question_answer 1) The internal resistance of a cell is the resistance of:
A)
electrolyte used in cell
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B)
electrodes of the cell
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C)
material used in cell
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D)
vessel of the cell
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question_answer 2) A device for generating an alternating current of d desired frequency is known as:
A)
an oscillator
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B)
an amplifier
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C)
a rectifier
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D)
none of these
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question_answer 3) The angle of minimum deviation for a thin prism with respect to air and when dipped in water will be:\[\left( _{a}{{\mu }_{g}}=\frac{3}{2},\,{{\,}_{a}}{{\mu }_{w}}=\frac{4}{3} \right)\]
A)
\[\frac{1}{4}\]
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B)
\[\frac{1}{8}\]
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C)
\[\frac{1}{3}\]
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D)
\[\frac{1}{2}\]
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question_answer 4) Escape velocity of a body when projected from the earth's surface is \[11.2\,\,km/s\]. If it is projected at an angle of \[{{50}^{o}}\] from the horizontal, the escape velocity is:
A)
\[11.8\,\,km/s\]
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B)
\[16.5\,\,km/s\]
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C)
\[11.2\,\,km/s\]
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D)
\[14.5\,\,km/s\]
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question_answer 5) A diamagnetic substance is brought near a strong magnet, then it is:
A)
attracted by a magnet
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B)
repelled by a magnet
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C)
repelled by north pole and attracted by south pole
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D)
attracted by north pole and repelled by south pole
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question_answer 6) The ratio of intensities of two waves is \[9:16\]. If they interfere, the ratio of maximum to minimum intensity will be:
A)
\[4:1\]
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B)
\[1:25\]
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C)
\[1:3\]
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D)
\[49:1\]
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question_answer 7) The sun emits a light with maximum wavelength\[510\,\,nm\] while another star emits a light with maximum wavelength of \[350\,\,nm\]. The ratio of surface temperature of sun and the star will be:
A)
\[0.69\]
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B)
\[0.46\]
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C)
\[1.45\]
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D)
\[2.1\]
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question_answer 8) If the equation of Motion of standing wave is\[y=0.3\sin (314t-1.57x)\], then the velocity of standing wave is:
A)
\[400\,\,unit\]
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B)
\[350\,\,unit\]
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C)
\[209\,\,unit\]
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D)
\[200\,\,unit\]
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question_answer 9) For driving current of \[2\,\,A\] for \[6\min \] in a circuit, \[1000\,\,J\] of work is to be done. The emf-of the source in the circuit is:
A)
\[2.03\,\,V\]
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B)
\[2.54\,\,V\]
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C)
\[1.25\,\,V\]
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D)
\[1.39\,\,V\]
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question_answer 10) The moment of momentum for an electron in second orbit of hydrogen atom as per Bohr's model is:
A)
\[\frac{h}{\pi }\]
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B)
\[2\pi h\]
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C)
\[\frac{2h}{\pi }\]
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D)
\[\frac{\pi }{h}\]
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question_answer 11) The latent heat of vaporisation of water is\[2250\,\,J/kg\]. If the work done in the process of vaporisation of \[1\,\,kg\] is \[168\,\,J\], then increase in internal energy will be:
A)
\[1904\,\,J\]
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B)
\[1984\,\,J\]
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C)
\[3202\,\,J\]
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D)
\[2082\,\,J\]
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question_answer 12) Huygen's wave theory of light could not explain:
A)
photoelectric effect
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B)
interference
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C)
diffraction
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D)
polarization
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question_answer 13) In a triode valve, when the plate potential is increased from \[200\,\,V\] to \[220\,\,V\] and-grid potential is decreased from \[-0.5\,\,V\] to \[-\text{ }1.3\,\,V,\] there is no change in plate current. The amplification factor of the triode is:
A)
\[25\]
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B)
\[14\]
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C)
\[11\]
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D)
\[73\]
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question_answer 14) A bar magnet of magnetic moment \[220\,\,A{{m}^{2}}\] is suspended in a magnetic field of intensity\[0.25\,\,N/Am\]. The couple required to deflect it through \[{{30}^{o}}\] is:
A)
\[27.5\,\,Nm\]
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B)
\[20.25\,\,Nm\]
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C)
\[47.63\,\,Nm\]
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D)
\[12\,\,Nm\]
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question_answer 15) A plano-convex lens has refractive index \[1.5\] and radius of curvature \[50\,\,cm\]. What is focal length of lens?
A)
\[100\,\,cm\]
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B)
\[200\,\,cm\]
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C)
\[178\,\,cm\]
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D)
\[150\,\,cm\]
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question_answer 16) A source and an observer move away from each other, with a velocity of \[20\,\,m/s\]. If the apparent frequency heard by the observer is \[1840\,\,Hz\], the actual frequency of the source is: (Velocity of sound in\[=340\,\,m/s)\]:
A)
\[2486\,\,Hz\]
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B)
\[2070\,\,Hz\]
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C)
\[2134\,\,Hz\]
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D)
\[1872\,\,Hz\]
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question_answer 17) The speed of wave in a medium is \[650\,\,m/s\]. If \[3500\] waves are passing through a point in the medium in \[1.67\,\,\min \], then its wavelength will be:
A)
\[16.25\,\,m\]
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B)
\[14.29\,\,m\]
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C)
\[18.57\,\,m\]
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D)
\[20.50\,\,m\]
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question_answer 18) The body is projected at such angle that the horizontal range is three times the greatest height. The angle of projection is:
A)
\[{{43}^{o}}8'\]
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B)
\[{{25}^{o}}8'\]
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C)
\[{{33}^{o}}7'\]
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D)
\[{{53}^{o}}1'\]
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question_answer 19) On the horizontal surface of a truck, a block of mass \[1\,\,kg\] is placed \[(\mu =0.6)\] and truck is moving with acceleration \[5m/{{s}^{2}}\]. The frictional force acting on the block will be: \[(g=10\,\,m/{{s}^{2}})\]
A)
\[6\,\,N\]
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B)
\[5.88\,\,N\]
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C)
\[7\,\,N\]
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D)
\[9\,\,N\]
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question_answer 20) Calculate the work done when a force\[\overset{\to }{\mathop{\mathbf{F}}}\,=2\widehat{\mathbf{i}}+3\widehat{\mathbf{j}}-5\widehat{\mathbf{k}}\]. units acts on a body producing a displacement \[\overset{\to }{\mathop{\mathbf{s}}}\,=2\widehat{\mathbf{i}}+4\widehat{\mathbf{j}}+3\widehat{\mathbf{k}}\] units:
A)
\[1\,\,unit\]
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B)
\[20\,\,unit\]
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C)
\[5\,\,unit\]
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D)
\[zero\]
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question_answer 21) The efficiency of Carnot engine is, \[50%\] and temperature of sink is \[500\,\,K\]. If the temperature of source is kept constant and its efficiency is to be raised to \[60%\], then the required temperature of the sink will be:
A)
\[600\,\,K\]
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B)
\[400\,\,K\]
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C)
\[500\,\,K\]
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D)
\[100\,\,K\]
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question_answer 22) What happens to the internal energy of a gas during isothermal expansion?
A)
Internal energy will decrease
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B)
Internal energy will increase
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C)
Internal energy will become zero
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D)
Internal energy will remain same
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question_answer 23) \[100\,\,g\] ice is mixed with \[100\,\,g\] of water at \[{{100}^{o}}C\]. What will be the final temperature of the mixture?
A)
\[{{10}^{o}}C\]
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B)
\[{{27}^{o}}C\]
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C)
\[{{14}^{o}}C\]
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D)
none of these
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question_answer 24) Black hole consists of:
A)
ozone layer
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B)
super dense planetary material
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C)
upper surface of atmosphere
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D)
none of the above
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question_answer 25)
Three resistors \[2\,\,\Omega ,\,\,\,3\,\,\Omega \] and \[4\,\,\Omega \] are connected as shown in the given diagram. The equivalent resistance will be:
A)
\[\frac{12}{13}\]
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B)
\[\frac{11}{10}\]
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C)
\[2\]
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D)
\[\frac{10}{11}\]
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question_answer 26) If an electron jumps from first orbit to third orbit of hydrogen atom it will:
A)
not loose energy
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B)
release energy
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C)
absorb energy
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D)
not gain energy
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question_answer 27) A body of mass \[10\,\,kg\] moving with velocity \[10\,\,m/s\] collides with a stationary body of mass\[5\,\,kg\]. After collision both bodies stick to each other, velocity of the joint body after collision is:
A)
\[\frac{3}{10}m/s\]
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B)
\[20\,\,m/s\]
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C)
\[\frac{20}{3}m/s\]
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D)
\[15\,\,m/s\]
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question_answer 28) If a body starts from rest and travels \[110\,\,cm\] in the \[9th\] second, then acceleration of the body is:
A)
\[0.13m/{{s}^{2}}\]
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B)
\[0.16m/{{s}^{2}}\]
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C)
\[0.18m/{{s}^{2}}\]
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D)
\[0.34m/{{s}^{2}}\]
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question_answer 29) It the momentum of a particle is doubled, then its de-Broglie wavelength will:
A)
become four times
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B)
become half
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C)
become two times
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D)
remain unchanged
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question_answer 30) Dimensions of torque are:
A)
\[[{{M}^{2}}{{L}^{2}}{{T}^{-2}}]\]
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B)
\[[M{{L}^{2}}{{T}^{-2}}]\]
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C)
\[[M{{L}^{2}}{{T}^{-1}}]\]
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D)
\[[M{{L}^{0}}{{T}^{-2}}]\]
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question_answer 31) Two vectors have magnitudes \[3\] and \[5\]. If angle between them is \[{{60}^{o}}\], then the dot product of two vectors will be:
A)
\[7.5\]
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B)
\[6.5\]
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C)
\[8.4\]
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D)
\[7.9\]
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question_answer 32) The kinetic energy of \[1\,\,g\] molecule of a gas, at normal temperature and pressure is:\[(R=8.321\,\,J/mol\text{-}K)\]
A)
\[1.2\times {{10}^{2}}J\]
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B)
\[3.4\times {{10}^{3}}J\]
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C)
\[1.66\times {{10}^{4}}J\]
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D)
\[2.97\times {{10}^{4}}J\]
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question_answer 33) If the coefficient of cubical expansion is \[x\] times of the coefficient of superficial expansion, then value of \[x\] is:
A)
\[2.7\]
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B)
\[2\]
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C)
\[1.5\]
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D)
\[9.5\]
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question_answer 34) \[X-\]ray will not show the phenomenon of:
A)
interference
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B)
deflection by electric field
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C)
diffraction
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D)
polarisation
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question_answer 35) Bernoulli's theorem is based on:
A)
conservation of mass, energy and momentum
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B)
conservation of mass
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C)
conservation of momentum
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D)
conservation of energy
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question_answer 36) In bringing an electron towards another electron, the electrostatic potential energy of the system:
A)
decreases
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B)
increases
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C)
remains same
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D)
becomes zero
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question_answer 37) The half-life of radium is \[1600\,\,yr\]. What is the mean life and disintegration constant of radium?
A)
\[2309\,\,yr,\,\,\frac{1}{2309}/yr\]
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B)
\[3309\,\,yr,\,\,\frac{1}{3309}/yr\]
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C)
\[1309\,\,yr,\,\,\frac{1}{1309}/yr\]
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D)
none of the above
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question_answer 38) Energy obtained when \[1\,\,mg\] mass is completely converted in to energy will be:
A)
\[9\times {{10}^{13}}J\]
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B)
\[3\times {{10}^{8}}J\]
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C)
\[3\times {{10}^{15}}J\]
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D)
\[9\times {{10}^{15}}J\]
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question_answer 39) A ray of light is incident on a surface of a plate of glass of refractive index \[1.5\] at polarising angle. The angle of refraction of the ray will be:
A)
\[{{53.7}^{o}}\]
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B)
\[{{43.7}^{o}}\]
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C)
\[{{33.7}^{o}}\]
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D)
none of these
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question_answer 40) A closed organ pipe and an open organ pipe are tuned to the same fundamental frequency. The ratio of their lengths is:
A)
\[1:2\]
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B)
\[4:1\]
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C)
\[1:4\]
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D)
\[2:1\]
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question_answer 41) A particle is moving along a circular path of radius \[5\,\,m\] with uniform speed \[5\,\,m/s\]. What will be the average acceleration when the particle completes half revolution?
A)
\[\frac{10}{\pi }m/{{s}^{2}}\]
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B)
\[10\,\,m/{{s}^{2}}\]
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C)
\[10\pi \,\,m/{{s}^{2}}\]
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D)
\[Zero\]
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question_answer 42)
A body of mass \[m\] is attached between two springs of force constants \[{{k}_{1}}\] and \[{{k}_{2}}\] as Shown in figure. The other ends of the springs are fixed to firm supports. The frequency of the oscillation is:
A)
\[n=\frac{1}{2\pi }\sqrt{\frac{{{k}_{1}}-{{k}_{2}}}{m}}\]
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B)
\[n=\frac{1}{2\pi }\sqrt{\frac{{{k}_{1}}{{k}_{2}}}{m}}\]
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C)
\[n=\frac{1}{2\pi }\sqrt{\frac{{{k}_{1}}+{{k}_{2}}}{m}}\]
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D)
none of the above
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question_answer 43) In a \[p-\]type semicoriductor, germanium is doped with:
A)
boron
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B)
gallium
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C)
aluminium
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D)
all of these
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question_answer 44) In a full wave rectifier circuit operating from \[50\,\,Hz\] mains frequency, what is the fundamental frequency in the ripple?
A)
\[50\,\,Hz\]
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B)
\[100\,\,Hz\]
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C)
\[25\,\,Hz\]
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D)
\[70\,\,Hz\]
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question_answer 45) An ideal gas at \[{{27}^{o}}C\] is compressed adiabatically to \[\frac{8}{27}\] of its original volume. The rise in temperature will be\[\left( \gamma =\frac{5}{3} \right)\].
A)
\[{{480}^{o}}C\]
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B)
\[{{275}^{o}}C\]
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C)
\[{{450}^{o}}C\]
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D)
\[{{375}^{o}}C\]
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question_answer 46) When you make ice cubes, entropy of water:
A)
does not change
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B)
increases
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C)
decreases
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D)
may either increase or decrease depending on the process used
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question_answer 47) The focal length of the objective lens and eye-piece of an astronomical telescope are \[2\,\,m\] and\[0.05\,\,m\]. Find the length of the telescope.
A)
\[2.05\,\,m\]
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B)
\[1.16\,\,m\]
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C)
\[1.05\,\,m\]
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D)
\[2.9\,\,m\]
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question_answer 48)
Two identical batteries, each of emf \[2\,\,V\] and internal resistance \[1\Omega \] pass a current through external, resistance\[R=0.5\Omega \]. The maximum power that can be developed across \[R\] using these batteries is:
A)
\[3.2\,\,W\]
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B)
\[8.2\,\,W\]
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C)
\[4\,\,W\]
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D)
\[2\,\,W\]
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question_answer 49) At what height from the earth's surface, the acceleration due to gravity will be half the value of \[g\] at surface? \[(R=6400\,\,km)\]
A)
\[6400\,\,km\]
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B)
\[8200\,\,km\]
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C)
\[4800\,\,km\]
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D)
\[1600\,\,km\]
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question_answer 50) In a semiconducting material the motilities of electrons and holes are \[{{\mu }_{e}}\] and \[{{\mu }_{h}}\] respectively which of the following is true?
A)
\[{{\mu }_{e}}>{{\mu }_{h}}\]
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B)
\[{{\mu }_{e}}<{{\mu }_{h}}\]
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C)
\[{{\mu }_{e}}={{\mu }_{h}}\]
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D)
\[{{\mu }_{e}}<0,\,\,{{\mu }_{h}}>0\]
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question_answer 51) Tyndall effect is shown by:
A)
solution
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B)
precipitate
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C)
sol
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D)
none of these
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question_answer 52) In reaction,\[MnO_{4}^{-}+{{H}^{+}}+{{C}_{2}}O_{4}^{2-}\xrightarrow{{}}M{{n}^{2+}}\]\[+{{H}_{2}}O+C{{O}_{2}}\]What is happening?
A)
Reduction of\[Mn\]
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B)
Reduction of\[{{C}_{2}}O_{4}^{2-}\]
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C)
Oxidation of\[Mn\]
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D)
None of these
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question_answer 53) In which of the following ionic bond is present?
A)
\[B{{F}_{3}}\]
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B)
\[CC{{l}_{4}}\]
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C)
\[HCl\]
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D)
\[BaC{{l}_{2}}\]
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question_answer 54) Deficiency of vitamin \[E\] causes:
A)
scurvy
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B)
beri-beri
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C)
sterility
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D)
xerophthalmia
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question_answer 55) The reaction of Lucas reagent is fast with:
A)
\[C{{H}_{3}}C{{H}_{2}}OH\]
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B)
\[{{(C{{H}_{3}})}_{3}}COH\]
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C)
\[{{(C{{H}_{3}})}_{2}}CHOH\]
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D)
\[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}OH\]
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question_answer 56) \[IUPAC\] name of the compound is: \[H-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{2}}-C{{H}_{2}}-COOH\]
A)
3-oxo-butanoic acid
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B)
4-oxo-propanoic acid
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C)
3-formyl-propanoic acid
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D)
none of the above
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question_answer 57) Tollen's reagent is:
A)
alkaline \[CuS{{O}_{4}}\] solution
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B)
ammoniacal cuproxide solution
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C)
aqueous solution of sodium cupritartarate
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D)
ammoniacal \[AgN{{O}_{3}}\] solution
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question_answer 58) Epsom salt is:
A)
\[MgS{{O}_{4}}\cdot 2{{H}_{2}}O\]
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B)
\[BaS{{O}_{4}}\cdot 2{{H}_{2}}O\]
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C)
\[MgS{{O}_{4}}\cdot 7{{H}_{2}}O\]
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D)
\[CaS{{O}_{4}}\cdot 2{{H}_{2}}O\]
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question_answer 59) Which of the following carbonate decompose most easily on heating?
A)
\[R{{b}_{2}}C{{O}_{3}}\]
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B)
\[{{K}_{2}}C{{O}_{3}}\]
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C)
\[N{{a}_{2}}C{{O}_{3}}\]
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D)
\[MgC{{O}_{3}}\]
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question_answer 60) In an isothermal expansion of an ideal gas:
A)
\[W=0\]
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B)
\[\Delta E=0\]
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C)
\[q=0\]
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D)
\[\Delta V=0\]
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question_answer 61) The degree of hydrolysis of \[0.01\,\,M\,\,N{{H}_{4}}Cl\] is:\[({{K}_{h}}=2.5\times {{10}^{-9}})\]
A)
\[5\times {{10}^{-5}}\]
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B)
\[5\times {{10}^{-4}}\]
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C)
\[5\times {{10}^{-3}}\]
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D)
\[5\times {{10}^{-7}}\]
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question_answer 62) The number of gram equivalent of \[{{H}_{2}}S{{O}_{4}}\] in \[1000\,\,mL\,\,3M\] solution, is:
A)
\[3\]
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B)
\[6\]
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C)
\[4\]
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D)
\[1.5\]
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question_answer 63) The radioactive isotope used in cancer therapy, is:
A)
\[{{I}^{128}}\]
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B)
\[C{{o}^{60}}\]
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C)
\[C{{o}^{59}}\]
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D)
\[{{p}^{32}}\]
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question_answer 64) The expression of angular momentum of an electron in a Bohr's orbit is:
A)
\[\frac{n\,\,h}{3\,\,\pi }\]
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B)
\[\frac{n\,\,h}{2\,\,\pi }\]
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C)
\[\frac{h}{4\pi }\]
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D)
\[\sqrt{l(l+1)}\cdot \frac{h}{2\pi }\]
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question_answer 65) Which of the following is called Hofmann's bromamide reaction?
A)
\[C{{H}_{3}}CHN+2{{H}_{2}}O\xrightarrow{{}}C{{H}_{3}}COO+N{{H}_{3}}\]
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B)
\[C{{H}_{3}}CN+4H\xrightarrow{Na/ErOH}C{{H}_{3}}C{{H}_{2}}N{{H}_{2}}\]
done
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C)
\[C{{H}_{3}}CON{{H}_{2}}\xrightarrow{B{{r}_{2}}/NaOH}C{{H}_{3}}N{{H}_{2}}\]
done
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D)
\[C{{H}_{3}}COCl+C{{H}_{3}}OH\xrightarrow{{}}\]\[C{{H}_{3}}COOC{{H}_{3}}+HCl\]
done
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question_answer 66) Which one among the following contains a phenolic \[-OH\] group?
A)
Oxalic acid
done
clear
B)
Formic acid
done
clear
C)
Picric acid
done
clear
D)
Citric acid
done
clear
View Answer play_arrow
question_answer 67) In the reaction, product \['X'\] is: \[C{{H}_{3}}-C\equiv CH+{{H}_{2}}O\xrightarrow{{{H}^{+}}/H{{g}^{2+}}}X\]
A)
\[C{{H}_{3}}C{{H}_{2}}CHO\]
done
clear
B)
\[C{{H}_{3}}C{{H}_{2}}COOH\]
done
clear
C)
\[C{{H}_{3}}-C(OH)=CHOH\]
done
clear
D)
\[C{{H}_{3}}COC{{H}_{3}}\]
done
clear
View Answer play_arrow
question_answer 68) Which is an amphoteric oxide?
A)
\[MgO\]
done
clear
B)
\[{{K}_{2}}O\]
done
clear
C)
\[A{{l}_{2}}{{O}_{3}}\]
done
clear
D)
\[CuO\]
done
clear
View Answer play_arrow
question_answer 69) The oxidation number of \[S\] in\[{{H}_{2}}{{S}_{2}}{{O}_{8}}\] is:
A)
\[+6\]
done
clear
B)
\[-6\]
done
clear
C)
\[+4\]
done
clear
D)
\[+8\]
done
clear
View Answer play_arrow
question_answer 70) Bleaching powder is obtained by treating chlorine with:
A)
\[CaC{{O}_{3}}\]
done
clear
B)
\[Ca{{(OH)}_{2}}\]
done
clear
C)
\[CaO\]
done
clear
D)
none of these
done
clear
View Answer play_arrow
question_answer 71) For reaction,\[PC{{l}_{3}}(g)+C{{l}_{2}}(g)PC{{l}_{5}}(g)\]the value of\[{{K}_{c}}\]at\[{{250}^{o}}C\]is\[26\]. At the same temperature, the value of \[{{K}_{p}}\] is:
A)
\[0.46\]
done
clear
B)
\[0.61\]
done
clear
C)
\[0.95\]
done
clear
D)
\[0.73\]
done
clear
View Answer play_arrow
question_answer 72) The volume of a gas is reduced to \[1.0\,\,L\] at \[{{25}^{o}}C\] and \[1\,\,atm\] pressure. Its pressure at \[{{35}^{o}}C\] would be:
A)
\[0.96\,\,atm\]
done
clear
B)
\[1.03\,\,atm\]
done
clear
C)
\[2.04\,\,atm\]
done
clear
D)
\[3.08\,\,atm\]
done
clear
View Answer play_arrow
question_answer 73) The strongest acid among the following is:
A)
\[C{{H}_{3}}COOH\]
done
clear
B)
\[C{{H}_{2}}ClCOOH\]
done
clear
C)
\[C{{H}_{2}}FCOOH\]
done
clear
D)
\[C{{H}_{3}}C{{H}_{2}}COOH\]
done
clear
View Answer play_arrow
question_answer 74) The compressibility factor for an ideal gas is:
A)
\[<1\]
done
clear
B)
\[=1\]
done
clear
C)
\[>1\]
done
clear
D)
always\[2\]
done
clear
View Answer play_arrow
question_answer 75) The standard reduction potential of\[L{{i}^{+}},\,B{{a}^{2+}},\,\,N{{a}^{+}}\]and\[M{{g}^{2+}}\]are\[-3.05,\,\,-2.73,\]\[-2.71\] and \[-2.37\] volts respectively. Which one is the strongest reducing agent?
A)
\[Li\]
done
clear
B)
\[Na\]
done
clear
C)
\[Mg\]
done
clear
D)
\[Ba\]
done
clear
View Answer play_arrow
question_answer 76) The unit of rate constant for 1st order reaction is:
A)
\[mol\,\,{{L}^{-1}}{{s}^{-1}}\]
done
clear
B)
\[mo{{l}^{-1}}L{{s}^{-1}}\]
done
clear
C)
\[{{s}^{-1}}\]
done
clear
D)
\[mo{{l}^{2}}{{L}^{-2}}{{s}^{-1}}\]
done
clear
View Answer play_arrow
question_answer 77) In which of the following, the dipole moment is zero?
A)
\[{{H}_{2}}{{O}_{2}}\]
done
clear
B)
\[C{{O}_{2}}\]
done
clear
C)
\[S{{O}_{2}}\]
done
clear
D)
\[N{{H}_{3}}\]
done
clear
View Answer play_arrow
question_answer 78) The bond order of\[O_{2}^{+}\]is:
A)
\[2\]
done
clear
B)
\[2.5\]
done
clear
C)
\[1.5\]
done
clear
D)
\[0.5\]
done
clear
View Answer play_arrow
question_answer 79) Addition of \[HgC{{l}_{2}}\] to \[SnC{{l}_{2}}\] gives a black colour due to:
A)
oxidation of\[Sn\]
done
clear
B)
reduction of\[HgC{{l}_{2}}\]
done
clear
C)
formation of amalgam
done
clear
D)
oxidation of\[Hg\]
done
clear
View Answer play_arrow
question_answer 80) Which one of the following is a trihydric alcohol containing only secondary hydroxyl group?
A)
\[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}}\,-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,H-C{{H}_{2}}OH\]
done
clear
B)
\[\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,{{H}_{2}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,H-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,{{H}_{2}}\]
done
clear
C)
\[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,H-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,H-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,H-C{{H}_{3}}\]
done
clear
D)
None of the above
done
clear
View Answer play_arrow
question_answer 81) How, many sigma and it-bonds are there in the following compound? \[C{{H}_{2}}=CH-C\equiv C-\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}\,=C{{H}_{2}}\]
A)
\[11\sigma ,\,\,4\pi \]
done
clear
B)
\[12\sigma ,\,\,3\pi \]
done
clear
C)
\[14\sigma ,\,\,4\pi \]
done
clear
D)
\[15\sigma ,\,\,4\pi \]
done
clear
View Answer play_arrow
question_answer 82) In the nitration of benzene, the reactive species is:
A)
\[N{{O}_{2}}\]
done
clear
B)
\[NO_{2}^{+}\]
done
clear
C)
\[NO_{2}^{-}\]
done
clear
D)
\[N{{O}^{-}}\]
done
clear
View Answer play_arrow
question_answer 83) Reaction of phenol with\[CC{{l}_{4}}\]and\[NaOH\], followed by hydrolysis is likely to give:
A)
done
clear
B)
done
clear
C)
done
clear
D)
done
clear
View Answer play_arrow
question_answer 84) In the reaction, \[_{92}{{U}^{238}}{{\xrightarrow{{}}}_{82}}P{{b}^{206}}\], the number of \[\alpha \] and \[\beta -\]particles emitted are:
A)
\[7\alpha ,\,\,5\beta \]
done
clear
B)
\[6\alpha ,\,\,4\beta \]
done
clear
C)
\[4\alpha ,\,\,3\beta \]
done
clear
D)
\[8\alpha ,\,\,6\beta \]
done
clear
View Answer play_arrow
question_answer 85) Which is the correct Gibb's Helmholtz equation?
A)
\[\Delta H=\Delta G=T\cdot \Delta S\]
done
clear
B)
\[\Delta S=\frac{1}{T}[\Delta G-\Delta H]\]
done
clear
C)
\[\Delta S=\frac{1}{T}[\Delta H-\Delta G]\]
done
clear
D)
\[-\Delta G=\Delta H-T\cdot \Delta S\]
done
clear
View Answer play_arrow
question_answer 86) Vinegar is:
A)
\[8-10%\] acetic acid
done
clear
B)
\[6-10%\] ethyl alcohol'
done
clear
C)
glacial acetic acid
done
clear
D)
\[10%\] formic acid
done
clear
View Answer play_arrow
question_answer 87) Decreasing order of electron affinity of halogens is:
A)
\[Cl>Br>F>I\]
done
clear
B)
\[Cl>F>Br>I\]
done
clear
C)
\[Br>Cl>F>I\]
done
clear
D)
\[F>Cl>Br>I\]
done
clear
View Answer play_arrow
question_answer 88) Which of the following is an acidic salt?
A)
\[N{{a}_{2}}S{{O}_{4}}\]
done
clear
B)
\[Pb(OH)Cl\]
done
clear
C)
\[BaC{{l}_{2}}\]
done
clear
D)
\[N{{a}_{2}}HP{{O}_{4}}\]
done
clear
View Answer play_arrow
question_answer 89) Which one is the Lewis acid?
A)
\[{{H}_{2}}O\]
done
clear
B)
\[AlC{{l}_{3}}\]
done
clear
C)
\[RN{{H}_{2}}\]
done
clear
D)
\[N{{H}_{3}}\]
done
clear
View Answer play_arrow
question_answer 90) \[720\,\,g\] water contain the number of moles:
A)
\[2\]
done
clear
B)
\[190\]
done
clear
C)
\[40\]
done
clear
D)
\[55\]
done
clear
View Answer play_arrow
question_answer 91) \[2HCHO\xrightarrow{50%NaOH}C{{H}_{3}}OH+HCOONa\] This reaction is called:
A)
aldol condensation
done
clear
B)
Tischenko reaction
done
clear
C)
Cannizaro reaction
done
clear
D)
Reimer Tiemann reaction
done
clear
View Answer play_arrow
question_answer 92) The geometry of the molecule having \[s\] and \[p-\]characters equal to \[25%\] and \[75%\] respectively, is:
A)
trigonal
done
clear
B)
linear
done
clear
C)
tetrahedral
done
clear
D)
octahedral
done
clear
View Answer play_arrow
question_answer 93) Impossible configuration is:
A)
\[1{{s}^{2}},\,\,2{{s}^{2}}2{{p}^{2}},\,\,3{{s}^{2}}\]
done
clear
B)
\[1{{s}^{2}},\,\,2{{s}^{2}}\]
done
clear
C)
\[1{{s}^{2}},\,\,2{{s}^{2}}2{{p}^{6}}\]
done
clear
D)
None of these
done
clear
View Answer play_arrow
question_answer 94) The solubility product of \[PbB{{r}_{2}}\] is \[10.8\times {{10}^{-5}}\]. It, is \[70%\] dissociated in saturated solution. The solubility of salt is:
A)
\[4.18\times {{10}^{-2}}\]
done
clear
B)
\[6.76\times {{10}^{-3}}\]
done
clear
C)
\[3.4\times {{10}^{-4}}\]
done
clear
D)
\[5.44\times {{10}^{-2}}\]
done
clear
View Answer play_arrow
question_answer 95) The latent heat of vaporisation of water is \[540\,\,cal\,\,{{g}^{-1}}\] at \[{{100}^{o}}C\]. What will be the entropy increase when one mole of water is evaporated at\[{{100}^{o}}C?\]
A)
\[28\,\,cal\,\,{{K}^{-1}}mo{{l}^{-1}}\]
done
clear
B)
\[26\,\,cal\,\,{{K}^{-1}}mo{{l}^{-1}}\]
done
clear
C)
\[540\,\,cal\,\,{{K}^{-1}}mo{{l}^{-1}}\]
done
clear
D)
\[1.82\,\,cal\,\,{{K}^{-1}}mo{{l}^{-1}}\]
done
clear
View Answer play_arrow
question_answer 96) The brown ring in the test of nitrate is formed due to:
A)
\[{{[Fe{{({{H}_{2}}O)}_{5}}N{{O}_{2}}]}^{2+}}\]
done
clear
B)
\[Fe{{(N{{O}_{3}})}_{3}}\]
done
clear
C)
\[{{[Fe{{({{H}_{2}}O)}_{5}}NO]}^{2+}}\]
done
clear
D)
\[{{[Fe({{H}_{2}}O){{(NO)}_{5}}]}^{2+}}\]
done
clear
View Answer play_arrow
question_answer 97) The corrosive sublimate is :
A)
\[Hg\]
done
clear
B)
\[H{{g}_{2}}O\]
done
clear
C)
\[H{{g}_{2}}C{{l}_{2}}\]
done
clear
D)
\[HgC{{l}_{2}}\]
done
clear
View Answer play_arrow
question_answer 98) The half-life of radium is\[1580\,\,yr\]. Its average life is:
A)
\[2.275\times {{10}^{3}}yr\]
done
clear
B)
\[3.735\times {{10}^{2}}yr\]
done
clear
C)
\[1.62\times {{10}^{3}}yr\]
done
clear
D)
\[7.28\times {{10}^{2}}yr\]
done
clear
View Answer play_arrow
question_answer 99) Cobalt is present in:
A)
vitamin\[{{B}_{12}}\]
done
clear
B)
vitamin\[{{B}_{6}}\]
done
clear
C)
vitamin\[{{B}_{2}}\]
done
clear
D)
vitamin\[{{B}_{1}}\]
done
clear
View Answer play_arrow
question_answer 100) Adipic acid and hexamethylene diamine, on polymerisation gives:
A)
nylon\[-6\]
done
clear
B)
Dacron
done
clear
C)
nylon\[-66\]
done
clear
D)
bakelite
done
clear
View Answer play_arrow
question_answer 101) If \[z=x+iy\], then the area of a triangle whose vertices are points \[z,\,\,iz\] and \[z+iz\] is:
A)
\[2|z{{|}^{2}}\]
done
clear
B)
\[\frac{1}{2}|z{{|}^{2}}\]
done
clear
C)
\[|z{{|}^{2}}\]
done
clear
D)
\[\frac{3}{2}|z{{|}^{2}}\]
done
clear
View Answer play_arrow
question_answer 102) If the-complex number \[{{z}_{1}},\,\,{{z}_{2}}\] and \[{{z}_{3}}\] represent the vertices of an equilateral triangle such that \[|{{z}_{1}}|=|{{z}_{2}}|=|{{z}_{3}}|\], then \[{{z}_{1}}+{{z}_{2}}+{{z}_{3}}\] is equal to:
A)
\[0\]
done
clear
B)
\[1\]
done
clear
C)
\[-1\]
done
clear
D)
none of these
done
clear
View Answer play_arrow
question_answer 103) If\[{{i}^{2}}=-1\], then the value of\[\sum\limits_{n=1}^{200}{{{i}^{n}}}\]is:
A)
\[50\]
done
clear
B)
\[-50\]
done
clear
C)
\[0\]
done
clear
D)
\[100\]
done
clear
View Answer play_arrow
question_answer 104) The sum to infinity of the series\[2+\frac{1}{2}+\frac{1}{3}+\frac{1}{{{2}^{2}}}+\frac{1}{{{3}^{2}}}+\frac{1}{{{2}^{3}}}+\frac{1}{{{3}^{3}}}+...\]
A)
\[3\]
done
clear
B)
\[4\]
done
clear
C)
\[\frac{7}{2}\]
done
clear
D)
\[\frac{9}{2}\]
done
clear
View Answer play_arrow
question_answer 105) If\[x>1,\,\,y>1,\,\,z>1\]are in\[GP\], then\[\frac{1}{1+\log x},\,\,\frac{1}{1+\log y},\,\,\frac{1}{1+\log z}\]are in:
A)
\[AP\]
done
clear
B)
\[HP\]
done
clear
C)
\[GP\]
done
clear
D)
none of these
done
clear
View Answer play_arrow
question_answer 106) If\[{{x}^{2}}-3x+2\]be a factor of\[{{x}^{4}}-p{{x}^{2}}+q\], then \[(p,\,\,q)\]is equal to:
A)
\[(3,\,\,4)\]
done
clear
B)
\[(4,\,\,5)\]
done
clear
C)
\[(4,\,\,3)\]
done
clear
D)
\[(5,\,\,4)\]
done
clear
View Answer play_arrow
question_answer 107) If\[a{{x}^{2}}+bx+c=0\]and\[b{{x}^{2}}+cx+a=0\], then a common root and\[a\ne 0\], then\[\frac{{{a}^{3}}+{{b}^{3}}+{{c}^{3}}}{abc}\]is equal to:
A)
\[1\]
done
clear
B)
\[2\]
done
clear
C)
\[3\]
done
clear
D)
\[4\]
done
clear
View Answer play_arrow
question_answer 108) If\[^{15}{{C}_{3r}}{{=}^{15}}{{C}_{r+3}}\], then the value of\[r\]is:
A)
\[3\]
done
clear
B)
\[4\]
done
clear
C)
\[5\]
done
clear
D)
\[8\]
done
clear
View Answer play_arrow
question_answer 109) The number of divisors of \[9600\] including \[1\] and \[9600\] are:
A)
\[60\]
done
clear
B)
\[58\]
done
clear
C)
\[48\]
done
clear
D)
\[46\]
done
clear
View Answer play_arrow
question_answer 110) If\[{{a}_{n}}=\sum\limits_{r=0}^{n}{\frac{1}{^{n}{{C}_{r}}}}\], then\[\sum\limits_{r=0}^{n}{\frac{r}{^{n}{{C}_{r}}}}\]is equal to:
A)
\[(n-1){{a}_{n}}\]
done
clear
B)
\[n{{a}_{n}}\]
done
clear
C)
\[\frac{1}{2}n{{a}_{n}}\]
done
clear
D)
none of these
done
clear
View Answer play_arrow
question_answer 111) 6th term in expansion of\[{{\left( 2{{x}^{2}}-\frac{1}{3{{x}^{2}}} \right)}^{10}}\]is:
A)
\[\frac{4580}{17}\]
done
clear
B)
\[-\frac{896}{27}\]
done
clear
C)
\[\frac{5580}{17}\]
done
clear
D)
none of these
done
clear
View Answer play_arrow
question_answer 112) In the expansion of\[{{(1+x)}^{m}}{{(1-x)}^{n}}\], the coefficient of \[x\] and\[{{x}^{2}}\]are \[3\] and \[-6\] respectively, then \[m\] is equal to:
A)
\[6\]
done
clear
B)
\[9\]
done
clear
C)
\[12\]
done
clear
D)
\[24\]
done
clear
View Answer play_arrow
question_answer 113) \[(1+3){{\log }_{e}}3+\frac{1+{{3}^{2}}}{2!}{{({{\log }_{e}}3)}^{2}}\]\[+\frac{1+{{3}^{3}}}{3!}{{({{\log }_{e}}3)}^{3}}+...\infty \]is equal to:
A)
\[28\]
done
clear
B)
\[30\]
done
clear
C)
\[25\]
done
clear
D)
\[0\]
done
clear
View Answer play_arrow
question_answer 114) The sum of\[\frac{1}{2}+\frac{1}{3}+\frac{1}{{{2}^{3}}}+\frac{1}{5}\cdot \frac{1}{{{2}^{5}}}+...\infty \]is:
A)
\[{{\log }_{e}}\sqrt{\frac{3}{2}}\]
done
clear
B)
\[{{\log }_{e}}\sqrt{3}\]
done
clear
C)
\[{{\log }_{e}}\sqrt{\frac{7}{2}}\]
done
clear
D)
\[{{\log }_{e}}3\]
done
clear
View Answer play_arrow
question_answer 115) \[\left| \begin{matrix} 1 & a & {{a}^{2}}-bc \\ 1 & b & {{b}^{2}}-ac \\ 1 & c & {{c}^{2}}-ac \\ \end{matrix} \right|\]is equal to:
A)
\[0\]
done
clear
B)
\[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc\]
done
clear
C)
\[3abc\]
done
clear
D)
\[{{(a+b+c)}^{3}}\]
done
clear
View Answer play_arrow
question_answer 116) \[x+ky-z=0\],\[3x-ky-z=0\]and\[x-3y+z=0\] has non-zero solution for \[k\] is equal to:
A)
\[-1\]
done
clear
B)
\[0\]
done
clear
C)
\[1\]
done
clear
D)
\[2\]
done
clear
View Answer play_arrow
question_answer 117) If\[A=\left| \begin{matrix} 1 & -2 & 3 \\ 0 & -1 & 4 \\ -2 & 2 & 1 \\ \end{matrix} \right|\], then\[{{(A')}^{-1}}\] is equal to:
A)
\[\left[ \begin{matrix} -9 & -8 & -2 \\ 8 & 7 & 2 \\ -5 & -4 & -1 \\ \end{matrix} \right]\]
done
clear
B)
\[\left[ \begin{matrix} 1 & -1 & -2 \\ -2 & -1 & 2 \\ 3 & 4 & 1 \\ \end{matrix} \right]\]
done
clear
C)
\[\left[ \begin{matrix} -9 & 8 & 5 \\ -8 & 7 & -4 \\ 2 & 2 & -1 \\ \end{matrix} \right]\]
done
clear
D)
\[\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{matrix} \right]\]
done
clear
View Answer play_arrow
question_answer 118) Inverse matrix of\[\left[ \begin{matrix} 4 & 7 \\ 1 & 2 \\ \end{matrix} \right]\]is equal to:
A)
\[\left[ \begin{matrix} 2 & -7 \\ -1 & 4 \\ \end{matrix} \right]\]
done
clear
B)
\[\left[ \begin{matrix} 2 & -1 \\ -7 & 4 \\ \end{matrix} \right]\]
done
clear
C)
\[\left[ \begin{matrix} -2 & 7 \\ 1 & -4 \\ \end{matrix} \right]\]
done
clear
D)
\[\left[ \begin{matrix} -2 & 1 \\ 7 & -4 \\ \end{matrix} \right]\]
done
clear
View Answer play_arrow
question_answer 119) If \[A\] lies in the second quadrant and\[3\tan A+4=0\], then value of\[2\cot A-5\cos A+\sin A\]is equal to:
A)
\[-53/10\]
done
clear
B)
\[-7/10\]
done
clear
C)
\[7/10\]
done
clear
D)
\[23/10\]
done
clear
View Answer play_arrow
question_answer 120) If\[\sin \theta +\cos \theta =1\], then the general value of\[\theta \]is:
A)
\[2n\pi \]
done
clear
B)
\[n\pi +{{(-1)}^{n}}\frac{\pi }{4}-\frac{\pi }{4}\]
done
clear
C)
\[2n\pi +\frac{\pi }{2}\]
done
clear
D)
none of these
done
clear
View Answer play_arrow
question_answer 121) \[\cos \left[ 2{{\cos }^{-1}}\frac{1}{5}+{{\sin }^{-1}}\frac{1}{5} \right]\]is equal to:
A)
\[\frac{2\sqrt{6}}{5}\]
done
clear
B)
\[\frac{-2\sqrt{6}}{5}\]
done
clear
C)
\[\frac{1}{5}\]
done
clear
D)
\[\frac{-1}{5}\]
done
clear
View Answer play_arrow
question_answer 122) From a roof of a \[15\,\,m\] high house the angle of elevation of a point located \[15\,\,m\] distant to the base of the house is:
A)
\[{{45}^{o}}\]
done
clear
B)
\[{{30}^{o}}\]
done
clear
C)
\[{{60}^{o}}\]
done
clear
D)
\[{{90}^{o}}\]
done
clear
View Answer play_arrow
question_answer 123) If \[A\] and \[B\] are two fixed point and \[P\] is a variable point such that\[PA+PB=4\], then the locus of \[P\] is a/an:
A)
parabola
done
clear
B)
ellipse
done
clear
C)
hyperbola
done
clear
D)
none of these
done
clear
View Answer play_arrow
question_answer 124) A line passes through \[(2,\,\,2)\] and is perpendicular to the line \[3x+y=3\], its \[y-\]intercept is:
A)
\[1/3\]
done
clear
B)
\[2/3\]
done
clear
C)
\[1\]
done
clear
D)
\[4/3\]
done
clear
View Answer play_arrow
question_answer 125) The angle between the pair of straight lines \[{{x}^{2}}-{{y}^{2}}-2xy-1=0\]is :
A)
\[{{90}^{o}}\]
done
clear
B)
\[{{60}^{o}}\]
done
clear
C)
\[{{75}^{o}}\]
done
clear
D)
\[{{36}^{o}}\]
done
clear
View Answer play_arrow
question_answer 126) The point of intersection of the line \[4x-3y-10=0\] and the circle \[{{x}^{2}}+{{y}^{2}}-2x+4y-20=0\] are:
A)
\[(-2,\,\,-6),\,\,(4,\,\,2)\]
done
clear
B)
\[(2,\,\,6),\,\,(-4,\,\,-2)\]
done
clear
C)
\[(-2,\,\,6),\,\,(-4,\,\,2)\]
done
clear
D)
none of the above
done
clear
View Answer play_arrow
question_answer 127) The focus of the parabola\[{{y}^{2}}=4y-4x\]is:
A)
\[(0,\,\,2)\]
done
clear
B)
\[(1,\,\,2)\]
done
clear
C)
\[(2,\,\,0)\]
done
clear
D)
\[(2,\,\,1)\]
done
clear
View Answer play_arrow
question_answer 128) The eccentricity of the ellipse\[4{{x}^{2}}+9{{y}^{2}}+8x+36y+4=0\]is:
A)
\[5/6\]
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B)
\[3/5\]
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C)
\[\sqrt{2}/3\]
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D)
\[\sqrt{5}/3\]
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question_answer 129) The angle of intersection of the curves\[{{y}^{2}}=2x/\pi \]and\[y=\sin x\]is:
A)
\[{{\cot }^{-1}}(-1/\pi )\]
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B)
\[{{\cot }^{-1}}\pi \]
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C)
\[{{\tan }^{-1}}(-\pi )\]
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D)
\[{{\cot }^{-1}}\left( \frac{1}{\pi } \right)\]
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question_answer 130) The projection of any line on coordinate axes be respectively \[3,\,\,\,4,\,\,\,5,\] then its length is:
A)
\[12\]
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B)
\[50\]
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C)
\[5\sqrt{2}\]
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D)
none of these
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question_answer 131) If the direction ratios of a line are \[1,\,\,-3,\,\,2,\] then the direction cosines of the line are :
A)
\[\frac{1}{\sqrt{14}},\,\,\frac{-3}{\sqrt{14}},\,\,\frac{2}{\sqrt{14}}\]
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B)
\[\frac{1}{\sqrt{14}},\,\,\frac{2}{\sqrt{14}},\,\,\frac{3}{\sqrt{14}}\]
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C)
\[\frac{-1}{\sqrt{14}},\,\,\frac{3}{\sqrt{14}},\,\frac{-2}{\sqrt{14}}\]
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D)
\[\frac{-1}{\sqrt{14}},\,\,\frac{-2}{\sqrt{14}},\,\,\frac{-3}{\sqrt{14}}\]
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question_answer 132) The area of triangle whose vertices are\[A(1,\,\,-1,\,\,2),\,\,\,B(2,\,\,1,\,\,-1)\]and\[C(3,\,\,-1,\,\,2)\]is:
A)
\[13\,\,sq\,\,unit\]
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B)
\[\sqrt{13}\,\,sq\,\,unit\]
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C)
\[56\,\,sq\,\,unit\]
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D)
\[\sqrt{6}\,\,sq\,\,unit\]
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question_answer 133) \[|(\overset{\to }{\mathop{\mathbf{a}}}\,\times \overset{\to }{\mathop{\mathbf{b}}}\,)\cdot \overset{\to }{\mathop{\mathbf{c}}}\,|=|\overset{\to }{\mathop{\mathbf{a}}}\,||\overset{\to }{\mathop{\mathbf{b}}}\,||\overset{\to }{\mathop{\mathbf{c}}}\,|\]if:
A)
\[\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,=\overset{\to }{\mathop{\mathbf{b}}}\,\cdot \overset{\to }{\mathop{\mathbf{c}}}\,=0\]
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B)
\[\overset{\to }{\mathop{\mathbf{b}}}\,\cdot \overset{\to }{\mathop{\mathbf{c}}}\,=\overset{\to }{\mathop{\mathbf{c}}}\,\cdot \overset{\to }{\mathop{\mathbf{a}}}\,=0\]
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C)
\[\overset{\to }{\mathop{\mathbf{c}}}\,\cdot \overset{\to }{\mathop{\mathbf{a}}}\,=\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,=0\]
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D)
\[\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,=\overset{\to }{\mathop{\mathbf{b}}}\,\cdot \overset{\to }{\mathop{\mathbf{c}}}\,=\overset{\to }{\mathop{\mathbf{c}}}\,\cdot \overset{\to }{\mathop{\mathbf{a}}}\,=0\]
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question_answer 134) The angle between the vectors \[(2\widehat{\mathbf{i}}+6\widehat{\mathbf{j}}+3\widehat{\mathbf{k}})\] and\[(12\widehat{\mathbf{i}}-4\widehat{\mathbf{j}}+3\widehat{\mathbf{k}})\]is:
A)
\[{{\cos }^{-1}}\left( \frac{1}{10} \right)\]
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B)
\[{{\cos }^{-1}}\left( \frac{9}{11} \right)\]
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C)
\[{{\cos }^{-1}}\left( \frac{9}{91} \right)\]
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D)
\[{{\cos }^{-1}}\left( \frac{1}{9} \right)\]
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question_answer 135) Domain of the function\[\sin \log \left( \frac{\sqrt{4-{{x}^{2}}}}{1-x} \right)\]is:
A)
\[[-2,\,\,1]\]
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B)
\[(-2,\,\,1)\]
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C)
\[[-2,\,\,1)\]
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D)
\[(-2,\,\,1]\]
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question_answer 136) If\[f(9)=9,\,\,f'(9)=4\]and\[\underset{x\to 9}{\mathop{\lim }}\,\frac{f(x)-9}{x-9}=4\]then \[\underset{x\to 9}{\mathop{\lim }}\,\frac{\sqrt{f(x)}-3}{\sqrt{x}-3}\]is equal to:
A)
\[2\]
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B)
\[4\]
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C)
\[-2\]
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D)
\[-4\]
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question_answer 137) Let \[f(x)\] be defined for all \[x>0\] and be continuous, let \[f(x)\] satisfy\[f\left( \frac{x}{y} \right)=f(x)-f(y)\]for all \[x,\,\,y,\] then:
A)
\[f(x)=\log x\]
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B)
\[f(x)\]is bounded
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C)
\[f\left( \frac{1}{2} \right)\to 0\]as\[x\to 0\]
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D)
\[x\,\,f(x)\to 1\]as\[x\to 0\]
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question_answer 138) The domain of the function\[y=\frac{1}{\sqrt{|x|-x}}\]is:
A)
\[(-\infty ,\,\,0)\]
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B)
\[(+\infty ,\,\,0)\]
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C)
\[(-\infty ,\,\,-1)\]
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D)
\[(-\infty ,\,\,\infty )\]
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question_answer 139) Differential coefficient of \[{{\sin }^{-1}}\frac{1-x}{1+x}\] with respect to\[\sqrt{x}\]is:
A)
\[\frac{1}{2\sqrt{x}}\]
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B)
\[\frac{\sqrt{x}}{\sqrt{1-x}}\]
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C)
\[1\]
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D)
none of these
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question_answer 140) The number that exceeds its square by the greatest number is:
A)
\[-1\]
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B)
\[0\]
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C)
\[\frac{1}{2}\]
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D)
\[1\]
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question_answer 141) \[\int{\frac{{{\sin }^{8}}x-{{\cos }^{8}}x}{1-2{{\sin }^{2}}x{{\cos }^{2}}x}dx}\]is equal to:
A)
\[\sin 2x+c\]
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B)
\[-\frac{1}{2}\sin 2x+c\]
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C)
\[\frac{1}{2}\sin 2x+c\]
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D)
\[-\sin 2x+c\]
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question_answer 142) If\[f(x)=A\sin \left( \frac{\pi x}{2} \right)+B,\,\,\,f'\left( \frac{1}{2} \right)=\sqrt{2}\]and\[\int_{0}^{1}{f(x)}dx=\frac{2A}{\pi }\], then the constants \[A\] and \[B\] are respectively:
A)
\[\frac{\pi }{2}\]and\[\frac{\pi }{2}\]
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B)
\[\frac{2}{\pi }\]and\[\frac{3}{\pi }\]
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C)
\[\frac{4}{\pi }\]and\[0\]
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D)
\[0\]and\[\frac{-4}{\pi }\]
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question_answer 143) Let\[f(x)=x-[x]\]for all real number, where\[[x]\]is the integral part of\[x\], then\[\int_{-1}^{1}{f(x)}dx\]is equal to:
A)
\[1\]
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B)
\[2\]
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C)
\[0\]
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D)
\[1/2\]
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question_answer 144) A solution of the differential equation\[{{\left( \frac{dy}{dx} \right)}^{2}}-x\frac{dy}{dx}+y=0\]is:
A)
\[y=2\]
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B)
\[y=2x\]
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C)
\[y=2x-4\]
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D)
\[y=2{{x}^{2}}-4\]
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question_answer 145) If \[A\] and \[B\] are two independent events, then \[P(A+B)\] is equal to:
A)
\[P(A)+P(B)-P(A)P(B)\]
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B)
\[P(A)-P(B)\]
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C)
\[P(A)+P(B)\]
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D)
\[P(A)+P(B)+P(A)P(B)\]
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question_answer 146) A bag contains \[6\] red, \[5\] white and \[4\] black balls, two balls are drawn the probability that none of them is red, is:
A)
\[12/35\]
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B)
\[6/35\]
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C)
\[4/35\]
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D)
none of these
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question_answer 147) If\[P(A)=0.65,\,\,P(B)=0.15\], then\[P(\bar{A})+P(\bar{B})\]is equal to:
A)
\[1.5\]
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B)
\[1.2\]
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C)
\[0.8\]
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D)
none of these
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question_answer 148) If the regression equations of the variables \[x\]and \[y\] be \[x=19.13-0.83y\] and\[y=11.64-0.50x\], then the correlation coefficient between x and y is:
A)
\[0.66\]
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B)
\[-0.64\]
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C)
\[0.001\]
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D)
\[-0.001\]
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question_answer 149) The roots of \[x+{{\log }_{10}}x=3.375\] is approximately:
A)
\[2.09\]
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B)
\[2.909\]
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C)
\[2.990\]
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D)
\[3.003\]
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question_answer 150) After second iteration of Newton-Raphson method, the positive root of equation \[{{x}^{2}}=3\](taking initial approximation\[\frac{3}{2}):\]
A)
\[3/2\]
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B)
\[7/4\]
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C)
\[97/56\]
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D)
\[347/200\]
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