question_answer 1) A solenoid of length 0.6 m has a radius of \[1\text{ }cm\] and is made up of 600 turns. It carries a current of \[6\text{ }A\]. What is the magnitude of the magnetic field inside the solenoid?
A)
\[7.54\times {{10}^{-3}}T~\]
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B)
\[10.84\times {{10}^{-3}}\,\,T\]
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C)
\[4.87\times {{10}^{-3}}\,\,T\]
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D)
\[2.36\times {{10}^{-2}}\,\,T\]
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question_answer 2) The bus moving with a speed of \[42\text{ }km/h\]is brought to a stop by brakes after\[6\text{ }m\]. If the same bus is moving at a speed of \[90\text{ }km/h,\] then the minimum stopping distance is
A)
\[15.48\text{ }m\]
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B)
\[18.64\text{ }m\]
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C)
\[22.13\text{ }m\]
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D)
\[27.55\text{ }m\]
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question_answer 3) A \[15pF\] capacitor is connected to a \[60\text{ }V\] battery. How much electrostatic energy is stored?
A)
\[2.77\times {{10}^{-8}}\,J\]
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B)
\[1.77\times {{10}^{-8}}\,J\]
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C)
\[2.35\times {{10}^{-8}}\,J\]
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D)
\[1.35\times {{10}^{-8}}\,J\]
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question_answer 4) In a video signal for transmission of picture, what value of bandwidth is used " in communication system?
A)
\[2.4\text{ }MHz\]
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B)
\[4.2\text{ }MHz\]
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C)
\[4.2\text{ }MHz\]
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D)
\[42\text{ }MHz\]
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question_answer 5) A straight wire of mass 300 g and length \[2.5\text{ }m\]carries a current of \[3.5\text{ }A\]. It is suspended in mid-air by a uniform horizontal magnetic field B. What is the magnitude of the magnetic field?
A)
\[0.654\text{ }T\]
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B)
\[0.336\text{ }T\]
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C)
\[1.576\text{ }T\]
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D)
\[0.939\text{ }T\]
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question_answer 6) When longitudinal wave propagates, what happens in the region of compressions and rarefactions?
A)
Density varies
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B)
Density remains constant
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C)
There is heat transfers
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D)
Boyle's law is obeyed
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question_answer 7) If the temperature of the body is increased by \[10%,\] the percentage increase in the emitted indication will be
A)
\[46%\]
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B)
\[40%\]
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C)
\[30%\]
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D)
\[80%\]
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question_answer 8) A galaxy is moving away from an observe on the earth so that sodium light of wavelength \[5892\overset{\text{o}}{\mathop{\text{A}}}\,\] is observed at \[5896\overset{\text{o}}{\mathop{\text{A}}}\,\]. The speed of galaxy is
A)
\[306\,\,km/s\]
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B)
\[204\text{ }km/s\]
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C)
\[185\,km/s\]
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D)
\[158\text{ }km/s\]
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question_answer 9) The correct order of arrangement of electromagnetic waves according to their wavelength is
A)
gamma rays < microwaves < AM radiowaves < FM radiowaves
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B)
microwaves < AM radiowaves < FM radiowaves < gamma rays
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C)
gamma rays < AM radiowaves < FM radiowaves < microwaves
done
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D)
gamma rays < microwaves < FM radiowaves < AM radiowaves
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question_answer 10) A constant retarding force of \[80\text{ }N\]is applied to a body of mass \[50\text{ }kg\]which is moving initially with a speed of\[20\text{ }m/s\]. What would be the time required by the body to come to rest?
A)
\[15\,\,s\]
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B)
\[14\,\,s\]
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C)
\[12.5\,\,s\]
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D)
\[1\,8\,\,s\]
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question_answer 11) Light from a point source in air falls on a spherical glass surface (\[n=1.67\]and radius of curvature \[~=25\text{ }cm\]). The distance of the light source from the glass surface is \[95\text{ }cm\]. At what position, the image is formed?
A)
\[75.45\text{ }cm\]
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B)
\[90.50\text{ }cm\]
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C)
\[105.25\text{ }cm\]
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D)
\[99.40\text{ }cm\]
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question_answer 12) The length of the wire is increase by 2% by applying a load of\[2.5\text{ }kg-wt\]. What is the linear strain produced in the wire?
A)
\[0.1\]
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B)
\[0.01\]
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C)
\[0.2\]
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D)
\[0.02\]
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question_answer 13) The half life of an old rock element is 5800 years. In how many years its sample of \[25\text{ }g\]is reduced to \[6.25\text{ }g\].
A)
\[2900\text{ }years\]
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B)
\[5800\text{ }years\]
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C)
\[11600\text{ }years\]
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D)
\[23200\text{ }years\]
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question_answer 14) The earth takes \[24\text{ }h\]to rotate once about its axis. How much time does the sun take to shift by \[{{5}^{o}}\] when viewed from the earth?
A)
\[20\text{ }min\]
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B)
\[15\text{ }min\]
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C)
\[10\text{ }min\]
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D)
\[5\text{ }min\]
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question_answer 15) Which of the following is a dimension less quantity?
A)
Magnetic flux density
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B)
Electric flux density
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C)
Lumen flux density
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D)
Optical density
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question_answer 16) A crane lifts weight of \[75\text{ }kg\]to a height of \[15\text{ }m\] in\[15\text{ }s\]. The power of the crane is (assuming \[g=9.8\,m/{{s}^{2}}\])
A)
\[635\,\,W\]
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B)
\[735\,\,W\]
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C)
\[835\,\,W\]
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D)
\[1135\,\,W\]
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question_answer 17) The escape velocity from the surface of the earth is\[11.2\text{ }km{{s}^{-1}}\]. What is the escape velocity in a planet whose radius is three times that of the earth and on which the acceleration due to gravity is three times of that on the earth?
A)
\[11.2\text{ }km{{s}^{-1}}\]
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B)
\[22.4\text{ }km{{s}^{-1}}\]
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C)
\[33.6\text{ }km{{s}^{-1}}\]
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D)
\[5.6\text{ }km{{s}^{-1}}\]
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question_answer 18) What is the dimensional formula for Work?
A)
\[[ML{{T}^{-2}}]\]
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B)
\[[M{{L}^{2}}{{T}^{-2}}]\]
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C)
\[[M{{L}^{3}}{{T}^{-2}}]\]
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D)
\[[M{{L}^{2}}{{T}^{-1}}]\]
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question_answer 19) When the gas expands with temperature using the relation \[V=K{{T}^{2/3}}\] for the temperature change of \[40\text{ }K,\] the work done is
A)
\[20.1\,\,R\]
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B)
\[30.2\,\,R\]
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C)
\[26.6\,\,R\]
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D)
\[35.6\,\,R\]
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question_answer 20) The resonant frequency of a L-C-R circuit depends upon
A)
L and R
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B)
C and R
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C)
L and C
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D)
L, C and R
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question_answer 21) A wheel with 30 metallic spokes each of \[7.0\text{ }m\] long is rotated with a speed of \[120\text{ }rev/min,\] in a plane normal to the horizontal component of the earth's magnetic field Hg /at a place. If \[{{H}_{E}}=0.8G\]at the place what is the induced emf between the axis and the rim of the wheel? (Give \[1G={{10}^{-4}}\text{ }T\])
A)
\[2.46\times {{10}^{-4}}V\]
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B)
\[6.28\times {{10}^{-4}}V\]
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C)
\[5.76\times {{10}^{-5}}V\]
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D)
\[4.92\times {{10}^{-4}}V\]
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question_answer 22) In a circuit, 3 resistors of resistance \[1.2\Omega \]\[1.2\,\,\Omega ,\]\[2\,\,\Omega ,\] \[3\,\,\Omega ,\] are connected in parallel. The value of equivalent resistance is
A)
less than \[1.2\,\Omega \]
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B)
greater than \[1.2\,\Omega \]
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C)
between \[1.2\,\Omega \] and \[2\,\Omega \]
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D)
between \[2\,\Omega \] and \[3\,\Omega \]
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question_answer 23) The magnetic field is absent in which one of the following physical situation?
A)
Surface of neutron star
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B)
Surface of the earth
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C)
Human nerve fiber
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D)
At some point on the axis of bar magnet
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question_answer 24) What amount of energy is associated with mass of\[2.5\text{ }kg\]?
A)
\[6.27\times {{10}^{17}}\,\,J\]
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B)
\[4.27\times {{10}^{17}}J\]
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C)
\[0.27\times {{10}^{17}}\,J\]
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D)
\[2.27\times {{10}^{17}}\,J\]
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question_answer 25) The ratio of radii of nuclei of two atoms of element of atomic mass numbers 27 and 64 is
A)
\[3:4\]
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B)
\[4:3\]
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C)
\[9:16\]
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D)
\[16:9\]
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question_answer 26) MSI integrated chip contains
A)
less than 10 gates
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B)
10 to 100 gates
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C)
100 to 1000 gates
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D)
1000 to 10000 gates
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question_answer 27) What is the torque of a force \[3\hat{i}+7\hat{j}+4\hat{k}\] about the origin, if the force acts on a particle whose position vector is \[2\hat{i}+2\hat{j}+1\hat{k}\]?
A)
\[\hat{i}-5\hat{j}+8\hat{k}\]
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B)
\[2\hat{i}+2\hat{j}+2\hat{k}\]
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C)
\[\hat{i}+\hat{j}+\hat{k}\]
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D)
\[3\hat{i}+2\hat{j}+3\hat{k}\]
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question_answer 28) A message signal of frequency \[20\text{ }kHz\] and peak voltage of \[15\text{ }V\]is used to modulate a carrier wave of \[1000\text{ }kHz\]and peak voltage of\[30\text{ }V\]. The modulation index and upper side band are respectively
A)
\[0.50\]and \[1020\text{ }kHz\]
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B)
\[0.66\]and \[1020\text{ }kHz\]
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C)
\[0.50\]and \[980\text{ }kHz\]
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D)
\[0.66\]and \[980\text{ }kHz\]
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question_answer 29) Calculate, the efficiency of the engine, if Carnot cycle operates at \[{{T}_{1}}=550\,K\] and \[{{T}_{2}}=320\,K\] producing \[2.3\text{ }kJ\]of mechanical work per cycle?
A)
\[0.418\]
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B)
\[0.622\]
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C)
\[0.823\]
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D)
\[0.902\]
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question_answer 30) Which of the following device is the application of photoelectric effect?
A)
Light emitting diode
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B)
Diode
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C)
Photocell
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D)
Transistor
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question_answer 31) The waves used for Line-of-Sight (LOS) communication are
A)
ground waves
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B)
space waves
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C)
sound waves
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D)
sky waves
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question_answer 32) The inductance L of a solenoid depends upon its radius R as
A)
\[L\propto R\]
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B)
\[L\propto 1/R\]
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C)
\[L\propto {{R}^{2}}\]
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D)
\[L\propto {{R}^{3}}\]
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question_answer 33) How much revolution does the engine make during the time when a motor wheel with angular speed is increased from \[720\text{ }rpm\]to \[2820\text{ }rpm\]in \[1,4\,s\]?
A)
\[354\]
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B)
\[490\]
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C)
\[413\]
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D)
\[620\]
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question_answer 34) If the pressure at half of the lake is equal to 1/3 pressure at the bottom of the lake, what is the depth of the lake? (Assume \[g=10\text{ }m/{{s}^{2}}\]and \[1\text{ }atm=1\times {{10}^{5}};\] \[\rho \]p water\[={{10}^{3}}\])
A)
\[9.6\text{ }m\]
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B)
\[7.5\text{ }m\]
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C)
\[4.4\text{ }m\]
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D)
\[3.2\text{ }m\]
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E)
Not Available
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question_answer 35) The value of Rydberg constant is
A)
\[1.997\times {{10}^{7}}\text{ }{{m}^{-1}}\]
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B)
\[1.097\times {{10}^{-7}}\text{ }m\]
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C)
\[1.097\times {{10}^{7}}{{m}^{-1}}\]
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D)
\[19.97\times {{10}^{7}}\,{{m}^{-1}}\]
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question_answer 36) A car moving on a straight road covers \[1/3\] of the distance with \[25\text{ }km/h\] and rest with'\[75\text{ }km/h\]. The average speed is
A)
\[25\text{ }km/h\]
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B)
45 km/h
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C)
\[55\text{ }km/h\]
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D)
\[~75\text{ }km/h\]
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question_answer 37) The distance at which average radius of the earth orbit subtends an angle of \[1\text{ }arc\]second is
A)
parsec
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B)
astronomical unit
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C)
light year
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D)
unified atomic unit
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question_answer 38) What happens to the acceleration due to gravity with the increase in altitude from the surface of the earth?
A)
Increase
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B)
Decrease
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C)
First decrease and then increase
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D)
Remains same
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question_answer 39) Lenz's law is a consequence of the law of conservation of.
A)
charge
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B)
mass
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C)
momentum
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D)
energy
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question_answer 40) The angle between the true geographic north and the north shown by a compass needle is called as
A)
inclination
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B)
magnetic declination
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C)
angle of meridian
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D)
magnetic pole
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question_answer 41) An air bubble of \[2\text{ }c{{m}^{3}}\]rises from the bottom of a lake of \[32\text{ }m\]at a temperature of \[{{9}^{o}}C\]. When the bubble reaches the surface of the lake from the bottom of the lake, what volume does it grows for which temperature is \[{{30}^{o}}C\](assume \[g=10m/{{s}^{2}}\]and density\[\rho ={{10}^{3}}\text{ }kg/{{m}^{3}}\])
A)
\[5.937\text{ }c{{m}^{3}}\]
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B)
\[8.937\text{ }c{{m}^{3}}\]
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C)
\[~12.937\,\,c{{m}^{3}}\]
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D)
\[16.937\,\,c{{m}^{3}}\]
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question_answer 42) Which quantity is transmitted with propagation of longitudinal waves through a medium?
A)
Dispersion
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B)
Energy
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C)
Matter
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D)
Frequency
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question_answer 43) A monochromatic light of frequency \[3\times {{10}^{14}}\,\,Hz\] is produced by a Laser, emits the power of \[3\times {{10}^{-3}}W\]. Find, how many number of photons are emitted per second
A)
\[1.5\times {{10}^{16}}\]
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B)
\[2.5\times {{10}^{16}}\]
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C)
\[4.5\times {{10}^{16}}\]
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D)
\[8.5\times {{10}^{16}}\]
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question_answer 44) A mountaineer standing on the edge of a cliff \[441\,\,m\]above the ground throws a stone horizontally with an initial speed of \[20\text{ }m/s\]. What is the speed with which the stone reaches the ground?
A)
\[90\text{ }m/s\]
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B)
\[95.08\text{ }m/s\]
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C)
\[85\text{ }m/s\]
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D)
\[92\text{ }m/s\]
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question_answer 45) A zener diode is used as
A)
an amplifier
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B)
a rectifier
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C)
a voltage regulator
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D)
a light emitting device
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question_answer 46) In which of the following does the intensity of sound vary with time?
A)
Doppler effect
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B)
Beats
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C)
Transverse waves
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D)
Longitudinal waves
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question_answer 47) A solid cylindrical of mass \[30\text{ }kg\]rotates about its axis with an angular speed of \[50\text{ }rad/s\]. What is the KE associated with the rotation of the cylinder,(if the radius of the cylinder is\[0.30\,\,m\]?
A)
\[1500.5\text{ }J\]
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B)
\[1687.5\text{ }J\]
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C)
\[2000.7\text{ }J~\]
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D)
\[1350.0\text{ }J\]
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question_answer 48) The circuits that make rippled AC to pure DC are known as
A)
DC converters
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B)
junction diodes
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C)
bipolar transistors
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D)
filters
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question_answer 49) A string of mass \[3\text{ }kg\]is under tension of\[400\text{ }N\] The length of the stretched string is \[25\text{ }cm\]. If the transverse jerk is stuck at one end of the string' how long does the disturbance take to reach the other end?
A)
\[0.047\,\,s\]
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B)
\[0.055\,\,s\]
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C)
\[0.034\text{ }s\]
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D)
\[0.065\text{ }s\]
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question_answer 50) The total energy of an electron in 4th orbit of hydrogen atom is
A)
\[-13.6\,\,eV\]
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B)
\[-3.4\,\,eV\]
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C)
\[-1.51\,\,eV\]
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D)
\[-0.85\,\,eV\]
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question_answer 51) The graph between voltage and current across a conductor that follows Ohm's law is
A)
straight line
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B)
parabolic
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C)
sine-curve
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D)
cos-curve
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question_answer 52) An athlete throws the shot-put of mass \[4\text{ }kg\]with initial speed of \[2.2\text{ }m{{s}^{-1}}\] at \[{{41}^{o}}\] from a height of \[1.3\text{ }m\]from the ground. What is the KE of the shot-put when it reaches the ground? (Ignoring the air resistance and gravity \[g=9.8m/{{s}^{2}}\])
A)
\[42.84\text{ }J\]
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B)
\[52.84\text{ }J\]
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C)
\[62.84\text{ }J\]
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D)
\[72.84\text{ }J\]
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question_answer 53) Two bulbs operating on standard voltage \[110V\] have resistances in the ratio\[9:16\]. The ratio of brightness of light from them is
A)
\[9:16\]
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B)
\[16:9\]
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C)
\[3:4\]
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D)
\[4:3\]
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question_answer 54) The neutral point on potentiometer's scale for two cells of EMF \[2.1\] and E volts is observed at distances \[40\text{ }cm\]and \[56\text{ }cm\]respectively. The value of E is
A)
\[2.10\,\,V\]
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B)
\[2.94\,\,V\]
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C)
\[1.50\,\,V\]
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D)
\[~1.20\,\,V\]
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question_answer 55) Which one of the following equation is Torricelli law?
A)
\[P=\rho gh\]
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B)
\[v=\sqrt{2hg}\]
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C)
\[\eta {{R}_{e}}=\rho vd\]
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D)
\[S\,(2dI)=Fd\]
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question_answer 56) Which of the law representing Maxwell's third equation?
A)
Gauss's law for electricity
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B)
Ampere-Maxwell law
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C)
Gauss's law of magnetism
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D)
Faraday's law
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question_answer 57) A silver wire has a resistance of \[1.6\text{ }\Omega \]. At \[{{25.5}^{o}}C,\] and a resistance of \[2.5\text{ }\Omega \]. at \[{{100}^{o}}C,\] then temperature coefficient of resistivity of silver is
A)
\[5.55\times {{10}^{-3}}\,{{\,}^{o}}C\]
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B)
\[7.55\times {{10}^{-3}}\,{{\,}^{o}}C\]
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C)
\[11.75\times {{10}^{-2}}\,{{\,}^{o}}C\]
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D)
\[15.5\times {{10}^{-3}}\,{{\,}^{o}}C\]
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question_answer 58) When a particle returns to its initial point, its
A)
displacement is zero
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B)
average velocity is zero
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C)
distance is zero
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D)
average speed is zero
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question_answer 59) A body weight \[45\text{ }N\]on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half of the radius of the earth?
A)
\[20\,\,N\]
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B)
\[45\,\,N\]
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C)
\[40\text{ }N\]
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D)
\[90\text{ }N\]
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question_answer 60) The angle of a prism is \[{{42}^{o}}\] and refractive index of its material is\[3/2\]. Then, angle of minimum deviation for this prism is
A)
\[{{63}^{o}}\]
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B)
\[{{42}^{o}}\]
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C)
\[{{28}^{o}}\]
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D)
\[{{21}^{o}}\]
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question_answer 61) A conducting sphere of radius \[5\text{ }cm\]has an unknown charge. The electric field at \[10\text{ }cm\] from the centre of the sphere is \[1.8\times {{10}^{3}}\text{ }N/C\] and points radially inward. What is the net charge on the sphere?
A)
\[1.8\,\,nC\]
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B)
\[2\,\,nC\]
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C)
\[1\,\,nC\]
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D)
\[1.5\,\,nC\]
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question_answer 62) For transistors the value of \[\beta \] is 50 then, the value of a is
A)
\[50/51\]
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B)
\[49/50\]
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C)
\[51/50\]
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D)
\[50/49\]
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question_answer 63) An infinite line charge produces a field of \[18\times {{10}^{5}}\text{ }N/C\]at a distance of \[4\text{ }cm\]. What is the linear charge density?
A)
\[18\,\mu \,C/m\]
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B)
\[5\,\mu \,C/m\]
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C)
\[4\,\mu \,C/m\]
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D)
\[10\,\mu \,C/m\]
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question_answer 64) What is the fraction of molecular volume to the actual volume occupied by oxygen gas at STP? Given, the diameter of oxygen molecule is \[2\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\].
A)
\[1.75\times {{10}^{-4}}\]
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B)
\[1.5\times {{10}^{-4}}\]
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C)
\[12\times {{10}^{-4}}\]
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D)
\[1.125\times {{10}^{-4}}\]
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question_answer 65) A \[400\text{ }pF\]capacitor is charged by a' \[100\text{ }V\] supply. How much electrostatic energy is lost in the process of disconnecting from the supply and connecting another uncharged \[400\text{ }pF\] capacitor?
A)
\[{{10}^{-5}}\,\,J\]
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B)
\[{{10}^{-6}}\,\,J\]
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C)
\[{{10}^{-7}}\,\,J\]
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D)
\[{{10}^{-4}}\,\,J\]
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question_answer 66) The ratio of magnitude of electric displacement and electric field (E) is
A)
charge density
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B)
permittivity
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C)
electric susceptibility
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D)
dielectric constant
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question_answer 67) An object is gently placed on a long converges belt moving with \[11\text{ }m{{s}^{-1}}\]. If the coefficient of friction is \[0.4,\] then the block will slide in the belt up to a distance of
A)
\[10.21\,\,m\]
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B)
\[15.43\,\,m\]
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C)
\[20.3\text{ }m\]
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D)
\[25.6\text{ }m\]
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question_answer 68) A spring balance has a scale that reads from \[0\]to\[60\text{ }kg\]. The length of the scale is \[30\text{ }cm\]. A body suspended from this balance and when displaced and released, oscillates with a period of \[0.8\text{ }s,\] what is the weight of the body when oscillating?
A)
\[350.67\text{ }N\]
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B)
\[540.\text{ }11\text{ }N\]
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C)
\[311.24\,\,N\]
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D)
\[300.5\text{ }N\]
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question_answer 69) The magnetic needle has magnetic moment \[8.7\times {{10}^{-2}}\text{ }A-{{m}^{2}}\]and moment of inertia\[11.5\times {{10}^{-6}}\text{ }kg-{{m}^{2}}\]. It performs 10 complete oscillations in \[6.70\text{ }s,\] what is the magnitude of the magnetic field?
A)
\[0.012\text{ }T\]
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B)
\[0.120\text{ }T\]
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C)
\[1.200\,\,T\]
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D)
\[2.10\,\,T\]
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question_answer 70) The distance for which ray optics is good approximation for an aperture \[5\,\,mm\]and wavelength \[5000\overset{\text{o}}{\mathop{\text{A}}}\,\]is
A)
\[18\,m\]
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B)
\[30\,\,m\]
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C)
\[38\,\,m\]
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D)
\[50\,\,m\]
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question_answer 71) A compound microscope has a magnification of\[30\]. The focal length of the eye-piece is \[5\text{ }cm\] If the final image is formed at the least distance of distinct vision \[(25\,\,cm)\] the magnification produced by the objective is
A)
\[10\]
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B)
\[7.5\]
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C)
\[5\]
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D)
\[15\]
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question_answer 72) Which of the following relation is called mirror equation?
A)
\[u/v+f/u=1f\]
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B)
\[1/v+1/u=1f\]
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C)
\[1/f+u=1/v\]
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D)
\[uf+vf=uv\]
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question_answer 73) A stone of mass \[0.05\text{ }kg\] is thrown vertically upwards. What is the direction and magnitude of the net force on the stone during its upward motion?
A)
\[0.49\text{ }N\]vertically downward direction
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B)
\[0.49\text{ }N\] vertically upwards direction
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C)
\[0.05\text{ }N\]vertically downwards direction
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D)
\[9.8\text{ }N\]vertically upwards direction
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question_answer 74) Two different coils have self-inductance \[{{L}_{1}}=8\,\,mH,\]\[{{L}_{2}}=2\,\,mH,\] The current in one coil is increased at a constant rate. The current in the second coil is also increased at the same rate. At a certain instant of time, the power given to the two coils is the same. At that time the current, the induced voltage and the energy stored in the first coil are \[{{i}_{1}},\,\,{{V}_{1}}\] and \[{{W}_{1}}\] respectively. Corresponding values for the second coil at the same instant are \[{{i}_{2}},\,{{V}_{2}}\] and \[{{W}_{2}}\] respectively. Then,
A)
\[{{W}_{2}}/{{W}_{1}}=8\]
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B)
\[{{W}_{2}}/{{W}_{1}}=1/8\]
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C)
\[{{W}_{2}}/{{W}_{1}}=4\]
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D)
\[{{W}_{2}}/{{W}_{1}}=1/4\]
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question_answer 75) A concave mirror of focal length 'f produces a real image n times the size of the object. The distance of the object from the mirror is
A)
\[(n-1)f\]
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B)
\[(n+1)f\]
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C)
\[(n+1)f/n\]
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D)
\[(n-1)f/n\]
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question_answer 76) Which of the following mentioned is a type of hydrocarbon?
A)
Saturated hydrocarbons
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B)
Unsaturated hydrocarbons
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C)
Aromatic hydrocarbons
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D)
All of the above
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question_answer 77) The process of formation of polymers from respective monomers is called
A)
polyacrylonitrile
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B)
copolymerisation
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C)
polymerization
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D)
None of the above
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question_answer 78) Energy of one mole of photons of radiation whose frequency is \[5\times {{10}^{14}}\,Hz\]is
A)
\[199.51\text{ }kJ\text{ }mo{{l}^{-1}}\]
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B)
\[~189.51\text{ }kJ\,mo{{l}^{-1}}\]
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C)
\[198.51\,kJ\,mo{{l}^{-1}}\]
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D)
\[188.51\,kJ\,mo{{l}^{-1}}\]
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question_answer 79) The total number of orbitals associated with the principal quantum number \[n=3\]is
A)
9
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B)
8
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C)
5
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D)
7
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question_answer 80) Mass number of an atom is the sum of
A)
number of protons + number of neutrons + number of electrons
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B)
number of protons + number of neutrons
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C)
number of protons + number of electrons
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D)
number of electrons + number of neutrons
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question_answer 81) Which of the following is used in the manufacture of alloys?
A)
Lithium
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B)
Hatides
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C)
Plaster of Paris
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D)
Beryllium
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question_answer 82) Williamson's synthesis is used to prepare
A)
acetone
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B)
PVC
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C)
ethers
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D)
bakelite
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question_answer 83) Which acid is present in vinegar?
A)
Formic acid
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B)
Acetic acid
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C)
Butyric acid
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D)
Tartaric acid
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question_answer 84) What is the percentage of free space in body centered cubic unit cell?
A)
32%
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B)
20%
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C)
34%
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D)
28%
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question_answer 85) In the formation of\[\pi -\]bond, the atomic orbitals overlap in such a way that
A)
their axes remain parallel to each other and perpendicular to the internuclear axis
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B)
their axes remain parallel to each other and parallel to the internuclear axis
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C)
their axes remain perpendicular to each other and parallel to the internuclear axis
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D)
their axes remain perpendicular to each other and perpendicular to the internuclear axis
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question_answer 86) What elements are present in\[f-\]block series?
A)
Lanthanoids
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B)
Actinoids
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C)
Lanthanoids and actinoids
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D)
Lipids
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question_answer 87) What colour is imparted into the flame when lithium is burnt?
A)
Golden yellow
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B)
Brick red
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C)
Crimson red
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D)
Grassy green
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question_answer 88) Which among the following is a non-colligative property?
A)
Elevation in boiling point
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B)
Osmotic pressure
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C)
Refractive index
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D)
Lowering of vapour pressure
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question_answer 89) Ethylene can be converted into alcohol by treatment of
A)
\[Aq.\text{ }KOH\]
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B)
\[{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]as catalyst
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C)
Moist silver oxide
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D)
\[~Zn/HCl\]
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question_answer 90) Negatively charged particles are called
A)
electrons
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B)
protons
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C)
neutrons
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D)
None of these
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question_answer 91) Atoms with identical atomic number but different atomic mass number are known as
A)
polymers
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B)
isobars
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C)
isotopes
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D)
isomers
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question_answer 92) The colour of transition metal compound is due to
A)
complete ns subshell
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B)
small size metal ions
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C)
incomplete \[(n-1)\,d\]subshell
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D)
absorption of light in UV region
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question_answer 93) The mixture of reactants and products in the equilibrium state is called?
A)
Chemical mixture
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B)
Equilibrium mixture
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C)
Chemical equilibrium
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D)
Dynamic equilibrium
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question_answer 94) Among the following molecule which has the zero dipole moment?
A)
\[B{{F}_{3}}\]
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B)
\[{{H}_{2}}O\]
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C)
\[N{{F}_{3}}\]
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D)
\[Cl{{O}_{2}}\]
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question_answer 95) Who has synthesised the organic compound 'urea' for the first time?
A)
Friedrich Wohler
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B)
Berzelius
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C)
Kolbe
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D)
Berthelot
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question_answer 96) How much is the pH of human blood?
A)
5.2
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B)
8.3
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C)
6.3
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D)
7.4
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question_answer 97) A reagent which lowers the oxidation number of an element in a given substance in known as
A)
oxidising agent
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B)
reduction
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C)
reducing agent
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D)
oxidation
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question_answer 98) Sodium carbonate is manufactured by
A)
Castner-Kellner
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B)
Solvay process
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C)
oxidation
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D)
transmission process
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question_answer 99) EDTA can form complex with how many number of donor atoms?
A)
One
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B)
Two
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C)
Six
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D)
Three
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question_answer 100) Henry's law constant value for\[{{O}_{2}}\] in water is
A)
46.82
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B)
43.86
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C)
88.84
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D)
76.48
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question_answer 101) Polycondensation products of dicarboxylic acids and diols are
A)
polyamides
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B)
neoprene
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C)
glyptal
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D)
polyesters
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question_answer 102) The attractive force which holds various constituents together in different chemical species is called
A)
valence bond
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B)
chemical bond
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C)
atomic bond
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D)
electrovalent bond
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question_answer 103) What are lanthanides and actinides?
A)
Inner transition element
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B)
Noble gas
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C)
Normal element
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D)
Transition element
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question_answer 104) Compounds having the same molecular formula but different structures are classified as
A)
functional group isomers
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B)
structural isomers
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C)
optical isomerism
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D)
Metamerism
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question_answer 105) Gas constant is equal to the
A)
product of two specific heat
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B)
difference of two specific heat
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C)
ratio of two specific heat
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D)
sum of two specific heat
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question_answer 106) The colour in the coordination compounds can be readily explained in terms of
A)
spectrochemistry
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B)
chelate effect
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C)
crystal field theory
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D)
None of the above
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question_answer 107) Paramagnetism is exhibited due to which one of the following reason?
A)
Presence of unpaired electrons
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B)
Presence of completely filled electronic subshell
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C)
By non-transition element
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D)
By elements with noble gas configuration
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question_answer 108) Which one of the following acid does not have a carboxylic group?
A)
Methanoic acid
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B)
Ethanoic acid
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C)
Propanoic acid
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D)
Picric acid
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question_answer 109) How will you define the specific heat at constant volume?
A)
The amount of heat required to raise the temperature of unit mass of gas through one degree at constant pressure
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B)
The amount of heat required to raise the temperature of 1 kg of water through one degree
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C)
The amount of heat required to raise the temperature of unit mass of gas through one degree at constant volume
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D)
All of the above
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question_answer 110) The chief commercial use of amines as intermediates in the synthesis of
A)
medicines
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B)
fibers
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C)
medicines and fibers
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D)
proteins
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question_answer 111) Silver, gold, platinum, iron, copper and titanium are part of the
A)
minerals
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B)
transition metals
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C)
salts
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D)
All of these
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question_answer 112) Wood spirit is known as
A)
Ethanol
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B)
Methanol
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C)
Propanol
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D)
None of these
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question_answer 113) What is the value of 1/n in Freundlich adsorption isotherm2
A)
Between 2 and 4 in all cases
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B)
Between 0 and 1 in all cases
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C)
1 in case of chemisorptions
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D)
1 in case of physical adsorption
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question_answer 114) What is the product of reaction between calcium carbide and water?
A)
Ethylene
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B)
Acetylene
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C)
Methane
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D)
Benzene
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question_answer 115) The crystal lattice of electrovalent compound is composed of
A)
oppositely charged ions
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B)
both molecules and ions
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C)
molecules
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D)
atoms
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question_answer 116) Anti-Markownikoff addition of HBr is observed in
A)
propene
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B)
but-2-ene
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C)
pent-2-ene
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D)
All of these
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question_answer 117) What kind of isomerism is exhibited by the compounds\[C{{H}_{3}}C{{H}_{2}}CHO\]and \[C{{H}_{3}}COC{{H}_{3}}?\]
A)
Geometrical isomerism
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B)
Functional isomers
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C)
Tautomers
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D)
Metamers
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question_answer 118) Mass of a proton is
A)
0.00727 amu
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B)
1.0087 amu
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C)
0.00054 amu
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D)
1.00727 amu
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question_answer 119) The concentration of hydrogen ion in a sample of soft drink is \[3.8\times {{10}^{-3}}M.\] What is its pH?
A)
\[3.84\]
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B)
\[2.42\]
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C)
\[4.44\]
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D)
\[1.42\]
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question_answer 120) Which factor has no influence on the rate of reaction?
A)
Molecularity
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B)
Temperature
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C)
Concentration of reactant
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D)
Nature of reactant
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question_answer 121) What kinds of bonds are present in ethene molecule?
A)
1 pi and 5 sigma bonds
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B)
1 pi and 3 sigma bonds
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C)
1 sigma and 1 pi bonds
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D)
3 sigma and 3 pi bonds
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question_answer 122) r. The smallest quantity of energy that can be emitted or absorbed in the form of electromagnetic radiation is known as
A)
quantum
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B)
photon
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C)
spectrum
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D)
photoelectron
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question_answer 123) Food preservatives prevent spoilage of food due to microbial growth. The most commonly used preservatives are
A)
table salt, sugar
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B)
vegetable oils and sodium benzoate
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C)
\[{{C}_{6}}{{H}_{5}}COONa\]
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D)
All of the above
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question_answer 124) Based on which method amines are prepared?
A)
Reduction of nitro compounds
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B)
Ammonolysis of alkyl halides
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C)
Reduction of nitrites and amides
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D)
All of the above
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question_answer 125) All substances that conduct electricity in aqueous solutions are called?
A)
Electrolytes
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B)
Acids
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C)
Buffers
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D)
Catalyst
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question_answer 126) In which year, IUPAC draft recommends that anionic ligands will end with-ido so that chloro would become chloride
A)
1994
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B)
1984
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C)
2000
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D)
2004
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question_answer 127) Use of chemicals for therapeutic effect is called
A)
medicines
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B)
chemotherapy
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C)
drug-target interaction
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D)
phototherapy
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question_answer 128) What is the type of hybridisation found in methane?
A)
\[s{{p}^{3}}\]
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B)
\[s{{p}^{2}}\]
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C)
\[sp\]
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D)
None of these
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question_answer 129) Addition of oxygen to an element or a compound is termed as
A)
oxidation
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B)
reduction
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C)
ionisation
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D)
redox reaction
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question_answer 130) Molality of 2.5 g of ethanoic acid \[(C{{H}_{3}}COOH)\] in 75 g of benzene is
A)
\[~0.565\text{ }mol\text{ }k{{g}^{-1}}\]
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B)
\[~0.656\text{ }mol\text{ }k{{g}^{-1}}\]
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C)
\[~0.556\text{ }mol\text{ }k{{g}^{-1}}\]
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D)
\[0.665\text{ }mol\text{ }k{{g}^{-1}}\]
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question_answer 131) It has been found that for a chemical reaction with rise in temperature by\[{{10}^{o}},\]the rate constant is
A)
nearly doubled
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B)
nearly tripled
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C)
increases 5 times
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D)
increases 4 times
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question_answer 132) Carbonyl compounds are constituents of
A)
fabrics, drugs
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B)
fabrics, plastics
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C)
flavourings, plastics
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D)
All of these
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question_answer 133) What is IUPAC name of \[iso-\]propylamine?
A)
Propan-2-amine
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B)
Ethanamine
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C)
2-aminotoluene
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D)
Propan-1 -amine
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question_answer 134) lonization energy and electron affinity are defined at
A)
enthalpy
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B)
spontaneity
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C)
equilibrium
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D)
absolute zero
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question_answer 135) When acetaldehyde is heated with dilute sodium hydroxide solution, the product is
A)
ethanol and sodium acetate
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B)
paraldehyde
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C)
aldol
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D)
brown resin
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question_answer 136) Monovalent sodium and potassium ions, divalent magnesium and calcium ions are found in
A)
lipids
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B)
biological fluids
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C)
fats
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D)
enzymes
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question_answer 137) The removal of an electron from an atom results in the formation of
A)
anion
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B)
anode
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C)
cation
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D)
cathode
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question_answer 138) Which compound is responsible for perfumery?
A)
Ketones
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B)
Ethers
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C)
Alcohols
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D)
Esters
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question_answer 139) Which is the metal present in the coordination compound chlorophyll?
A)
Ca
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B)
Mg
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C)
K
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D)
Na
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question_answer 140) 45 g of ethylene glycol \[({{C}_{2}}{{H}_{6}}{{O}_{2}})\] is mixed with 600 g of water, what is the depression of freezing point?
A)
7.9 K
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B)
2.5 K
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C)
6.6 K
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D)
2.2 K
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question_answer 141) In \[\text{B}{{\text{r}}_{\text{3}}}{{\text{O}}_{\text{8}}}\]compound, oxidation number of bromine is
A)
16/13
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B)
26/3
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C)
24/3
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D)
16/3
done
clear
View Answer play_arrow
question_answer 142) How many octahedral void(s) are present per atom in a cubic close - packed structure?
A)
3
done
clear
B)
4
done
clear
C)
1
done
clear
D)
2
done
clear
View Answer play_arrow
question_answer 143) Lithium shows diagonal relationship with
A)
sodium
done
clear
B)
magnesium
done
clear
C)
calcium
done
clear
D)
aluminium
done
clear
View Answer play_arrow
question_answer 144) Why d-block element form complexes?
A)
Due to large size and high nuclear charge
done
clear
B)
Due to small size and low nuclear charge
done
clear
C)
Due to small size and high nuclear charge
done
clear
D)
None of the above
done
clear
View Answer play_arrow
question_answer 145) What is conductance?
A)
Inverse of resistance
done
clear
B)
Proportional of resistance
done
clear
C)
Equal of resistivity
done
clear
D)
Equal of resistance
done
clear
View Answer play_arrow
question_answer 146) Which is the correct statement about solid?
A)
Very high compressibility
done
clear
B)
Maximum intermolecular distance
done
clear
C)
Definite mass but no definite volume
done
clear
D)
Maximum intermolecular force of attraction
done
clear
View Answer play_arrow
question_answer 147) The enthalpy change accompanying a reaction is called
A)
reaction enthalpy
done
clear
B)
standard enthalpy
done
clear
C)
thermochemical equation
done
clear
D)
enthalpy of atomization
done
clear
View Answer play_arrow
question_answer 148) According to IUPAC system, what is the correct name of the compound\[[Cr{{(N{{H}_{3}})}_{3}}{{({{H}_{2}}O)}_{3}}]C{{l}_{3}}\]
A)
triamminetriaquachromium \[(III)\] chloride
done
clear
B)
triamminetriaquachromiumchloride \[(III)\]
done
clear
C)
tetraammoniumtriaquachromium \[(III)\] chloride
done
clear
D)
None of the above
done
clear
View Answer play_arrow
question_answer 149) The relative ease of dehydration of alcohols follows following order
A)
tertiary > secondary > primary
done
clear
B)
primary > secondary > tertiary
done
clear
C)
secondary > tertiary > primary
done
clear
D)
tertiary > primary > secondary
done
clear
View Answer play_arrow
question_answer 150) What is the unit of zero order reaction?
A)
\[mol\,L\,{{s}^{-1}}\]
done
clear
B)
\[{{S}^{-1}}\]
done
clear
C)
\[L\,mo{{l}^{-1}}{{s}^{-1}}\]
done
clear
D)
None of the above
done
clear
View Answer play_arrow
question_answer 151) Find the value of \[\cos \,\,(29\pi /3)?\]
A)
\[1\]
done
clear
B)
\[0\]
done
clear
C)
\[\frac{\sqrt{3}}{2}\]
done
clear
D)
\[1/2\]
done
clear
View Answer play_arrow
question_answer 152) Find the derivative of \[\sqrt{2}x+2\sqrt{x}-\frac{1}{x}\]?
A)
\[\sqrt{2}+1/\sqrt{x}(1-1/2x)\]
done
clear
B)
\[\sqrt{2}-1/\sqrt{x}(1+1/2x)\]
done
clear
C)
\[\sqrt{2}-1/\sqrt{x}(1-1/2x)\]
done
clear
D)
\[\sqrt{2}+1/\sqrt{x}(1+1/2x)\]
done
clear
View Answer play_arrow
question_answer 153) Solve \[\frac{dy}{dx}+\frac{y}{x}={{x}^{3}}\]
A)
\[y=\frac{{{x}^{4}}}{5}+Cx\]
done
clear
B)
\[y=\frac{{{x}^{3}}}{3}+Cx\]
done
clear
C)
\[y=\frac{{{x}^{3}}}{3}+C\]
done
clear
D)
\[y=\frac{{{x}^{4}}}{4}+x\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
question_answer 154) Given two vectors are \[\hat{i}-\hat{j}\] and \[\hat{i}+2\hat{j},\] the unit vector is coplanar with the two vectors and perpendicular to the first. Find the vector?
A)
\[+\frac{1}{\sqrt{2}}\,(i+k)\]
done
clear
B)
\[+\frac{1}{\sqrt{5}}\,(2i+j)\]
done
clear
C)
\[+\frac{1}{\sqrt{2}}\,(i+j)\]
done
clear
D)
\[+\frac{1}{\sqrt{2}}\,(2i+3j)\]
done
clear
View Answer play_arrow
question_answer 155) Solve the linear programming problem: max \[Z=x+2y\]subject to constraints: \[x-y\le 10,\]\[2x+3y\le 20.\],
A)
\[max\text{ }Z=10~\]
done
clear
B)
\[max\text{ }Z=30\]
done
clear
C)
\[max\text{ }2=40\]
done
clear
D)
\[max\text{ }Z=50\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
question_answer 156) Find the intersection of the spheres \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+7x-2y-z=13\] and \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-3x+3y+4z=8\]
A)
\[x-y-z=1\]
done
clear
B)
\[x-2y-z=1\]
done
clear
C)
\[x-y-2z=1\]
done
clear
D)
\[2x-y-z=1\]
done
clear
View Answer play_arrow
question_answer 157) Convert \[(i+1)/(\cos \,\pi /4)-i\,\sin (\pi /4)\] in polar form?
A)
\[\cos \,(\pi /4)+i\,sin\,(\pi /4)\]
done
clear
B)
\[\cos \,(\pi /2)+i\,\sin \,(\pi /2)\]
done
clear
C)
\[\sqrt{2}\,(\cos \,(\pi /4)+i\,\sin (\pi /4))\]
done
clear
D)
\[\sqrt{2}\,(\cos \,(\pi /2)\,+\,i\,\sin (\pi /2))\]
done
clear
View Answer play_arrow
question_answer 158) Solve \[{{\sin }^{-1}}\,2x+{{\cos }^{-1}}\,2x+2\,{{\tan }^{-1}}\,x=\pi \]
A)
\[1\]
done
clear
B)
\[0\]
done
clear
C)
\[-1\]
done
clear
D)
\[1/\sqrt{2}\]
done
clear
View Answer play_arrow
question_answer 159) For what values of x, the numbers \[-1,\,x,-3/4\] are in GP?
A)
\[3/2\]
done
clear
B)
\[\sqrt{3}/4\]
done
clear
C)
\[\sqrt{3}/2\]
done
clear
D)
\[3/\sqrt{2}\]
done
clear
View Answer play_arrow
question_answer 160) \[{{(1+i)}^{3}}+{{(1-i)}^{3}}\]
A)
\[1\]
done
clear
B)
\[-2\]
done
clear
C)
\[0\]
done
clear
D)
\[-4\]
done
clear
View Answer play_arrow
question_answer 161) Find the length of the diagonal of the parallelepiped formed by planes drawn through the points \[(2,3,5)\] and \[(5,9,7),\] parallel to the co-ordinate planes?
A)
\[\sqrt{38}\] units
done
clear
B)
\[7\]nits
done
clear
C)
\[\sqrt{155}\] units
done
clear
D)
\[13\]units
done
clear
View Answer play_arrow
question_answer 162) If \[g(x)=({{x}^{2}}+2x+3)\,f(x),\,\,f(0)=5\] and \[{{\lim }_{x\to 0}}\,\frac{f(x)-5)}{x}=4,\]then \[f'(0)\] equal to
A)
\[22\]
done
clear
B)
\[18\]
done
clear
C)
\[20\]
done
clear
D)
\[25\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
question_answer 163) Find \[\int{\frac{1}{\sqrt{7-{{x}^{2}}}}\,dx}\]
A)
\[\frac{1}{2\sqrt{7}}\,\log \,\left| \frac{\sqrt{7+x}}{\sqrt{7-x}} \right|+C\]
done
clear
B)
\[{{\sin }^{-1}}\,\left( \frac{x}{\sqrt{7}} \right)+C\]
done
clear
C)
\[\log |x+\sqrt{{{x}^{2}}-7}|+C\]
done
clear
D)
\[\frac{1}{2\sqrt{7}}\log \,\left| \frac{x-\sqrt{7}}{x+\sqrt{7}} \right|+C\]
done
clear
View Answer play_arrow
question_answer 164) Find the range of the function \[f:[0,\,1]\to R,\,\,f(x)={{x}^{3}}-{{x}^{2}}+4x+2{{\sin }^{-1}}x\]?
A)
\[[-(\pi +2),\,0]\]
done
clear
B)
\[[0,4+\pi ]\]
done
clear
C)
\[[2,3]\]
done
clear
D)
\[(0,\,2+\pi ]\]
done
clear
View Answer play_arrow
question_answer 165) Solve the inequality \[3x+2>-16,\,2x-3\le 11\]
A)
\[(-6,7)\]
done
clear
B)
\[[-6,7)\]
done
clear
C)
\[(-6,7]\]
done
clear
D)
[-6, 7]
done
clear
View Answer play_arrow
question_answer 166) Events A, B and C are mutually exclusive events such that \[P(A)=(3x+1)/3,\] \[P(B)=(x-1)/4,\] \[P(C)=(1-2x)/2,\] Find the set of possible value of x in the interval.
A)
\[[-1/3,\,\,1/2]\]
done
clear
B)
\[[1/3,\,2/3]\]
done
clear
C)
\[[1/3,\,13/3]\]
done
clear
D)
\[[0,1]\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
question_answer 167) If \[{{\cos }^{-1}}(2-{{x}^{2}})/(1+{{x}^{2}})+{{\tan }^{-1}}x=\pi /2,\], then x is equal to?
A)
\[0\]
done
clear
B)
\[1\]
done
clear
C)
\[\frac{1}{\sqrt{3}}\]
done
clear
D)
\[\sqrt{3}\]
done
clear
View Answer play_arrow
question_answer 168) There are 7 horses in a race, Mr. X selected 2 horses at random and bet on them. The probability that Mr. X selected the winning horse, is
A)
\[1/7\]
done
clear
B)
\[4/7\]
done
clear
C)
\[3/7\]
done
clear
D)
\[2/7\]
done
clear
View Answer play_arrow
question_answer 169) If \[{{x}^{y}}={{e}^{(x-y)}},\] then find \[dy/dx\]
A)
\[\log x/{{(1+\log x)}^{2}}\]
done
clear
B)
\[(\log x)\,/\,(1+\log x)\]
done
clear
C)
\[(1-\log x)\,/\,(1+\log x)\]
done
clear
D)
\[(\log x)\,/\,{{(1-\log x)}^{2}}\]
done
clear
View Answer play_arrow
question_answer 170) The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively, find the value of \[P(X=1)\].
A)
\[1/4\]
done
clear
B)
\[1/16\]
done
clear
C)
\[1/8\]
done
clear
D)
\[1/32\]
done
clear
View Answer play_arrow
question_answer 171) Find the domain of the function \[f(x)=({{x}^{2}}+1)/({{x}^{2}}-3x+3)?\]
A)
\[R-\{1,\,\,2\}\]
done
clear
B)
\[R-\{1,\,\,4\}\]
done
clear
C)
\[R\]
done
clear
D)
\[R-\{\,1\,\}\]
done
clear
View Answer play_arrow
question_answer 172) Let \[A\,\,(2,\,\,-3)\]and \[B\,\,(-2,\,\,1)\] be vertices of a triangle ABC. If the centroid of this triangle moves on the line 2x + 3y = 1, then the locus of the vertex C is the line
A)
\[3x-2y=3\]
done
clear
B)
\[2x+3y=9\]
done
clear
C)
\[2x-3y=7\]
done
clear
D)
\[3x-2y=5\]
done
clear
View Answer play_arrow
question_answer 173) Find \[^{n}{{C}_{21}}\] if \[^{n}{{C}_{10}}{{=}^{n}}{{C}_{11}}.\]
A)
\[1\]
done
clear
B)
\[0\]
done
clear
C)
\[11\]
done
clear
D)
\[10\]
done
clear
View Answer play_arrow
question_answer 174) 9th term in \[n(n-4)/({{n}^{2}}+1)\] is
A)
\[55/82\]
done
clear
B)
\[40/82\]
done
clear
C)
\[45/82\]
done
clear
D)
\[36/82\]
done
clear
View Answer play_arrow
question_answer 175) Find the area of the triangle with vertices \[(2,3),\]\[(0,\,\,1)\]and \[(1,\,\,2)\].
A)
\[{\scriptstyle{}^{1}/{}_{2}}\]sq. unit
done
clear
B)
\[1\] sq. unit
done
clear
C)
\[2\] sq. units
done
clear
D)
\[2\,\,{\scriptstyle{}^{1}/{}_{2}}\]sq. units
done
clear
E)
None of these
done
clear
View Answer play_arrow
question_answer 176) Solve the system of linear equations \[x+y=1,\]\[x-2y=4\].
A)
\[x=2,y=-5\]
done
clear
B)
\[x=1,y=2\]
done
clear
C)
\[x=2,\,y=-1\]
done
clear
D)
\[x=-1,y=2\]
done
clear
View Answer play_arrow
question_answer 177) Find \[\frac{dy}{dx},\] if \[y={{\sin }^{2}}x+{{\cos }^{4}}x\]
A)
\[\frac{-\sin \,4x}{4}\]
done
clear
B)
\[\frac{-\sin \,2x}{2}\]
done
clear
C)
\[\frac{\sin \,4x}{4}\]
done
clear
D)
\[\frac{-\sin \,4x}{2}\]
done
clear
View Answer play_arrow
question_answer 178) A manufacturer has \[500\text{ }L\]of a \[10%\]solution of acid, find the range of 40% acid to be added to it y such that the acid content in the resultant mixture will be more than \[15%\] but less than \[20%\] .
A)
More than \[250\text{ }L\]and less than \[~300\]
done
clear
B)
More than \[300\text{ }L\] and less than \[400\]
done
clear
C)
More than \[100\text{ }L\] and less than \[250\]
done
clear
D)
More than \[250\text{ }L\]and less than \[350\]
done
clear
View Answer play_arrow
question_answer 179) If the eccentricity of an ellipse with its centre at the origin is \[1/2\] and one of its directrices is\[x=4,\]then find the equation of the ellipse
A)
\[3{{x}^{2}}+4{{y}^{2}}=1\]
done
clear
B)
\[4{{x}^{2}}+3{{y}^{2}}=12\]
done
clear
C)
\[3{{x}^{2}}+4{{y}^{2}}=12\]
done
clear
D)
\[4{{x}^{2}}+3{{y}^{2}}=12\]
done
clear
View Answer play_arrow
question_answer 180) Integrate \[\frac{{{\sec }^{2}}\,({{\sin }^{-1}}x)}{\sqrt{1-{{x}^{2}}}}\]
A)
\[\sin \,({{\tan }^{-1}}x)+C\]
done
clear
B)
\[\tan \,({{\sec }^{-1}}x)+C\]
done
clear
C)
\[\tan \,({{\sin }^{-1}}x)+C\]
done
clear
D)
\[-\tan \,(co{{s}^{-1}}x)+C\]
done
clear
View Answer play_arrow
question_answer 181) A circle with centre \[(0,\,\,3)\] is passing through the foci of the ellipse \[{{x}^{2}}/16+{{y}^{2}}/9=1.\] Find the radius of the circle.
A)
\[7/2\] units
done
clear
B)
\[3\] units
done
clear
C)
\[4\] units
done
clear
D)
\[\sqrt{12}\] units
done
clear
View Answer play_arrow
question_answer 182) Which term of the series \[\sqrt{2},2/3,\,2\sqrt{2}/9,....\]is \[16/2187\]?
A)
10th term
done
clear
B)
8th term
done
clear
C)
9th term
done
clear
D)
11th term
done
clear
View Answer play_arrow
question_answer 183) Integrate \[\frac{1}{{{x}^{3}}\,({{x}^{2}}-1)}\]
A)
\[\frac{1}{3}\log \left| \frac{{{x}^{3}}}{{{x}^{3}}-1} \right|+C\]
done
clear
B)
\[\frac{1}{3}\log \left| \frac{1-{{x}^{3}}}{{{x}^{3}}} \right|+C\]
done
clear
C)
\[\log \left| \frac{{{x}^{3}}}{{{x}^{3}}-1} \right|+C\]
done
clear
D)
\[\frac{1}{3}\log \left| \frac{{{x}^{3}}-1}{{{x}^{3}}} \right|+C\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
question_answer 184) Evaluate \[\underset{x\to 3}{\mathop{\lim }}\,\frac{3-x}{\sqrt{4+x}-\sqrt{1+2x}}\]
A)
\[0\]
done
clear
B)
\[7\sqrt{2}\]
done
clear
C)
\[4\sqrt{7}\]
done
clear
D)
\[2\sqrt{7}\]
done
clear
View Answer play_arrow
question_answer 185) \[\int{{{\sec }^{3}}\,\,x\,\,dx}\]
A)
\[1/2[\sec x\tan x-\log |\sec x+\tan x|]+C\]
done
clear
B)
\[1/2[\sec x\tan x+\log |\sec x-\tan x|]+C\]
done
clear
C)
\[1/2[\sec x\tan x-\log |\sec x-\tan x|]+C\]
done
clear
D)
\[1/2[\sec x\tan x+\log |\sec x+\tan x|]+C\]
done
clear
View Answer play_arrow
question_answer 186) The sum of first three terms of a GP is 7/9 and their product is\[~-8/27\]. Find the common ratio of the series
A)
\[r=-2/3\] or \[-3/2\]
done
clear
B)
\[r=-2/3\] or \[3/2\]
done
clear
C)
\[r=2/3\] or \[-3/2\]
done
clear
D)
\[r=2/3\] or \[3/2\]
done
clear
View Answer play_arrow
question_answer 187) Differentiate \[\sin \,\,(\sin \,\,2x).\]
A)
\[2\,\cos \,2x.\,\cos \,2x\]
done
clear
B)
\[2\,\cos \,2x.\,\cos \,(\sin \,2x)\]
done
clear
C)
\[2\,\cos \,2x.\sin 2x\]
done
clear
D)
\[\cos \,2x.\cos \,(\sin 2x)\]
done
clear
View Answer play_arrow
question_answer 188) In a moderately a symmetrical distribution, the mean and median are 36 and 34 respectively, find out, the value of empirical mode.
A)
\[30\]
done
clear
B)
\[32\]
done
clear
C)
\[42\]
done
clear
D)
\[22\]
done
clear
View Answer play_arrow
question_answer 189) If \[\sin y=x\sin (a+y),\] then find \[dy/dx\].
A)
\[{{\sin }^{2}}\,(a+y)/\sin a\]
done
clear
B)
\[\sin a/{{\sin }^{2}}\,(a+y)\]
done
clear
C)
\[\sin a/{{\sin }^{2}}\,(a-y)\]
done
clear
D)
\[{{\sin }^{2}}(a-y)\sin a\]
done
clear
View Answer play_arrow
question_answer 190) Solve the inequality \[2x-5\le (4x-7)/3?\]
A)
\[x\in (-\infty ,\,4)\]
done
clear
B)
\[x\in (-\infty ,\,4]\]
done
clear
C)
\[x\in (-\infty ,\,8]\]
done
clear
D)
\[x\in (-\infty ,\,-4]\]
done
clear
View Answer play_arrow
question_answer 191) If u , v and w are three non-coplanar vectors, then \[(u+v-w).\,[(u-v)\times (v-w)]\]equals to
A)
\[u.\,\,w\times u\]
done
clear
B)
\[u.\,\,v\times w\]
done
clear
C)
\[0\]
done
clear
D)
\[3\,u.\,\,v\times w\]
done
clear
View Answer play_arrow
question_answer 192) If \[y=x{{e}^{2y}},\]then find \[dy/dx\].
A)
\[y/(x(1-2x))\]
done
clear
B)
\[x/(y\,(1-2x))\]
done
clear
C)
\[x/(y(1-2y))\]
done
clear
D)
\[y/(x(1-2y))\]
done
clear
View Answer play_arrow
question_answer 193) A line makes the same angle 6 with each of the x and z-axis. If it makes the angle \[\beta \] with y-axis such that \[{{\sin }^{2}}\beta =3\,{{\sin }^{2}}\theta ,\] then \[{{\cos }^{2}}\,\theta \] equals
A)
\[3/5\]
done
clear
B)
\[1/5\]
done
clear
C)
\[2/5\]
done
clear
D)
\[2/3\]
done
clear
View Answer play_arrow
question_answer 194) The two curves \[{{x}^{3}}-3x{{y}^{2}}+2=0\] and \[3{{x}^{2}}y-{{y}^{2}}-2=0\]
A)
touch each other
done
clear
B)
cut a an angle \[\pi /4\]
done
clear
C)
cut at an angle \[\pi /3\]
done
clear
D)
cut at an angle \[\pi /2\]
done
clear
View Answer play_arrow
question_answer 195) . Solve for \[x,\,\,{{\tan }^{-1}}(1/x)=\pi +{{\tan }^{-1}}x,\,\,0<x<1\]
A)
not defined
done
clear
B)
\[\sqrt{3}\]
done
clear
C)
\[\pm \,1\]
done
clear
D)
\[0\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
question_answer 196) Solve the equation \[{{x}^{2}}-\sqrt{3}x+1=0\]
A)
\[x=(-\sqrt{3}\,\,\pm \,\,2i)/2\]
done
clear
B)
\[x=(-\sqrt{3}\,\,\pm \,i)/2\]
done
clear
C)
\[x=(-\sqrt{3}\,\,\pm \,i)\]
done
clear
D)
\[x=(\sqrt{3}\,\,\pm \,i)/2\]
done
clear
View Answer play_arrow
question_answer 197) Differentiate \[{{x}^{-3}}\,(2+7x)\]
A)
\[\frac{-1}{{{x}^{4}}}\,(3+7x)\]
done
clear
B)
\[\frac{-2}{{{x}^{3}}}\,(2+7x)\]
done
clear
C)
\[\frac{2}{{{x}^{4}}}\,(2+7x)\]
done
clear
D)
\[\frac{-2}{{{x}^{4}}}\,(3+7x)\]
done
clear
View Answer play_arrow
question_answer 198) The probability that A speaks the truth is \[3\text{ }/5\] and probability that B speaks the truth is\[3\text{ }/4\] Find the probability that they contradict each other when; asked to speak a fact.
A)
\[3/20\]
done
clear
B)
\[4/5\]
done
clear
C)
\[9/20\]
done
clear
D)
\[7/20\]
done
clear
View Answer play_arrow
question_answer 199) Find the multiplicative-inverse of \[5-6i\]
A)
\[-(5/61)+(6/61)i\]
done
clear
B)
\[(5/61)+(6/61)i\]
done
clear
C)
\[(5/61)-(6/61)i\]
done
clear
D)
\[-(5/61)+(6/61)i\]
done
clear
View Answer play_arrow
question_answer 200) Find the sum to n terms of the series whose nth term is \[{{n}^{2}}-2\text{ }n\].
A)
\[2n\,(n-1)\]
done
clear
B)
\[2n(n+1)\]
done
clear
C)
\[2{{n}^{2}}(n+1)\]
done
clear
D)
\[2{{n}^{2}}(n-1)\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
question_answer 201) A plane which passes through the point \[(3,\,2,\,0)\]and the line \[(x-4)/1=(y-7)/5=(z-4)/4\] is
A)
\[x+y+z=1\]
done
clear
B)
\[x+2y-z=1\]
done
clear
C)
\[x-y+z=1\]
done
clear
D)
\[2x-y+z=5\]
done
clear
View Answer play_arrow
question_answer 202) Find the value of \[\sin \,(2\,{{\tan }^{-1}}x),\,|x|\le 1\]
A)
\[1/x\]
done
clear
B)
\[x\]
done
clear
C)
\[1/{{x}^{2}}\]
done
clear
D)
\[2x/(1+{{x}^{2}})\]
done
clear
View Answer play_arrow
question_answer 203) In a group of students, 40 students choose Physics, 30 students choose Chemistry and 15 students choose both. Each of the students choose either Physics or Chemistry. How many students are there in the group?
A)
\[60\]
done
clear
B)
\[70\]
done
clear
C)
\[75\]
done
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D)
\[55\]
done
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question_answer 204) Discuss the continuity of the function \[f(x)=\sin 2x-1\]at the point \[x=0,\]and\[x=\pi \].
A)
Continuous at \[x=0,\,\pi \]
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B)
Discontinuous at \[x=0\]but continuous at \[x=\pi \]
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C)
Continuous at \[x=0\] but discontinuous at \[x=\pi \]
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D)
Discontinuous at \[x=0,\,\pi \]
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question_answer 205) The value of \[2{{\cot }^{2}}\,(\pi /6)+\,4\,{{\tan }^{2}}(\pi /6)\]\[-3\,\text{cosec }\pi \text{/6}\] is
A)
\[2\]
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B)
\[4\]
done
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C)
\[4/3\]
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D)
\[3/4\]
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question_answer 206) If \[A=\left[ \begin{matrix} 2 & -1 \\ 1 & 2 \\ \end{matrix} \right],\]then \[{{A}^{2}}+2A-3I=?\]
A)
\[\left[ \begin{matrix} 4 & -6 \\ 6 & 4 \\ \end{matrix} \right]\]
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B)
\[0\]
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C)
\[\left[ \begin{matrix} -6 & 2 \\ -2 & 6 \\ \end{matrix} \right]\]
done
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D)
\[5l\]
done
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question_answer 207) The sum of first 8 terms of the geometric series \[2+6+18+54+.....\]is
A)
\[6506\]
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B)
\[5650\]
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C)
\[6650\]
done
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D)
\[6560\]
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question_answer 208) Let \[A\{1,2,3,4,5\}.\]Find the domain in the relation from A to A by \[R=\{(x,y):y=2x-1\}.\]
A)
\[\{1,2,3\}\]
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B)
\[\{1,2\}\]
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C)
\[\{1,3,5\}\]
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D)
\[\{2,4\}\]
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question_answer 209) Find \[\cos \,(x/2),\] if \[\tan \,x=5/12,\,x\] in quadrant III
A)
\[5/\sqrt{13}\]
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B)
\[5/\sqrt{26}\]
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C)
\[5/13\]
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D)
\[5/26\]
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E)
None of these
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question_answer 210) \[\int{{{\sin }^{-1}}\,\,\cos \,\,3x\,\,dx}\]is
A)
\[\frac{3\pi }{2}x-\frac{{{x}^{2}}}{2}+C\]
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B)
\[\frac{\pi }{2}x-\frac{{{x}^{2}}}{2}+C\]
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C)
\[\frac{3\pi }{2}x+\frac{{{x}^{2}}}{2}+C\]
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D)
\[\frac{\pi }{2}x+\frac{{{x}^{3}}}{3}+C\]
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E)
None of these
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question_answer 211) If a, b, c are three vectors such that \[a\text{ }\times \text{b}=c\] and\[b\text{ }\times c=a\],then
A)
\[a\ne b\ne c\]
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B)
\[a=b=c\]
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C)
\[a\ne b\text{ }\ne \text{ }c\ne 1\]
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D)
a, b, c are orthogonal in pairs
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question_answer 212) Determine n, if \[^{2n}{{C}_{2}}{{:}^{n}}{{C}_{2}}:\,\,\,\,=\,\,9:2\]
A)
\[5\]
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B)
\[4\]
done
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C)
\[3\]
done
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D)
\[2\]
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question_answer 213) \[\underset{x\to 0}{\mathop{\lim }}\,\,\,\frac{{{\sin }^{-1}}\,(x-2)}{{{x}^{2}}-4}\]is equal to
A)
\[0\]
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B)
\[2\]
done
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C)
\[1/2\]
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D)
\[1\]
done
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question_answer 214) If \[a\ne 0\]and the line \[2bx+3cy+4d=0\] passes through the points of intersection of the parabolas\[{{y}^{2}}=4ax\]and \[{{x}^{2}}=4ay,\]then
A)
\[{{d}^{2}}+{{(2b-3c)}^{2}}=0\]
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B)
\[{{d}^{2}}+{{(3b-2c)}^{2}}=0\]
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C)
\[{{d}^{2}}+{{(2b+3c)}^{2}}=0\]
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D)
\[{{d}^{2}}+{{(3b-2c)}^{2}}=0\]
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question_answer 215) If \[f(x)={{x}^{3}}-1,\] then find \[[f(3)+f(2)]/11\]
A)
\[1\]
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B)
\[2\]
done
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C)
\[3\]
done
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D)
\[4\]
done
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question_answer 216) The intercept- on the line \[y=x\]by the circle \[{{x}^{2}}+{{y}^{2}}-2x=0\]is AB. Find the equation of the circle on AB as a diameter?
A)
\[{{x}^{2}}+{{y}^{2}}+x+y=0\]
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B)
\[{{x}^{2}}+{{y}^{2}}-x-y=0\]
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C)
\[{{x}^{2}}+{{y}^{2}}+x-y=0\]
done
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D)
\[{{x}^{2}}+{{y}^{2}}-x+y=0\]
done
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question_answer 217) Compute the product \[\left[ \begin{matrix} -1 & 3 & 0 \\ 2 & 1 & 4 \\ \end{matrix} \right]\times \left[ \begin{matrix} 1 & 3 \\ 0 & 2 \\ -2 & -1 \\ \end{matrix} \right]\]
A)
\[\left[ \begin{matrix} 1 & 3 \\ 6 & -4 \\ \end{matrix} \right]\]
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B)
\[\left[ \begin{matrix} -1 & -3 \\ 6 & 4 \\ \end{matrix} \right]\]
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C)
\[\left[ \begin{matrix} -1 & 3 \\ -6 & 4 \\ \end{matrix} \right]\]
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D)
\[\left[ \begin{matrix} -1 & 3 \\ -6 & -4 \\ \end{matrix} \right]\]
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question_answer 218) Find the values of x, y and z from the following equations \[\left[ \begin{matrix} 4 & x-z \\ 2+y & xz \\ \end{matrix} \right]=\left[ \begin{matrix} 4 & 3 \\ -1 & 10 \\ \end{matrix} \right]\]
A)
\[x=-5,\text{ }y=3,\text{ }z=2\]
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B)
\[x=5,y=-3,z=2\]
done
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C)
\[x=5,y=3,\text{ }z=-2\]
done
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D)
\[x=5,y=-3,z=-2\]
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question_answer 219) Let \[A=\{1,\,\,2\,\{a,\,\,b\},\,\,3,\,\,4\},\] which among the following statements is incorrect?
A)
\[\{a,\,b\}\subset A\]
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B)
\[\{a,\,b\}\in A\]
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C)
\[\{\{a,\,b\}\}\subset A\]
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D)
\[\phi \,\,\in \,\,A\]
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question_answer 220) The probability of India winning a test match against South Africa is \[1/2\]assuming independence form match to match played. The probability that in a match series India's second win occurs at the third day is
A)
\[1/8\]
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B)
\[1/2\]
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C)
\[1/4\]
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D)
\[2/3\]
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question_answer 221) In an experiment with 15 observations on x the following results are available \[\Sigma {{x}^{2}}=2830,\] \[\Sigma x=170.\] One observation that was 20, was found to be wrong and was replaced by correct value 30. Find the correct variance.
A)
\[78'\]
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B)
\[186\]
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C)
\[158\]
done
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D)
\[18\]
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question_answer 222) If a circle passes through the point \[(a,b)\] and cuts the circle \[{{x}^{2}}+{{y}^{2}}=4\]orthogonally, then the locus of its centre is
A)
\[2ax+2by-({{a}^{2}}+{{b}^{2}}+4)=0\]
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B)
\[2ax+2by+({{a}^{2}}+{{b}^{2}}+4)=0\]
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C)
\[2ax-2by+({{a}^{2}}+{{b}^{2}}+4)=0\]
done
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D)
2ax \[2ax-2by-({{a}^{2}}+{{b}^{2}}+4)=0\]
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question_answer 223) Find the radius of the circle in which the sphere \[{{x}^{2}}+\text{ }{{y}^{2}}+\text{ }{{z}^{2}}+2x-2y-4z=19\]is cut by the plane\[x+2y+2z+7=0\].
A)
\[2\]
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B)
\[3\]
done
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C)
\[1\]
done
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D)
\[4\]
done
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question_answer 224) Let \[A=\{1,2,3,4\}\] and R be the relation on A defined by \[\{(a,b);\,\,a,\,b\,\in A,\,\,a\times b\] is an even number}, then find the range of R.
A)
\[\{1,2,3,4\}\]
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B)
\[\{2,\,\,4\}\]
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C)
\[\{2,\,\,3,\,\,4\}\]
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D)
\[\{1,\,\,2,\,\,4\}\]
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