Solved papers for BCECE Engineering BCECE Engineering Solved Paper-2011

done BCECE Engineering Solved Paper-2011

  • question_answer1) Which of the following pairs have identical dimensions?

    A) Momentum and force

    B) Pressure and surface tension

    C) Moment of force and angular momentum

    D) Surface tension and surface energy

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  • question_answer2) A train 100 m long travelling at 40 m/s starts overtaking another train 200 m long travelling at 30 m/s. The time taken by the first train to pass the second train completely is

    A) 30 s

    B) 40 s

    C) 50 s

    D) 60 s

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  • question_answer3) A constant power P is applied to a particle of mass m. The distance travelled by the particle when its velocity increases from \[{{v}_{1}}\] to \[{{v}_{2}}\] is (neglect friction)

    A) \[\frac{\text{m}}{\text{3P}}\text{(v}\,_{\text{2}}^{\text{3}}\text{-v}\,_{\text{1}}^{\text{3}}\text{)}\]

    B) \[\frac{\text{m}}{\text{3P}}\text{(}{{\text{v}}_{2}}\text{-}{{\text{v}}_{1}}\text{)}\]

    C) \[\frac{3P}{m}\text{(v}\,_{2}^{2}\text{-v}\,_{1}^{2}\text{)}\]

    D) \[\frac{m}{3P}\text{(v}\,_{2}^{2}\text{-v}\,_{1}^{2}\text{)}\]

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  • question_answer4) A spring of constant \[5\,\times {{10}^{3}}\,N/m\] is stretched initially by 5 cm from the unstretched position. Then the work required to stretch it further by another 5 cm is

    A) 6.25 Nm

    B) 12.5 Nm

    C) 18.75 Nm

    D) 25.00 Nm

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  • question_answer5) Four spheres each having mass m and radius r are placed with their centres on the four comers of a square of side a. Then the moment of inertia of the system about an axis along one of the sides of the square is

    A) \[\frac{8}{5}m{{r}^{2}}\]

    B) \[\frac{8}{5}m{{r}^{2}}+m{{a}^{2}}\]

    C) \[\frac{8}{5}m{{r}^{2}}+2m{{a}^{2}}\]

    D) \[\frac{4}{5}m{{r}^{2}}+4m{{a}^{2}}\]

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  • question_answer6) If an artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth, the height of the satellite above the surface of the earth is

    A) \[2R\]

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

    C) \[R\]

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

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  • question_answer7) A 2 kg copper block is heated to \[500{}^\circ C\] and then it is placed on a large block of ice at \[0{}^\circ C\]. If the specific heat capacity of copper is 400 J/kg/C and latent heat of water is \[3.5\times {{10}^{5}}J/kg\]. The amount of ice that can melt is

    A) 7/8 kg

    B) 7/5 kg

    C) 8/7 kg

    D) 5/7 kg

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  • question_answer8) Number of waves in 8 cm of vacuum is same as number of waves in x cm of a medium. Refractive index of medium is 4/3, then the value x is

    A) 32/3 cm

    B) 12 cm

    C) 6 cm

    D) 4 cm

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  • question_answer9) Consider a gas with density \[\rho \] and \[\overline{\text{c}}\] as the root mean square velocity of its molecules contained in a volume. If the system moves as whole with velocity v, then the pressure exerted by the gas is

    A) \[\frac{1}{3}\rho {{\overline{\text{c}}}^{2}}\]

    B) \[\frac{1}{3}\rho {{(c+v)}^{2}}\]

    C) \[\frac{1}{3}\rho {{(\overline{c}-v)}^{2}}\]

    D) \[\frac{1}{3}\rho {{({{\overline{c}}^{2}}-v)}^{2}}\]

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  • question_answer10) At 127?C radiated energy is \[2.7\,\times {{10}^{-3}}\,J/s\]. At what temperature radiated energy is \[4.32\,\times {{10}^{6}}J/s\]?

    A) 400 K

    B) 4000 K

    C) 80000 K

    D) 40000 K

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  • question_answer11) The minimum phase difference between two simple harmonic oscillations,

    A) \[{{y}_{1}}=\frac{1}{2}\sin \,\omega t+\frac{\sqrt{3}}{2}\cos \,\omega t\] \[{{y}_{2}}=\sin \,\omega t+\,\omega t,\,\text{is}\] \[\frac{7\pi }{12}\]

    B) \[\frac{\pi }{12}\]

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

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

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  • question_answer12) A rubber cord catapult has cross-sectional area \[25\,m{{m}^{2}}\] and initial length of rubber cord is 10 cm. It is stretched to 5 cm and then released to project a missile of mass 5 g. Taking \[{{Y}_{rubber}}\,=5\times {{10}^{8}}N{{m}^{-2}},\] velocity of projected missile is

    A) \[20\,m{{s}^{-1}}\]

    B) \[100\,m{{s}^{-1}}\]

    C) \[250\,m{{s}^{-1}}\]

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

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  • question_answer13) The material of a wire has a density of \[1.4\,g/c{{m}^{3}}\]. If it is not wetted by a liquid of surface tension 44 dyne/cm, then the maximum radius of the wire which can float on the surface of liquid is

    A) \[\frac{10}{28}cm\]

    B) \[\frac{10}{14}cm\]

    C) \[\frac{10}{7}cm\]

    D) \[0.7cm\]

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  • question_answer14) Binding energy of satellite is \[4\times {{10}^{8}}J\]. Its PE is

    A) \[-4\times {{10}^{8}}J\]

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

    C) \[8\times {{10}^{8}}J\]

    D) \[4\times {{10}^{8}}J\]

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  • question_answer15) A current of 0.01 mA passes through the potentiometer wire of a resistivity of \[{{10}^{9}}\Omega \] and area of cross-section \[{{10}^{-2}}c{{m}^{2}}\]. The potential gradient is

    A) \[\text{1}{{\text{0}}^{\text{9}}}\text{V/m}\]

    B) \[\text{1}{{\text{0}}^{11}}\text{V/m}\]

    C) \[\text{1}{{\text{0}}^{10}}\text{V/m}\]

    D) \[\text{1}{{\text{0}}^{8}}\text{V/m}\]

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  • question_answer16) A particle of mass m attached with a string of length l is just revolving on the vertical circle without slacking of the string. If \[{{v}_{A,}}{{v}_{B}}\] and\[{{v}_{D}}\] are speeds at positions A, B and D, then

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

    B) tension in string at D = 3 mg

    C) \[{{v}_{D}}=\sqrt{3gl}\]

    D) All of the above

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  • question_answer17) A bucket of water is being revolved in vertical circle of radius 1 m. Minimum frequency required to prevent the water from getting down the path is \[(g=10m/{{s}^{2}})\]

    A) \[\frac{2\pi }{\sqrt{10}}\]

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

    C) \[\frac{\sqrt{10}}{2\pi }\]

    D) \[\frac{\sqrt{5}}{2\pi }\]

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  • question_answer18) A round disc of moment of inertia \[{{I}_{2}}\] about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia \[{{l}_{1}}\] rotating with an angular velocity co about the same axis. The final angular velocity of the combination of discs is

    A) \[\frac{{{I}_{2}}\omega }{{{I}_{1}}+{{I}_{2}}}\]

    B) \[\omega \]

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

    D) \[\frac{({{I}_{1}}+{{I}_{2}})\omega }{{{I}_{1}}}\]

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  • question_answer19) Two discs have same mass and thickness. Their materials are of densities \[{{\rho }_{1}}\] and \[{{\rho }_{2.}}\] The ratio of their moment of inertia about central axis will be

    A) \[{{\rho }_{1}}:{{\rho }_{2}}\]

    B) \[{{\rho }_{1}}:{{\rho }_{2}}:1\]

    C) \[1:{{\rho }_{1}}\,{{\rho }_{2}}\]

    D) \[{{\rho }_{2}}:\,{{\rho }_{1}}\]

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  • question_answer20) A 4 m long wire of resistance \[8\,\Omega \] is connected in series with a battery of emf 2 V and a resistor of \[7\Omega .\] The internal resistance of the battery is \[1\Omega .\] What is the potential gradient along the wire?

    A) \[1.00\,V{{m}^{-1}}\]

    B) \[0.75\,V{{m}^{-1}}\]

    C) \[0.50\,V{{m}^{-1}}\]

    D) \[0.25\,V{{m}^{-1}}\]

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  • question_answer21) A uniform wire of \[16\,\Omega \] resistance is made into the form of a square. Two opposite corners of the square are connected by a wire of resistance \[16\,\Omega .\] The effective resistance between the other two opposite comers is

    A) \[32\,\Omega \]

    B) \[16\,\Omega \]

    C) \[8\,\Omega \]

    D) \[4\,\Omega \]

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  • question_answer22) A \[6\times {{10}^{-4}}\,F\] parallel plate air capacitor is connected to a 500 V batten. When air is replaced by another dielectric material, \[7.5\,\times {{10}^{-4}}C\] charge flows into the capacitor. The value of the dielectric constant of the material is

    A) 1.5

    B) 2.0

    C) 1.0025

    D) 3.5

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  • question_answer23) The 90 pF capacitor is connected to a 12 V battery. How many electrons are transferred from one plate to another?

    A) \[1.1\,\times {{10}^{9}}\]

    B) \[6.7\,\times {{10}^{9}}\]

    C) \[4\times {{10}^{19}}\]

    D) \[5\times {{10}^{19}}\]

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  • question_answer24) Given mass number of gold = 197, Density of gold \[=19.7\,g/c{{m}^{3}}\] Avogadros number \[=6\times {{10}^{23}}\]. The radius of the gold atom is approximately

    A) \[1.5\times {{10}^{-8}}m\]

    B) \[1.7\times {{10}^{-9}}m\]

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

    D) \[1.5\times {{10}^{-12}}m\]

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  • question_answer25) In Youngs double slit experiment, two slits are separated by 1 m. The slits are illuminated by a light of wavelength 650 nm. The source of light is placed symmetrically with respect to the two slits. Interference pattern is observed on a screen at a distance of 1 m from the slits. The distance between the third dark fringe and the fifth bright fringe from the centre of the pattern will be

    A) 1.62 mm

    B) 2.62 mm

    C) 5.62 mm

    D) 3.62 mm

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  • question_answer26) R is a radius of a planet and p is its density. The escape velocity on its surface will be

    A) \[{{R}^{2}}\sqrt{4\pi G\rho /3}\]

    B) \[R\sqrt{4\pi G\rho /3}\]

    C) \[{{R}^{2}}\sqrt{8\pi G\rho /3}\]

    D) \[R\sqrt{8\pi G\rho /3}\]

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  • question_answer27) A satellite is moving in a circular orbit at a certain height above the earths surface. It takes \[5.26\,\times {{10}^{3}}\,s\] to complete one revolution with a centripetal acceleration equal to \[9.32\,\,m/{{s}^{2}}\]. The height of satellite orbiting above the earth is (Earths radius \[=6.37\,\times {{10}^{6}}\,m\])

    A) 220 km                

    B) 160 km

    C)  70 km                  

    D) 120 km

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  • question_answer28) The surface tension of soap solution is 0.03 N/m. The amount of work done in forming a bubble of radius 5 cm is

    A) 3.77 J

    B) 1.885 J

    C) \[0.95\times {{10}^{-3}}J\]

    D) \[1.9\times {{10}^{-3}}J\]

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  • question_answer29) The minimum velocity of capillary waves on the surface of water is (surface tension of water is \[=7.2\,\times {{10}^{-2}}N/m\])

    A) 0.23 m/s

    B) 0.46 m/s

    C) 0.69 m/s

    D) 0.92 m/s

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  • question_answer30) 30. A wire has a breaking stress of\[6\times {{10}^{5}}N/{{m}^{2}}\] and a density of \[3\times {{10}^{4}}kg/{{m}^{3}}\]. The length of the wire of the same material which will break under its town weight, (if \[g=10\,m/{{s}^{2}}\]) is

    A) 2000 m

    B) 2500 m

    C) 20 m

    D) 2 m

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  • question_answer31) A man measures the period of simple pendulum inside a stationary lift and finds it to be T second. If the lift accelerates downwards with acceleration of \[\frac{g}{4},\] the period of oscillation will be

    A) \[T\times \frac{\sqrt{3}}{2}s\]

    B) \[T\times \frac{2}{\sqrt{3}}s\]

    C) \[\frac{T}{2}s\]

    D) \[\sqrt{T}s\]

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  • question_answer32) A spherical black body with a radius of 12 cm radiates 450 W power at 500 K. If the radius were halved and temperature be doubled, the power radiated in watt would be

    A) 1800

    B) 900

    C) 3600

    D) 850

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  • question_answer33) If the emissive power of black surface at same temperature is \[400\,W/{{m}^{2}},\] the emissive and absorptive powers of the surface assuming it was initially ordinary surface, are (Given, Mass of the body m = 4.2 kg, area of body \[=5\times {{10}^{-2}}{{m}^{2}},\] rate of cooling \[\frac{d\theta }{dt}=\frac{1}{12}\times {{10}^{-2}}{{\,}^{\text{o}}}\text{C/min,}\] specific heat\[s=420J/kg{{\,}^{\text{0}}}\text{C)}\]

    A) e=\[a\]= 0.0735              

    B)  e = \[a\] = 0.0435

    C) e =\[a\]=0.0535   

    D) e=\[a\]= 0.0235

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  • question_answer34) The expression for total kinetic energy per unit volume of gas is

    A) \[\frac{E}{V}=\frac{P}{2}\]

    B) \[\frac{E}{V}=\frac{1}{3}P\]

    C) \[\frac{E}{V}=\frac{2}{3}P\]

    D) \[\frac{E}{V}=\frac{3}{2}P\]

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  • question_answer35) A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300 K. The ratio of the average rotational KE per. oxygen molecule that per nitrogen molecule is

    A) 1 : 1

    B) 1 : 2

    C) 2 : 1

    D) depends on the moments of inertia of the two molecules

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  • question_answer36) The wavelength and frequency of beam of light in water of refractive index 4/3 having wavelength 0.48 micron in air are

    A) \[0.16\,\times {{10}^{-6}}\,m,\,\,6.25\,\times {{10}^{14}}\,Hz\]

    B) \[0.36\,\times {{10}^{-6}}\,m,\,\,6.25\,\times {{10}^{14}}\,Hz\]

    C) \[0.36\,\times {{10}^{-6}}\,m,\,\,3.25\,\times {{10}^{14}}\,Hz\]

    D) \[0.26\,\times {{10}^{-6}}\,m,\,\,3.25\,\times {{10}^{14}}\,Hz\]

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  • question_answer37) A ray of light is incident on glass slab making an angle of incidence sin\[^{-1}\left( \frac{\sqrt{3}}{2} \right).\] What will be the angle of refraction in glass of refractive index 1.5?

    A) \[40{}^\circ \text{ }18\]

    B) \[24{}^\circ \text{ }49\]

    C) \[25{}^\circ \text{ }17\]

    D) \[35{}^\circ \text{ }16\]

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  • question_answer38) An electron at rest is accelerated through a potential difference of 200 V. If the electron acquires a velocity \[8.4\,\times {{10}^{6}}\,m/s,\] the value of e/m of electron is

    A) \[1.76\,\times {{10}^{-4}}C/kg\]

    B) \[1.76\,\times {{10}^{14}}C/kg\]

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

    D) \[1.76\,\times {{10}^{-16}}C/kg\]

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  • question_answer39) A radio transmitter operates at a frequency of 880 kHz and power of 10 kW. The number of photons emitted per second is

    A) \[13.27\,\times {{10}^{4}}\]

    B) \[13.27\,\times {{10}^{34}}\]

    C) \[1327\,\times {{10}^{34}}\]

    D) \[1.71\times {{10}^{31}}\]

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  • question_answer40) What is the voltage gain in a common emitter amplifier, when input resistance is \[3\,\Omega \] and load resistance is \[24\,\Omega \] with \[\beta =60\,?\]

    A) 480

    B) 2.4

    C) 4.8

    D) 8.4

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  • question_answer41) The input resistance or a common emitter transistor amplifier, if the output resistance is \[500\,k\Omega ,\], the current gain \[\alpha \] = 0.98 and the power gain is \[6.0625\,\times {{10}^{6}},\] is

    A) 198 \[\Omega \]

    B) \[300\,\Omega \]

    C) \[100\,\Omega \]

    D) \[400\,\Omega \]

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  • question_answer42) Which of the following transitions in hydrogen atom produces longest wavelength of radiation (or photon of minimum energy)?

    A) \[n=2,p=4\]

    B) \[n=3,p=4\]

    C) \[n=6,p=8\]

    D) \[n=5,p=6\]

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  • question_answer43) If\[\left( \frac{0.51\times {{10}^{-10}}}{4} \right)\]m, is the radius of smallest electron orbit in hydrogen like atom, then this atom is

    A) H-atom

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

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

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

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  • question_answer44) A series resonant circuit contains \[L=\frac{5}{\pi }mH,\] \[C=\frac{200}{\pi }\mu F\] and R = 100 \[\Omega \] If a source of emf It e = 200 sin 1000 \[1000\,\pi t\] is applied, then the rms current is

    A) 2 A

    B) 200\[\sqrt{2}\] A

    C) 100\[\sqrt{2}\] A

    D) 1.41 A

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  • question_answer45) A rod of length 1.0 m is rotated in a plane perpendicular to a uniform magnetic field of induction 0.25 T with a frequency of 12 rev/s. The induced emf across the ends of the rod is

    A) 18.89 V

    B) 3 V

    C) 15 V

    D) 9.42 V

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  • question_answer46) A ferromagnetic material is heated above its curie temperature. Which one is a correct statement?

    A) Ferromagnetic domains are perfectly arranged

    B) Ferromagnetic domains become random

    C) Ferromagnetic domains are not influenced

    D) Ferromagnetic material changes into diamagnetic material

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  • question_answer47) A material is placed in a magnetic field and. It is thrown out of it. Then the material is

    A) paramagnetic

    B) diamagnetic

    C) ferromagnetic

    D) non-magnetic

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  • question_answer48) A charged particle of mass m and charge q is accelerated through a potential difference of V volt. It enters a region of uniform magnetic field which is directed perpendicular to the direction of motion of the particle. The particle will move on a circular path of radius given by

    A) \[\sqrt{\frac{Vm}{q{{B}^{2}}}}\]

    B) \[\frac{2Vm}{q{{B}^{2}}}\]

    C) \[\sqrt{\frac{2Vm}{q}}.\left( \frac{1}{B} \right)\]

    D) \[\sqrt{\frac{Vm}{q}}.\left( \frac{1}{B} \right)\]

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  • question_answer49) An electron moves at right angle to a magnetic field of \[1.5\times {{10}^{-2}}T\] with a speed of \[6\times {{10}^{7}}\,m/s\]. If the specific charge on the electron is \[1.7\,\times {{10}^{11}}\,C/kg,\] the radius of the circular path will be

    A) 2.9 cm

    B) 3.9 cm

    C) 2.35 cm

    D) 2 cm

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  • question_answer50) In a circuit, 5 percent of total current passes through a galvanometer. If resistance of the galvanometer is G. Then the value of the shunt is

    A) 19 G

    B) 20 G

    C) \[\frac{G}{20}\]

    D) \[\frac{G}{19}\]

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  • question_answer51) Given, C (diamond)\[+\,{{O}_{2}}\xrightarrow{{}}C{{O}_{2}};\Delta H =-395\,kJ\] C (graphite) \[+\,{{O}_{2}}\xrightarrow{{}}C{{O}_{2}};\Delta H =-393\,kJ\] The heat of formation of diamond from graphite is

    A) \[+\,2.0\,kJ\]                    

    B) \[-1.5\,kJ\]        

    C) \[-788\,kJ\]       

    D) \[788\,kJ\]

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  • question_answer52) The type of isomerism observed in benzaldoxime is

    A) optical

    B) functional

    C) geometrial

    D) tautomerism

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  • question_answer53) Sodium metal is prepared commercially by electrolysis of fused NaCl by

    A) Downs process

    B) Nelson cell

    C) Solvay process

    D) Castner and Kellners cell

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  • question_answer54) The value of \[x\] is maximum for

    A) \[MgS{{O}_{4}}.\,x\,{{H}_{2}}O\]

    B) \[CaS{{O}_{4}}.\,x\,{{H}_{2}}O\]

    C) \[BaS{{O}_{4}}.\,x\,{{H}_{2}}O\]

    D) All have the same value of \[x\]

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  • question_answer55) Heating of ore in absence of air below its melting point is called

    A) leaching

    B) roasting

    C) smelting

    D) calcination

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  • question_answer56) In fluorine group of Periodic Table, on going down

    A) ionic radius increases

    B) electronegativity increases

    C) ionization potential increases

    D) reactivity increases

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  • question_answer57) The ether that undergoes electrophilic substitution reactions is

    A) \[C{{H}_{3}}O{{C}_{2}}{{H}_{5}}\]

    B) \[{{C}_{6}}{{H}_{5}}OC{{H}_{3}}\]

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

    D) \[{{C}_{2}}{{H}_{5}}O{{C}_{2}}{{H}_{5}}\]

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  • question_answer58) The order of reactivity of alcohols towards sodium metal is

    A) Primary > Secondary > Tertiary

    B) Primary < Secondary < Tertiary

    C) Primary < Secondary > Tertiary

    D) Primary > Secondary < Tertiary

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  • question_answer59) If one mole of a substance is present in 1 kg of solvent then its concentration is called

    A) molar cone.

    B) molal cone.

    C) normality

    D) strength wt/wt.

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  • question_answer60) If the pressure and absolute temperature of 2 L of carbondioxide gas are doubled, the value of the gas would become

    A) 2 L

    B) 4 L

    C) 5 L

    D) 7 L

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  • question_answer61) \[C{{H}_{3}}CO{{O}^{-}}\] ion is a

    A) weak conjugate base

    B) strong conjugate base

    C) weak conjugate acid

    D) strong conjugate add

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  • question_answer62) The hybrid state of C in charcoal is

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

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

    C) \[sp\]

    D) No specific state

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  • question_answer63) The shape of \[\text{Cl}{{\text{F}}_{\text{3}}}\]molecule is

    A) triangular planar

    B) pyramidal

    C) T-shape

    D) trigonal bipyramidal

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  • question_answer64) Equivalent weight of crystalline oxalic acid is

    A) 90

    B) 63

    C) 53

    D) 45

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  • question_answer65) If \[x\,\text{mol}\,{{\text{L}}^{-1}}\]is the solubility of \[\text{KAl(S}{{\text{O}}_{\text{4}}}{{\text{)}}_{\text{2}}}\] then \[{{\text{K}}_{\text{sp}}}\]is equal to

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

    B) \[4{{x}^{4}}\]

    C) \[{{x}^{4}}\]

    D) \[4{{x}^{3}}\]

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  • question_answer66) In the reaction, \[{{N}_{2}}(g)+{{O}_{2}}(g)2NO(g)-180.7\,kJ,\] on increasing the temperature, the production of NO

    A) increases

    B) decreases

    C) remains same

    D) Cannot be predicted

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  • question_answer67) In an experiment, 20 mL of decinormal \[HCl\] solution was added to 10 mL of a decinormal \[\text{AgN}{{\text{O}}_{\text{3}}}\]solution. \[\text{AgCl}\]was precipitated out and the excess acid was titrated against a decinormal \[\text{NaOH}\] solution. Volume of \[\text{NaOH}\].required for this back titration is

    A) 10 mL

    B) 5 mL

    C) 20 mL

    D) 30 mL

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  • question_answer68) Consider the following statements.

    I. The colour of the hydrophobic sol depends on the wavelength of the light scattered by the dispersed particle.
    II. The smaller the gold number value of a hydrophilic colloid, the greater is its protective power.
    III. The movement of sol particle under an applied electric potential is called electro osmosis.
    Which of the above statements are correct?

    A) I and II

    B) I and III

    C) II and III

    D) I, II and III

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  • question_answer69) Natural gas is

    A) \[CO+{{H}_{2}}\]

    B) \[CO+{{N}_{2}}\]

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

    D) None of these

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  • question_answer70) Colemanite is

    A) \[N{{a}_{2}}{{B}_{4}}{{O}_{7}}.10{{H}_{2}}O\]

    B) \[C{{a}_{2}}{{B}_{6}}{{O}_{11}}.5{{H}_{2}}O\]

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

    D) \[{{H}_{3}}B{{O}_{3}}\]

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  • question_answer71) Arsenic drugs are mainly used in the treatment of

    A) jaundice

    B) typhoid

    C) syphilis

    D) cholera

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  • question_answer72) Which of the following statements is not correct?

    A) Methylamine is more basic than \[\text{N}{{\text{H}}_{\text{3}}}\]

    B) Amines form hydrogen bonds

    C) Ethylamine has higher boiling point than propane

    D) Dimethylamine is less basic than methylamine

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  • question_answer73) Which one of the following will be most basic?

    A) Aniline

    B) p-methoxyaniline

    C) p-nitroaniline

    D) Benzylamine

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  • question_answer74) The final product of oxidation of 2-propanol with hot cone. \[\text{HN}{{\text{O}}_{\text{3}}}\]is

    A) propanal

    B) ethanoic acid

    C) propanone

    D) ethanol

    View Answer play_arrow
  • question_answer75) Bimolecular reduction of acetone gives

    A) diacetoneamine

    B) pinacol

    C) chloretone

    D) propane

    View Answer play_arrow
  • question_answer76) Aldehydes and ketones give addition reaction with

    A) hydrazine

    B) phenyl hydrazine

    C) semicarbazide

    D) hydrogen cyanide

    View Answer play_arrow
  • question_answer77) Amongst the following, the compound which is most difficult to sulphonate is

    A) benzene

    B) nitrobenzene

    C) toluene

    D) chlorobenzene

    View Answer play_arrow
  • question_answer78) Acetonitrile is prepared by treating an alcoholic solution of methyl iodide with

    A) silver cyanide

    B) potassium cyanide

    C) hydrogen cyanide

    D) ammonia

    View Answer play_arrow
  • question_answer79) During polymerization of acetylene to benzene, the state of hybridisation of carbon changes from

    A) \[s{{p}^{2}}\]to \[sp\]

    B) \[s{{p}^{3}}\]to \[sp\]

    C) \[sp\]to \[s{{p}^{3}}\]

    D) \[sp\]to \[s{{p}^{2}}\]

    View Answer play_arrow
  • question_answer80) Which one of the following series contains electrophiles only?

    A) \[{{H}_{2}}O,S{{O}_{3}},{{H}_{3}}{{O}^{+}}\]

    B) \[N{{H}_{3}},{{H}_{2}}O,AlC{{l}_{3}}\]

    C) \[AlC{{l}_{3}},S{{O}_{3}},\overset{+}{\mathop{N}}\,{{O}_{2}}\]

    D) \[{{H}_{2}}O,\overset{+}{\mathop{C}}\,l,N{{H}_{3}}\]

    View Answer play_arrow
  • question_answer81) The equilibrium constants for the reactions \[{{N}_{2}}+3{{H}_{2}}2N{{H}_{3}}\] and \[\frac{1}{2}{{N}_{2}}+\frac{3}{2}{{H}_{2}}N{{H}_{3}}\] are\[{{K}_{1}}\]and \[{{K}_{2}}\]respectively. Which one of the following is the correct relationship?

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

    B) \[{{K}_{1}}=\frac{1}{2}{{K}_{2}}\]

    C) \[{{K}_{2}}=\sqrt{{{K}_{1}}}\]

    D) \[{{K}_{1}}={{K}_{2}}\]

    View Answer play_arrow
  • question_answer82) When we increase the temperature, the rate of reaction increases because of

    A) more number of collisions

    B) decrease in mean free path

    C) more number of energetic electrons

    D) less number of energetic electrons

    View Answer play_arrow
  • question_answer83) The pH of buffer of \[\text{N}{{\text{H}}_{\text{4}}}\text{Cl}\]type is given by

    A) \[pH=p{{K}_{b}}\]

    B) \[pH=1/2p{{K}_{b}}-1/2\,\log [salt]/[base]\]

    C) \[pH=14-p{{K}_{b}}-\log [salt]/[base]\]

    D) \[pH=pOH-p{{K}_{b}}+\log [salt]/[base]\]

    View Answer play_arrow
  • question_answer84) Azimuthal quantum number determines the

    A) size

    B) spin

    C) orientation

    D) angular momentum of orbitals

    View Answer play_arrow
  • question_answer85) The formation of colloid from suspension is called

    A) peptisation

    B) condensation

    C) sedimentation

    D) fragmentation

    View Answer play_arrow
  • question_answer86) Other things being equal, the EMF of a Daniell cell may be increased by

    A) keeping low temperature

    B) using large copper electrodes

    C) using large zinc electrodes

    D) decreasing concentration of \[\text{C}{{\text{u}}^{\text{2+}}}\]ions

    View Answer play_arrow
  • question_answer87) Which one of the following can be considered as a weak electrolyte?

    A) \[\text{NaCl}\]

    B) \[\text{HCl}\]

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

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

    View Answer play_arrow
  • question_answer88) lodoform can be prepared from all except

    A) acetaldehyde

    B) 3-methyl-2-butanone

    C) iso-butyl alcohol

    D) acetophenone

    View Answer play_arrow
  • question_answer89) The end product C in the following sequence of chemical reactions is \[C{{H}_{3}}COOH\xrightarrow{CaC{{O}_{3}}}A\xrightarrow{Heat}B\xrightarrow{N{{H}_{2}}OH}C\]

    A) acetaldehyde oxime

    B) formaldehyde oxime

    C) methyl nitrate

    D) acetoxime

    View Answer play_arrow
  • question_answer90) Synthetic human hair wigs are made from a copolymer of vinyl chloride and acrylonitrile and is called

    A) PVC

    B) polyacrylonitrile

    C) cellulose

    D) dynel

    View Answer play_arrow
  • question_answer91) Which one of the following is not an example of chain growth polymer?

    A) Neoprene

    B) Buna-S

    C) PMMA

    D) Glyptal

    View Answer play_arrow
  • question_answer92) Most abundant water pollutant is

    A) detergents

    B) industrial wastes

    C) pesticides

    D) oil spills

    View Answer play_arrow
  • question_answer93) Paulings electronegativity values for elements are useful in predicting

    A) polarity of the molecules

    B) position in the EMF series

    C) coordination numbers

    D) dipole moments

    View Answer play_arrow
  • question_answer94) A neutral ferilizer among the following is

    A) CAN

    B) ammonium sulphate

    C) ammonium nitrate

    D) Urea

    View Answer play_arrow
  • question_answer95) Transition metal with low oxidation number will act as

    A) an oxidizing agent

    B) a base

    C) an acid

    D) None of these

    View Answer play_arrow
  • question_answer96) In \[\text{LiAl}{{\text{H}}_{\text{4}}}\text{,}\]the ligand is

    A) H

    B) \[{{\text{H}}^{\text{+}}}\]

    C) \[{{\text{H}}^{-}}\]

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

    View Answer play_arrow
  • question_answer97) Iodide of Millons base is

    A) \[\text{Hg}{{\text{I}}_{\text{2}}}\]

    B) \[{{\text{K}}_{\text{2}}}\text{Hg}{{\text{I}}_{\text{4}}}\]

    C) \[\text{N}{{\text{H}}_{\text{4}}}\text{HgO}\text{.HgI}\]

    D) \[\text{N}{{\text{H}}_{\text{4}}}\text{I}\]

    View Answer play_arrow
  • question_answer98) Ce-58 is a member of

    A) \[s-\]block elements

    B) \[p-\]block elements

    C) \[d-\]block elements

    D) \[f-\]block elements

    View Answer play_arrow
  • question_answer99) Complete hydrolysis of \[\text{Xe}{{\text{F}}_{\text{2}}}\]gives

    A) Xe

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

    C) HF

    D) All of these

    View Answer play_arrow
  • question_answer100) The alloy best suited for making metre scales is

    A) stainless steel

    B) invar

    C) alnicos

    D) tungsten steel

    View Answer play_arrow
  • question_answer101) The value of \[\sum\limits_{n=1}^{13}{({{i}^{n}}+{{i}^{n+1}}),}\]where \[i=\sqrt{-1}\] equals

    A) \[i\]

    B) \[i-1\]

    C) \[-i\]

    D) 0

    View Answer play_arrow
  • question_answer102) If \[4{{\sin }^{-1}}x+{{\cos }^{-1}}x=\pi ,\] then the value of \[x\]is

    A) 0

    B) \[1/2\]

    C) 1

    D) \[-\text{ }1\]

    View Answer play_arrow
  • question_answer103) There are n different books and p copies of each. The number of ways in which a selection can be made from them, is

    A) \[{{n}^{p}}\]

    B) \[{{p}^{n}}\]

    C) \[{{(p+1)}^{n}}-1\]

    D) \[{{(n+1)}^{p}}-1\]

    View Answer play_arrow
  • question_answer104) The circle \[{{S}_{1}}\]with centre \[{{C}_{1}}({{a}_{1}},{{b}_{1}})\]and radius \[{{r}_{1}}\]touches externally the circle \[{{S}_{2}}\]with centre \[{{C}_{2}}({{a}_{2}},{{b}_{2}})\]and radius \[{{r}_{2}}.\] If the tangent at their common point passes through the origin, then

    A) \[(a_{1}^{2}+a_{2}^{2})+(b_{1}^{2}+b_{2}^{2})=r_{1}^{2}+r_{2}^{2}\]

    B) \[(a_{1}^{2}-a_{2}^{2})+(b_{1}^{2}-b_{2}^{2})=r_{1}^{2}-r_{2}^{2}\]

    C) \[{{(a_{1}^{2}-{{b}_{2}})}^{2}}+(a_{2}^{2}+b_{2}^{2})=r_{1}^{2}+r_{2}^{2}\]

    D) \[(a_{1}^{2}-b_{1}^{2})+(a_{1}^{2}+b_{2}^{2})=r_{1}^{2}+r_{2}^{2}\]

    View Answer play_arrow
  • question_answer105) If three vectors a, b, c are such that \[a\ne 0\]and \[a\times b=2(a\times c),|a|=|c|=1,|b|=4\]and the angle between b and c is \[{{\cos }^{-1}}\left( \frac{1}{4} \right).\]Also \[b-2c=\lambda a,\]then find the value of \[\lambda \]

    A) \[~\pm \,4\]

    B) 14

    C) \[\pm \text{ }2~\]

    D) 12

    View Answer play_arrow
  • question_answer106) A vector which makes equal angle with the vectors \[1/3(i-2j+2k),1/5(-4i-3k)\]and j is

    A) \[5i+j+jk\]

    B) \[-6i+j+5k\]

    C) \[5i-j-5k\]

    D) \[5i+j-5k\]

    View Answer play_arrow
  • question_answer107) If \[a.b=0\]and \[a+b\]makes an angle of \[{{30}^{o}}\] with a, then

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

    B) \[|a|=2|b|\]

    C) \[|a|=\sqrt{3}|b|\]

    D) None of these

    View Answer play_arrow
  • question_answer108) In Simpsons one-third rule the curve \[y=f(x)\]is assumed to be a

    A) circle

    B) parabola

    C) hyperbola

    D) None of these

    View Answer play_arrow
  • question_answer109) Objective of LPP is

    A) a constraint

    B) a function to be optimized

    C) a relation between the variables

    D) None of the above

    View Answer play_arrow
  • question_answer110) The variance of first \[n\] natural number is

    A) \[\frac{{{n}^{2}}+1}{12}\]

    B) \[\frac{{{n}^{2}}-1}{12}\]

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

    D) None of these

    View Answer play_arrow
  • question_answer111) In Boolean algebra, which of the following statement is correct

    A) \[(a+b)=a+b\]

    B) \[(a+b)=a.b\]

    C) \[(a+b)=(a.b)\]

    D) None of the above

    View Answer play_arrow
  • question_answer112) The function \[{{x}^{x}}\]decreases in the interval

    A) (0, e)

    B) (0, 1)

    C) (0, 1/e)

    D) None of these

    View Answer play_arrow
  • question_answer113) The period of the function \[f(x)=(\sin 3x)+|\cos 6x|\]is

    A) \[\pi \]

    B) \[2\pi /3\]

    C) \[2\pi \]

    D) \[\pi /2\]

    View Answer play_arrow
  • question_answer114) The differential equation representing the family of curves \[{{y}^{2}}=2x(x+\sqrt{c}),\]where c is a positive perimeter, is of

    A) order 1, degree 3

    B) order 2, degree 2

    C) degree 3, order 3

    D) degree 4, order 4

    View Answer play_arrow
  • question_answer115) If \[\int_{{}}^{{}}{\sqrt{1+\sin x}}.f(x)dx=\frac{2}{3}{{(1+\sin x)}^{3/2}}+C,\] then \[f(x)\] is equal to

    A) \[\cos x\]

    B) \[\sin x\]

    C) \[\tan x\]

    D) 1

    View Answer play_arrow
  • question_answer116) \[\int_{{}}^{{}}{x\sqrt{\frac{1-x}{1+x}}}dx\]is equal to

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

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

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

    D) None of the above

    View Answer play_arrow
  • question_answer117) If \[x=\sec \theta -\cos \theta \]and \[y={{\sec }^{n}}\theta -{{\cos }^{n}}\theta ,\]then \[{{\left( \frac{dy}{dx} \right)}^{2}}\]is

    A) \[\frac{{{n}^{2}}({{y}^{2}}+4)}{{{x}^{2}}+4}\]

    B) \[\frac{{{n}^{2}}({{y}^{2}}-4)}{{{x}^{2}}}\]

    C) \[n\frac{({{y}^{2}}-4)}{{{x}^{2}}-4}\]

    D) \[{{\left( \frac{ny}{x} \right)}^{2}}-4\]

    View Answer play_arrow
  • question_answer118) The area formed by triangular shaped region bounded by the curves \[y=\sin x,y=\cos x\]and \[x=0\]is

    A) \[(\sqrt{2}-1)sq\,unit\]

    B) \[\text{1}\,\text{sq}\,\text{unit}\]

    C) \[\sqrt{\text{2}}\,\text{sq}\,\text{units}\]

    D) \[(\sqrt{2}+1)\,sq\,unit\]

    View Answer play_arrow
  • question_answer119) Find the value of \[\int_{0}^{\pi /2}{\frac{dx}{1+{{\tan }^{3}}x}}\]

    A) 0

    B) 1

    C) \[\pi /2\]

    D) \[\pi /4\]

    View Answer play_arrow
  • question_answer120) The angle of intersection of the curve \[y={{x}^{2}}\] and \[6y=7-{{x}^{3}}\]at \[(1,1)\] is

    A) \[\pi /4\]

    B) \[\pi /3\]

    C) \[\pi /2\]

    D) None of these

    View Answer play_arrow
  • question_answer121) If \[{{I}_{m,n}}=\int_{0}^{1}{{{x}^{m}}{{(\log x)}^{n}}}dx,\]then it is equal to

    A) \[\frac{n}{n+1}{{I}_{m,n}}_{-1}\]

    B) \[\frac{-m}{n+1}{{I}_{m,n-1}}\]

    C) \[\frac{-n}{m+1}{{I}_{m,n-1}}\]

    D) None of the above

    View Answer play_arrow
  • question_answer122) \[\frac{d}{dx}\cos e{{c}^{-1}}\left( \frac{1+{{x}^{2}}}{2x} \right)\]is equal to

    A) \[\frac{-2}{(1+{{x}^{2}})},x\ne 0\]

    B) \[\frac{2}{(1+{{x}^{2}})},x\ne 0\]

    C) \[\frac{2(1-{{x}^{2}})}{(1+{{x}^{2}})|1-{{x}^{2}}|},x\ne \pm 1,0\]

    D) None of the above

    View Answer play_arrow
  • question_answer123) If \[\underset{x\to 0}{\mathop{\lim }}\,\phi (x)={{a}^{3}},a\ne 0,\] then \[\underset{x\to 0}{\mathop{\lim }}\,\phi (x/a)\] is equal to

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

    B) \[1/{{a}^{3}}\]

    C) \[1/{{a}^{2}}\]

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

    View Answer play_arrow
  • question_answer124) If \[(1+tan\theta )(1+tan\phi )=2,\]then \[(\theta +\phi )\]is equal to

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

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

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

    D) \[~{{75}^{o}}\]

    View Answer play_arrow
  • question_answer125) If in a\[\Delta A B C,\cos A+\cos B+\cos C=3/2,\] then triangle is

    A) right angled         

    B) isosceles                              

    C) acute                                    

    D) equilateral

    View Answer play_arrow
  • question_answer126) If the line \[x-1=0\]is the directrix of parabola \[{{y}^{2}}-kx+8=0,\] then one of the value of \[k\]is

    A) 1/8

    B) 8

    C) 4

    D) 1/4

    View Answer play_arrow
  • question_answer127) The centre of the sphere through the points \[(0,3,4),(0,5,0),(4,0,3)\]and \[(-3,4,0)\]is

    A) \[(1/4,3,7/4)\]

    B) (0, 0, 0)

    C) \[(-4,3,0)\]

    D) None of the above

    View Answer play_arrow
  • question_answer128) Solve \[(y\,\log \,x-1)ydx=x\,dy\]

    A) \[y(\log ex+cx)=1\]

    B) \[y(\log ex+cx)\]

    C) \[y(\log ex-(x))=-1\]

    D) None of the above

    View Answer play_arrow
  • question_answer129) If \[f(x)=\int_{-1}^{x}{|t|dt,x\ge -1,}\]then

    A) \[f\]and\[f\] are continuous for \[x+1>0\]

    B) \[f\]is continuous but \[f\] is not continuous for \[x+1>0\]

    C) \[f\] and\[f\] are not continuous at \[x=0\]

    D) \[f\]is continuous at \[x=0\]but\[f\] is not so

    View Answer play_arrow
  • question_answer130) AB, AC are tangents to a parabola \[{{y}^{2}}=4ax,\]If \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\] are the lengths of perpendiculars from A, B, C on any tangents to the parabola, then

    A) \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\]are in GGP

    B) \[{{l}_{2}},{{l}_{1}},{{l}_{3}}\]are in GP

    C) \[{{l}_{3}},{{l}_{1}},{{l}_{2}}\]are in GP

    D) \[{{l}_{3}},{{l}_{2}},{{l}_{1}}\]are in GP

    View Answer play_arrow
  • question_answer131) A family of lines is given by \[(1+2\lambda )x+(1-\lambda )y+\lambda =0,\,\lambda \] being the parameter. The line belonging to this family at the maximum distance from the point\[(1,4)\]is

    A) \[4x-y+1=0\]

    B) \[33x+12y+7=0\]

    C) \[12x+33y=7\]

    D) None of these

    View Answer play_arrow
  • question_answer132) If the eccentricity of the hyperbola \[{{x}^{2}}-{{y}^{2}}{{\sec }^{2}}\alpha =5\]is \[\sqrt{3}\]times the eccentricity of the ellipse \[{{x}^{2}}{{\sec }^{2}}\alpha +{{y}^{2}}=25,\]then the value of \[\alpha \] is

    A) \[\pi /6\]

    B) \[\pi /4\]

    C) \[\pi /3\]

    D) \[\pi /2\]

    View Answer play_arrow
  • question_answer133) Lines of regressions of \[y\] on \[x\] and \[x\] on \[y\] are respectively \[y=ax+b\]and\[x=\alpha y+\beta ,\] If mean of \[x\]and\[y\] series is same, then its value. is

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

    B) \[\frac{1-a}{b}\]

    C) \[\frac{\beta }{1-\beta }\]

    D) \[\frac{a}{1-\alpha }\]

    View Answer play_arrow
  • question_answer134) A solution of the differential equation \[{{\left( \frac{dy}{dx} \right)}^{2}}-x\frac{dy}{dx}+y=0\]is

    A) \[y=2\]

    B) \[y=2x\]

    C) \[y=2x-4\]

    D) \[y=2{{x}^{2}}-4\]

    View Answer play_arrow
  • question_answer135) The relation between the time t and distance \[x\] is given by \[t=p{{x}^{2}}+qx,\]where p and q are constants. The relation between velocity v and acceleration \[f\] is

    A) \[f\propto v\]

    B) \[f\propto {{v}^{4}}\]

    C) \[f\propto {{v}^{2}}\]

    D) \[f\propto {{v}^{3}}\]

    View Answer play_arrow
  • question_answer136) The product of\[{{x}^{1/2}}.{{x}^{1/4}},{{x}^{1/8}}....\infty \]equals

    A) 0

    B) 1

    C) \[x\]

    D) \[\infty \]

    View Answer play_arrow
  • question_answer137) If the equation \[{{x}^{2}}+ix+a=0,\]\[{{x}^{2}}-2x+ia=0,a\ne 0\]have a common root, then

    A) a is real

    B) \[a=1/2+i\]

    C) \[a=1/2-i\]

    D) the other root is also common

    View Answer play_arrow
  • question_answer138) The distance between the lines \[y=2x+4\]and \[3y=6x-5\] is equal to

    A) 1

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

    C) \[\frac{17\sqrt{5}}{15}\]

    D) \[\frac{17}{\sqrt{3}}\]

    View Answer play_arrow
  • question_answer139) The equation\[\frac{{{x}^{2}}}{12-k}+\frac{{{y}^{2}}}{8-k}=1\]represents

    A) a hyperbola, if k < 8

    B) an ellipse, if \[k>8\]

    C) a hyperbola, if \[8<k<12\]

    D) None of the above

    View Answer play_arrow
  • question_answer140) The series \[\frac{1}{(n+1)}+\frac{1}{2{{(n+1)}^{2}}}+\frac{1}{3{{(n+1)}^{3}}}+...\] has the same sum as the series

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

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

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

    D) None of the above

    View Answer play_arrow
  • question_answer141) The sum of the infinite series \[\frac{2}{3!}+\frac{4}{5!}+\frac{6}{7!}+\frac{8}{9!}+....\infty \]is

    A) \[e\]

    B) \[{{e}^{-1}}\]

    C) \[2e\]

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

    View Answer play_arrow
  • question_answer142) If the roots of the equation \[a(b-c){{x}^{2}}+b(c-a)x+c(a-b)=0\]are equal, then a, b, c are in

    A) AP

    B) GP

    C) HP

    D) None of these

    View Answer play_arrow
  • question_answer143) The probability that a person will hit a target in shooting practice is 0.3. If he shoots 10 times, then the probability of his shooting the target is

    A) 1

    B) \[1-{{(0.7)}^{10}}\]

    C) \[{{(0.7)}^{10}}\]

    D) \[{{(0.3)}^{10}}\]

    View Answer play_arrow
  • question_answer144) Let A and B be two events such that\[P(A)=0.3\] and \[P(A\cup B)=0.8\]If A and B. are independent events. Then, \[P(B)\] is equal to

    A) 5/7

    B) 2/3

    C) 1

    D) None of these

    View Answer play_arrow
  • question_answer145) The number of distinct real roots of \[\left| \begin{matrix} \sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & \cos x & \sin x \\ \end{matrix} \right|=0\]in the interval\[x\in \left[ \frac{-\pi }{4},\frac{\pi }{4} \right]\]is

    A) 0

    B) 2

    C) 1

    D) 3

    View Answer play_arrow
  • question_answer146) If \[A=\left| \begin{matrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \\ \end{matrix} \right|,\] then the value of\[|A||adj(A)|\]is

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

    B) \[{{a}^{6}}\]

    C) \[{{a}^{9}}\]

    D) \[{{a}^{27}}\]

    View Answer play_arrow
  • question_answer147) The term independent of \[x\]in \[{{\left[ \sqrt{\frac{x}{3}}+\sqrt{\frac{3}{2{{x}^{2}}}} \right]}^{10}}\] is

    A) \[{{\,}^{10}}{{C}_{1}}\]

    B) \[5/12\]

    C) 1

    D) None of these

    View Answer play_arrow
  • question_answer148) \[\frac{\frac{1}{2}.\frac{2}{2}}{{{1}^{3}}}+\frac{\frac{2}{2}.\frac{3}{2}}{{{1}^{3}}+{{2}^{3}}}+\frac{\frac{3}{2}.\frac{4}{2}}{{{1}^{3}}+{{2}^{3}}+{{3}^{3}}}+...\]upto \[n\] terms

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

    B) \[\frac{n}{n+1}\]

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

    D) \[\frac{(n+1)}{n}\]

    View Answer play_arrow
  • question_answer149) The solution of the equation \[{{\cos }^{2}}\theta +\sin \theta +1=0,\] lies in the interval

    A) \[\left( \frac{-\pi }{4},\frac{\pi }{4} \right)\]

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

    C) \[\left( \frac{3\pi }{4},\frac{5\pi }{4} \right)\]

    D) \[\left( \frac{5\pi }{4},\frac{7\pi }{4} \right)\]

    View Answer play_arrow
  • question_answer150) \[{{\log }_{3}}2,lo{{g}_{6}}2,{{\log }_{12}}2\]are in

    A) AP

    B) GP

    C) HP

    D) None of these

    View Answer play_arrow



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