question_answer 1) A rectangular coil of 100 turns and size \[0.1\times 0.05\] m is placed perpendicular to a magnetic field of 0.1 T. The induced emf when the field drops to 0.05 T in 0.05 s is
A)
0.5 V
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B)
1.0 V
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C)
1.5 V
done
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D)
2.0 V
done
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question_answer 2) A paramagnetic substance is placed in a weak magnetic field and its absolute temperature T is increased. As a result, its magnetization
A)
increases in proportion to T
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B)
decreases in proportion to \[\frac{1}{T}\]
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C)
increases in proportion to\[{{T}^{2}}\]
done
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D)
decreases in proportion to \[\frac{1}{{{T}^{2}}}\]
done
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question_answer 3) The current through n bulb is increased by. Assuming that the resistance of the filament remains unchanged the power of the bulb will
A)
increase by 1%
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B)
decrease by 1%
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C)
increase by 2%
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D)
decrease by 2%
done
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question_answer 4) You are given two resistances \[{{R}_{1}}\] and\[{{R}_{2}}\] By using them singly in series and In parallel you can obtain four resistances of \[1.5\,\Omega ,\,2\,\Omega ,\,6\,\Omega \] and 8 \[\Omega .\] The values of \[{{R}_{1}}\] and \[{{R}_{2}}\] are
A)
\[1\,\,\Omega ,\,7\,\Omega \]
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B)
\[1.5\,\,\Omega ,\,6.5\,\Omega \]
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C)
\[3\,\,\Omega ,\,5\,\Omega \]
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D)
\[2\,\,\Omega ,\,6\,\Omega \]
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question_answer 5) A wire often the \[l\] carrying a current \[I\] A is bent into a circle. The magnitude of the magnetic moment is
A)
\[\frac{l{{I}^{2}}}{2\pi }\]
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B)
\[\frac{l{{I}^{2}}}{4\pi }\]
done
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C)
\[\frac{{{l}^{2}}I}{2\pi }\]
done
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D)
\[\frac{{{l}^{2}}I}{4\pi }\]
done
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question_answer 6) A parallel beam of white light is reflected from a thin wedge-shaped film. The colour of the fringe the edge of the wedge will be
A)
white
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B)
red
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C)
black
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D)
violet
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question_answer 7) An object is placed at the focus of a convex mirror. If its focal length is 20 cm, the distance of mirror is
A)
20 cm
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B)
10 cm
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C)
40 cm
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D)
None of these
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question_answer 8) A convex lens of glass (\[\mu =1\] of 8 cm when place in has a focal length of lens when air. What is the focal \[\left( \mu =\frac{4}{3} \right)?\]
A)
\[4cm\]
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B)
\[8\,cm\]
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C)
\[16\,cm\]
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D)
\[32\,cm\]
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question_answer 9) An LCR series circuit, connected to a source E, is resonance. Then
A)
the voltage across R is zero
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B)
the voltage across R equals applied voltage
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C)
the voltage across C is zero
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D)
the voltage across L equals applied voltage
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question_answer 10) What will be the colour of the sky as seen from the earth if there were no atmosphere?
A)
Black
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B)
Blue
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C)
Orange
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D)
Red
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question_answer 11) In a single slit diffraction experiment, the width of the slit is made double its original width. Then the central maximum on the diffraction pattern will become
A)
narrower and fainter
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B)
narrower and brighter
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C)
broader and fainter
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D)
broader and brighter
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question_answer 12) An \[\alpha -\]particle and a deuteron projected with equal kinetic energies describe circular paths or radii \[{{r}_{1}}\] and\[{{r}_{2}}\] respectively in a uniform magnetic field. The ratio\[{{\text{r}}_{\text{1}}}\text{/}{{\text{r}}_{\text{2}}}\] is
A)
1
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B)
2
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C)
\[\frac{1}{\sqrt{2}}\]
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D)
\[\sqrt{2}\]
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question_answer 13) The energy in monochromatic X-rays of wavelength \[1\,\overset{\text{o}}{\mathop{\text{A}}}\,\] is roughly equal to
A)
\[\text{2 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-15}}}\text{J}\]
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B)
\[\text{2 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-16}}}\text{J}\]
done
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C)
\[\text{2 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-17}}}\text{J}\]
done
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D)
\[\text{2 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-18}}}\text{J}\]
done
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question_answer 14) The de-Broglie wavelength of a neutron at 927°C is \[\lambda \]. What will be its wavelength at 27°C?
A)
\[\frac{\lambda }{2}\]
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B)
\[\lambda \]
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C)
\[2\lambda \]
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D)
None of these
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question_answer 15) A telescope has an objective of focal length 100 cm and an eye-piece of focal length 5 cm. What is the magnifying power of the telescope when it is in normal adjustment?
A)
0.2
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B)
2.0
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C)
20
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D)
200
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question_answer 16) An isotropic source of 2 candela produces a light flux equal to
A)
\[2\pi \] lumen
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B)
\[4\pi \] lumen
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C)
\[6\pi \] lumen
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D)
\[8\pi \] lumen
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question_answer 17) No photoelectrons are emitted from a metal if the wavelength of the light exceeds 600 nm. The work function of the metal is approximately equal to
A)
\[\text{3 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-16}}}\text{J}\]
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B)
\[\text{3 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-19}}}\text{J}\]
done
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C)
\[\text{3 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-20}}}\text{J}\]
done
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D)
\[\text{3 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-22}}}\text{J}\]
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question_answer 18) In Rutherfords\[\alpha -\]particle experiment with thin gold foil, 8100 scintillations per minute are observed at an angle of 60°. The number of scintillations per minute at an angle of 120° will be
A)
900
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B)
2025
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C)
32400
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D)
4050
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question_answer 19)
Which of the following gates has the truth table
A
B
X
0
0
1
1
0
1
0
1
1
1
1
0
A)
NAND
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B)
NOR
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C)
XOR
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D)
AND
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question_answer 20) Which of the junction diodes shown below are forward biased?
A)
done
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B)
done
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C)
done
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D)
done
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question_answer 21) A uniform rod or mass m and length l is held \[{{60}^{\text{o}}}\] with the vertical. . What will be the potential this position?
A)
Zero
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B)
\[\frac{mgl}{4}\]
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C)
\[\frac{mgl}{2}\]
done
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D)
\[mgl\]
done
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question_answer 22) A sphere roils down an inclined plane without slipping. What fraction of its total energy is rotational?
A)
\[\frac{2}{7}\]
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B)
\[\frac{3}{7}\]
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C)
\[\frac{4}{7}\]
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D)
\[\frac{5}{7}\]
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question_answer 23) 23. From the top of a building 40 m tall, a boy projects a Stone vertically upwards with an initial velocity \[10\,m{{s}^{-1}}\] such that it eventually falls to the ground. After how long will the stone strike the ground? Take \[g=10\,m{{s}^{-2}}\]
A)
1 s
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B)
2 s
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C)
3 s
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D)
4 s
done
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question_answer 24) A 150 m long train is travelling from east to west at a speed of \[20\,m{{s}^{-1}}\]. A bird is flying from west to east at a speed of \[5\,m{{s}^{-1}}\]. How long wilt the bird take to cross the train?
A)
6 s
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B)
7.5 s
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C)
10 s
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D)
30 s
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question_answer 25) An elastic spring has a length \[{{l}_{1}}\] when it is stretched with a force of 2 N and a length of \[{{l}_{2}}\] when it is stretched with a force of 3N. What will be the length of the spring if it is stretched with force of 5N?
A)
\[(l{{ }_{1}}+{{l}_{2}})\]
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B)
\[\frac{1}{2}(l{{ }_{1}}+{{l}_{2}})\]
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C)
\[(3l{{ }_{2}}-2{{l}_{1}})\]
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D)
\[(3l{{ }_{1}}-2{{l}_{2}})\]
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question_answer 26) The density of water at the surface of ocean is \[\rho \] If the bulk modulus of water is B, what is the density of ocean water at a depth where the pressure is\[n{{p}_{0,}}\] where\[{{p}_{0,}}\] is the atmospheric pressure?
A)
\[\frac{\rho B}{B-(n-1){{P}_{0}}}\]
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B)
\[\frac{\rho B}{B+(n-1)P0}\]
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C)
\[\frac{\rho B}{B-n{{P}_{0}}}\]
done
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D)
\[\frac{\rho B}{B+n{{P}_{0}}}\]
done
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question_answer 27) What is the torque of force \[\mathbf{\hat{F}}=-3\mathbf{\hat{i}}+\mathbf{\hat{j}}+5\mathbf{\hat{k}}\] acting at point whose position vector is\[\mathbf{\vec{r}}=7\mathbf{\hat{i}}+3\mathbf{\hat{j}}+\mathbf{\hat{k}}?\]
A)
\[14\mathbf{\hat{i}}-38\mathbf{\hat{j}}+16\mathbf{\hat{k}}\]
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B)
\[4\mathbf{\hat{i}}+4\mathbf{\hat{j}}+6\mathbf{\hat{k}}\]
done
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C)
\[-14\mathbf{\hat{i}}+38\mathbf{\hat{j}}-6\mathbf{\hat{k}}\]
done
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D)
\[-21\mathbf{\hat{i}}+3\mathbf{\hat{j}}+5\mathbf{\hat{k}}\]
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question_answer 28) Two satellites of masses 3M and M orbit the earth in circular orbits of radii r and 3r respectively. The ratio of their speeds is
A)
1 : 1
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B)
\[\sqrt{3}\]: 1
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C)
3 : 1
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D)
9 : 1
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question_answer 29) The dimensions of Reynoldss constant are
A)
\[\text{ }\!\![\!\!\text{ }{{\text{M}}^{\text{o}}}{{\text{L}}^{\text{o}}}{{\text{T}}^{\text{o}}}\text{ }\!\!]\!\!\text{ }\]
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B)
\[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{-1}}{{\text{T}}^{-1}}\text{ }\!\!]\!\!\text{ }\]
done
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C)
\[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{-1}}{{\text{T}}^{-2}}\text{ }\!\!]\!\!\text{ }\]
done
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D)
\[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{-2}}{{\text{T}}^{-2}}\text{ }\!\!]\!\!\text{ }\]
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question_answer 30) The surface tension of soap solution is \[\sigma \]. What is the work done in blowing soap bubble of radius r?
A)
\[\pi {{r}^{2}}\sigma \]
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B)
\[2\pi {{r}^{2}}\sigma \]
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C)
\[4\pi {{r}^{2}}\sigma \]
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D)
\[8\pi {{r}^{2}}\sigma \]
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question_answer 31) The ratio of nns speed of \[{{O}_{2}}\] to \[{{H}_{2}}\] is
A)
\[\frac{1}{4}\]
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B)
4
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C)
2
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D)
\[\frac{1}{2}\]
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question_answer 32) Two rods A and B of different materials are welded together as shown in figure. If their thermal conductivities are \[{{K}_{1}}\] and\[{{K}_{2}}\] the thermal conductivity of the composite rod will be
A)
\[2({{K}_{1}}+{{K}_{2}})\]
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B)
\[\frac{3}{2}({{K}_{1}}+{{K}_{2}})\]
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C)
\[({{K}_{1}}+{{K}_{2}})\]
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D)
\[\frac{1}{2}({{K}_{1}}+{{K}_{2}})\]
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question_answer 33) The wavelength of the radiation emitted by a body depends upon
A)
the nature of its surface
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B)
the area of its surface
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C)
the temperature of its surface
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D)
All the above factors
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question_answer 34)
An ideal monoatomic gas is taken around the cycle ABCDA as shown in the p- V diagram. The work done during the cycle is given by
A)
\[\frac{1}{2}pV\]
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B)
\[pV\]
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C)
\[2pV\]
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D)
\[4pV\]
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question_answer 35) An ideal gas at pressure p is adiabaticalty compressed so that its density becomes n times the initial value. The final pressure of the gas will be\[\left( \gamma =\frac{{{C}_{P}}}{{{C}_{V}}} \right)\]
A)
\[{{n}^{\gamma }}P\]
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B)
\[{{n}^{-\gamma }}P\]
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C)
\[{{n}^{(-\gamma -1)}}P\]
done
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D)
\[{{n}^{(1-\gamma )}}P\]
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question_answer 36) The displacement of a travelling wave is given by\[y=2\,\cos \,2\pi \,(10t-\,0.008\,x\,+\,.35)\] where, x and y are in centimetre and t in second. What is the phase difference between oscillatory motion at two points separated by a distance of 4 m?
A)
\[2\pi \]
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B)
\[4\pi \]
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C)
\[6\pi \]
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D)
\[8\pi \]
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question_answer 37) A bimetallic strip consists of brass and iron when it is heated it bends into an arc with brass on the convex and iron on the concave side of the arc. This happens because
A)
brass has a higher specific heat capacity than iron
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B)
density of brass is more than that of iron
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C)
it is easier to bend an iron strip than a brass strip of the same size
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D)
brass has a higher coefficient of linear expansion than iron
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question_answer 38) Three sound waves of equal amplitudes have frequencies (v -1), v, (v + 1). They superpose to give beats. The number of beats produced per second will be
A)
v
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B)
v/2
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C)
2
done
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D)
1
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question_answer 39) Which of the following functions does not represent a stationary wave? Here a, b and c are constants.
A)
\[y=a\,\cos bx\,\sin ct\]
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B)
\[y=a\sin bx\,\cos \,ct\]
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C)
\[y=a\,\sin (bx+ct)\]
done
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D)
\[y=a\sin (bx+ct)\,+a\,\sin \,(bx-ct)\]
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question_answer 40) The velocity of sound is greatest in
A)
water
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B)
air
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C)
vacuum
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D)
steel
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question_answer 41) Due to Doppler effect, the shift in wavelength observed is \[0.1\,\overset{\text{o}}{\mathop{\text{A}}}\,,\] for a star producing wavelength \[6000\overset{\text{o}}{\mathop{\text{A}}}\,\]. The velocity of recession of star will be
A)
\[2.5\,km{{s}^{-1}}\]
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B)
\[10\,km{{s}^{-1}}\]
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C)
\[5\,km{{s}^{-1}}\]
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D)
\[20\,km{{s}^{-1}}\]
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question_answer 42) A body executing linear simple harmonic motion has a velocity of \[3\,m{{s}^{-1}}\] when its displacement is 4 cm and a velocity of \[4\,m{{s}^{-1}}\] when its displacement is 3 cm. What is the amplitude of oscillation?
A)
5 cm
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B)
7.5 cm
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C)
10 cm
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D)
12.5 cm
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question_answer 43) Two masses \[{{m}_{1}}\] and\[{{m}_{2}}\] are suspended together by a massless spring of force constant k, as shown in figure. When the masses are in equilibrium, mass \[{{m}_{1}}\]is removed without disturbing the system. The angular frequency of oscillation of mass \[{{m}_{2}}\] is
A)
\[\sqrt{\frac{k}{{{m}_{2}}}}\]
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B)
\[\sqrt{\frac{k}{{{m}_{1}}}}\]
done
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C)
\[\sqrt{\frac{k{{m}_{1}}}{m\,_{2}^{2}}}\]
done
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D)
\[\sqrt{\frac{k{{m}_{2}}}{m_{1}^{2}\,}}\]
done
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question_answer 44) The intensity level of a sound wave is defined by an arbitrary scale. The zero of the scale is taken at the sound wave intensity
A)
\[\text{1 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-10}}}\,\text{W}{{\text{m}}^{\text{-2}}}\]
done
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B)
\[\text{1 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-12}}}\,\text{W}{{\text{m}}^{\text{-2}}}\]
done
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C)
\[\text{1 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-14}}}\,\text{W}{{\text{m}}^{\text{-2}}}\]
done
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D)
\[\text{1 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-16}}}\,\text{W}{{\text{m}}^{\text{-2}}}\]
done
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question_answer 45) A pendulum bob of mass m carrying a charge q is at rest with its string making an angle \[\theta \] with the vertical in a uniform horizontal electric field E. The tension in the siring is
A)
\[\frac{\text{mg}}{\text{sin}}\text{and}\frac{\text{qE}}{\text{cos}\,}\]
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B)
\[\frac{\text{mg}}{\text{cos}}\text{and}\frac{\text{qE}}{\sin \,}\]
done
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C)
\[\frac{\text{qE}}{mg}\]
done
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D)
\[\frac{mg}{\text{qE}}\]
done
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question_answer 46) A galvanometer of resistance 10 \[\Omega \] gives full-scale deflection when 1 mA current passes through it. The resistance required to convert it into a voltmeter reading upto 2.5 V is
A)
\[24.9\,\Omega \]
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B)
\[249\,\Omega \]
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C)
\[2490\,\Omega \]
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D)
\[24900\,\Omega \]
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question_answer 47) The current inside an electrolytic cell is carried by
A)
positive ions
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B)
negative ions
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C)
both positive and negative ions
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D)
electrons
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question_answer 48) The electric potential V (in volt) varies with x (in metre) according to the relation \[V=(5+4{{x}^{2}})\]. The force experienced by a negative charge of 2x10-6C located at a =0.5 m is
A)
\[\text{2 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-6}}}\text{N}\]
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B)
\[\text{4 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-6}}}\text{N}\]
done
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C)
\[\text{6 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-6}}}\text{N}\]
done
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D)
\[\text{8 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-6}}}\text{N}\]
done
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question_answer 49) A parallel plate capacitor of plate area A has a charge Q. The force on each plate of the capacitor is
A)
\[\frac{2{{Q}^{2}}}{{{\varepsilon }_{0}}A}\]
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B)
\[\frac{{{Q}^{2}}}{{{\varepsilon }_{0}}A}\]
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C)
\[\frac{{{Q}^{2}}}{2{{\varepsilon }_{0}}A}\]
done
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D)
Zero
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question_answer 50) In Millikans oil drop experiment, an oil drop is observed to move vertically upwards. The upward motion of the drop is due to
A)
gravity
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B)
viscosity
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C)
buoyancy
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D)
electric field
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question_answer 51) Which one of these is an important polysaccharide present in plants?
A)
Glucose
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B)
Glycogen
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C)
Sucrose
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D)
Starch
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question_answer 52) Cannizaro reaction would be given by
A)
\[{{C}_{6}}{{H}_{5}}CHO\]
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B)
\[C{{H}_{3}}COC{{H}_{3}}\]
done
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C)
\[C{{H}_{3}}CHO\]
done
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D)
\[{{C}_{2}}{{H}_{5}}CO{{C}_{2}}{{H}_{5}}\]
done
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question_answer 53) \[C{{H}_{3}}C\equiv CH\xrightarrow[+H{{g}^{2+}},60{{\,}^{o}}C]{{{H}_{2}}S{{O}_{4}}}\]?
A)
\[C{{H}_{3}}CHO\]
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B)
\[C{{H}_{3}}COOH\]
done
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C)
\[C{{H}_{3}}COC{{H}_{3}}\]
done
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D)
\[C{{H}_{3}}C{{H}_{2}}COOH\]
done
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question_answer 54) In which of the following can peroxide effect operate?
A)
\[C{{H}_{3}}C{{H}_{2}}CH=C{{H}_{2}}+HCl\]
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B)
\[C{{H}_{3}}C{{H}_{2}}CH=C{{H}_{2}}+HBr\]
done
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C)
\[C{{H}_{3}}CH=CH.C{{H}_{3}}+HBr\]
done
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D)
\[C{{H}_{3}}C{{H}_{2}}CH=C{{H}_{2}}+HI\]
done
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question_answer 55) The term quaternary structure is used in the context of
A)
carbohydrates
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B)
vitamins
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C)
proteins
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D)
nucleic acids
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question_answer 56) Aspirin is
A)
antibiotic
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B)
sedative
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C)
tranquilizer
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D)
antipyretic
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question_answer 57) The following is a coordination compound of iron
A)
chlorophyll
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B)
Mohrs salt
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C)
haemoglobin
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D)
vitamin \[{{B}_{12}}\]
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question_answer 58) This metal is extracted from its ore by formation of a cyanide complex
A)
\[Ag\]
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B)
\[Cu\]
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C)
\[Al\]
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D)
\[Zn\]
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question_answer 59) Smoke is an example of
A)
emulsion
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B)
aerosol
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C)
gel
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D)
foam
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question_answer 60) Propan-2-ol + ethanoic acid\[\xrightarrow{{}}\]
A)
\[{{(C{{H}_{3}})}_{2}}CHCOOC{{H}_{3}}\]
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B)
\[C{{H}_{3}}COOCH{{(C{{H}_{3}})}_{2}}\]
done
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C)
\[C{{H}_{3}}COOC{{H}_{2}}C{{H}_{3}}\]
done
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D)
\[{{(C{{H}_{3}})}_{2}}CHCOOC{{H}_{2}}C{{H}_{3}}\]
done
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question_answer 61) Which of the following gives RNC when treated with \[CHC{{l}_{3}}\]and KOH?
A)
\[RN{{H}_{2}}\]
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B)
\[{{R}_{2}}NH\]
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clear
C)
\[{{R}_{4}}{{N}^{+}}C{{l}^{-}}\]
done
clear
D)
\[{{R}_{3}}N\]
done
clear
View Answer play_arrow
question_answer 62) Which of the following is a soap?
A)
Sodium acetate
done
clear
B)
Magnesium butyrate
done
clear
C)
Sodium palmitate
done
clear
D)
Palmitic acid
done
clear
View Answer play_arrow
question_answer 63) The C-C bond dissociation energy in kcal/mol is
A)
8.1
done
clear
B)
0.81
done
clear
C)
81
done
clear
D)
810
done
clear
View Answer play_arrow
question_answer 64) A compound has four \[s{{p}^{3}}\]hybridized covalent bonds. Its shape is
A)
linear
done
clear
B)
square planar
done
clear
C)
octahedral
done
clear
D)
tetrahedral
done
clear
View Answer play_arrow
question_answer 65) The resonance energy of benzene in kcal/mol is about
A)
\[\approx 20\]
done
clear
B)
\[\approx 40\]
done
clear
C)
\[\approx 60\]
done
clear
D)
\[\approx 80\]
done
clear
View Answer play_arrow
question_answer 66) 1 mole of \[\text{C}{{\text{O}}_{\text{2}}}\]contains
A)
\[6\times {{10}^{23}}\]atoms of C
done
clear
B)
\[6\times {{10}^{23}}\]atoms of O
done
clear
C)
\[18\times {{10}^{23}}\]molecules of \[C{{O}_{2}}\]
done
clear
D)
3 g-atoms of \[C{{O}_{2}}\]
done
clear
View Answer play_arrow
question_answer 67) Rutherfords famous experiment with \[\alpha -\]particles used this metal
A)
Ni
done
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B)
Au
done
clear
C)
Fe
done
clear
D)
Zn
done
clear
View Answer play_arrow
question_answer 68) The charge on an electron in Coulombs is
A)
\[1.602\times {{10}^{-19}}\]
done
clear
B)
\[1.062\times {{10}^{-19}}\]
done
clear
C)
\[1.620\times {{10}^{-19}}\]
done
clear
D)
\[1.006\times {{10}^{-19}}\]
done
clear
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question_answer 69) The number of subshells for a shell with principal quantum number \[n\] is
A)
\[n\]
done
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B)
\[~n+1\]
done
clear
C)
\[n-1\]
done
clear
D)
\[2{{n}^{2}}\]
done
clear
View Answer play_arrow
question_answer 70) Which of the following pairs of atomic numbers represents s-block elements?
A)
7, 15
done
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B)
6, 12
done
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C)
9, 17
done
clear
D)
3, 11
done
clear
View Answer play_arrow
question_answer 71) For a system in equilibrium
A)
\[\Delta G=0\]
done
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B)
\[\Delta G>0\]
done
clear
C)
\[\Delta G<0\]
done
clear
D)
\[\Delta H=0\]
done
clear
View Answer play_arrow
question_answer 72) Which of the following will produce the highest rise in temperature?
A)
\[\text{64}\,\text{mL}\,\text{1M}\,\text{NaOH}\,\text{+}\,\text{33}\,\text{mL}\]of \[\text{0}\text{.5}\,\text{M}\,{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]
done
clear
B)
\[\text{33}\,\text{mL}\]of \[\text{1}\,\text{M}\,\text{NaOH}\,\text{+}\,\text{67}\,\text{mL}\,\]of \[\text{0}\text{.5}\,\text{M}\,{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]
done
clear
C)
\[\text{40}\,\text{mL}\]of \[\text{1}\,\text{M}\,\text{NaOH}\,\text{+}\,\text{60}\,\text{mL}\]of \[\text{0}\text{.5}\,\text{M}\,{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]
done
clear
D)
\[\text{50}\,\text{mL}\]of \[\text{1}\,\text{M}\,\text{NaOH}\,\text{+}\,\text{50}\,\text{mL}\]of \[\text{0}\text{.5}\,\text{M}\,{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]
done
clear
View Answer play_arrow
question_answer 73) The standard for atomic mass is
A)
\[_{1}^{1}H\]
done
clear
B)
\[_{6}^{12}C\]
done
clear
C)
\[_{6}^{14}C\]
done
clear
D)
\[_{8}^{16}O\]
done
clear
View Answer play_arrow
question_answer 74) Which of the following involves absorption of energy?
A)
\[Cl+{{e}^{-}}\xrightarrow{{}}C{{l}^{-}}\]
done
clear
B)
\[{{O}^{-}}+{{e}^{-}}\xrightarrow{{}}{{O}^{2-}}\]
done
clear
C)
\[O+{{e}^{-}}\xrightarrow{{}}{{O}^{-}}\]
done
clear
D)
\[S+{{e}^{-}}\xrightarrow{{}}{{S}^{-}}\]
done
clear
View Answer play_arrow
question_answer 75) The successive ionization energies of an element are 800, 2,000, 3,600, 25,000 and 32,000 kJ/mol. The number of valence electrons are
A)
5
done
clear
B)
2
done
clear
C)
3
done
clear
D)
4
done
clear
View Answer play_arrow
question_answer 76) The first order rate constant for the decomposition of \[{{\text{N}}_{\text{2}}}{{\text{O}}_{\text{5}}}\]is \[6.2\times {{10}^{-4}}{{s}^{-1}}.\] The half-life in seconds is nearly
A)
1117.7
done
clear
B)
111.7
done
clear
C)
223
done
clear
D)
160
done
clear
View Answer play_arrow
question_answer 77) The rate constant of a reaction is \[1\times {{10}^{-2}}mo{{l}^{-2}}{{L}^{2}}{{s}^{-1}}.\] The order of the reaction is
A)
0
done
clear
B)
1
done
clear
C)
2
done
clear
D)
3
done
clear
View Answer play_arrow
question_answer 78) The oxidation number of O in \[\text{O}{{\text{F}}_{\text{2}}}\]is
A)
\[-2\]
done
clear
B)
\[+\,1\]
done
clear
C)
\[+\,2\]
done
clear
D)
\[-1\]
done
clear
View Answer play_arrow
question_answer 79) The correct relationship is
A)
\[{{K}_{C}}=n\times {{K}_{p}}\]
done
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B)
\[{{K}_{p}}={{K}_{C}}{{(RT)}^{\Delta {{n}_{g}}}}\]
done
clear
C)
\[{{K}_{p}}=n\times {{K}_{C}}\]
done
clear
D)
\[{{K}_{C}}-{{K}_{p}}={{(RT)}^{\Delta N}}\]
done
clear
View Answer play_arrow
question_answer 80) W. For the reaction, \[2B+AC,\] the equilibrium constant is
A)
\[\frac{[A]{{[B]}^{3}}}{[C]}\]
done
clear
B)
\[\frac{[C]}{[A][2B]}\]
done
clear
C)
\[\frac{[C]}{[A]{{[B]}^{2}}}\]
done
clear
D)
\[\frac{[A][B]}{[C]}\]
done
clear
View Answer play_arrow
question_answer 81) A buffer contains equal concentrations of \[{{X}^{-}}\] and HX. The \[{{K}_{a}}\]for HX is \[{{10}^{-8}}.\] The pH of the buffer is
A)
3
done
clear
B)
8
done
clear
C)
7
done
clear
D)
11
done
clear
View Answer play_arrow
question_answer 82) The metal which gives \[{{\text{H}}_{\text{2}}}\]on treatment with acid as well as \[NaOH\] is
A)
Fe
done
clear
B)
Cu
done
clear
C)
Zn
done
clear
D)
Hg
done
clear
View Answer play_arrow
question_answer 83) Which is isoelectronic with hydride ion?
A)
He
done
clear
B)
\[\text{H}{{\text{e}}^{+}}\]
done
clear
C)
Li
done
clear
D)
\[{{H}^{+}}\]
done
clear
View Answer play_arrow
question_answer 84) A solution of Na in liquid\[\text{N}{{\text{H}}_{\text{3}}}\] is
A)
green
done
clear
B)
blue
done
clear
C)
pink
done
clear
D)
yellow
done
clear
View Answer play_arrow
question_answer 85) The oxide which gives \[{{\text{H}}_{\text{2}}}{{\text{O}}_{\text{2}}}\]on treatment with dilute acid is
A)
\[Pb{{O}_{2}}\]
done
clear
B)
\[Ti{{O}_{2}}\]
done
clear
C)
\[Mn{{O}_{2}}\]
done
clear
D)
\[N{{a}_{2}}{{O}_{2}}\]
done
clear
View Answer play_arrow
question_answer 86) During the electrolysis of fused \[NaCl,\] this happens at cathode
A)
oxidation of\[N{{a}^{+}}\]
done
clear
B)
reduction of\[N{{a}^{+}}\]
done
clear
C)
reduction of \[C{{l}^{-}}\]
done
clear
D)
oxidation of \[C{{l}^{-}}\]
done
clear
View Answer play_arrow
question_answer 87) Which of the following-s a colored gas?
A)
\[{{N}_{2}}O\]
done
clear
B)
\[NO\]
done
clear
C)
\[{{H}_{2}}\]
done
clear
D)
\[N{{O}_{2}}\]
done
clear
View Answer play_arrow
question_answer 88) This compound gives off \[{{\text{O}}_{\text{2}}}\]on moderate heating
A)
\[HgO\]
done
clear
B)
\[ZnO\]
done
clear
C)
\[CaO\]
done
clear
D)
\[A{{l}_{2}}{{O}_{3}}\]
done
clear
View Answer play_arrow
question_answer 89) Plaster of Paris is hardened by
A)
liberating \[C{{O}_{2}}\]
done
clear
B)
hydration
done
clear
C)
dehydration
done
clear
D)
changing into \[CaC{{O}_{3}}\]
done
clear
View Answer play_arrow
question_answer 90) The least ionic chloride is formed by
A)
Mg
done
clear
B)
Ca
done
clear
C)
Be
done
clear
D)
Sr
done
clear
View Answer play_arrow
question_answer 91) Aluminium bronze has
A)
90% Cu
done
clear
B)
50% Ni
done
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C)
90% Sn
done
clear
D)
50% Cu
done
clear
View Answer play_arrow
question_answer 92) In the thermite welding, this is used
A)
Ca
done
clear
B)
Al + Fe
done
clear
C)
Fe
done
clear
D)
\[Al+F{{e}_{2}}{{O}_{3}}\]
done
clear
View Answer play_arrow
question_answer 93) \[{{\text{K}}_{\text{2}}}\text{C}{{\text{O}}_{\text{3}}}\]cannot be prepared by Solvay-ammonia process because
A)
\[{{\text{K}}_{\text{2}}}\text{C}{{\text{O}}_{\text{3}}}\]is fairly soluble in water
done
clear
B)
it has no water of crystallization
done
clear
C)
\[\text{KHC}{{\text{O}}_{\text{3}}}\] is highly soluble in water
done
clear
D)
\[{{\text{K}}_{\text{2}}}\text{C}{{\text{O}}_{\text{3}}}\]decomposes in \[{{\text{H}}_{\text{2}}}\text{O}\]
done
clear
View Answer play_arrow
question_answer 94) Glaubers salt is
A)
\[N{{a}_{2}}S{{O}_{4}}.10{{H}_{2}}O\]
done
clear
B)
\[FeS{{O}_{4}}.7{{H}_{2}}O\]
done
clear
C)
\[ZnS{{O}_{4}}.7{{H}_{2}}O\]
done
clear
D)
\[MgS{{O}_{4}}.7{{H}_{2}}O\]
done
clear
View Answer play_arrow
question_answer 95) The salt responsible for permanent hardness of \[{{\text{H}}_{\text{2}}}\text{O}\]is
A)
\[N{{a}_{2}}S{{O}_{4}}\]
done
clear
B)
\[MgHC{{O}_{3}}\]
done
clear
C)
\[NaCl\]
done
clear
D)
\[MgC{{l}_{2}}\]
done
clear
View Answer play_arrow
question_answer 96) Which of the following carbonium ion is most stable?
A)
\[{{C}_{6}}{{H}_{5}}\overset{+}{\mathop{C}}\,{{H}_{2}}\]
done
clear
B)
\[{{(C{{H}_{3}})}_{3}}\overset{+}{\mathop{C}}\,\]
done
clear
C)
\[{{(C{{H}_{3}})}_{2}}\overset{+}{\mathop{C}}\,H\]
done
clear
D)
\[C{{H}_{3}}\overset{+}{\mathop{C}}\,{{H}_{2}}\]
done
clear
View Answer play_arrow
question_answer 97) Which of the following reacts in presence of anhydrpus \[\text{AlC}{{\text{l}}_{\text{3}}}\]to give acetophenone?
A)
\[{{C}_{6}}{{H}_{6}}+C{{H}_{3}}COC{{H}_{3}}\]
done
clear
B)
\[{{C}_{6}}{{H}_{5}}OH+C{{H}_{3}}COC{{H}_{3}}\]
done
clear
C)
\[{{C}_{6}}{{H}_{5}}OH+C{{H}_{3}}COOH\]
done
clear
D)
\[{{C}_{6}}{{H}_{6}}+C{{H}_{3}}COCl\]
done
clear
View Answer play_arrow
question_answer 98) The isomers which can be interconverted through rotation around a single bond are
A)
conformers
done
clear
B)
diastereoisomers
done
clear
C)
enantiomers
done
clear
D)
position isomers
done
clear
View Answer play_arrow
question_answer 99) Phenol is the component of this fraction upon fractional distillation of petroleum
A)
light oil
done
clear
B)
middle oil
done
clear
C)
heavy oil
done
clear
D)
pitch
done
clear
View Answer play_arrow
question_answer 100) Ethyl chloride on treatment with alcoholic alkali gives
A)
\[{{C}_{2}}{{H}_{6}}\]
done
clear
B)
\[C{{H}_{3}}CHO\]
done
clear
C)
\[{{C}_{2}}{{H}_{5}}OH\]
done
clear
D)
\[C{{H}_{2}}=C{{H}_{2}}\]
done
clear
View Answer play_arrow
question_answer 101) The area of the figure bounded by \[{{y}^{2}}=2x+1\] and \[x-y=1\]is
A)
\[\frac{2}{3}\]
done
clear
B)
\[\frac{4}{3}\]
done
clear
C)
\[\frac{8}{3}\]
done
clear
D)
\[\frac{11}{3}\]
done
clear
View Answer play_arrow
question_answer 102) The order of the differential equation of all tangent lines to the parabola \[y={{x}^{2}}\]is
A)
1
done
clear
B)
2
done
clear
C)
3
done
clear
D)
4
done
clear
View Answer play_arrow
question_answer 103) \[\int_{{}}^{{}}{\frac{dx}{\sqrt{(1-x)(x-2)}}}\]is equal to
A)
\[{{\sin }^{-1}}(2x-3)+C\]
done
clear
B)
\[{{\sin }^{-1}}(2x+5)+C\]
done
clear
C)
\[{{\sin }^{-1}}(3-2x)+C\]
done
clear
D)
\[{{\sin }^{-1}}(5-2x)+C\]
done
clear
View Answer play_arrow
question_answer 104) \[\int_{{}}^{{}}{\frac{({{\sec }^{2}}x-7)}{{{\sin }^{7}}x}}dx\]is equal to
A)
\[\frac{\tan x}{{{\sin }^{7}}x}+C\]
done
clear
B)
\[\frac{\cos x}{{{\sin }^{7}}x}+C\]
done
clear
C)
\[\frac{\sin x}{{{\cos }^{7}}x}+C\]
done
clear
D)
\[\frac{\sin x}{{{\tan }^{7}}x}+C\]
done
clear
View Answer play_arrow
question_answer 105) \[\int_{-3}^{2}{\{|x+1|+|x+2|+||x-1|\}}\,dx\]is equal to
A)
\[\frac{31}{2}\]
done
clear
B)
\[\frac{35}{2}\]
done
clear
C)
\[\frac{37}{2}\]
done
clear
D)
\[\frac{39}{2}\]
done
clear
View Answer play_arrow
question_answer 106) The variance of first \[n\]natural numbers is
A)
\[\frac{{{n}^{2}}+1}{12}\]
done
clear
B)
\[\frac{{{n}^{2}}-1}{12}\]
done
clear
C)
\[\frac{(n+1)(2n+1)}{6}\]
done
clear
D)
\[{{\left[ \frac{n(n+1)}{2} \right]}^{2}}\]
done
clear
View Answer play_arrow
question_answer 107) A particular solution of \[\log \left( \frac{dy}{dx} \right)=3x+4y,y(0)=0\]is
A)
\[{{e}^{3x}}+3{{e}^{-4y}}=4\]
done
clear
B)
\[4{{e}^{3x}}-3{{e}^{-4y}}=3\]
done
clear
C)
\[3{{e}^{3x}}+4{{e}^{-4y}}=7\]
done
clear
D)
\[4{{e}^{3x}}+3{{e}^{-4y}}=7\]
done
clear
View Answer play_arrow
question_answer 108) The equation of the curve whose subnormal is equal to a constant a is
A)
\[y=ax+b\]
done
clear
B)
\[{{y}^{2}}=2ax+2b\]
done
clear
C)
\[a{{y}^{2}}-{{x}^{3}}=a\]
done
clear
D)
None of these
done
clear
View Answer play_arrow
question_answer 109) If the standard deviation of a variable X is \[\sigma ,\]then the standard deviation of \[\sigma ,\](a, b, c are constants) is
A)
\[\frac{a}{c}\sigma \]
done
clear
B)
\[\left| \frac{a}{c} \right|\sigma \]
done
clear
C)
\[\left| \frac{c}{a} \right|\sigma \]
done
clear
D)
\[\frac{c}{a}\sigma \]
done
clear
View Answer play_arrow
question_answer 110) If \[\sin \alpha ,\cos \alpha \]are the roots of the equation\[a{{x}^{2}}+bx+c=0,(c\ne 0),\]the
A)
\[{{a}^{2}}-{{b}^{2}}+2ac=0\]
done
clear
B)
\[{{(a+c)}^{2}}={{b}^{2}}-{{c}^{2}}\]
done
clear
C)
\[{{a}^{2}}+{{b}^{2}}-2ac=0\]
done
clear
D)
\[{{(a-c)}^{2}}={{b}^{2}}+{{c}^{2}}\]
done
clear
View Answer play_arrow
question_answer 111) If \[\alpha ,\beta ,\gamma \]are such that \[\alpha +\beta +\gamma =2,\]\[{{\alpha }^{2}}+{{\beta }^{2}}+{{\gamma }^{2}}=6,\]\[{{\alpha }^{3}}+{{\beta }^{3}}+{{\gamma }^{3}}=8,\]then \[{{\alpha }^{4}}+{{\beta }^{4}}+{{\gamma }^{4}}\]is equal to
A)
7
done
clear
B)
12
done
clear
C)
18
done
clear
D)
36
done
clear
View Answer play_arrow
question_answer 112) The equation \[\bar{z}=\bar{a}+\frac{{{r}^{2}}}{(z-a)},r>0\] represents
A)
an ellipse
done
clear
B)
a parabola
done
clear
C)
a circle
done
clear
D)
_ a straight line through point \[\bar{a}\]
done
clear
View Answer play_arrow
question_answer 113) If \[\frac{3}{2+\cos \theta +i\sin \theta }=a+ib,\]then \[[{{(a-2)}^{2}}+{{b}^{2}}]\]is equal to
A)
0
done
clear
B)
1
done
clear
C)
\[-1\]
done
clear
D)
2
done
clear
View Answer play_arrow
question_answer 114) The value of \[4+5{{\left( -\frac{1}{2}+\frac{i\sqrt{3}}{2} \right)}^{334}}+3{{\left( -\frac{1}{2}+\frac{i\sqrt{3}}{2} \right)}^{365}}\]is
A)
\[1-i\sqrt{3}\]
done
clear
B)
\[-1+i\sqrt{3}\]
done
clear
C)
\[i\sqrt{3}\]
done
clear
D)
\[-i\sqrt{3}\]
done
clear
View Answer play_arrow
question_answer 115) If in the expansion of \[{{(a-2b)}^{n}},\] the sum of 4th and 5th term is zero, then the value of\[\frac{a}{b}\] is
A)
\[\frac{n-4}{5}\]
done
clear
B)
\[\frac{2(n-4)}{5}\]
done
clear
C)
\[\frac{5}{n-4}\]
done
clear
D)
\[\frac{5}{2(n-4)}\]
done
clear
View Answer play_arrow
question_answer 116) If\[A=\left[ \begin{matrix} a & b \\ c & d \\ \end{matrix} \right]\]is such that \[|A|=0\] and\[{{A}^{2}}-(a+d)A+kI=0,\] then \[k\]is equal to
A)
\[b+c\]
done
clear
B)
\[a+d\]
done
clear
C)
\[ab+cd\]
done
clear
D)
zero
done
clear
View Answer play_arrow
question_answer 117) The sum of series\[1+\frac{3}{2}+\frac{7}{4}+\frac{15}{8}+\frac{31}{16}+...\]is equal to
A)
\[2(n-1)+\frac{1}{{{2}^{n-1}}}\]
done
clear
B)
\[2n-\frac{1}{{{2}^{n}}}\]
done
clear
C)
\[2+\frac{1}{{{2}^{n}}}\]
done
clear
D)
\[2n-1+\frac{1}{{{2}^{n}}}\]
done
clear
View Answer play_arrow
question_answer 118) The number of meaningful solutions of \[{{\log }_{4}}(x-1)={{\log }_{2}}(x-3)\]is
A)
3
done
clear
B)
2
done
clear
C)
1
done
clear
D)
zero
done
clear
View Answer play_arrow
question_answer 119) The number of ways of arranging letters of the word HAVANA so that V and N do not appear together is
A)
60
done
clear
B)
80
done
clear
C)
100
done
clear
D)
120
done
clear
View Answer play_arrow
question_answer 120) A man is known to speak the truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six is
A)
\[\frac{3}{8}\]
done
clear
B)
\[\frac{1}{5}\]
done
clear
C)
\[\frac{3}{4}\]
done
clear
D)
\[\frac{1}{2}\]
done
clear
View Answer play_arrow
question_answer 121) The expression \[{{\cos }^{2}}(A-B)+co{{s}^{2}}B-2\cos (A-B)cos\,A\,cos\,B\]is independent of
A)
A
done
clear
B)
B
done
clear
C)
both A and B
done
clear
D)
neither A nor B
done
clear
View Answer play_arrow
question_answer 122) If the system of equations \[ax+y=3,\]\[x+2y=3,3x+4y=7\]is consistent, then value of a is equal to
A)
2
done
clear
B)
1
done
clear
C)
-1
done
clear
D)
0
done
clear
View Answer play_arrow
question_answer 123) If \[\left| \begin{matrix} x-1 & 5x & 7 \\ {{x}^{2}}-1 & x-1 & 8 \\ 2x & 3x & 0 \\ \end{matrix} \right|=a{{x}^{3}}+b{{x}^{2}}+cx+d,\]then c is equal to
A)
\[-1\]
done
clear
B)
12
done
clear
C)
15
done
clear
D)
17
done
clear
View Answer play_arrow
question_answer 124) If \[a,b,c>0,\]the minimum value of \[\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\]is
A)
1
done
clear
B)
\[\frac{3}{2}\]
done
clear
C)
2
done
clear
D)
\[\frac{5}{2}\]
done
clear
View Answer play_arrow
question_answer 125) If \[\tan {{1}^{o}}\tan {{2}^{o}}...tan{{2}^{o}}....\tan {{89}^{o}}={{x}^{2}}-8,\]then the value of \[x\]can be
A)
\[\pm \,1\]
done
clear
B)
\[\pm \,\,2\]
done
clear
C)
\[\pm \,\,3\]
done
clear
D)
\[\pm \,\,4\]
done
clear
View Answer play_arrow
question_answer 126) If \[\sin (x+3\alpha )=3\sin (\alpha -x),\]then
A)
\[\tan \,x=\tan \alpha \]
done
clear
B)
\[\tan \,x={{\tan }^{2}}\alpha \]
done
clear
C)
\[\tan x={{\tan }^{3}}\alpha \]
done
clear
D)
\[\tan x=3\tan \alpha \]
done
clear
View Answer play_arrow
question_answer 127) In a \[\Delta ABC,2{{a}^{2}}+4{{b}^{2}}+{{c}^{2}}=4ab+2ac,\]then \[\cos \,B\]is equal to
A)
0
done
clear
B)
\[\frac{1}{8}\]
done
clear
C)
\[\frac{3}{8}\]
done
clear
D)
\[\frac{7}{8}\]
done
clear
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question_answer 128) Let A and B be two events such that \[P(A)=0.3\]and \[p(A\cup B)=0.8.\]If A and B are independent events, then \[P(B)\] is
A)
\[\frac{3}{7}\]
done
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B)
\[\frac{4}{7}\]
done
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C)
\[\frac{5}{7}\]
done
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D)
\[\frac{6}{7}\]
done
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question_answer 129) A bag contains 4 brown and 5 white balls. A man pulls two balls at random without replacement. The probability that the man gets both the balls of the same colour is
A)
\[\frac{5}{108}\]
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B)
\[\frac{1}{6}\]
done
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C)
\[\frac{5}{18}\]
done
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D)
\[\frac{4}{9}\]
done
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question_answer 130) The value of expression\[\frac{1}{\cos {{290}^{o}}}+\frac{1}{\sqrt{3}\sin {{250}^{o}}}\] is equal to
A)
\[\frac{\sqrt{3}}{4}\]
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B)
\[\frac{4}{\sqrt{3}}\]
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C)
\[\frac{2}{\sqrt{3}}\]
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D)
\[\frac{\sqrt{3}}{2}\]
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question_answer 131) An equation of a line through the point (1, 2) whose distance from the point (3, 1) has the greatest value is
A)
\[y=2x\]
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B)
\[y=x+1\]
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C)
\[x+2y=5\]
done
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D)
\[y=3x-1\]
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question_answer 132) A line is drawn through the point P(3,11) to cut the circle \[{{x}^{2}}+{{y}^{2}}=9\]at A and B. Then, \[PA.PB\]is equal to
A)
9
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B)
121
done
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C)
205
done
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D)
139
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question_answer 133) If the tangent at point P on the circle \[{{x}^{2}}+{{y}^{2}}+6x+6y-2=0\] meets the straight line \[5x-2y+6=0\] at a point Q on the. \[y-\]axis, then length PQ is
A)
4
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B)
\[2\sqrt{5}\]
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C)
5
done
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D)
\[3\sqrt{5}\]
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question_answer 134) In a triangle ABC, \[a:\text{ }b:\text{ }c\text{ }=\text{ }4:\text{ }5:\text{ }6.\]The ratio of the radius of the circumcircle to that of the incircle is
A)
\[\frac{15}{4}\]
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B)
\[\frac{11}{5}\]
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C)
\[\frac{16}{7}\]
done
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D)
\[\frac{16}{3}\]
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question_answer 135) If \[4{{\sin }^{-1}}x+{{\cos }^{-1}}x=\pi ,\]then \[x\]is equal to
A)
\[-\frac{1}{2}\]
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B)
0
done
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C)
\[\frac{1}{2}\]
done
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D)
1
done
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question_answer 136) The Value of \[\cos \left( \frac{1}{2}{{\cos }^{-1}}\frac{1}{8} \right)\] is equal to
A)
\[\frac{3}{4}\]
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B)
\[-\frac{3}{4}\]
done
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C)
\[\frac{1}{16}\]
done
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D)
\[\frac{1}{4}\]
done
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question_answer 137) The vectors \[\vec{a}=\hat{i}+\hat{j}+m\hat{k},\]\[\vec{b}=\hat{i}+\hat{j}+(m+1)\hat{k}\] and \[\vec{c}=\hat{i}-\hat{j}+m\hat{k}\] are coplanar, if \[m\]is equal to
A)
1
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B)
4
done
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C)
3
done
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D)
no value of m for which vectors are coplanar
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question_answer 138) If|\[|\vec{a}|=2,|\vec{b}|=3,|\vec{c}|=4\]and \[\vec{a}+\vec{b}+\vec{c}=0,\] then the value of \[\vec{b}.\vec{c}+\vec{c}.\vec{a}+\vec{a}+\vec{a}.\vec{b}\]is equal to
A)
\[\frac{19}{2}\]
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B)
\[-\frac{19}{2}\]
done
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C)
\[\frac{29}{2}\]
done
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D)
\[-\frac{29}{2}\]
done
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question_answer 139) The line \[x+y=6\]is a normal to the parabola \[{{y}^{2}}=8x\]at the point
A)
\[(18,-12)\]
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B)
\[(4,2)\]
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C)
\[(2,4)\]
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D)
\[(8,8)\]
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question_answer 140) If\[{{F}_{1}}=(3,0),{{F}_{2}}=(-3,0)\] and P is any point on the curve \[16{{x}^{2}}+25{{y}^{2}}=400,\] then \[P{{F}_{1}}+P{{F}_{2}}\]is equal to
A)
6
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B)
8
done
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C)
10
done
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D)
12
done
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question_answer 141) If e and\[{{e}_{1}}\]are the eccentricities of a hyperbola and its conjugate, then\[\frac{1}{{{e}^{2}}}+\frac{1}{e_{1}^{2}}\] is equal to
A)
\[-1\]
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B)
0
done
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C)
1
done
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D)
2
done
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question_answer 142) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{1-{{\cos }^{3}}x}{x\sin \cos x}\]is equal to
A)
\[\frac{2}{5}\]
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B)
\[\frac{3}{5}\]
done
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C)
\[\frac{3}{2}\]
done
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D)
\[\frac{3}{4}\]
done
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question_answer 143) If \[y={{\cos }^{-1}}(\cos \,x),\]then \[y(x)\]is equal to
A)
1 for all \[x\]
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B)
\[-1\]for all \[x\]
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C)
1 in 2nd and 3rd quadrant
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D)
\[-1\]in 3rd and 4th quadrant
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question_answer 144) If the vectors \[\overrightarrow{AB}=3\hat{i}+4\hat{k}\] and =\[\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}\]are the sides of a \[\Delta ABC,\] then the length of the median through A is
A)
\[\sqrt{14}\]
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B)
\[\sqrt{18}\]
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C)
\[\sqrt{29}\]
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D)
4
done
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question_answer 145) The period of the function\[f(x)=\cos e{{c}^{2}}3x+\cot 4x\]is
A)
\[\frac{\pi }{3}\]
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B)
\[\frac{\pi }{4}\]
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C)
\[\frac{\pi }{6}\]
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D)
\[\pi \]
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question_answer 146) The graph of the function\[f(x)={{\log }_{a}}(x+\sqrt{{{x}^{2}}+1})\] is symmetric about
A)
\[x-\]axis
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B)
origin
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C)
\[y-\]axis
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D)
the line \[y=x\]
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question_answer 147) The difference between the greatest and least values of the function\[f(x)=\cos x+\frac{1}{2}\cos 2x-\frac{1}{3}\cos 3x\]is
A)
\[\frac{2}{3}\]
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B)
\[\frac{8}{7}\]
done
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C)
\[\frac{3}{8}\]
done
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D)
\[\frac{9}{4}\]
done
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question_answer 148) \[f(x)=\left\{ \begin{matrix} a{{x}^{2}}+b, & b\ne 0,x\le 1 \\ b{{x}^{2}}+ax+c, & x>1 \\ \end{matrix} \right.\] then\[f(x)\] is continuous and differentiable at \[x=1\]if
A)
\[c=0,\,a=2b\]
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B)
\[a=b,\,c\in R\]
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C)
\[a=b,c=0\]
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D)
\[a=b,c\ne 0\]
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question_answer 149) Let \[g(x)\]be the inverse of function \[f(x)\] and \[f(x)=\frac{1}{1+{{x}^{3}}},\] then \[g(x)\]is equal to
A)
\[\frac{1}{1+{{\{g(x)\}}^{3}}}\]
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B)
\[\frac{1}{1+{{\{f(x)\}}^{3}}}\]
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C)
\[1+{{\{g(x)\}}^{3}}\]
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D)
\[1+{{\{f(x)\}}^{3}}\]
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question_answer 150) If \[\theta \] is the semi vertical angle of a cone of maximum volume and given slant height, then\[\tan \,\theta \]is given by
A)
2
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B)
1
done
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C)
\[\sqrt{2}\]
done
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D)
\[\sqrt{3}\]
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