Solved papers for BCECE Engineering BCECE Engineering Solved Paper-2007

done BCECE Engineering Solved Paper-2007

  • question_answer1) A body is projected at such angle that the horizontal range is three times the greatest height. The angle of projection is

    A) \[{{42}^{o}}8\]

    B) \[{{53}^{o}}7\]

    C) \[{{33}^{o}}7\]

    D) \[{{25}^{o}}8\]

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  • question_answer2) A gas bubble formed from an explosion under water oscillates with a period T proportional to \[{{P}^{a}}{{d}^{b}}{{E}^{c}},\]where P is pressure, d is the density of water and E is the total energy of explosion. The value of a, b, c are

    A) \[a=1,\,\,\,\,\,b=1,\,\,\,\,c=2\]

    B) \[a=1,\,\,\,\,\,b=2,\,\,\,\,c=1\]

    C) \[a=\frac{5}{6},\]\[b=\frac{1}{2},c=\frac{1}{3}\]

    D) \[a=-\frac{5}{6},b=\frac{1}{2},c=\frac{1}{3}\]

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  • question_answer3) A particle moving with a uniform acceleration travels 24 A and 64m in the first two consecutive interval of 4s each. Its initial velocity will be

    A) 5 m/s

    B) 3 m/s

    C) 1 m/s

    D) 4 m/s

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  • question_answer4) Two equal vectors have a resultant equal to either of them, then the angle between them will be

    A) \[~{{120}^{o}}\]

    B) \[~{{110}^{o}}\]

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

    D) \[~150{}^\circ \]

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  • question_answer5) If the radius of earth of R then the height h at which the value of g becomes one fourth, will be

    A) \[~~\frac{R}{8}~~~\]

    B) \[~~\frac{3R}{8}~~~\]

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

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

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  • question_answer6) A body moves a distance of 10 m along a straight line under a action of 5 N force. If work done is 25 J, then angle between the force and direction of motion of the body will be

    A) \[{{75}^{o}}\]

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

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

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

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  • question_answer7) If 150 J of heat is added to a system work done by the system is 110 J, the in internal energy will be

    A) 40 J

    B) 110 J

    C) 150 J

    D) 260 J

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  • question_answer8) Sum of the two binary numbers \[{{(100010)}_{2}}\]and \[{{(11011)}_{2}}\]is \[{{(11011)}_{2}}\]is

    A) \[{{(111111)}_{2}}\]

    B) \[{{(101111)}_{2}}\]

    C) \[{{(111001)}_{2}}\]

    D) \[{{(111101)}_{2}}\]

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  • question_answer9) What is the velocity of the bob of pendulum at its mean position, if it is a1 to vertical height of 10 cm? \[(g=9.8\,m/{{s}^{2}})\]

    A) \[2.2\text{ }m/s\]

    B) \[1.8\text{ }m/s\]

    C) \[1.4\text{ }m/s\]

    D) \[0.6\text{ }m/s\]

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  • question_answer10) A body cools from \[60{{\,}^{o}}C\] to \[50{{\,}^{o}}C\] in 1 the room temperature is\[25{{\,}^{o}}C\] and assuming Newton law of cooling to hold g temperature of the body at the end of the next 10 min will be

    A) \[~45{{\,}^{o}}C\]

    B) \[~42.85{{\,}^{o}}C\]

    C) \[40{{\,}^{o}}C\]

    D) \[~38.5{{\,}^{o}}C\]

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  • question_answer11) At \[27{}^\circ C\] a gas suddenly compressed such that its pressure becomes \[\frac{1}{8}\text{th}\] of original pressure. The temperature of the gas will be \[(\gamma =5/3)\]

    A) \[-142{{\,}^{o}}C\]

    B) \[300\,K\]

    C) \[327{{\,}^{o}}C\]

    D) \[420\,K\]

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  • question_answer12) An ideal refrigerator has a freezer at a temperature of \[-\text{ }13{{\,}^{o}}C.\] The coefficient of performance of the engine is 5. The temperature of the air (to which heat is rejected) will be

    A) \[325{{\,}^{o}}C\]

    B) 325 K

    C) \[~39{{\,}^{o}}C\]

    D) \[320{{\,}^{o}}C\]

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  • question_answer13) In a capacitor of capacitance \[20\,\mu F\] the distance between the plates is 2 mm. If a dielectric slab of width 1 mm and dielectric constant 2 is inserted between the plates, then the new capacitance will be

    A) \[22\,\mu F\]

    B) \[26.6\,\mu F\]

    C) \[52.2\text{ }\mu \text{F}\]

    D) \[~13\text{ }\mu \text{F}\]

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  • question_answer14) An automobile spring extends 0.2 m for 5000 N load. The ratio of potential energy stored in this spring when it has been compressed by 0.2 m to the potential energy stored in a \[10\,\mu F\] capacitor at a potential difference of 10000 V will be

    A) 1/4

    B) 1

    C) 1/2

    D) 2

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  • question_answer15) A solid metallic sphere has a charge + 3Q. Concentric with this sphere is a conducting spherical shell having charge - Q. The radius of the sphere is a and that of the spherical shell is \[b(b>a).\]What is the electric field at a distance \[R(a<R<b)\]from the centre?

    A) \[\frac{4Q}{2\pi \,{{\varepsilon }_{0}}{{R}^{2}}}\]

    B) \[\frac{3Q}{4\pi \,{{\varepsilon }_{0}}{{R}^{2}}}\]

    C) \[\frac{3Q}{2\pi \,{{\varepsilon }_{0}}{{R}^{2}}}\]

    D) \[\frac{Q}{2\pi \,{{\varepsilon }_{0}}R}\]

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  • question_answer16) Output \[Y\]is given by:

    A) \[(\bar{X}.\bar{Y}).Z\]

    B) \[(X+Y)Z\]

    C) \[(X+Y)\bar{Z}\]

    D) \[\bar{X}.\bar{Y}+Z\]

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  • question_answer17) In a network as shown in the figure, the potential difference across the resistance 2R is (the cell has an emf of E volts and has no internal resistance)

    A) 2E

    B) \[\frac{4E}{7}\]

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

    D) \[E\]

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  • question_answer18) The resistance of a galvanometer coil is R, then the shunt resistance required to convert it into a ammeter of range 4 times, will be

    A) 4R

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

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

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

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  • question_answer19) The instrument used by doctors for endoscopy works on the principle of

    A) total internal reflection

    B) reflection

    C) refraction

    D) none of the above

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  • question_answer20) A meter stick is held vertically with one end on the floor and is then allowed to fall. Assuming that the end on the floor the stick does not slip, the velocity of the other end when it hits the floor, will be

    A) \[10.8\text{ }m/s\]

    B) \[~5.4\text{ }m/s\]

    C) \[~2.5\text{ }m/s\]

    D) none of these

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  • question_answer21) If the coefficient of static friction between the tyres and road is 0.5, what is the shortest distance in which an automobile can be stopped when travelling at 72 km/h?

    A) 50 m

    B) 60 m

    C) 40.8 m

    D) 80.16 m

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  • question_answer22) A bullet fired at an angle of \[{{30}^{o}}\] with the horizontal hits the ground 3 km away. By adjusting its angle of projection, can one hope to hit a target 5 km away. Assume the muzzle speed to be same and the air resistance is negligible

    A) possible to hit a target 5 km away

    B) not possible to hit a target 5 km away

    C) prediction is not possible

    D) none of the above

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  • question_answer23) Two springs of spring constant 1500 N/m and 3000 N/m respectively are stretched with the same force. They will have potential energy in ratio

    A) 1 : 2

    B) 2 : 1

    C) 1 : 4

    D) 4 : 1

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  • question_answer24) The elastic energy stored in a wire of Youngs modulus Y is

    A) \[\frac{\text{1}}{\text{2}}\text{Y}\,\text{ }\!\!\times\!\!\text{ }\,\text{stress}\,\text{ }\!\!\times\!\!\text{ strain}\,\text{ }\!\!\times\!\!\text{ }\,\text{volume}\]

    B) \[\frac{{{\text{(stress)}}^{\text{2}}}\text{ }\!\!\times\!\!\text{ }\,\text{volume}}{\text{2Y}}\]

    C) \[stress\times strain\times volume\]

    D) \[Y\times \frac{{{(stress)}^{2}}}{volume}\]

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  • question_answer25) A soap bubble A of radius 0.03 and another bubble B of radius 0.04 m are brought together so that the combined bubble has a common interface of radius r, then the value of r is

    A) 0.24 m

    B) 0.48 m

    C) 0.12m

    D) none of these

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  • question_answer26) An air bubble of radius \[{{10}^{-2}}\,m\] is rising up at a steady rate of \[2\times {{10}^{-3}}m/s\] through a liquid of density \[1.5\times {{10}^{3}}kg/{{m}^{3}},\] the coefficient of viscosity neglecting the density of. air, will be \[(g=10\,m/{{s}^{2}})\]

    A) 23.2 units

    B) 83.5 units

    C) 334 units

    D) 167 units

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  • question_answer27) A Carnot reversible engine converts 1/6 of heat input into work. When the temperature of the sink is reduced by 62 K, the efficiency of Carnots cycle becomes 1/3. The temperature of the source and sink will be

    A) \[372\text{ }K,\text{ }310\text{ }K\]

    B) \[~181\text{ }K,\text{ }150\text{ }K\]

    C) \[~472\text{ }K,\text{ }410\text{ }K\]

    D) none of the above

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  • question_answer28) The ratio of the coefficient of thermal conductivity of two different materials is \[5:3.\] If the thermal resistance of the rods of same thickness of these materials is same, then the ratio of the length of these rods will be

    A) 3 : 5

    B) 5 : 3

    C) 3 : 4

    D) 3 : 2

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  • question_answer29) Compressional wave pulses are sent to the bottom of sea from a ship and the echo is heard after 2 s. If bulk modulus of elasticity of water is \[2\times {{10}^{9}}\text{ }N/{{m}^{2}}\]and mean temperature is \[4{{\,}^{o}}C,\] the depth of the sea will be

    A) 1014 m

    B) 1414 m

    C) 2828 m

    D) none of these

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  • question_answer30) Sound waves of \[f=600\,Hz\]fall normally on a perfectly reflecting wall. The shortest distance from the wall at which all particles will have maximum amplitude of vibration will be (speed of sound = 300 m/s)

    A) \[\frac{7}{8}m\]

    B) \[\frac{3}{8}m\]

    C) \[\frac{1}{8}m\]

    D) \[\frac{1}{4}m\]

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  • question_answer31) A pipe closed at one end produces a fundamental note of 412 Hz. It is cut into two pieces of equal length the fundamental notes produced by the two pieces are

    A) \[~824\text{ }Hz,\text{ }1648\text{ }Hz\]

    B) \[~412\text{ }Hz,\text{ }824\text{ }Hz\]

    C) \[~206\text{ }Hz,\text{ }412\text{ }Hz\]

    D) \[216\text{ }Hz,\text{ }824\text{ }Hz\]

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  • question_answer32) The refractive index of water and glycerine are 1.33 and 1.47 respectively. What is the critical angle for a light ray going from the later to the former?

    A) \[60{}^\circ 48\]

    B) \[64{}^\circ 48\]

    C) \[74{}^\circ 48\]

    D) None of these

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  • question_answer33) Lenses of power 3 D and -5D are combined to form a compound lens. An object is placed at a distance of 50 cm from this lens. Its image will be formed at a distance from the lens, will be

    A) 25 cm

    B) 20 cm

    C) 30 cm

    D) 40 cm

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  • question_answer34) If fringes width \[\lambda =5.89\times {{10}^{-5}}\] mm is 0.431 mm and shift of white central fringe on introducing a mica sheet in one path is 1.89 mm. Thickness of the mica sheet will be \[(\mu =1.59)\]

    A) \[4.38\,\times {{10}^{-6}}m\]

    B) \[5.38\,\times {{10}^{-6}}m\]

    C) \[6.38\,\times {{10}^{-6}}m\]

    D) none of these

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  • question_answer35) A body is orbiting around earth at a mean radius which is two times as greater as the parking orbit of a satellite, the period of body is

    A) 4 days

    B) 16 days

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

    D) 64 days

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  • question_answer36) A radioactive substance has half-life of 60 min. During 3 h, the fraction of the substance that has to be decayed, will be

    A) 87.5%

    B) 52.5%

    C) 25.5%

    D) 8.5%

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  • question_answer37) Voltage in the secondary coil of a transformer does not depend upon

    A) frequency of the source

    B) voltage in the primary coil

    C) ratio of number of turns in the two coils

    D) both (b) and (c)

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  • question_answer38) When n-p-n transistor is used as an amplifier

    A) electrons move from emitter to base

    B) electrons move from base to emitter

    C) electrons move from collector to base

    D) holes move from base to emitter

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  • question_answer39) \[_{\text{7}}{{\text{N}}^{\text{14}}}\]is bombarded with \[_{2}H{{e}^{\text{4}}}.\] The resulting nucleus is \[_{8}{{O}^{17}}\] with the emission of

    A) neutrino

    B) antineutrino

    C) proton

    D) neutron

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  • question_answer40) In the given figure the steady state current in the circuit is

    A) Zero                                     

    B) 0.6 A                    

    C) 0.9 A                    

    D) 1.5 A

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  • question_answer41) The time of vibration of a dip needle vibration in the vertical plane in the magnetic meridian is 3 s. When the same magnetic needle is made to vibrate in the horizontal plane, the time of vibration is 3\[\sqrt{2}\]s. Then angle of dip will be

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

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

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

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

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  • question_answer42) The inductance of the oscillatory circuit of a radio station is 10 mH and its capacitance is 0.25 \[\mu F\].Taking the effect of resistance negligible, wavelength of the broadcasted waves will be (velocity of light \[=3.0\,\times {{10}^{8}}\,m/s,\,\pi =3.14\])

    A) \[9.42\,\times {{10}^{4}}\,m\]

    B) \[18\,\times 8.\,{{10}^{4}}m\]

    C) \[4.5\,\times {{10}^{4}}\,m\]

    D) none of these

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  • question_answer43) The \[{{K}_{\alpha }}\] line of singly ionized calcium has a wavelength of 393.3 nm as measured on earth. In the spectrum of one of the observed galaxies, the spectral line is located at 401.8 nm. The speed with which this galaxy is moving away from us, will be

    A) 7400 m/s

    B) \[32.\,4\times {{10}^{2}}m/s\]

    C) 6480 km/s

    D) none of these

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  • question_answer44) In a common-base circuit of a transistor current amplification factor is 0.95. The base current when emitter current is 2 mA, will be

    A) 0.2mA

    B) 0.1mA

    C) 0.002 mA

    D) none of these

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  • question_answer45) Cathode rays of velocity \[{{10}^{6}}\,m/s\] describe an approximate circular path of radius 1 m in an electric field 300 V/cm. If the velocity of the cathode rays are doubled. The value of electric field so that the rays describe the same circular path, will be

    A) 2400 V/cm

    B) 600 V/cm

    C) 1200 V/cm

    D) 12000 V/cm

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  • question_answer46) Light of wavelength \[5000\overset{\text{o}}{\mathop{\text{A}}}\,\] falling on a sensitive surface. If the surface has received \[{{10}^{-7}}J\] of energy, then the number of photons falling on the surface will be:

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

    B) \[2.5\,\times {{10}^{11}}\]

    C) \[3\times {{10}^{11}}\]

    D) none of these

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  • question_answer47) An X-ray machine is opearated at 40 kV. The short wavelength limit of continuous X-rays will be \[(h=6.63\,\times {{10}^{-34}}\,Js,\,\,c=3\times {{10}^{8}}m/s,\,e=1.6\times {{10}^{-19}}C)\]

    A) \[0.31\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

    B) \[0.62\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

    C) \[0.155\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

    D) \[0.62\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

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  • question_answer48) The wavelength of the first spectral line of sodium is \[5896\,\overset{\text{o}}{\mathop{\text{A}}}\,\]. The first excitation potential of sodium atom will be \[(h=6.63\times {{10}^{-34}}\,Js)\]

    A) 4.2 V

    B) 3.5 V

    C) 2.1 V

    D) None of these

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  • question_answer49) If 200 MeV energy is released in the fission of a single nucleus of \[_{92}{{U}^{235}}\]. How much fission must occur per second to produce a power of 1kW?

    A) \[3.125\,\times {{10}^{13}}\]

    B) \[6.250\,\times {{10}^{13}}\]

    C) \[1.525\,\times {{10}^{13}}\]

    D) None of these

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  • question_answer50) The energy supplied to calculate by state electricity board during an average November day was 40 mkh. If this energy could be obtained by the conversion of matter, how much mass will be annihilated?

    A) 3.2 g

    B) 6.4 g

    C) 1.6 g

    D) 2.5 g

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  • question_answer51) Which one of the following represents noble gas configuration?

    A) \[1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},3{{s}^{2}}3{{p}^{6}}3{{d}^{10}},4{{s}^{2}}4{{p}^{6}}4{{d}^{10}},\]\[5{{s}^{2}},5{{p}^{6}}5{{d}^{6}},6{{s}^{2}}\]

    B) \[1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},3{{s}^{2}}3{{p}^{6}}3{{d}^{10}},4{{s}^{2}}4{{p}^{6}}4{{d}^{10}},\]\[5{{s}^{2}}5{{p}^{6}}5{{d}^{1}},6{{s}^{2}}\]

    C) \[1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},3{{s}^{2}}3{{p}^{6}}3{{d}^{10}},4{{s}^{2}}4{{p}^{6}}4{{d}^{10}}\]\[5{{s}^{2}}5{{p}^{6}}\]

    D) \[1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},3{{s}^{2}}3{{p}^{6}}3{{d}^{10}},4{{s}^{2}}4{{p}^{6}}4{{f}^{14}},\]\[5{{s}^{2}}5{{p}^{6}}5{{d}^{1}}\]

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  • question_answer52) The number of unpaired electrons in \[\text{Ni(CO}{{\text{)}}_{\text{4}}}\]

    A) 0

    B) 1

    C) 3

    D) 4

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  • question_answer53) Nitrobenzene on treatment with zinc dust and aqueous ammonium chloride gives

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

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

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

    D) \[{{C}_{6}}{{H}_{5}}NHOH\]

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  • question_answer54) Which one of the following is a correct statement?

    A) All metal nitrates are insoluble in water

    B) Solubility depends on temperature

    C) All metal nitrates are soluble in water

    D) All metal nitrates are soluble in alcohol

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  • question_answer55) Methyl \[-\alpha -D-\]glucoside and methyl\[-\beta -D-\]glucoside are

    A) epimers

    B) anomers

    C) enantiomers

    D) conformational diastereomers

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  • question_answer56) Which one of the following shows maximum value of paramagnetic behaviour?

    A) \[{{[Sc{{(CN)}_{6}}]}^{3-}}\]

    B) \[{{[Co{{(CN)}_{6}}]}^{3-}}\]

    C) \[{{[Fe{{(CN)}_{6}}]}^{4-}}\]

    D) \[{{[Cr{{(CN)}_{6}}]}^{3-}}\]

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  • question_answer57) Carbolic acid is

    A) \[~HCOOH\]

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

    C) \[~{{C}_{6}}{{H}_{5}}COOH\]

    D) \[~{{C}_{6}}{{H}_{5}}OH\]

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  • question_answer58) The solubility product of \[BaC{{l}_{2}}\] is \[4\times {{10}^{-9}}.\] Its solubility in mol/L is

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

    B) \[4\times {{10}^{-9}}\]

    C) \[1\times {{10}^{-3}}\]

    D) \[1\times {{10}^{-9}}\]

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  • question_answer59) Which one can differentiate between \[{{C}_{2}}{{H}_{5}}OH\] and\[C{{H}_{3}}OH\]?

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

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

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

    D) \[HCl\]

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  • question_answer60) Zinc and cold dil. \[HN{{O}_{3}}\] reacts to produce

    A) NO

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

    C) \[N{{H}_{4}}N{{O}_{3}}\]

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

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  • question_answer61) For the reaction, \[{{H}_{2}}+{{I}_{2}}2HI,\]the equilibrium concentration of \[{{H}_{2}},{{I}_{2}}\]and HI are 8.0, 3.0 and 28.0 mol/L respectively. The equilibrium constant is

    A) 28.34

    B) 32.66

    C) 34.78

    D) 38.88

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  • question_answer62) Tincture of iodine is

    A) aqueous solution bf \[{{I}_{2}}\]

    B) solution of \[{{I}_{2}}\] in aqueous \[KI\]

    C) alcoholic solution of \[{{I}_{2}}\]

    D) aqueous solution of \[KI\]

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  • question_answer63) The chemical formula of plaster of Paris is

    A) \[CaS{{O}_{4}}.\frac{1}{2}{{H}_{2}}O\]

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

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

    D) \[CaS{{O}_{4}}.3{{H}_{2}}O\]

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  • question_answer64) Which one of the following has square planar structure?

    A) \[{{[Ni{{(CN)}_{4}}]}^{2-}}\]

    B) \[[Ni{{(CO)}_{4}}]\]

    C) \[{{[NiC{{l}_{4}}]}^{2-}}\]

    D) All of the above

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  • question_answer65) The oxidation number of chromium in potassium dichromate is

    A) + 2

    B) + 4

    C) + 6

    D) + 8

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  • question_answer66) The electronic configuration of most electronegative element? is

    A) \[1{{s}^{2}},2{{s}^{2}}2{{p}^{5}}\]

    B) \[1{{s}^{2}},2{{s}^{2}}2{{p}^{4}},3{{s}^{1}}\]

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

    D) \[1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},3{{s}^{2}}3{{p}^{5}}\]

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  • question_answer67) The molecular formula \[{{C}_{3}}{{H}_{9}}N\]cannot represent

    A) \[{{1}^{o}}\]amine

    B) \[{{2}^{o}}\]amine

    C) \[{{3}^{o}}\]amine

    D) quaternary salt

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  • question_answer68) The bond length between \[C-C\]bond in \[s{{p}^{2}}\]hybridized molecule is

    A) \[1.2\overset{\text{o}}{\mathop{\text{A}}}\,\]

    B) \[1.39\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]

    C) \[1.33\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]

    D) \[~1.54\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]

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  • question_answer69) The energy ratio of a photon of wavelength \[\text{3000 }\overset{\text{o}}{\mathop{\text{A}}}\,\]and \[\text{6000 }\overset{\text{o}}{\mathop{\text{A}}}\,\]is

    A) 1 : 1

    B) 2 : 1

    C) 1 : 2

    D) 1 : 4

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  • question_answer70) Gas equation \[PV=nRT\]is obeyed by ideal gas in

    A) adiabatic process

    B) isothermal process

    C) both (a) and (b)

    D) none of the above

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  • question_answer71) Clemmensens reduction of ketones is carried out in

    A) \[LiAl{{H}_{4}}\]in \[{{H}_{2}}O\]

    B) glycol and KOH

    C) \[Zn-Hg\]and \[HCl\]

    D) \[{{H}_{2}}\]and \[Pd\]catalyst

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  • question_answer72) The planar structure of \[B{{F}_{3}}\]can be explained by the fact that \[B{{F}_{3}}\] is

    A) \[sp-\]hybridized

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

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

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

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  • question_answer73) Reduction of aniline with acetyl chloride in presence of \[\text{NaOH}\]produce

    A) aniline hydrochloride

    B) acetanilide

    C) p-chloroaniline

    D) a red dye

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  • question_answer74) Which of the following compounds has the highest boiling point?

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

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

    C) \[C{{H}_{3}}CH(C{{H}_{3}})C{{H}_{2}}Cl\]

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

    View Answer play_arrow
  • question_answer75) An unknown compound D first oxidized to aldehyde and then acetic acid by a dilute solution of \[{{K}_{2}}C{{r}_{2}}{{O}_{7}}\]and \[{{H}_{2}}S{{O}_{4}}.\]The compound D is

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

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

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

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

    View Answer play_arrow
  • question_answer76) Which of the following is not possible?

    A) \[n=2,\,l=1,m=0\]

    B) \[n=2,\,l=0,m=-1\]

    C) \[n=3,\,l=0,m=0\]

    D) \[n=3,\,l=1,m=-1\]

    View Answer play_arrow
  • question_answer77) A gas expands isothermally against a constant external pressure of 1 atm from a volume of \[10\,d{{m}^{3}}\]to a volume of \[20\,d{{m}^{3}}.\] It absorbs 300 J of thermal energy from its surroundings. The \[\Delta U\]is

    A) \[-312\,J\]

    B) \[+\,123J\]

    C) \[-213\,J\]

    D) \[+\,231\,J\]

    View Answer play_arrow
  • question_answer78) Phenol is more acidic than alcohol because

    A) phenol is more soluble in polar solvents

    B) alcohol does not lose hydrogen atom

    C) phenoxide ion is stabilized by resonance

    D) phenoxide ion do not exhibit resonance

    View Answer play_arrow
  • question_answer79) The element having highest electron affinity

    A) bromine

    B) iodine

    C) fluorine

    D) chlorine

    View Answer play_arrow
  • question_answer80) Bakelite is prepared by the reaction between

    A) phenol and formaldehyde

    B) urea and formaldehyde

    C) ethylene and glycol

    D) tetramethylene and glycol

    View Answer play_arrow
  • question_answer81) Which one of the following is a conjugated protein?

    A) Phosphoprotein

    B) Glycoprotein

    C) Chromoprotein

    D) All of the above

    View Answer play_arrow
  • question_answer82) Iodine test is shown by

    A) glucose

    B) starch

    C) glycogen

    D) polypeptide

    View Answer play_arrow
  • question_answer83) A fruity smell is obtained by the reaction of ethanol with

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

    B) \[PC{{l}_{5}}\]

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

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

    View Answer play_arrow
  • question_answer84) Cyanide process is used for extraction of

    A) Ag

    B) Ni

    C) Pt

    D) Zn

    View Answer play_arrow
  • question_answer85) An acid solution of 0.005 M has a pH of 5. The degree of ionization of acid is

    A) \[0.1\times {{10}^{-2}}\]

    B) \[0.2\times {{10}^{-2}}\]

    C) \[0.5\times {{10}^{-4}}\]

    D) \[0.6\times {{10}^{-6}}\]

    View Answer play_arrow
  • question_answer86) Which metal gives hydrogen gas on heating with hot concentrated alkali?

    A) Ag

    B) Ni

    C) Zn

    D) Cu

    View Answer play_arrow
  • question_answer87) The conversion of ethyl chloride into diethyl ether takes place by

    A) Williamsons synthesis

    B) Perkins reaction

    C) Wurtz reaction

    D) Grignard reaction

    View Answer play_arrow
  • question_answer88) \[CHC{{l}_{3}}+{{C}_{6}}{{H}_{5}}N{{H}_{2}}+3NaOH\xrightarrow{{}}A\] \[+\,3B\,+3C\] In the above reaction, the product A is

    A) chlorobenzene

    B) phenyl isocyanide

    C) phenyl cyanide

    D) phenyl chloride

    View Answer play_arrow
  • question_answer89) A gas is found to have a formula \[{{[CO]}_{x}}.\]Its vapour density is 70, the \[x\] is

    A) 3.0

    B) 3.5

    C) 5.0

    D) 6.5

    View Answer play_arrow
  • question_answer90) Which of the following is used as purgative?

    A) \[HgS\]

    B) \[H{{g}_{2}}C{{l}_{2}}\]

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

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

    View Answer play_arrow
  • question_answer91) Least stable oxide of chlorine is

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

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

    C) \[C{{l}_{2}}{{O}_{7}}\]

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

    View Answer play_arrow
  • question_answer92) The sides of safety matches contains

    A) red phosphorus + sand powder

    B) \[{{P}_{4}}{{S}_{3}}\]

    C) \[C{{a}_{3}}{{(PO)}_{4}}+\text{glass}\,\text{pieces}\]

    D) \[KCl{{O}_{3}},KN{{O}_{3}},\] sulphur + antimony

    View Answer play_arrow
  • question_answer93) Chemically aspirin is known as

    A) salicylic acid

    B) salicylaldehyde

    C) 2-acetoxybenzoic acid

    D) phenyl salicylate

    View Answer play_arrow
  • question_answer94) Gun metal is

    A) \[Cu+Zn\]

    B) \[Cu+Sn+Zn\]

    C) \[Cu+Sn\]

    D) \[Zn+Sn\]

    View Answer play_arrow
  • question_answer95) Which cannot be oxidized by\[{{H}_{2}}{{O}_{2}}\]?

    A) \[N{{a}_{2}}S{{O}_{3}}\]

    B) \[PbS\]

    C) \[KI\]

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

    View Answer play_arrow
  • question_answer96) The gas not absorbed by coconut charcoal is

    A) He

    B) Ne

    C) Ar

    D) Kr

    View Answer play_arrow
  • question_answer97) KI and \[CuS{{O}_{4}}\]solutions on mixing produce

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

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

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

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

    View Answer play_arrow
  • question_answer98) Vitamin \[{{B}_{12}}\]contains

    A) Co

    B) Mn

    C) Mg

    D) Fe

    View Answer play_arrow
  • question_answer99) Water glass is

    A) glass made of water

    B) sodium silicate

    C) calcium formate

    D) pyrex glass

    View Answer play_arrow
  • question_answer100) Purification of alumina takes place by

    A) Bosch process

    B) Halls process

    C) Hoopes process

    D) Quartation process

    View Answer play_arrow
  • question_answer101) If \[f(x)=f(a-x)\] and \[g(x)+g(a-x)=2,\]then the value of \[\int\limits_{0}^{a}{f(x)g(x)dx}\] is

    A) \[\int_{0}^{a}{f(x)dx}\]

    B) \[\int_{0}^{a}{g(x)dx}\]

    C) \[\int_{0}^{a}{[g(x)-f(x)]dx}\]

    D) \[\int_{0}^{a}{[g(x)+f(x)]dx}\]

    View Answer play_arrow
  • question_answer102) The differential equation of the family of the curves \[{{x}^{2}}+{{y}^{2}}-2ax=0\]is

    A) \[{{x}^{2}}-{{y}^{2}}-2ax=0\]

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

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

    D) none of the above

    View Answer play_arrow
  • question_answer103) A body falls freely from the top of a tower and during the last second of its flight it falls \[\frac{\text{5}}{\text{9}}\text{th}\]of the whole distance. The height of the tower and time of motion are respectively

    A) 44.1 m and 3s

    B) 44.1m and 5s

    C) 4.41 m and 3s

    D) none of the above

    View Answer play_arrow
  • question_answer104) The sum of the series \[\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+...\]upto \[n\] term is

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

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

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

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

    View Answer play_arrow
  • question_answer105) The equation of the plane passing through the mid point of the line of join of the points (1, 2, 3) and (3, 4, 5) and perpendicular to it is

    A) \[x+y+z=9\]

    B) \[x+y+z=-9\]

    C) \[2x+3y+4z=9\]

    D) \[2x+3y+4z=-9\]

    View Answer play_arrow
  • question_answer106) The equation of the circle concentric to the circle \[2{{x}^{2}}+2{{y}^{2}}-3x+6y+2=0\] and having area double the area of this circle, is

    A) \[8{{x}^{2}}+8{{y}^{2}}-24x+48y-13=0\]

    B) \[16{{x}^{2}}+16{{y}^{2}}+24x-48y-13=0\]

    C) \[16{{x}^{2}}+16{{y}^{2}}-24x+48y-13=0\]

    D) \[8{{x}^{2}}+8{{y}^{2}}+24x-48y-13=0\]

    View Answer play_arrow
  • question_answer107) The domain of the function \[f(x)=\frac{{{\cos }^{-1}}x}{[x]}\]is

    A) \[[-1,0)\cup \{1\}\]

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

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

    D) none of these

    View Answer play_arrow
  • question_answer108) Let \[f(x)=\left\{ \begin{matrix} \frac{\tan x-\cot x}{x-\frac{\pi }{4}}, & x\ne \frac{\pi }{4} \\ a, & x=\frac{\pi }{4} \\ \end{matrix} \right.\] the value of a so that \[f(x)\] is continuous at\[x=\frac{\pi }{4}\]

    A) 2

    B) 4

    C) 3

    D) 1

    View Answer play_arrow
  • question_answer109) If e and e are the eccentricities of hyperbolas\[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{^{2}}}}{{{b}^{2}}}=1\] and its conjugate hyperbola, then the value of \[\frac{1}{{{e}^{2}}}+\frac{1}{e{{}^{2}}}\]is

    A) 0

    B) 1

    C) 2

    D) none of these

    View Answer play_arrow
  • question_answer110) The value of the\[\int_{{}}^{{}}{\frac{\sin x+\cos x}{3+\sin 2x}}dx\]is

    A) \[\frac{1}{4}\ln \left( \frac{2-\sin x+\cos x}{2+\sin x+\cos x} \right)+c\]

    B) \[\frac{1}{2}\ln \]\[\left( \frac{2+\sin x}{2-\sin x} \right)+c\]

    C) \[\frac{1}{4}\ln \]\[\left( \frac{1+\sin x}{1-\sin x} \right)+c\]

    D) none of the above

    View Answer play_arrow
  • question_answer111) If forces of magnitude 12 kg-wt, 5 kg-wt and 13 kg-wt act at a point are in equilibrium, then the angle between the first two forces is

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

    B) \[~{{90}^{o}}\]

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

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

    View Answer play_arrow
  • question_answer112) For a party 8 guests are invited by a husband and his wife. They sit in a row for dinner. The probability that the husband and his wife sit together is

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

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

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

    D) \[\frac{4}{9}\]

    View Answer play_arrow
  • question_answer113) If\[{{I}_{m}}\left( \frac{z-1}{2z+1} \right)=-4,\]then locus of z is

    A) ellipse

    B) parabola

    C) straight line

    D) circle

    View Answer play_arrow
  • question_answer114) The equation \[(x-b)(x-c)+(x-a)(x-b)\]\[+\,(x-a)(x-c)=0\] has all its roots

    A) positive

    B) real

    C) imaginary

    D) negative

    View Answer play_arrow
  • question_answer115) The sum of coefficients of the expansion\[{{\left( \frac{1}{x}+2x \right)}^{n}}\]is 6561. The coefficient of term independent of \[x\] is

    A) \[16\,{{\,}^{8}}{{C}_{4}}\]

    B) \[^{8}{{C}_{4}}\]

    C) \[^{8}{{C}_{5}}\]

    D) none of these

    View Answer play_arrow
  • question_answer116) The area enclosed between the curves \[y=x\] and \[y=2x-{{x}^{2}}\]is (in sq. unit)

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

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

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

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

    View Answer play_arrow
  • question_answer117) There are 12 white and 12 red balls in a bag. Balls are drawn one by one with replacement from the bag. The probability that 7th drawn ball is 4th white is

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

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

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

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

    View Answer play_arrow
  • question_answer118) In an ellipse the angle between the lines joining the foci with the positive end of minor axis is a right angle, the eccentricity of the ellipse is

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

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

    C) \[\sqrt{2}\]

    D) \[\sqrt{3}\]

    View Answer play_arrow
  • question_answer119) If \[|\vec{a}|=3,\,\,\,|\vec{b}|=5\]and \[|\vec{c}|=4\]then and \[\vec{a}+\vec{b}+\vec{c}=0,\] then the value of \[\vec{a}+\vec{b}+\vec{c}=0,\]then the value of \[\vec{a}.\vec{b}\,+\,\vec{b}.\vec{c}\]is equal to

    A) 0

    B) -25

    C) 25

    D) none of these

    View Answer play_arrow
  • question_answer120) The equation of a line is\[6x-2=3y-1=2z-2.\]The direction ratios of the line are

    A) 1, 2, 3

    B) 1, 1, 1

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

    D) \[\frac{1}{3},\frac{-1}{3},\frac{1}{3}\]

    View Answer play_arrow
  • question_answer121) For the circuit shown below, the Boolean polynomial is

    A) \[(\tilde{\ }p\vee q)\vee (p\vee \tilde{\ }q)\]

    B) \[(\tilde{\ }p\wedge p)\wedge (\tilde{\ }q\wedge q)\]

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

    D) \[(\tilde{\ }p\wedge q)\vee (q\wedge \tilde{\ }q)\]

    View Answer play_arrow
  • question_answer122) The value of \[\int_{{}}^{{}}{\frac{dx}{x+\sqrt{x-1}}}\]is

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

    B) \[\log (x+\sqrt{x-1})+c\]

    C) \[\log (x+\sqrt{x-1})-\frac{2}{\sqrt{3}}{{\tan }^{-1}}\]

    D) \[\left( \frac{2\sqrt{x-1}+1}{\sqrt{3}} \right)\] none of the above

    View Answer play_arrow
  • question_answer123) If \[y={{\sin }^{-1}}\frac{x}{2}+{{\cos }^{-1}}\frac{x}{2},\]then the value of \[\frac{dy}{dx}\]is

    A) 1

    B) -1

    C) 0

    D) 2

    View Answer play_arrow
  • question_answer124) In Boolean algebra, the unit element 1

    A) has two values

    B) is unique

    C) has at least two values

    D) none of the above

    View Answer play_arrow
  • question_answer125) On one bank of river there is a tree. On another bank, an observer makes an angle of elevation of \[{{60}^{o}}\] at the top of the tree. The angle of elevation of the top of the tree at a distance 20 m away from the bank is 30?. The width of the river is

    A) 20 m

    B) 10 m

    C) 5 m

    D) 1 m

    View Answer play_arrow
  • question_answer126) The magnitude of cross product of two vectors is \[\sqrt{3}\]times the dot product. The angle between the vectors is

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

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

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

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

    View Answer play_arrow
  • question_answer127) If \[{{D}_{r}}=\left| \begin{matrix} r & 1 & \frac{n(n+1)}{2} \\ 2r-1 & 4 & {{n}^{2}} \\ {{2}^{r-1}} & 5 & {{2}^{n-}}-1 \\ \end{matrix} \right|,\]then the value of \[\sum\limits_{r=0}^{n}{{{D}_{r}}}\]is

    A) 0

    B) 1

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

    D) none of these

    View Answer play_arrow
  • question_answer128) If\[\left| \begin{matrix} -12 & 0 & \lambda \\ 0 & 2 & -1 \\ 2 & 1 & 15 \\ \end{matrix} \right|=-360,\]then the value of \[\lambda \]is

    A) \[-1\]

    B) \[-2\]

    C) \[-3\]

    D) \[4\]

    View Answer play_arrow
  • question_answer129) If \[A=\left[ \begin{matrix} 1 & x \\ {{x}^{2}} & 4y \\ \end{matrix} \right]\]and \[B\,=\left[ \begin{matrix} -3 & 1 \\ 1 & 0 \\ \end{matrix} \right]\]adj.\[A+B=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right],\] then the value of \[x\]and \[y\]are

    A) 1, 1

    B) \[\pm \,1,1\]

    C) \[1,0\]

    D) none of these

    View Answer play_arrow
  • question_answer130) If \[{{\tan }^{-1}}\frac{1-x}{1+x}=\frac{1}{2}{{\tan }^{-1}}x,\]then values of \[x\]is

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

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

    C) \[\sqrt{3}\]

    D) 2

    View Answer play_arrow
  • question_answer131) If \[{{x}^{2/3}}-7{{x}^{1/3}}+10=0\]then, the value of \[x\] is

    A) \[\{125\}\]

    B) \[\{8\}\]

    C) \[\phi \]

    D) \[\text{ }\!\!\{\!\!\text{ 125,8 }\!\!\}\!\!\text{ }\]

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  • question_answer132) The value of \[\underset{\alpha \to 0}{\mathop{\lim }}\,\frac{\begin{align} & \cos e{{c}^{-1}}(sec\alpha )+co{{t}^{-1}}(tan\alpha ) \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+co{{t}^{-1}}\cos (si{{n}^{-1}}\alpha ) \\ \end{align}}{\alpha }\]is

    A) 0

    B) \[-1\]

    C) \[-2\]

    D) 1

    View Answer play_arrow
  • question_answer133) If the second term in the expansion\[{{\left[ \sqrt[13]{a}\frac{a}{\sqrt{{{a}^{-1}}}} \right]}^{n}}\]is \[14{{a}^{5/2}},\] then the value of \[\frac{{{\,}^{n}}C{{\,}_{3}}}{{{\,}^{n}}{{C}_{2}}}\]is

    A) 4

    B) 3

    C) 12

    D) 6

    View Answer play_arrow
  • question_answer134) One of the diameter of the circle \[{{x}^{2}}+{{y}^{2}}-12x+4y+6=0\] is given by

    A) \[~x+y=0\]

    B) \[~x+3y=0\]

    C) \[x=y\]

    D) \[3x+2y=0\]

    View Answer play_arrow
  • question_answer135) Point D, E are taken on the side BC of the triangle ABC, such that \[BD=DE=EC.\]If \[\angle BAD=x,\angle DAE=y,\angle EAC=z,\] then the value of \[\frac{\sin (x+y)\sin (y+z)}{\sin x\sin \,z}\] is equal to

    A) 1

    B) 2

    C) 4

    D) none of these

    View Answer play_arrow
  • question_answer136) The number of real solution of\[{{\tan }^{-1}}\sqrt{x(x+1)}+{{\sin }^{-1}}\sqrt{{{x}^{2}}+x+1}=\frac{\pi }{2}\]is

    A) zero

    B) one

    C) two

    D) infinite

    View Answer play_arrow
  • question_answer137) The equation \[{{\sin }^{-1}}x-{{\cos }^{-1}}x={{\cos }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\] has

    A) no solution

    B) unique solution

    C) infinite number of solution

    D) none of the above

    View Answer play_arrow
  • question_answer138) In a \[\Delta ABC,\,a,c,A\]are given and \[{{b}_{1}},{{b}_{2}}\]are two values, if the third side b such that \[{{b}_{2}}=2{{b}_{1}}\]then sin A is equal to

    A) \[\sqrt{\frac{9{{a}^{2}}-{{c}^{2}}}{8{{a}^{2}}}}\]

    B) \[\sqrt{\frac{9{{a}^{2}}-{{c}^{2}}}{8{{c}^{2}}}}\]

    C) \[\sqrt{\frac{9{{a}^{2}}+{{c}^{2}}}{8{{a}^{2}}}}\]

    D) none of these

    View Answer play_arrow
  • question_answer139) A variable chord is drawn through the origin to the circle \[{{x}^{2}}+{{y}^{2}}-2ax=0.\]The locus of the centre of the circle drawn on this chord as diameter is

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

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

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

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

    View Answer play_arrow
  • question_answer140) If \[1,{{a}_{1}},{{a}_{2}},...,{{a}_{n-1}}\]are the n roots of unity, then the value of \[(1-{{a}_{1}})(1-{{a}_{2}})(1-{{a}_{3}})......(1-{{a}_{n-1}})\] is equal to

    A) \[\sqrt{3}\]

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

    C) \[n\]

    D) 0

    View Answer play_arrow
  • question_answer141) Let a, b, c be real. If \[a{{x}^{2}}+bx+c=0\]has two real roots \[\alpha \]and\[\beta ,\]where \[a<-1\]and \[\beta >1,\]then \[1+\frac{c}{a}+\left| \frac{b}{a} \right|\]is

    A) \[<0\]

    B) \[>0\]

    C) \[\le 0\]

    D) none of these

    View Answer play_arrow
  • question_answer142) Number of divisiors of the form \[(4n+2),n\ge 0\] of the integer 240 is

    A) 4

    B) 8

    C) 10

    D) 3

    View Answer play_arrow
  • question_answer143) The expression \[{{\{x+{{({{x}^{3}}-1)}^{1/2}}\}}^{5}}\]\[+\,{{\{x-{{({{x}^{3}}-1)}^{1/2}}\}}^{5}}\] is a polynomial of degree

    A) 5

    B) 6

    C) 7

    D) 8

    View Answer play_arrow
  • question_answer144) Let a, b, c be positive and not all equal, the value of the determinant \[\left| \begin{matrix} a & b & c \\ b & c & a \\ c & a & b \\ \end{matrix} \right|\]is

    A) \[\text{+}\,\text{ve}\]

    B) \[-\text{ve}\]

    C) zero

    D) none of these

    View Answer play_arrow
  • question_answer145) \[\underset{h\to 0}{\mathop{\lim }}\,\frac{{{(a+h)}^{2}}\sin (a+h)-{{a}^{2}}\sin a}{h}\]is equal to

    A) \[2a\,\sin \,a\]

    B) \[{{a}^{2}}\cos \,a\]

    C) \[{{a}^{2}}\cos a+2a\,\,\sin \,a\]

    D) none of these

    View Answer play_arrow
  • question_answer146) If \[f(x)=x(\sqrt{x}+\sqrt{x+1}),\]then

    A) \[f(x)\]is continuous but not differentiable at \[x=0\]

    B) \[f(x)\] is differentiable at \[x=0\]

    C) \[f(x)\]is not differentiable at \[x=0\]

    D) none of these

    View Answer play_arrow
  • question_answer147) If \[y\]is a function of \[x\]and \[\log (x+y)=2xy,\] then the value of \[y(0)\]is equal to

    A) 1

    B) -1

    C) 2

    D) 0

    View Answer play_arrow
  • question_answer148) The angle between the tangent drawn from the point (1, 4) to the parabola \[{{y}^{2}}=4x\]is

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

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

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

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

    View Answer play_arrow
  • question_answer149) If \[y=a\log x+b{{x}^{2}}+x\]has its extremum value at \[x=-1\]and \[x=2,\]then

    A) \[x=-1\]and \[x=2,\]

    B) \[a=2,\,b=-\frac{1}{2}\]

    C) \[a=2,=-\frac{1}{2}\]

    D) none of the above

    View Answer play_arrow
  • question_answer150) The value of \[\int_{{}}^{{}}{\frac{dx}{{{x}^{2}}{{({{x}^{4}}+1)}^{3/4}}}}\]is

    A) \[-\frac{{{({{x}^{4}}+1)}^{1/4}}}{x}+c\]

    B) \[\frac{{{({{x}^{4}}+1)}^{1/4}}}{x}+c\]

    C) zero

    D) none of the above

    View Answer play_arrow

   

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