) \[{{K}_{p}}\]and\[{{K}_{c}}\]are related as:

    A) \[{{K}_{p}}={{K}_{c}}{{(RT)}^{\Delta n}}\]

    B) \[{{K}_{c}}={{K}_{p}}{{(RT)}^{\Delta n}}\]

    C) \[{{K}_{p}}+{{K}_{c}}={{(RT)}^{\Delta n}}\]

    D) \[{{K}_{c}}={{K}_{c}}\]

    E) \[{{K}_{c}}.{{K}_{c}}={{(RT)}^{\Delta n}}\]

    View Answer play_arrow
  • question_answer120) \[\underset{(anode)}{\mathop{Zn(s)|}}\,Z{{n}^{2+}}(aq)||C{{u}^{2+}}\underset{(cathode)}{\mathop{(aq)|Cu}}\,(s)\]is:

    A) Weston cell

    B) Daniel cell

    C) Calomel cell

    D) Faraday cell

    E) Standard cell

    View Answer play_arrow
  • question_answer121) The pH of\[0.005\text{ }M\text{ }{{H}_{2}}S{{O}_{4}}\]is:

    A) 2.5

    B) 1.5

    C) 1.0

    D) 2.0

    E) none of these

    View Answer play_arrow
  • question_answer122) If the n th term of the geometric progression, \[5,-\frac{5}{2},\frac{5}{4},\frac{5}{8},....\]is\[\frac{5}{1024},\]then the value of n is:

    A) 11

    B) 10

    C) 9

    D) 4

    E) 7

    View Answer play_arrow
  • question_answer123) If a, b and c are respectively the p th, q th and r th terms of an AP, then\[\left| \begin{matrix} a & p & 1 \\ b & q & 1 \\ c & r & 1 \\ \end{matrix} \right|\]is equal to:

    A) 1

    B) \[-1\]

    C) 0

    D) \[pqr\]

    E) \[p+q+r\]

    View Answer play_arrow
  • question_answer124) The sum of infinite terms of the geometric progression\[\frac{\sqrt{2}+1}{\sqrt{2}-1},\frac{1}{2-\sqrt{2}}=\frac{1}{2},....\]is:

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

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

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

    D) \[3\sqrt{2}+\sqrt{5}\]

    E) \[0\]

    View Answer play_arrow
  • question_answer125) The two geometric means between the numbers 1 and 64 are:

    A) 1 and 64

    B) 4 and 16

    C) 2 and 16

    D) 8 and 16

    E) 3 and 16

    View Answer play_arrow
  • question_answer126) The number of ways in which 5 boys and 3 girls be seated in a row so that each girl is between two boys, is:

    A) 2880

    B) 1880

    C) 3800

    D) 2800

    E) 2000

    View Answer play_arrow
  • question_answer127) If n and r are two positive integers such that \[n\ge r,\]then\[^{n}{{C}_{r-1}}{{+}^{n}}{{C}_{r}}\]is equal to:

    A) \[^{n}{{C}_{n-1}}\]

    B) \[^{n}{{C}_{r}}\]

    C) \[^{n-1}{{C}_{r}}\]

    D) \[^{n+1}{{C}_{r}}\]

    E) \[^{n-1}{{C}_{r-1}}\]

    View Answer play_arrow
  • question_answer128) If\[^{43}{{C}_{r-6}}{{=}^{43}}{{C}_{3r+1}},\]then the value of r is:

    A) 12

    B) 8

    C) 6

    D) 10

    E) 14

    View Answer play_arrow
  • question_answer129) The number of straight lines that can be formed by joining 20 points of which 4 points are collinear, is:

    A) 183

    B) 186

    C) 197

    D) 190

    E) 185

    View Answer play_arrow
  • question_answer130) The number of ways in which a committee of 6 members can be formed from 8 gentlemen and 4 ladies so that the committee contains at least 3 ladies, is:

    A) 252

    B) 672

    C) 444

    D) 420

    E) 250

    View Answer play_arrow
  • question_answer131) If\[1+\frac{1+2}{2}+\frac{1+2+3}{3}+.....\]to n terms is S, then S is equal to:

    A) \[\frac{n(n+3)}{4}\]

    B) \[\frac{n(n+2)}{4}\]

    C) \[\frac{n(n+1)(n+2)}{6}\]

    D) \[{{n}^{2}}\]

    E) \[0\]

    View Answer play_arrow
  • question_answer132) Let\[A=\{x:{{x}^{2}}-5x+6=0\},\] B={2,4},C={4, 5}, then\[A\times (B\cap C)\]is:

    A) {(2, 4), (3, 4)}

    B) {(4, 2), (4, 3)}

    C) {(2, 4), (3s 4), (4, 4)}

    D) {(2, 2), (3, 3), (4, 4), (5, 5)}

    E) null set

    View Answer play_arrow
  • question_answer133) In a city 20 per cent of the population travels by car, 50 per cent travels by bus and 10 per cent travels by both car and bus. The persons travelling by car or bus is:

    A) 80 per cent

    B) 40 per cent

    C) 60 per cent

    D) 70 per cent

    E) 30 per cent

    View Answer play_arrow
  • question_answer134) If\[f(x)=\frac{2x+1}{3x-2},\]then\[(f\,\,o\,\,f)(2)\]is equal to:

    A) 1

    B) 3

    C) 4

    D) 2

    E) none of these

    View Answer play_arrow
  • question_answer135) Which one of the following is a bijective function on the set of real numbers?

    A) \[2x-5\]

    B) \[|x|\]

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

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

    E) \[{{x}^{4}}-{{x}^{2}}+1\]

    View Answer play_arrow
  • question_answer136) If\[f(x)=\log \frac{1+x}{1-x},\]then\[f(x)\]is:

    A) even

    B) \[f({{x}_{1}})f({{x}_{2}})=f({{x}_{1}}+{{x}_{2}})\]

    C) \[\frac{f({{x}_{1}})}{f({{x}_{2}})}=f({{x}_{1}}-{{x}_{2}})\]

    D) odd

    E) neither even nor odd

    View Answer play_arrow
  • question_answer137) Let the function\[f\]be defined by\[f(x)=\frac{2x+1}{1-3x}\]Then\[{{f}^{-1}}(x)\]is:

    A) \[\frac{x-1}{3x+2}\]

    B) \[\frac{3x+1}{x-1}\]

    C) \[\frac{x+1}{3x-2}\]

    D) \[\frac{2x+1}{1-3x}\]

    E) \[\frac{1-3x}{2x+1}\]

    View Answer play_arrow
  • question_answer138) If\[\sqrt{a+ib}=x+iy,\]then a possible value of\[\sqrt{a+ib}\]is:

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

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

    C) \[x+iy\]

    D) \[x-iy\]

    E) \[\sqrt{{{x}^{2}}-{{y}^{2}}}\]

    View Answer play_arrow
  • question_answer139) If\[(1+i)(1+2i)(1+3i)....(1+ni)=a+ib,\]then\[2\times 5\times 10\times .....\times (1+{{n}^{2}})\]is equal to:

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

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

    C) \[\sqrt{{{a}^{2}}-{{b}^{2}}}\]

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

    E) \[a+b\]

    View Answer play_arrow
  • question_answer140) If\[{{i}^{2}}=-1,\]then the sum\[i+{{i}^{2}}+{{i}^{3}}+...\]upto 1000 terms is equal to:

    A) 1

    B) \[-1\]

    C) i

    D) \[-i\]

    E) 0

    View Answer play_arrow
  • question_answer141) \[{{\left( \frac{1+\sin \theta +i\cos \theta }{1+\sin \theta -i\cos \theta } \right)}^{n}}\]is equal to:

    A) \[\cos \left( \frac{n\pi }{2}-n\theta \right)+i\sin \left( \frac{n\pi }{2}-n\theta \right)\]

    B) \[\cos \left( \frac{n\pi }{2}+n\theta \right)+i\sin \left( \frac{n\pi }{2}+n\theta \right)\]

    C) \[\sin \left( \frac{n\pi }{2}-n\theta \right)+i\cos \left( \frac{n\pi }{2}-n\theta \right)\]

    D) \[\cos \left( \frac{n\pi }{2}+2n\theta \right)+i\sin \left( \frac{n\pi }{2}+2n\theta \right)\]

    E) \[\cos n\theta +i\sin n\theta \]

    View Answer play_arrow
  • question_answer142) If\[\omega \] is a non-real cube root of unity, then\[(a+b)(a+b\omega )(a+b{{\omega }^{2}})\] is equal to:

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

    B) \[{{a}^{3}}-{{b}^{3}}\]

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

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

    E) 0

    View Answer play_arrow
  • question_answer143) If\[{{z}_{1}}\]and\[{{z}_{2}}\]are any two complex numbers, then which one of the following is true?

    A) \[|{{z}_{1}}+{{z}_{2}}|=|{{z}_{1}}|+|{{z}_{2}}|\]

    B) \[|{{z}_{1}}-{{z}_{2}}|=|{{z}_{1}}|-|{{z}_{2}}|\]

    C) \[|{{z}_{1}}-{{z}_{2}}|\le |{{z}_{1}}|+|{{z}_{2}}|\]

    D) \[|{{z}_{1}}-{{z}_{2}}|\le |{{z}_{1}}|-|{{z}_{2}}|\]

    E) \[\left| \frac{{{z}_{1}}}{{{z}_{2}}} \right|\ne \left| \frac{{{z}_{1}}}{{{z}_{2}}} \right|,\]where\[{{z}_{2}}\ne 0\]

    View Answer play_arrow
  • question_answer144) If\[\alpha \]and\[\beta \]are the roots of the equation\[{{x}^{2}}+2x+4=0,\]then\[\frac{1}{{{\alpha }^{3}}}+\frac{1}{{{\beta }^{3}}}\]is equal to:

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

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

    C) \[32\]

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

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

    View Answer play_arrow
  • question_answer145) If\[{{x}^{2}}+ax+10=0\]and\[{{x}^{2}}+bx-10=0\]have a common root, then\[{{a}^{2}}-{{b}^{2}}\]is equal to:

    A) 10

    B) 20

    C) 30

    D) 40

    E) 50

    View Answer play_arrow
  • question_answer146) If\[2+i\]is a root of the equation \[{{x}^{3}}-5{{x}^{2}}+9x-5=0,\]then the other roots are:

    A) 1 and\[2-i\]

    B) -1 and\[3+i\]

    C) 0 and 1

    D) -1 and\[i-2\]

    E) none of these

    View Answer play_arrow
  • question_answer147) The equation of the smallest degree with real coefficients having\[1+i\]as one of the roots, is:

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

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

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

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

    E) none of these

    View Answer play_arrow
  • question_answer148) The least integer k which makes the roots of the equation\[{{x}^{2}}+5x+k=0\]imaginary, is:

    A) 4

    B) 5

    C) 3

    D) 7

    E) 8

    View Answer play_arrow
  • question_answer149) If\[{{x}^{2}}+px+q=0\]is the quadratic equation whose roots are\[a-2\]and\[b-2\]where a and b are the roots of\[{{x}^{2}}-3x+1=0,\]then:

    A) \[p=1,q=5\]

    B) \[p=5,q=1\]

    C) \[p=1,q=1\]

    D) \[p=1,q=-1\]

    E) none of these

    View Answer play_arrow
  • question_answer150) The number of terms of the AP series 3, 7, 11, 15, ... to be taken so that the sum is 406, is:

    A) 5

    B) 10

    C) 12

    D) 14

    E) 20

    View Answer play_arrow
  • question_answer151) If the progression 3, 10, 17, ... and 63, 65, 67,... are such that their n th term are equal, then n is equal to:

    A) 13

    B) 15

    C) 9

    D) 8

    E) 11

    View Answer play_arrow
  • question_answer152) A force of magnitude 5 unit acting along the vector\[2\hat{i}-2\hat{j}+\hat{k}\]displaces the point of application from (1, 2, 3) to (5, 3, 7). Then the work done is:

    A) 50/7 unit

    B) 50/3 unit

    C) 25/3 unit

    D) 25/4 unit

    E) 3/50 unit

    View Answer play_arrow
  • question_answer153) An unit vector perpendicular to both\[\hat{i}+\hat{j}\] and \[\hat{j}+\hat{k}\] is:

    A) \[\hat{i}-\hat{j}+\hat{k}\]

    B) \[\hat{i}+\hat{j}+\hat{k}\]

    C) \[\frac{\hat{i}+\hat{j}-\hat{k}}{\sqrt{3}}\]

    D) \[\frac{\hat{i}-\hat{j}+\hat{k}}{\sqrt{3}}\]

    E) none of these

    View Answer play_arrow
  • question_answer154) The area of the triangle whose vertices are (1, 2, 3), (2, 5, -1) and (-1, 1, 2) is:

    A) 150 sq unit

    B) 145 sq unit

    C) \[\frac{\sqrt{155}}{2}\]sq unit

    D) \[\frac{155}{2}\]sq unit

    E) \[\frac{\sqrt{165}}{2}\]sq unit

    View Answer play_arrow
  • question_answer155) For any three vectors\[\overrightarrow{a},\overrightarrow{b},\overrightarrow{c},\] \[\overrightarrow{a}\times (\overrightarrow{b}+\overrightarrow{c})+\overrightarrow{b}\times (\overrightarrow{c}+\vec{a})+\vec{c}\times (\overrightarrow{a}+\overrightarrow{b})\]is:

    A) \[\vec{0}\]

    B) \[\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}\]

    C) \[\overrightarrow{a}.(\overrightarrow{b}\times \overrightarrow{c})\]

    D) \[(\overrightarrow{a}\times \overrightarrow{b}).\overrightarrow{c}\]

    E) none of these

    View Answer play_arrow
  • question_answer156) The equation of the plane passing through the intersection of the planes\[x+2y+3z+4=0\] and\[4x+3y+2z+1=0\]and the origin is:

    A) \[3x+2y+z+1=0\]

    B) \[3x+2y+z=0\]

    C) \[2x+3y+\text{ }z=0\]

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

    E) none of the above

    View Answer play_arrow
  • question_answer157) If\[\overrightarrow{a},\text{ }\overrightarrow{b},\text{ }\overrightarrow{c}\]are any three vectors, then \[[\overrightarrow{a}\,\text{+}\,\overrightarrow{b}\,\,\overrightarrow{b}\,+\,\overrightarrow{c}\,\overrightarrow{c}\,+\,\overrightarrow{a}]\] is equal to:

    A) \[[\overrightarrow{a}\,\,\overrightarrow{b}\,\,\overrightarrow{c}]\]

    B) \[0\]

    C) \[2[\overrightarrow{a}\,\,\overrightarrow{b}\,\,\overrightarrow{c}]\]

    D) \[{{[\overrightarrow{a}\,\,\overrightarrow{b}\,\,\overrightarrow{c}]}^{2}}\]

    E) \[(\overrightarrow{a}\,\times \,\overrightarrow{b})\times \,\,\overrightarrow{c}\]

    View Answer play_arrow
  • question_answer158) The volume of the parallelepiped whose coterminous edges are\[\hat{i}-\hat{j}+\hat{k},2\hat{i}-4\hat{j}+5\hat{k}\] and\[3\hat{i}-5\hat{j}+2\hat{k}\]is:

    A) 4 cu unit

    B) 3 cu unit

    C) 2 cu unit

    D) 1 cu unit

    E) 8 cu unit

    View Answer play_arrow
  • question_answer159) If \[\left( \frac{1}{2},\,\frac{1}{3},\,n \right)\] are the direction cosines of a line, then the value of n is:

    A) \[\frac{\sqrt{23}}{6}\]

    B) \[\frac{23}{36}\]

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

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

    E) \[\frac{1}{6}\]

    View Answer play_arrow
  • question_answer160) For any vector\[\overrightarrow{a},\hat{i}\times (\overrightarrow{a}\times \hat{i})+\hat{j}\times (\overrightarrow{a}\times \hat{j})\]\[+\hat{k}\times (\overrightarrow{a}\times \hat{k})\]is equal to:

    A) \[\overrightarrow{0}\]

    B) \[\overrightarrow{a}\]

    C) \[2\overrightarrow{a}\]

    D) \[3\overrightarrow{a}\]

    E) \[4\overrightarrow{a}\]

    View Answer play_arrow
  • question_answer161) The equation of the plane passing through (2, 3, 4) and parallel to the plane \[5x-6y+7z=3\]is:

    A) \[5x-6y+7z+20=0\]

    B) \[5x-6y+7z-20=0\]

    C) \[5x+6y-7z+3=0\]

    D) \[5x+6y+7z+3=0\]

    E) \[5x+6y+7z-3=0\]

    View Answer play_arrow
  • question_answer162) The first three terms in the expansion of\[{{(1+ax)}^{n}}(n\ne 0)\]are\[1,6x\]and\[16{{x}^{2}}\].Then the values of a and n are respectively:

    A) 2 and 9

    B) 3 and 2

    C) \[\frac{2}{3}\]and 9

    D) \[\frac{3}{2}\]and 6

    E) \[\frac{-2}{3}\] and 9

    View Answer play_arrow
  • question_answer163) Value of the determinant \[\left| \begin{matrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \\ \end{matrix} \right|\]is:

    A) \[1+abc+ab+bc+ca\]

    B) \[abc\]

    C) \[4abc\]

    D) \[abc\left( \frac{1}{a}+\frac{1}{b}+\frac{1}{c} \right)\]

    E) \[abc\left( 1+\frac{1}{a}+\frac{1}{b}+\frac{1}{c} \right)\]

    View Answer play_arrow
  • question_answer164) If the value of the determinant \[\left| \begin{matrix} x+1 & 1 & 1 \\ 2 & x+2 & 2 \\ 3 & 3 & x+3 \\ \end{matrix} \right|\]is equal to zero, then\[x\]is:

    A) 0 and\[-6\]

    B) 0 and 6

    C) 6

    D) \[-6\]

    E) \[0\]

    View Answer play_arrow
  • question_answer165) The value of a for which the matrix\[A=\left[ \begin{matrix} a & 2 \\ 2 & 4 \\ \end{matrix} \right]\]is singular:

    A) \[a\ne 1\]

    B) \[a=1\]

    C) \[a=0\]

    D) \[a=-1\]

    E) none of these

    View Answer play_arrow
  • question_answer166) If \[A=\left[ \begin{matrix} 2 & -1 \\ -1 & 2 \\ \end{matrix} \right]\]and\[I\]is the unit matrix of order two, then\[{{A}^{2}}\]is equal to:

    A) \[4A-3I\]

    B) \[3A-4I\]

    C) \[A-I\]

    D) \[A+I\]

    E) none of these

    View Answer play_arrow
  • question_answer167) If A and B are two square matrices of the same order, then\[{{(A-B)}^{2}}\]:

    A) \[{{A}^{2}}-AB-BA+{{B}^{2}}\]

    B) \[{{A}^{2}}-2AB+{{B}^{2}}\]

    C) \[{{A}^{2}}-2BA+{{B}^{2}}\]

    D) \[{{A}^{2}}-{{B}^{2}}\]

    E) \[{{A}^{2}}+{{B}^{2}}\]

    View Answer play_arrow
  • question_answer168) If\[P=\left[ \begin{matrix} i & 0 & -i \\ 0 & -i & i \\ -i & i & 0 \\ \end{matrix} \right]\]and\[Q=\left[ \begin{matrix} -i & i \\ 0 & 0 \\ i & -i \\ \end{matrix} \right],\]then PQ is equal to:

    A) \[\left[ \begin{matrix} -2 & 2 \\ 1 & -1 \\ 1 & -1 \\ \end{matrix} \right]\]

    B) \[\left[ \begin{matrix} 2 & -2 \\ -1 & 1 \\ -1 & 1 \\ \end{matrix} \right]\]

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

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

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

    View Answer play_arrow
  • question_answer169) If\[I\]is the unit matrix of order 10, then the determinant of\[\lambda \]is equal to:

    A) 10

    B) 1

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

    D) 9

    E) 0

    View Answer play_arrow
  • question_answer170) If the vectors\[3\hat{i}+\lambda \hat{j}+\hat{k}\]and\[2\hat{i}-\hat{j}+8\hat{k}\]are perpendicular, then\[\lambda \]is:

    A) \[-14\]

    B) \[7\]

    C) \[14\]

    D) \[\frac{1}{7}\]

    E) \[\frac{1}{14}\]

    View Answer play_arrow
  • question_answer171) The projection of the vector\[\hat{i}+\hat{j}+\hat{k}\]along the vector\[\hat{j}\] is:

    A) 1

    B) 0

    C) 2

    D) \[-1\]

    E) \[-2\]

    View Answer play_arrow
  • question_answer172) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{1-\cos mx}{1-\cos mx}\]is equal to:

    A) \[\frac{m}{n}\]

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

    C) \[0\]

    D) \[\frac{{{n}^{2}}}{{{m}^{2}}}\]

    E) \[\frac{n}{m}\]

    View Answer play_arrow
  • question_answer173) Which of the following is not true?

    A) a polynomial function is always continuous

    B) a continuous function is always differentiable

    C) a differentiable function is always continuous

    D) \[{{e}^{x}}\]is continuous for all\[x\]

    E) \[log\text{ }x\]is continuous for all\[x\]greater than zero

    View Answer play_arrow
  • question_answer174) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{a}^{x}}-{{b}^{x}}}{{{e}^{x}}-1}\]is equal to:

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

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

    C) \[\log ab\]

    D) \[\log (a+b)\]

    E) 0

    View Answer play_arrow
  • question_answer175) The derivative of\[{{x}^{6}}+{{6}^{x}}\]with respect to\[x\]is:

    A) \[12x\]

    B) \[x+4\]

    C) \[6{{x}^{5}}+{{6}^{x}}log\text{ }6\]

    D) \[6{{x}^{5}}+{{x}^{{{6}^{x-1}}}}\]

    E) none of these

    View Answer play_arrow
  • question_answer176) If\[x=a\text{ }co{{s}^{4}}\theta ,\text{ }y=a\text{ }si{{n}^{4}}\theta ,\]then y at \[\theta =\frac{3\pi }{4}\]is:

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

    B) 1

    C) \[-1\]

    D) \[-{{a}^{2}}\]

    E) \[\pi \]

    View Answer play_arrow
  • question_answer177) If\[\sin y+{{e}^{-x\cos y}}=e,\]then\[\frac{dy}{dx}\]at\[(1,\pi )\]is:

    A) \[\sin y\]

    B) \[-x\cos y\]

    C) \[e\]

    D) \[\sin y-x\cos y\]

    E) \[\sin y+x\cos y\]

    View Answer play_arrow
  • question_answer178) If\[x={{\sin }^{-1}}(3t-4{{t}^{3}})\]and\[y={{\cos }^{-1}}(\sqrt{1-{{t}^{2}}}),\]then\[\frac{dy}{dx}\]is equal to:

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

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

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

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

    E) \[0\]

    View Answer play_arrow
  • question_answer179) The second derivative of\[a{{\sin }^{3}}t\]with respect to\[a{{\cos }^{3}}t\]at\[t=\frac{\pi }{4}\]is:

    A) \[\frac{4\sqrt{2}}{3a}\]

    B) \[2\]

    C) \[\frac{1}{12a}\]

    D) \[0\]

    E) none of these

    View Answer play_arrow
  • question_answer180) The equation of the tangent to the curve \[(1+{{x}^{2}})y=2-x\]where it crosses the\[x-\]axis, is:

    A) \[x+5y=2\]

    B) \[x-5y=2\]

    C) \[5x-y=2\]

    D) \[5x+y-2=0\]

    E) \[x-5y=0\]

    View Answer play_arrow
  • question_answer181) The sides of an equilateral triangle are increasing at the rate of 2 cm/s. The rate at which the area increases, when the side is 10 cm, is:

    A) \[\sqrt{3}\,sq\text{ }cm/s\]

    B) 10 sq cm/s

    C) \[10\sqrt{3}\,sq\text{ }cm/s\]

    D) \[\frac{10}{\sqrt{3}}\,sq\text{ }cm/s\]

    E) \[10\sqrt{2}\,sq\text{ }cm/s\]

    View Answer play_arrow
  • question_answer182) The differential equation for which\[y=a\text{ }cos\text{ }x+b\text{ }sin\text{ }x\] is a solution, is:

    A) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+y=0\]

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

    C) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+(a+b)y=0\]

    D) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=(a+b)y\]

    E) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=(a-b)y\]

    View Answer play_arrow
  • question_answer183) The solution of\[\frac{dy}{dx}+p(x)y=0\]is:

    A) \[y=c{{e}^{\int{p\,dx}}}\]

    B) \[y=c{{e}^{-\int{p\,dx}}}\]

    C) \[x=c{{e}^{-\int{p\,dy}}}\]

    D) \[x=c{{e}^{\int{p\,dy}}}\]

    E) none of these

    View Answer play_arrow
  • question_answer184) The differential equation of the family of lines passing through the origin is:

    A) \[x\frac{dy}{dx}+y=0\]

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

    C) \[\frac{dy}{dx}=y\]

    D) \[\frac{dy}{dx}=x\]

    E) \[x\frac{dy}{dx}-y=0\]

    View Answer play_arrow
  • question_answer185) The solution of\[\frac{dy}{dx}+y={{e}^{-x}};y(0)=0\]is:

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

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

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

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

    E) \[y=x{{e}^{x}}\]

    View Answer play_arrow
  • question_answer186) A batsman scores runs in 10 innings 34, 38, 42, 46, 44, 46, 48, 54, 55, 63, 46. Then the mean deviation is:

    A) 8.6

    B) 6.4

    C) 10.6

    D) 9.6

    E) 7.6

    View Answer play_arrow
  • question_answer187) A coin is tossed 10 times. The probability of getting exactly 6 heads is:

    A) \[\frac{512}{105}\]

    B) \[\frac{105}{512}\]

    C) \[\frac{100}{513}\]

    D) \[^{10}{{C}_{6}}\]

    E) \[^{10}{{C}_{4}}\,\times 6!\]

    View Answer play_arrow
  • question_answer188) If\[P(A)=\frac{2}{3},P(B)=\frac{1}{2}\]and\[P(A\cup B)=\frac{5}{6},\]then events A and B are:

    A) mutually exclusive

    B) independent as well as mutually exclusive

    C) independent

    D) dependent only on A

    E) dependent only on B

    View Answer play_arrow
  • question_answer189) For the data

    \[x\] 4 7 8 3 4
    \[y\] 5 8 6 3 5
    the Karl Pearson coefficient is:

    A) \[\frac{63}{\sqrt{94\times 66}}\]

    B) \[63\]

    C) \[\frac{63}{\sqrt{94}}\]

    D) \[\frac{63}{\sqrt{66}}\]

    E) \[\frac{1}{\sqrt{94\times 66}}\]

    View Answer play_arrow
  • question_answer190) The average weight of students in a class of 35 students is 40 kg. If the weight of the teacher be included, the average weight rises by\[\frac{1}{2}\]kg. The weight of the teacher is:

    A) 40.5 kg

    B) 50 kg

    C) 41 kg

    D) 40 kg

    E) 58 kg

    View Answer play_arrow
  • question_answer191) In a bivariate data\[\Sigma x=30,\Sigma y=400,\Sigma {{x}^{2}}=196,\Sigma xy=850\]and\[n=10\]. The regression coefficient of y on \[x\]is:

    A) \[-3.1\]

    B) \[-3.2\]

    C) \[-3.3\]

    D) \[-3.4\]

    E) \[-3.5\]

    View Answer play_arrow
  • question_answer192) \[\int_{-2}^{2}{|1-x{{|}^{2}}}dx\]is equal to:

    A) 4

    B) 2

    C) \[-2\]

    D) 0

    E) 1

    View Answer play_arrow
  • question_answer193) \[\int{\frac{\sqrt{\tan }x}{\sin x\cos x}}dx\]is equal to:

    A) \[2\tan x+c\]

    B) \[\sqrt{\cot x}+c\]

    C) \[2\sqrt{\tan x}+c\]

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

    E) \[\cot x+c\]

    View Answer play_arrow
  • question_answer194) \[\int{\frac{dx}{{{x}^{2}}+4x+13}}\]is equal to:

    A) \[\log ({{x}^{2}}+4x+130)+c\]

    B) \[\frac{1}{3}{{\tan }^{-1}}\left( \frac{x+2}{3} \right)+c\]

    C) \[\log (2x+4)+c\]

    D) \[\frac{1}{{{x}^{2}}+4x+13}+c\]

    E) \[\frac{2x+4}{{{({{x}^{2}}+4x+13)}^{2}}}+c\]

    View Answer play_arrow
  • question_answer195) \[\int_{0}^{1}{\frac{d}{dx}}\left[ {{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right) \right]dx\]is equal to:

    A) \[0\]

    B) \[\pi \]

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

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

    E) \[-\pi \]

    View Answer play_arrow
  • question_answer196) \[\int_{0}^{\frac{\pi }{2}}{\frac{\sin x}{\sin x+\cos x}}dx\]equals to:

    A) \[\pi \]

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

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

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

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

    View Answer play_arrow
  • question_answer197) The area bounded by the parabolas\[{{y}^{2}}=4ax\]and\[{{x}^{2}}=4ay\]is:

    A) \[\frac{8{{a}^{3}}}{3}sq\ unit\]

    B) \[\frac{16{{a}^{2}}}{3}sq\ unit\]

    C) \[\frac{32{{a}^{2}}}{3}sq\ unit\]

    D) \[\frac{64{{a}^{2}}}{3}sq\ unit\]

    E) \[\frac{128{{a}^{2}}}{3}sq\ unit\]

    View Answer play_arrow
  • question_answer198) The area of the region\[\{(x,y):{{x}^{2}}+{{y}^{2}}\le 1\le x+y\}\]is:

    A) \[\frac{{{\pi }^{2}}}{5}sq\,unit\]

    B) \[\frac{{{\pi }^{2}}}{2}sq\,unit\]

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

    D) \[\frac{\pi }{4}sq\,unit\]

    E) \[\left( \frac{\pi }{4}-\frac{1}{2} \right)sq\,unit\]

    View Answer play_arrow
  • question_answer199) The area bounded by the curve\[y=sin\text{ }x\]between the ordinates \[x=0,\,\,x=\pi \] and the\[x-\]axis is:

    A) 2 sq unit

    B) 4 sq unit

    C) 1 sq unit

    D) 3 sq unit

    E) 0

    View Answer play_arrow
  • question_answer200) The degree of the differential equation\[\frac{{{d}^{2}}y}{d{{x}^{2}}}+{{\left( \frac{dy}{dx} \right)}^{3}}+6y=0\]is:

    A) 1

    B) 3

    C) 2

    D) 5

    E) none of these

    View Answer play_arrow
  • question_answer201) The solution of the equation \[(2y-1)dx-(2x+3)dy=0\]is:

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

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

    C) \[\frac{2x-3}{2y-1}=c\]

    D) \[\frac{2y+1}{2x-3}=c\]

    E) \[\frac{2x+1}{2y-3}=c\]

    View Answer play_arrow
  • question_answer202) If \[f(x)=\left\{ \begin{matrix} \frac{{{x}^{2}}-9}{x-3} \\ 2x+k \\ \end{matrix} \right.\]if \[x\ne 3\]is continuous at otherwise\[x=3,\]then k is equal to:

    A) 3

    B) 0

    C) \[-6\]

    D) \[\frac{1}{6}\]

    E) \[-\frac{1}{6}\]

    View Answer play_arrow
  • question_answer203) The function\[f(x)=1-{{x}^{3}}-{{x}^{5}}\]is decreasing for:

    A) \[1\le x\le 5\]

    B) \[x\le 1\]

    C) \[x\ge 1\]

    D) all values of\[x\]

    E) \[0\le x\le 1\]

    View Answer play_arrow
  • question_answer204) \[\frac{d}{dx}({{x}^{x}})\]is equal to:

    A) \[log\text{ }x\]

    B) \[\log {{e}^{x}}\]

    C) \[{{x}^{x}}log\text{ }x\]

    D) \[{{x}^{x}}\log e\,x\]

    E) \[{{x}^{x}}\log \text{ }(1-x)\]

    View Answer play_arrow
  • question_answer205) If the displacements of a particle at time t is given by\[{{s}^{2}}=a{{t}^{2}}+2bt+c,\]then acceleration varies as:

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

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

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

    D) \[{{s}^{3}}\]

    E) \[{{s}^{2}}\]

    View Answer play_arrow
  • question_answer206) If PQ and PR are the two sides of a triangle, then the angle between them which gives maximum area of the triangle, is:

    A) \[\pi \]

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

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

    D) \[2\pi \]

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

    View Answer play_arrow
  • question_answer207) The function\[y=a(a-\cos x)\]is maximum when\[x\]is equal to:

    A) \[\pi \]

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

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

    D) \[-\frac{\pi }{6}\]

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

    View Answer play_arrow
  • question_answer208) \[\int{\frac{\sin x}{\sin (x-\alpha )}}dx\]is equal to:

    A) \[(x-\alpha )\cos \alpha +\sin \alpha \log \sin (x-\alpha )+c\]

    B) \[(x-\alpha )\cos x+\log \sin (x-\alpha )+c\]

    C) \[\sin (x-\alpha )+\sin x+c\]

    D) \[\cos (x-\alpha )+\cos x+c\]

    E) none of the above

    View Answer play_arrow
  • question_answer209) \[\int{{{13}^{x}}}dx\]is:

    A) \[\frac{{{13}^{x}}}{\log 13}+c\]

    B) \[{{13}^{x+1}}+c\]

    C) \[14x+c\]

    D) \[{{14}^{x+1}}+c\]

    E) none of these

    View Answer play_arrow
  • question_answer210) \[\int_{0}^{\frac{\pi }{2}}{\sin 2x}\log \tan x\,dx\]is equal to:

    A) \[\pi \]

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

    C) 1

    D) \[2\pi \]

    E) 0

    View Answer play_arrow
  • question_answer211) \[\int_{0}^{\frac{\pi }{2}}{x\sin x\,dx}\]is equal to:

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

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

    C) \[\pi \]

    D) 1

    E) 0

    View Answer play_arrow
  • question_answer212) The inclination of the straight line passing through the point\[(-3,6)\]and the midpoint of the line joining the points\[(4,-5)\]and\[(-2,9)\]

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

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

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

    D) \[\frac{3\pi }{4}\]

    E) \[\frac{5\pi }{6}\]

    View Answer play_arrow
  • question_answer213) A point moves such that the area of the triangle formed by it with the points (1, 5) and \[(3,-7)\]is 21 sq unit. Then locus of the point is:

    A) \[6x+y-32=0\]

    B) \[6x-y+32=0\]

    C) \[x+6y-32=0\]

    D) \[6x-y-32=0\]

    E) none of these

    View Answer play_arrow
  • question_answer214) The line\[\frac{x}{a}-\frac{y}{b}=1\]cuts the\[x-\]axis at P. The equation of the line through P perpendicular to the given line is:

    A) \[x+y=ab\]

    B) \[x+y=a+b\]

    C) \[ax+by={{a}^{2}}\]

    D) \[bx+ay={{b}^{2}}\]

    E) \[ax-by=ab\]

    View Answer play_arrow
  • question_answer215) The value of\[\lambda \]For which the lines\[3x+4y=5,\] \[2x+3y=4\]and\[\lambda x+4y=6\]meet at a point, is:

    A) 2

    B) 1

    C) 4

    D) 3

    E) 0

    View Answer play_arrow
  • question_answer216) Three vertices of a parallelogram taken in order are\[(-1,-6),(2,-5)\]and (7, 2). The fourth vertex is:

    A) (1, 4)

    B) (1, 1)

    C) (4, 4)

    D) (4, 1)

    E) 0

    View Answer play_arrow
  • question_answer217) The orthocentre of the triangle whose vertices are\[(5,-2),(-1,2)\]and (1, 4), is:

    A) \[\left( -\frac{1}{5},\frac{16}{5} \right)\]

    B) \[\left( \frac{14}{5},\frac{1}{5} \right)\]

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

    D) \[\left( \frac{14}{5},\frac{14}{5} \right)\]

    E) \[(5,14)\]

    View Answer play_arrow
  • question_answer218) Distance between the lines\[5x+3y-7=0\]and \[15x+9y+14=0\]is:

    A) \[\frac{35}{\sqrt{34}}\]

    B) \[\frac{1}{3\sqrt{34}}\]

    C) \[\frac{35}{3\sqrt{34}}\]

    D) \[\frac{35}{2\sqrt{34}}\]

    E) 35

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  • question_answer219) If the equation\[2{{x}^{2}}+7xy+3{{y}^{2}}-9x-7y\]\[+k=\]\[0\]represents a pair of lines, then k is equal to:

    A) 4

    B) 2

    C) 1

    D) \[-4\]

    E) none of these

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  • question_answer220) The angle between the lines\[2x-y+3=0\] and\[x+2y+3=0\]is:

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

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

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

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

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

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  • question_answer221) Distance between the pair of lines represented by the equation\[{{x}^{2}}-6xy+9{{y}^{2}}+\] \[3x-9y-4=0\]is:

    A) \[\frac{15}{\sqrt{10}}\]

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

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

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

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

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  • question_answer222) If\[tan\text{ }A+cot\text{ }A=4,\]then\[ta{{n}^{4}}A+co{{t}^{4}}A\]is equal to:

    A) 110

    B) 191

    C) 80

    D) 194

    E) 195

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  • question_answer223) If\[\tan \left( \frac{\theta }{2} \right)=t,\]then\[\left( \frac{1-{{t}^{2}}}{1+{{t}^{2}}} \right)\]is equal to:

    A) \[\cos \theta \]

    B) \[\sin \theta \]

    C) \[\sec \theta \]

    D) \[\cos \theta \]

    E) \[\tan \theta \]

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  • question_answer224) The period of the function\[y=sin\text{ }2x\]is:

    A) \[2\pi \]

    B) \[\pi \]

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

    D) \[4\pi \]

    E) \[3\pi \]

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  • question_answer225) If the angle of elevation of the top of a tower at a distance 500 m from its foot is 30?, then the height of the tower is:

    A) \[\frac{1}{\sqrt{3}}m\]

    B) \[500\sqrt{3}m\]

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

    D) \[\frac{1}{500}m\]

    E) \[\frac{500}{\sqrt{3}}m\]

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  • question_answer226) In triangle\[ABC,\text{ }a({{b}^{2}}+{{c}^{2}})cos\text{ }A+b({{c}^{2}}+{{a}^{2}})\] \[cos\text{ }B+c({{a}^{2}}+{{b}^{2}})cos\text{ }C\] is equal to:

    A) \[abc\]

    B) \[2\,abc\]

    C) \[3\,abc\]

    D) \[4\,abc\]

    E) 0

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  • question_answer227) The measures of the sides of a triangle are 3, 5 and 7. The greatest angle is:

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

    B) \[100{}^\circ \]

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

    D) \[120{}^\circ \]

    E) \[140{}^\circ \]

    View Answer play_arrow
  • question_answer228) If in triangle\[ABC,\text{ }cos\text{ }A=cos\text{ }B\text{ }cos\text{ }C,\]then \[cot\text{ }B\text{ }cot\text{ }C\]is equal to:

    A) 2

    B) 3

    C) 4

    D) 5

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

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  • question_answer229) If\[{{\tan }^{-1}}x+{{\tan }^{-1}}y+{{\tan }^{-1}}z=\pi ,\]then\[x+y+z\]is:

    A) \[xyz\]

    B) 0

    C) 1

    D) \[2xyz\]

    E) \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}\]

    View Answer play_arrow
  • question_answer230) If\[\theta ={{\sin }^{-1}}[\sin (-600{}^\circ )],\]then one of the possible values of\[\theta \]is:

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

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

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

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

    E) 0

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  • question_answer231) If \[x\sin 45{}^\circ {{\cos }^{2}}60{}^\circ =\frac{{{\tan }^{2}}60{}^\circ \cos ec30{}^\circ }{\sec 45{}^\circ {{\cot }^{2}}30{}^\circ }\]then\[x\]is equal to:

    A) 2

    B) 4

    C) 8

    D) 16

    E) 32

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  • question_answer232) The centre of a circle is\[(2,-3)\]and the circumference is\[10\pi \]Then the equation of the circle is:

    A) \[{{x}^{2}}+{{y}^{2}}+4x+6y+12=0.\]

    B) \[{{x}^{2}}+{{y}^{2}}-4x+6y+12=0\]

    C) \[{{x}^{2}}+{{y}^{2}}-4x+6y-12=0\]

    D) \[{{x}^{2}}+{{y}^{2}}-4x-6y-12=0\]

    E) \[{{x}^{2}}+{{y}^{2}}-4x-6y+12=0\]

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  • question_answer233) If the two circles\[2{{x}^{2}}+2{{y}^{2}}-3x+6y+k=0\]and\[{{x}^{2}}+{{y}^{2}}-4x+10y+16=0\]cut orthogonally, then the value of k is:

    A) 41

    B) 14

    C) 4

    D) 0

    E) 2

    View Answer play_arrow
  • question_answer234) The parabola\[{{y}^{2}}=x\]is symmetric about:

    A) \[x-\]axis

    B) \[y-\]axis

    C) both\[x\]and y axes

    D) the line\[y=x\]

    E) the line\[x=-y\]

    View Answer play_arrow
  • question_answer235) The equation of the parabola whose vertex is at\[(2,-1)\]and focus at\[(2,-3),\]is:

    A) \[{{x}^{2}}-4x-8y-12=0\]

    B) \[{{x}^{2}}-4x+8y+12=0\]

    C) \[{{x}^{2}}+8y=12\]

    D) \[{{x}^{2}}-4x+12=0\]

    E) none of the above

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  • question_answer236) The centroid of a triangle is (2, 7) and two of its vertices are (4, 8) and\[(-2,6)\]. The third vertex is:

    A) (0, 0)

    B) (4, 7)

    C) (7, 4)

    D) (7, 7)

    E) (4, 4)

    View Answer play_arrow
  • question_answer237) The line\[y=mx+c\]touches the curve\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1,\]if:

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

    B) \[{{c}^{2}}={{a}^{2}}{{m}^{2}}-{{b}^{2}}\]

    C) \[{{c}^{2}}={{b}^{2}}{{m}^{2}}-{{a}^{2}}\]

    D) \[{{a}^{2}}={{b}^{2}}{{m}^{2}}+{{c}^{2}}\]

    E) none of these

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  • question_answer238) The length of the tangent from a point on the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+{{c}_{1}}=0\]to the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+{{c}_{2}}=0\]is:

    A) \[\sqrt{{{c}_{2}}-{{c}_{1}}}\]

    B) \[{{c}_{2}}-{{c}_{1}}\]

    C) \[0\]

    D) \[{{c}_{1}}-{{c}_{2}}\]

    E) none of these

    View Answer play_arrow
  • question_answer239) The eccentricity of the conic\[9{{x}^{2}}+25{{y}^{2}}=225\] is:

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

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

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

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

    E) \[\frac{3}{5}\]

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  • question_answer240) The angles of a triangle are in the ratio\[1:3:5\]. Then the greatest angle is:

    A) \[\frac{5\pi }{9}\]

    B) \[\frac{2\pi }{9}\]

    C) \[\frac{7\pi }{9}\]

    D) \[\frac{11\pi }{9}\]

    E) \[\frac{\pi }{9}\]

    View Answer play_arrow
  • question_answer241) A circular wire of radius 7 cm is cut and bend again into an arc of a circle of radius 12 cm. Then angle subtended by the arc at the centre is:

    A) \[50{}^\circ \]

    B) \[210{}^\circ \]

    C) \[100{}^\circ \]

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

    E) \[30{}^\circ \]

    View Answer play_arrow

   



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