question_answer 1) One drop of soap bubble of diameter D breakes into 27 drops having surface tension T. The change in surface energy is
A)
\[2\pi T{{D}^{2}}\]
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B)
\[4\pi T{{D}^{2}}\]
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C)
\[\pi T{{D}^{2}}\]
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D)
\[8\pi T{{D}^{2}}\]
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question_answer 2) The period of a planet around sun is 27 times that of earth. The ratio of radius of planets orbit to the radius of earths orbit is
A)
4
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B)
9
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C)
64
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D)
27
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question_answer 3) Three particles each of mass m are kept at vertices of an equilateral triangle of side L. The gravitational field at centre due to these particles is
A)
zero
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B)
\[\frac{3GM}{{{L}^{2}}}\]
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C)
\[\frac{9GM}{{{L}^{2}}}\]
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D)
\[\frac{12}{\sqrt{3}}\frac{GM}{{{L}^{2}}}\]
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question_answer 4) In a turbulent flow, the velocity of the liquid in contact with the walls of the tube is
A)
zero
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B)
maximum
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C)
in between zero and maximum
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D)
equal to critical velocity
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question_answer 5) A charge q is fixed. Another charge Q is brought near it and rotated in a circle of radius r around it. Work done during rotation is
A)
zero
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B)
\[\frac{Qq}{4\pi G{{\varepsilon }_{0}}r}\]
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C)
\[\frac{Qq}{2\pi G{{\varepsilon }_{0}}r}\]
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D)
None of these
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question_answer 6) A diode having potential difference 0.5 V across its junction which does not depend on current, is connected in series with resistance of 20 \[\Omega \] across source. If 0.1 A current passes through resistance then what is the voltage of the source?
A)
1.5V
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B)
2.0V
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C)
2.5 V
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D)
5 V
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question_answer 7) Dipole is placed parallel to the electric field. If Q is the work done in rotating the dipole by 60°, then work done in rotating it by 180° is
A)
2W
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B)
3W
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C)
4W
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D)
W/2
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question_answer 8) An electron of charge e moves in a circular orbit of radius r around the nucleus at a frequency v. The magnetic moment associated with the orbital motion of the electron is
A)
\[\pi ve{{r}^{2}}\]
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B)
\[\frac{\pi v{{r}^{2}}}{e}\]
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C)
\[\frac{\pi v\,e}{r}\]
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D)
\[\frac{\pi v{{r}^{2}}}{v}\]
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question_answer 9) A and B are two identical spherical charged bodies which repel each other with force F, kept at a finite distance. A third uncharged sphere of the same size is brought in contact with sphere B and removed. It is then kept at mid-point of A and B. Find the magnitude of force on C.
A)
F/2
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B)
F/8
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C)
F
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D)
Zero
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question_answer 10) A wave equation is \[y=0.1\sin [100\pi t-kx]\]and wave velocity is 100 m/s, its wave number is equal to
A)
\[1{{m}^{-1}}\]
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B)
\[2{{m}^{-1}}\]
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C)
\[\pi {{m}^{-1}}\]
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D)
\[2\pi {{m}^{-1}}\]
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question_answer 11) Volume-temperature graph at atmospheric pressure for a monoatomic gas \[\left( V\text{ }in\text{ }{{m}^{3}},\text{ }T\text{ }in\text{ }{}^\circ C \right)\] is
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 12) An optically active compound
A)
rotates the plane polarized light
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B)
changing the direction of polarized light
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C)
do not allow plane polarized light to pass through
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D)
None of the above
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question_answer 13) Power applied to a particle varies with time as \[P=(3{{t}^{2}}-2t+1)\] W, where t is in second. Find the change in its kinetic energy between t = 1 s and t = 4 s.
A)
32 J
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B)
46 J
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C)
61 J
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D)
102 J
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question_answer 14) A hockey player receives a corner shot at a speed of 15 m/s at an angle of 30° with the y-axis and then shoots the ball of mass 100 g along the negative x-axis with a speed of 30 m/s. If it remains in contact with the hockey stick for 0.01 s, the force imparted to the ball in the x-direction is
A)
281.25 N
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B)
187.5N
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C)
562.5 N
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D)
375 N
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question_answer 15) Two equal charges are separated by a distance d. A third charge placed on a perpendicular bisector at x distance from centre will experience maximum coulomb force, when
A)
\[x=d/\sqrt{2}\]
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B)
\[x=d/2\]
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C)
\[x=d/2\sqrt{2}\]
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D)
\[x=d/2\sqrt{3}\]
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question_answer 16)
The equivalent resistance between points A and B of an infinite network of resistance s each of \[1\,\Omega ,\] connected as shown, is
A)
infinite
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B)
2\[\Omega \]
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C)
\[\frac{1+\sqrt{5}}{2}\Omega \]
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D)
zero
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question_answer 17) A circular current carrying coil has a radius R The distance from the centre of the coil off the axis of the coil, where the magnetic induction is I/8th of its value at the centre of the coil is
A)
\[\sqrt{3}R\]
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B)
\[R/\sqrt{3}\]
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C)
\[\left( \frac{2}{\sqrt{3}} \right)R\]
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D)
\[\frac{R}{2\sqrt{3}}\]
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question_answer 18) A point source of light is placed 4m below he surface of water of refractive index 5/ 3. The minimum diameter of a disc, which should be placed over the source, on the surface of water to cut-off all light coming out of water is
A)
infinite
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B)
6 m
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C)
4m
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D)
3m
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question_answer 19)
A ray falls on a prism ABC (AB =BC) and travels as shown in figure. The minimum refractive index of the prism material should be
A)
\[\frac{4}{3}\]
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B)
\[\sqrt{2}\]
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C)
1.5
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D)
\[\sqrt{3}\]
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question_answer 20) The plane face of a planoconvex lens is silvered. If u be the refractive index and R, the radius of curvature of curved surface, then the system will behave like a concave mirror of radius of curvature
A)
\[\mu R\]
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B)
\[\frac{R}{(\mu -1)}\]
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C)
\[\frac{{{R}^{2}}}{\mu }\]
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D)
\[\left[ \frac{(\mu +1)}{(\mu -1)} \right]R\]
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question_answer 21)
Two similar accumulators each of emf E and internal resistance r are connected as shown in the following figure. Then, the potential difference between x and y is
A)
2E
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B)
E
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C)
zero
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D)
None of these
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question_answer 22) A conducting circular loop is placed in a uniform magnetic field of induction B tesla with its plane normal to the field. Now, the radius of the loop starts shrinking at the rate\[\left( \frac{dr}{dt} \right)\]. Then, the induced emf at the instant when the radius is r, is
A)
\[\pi rB\left( \frac{dr}{dt} \right)\]
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B)
\[2\pi rB\left( \frac{dr}{dt} \right)\]
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C)
\[\pi {{r}^{2}}\left( \frac{dr}{dt} \right)\]
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D)
\[{{\left( \frac{\pi {{r}^{2}}}{2} \right)}^{2}}B\left( \frac{dr}{dt} \right)\]
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question_answer 23) The first excitation potential of a given atom is 10.2V. Then, ionization potential must be
A)
20.4V
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B)
13.6V
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C)
30.6V
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D)
40.8V
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question_answer 24) A train is approaching with velocity 25 m/s towards a pedestrian standing on the track, frequency of horn of train is 1 kHz. Frequency heard by the pedestrain is (v= 350 m/s)
A)
1077 Hz
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B)
1167 Hz
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C)
985 Hz
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D)
954 Hz
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question_answer 25) Intensity of wave A is 91, while of wave B is 7. What is maximum and minimum intensity in YDSE?
A)
82\[I\], 80\[I\]
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B)
8\[I\], 10\[I\]
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C)
16\[I\], 4\[I\]
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D)
4\[I\],\[I\]
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question_answer 26) What happens inside optical fibre?
A)
Diffraction
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B)
Polarization
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C)
Interference
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D)
Total internal reflection
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question_answer 27) A manometer connected to a closed tap reads\[3.5\times {{10}^{5}}\,N/{{m}^{2}}\]. When the valve is opened, the reading of manometer falls to \[3.0\times {{10}^{5}}\,N/{{m}^{2}}\], then velocity of flow of water is
A)
100 m/s
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B)
10 m/s
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C)
1m/s
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D)
\[10\sqrt{10}\]m/s
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question_answer 28) Water is moving with a speed of 5.18 \[m{{s}^{-1}}\] through a pipe with a cross-sectional area of 4.20\[c{{m}^{2}}\]. The water gradually descends 9.66 m as the pipe increase in area to 7.60\[c{{m}^{2}}\]. The speed of flow at the lower level is
A)
3.0\[m{{s}^{-1}}\]
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B)
5.7\[m{{s}^{-1}}\]
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C)
3.82\[m{{s}^{-1}}\]
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D)
2.86\[m{{s}^{-1}}\]
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question_answer 29) What is de-Broglie wavelength of electron having energy 10 keV?
A)
\[0.12\overset{\text{o}}{\mathop{\text{A}}}\,\]
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B)
\[1.2\overset{\text{o}}{\mathop{\text{A}}}\,\]
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C)
\[12.2\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
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D)
None of these
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question_answer 30) Find beat frequency? Motion of two particles is given by \[{{y}_{1}}=0.25\sin (310t)\] \[{{y}_{2}}=0.25\sin (316t)\]
A)
3
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B)
\[\frac{3}{\pi }\]
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C)
\[\frac{6}{\pi }\]
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D)
6
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question_answer 31) Half-life of radioactive substance is 3.20 h. What is the time taken for a 75% of substance to be used?
A)
6.38 h
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B)
12 h
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C)
4.18 day
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D)
1.2day
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question_answer 32)
A capacitor of capacitance 1 \[\mu F\] is filled with two dielectrics of dielectric constants 4 and 6. What is the new capacitance?
A)
10\[\mu F\]
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B)
5\[\mu F\]
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C)
4\[\mu F\]
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D)
7\[\mu F\]
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question_answer 33)
The given combination represents the following gate
A)
OR
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B)
XOR
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C)
NAND
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D)
NOR
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question_answer 34) In BJT, maximum current flows in which of the following?
A)
Emitter region
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B)
Base region
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C)
Collector region
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D)
Equal in all the regions
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question_answer 35) In semiconductors at a room temperature
A)
the valence band is partially empty and the conduction band is partially filled
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B)
the valence band is completely filled and the conduction band is partially filled
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C)
the valence band is completely filled
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D)
the conduction band is completely empty
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question_answer 36) If coil is open then L and R become
A)
\[\infty ,0\]
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B)
\[0,\infty \]
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C)
\[\infty ,\infty \]
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D)
0, 0
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question_answer 37) In a coil when current changes from 10A to 2A in time 0.1 s, induced emf is 3.28V. What is self-inductance of coil?
A)
4H
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B)
0.4H
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C)
0.04H
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D)
5H
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question_answer 38) Resistance of rod is 1\[\Omega \]. It is bent in form of square. What is resistance across adjoint corners?
A)
1\[\Omega \]
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B)
3\[\Omega \]
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C)
\[\frac{3}{16}\Omega \]
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D)
\[\frac{3}{4}\Omega \]
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question_answer 39) In a circuit L, C and R are connected in series with an alternating voltage source of frequency \[f\]. The current leads the voltage by \[45{}^\circ \]. The value of C is
A)
\[\frac{1}{2\pi f(2\pi fL+R)}\]
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B)
\[\frac{1}{\pi f(2\pi fL+R)}\]
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C)
\[\frac{1}{2\pi f(2\pi fL-R)}\]
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D)
\[\frac{1}{\pi f(2\pi fL-R)}\]
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question_answer 40) What is angle between electric field and equipotential surface?
A)
\[90{}^\circ \text{ }always\]
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B)
\[0{}^\circ \text{ }always\]
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C)
\[0{}^\circ \text{ }to\text{ }90{}^\circ \]
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D)
\[0{}^\circ \text{ }to\text{ }180{}^\circ \]
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question_answer 41) A ball falls from 20 m height on floor and rebounds to 5m. Time of contact is 0.02s. Find acceleration during impact.
A)
\[1200\,m/{{s}^{2}}\]
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B)
\[1000\,m/{{s}^{2}}\]
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C)
\[2000\,m/{{s}^{2}}\]
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D)
\[1500\,m/{{s}^{2}}\]
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question_answer 42) Two drops of equal radius coalesce to form a bigger drop. What is ratio of surface energy of bigger drop to smaller one?
A)
\[{{2}^{1/2}}:1\]
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B)
\[1:1\]
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C)
\[{{2}^{2/3}}:1\]
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D)
None of these
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question_answer 43) In any fission process the ratio \[\frac{mass\,of\,fission\,products}{mass\,of\,parent\,nucleus}is\]
A)
less than 1
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B)
greater than 1
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C)
equal to 1
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D)
depends on the mass of parent nucleus
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question_answer 44) In the phenomenon of diffraction of light. when blue light is used in the experiment instead of red light, then
A)
fringes will become narrower
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B)
fringes will become broader
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C)
no change in fringe width
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D)
None of the above
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question_answer 45) A glass slab \[(\mu =1.5)\] of thickness 6 cm is placed over a paper. What is the shift in the letters?
A)
4 cm
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B)
2 cm
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C)
1 cm
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D)
None of these
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question_answer 46) Two capacitors of capacitance C are connected in series. If one of them is filled with dielectric substance K, what is the effective capacitance?
A)
\[\frac{KC}{(1+K)}\]
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B)
C (K + 1)
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C)
\[\frac{2KC}{K+1}\]
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D)
None of these
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question_answer 47) A person is sitting in a lift accelerating upwards. Measured weight of person will be
A)
less than actual weight
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B)
equal to actual weight
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C)
more than actual weight
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D)
None of the above
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question_answer 48) By mistake a voltmeter is connected in series and an ammeter is connected in parallel with a resistance in an electrical circuit. What will happen to the instruments?
A)
Voltmeter is damaged
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B)
Ammeter is damaged
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C)
Both are damaged
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D)
None is damaged
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question_answer 49) The half-life of \[A{{t}^{215}}\]is 100 \[\mu s\]. If a sample contains 215 mg of \[A{{t}^{215}}\], the activity of the sample initially is
A)
\[{{10}^{2}}Bq\]
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B)
\[3\times {{10}^{10}}Bq\]
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C)
\[4.17\times {{10}^{24}}Bq\]
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D)
\[1.16\times {{10}^{5}}Bq\]
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question_answer 50) The ratio of minimum to maximum wavelength in Balmer series is
A)
5 : 9
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B)
5 : 36
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C)
1 : 4
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D)
3 : 4
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question_answer 51) A ball is released from the top of a tower. The ratio of work done by force of gravity in first, second and third second of the motion of the ball is
A)
1 : 2 : 3
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B)
1 : 4 : 9
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C)
1 : 3 : 5
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D)
1 : 5 : 3
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question_answer 52) A body of mass 2 kg moving with a velocity of 3 m/s collides head on with a body of mass 1 kg moving in opposite direction with a velocity of 4 m/s. After collision two bodies stick together and move with a common velocity which in m/s is equal to
A)
1/4
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B)
1/3
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C)
2/3
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D)
3/4
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question_answer 53) Two spheres P and Q, of same colour having radii 8 cm and 2 cm are maintained at temperatures \[127{}^\circ C\] and \[527{}^\circ C\] respectively. The energy radiated by P and Q is
A)
0.054
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B)
0.0034
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C)
1
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D)
2
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question_answer 54) A cane is taken out from a refrigerator at \[0{}^\circ C\]. The atmospheric temperature is \[25{}^\circ C\]. If \[{{t}_{1}}\] is the time taken to heat from \[0{}^\circ C\] to \[5{}^\circ C\] and \[{{t}_{2}}\] is the time taken from \[10{}^\circ C\] to \[15{}^\circ C\], then
A)
\[{{t}_{1}}>{{t}_{2}}\]
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B)
\[{{t}_{1}}<{{t}_{2}}\]
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C)
\[{{t}_{1}}={{t}_{2}}\]
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D)
there is no relation
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question_answer 55) If an electron and a photon propagate in the form of waves having the same wavelength, it implies that they have the same
A)
energy
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B)
momentum
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C)
velocity
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D)
angular momentum
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question_answer 56) The work function of a substance is 4.0 eV. The longest wavelength of light that can cause photoelectron emission from this substance is approximately
A)
540 nm
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B)
400 nm
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C)
310nm
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D)
220 nm
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question_answer 57) Work function of a metal is 2.1 eV. Which of the waves of the following wavelengths will be able to emit photoelectrons from its surface?
A)
\[4000\overset{\text{o}}{\mathop{\text{A}}}\,,\,\,7500\overset{\text{o}}{\mathop{\text{A}}}\,\]
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B)
\[5500\overset{\text{o}}{\mathop{\text{A}}}\,,\,6000\overset{\text{o}}{\mathop{\text{A}}}\,\]
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C)
\[4000\overset{\text{o}}{\mathop{\text{A}}}\,,\,6000\overset{\text{o}}{\mathop{\text{A}}}\,\]
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D)
None of the above
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question_answer 58) A laser beam of pulse power \[{{10}^{12}}\]W is focused on an object of area\[{{10}^{-4}}c{{m}^{2}}\]. The energy flux in watt/\[c{{m}^{2}}\] at the point of focus is
A)
\[{{10}^{20}}\]
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B)
\[{{10}^{16}}\]
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C)
\[{{10}^{8}}\]
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D)
\[{{10}^{4}}\]
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question_answer 59) A laser device produces amplification in the
A)
microwave region
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B)
ultraviolet or visible region
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C)
infrared region
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D)
None of the above
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question_answer 60) Which of the following circular rods. (given radius r and length 0 each made of the same material as whose ends are maintained at the same temperature will conduct most heat?
A)
\[r=2{{r}_{0}};l=2{{l}_{0}}\]
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B)
\[r=2{{r}_{0}};l={{l}_{0}}\]
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C)
\[r={{r}_{0}};l={{l}_{0}}\]
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D)
\[r={{r}_{0}};l=2{{l}_{0}}\]
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question_answer 61) Which of the following is diamagnetic?
A)
\[H_{2}^{+}\]
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B)
\[{{O}_{2}}\]
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C)
\[L{{i}_{2}}\]
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D)
\[He_{2}^{+}\]
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question_answer 62) Which of the following can participate in linkage isomerism?
A)
\[NO_{2}^{-}\]
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B)
\[{{H}_{2}}\overset{\centerdot \,\,\,\centerdot }{\mathop{N}}\,C{{H}_{2}}C{{H}_{2}}\overset{\centerdot \,\,\,\centerdot }{\mathop{N}}\,{{H}_{2}}\]
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C)
\[{{H}_{2}}O\]
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D)
\[:N{{H}_{3}}\]
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question_answer 63) By heating phenol with chloroform in alkali, it is converted into
A)
salicylic acid
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B)
salicylaldehyde
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C)
anisole
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D)
phenyl benzoate
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question_answer 64) Osmotic pressure observed when benzoic acid is dissolved in benzene is less than that expected from theoretical considerations. This is because
A)
benzoic acid is an organic solute
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B)
benzoic acid has higher molar mass than benzene
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C)
benzoic acid gets associated in benzene
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D)
benzoic acid gets dissociated in benzene
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question_answer 65) The formula mass of Moms salt is 392. The iron present in it is oxidized by\[KMn{{O}_{4}}\]in acid medium. The equivalent mass of Mohrs salt is
A)
392
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B)
31.6
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C)
278
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D)
156
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question_answer 66) Solubility product of a salt\[AB\]is\[1\times {{10}^{-8}}{{M}^{2}}\]in a solution in which the concentration of\[{{A}^{+}}\]ions is\[{{10}^{-3}}M\]. The salt will precipitate when the concentration of\[{{B}^{-}}\]ions is kept
A)
between\[{{10}^{-8}}M\]to\[{{10}^{-7}}M\]
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B)
between\[{{10}^{-7}}M\]to\[{{10}^{-8}}M\]
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C)
\[>{{10}^{-5}}M\]
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D)
\[<{{10}^{-8}}M\]
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question_answer 67) The decomposition of a certain mass of\[CaC{{O}_{3}}\]gave\[11.2\,\,d{{m}^{3}}\]of\[C{{O}_{2}}\]gas at STP. The mass of\[KOH\]required to completely I neutralize the gas is
A)
56 g
done
clear
B)
28 g
done
clear
C)
42 g
done
clear
D)
20 g
done
clear
View Answer play_arrow
question_answer 68) The basicity of aniline is less than that of cyclohexylamine. This is due to
A)
\[+R-\]effect of\[-N{{H}_{2}}\]group
done
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B)
\[-I-\]effect of\[-N{{H}_{2}}\]group
done
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C)
\[-R-\]effect of\[-N{{H}_{2}}\]group
done
clear
D)
hyperconjugation effect
done
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question_answer 69) A distinctive and characteristic functional group of fats is
A)
a peptide group
done
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B)
an ester group
done
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C)
an alcoholic group
done
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D)
a ketonic group
done
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question_answer 70) Which of the following compound is expected to be optically active?
A)
\[{{(C{{H}_{3}})}_{2}}CHCHO\]
done
clear
B)
\[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}CHO\]
done
clear
C)
\[C{{H}_{3}}C{{H}_{2}}CHBrCHO\]
done
clear
D)
\[C{{H}_{3}}C{{H}_{2}}CB{{r}_{2}}CHO\]
done
clear
View Answer play_arrow
question_answer 71) Which cycloalkane has the lowest heat of combustion per\[C{{H}_{2}}\]group?
A)
Cyclopropane
done
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B)
Cyclobutane
done
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C)
Cyclopentane
done
clear
D)
Cyclohexane
done
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question_answer 72) The physical states of dispersing phase and dispersion medium in colloid like pesticide spray respectively, are
A)
gas, liquid
done
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B)
solid, gas
done
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C)
liquid, solid
done
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D)
liquid, gas
done
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question_answer 73) Potassium dichromate is used
A)
in electroplating
done
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B)
as a reducing agent
done
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C)
it oxidizes ferrous ions into ferric ions in acidic media as an oxidizing agent
done
clear
D)
as an insecticide
done
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question_answer 74) Which one of the following statements is incorrect for the sucrose?
A)
It is obtained from cane sugar
done
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B)
It is not reducing sugar
done
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C)
On hydrolysis, it gives equal quantities of D-glucose and D-fructose
done
clear
D)
It gives aspartame when it is heated at\[{{210}^{o}}C\]
done
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View Answer play_arrow
question_answer 75) Inductive effect involves
A)
displacement of \[\sigma \]-electrons
done
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B)
delocalisation of \[\pi \]-electrons
done
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C)
delocalisation of \[\sigma \]-electrons
done
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D)
displacement of \[\pi \]-electrons
done
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question_answer 76) The atomic number of\[Ni\]and\[Cu\]are 28 and 29 respectively. The electronic configuration \[1{{s}^{2}},\,\,2{{s}^{2}},\,\,2{{p}^{6}},\,\,3{{s}^{2}}\,\,3{{p}^{6}}\,\,3{{d}^{10}}\]represents
A)
\[C{{u}^{+}}\]
done
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B)
\[C{{u}^{2+}}\]
done
clear
C)
\[N{{i}^{2+}}\]
done
clear
D)
\[Ni\]
done
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View Answer play_arrow
question_answer 77) In which of the following complex ion, the central metal ion is in a state of\[s{{p}^{3}}{{d}^{2}}\]hybridisation?
A)
\[{{[CoF]}^{3-}}\]
done
clear
B)
\[{{[CO{{(N{{H}_{3}})}_{6}}]}^{3+}}\]
done
clear
C)
\[{{[Fe{{(CN)}_{6}}]}^{3-}}\]
done
clear
D)
\[{{[Cr{{(N{{H}_{3}})}_{6}}]}^{3+}}\]
done
clear
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question_answer 78) The formation of\[O_{2}^{+}{{[Pt{{F}_{6}}]}^{-}}\]is the basis for the formation of xenon fluorides. This is because
A)
\[{{O}_{2}}\]and\[Xe\]have comparable sizes
done
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B)
Both\[{{O}_{2}}\]and\[Xe\]are gases
done
clear
C)
\[{{O}_{2}}\]and\[Xe\]have comparable ionization energies
done
clear
D)
Both (a) and (c)
done
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question_answer 79) The density of a gas is\[1.964\,\,g\,\,d{{m}^{-3}}\]at\[273\,\,K\]and\[76\,\,cm\,\,Hg\]. The gas is
A)
\[C{{H}_{4}}\]
done
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B)
\[{{C}_{2}}{{H}_{6}}\]
done
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C)
\[C{{O}_{2}}\]
done
clear
D)
\[Xe\]
done
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View Answer play_arrow
question_answer 80) \[\Delta {{G}^{o}}vs\,\,T\]plot in the Ellinghams diagram slopes downwards for the reactions
A)
\[Mg+\frac{1}{2}{{O}_{2}}\xrightarrow{{}}MgO\]
done
clear
B)
\[2Ag+\frac{1}{2}{{O}_{2}}\xrightarrow{{}}A{{g}_{2}}O\]
done
clear
C)
\[CO+\frac{1}{2}{{O}_{2}}\xrightarrow{{}}C{{O}_{2}}\]
done
clear
D)
All of the above
done
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question_answer 81) When a mixture of calcium benzoate and calcium acetate is dry distilled, the resulting compound is
A)
acetophenone
done
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B)
benzaldehyde
done
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C)
benzophenone
done
clear
D)
acetaldehyde
done
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question_answer 82) In a metallic crystal
A)
the valence electrons constitute a sea of mobile electrons
done
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B)
the valence electrons are localized in between the kernels
done
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C)
the valence electrons remain within the field of influence of their own kernels
done
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D)
None of the above
done
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question_answer 83) Which of the following is correct, based on molecular orbital theory for peroxide ion?
A)
Its bond order is one and it is paramagnetic
done
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B)
Its bond order is two and it is diamagnetic
done
clear
C)
Its bond order is one and it is diamagnetic
done
clear
D)
Its bond order is two and it is paramagnetic
done
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View Answer play_arrow
question_answer 84) Insulin regulates the metabolism of
A)
minerals
done
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B)
ammo acids
done
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C)
glucose
done
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D)
vitamins
done
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question_answer 85) Which of the following electrolyte will have maximum flocculation value for\[Fe{{(OH)}_{3}}\]sol?
A)
\[NaCl\]
done
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B)
\[N{{a}_{2}}S\]
done
clear
C)
\[{{(N{{H}_{4}})}_{3}}P{{O}_{4}}\]
done
clear
D)
\[{{K}_{2}}S{{O}_{4}}\]
done
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View Answer play_arrow
question_answer 86) The concentration of a reactant X decreases from\[0.1M\]to\[0.005M\]in 40 min. If the reaction follows first order kinetics, the rate of the reaction when the concentration of\[X\]is \[0.01\,\,M\]will be
A)
\[1.73\times {{10}^{-4}}M\,\,{{\min }^{-1}}\]
done
clear
B)
\[3.47\times {{10}^{-4}}M\,\,{{\min }^{-1}}\]
done
clear
C)
\[3.47\times {{10}^{-5}}M\,\,{{\min }^{-1}}\]
done
clear
D)
\[7.5\times {{10}^{-4}}M\,\,{{\min }^{-1}}\]
done
clear
View Answer play_arrow
question_answer 87) At\[pH=4\], glycine exists as
A)
\[{{H}_{3}}N-C{{H}_{2}}-CO{{O}^{-}}\]
done
clear
B)
\[{{H}_{3}}N-C{{H}_{2}}-COOH\]
done
clear
C)
\[{{H}_{2}}N-C{{H}_{2}}-COOH\]
done
clear
D)
\[{{H}_{2}}N-C{{H}_{2}}-CO{{O}^{-}}\]
done
clear
View Answer play_arrow
question_answer 88) Which of the following taking place in the blast furnace is endothermic?
A)
\[CaC{{O}_{3}}\xrightarrow{{}}CaO+C{{O}_{2}}\]
done
clear
B)
\[2C+{{O}_{2}}\xrightarrow{{}}2CO\]
done
clear
C)
\[C+{{O}_{2}}\xrightarrow{{}}C{{O}_{2}}\]
done
clear
D)
\[F{{e}_{2}}{{O}_{3}}+3CO\xrightarrow{{}}2Fe+3C{{O}_{2}}\]
done
clear
View Answer play_arrow
question_answer 89) The\[emf\,\,{{E}^{o}}\]of the following cells are: \[AG|A{{g}^{+}}(1M)||C{{u}^{2+}}(1M)|Cu;\,\,{{E}^{o}}=-0.46\,\,V\] \[Zn|Z{{n}^{2+}}(1M)||C{{u}^{2+}}(1M)|Cu;\,\,{{E}^{o}}=1.10\,\,V\] emf of the following cell is \[Zn|Z{{n}^{2+}}(1M)||A{{g}^{+}}(1M)|Ag\]
A)
\[0.64\,\,V\]
done
clear
B)
\[1.10\,\,V\]
done
clear
C)
\[1.56\,\,V\]
done
clear
D)
\[-0.64\,\,V\]
done
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View Answer play_arrow
question_answer 90) The formation of cyanohydrin from acetone is which type of reaction?
A)
Electrophilic substitution reaction
done
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B)
Electrophilic addition reaction
done
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C)
Nucleophilic addition reaction
done
clear
D)
Nucleophilic substitution reaction
done
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View Answer play_arrow
question_answer 91) Name the end product in the following series of reactions \[C{{H}_{3}}COOH\xrightarrow{N{{H}_{3}}}A\xrightarrow{Heat}B\xrightarrow[\Delta ]{{{P}_{4}}{{O}_{14}}}C\]
A)
\[C{{H}_{3}}OH\]
done
clear
B)
\[C{{H}_{4}}\]
done
clear
C)
\[C{{H}_{3}}COON{{H}_{4}}\]
done
clear
D)
\[C{{H}_{3}}CN\]
done
clear
View Answer play_arrow
question_answer 92) The presence of unpaired electron in phosphorous atom is explained by which principle?
A)
Aufbau principle
done
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B)
Faults exclusion principle
done
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C)
Hunds rule
done
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D)
Heisenbergs principle
done
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question_answer 93) If a cricket ball having mass of\[200\,\,g\]is thrown with a speed of\[3\times {{10}^{3}}\,\,cm/s\], then calculate the wavelength related to it.
A)
\[2.2\times {{10}^{-27}}cm\]
done
clear
B)
\[1.104\times {{10}^{-32}}cm\]
done
clear
C)
\[1.104\times {{10}^{-32}}cm\]
done
clear
D)
\[1.104\times {{10}^{-33}}cm\]
done
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View Answer play_arrow
question_answer 94) Which type of stacking pattern is found in sodium chloride crystal lattice?
A)
\[a-b-a-b\]
done
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B)
\[a-a-a\]
done
clear
C)
\[a-b-c-a-b-c\]
done
clear
D)
None of these
done
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View Answer play_arrow
question_answer 95) Equivalent weight of a bivalent metal is 37.2. The molecular weight of its chloride is
A)
412.2
done
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B)
216
done
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C)
145.4
done
clear
D)
108.2
done
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question_answer 96) Phenolphthalein is obtained by heating phthalic anhydride with \[conc.{{H}_{2}}S{{O}_{4}}\]and
A)
benzyl alcohol
done
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B)
benzene
done
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C)
phenol
done
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D)
benzoic acid
done
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question_answer 97) Freezing point of urea solution is\[-{{0.6}^{o}}C\]. How much urea\[(m.wt.=60g/mol)\]will be required to dissolve in 3 kg water? \[({{k}_{f}}={{1.5}^{o}}C\,\,kg\,\,mo{{l}^{-1}})\]
A)
24 g
done
clear
B)
36 g
done
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C)
60 g
done
clear
D)
72 g
done
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question_answer 98) If\[K<1.0\], what will be the value of\[\Delta {{G}^{o}}\]of the following?
A)
Zero
done
clear
B)
1.0
done
clear
C)
Positive
done
clear
D)
Negative
done
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View Answer play_arrow
question_answer 99) The normality of a solution containing 32.5 g of\[{{(COOH)}_{2}}\cdot 2{{H}_{2}}O\]per\[0.5\,\,L\]is
A)
\[10\,\,N\]
done
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B)
\[1\,\,N\]
done
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C)
\[2\,\,N\]
done
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D)
\[0.1\,\,N\]
done
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View Answer play_arrow
question_answer 100) For the titration of\[KOH\]vs\[{{(COOH)}_{2}}\cdot 2{{H}_{2}}O\], the suitable indicator is
A)
methyl orange
done
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B)
phenolphthalein
done
clear
C)
methyl red
done
clear
D)
All can be used
done
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question_answer 101) The radius of\[N{{a}^{+}}\]is\[95\,\,\text{pm}\]and that of\[C{{l}^{-}}\]ion is\[181\,\,\text{pm}\]. The coordination number of\[N{{a}^{+}}\]is
A)
8
done
clear
B)
6
done
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C)
4
done
clear
D)
unpredictable
done
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question_answer 102) In van der Waals equation of state of the gas law, the constant V is a measure of
A)
intermolecular repulsion
done
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B)
intermolecular attraction
done
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C)
volume occupied by the molecules
done
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D)
intermolecular collisions per unit volume
done
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View Answer play_arrow
question_answer 103) Which reaction intermediate is formed during the condensation reaction between acetaldehyde and formaldehyde?
A)
\[:C{{H}_{2}}CHO\]
done
clear
B)
\[\overset{+}{\mathop{C}}\,{{H}_{2}}CHO\]
done
clear
C)
\[\overset{+}{\mathop{C}}\,{{H}_{2}}OH\]
done
clear
D)
\[:\bar{C}HCHO\]
done
clear
View Answer play_arrow
question_answer 104) \[2,\,\,2\mathbf{-}\]dichloro propane on hydrolysis yields
A)
acetone
done
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B)
\[2,\,\,2\mathbf{-}\]propane diol
done
clear
C)
iso-propyl alcohol
done
clear
D)
acetaldehyde
done
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View Answer play_arrow
question_answer 105) Phenols are more acidic than alcohols because
A)
phenoxide ion is stabilized by resonance
done
clear
B)
phenols are more soluble in polar solvents
done
clear
C)
phenoxide ions do not exhibit resonance
done
clear
D)
alcohols do not lose H atoms at all
done
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View Answer play_arrow
question_answer 106) Lemon gives sour taste because of
A)
citric acid
done
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B)
tartaric acid
done
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C)
oxalic acid
done
clear
D)
acetic acid
done
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View Answer play_arrow
question_answer 107) When ammonium chloride is added to ammonia solution, the pH of the resulting solution will be
A)
increased
done
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B)
seven
done
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C)
decreased
done
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D)
unchanged
done
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View Answer play_arrow
question_answer 108) Which of the following has highest second ionization energy?
A)
Calcium
done
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B)
Chromium
done
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C)
Iron
done
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D)
Cobalt
done
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View Answer play_arrow
question_answer 109) The standard reduction potentials at\[298K\]for the following half-cell reactions are given below \[Z{{n}^{2+}}(aq)+2{{e}^{-}}Zn(s)-0.762\] \[C{{r}^{3+}}(aq)+3{{e}^{-}}Cr(s)-0.74\] \[2{{H}^{+}}(aq)+2{{e}^{-}}{{H}_{2}}(g)-0.00\] \[F{{e}^{3+}}(aq)+{{e}^{-}}F{{e}^{2+}}(aq)-0.77\] Which one of the following is the strongest reducing agent?
A)
\[Zn(s)\]
done
clear
B)
\[Cr(s)\]
done
clear
C)
\[{{H}_{2}}(g)\]
done
clear
D)
\[F{{e}^{2+}}(aq)\]
done
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question_answer 110) Following reaction, \[{{(C{{H}_{3}})}_{3}}CBr+{{H}_{2}}O\xrightarrow{{}}{{(C{{H}_{3}})}_{3}}COH+HBr\]is an example of
A)
elimination reaction
done
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B)
free radical substitution
done
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C)
nucleophilic substitution
done
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D)
electrophilic substitution
done
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question_answer 111) The unit of rate for a first order reaction is
A)
\[L\,\,{{s}^{-1}}\]
done
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B)
\[mo{{l}^{-1}}\,\,L\,\,{{s}^{-1}}\]
done
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C)
\[mol\,\,{{L}^{-1}}\,\,{{s}^{-1}}\]
done
clear
D)
\[mol\,\,{{s}^{-1}}\]
done
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View Answer play_arrow
question_answer 112) \[Iso-\]propyl amine with excess of acetyl chloride will give
A)
\[{{(C{{H}_{3}}CO)}_{2}}N-C-{{(C{{H}_{3}})}_{3}}\]
done
clear
B)
\[{{(C{{H}_{3}})}_{2}}CH-\underset{\begin{smallmatrix} | \\ H \end{smallmatrix}}{\mathop{N}}\,-COC{{H}_{3}}\]
done
clear
C)
\[{{(C{{H}_{3}})}_{2}}CHN{{(CO{{H}_{3}})}_{2}}\]
done
clear
D)
\[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ H \end{smallmatrix}}{\mathop{N}}\,-COC{{H}_{3}}\]
done
clear
View Answer play_arrow
question_answer 113) \[{{C}_{2}}{{H}_{5}}CHO\]and\[{{(C{{H}_{3}})}_{2}}CO\]can be distinguished by testing with
A)
phenyl hydrazine
done
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B)
hydroxyl amine
done
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C)
Fehling solution
done
clear
D)
sodium bisulphite
done
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View Answer play_arrow
question_answer 114) Glucose molecule reacts with\[X\]number of molecules of phenylhydrazine to yield osazone. The value of T is
A)
four
done
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B)
one
done
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C)
two
done
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D)
three
done
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question_answer 115) The oxidation number of chromium in\[Cr{{O}_{5}}\]is
A)
+3
done
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B)
+ 5
done
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C)
+ 10
done
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D)
+ 6
done
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View Answer play_arrow
question_answer 116) Liquor ammonia bottles are opened only after cooling. This is because
A)
it is a mild explosive
done
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B)
it generates high vapour pressure
done
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C)
Both (a) and (b)
done
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D)
it is lachrymatory
done
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View Answer play_arrow
question_answer 117) What will be the proportion of moles of metal \[(Cu:Ni:Ag)\]at cathode according to the second law of Faraday?
A)
\[1:2:1\]
done
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B)
\[2:2:1\]
done
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C)
\[1:2:2\]
done
clear
D)
\[1:1:2\]
done
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View Answer play_arrow
question_answer 118) Which equation is true to calculate the energy of activation, if the rate of reaction is doubled by increasing temperature from\[{{T}_{1}}K\]to\[{{T}_{2}}K\]?
A)
\[{{\log }_{10}}\frac{{{k}_{1}}}{{{k}_{2}}}=\frac{{{E}_{a}}}{2.303R}\left[ \frac{1}{{{T}_{1}}}-\frac{1}{{{T}_{2}}} \right]\]
done
clear
B)
\[{{\log }_{10}}\frac{{{k}_{2}}}{{{k}_{1}}}=\frac{{{E}_{a}}}{2.303R}\left[ \frac{1}{{{T}_{2}}}-\frac{1}{{{T}_{1}}} \right]\]
done
clear
C)
\[{{\log }_{10}}\frac{1}{2}=\frac{{{E}_{a}}}{2.303}\left[ \frac{1}{{{T}_{2}}}-\frac{1}{{{T}_{1}}} \right]\]
done
clear
D)
\[{{\log }_{10}}2=\frac{{{E}_{a}}}{2.303R}\left[ \frac{1}{{{T}_{1}}}-\frac{1}{{{T}_{2}}} \right]\]
done
clear
View Answer play_arrow
question_answer 119) For a reversible reaction : \[X(g)+3Y(g)2Z(g);\,\,\Delta H=-40kJ\] the standard entropies of\[X,\,\,Y\]and\[Z\]are 60, 40 and 50 \[J{{K}^{-1}}mo{{l}^{-1}}\]respectively. The temperature at which the above reaction attains equilibrium is about
A)
\[400\,\,K\]
done
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B)
\[500\,\,K\]
done
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C)
\[273\,\,K\]
done
clear
D)
\[373\,\,K\]
done
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View Answer play_arrow
question_answer 120) Which of the following gives aldol condensation reaction?
A)
\[{{C}_{6}}{{H}_{5}}OH\]
done
clear
B)
\[{{C}_{6}}{{H}_{5}}-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-{{C}_{6}}{{H}_{5}}\]
done
clear
C)
\[C{{H}_{3}}C{{H}_{2}}-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}\]
done
clear
D)
\[{{(C{{H}_{3}})}_{3}}C-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-{{C}_{6}}{{H}_{5}}\]
done
clear
View Answer play_arrow
question_answer 121) The range of the function\[f\left( x \right)={{x}^{2}}+\frac{1}{{{x}^{2}}+1}\]is
A)
\[[1,\,\,\infty )\]
done
clear
B)
\[[2,\,\,\infty )\]
done
clear
C)
\[\left[ \frac{3}{2},\,\,\infty \right)\]
done
clear
D)
None of these
done
clear
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question_answer 122) If\[f\left( x \right)=\left\{ \begin{matrix} a{{x}^{2}}+b, & b\ne 0,\,\,x\le 1 \\ b{{x}^{2}}+ax+c, & x>1 \\ \end{matrix} \right.\],then \[f\left( x \right)\]is continuous and differentiable at\[x=1\], if
A)
\[c=0,\,\,a=2b\]
done
clear
B)
\[a=b,\,\,c\in R\]
done
clear
C)
\[a=b,\,\,c=0\]
done
clear
D)
\[a=b,\,\,c\ne 0\]
done
clear
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question_answer 123) If a circle passes through the point\[(1,\,\,2)\]and cuts the circle\[{{x}^{2}}+{{y}^{2}}=4\]orthogonally, then the equation of the locus of its centre is
A)
\[{{x}^{2}}+{{y}^{2}}-3x-8y+1=0\]
done
clear
B)
\[{{x}^{2}}+{{y}^{2}}-2x-6y-7=0\]
done
clear
C)
\[2x+4y-9=0\]
done
clear
D)
\[2x+4y-1=0\]
done
clear
View Answer play_arrow
question_answer 124) If\[\int{f\left( x \right)}\sin x\cos x\,\,dx\] \[=\frac{1}{2({{b}^{2}}-{{a}^{2}})}\log [f(x)]+c,\] then\[f\left( x \right)\]is equal to
A)
\[\frac{1}{{{a}^{2}}{{\sin }^{2}}x+{{b}^{2}}{{\cos }^{2}}x}\]
done
clear
B)
\[\frac{1}{{{a}^{2}}{{\sin }^{2}}x-{{b}^{2}}{{\cos }^{2}}x}\]
done
clear
C)
\[\frac{1}{{{a}^{2}}{{\cos }^{2}}x-{{b}^{2}}{{\sin }^{2}}x}\]
done
clear
D)
\[\frac{1}{{{a}^{2}}{{\cos }^{2}}x+{{b}^{2}}{{\sin }^{2}}x}\]
done
clear
View Answer play_arrow
question_answer 125) The points representing complex number 2 for which\[\left| z-3 \right|=\left| z-5 \right|\]lie on the locus given by
A)
an ellipse
done
clear
B)
a circle
done
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C)
a straight line
done
clear
D)
None of the above
done
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View Answer play_arrow
question_answer 126) The value of\[\alpha \], for which the equation\[{{x}^{2}}-(\sin \alpha -2)x-(1+\sin \alpha )=0\]has roots whose sum of square is least, is
A)
\[\frac{\pi }{3}\]
done
clear
B)
\[\frac{\pi }{4}\]
done
clear
C)
\[\frac{\pi }{2}\]
done
clear
D)
\[\frac{\pi }{6}\]
done
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View Answer play_arrow
question_answer 127) For\[n\in N,\,\,{{10}^{n-2}}\ge 81n\], is
A)
\[n>5\]
done
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B)
\[n\ge 5\]
done
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C)
\[n<5\]
done
clear
D)
\[n>8\]
done
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View Answer play_arrow
question_answer 128) The two consecutive terms in the expansion of\[{{(3+2x)}^{74}}\]whose coefficients are equal are
A)
11, 12
done
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B)
7, 8
done
clear
C)
30, 31
done
clear
D)
None of these
done
clear
View Answer play_arrow
question_answer 129) The value of\[2.\overline{357}\]is
A)
\[\frac{2355}{999}\]
done
clear
B)
\[\frac{2355}{1000}\]
done
clear
C)
\[\frac{2355}{1111}\]
done
clear
D)
None of these
done
clear
View Answer play_arrow
question_answer 130) Let\[{{S}_{n}}=\frac{1}{{{1}^{3}}}+\frac{1}{{{1}^{3}}}+\frac{2}{{{2}^{3}}}+...+\frac{1+2+...+n}{{{1}^{3}}+{{2}^{3}}+...+n}\] \[n=1,2,3,...\]. Then,\[{{S}_{n}}\]is not greater than
A)
\[\frac{1}{2}\]
done
clear
B)
1
done
clear
C)
2
done
clear
D)
4
done
clear
View Answer play_arrow
question_answer 131) If\[E(\theta )=\left[ \begin{matrix} {{\cos }^{2}}\theta & \cos \theta \sin \theta \\ \cos \theta \sin \theta & {{\sin }^{2}}\theta \\ \end{matrix} \right]\]and\[\theta \]and\[\phi \] differ by an odd multiple of\[\frac{\pi }{2}\], then\[E(\theta )E(\phi )\]is a
A)
unit matrix
done
clear
B)
null matrix
done
clear
C)
diagonal matrix
done
clear
D)
None of the above
done
clear
View Answer play_arrow
question_answer 132) A parabola is drawn with its focus at\[(3,\,\,4)\]and vertex at the focus of the parabola\[{{y}^{2}}-12x-4y+4=0\]. The equation of the parabola is
A)
\[{{y}^{2}}-8x-6y+25=0\]
done
clear
B)
\[{{y}^{2}}-6x+8y-25=0\]
done
clear
C)
\[{{x}^{2}}-6x-8y+25=0\]
done
clear
D)
\[{{x}^{2}}+6x-8y-25=0\]
done
clear
View Answer play_arrow
question_answer 133) If\[p,\,\,p\]denote the lengths of the perpendiculars from the focus and the centre of an ellipse with semi major axis of length a respectively on a tangent to the ellipse and\[r\]denotes the focal distance of the point, then
A)
\[ap=rp+1\]
done
clear
B)
\[rp=ap\]
done
clear
C)
\[ap=rp+1\]
done
clear
D)
\[ap=rp\]
done
clear
View Answer play_arrow
question_answer 134) The equation of perpendicular bisectors of sides\[AB\]and\[AC\]of a\[\Delta ABC\]are\[x-y+5=0\] and\[x+2y=0\]respectively. If the coordinates of vertex\[A\]are\[(1,\,\,-2)\], the equation of\[BC\]is
A)
\[14x+23y-40=0\]
done
clear
B)
\[14x-23y+40=0\]
done
clear
C)
\[23x+14y-40=0\]
done
clear
D)
\[23x-14y+40=0\]
done
clear
View Answer play_arrow
question_answer 135) If\[\cos \theta =-\frac{\sqrt{3}}{2}\]and\[\sin \alpha =-\frac{3}{5}\], where\[\theta \]does not lie in the third quadrant, then \[\frac{2\tan \alpha +\sqrt{3}\tan \theta }{{{\cot }^{2}}\theta +\cos \alpha }\]is equal to
A)
\[\frac{7}{22}\]
done
clear
B)
\[\frac{5}{22}\]
done
clear
C)
\[\frac{9}{22}\]
done
clear
D)
\[\frac{22}{5}\]
done
clear
View Answer play_arrow
question_answer 136) A parallelogram is constructed on the vectors \[\overset{\to }{\mathop{\mathbf{a}}}\,=3\overset{\to }{\mathop{\alpha }}\,-\overset{\to }{\mathop{\beta }}\,,\,\,\overset{\to }{\mathop{\mathbf{b}}}\,=\overset{\to }{\mathop{\alpha }}\,+3\overset{\to }{\mathop{\beta }}\,\], if\[\left| \overset{\to }{\mathop{\alpha }}\, \right|=\left| \overset{\to }{\mathop{\beta }}\, \right|=2\]and angle between\[\overset{\to }{\mathop{\alpha }}\,\]and\[\overset{\to }{\mathop{\beta }}\,\]is\[\frac{\pi }{3}\], then length of a diagonal of the parallelogram is
A)
\[4\sqrt{5}\]
done
clear
B)
\[4\sqrt{3}\]
done
clear
C)
\[4\sqrt{17}\]
done
clear
D)
None of the above
done
clear
View Answer play_arrow
question_answer 137) The value of\[c\], so that for all real\[x\], the vectors\[cx\widehat{\mathbf{i}}-6\widehat{\mathbf{j}}+3\widehat{\mathbf{k}}\],\[x\widehat{\mathbf{i}}+2\widehat{\mathbf{j}}+2cx\widehat{\mathbf{k}}\]make an obtuse angle, are
A)
\[c<0\]
done
clear
B)
\[0<c<\frac{4}{3}\]
done
clear
C)
\[-\frac{4}{3}<c<0\]
done
clear
D)
\[c>0\]
done
clear
View Answer play_arrow
question_answer 138) The solution of the equation \[y-x\frac{dy}{dx}=a\left( {{y}^{2}}+\frac{dy}{dx} \right)\]
A)
\[y=c(x+a)(1-ay)\]
done
clear
B)
\[y=c(x+a)(1+ay)\]
done
clear
C)
\[y=c(x-a)(1+ay)\]
done
clear
D)
None of the above
done
clear
View Answer play_arrow
question_answer 139) The order of the differential equation whose general solution is given by\[y=({{c}_{1}}+{{c}_{2}})\cos (x+{{c}_{3}})-{{c}_{4}}{{e}^{x\_{{c}_{5}}}}\], where\[{{c}_{1}},\,\,{{c}_{2}},\,\,{{c}_{3}},\,\,{{c}_{4}},\,\,{{c}_{5}}\]are arbitrary constants, is
A)
4
done
clear
B)
3
done
clear
C)
2
done
clear
D)
5
done
clear
View Answer play_arrow
question_answer 140) If\[f(x)={{x}^{3}}+b{{x}^{2}}+cx+d\]and\[0<{{b}^{2}}<c\], then in\[(-\infty ,\,\,\infty )\]
A)
\[f(x)\]is strictly increasing function
done
clear
B)
\[f(x)\]has a local maxima
done
clear
C)
\[f(x)\]strictly decreasing function
done
clear
D)
\[f(x)\]is bounded
done
clear
View Answer play_arrow
question_answer 141) \[\frac{d}{dx}{{\sin }^{-1}}(x\sqrt{1-x}+\sqrt{x}\sqrt{1-{{x}^{2}}})\]
A)
\[-\frac{1}{2x\sqrt{1-x}}-\frac{1}{\sqrt{1-{{x}^{2}}}}\]
done
clear
B)
\[\frac{1}{2\sqrt{x}\sqrt{1-x}}-\frac{1}{\sqrt{1-{{x}^{2}}}}\]
done
clear
C)
\[\frac{1}{2\sqrt{x}\sqrt{1-x}}+\frac{1}{\sqrt{1-{{x}^{2}}}}\]
done
clear
D)
\[-\frac{1}{2\sqrt{x}\sqrt{1-x}}+\frac{1}{\sqrt{1-{{x}^{2}}}}\]
done
clear
View Answer play_arrow
question_answer 142) \[\int{\frac{x{{\tan }^{-1}}x}{{{(1+{{x}^{2}})}^{3}}}}dx\]is equal to
A)
\[\frac{x-{{\tan }^{-1}}x}{1-{{x}^{2}}}+c\]
done
clear
B)
\[\frac{x+{{\tan }^{-1}}x}{\sqrt{1-{{x}^{2}}}}+c\]
done
clear
C)
\[\frac{x-{{\tan }^{-1}}x}{\sqrt{1+{{x}^{2}}}}+c\]
done
clear
D)
\[\frac{x+\sqrt{1-{{x}^{2}}}}{\sqrt{1+{{x}^{2}}}}+c\]
done
clear
View Answer play_arrow
question_answer 143) Let\[A=\left[ \begin{matrix} 1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1 \\ \end{matrix} \right]\], where\[0\le \theta \le 2\pi \]. Then, the range of\[\left| A \right|\]is
A)
0
done
clear
B)
{2, 4}
done
clear
C)
[2, 4]
done
clear
D)
None of the above
done
clear
View Answer play_arrow
question_answer 144) If\[y=\left| \cos x \right|+\left| \sin x \right|\], then\[\frac{dy}{dx}\]at\[x=\frac{2\pi }{3}\]is
A)
0
done
clear
B)
1
done
clear
C)
\[\frac{1-\sqrt{3}}{2}\]
done
clear
D)
\[\frac{\sqrt{3}-1}{2}\]
done
clear
View Answer play_arrow
question_answer 145) \[\underset{n\to \infty }{\mathop{\lim }}\,\left( \frac{1}{1-{{n}^{2}}}+\frac{2}{1-{{n}^{2}}}+...+\frac{n}{1-{{n}^{2}}} \right)\]is equal to
A)
0
done
clear
B)
\[-\frac{1}{2}\]
done
clear
C)
\[\frac{1}{2}\]
done
clear
D)
None of these
done
clear
View Answer play_arrow
question_answer 146) Let\[f(x)=\left\{ \begin{matrix} \sin x, & x\ne n\pi \\ 2 & x=n\pi \\ \end{matrix} \right.\], where\[n\in I\]and\[g(x)=\left\{ \begin{matrix} {{x}^{2}}+1, & x\ne 2 \\ 3, & x=2 \\ \end{matrix} \right.\], then\[\underset{x\to 0}{\mathop{\lim }}\,g[f(x)]\]is
A)
1
done
clear
B)
0
done
clear
C)
3
done
clear
D)
does not exist
done
clear
View Answer play_arrow
question_answer 147) The intercept made by the tangent to the curve\[y=\int_{0}^{x}{|t|}\,\,dt\],which is parallel to the line \[y=2x\], on x-axis is equal to
A)
1
done
clear
B)
-2
done
clear
C)
2
done
clear
D)
None of these
done
clear
View Answer play_arrow
question_answer 148) If\[P={{x}^{3}}-\frac{1}{{{x}^{3}}}\]and\[Q=x-\frac{1}{x},\,\,x\in (0,\,\,x)\], then minimum value of\[\frac{P}{{{Q}^{2}}}\]is
A)
\[2\sqrt{3}\]
done
clear
B)
\[-2\sqrt{3}\]
done
clear
C)
does not exist
done
clear
D)
None of these
done
clear
View Answer play_arrow
question_answer 149) Locus of the point which divides double ordinate of the ellipse\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]in the ratio 1:2 internally, is
A)
\[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{9{{y}^{2}}}{{{b}^{2}}}=\frac{1}{9}\]
done
clear
B)
\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{9{{y}^{2}}}{{{b}^{2}}}=1\]
done
clear
C)
\[\frac{9{{y}^{2}}}{{{a}^{2}}}+\frac{9{{y}^{2}}}{{{b}^{2}}}=1\]
done
clear
D)
None of these
done
clear
View Answer play_arrow
question_answer 150) From any point on the hyperbola\[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\]tangents are drawn to the hyperbola\[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=2\]. The area cut-off by the chord of contact on the asymptotes is equal to
A)
\[\frac{ab}{2}\]
done
clear
B)
\[ab\]
done
clear
C)
\[2ab\]
done
clear
D)
\[4ab\]
done
clear
View Answer play_arrow
question_answer 151) The value of the sum of the series\[3{{\cdot }^{n}}{{C}_{0}}-8{{\cdot }^{n}}{{C}_{1}}+{{13}^{n}}{{C}_{2}}-18{{\cdot }^{n}}{{C}_{3}}+...\]upto\[(n+1)\]terms is
A)
0
done
clear
B)
\[{{3}^{n}}\]
done
clear
C)
\[{{5}^{n}}\]
done
clear
D)
None of these
done
clear
View Answer play_arrow
question_answer 152) If\[A\]is a skew-symmetric matrix, then trace of\[A\]is
A)
1
done
clear
B)
-1
done
clear
C)
0
done
clear
D)
None of these
done
clear
View Answer play_arrow
question_answer 153) The arbitrary constant on which the value of the determinant \[\left| \begin{matrix} 1 & \alpha & {{\alpha }^{2}} \\ \cos (p-d)a & \cos pa & \cos (p-d)a \\ \sin (p-d)a & \sin pa & \sin (p-d)a \\ \end{matrix} \right|\]does not depend, is
A)
\[\alpha \]
done
clear
B)
p
done
clear
C)
d
done
clear
D)
a
done
clear
View Answer play_arrow
question_answer 154) The sum of the first n terms of the series\[\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+...\]is equal to
A)
\[{{2}^{n}}-n+1\]
done
clear
B)
\[1-{{2}^{n}}\]
done
clear
C)
\[n+{{2}^{-n}}-1\]
done
clear
D)
\[{{2}^{n}}-1\]
done
clear
View Answer play_arrow
question_answer 155) The base of a cliff is circular. From the extremities of a diameter of the base angles of elevation of the top of the cliff are \[{{30}^{o}}\]and\[{{60}^{o}}\]. If the height of the cliff be 500 m, then the diameter of the base of the cliff is
A)
\[\frac{2000}{\sqrt{3}}m\]
done
clear
B)
\[\frac{1000}{\sqrt{3}}m\]
done
clear
C)
\[\frac{2000}{\sqrt{3}}m\]
done
clear
D)
\[1000\sqrt{3}\,m\]
done
clear
View Answer play_arrow
question_answer 156) The most general solutions of the equation\[\sec x-1=(\sqrt{2}-1)\tan x\]are given by
A)
\[n\pi +\frac{\pi }{8}\]
done
clear
B)
\[2n\pi ,\,\,2n\pi +\frac{\pi }{4}\]
done
clear
C)
\[2n\pi \]
done
clear
D)
None of these
done
clear
View Answer play_arrow
question_answer 157) The maximum value of\[\sin \left( x+\frac{\pi }{6} \right)+\cos \left( x+\frac{\pi }{6} \right)\]in the interval \[\left( 0,\,\frac{\pi }{2} \right)\] is attained at
A)
\[x=\frac{\pi }{12}\]
done
clear
B)
\[x=\frac{\pi }{6}\]
done
clear
C)
\[x=\frac{\pi }{3}\]
done
clear
D)
\[x=\frac{\pi }{2}\]
done
clear
View Answer play_arrow
question_answer 158) If\[{{z}_{r}}=\cos \frac{r\alpha }{{{n}^{2}}}+i\sin \frac{r\alpha }{2}\], where\[r=1,\,\,2,\,\,3,....,\,\,n,\]then\[\underset{n\to \infty }{\mathop{\lim }}\,\,\,{{z}_{1}},\,\,{{z}_{2}}...{{z}_{n}}\]is equal to
A)
\[\cos \alpha +i\sin \alpha \]
done
clear
B)
\[\cos \left( \frac{\alpha }{2} \right)-i\sin \left( \frac{\alpha }{2} \right)\]
done
clear
C)
\[{{e}^{i\alpha /2}}\]
done
clear
D)
\[\sqrt[3]{{{e}^{i\alpha }}}\]
done
clear
View Answer play_arrow
question_answer 159) Negation of Paris is in France and London is in England is
A)
Paris is in England and London is in France
done
clear
B)
Paris is not in France or London is not in England
done
clear
C)
Paris is in England or London is in France
done
clear
D)
None of the above
done
clear
View Answer play_arrow
question_answer 160) The area enclosed between the curves\[y={{x}^{3}}\]and\[y=\sqrt{x}\]is
A)
\[\frac{5}{3}sq\,\,unit\]
done
clear
B)
\[\frac{5}{4}sq\,\,unit\]
done
clear
C)
\[\frac{5}{12}sq\,\,unit\]
done
clear
D)
\[\frac{12}{5}sq\,\,unit\]
done
clear
View Answer play_arrow
question_answer 161) Find the equation of the bisector of the obtuse angle between the lines\[3x-4y+7=0\]and\[-12x-5y+2=0\],
A)
\[21x+77y-101=0\]
done
clear
B)
\[99x-27y+81=0\]
done
clear
C)
\[21x-77y+101=0\]
done
clear
D)
None of the above
done
clear
View Answer play_arrow
question_answer 162) The equation of curve passing through the point\[\left( 1,\frac{\pi }{4} \right)\]and having slope of tangent at any point\[(x,\,\,y)\]as\[\frac{y}{x}-{{\cos }^{2}}\left( \frac{y}{x} \right)\]is
A)
\[x={{e}^{1+\tan \left( \frac{y}{x} \right)}}\]
done
clear
B)
\[x={{e}^{1-\tan \left( \frac{y}{x} \right)}}\]
done
clear
C)
\[x={{e}^{1+\tan \left( \frac{x}{y} \right)}}\]
done
clear
D)
\[x={{e}^{1-\tan \left( \frac{x}{y} \right)}}\]
done
clear
View Answer play_arrow
question_answer 163) If\[P(n):2+4+6+...+(2n),\,\,n\in N\], then\[P(k)=k(k+1)+2\]implies \[P(k+1)=(k+1)(k+2)+2\]is true for all\[k\in N.\] So, statement\[P(n)=n(n+1)+2\]is true for
A)
\[n\ge 1\]
done
clear
B)
\[n\ge 2\]
done
clear
C)
\[n\ge 3\]
done
clear
D)
None of these
done
clear
View Answer play_arrow
question_answer 164) The differential equation of all non-vertical lines in a plane is
A)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}=0\]
done
clear
B)
\[\frac{{{d}^{2}}x}{d{{y}^{2}}}=0\]
done
clear
C)
\[\frac{dy}{dx}=0\]
done
clear
D)
\[\frac{dx}{dy}=0\]
done
clear
View Answer play_arrow
question_answer 165) The unit vector in ZOX plane and making angle \[{{45}^{o}}\]and \[{{60}^{o}}\]respectively with\[\overset{\to }{\mathop{\mathbf{a}}}\,=2\widehat{\mathbf{i}}+2\widehat{\mathbf{j}}-\widehat{\mathbf{k}}\]and\[\overset{\to }{\mathop{\mathbf{b}}}\,=0\widehat{\mathbf{i}}+\widehat{\mathbf{j}}-\widehat{\mathbf{k}}\], is
A)
\[-\frac{1}{\sqrt{2}}\widehat{\mathbf{i}}+\frac{1}{\sqrt{2}}\widehat{\mathbf{k}}\]
done
clear
B)
\[\frac{1}{\sqrt{2}}\mathbf{\hat{i}}-\frac{1}{\sqrt{2}}\mathbf{\hat{k}}\]
done
clear
C)
\[\frac{1}{3\sqrt{2}}\widehat{\mathbf{i}}+\frac{4}{3\sqrt{2}}\widehat{\mathbf{j}}+\frac{1}{3\sqrt{2}}\widehat{\mathbf{k}}\]
done
clear
D)
None of the above
done
clear
View Answer play_arrow
question_answer 166) If\[\int_{2}^{e}{\left( \frac{1}{\log x}-\frac{1}{{{(\log x)}^{2}}} \right)dx=a+\frac{b}{\log 2}}\],then
A)
\[a=e,\,\,b=-2\]
done
clear
B)
\[a=e,\,\,b=2\]
done
clear
C)
\[a=-e,\,\,b=2\]
done
clear
D)
None of these
done
clear
View Answer play_arrow
question_answer 167) The circle\[{{x}^{2}}+{{y}^{2}}-4x-4y+4=0\]is inscribed in a triangle which has two of its sides along the coordinate axes. If the locus of the circumcentre of the triangle is\[x+y-xy+k\sqrt{{{x}^{2}}+{{y}^{2}}}=0\], then the value of \[k\]is equal to
A)
2
done
clear
B)
1
done
clear
C)
-2
done
clear
D)
3
done
clear
View Answer play_arrow
question_answer 168) The points of discontinuity of tan x are
A)
\[n\pi ,\,\,n\in I\]
done
clear
B)
\[2n\pi ,\,\,n\in I\]
done
clear
C)
\[(2n+1)\frac{\pi }{2},\,\,n\in I\]
done
clear
D)
None of the above
done
clear
View Answer play_arrow
question_answer 169) The two curves\[{{x}^{3}}-3x{{y}^{2}}+2=0\]and\[3{{x}^{2}}y-{{y}^{3}}-2=0\]
A)
cut at right angles
done
clear
B)
touch each other
done
clear
C)
cut at an angle\[\frac{\pi }{3}\]
done
clear
D)
cut at an angle\[\frac{\pi }{4}\]
done
clear
View Answer play_arrow
question_answer 170) The period of the function \[f(x)=\frac{\sin 8x\cos x-\sin 6x\cos 3x}{\cos 2x\cos x-\sin 3x\sin 4x}\]
A)
\[\pi \]
done
clear
B)
\[2\pi \]
done
clear
C)
\[\frac{\pi }{2}\]
done
clear
D)
None of these
done
clear
View Answer play_arrow
question_answer 171) The derivative of\[f(\tan x)\]w.r.t.\[g(\sec x)\]at\[x=\frac{\pi }{4}\], where\[f(1)=2\]and\[g(\sqrt{2})=4\], is
A)
\[\frac{1}{\sqrt{2}}\]
done
clear
B)
\[\sqrt{2}\]
done
clear
C)
1
done
clear
D)
None of these
done
clear
View Answer play_arrow
question_answer 172) If\[a>0,\,\,b>0\]the maximum area of the triangle formed by the points\[O(0,\,\,0)\]\[A(a\cos \theta ,\,\,b\sin \theta )\]and\[B(a\cos \theta ,\,\,-b\sin \theta )\]is (in sq unit)
A)
\[\frac{ab}{2}\]when\[\theta =\frac{\pi }{4}\]
done
clear
B)
\[\frac{3ab}{4}\]when\[\theta =\frac{\pi }{4}\]
done
clear
C)
\[\frac{ab}{2}\]when\[\theta =-\frac{\pi }{2}\]
done
clear
D)
\[{{a}^{2}}{{b}^{2}}\]
done
clear
View Answer play_arrow
question_answer 173) If the two curves \[y={{a}^{x}}\]and\[y={{b}^{x}}\]intersect at an angle\[\alpha \], then tan a equals
A)
\[\frac{\log a-\log b}{1+\log a\log b}\]
done
clear
B)
\[\frac{\log a+\log b}{1-\log a\log b}\]
done
clear
C)
\[\frac{\log a-\log b}{1-\log a\log b}\]
done
clear
D)
None of these
done
clear
View Answer play_arrow
question_answer 174) The number of roots of the equation \[x-\frac{2}{x-1}=1-\frac{2}{x-1}\]
A)
1
done
clear
B)
2
done
clear
C)
0
done
clear
D)
infinitely many
done
clear
View Answer play_arrow
question_answer 175) The vector \[z=-4+5i\]is turned counter clockwise through an angle of\[{{180}^{o}}\]and stretched\[1\frac{1}{2}\]times. The complex number corresponding to newly obtained vector is
A)
\[-6+\frac{15}{2}i\]
done
clear
B)
\[6+\frac{15}{2}i\]
done
clear
C)
\[6-\frac{15}{2}i\]
done
clear
D)
None of these
done
clear
View Answer play_arrow
question_answer 176) If\[A=[{{a}_{ij}}]\]is a4\[4\times 4\]matrix\[{{C}_{ij}}\]is the cofactor of the element\[{{a}_{ij}}\]in\[\left| A \right|\], then the expression\[{{a}_{11}}{{C}_{11}}+{{a}_{12}}{{C}_{12}}+{{a}_{13}}{{C}_{13}}+{{a}_{14}}{{C}_{14}}\]equal to
A)
0
done
clear
B)
-1
done
clear
C)
1
done
clear
D)
\[\left| A \right|\]
done
clear
View Answer play_arrow
question_answer 177) If\[A=\left\{ x:\frac{\pi }{6}\le x\le \frac{\pi }{3} \right\}\]and \[f(x)=\cos x-x(1+x)\], then\[f(A)\]is equal to
A)
\[\left[ -\frac{\pi }{3},\,\,-\frac{\pi }{6} \right]\]
done
clear
B)
\[\left[ \frac{\pi }{6},\,\,\frac{\pi }{3} \right]\]
done
clear
C)
\[\left[ \frac{1}{2}-\frac{\pi }{3}\left( 1+\frac{\pi }{3} \right),\,\,\frac{\sqrt{3}}{2}-\frac{\pi }{6}\left( 1+\frac{\pi }{6} \right) \right]\]
done
clear
D)
\[\left[ \frac{1}{2}+\frac{\pi }{3}\left( 1-\frac{\pi }{3} \right),\,\,\frac{\sqrt{3}}{2}+\frac{\pi }{6}\left( 1-\frac{\pi }{6} \right) \right]\]
done
clear
View Answer play_arrow
question_answer 178) The contrapositive of\[(p\vee q)\Rightarrow r\]is
A)
\[\tilde{\ }r\Rightarrow (p\vee q)\]
done
clear
B)
\[r\Rightarrow (p\vee q)\]
done
clear
C)
\[\tilde{\ }r\Rightarrow (\tilde{\ }p\wedge \tilde{\ }q)\]
done
clear
D)
\[p\Rightarrow (q\vee r)\]
done
clear
View Answer play_arrow
question_answer 179) If the function\[f(x)=a{{x}^{3}}+b{{x}^{2}}+11x-6\]satisfies the condition of Rollers theorem in\[[1,\,\,3]\]and\[f\left( 2+\frac{1}{\sqrt{3}} \right)=0\], then the values of \[a,\text{ }b\]are respectively
A)
- 1, 6
done
clear
B)
- 2, 1
done
clear
C)
1, -6
done
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D)
\[-1,\,\,\frac{1}{2}\]
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question_answer 180) If\[f(x)=\cos (\log x)\], then \[f\left( \frac{1}{x} \right)f\left( \frac{1}{y} \right)-\frac{1}{2}\left[ f\left( \frac{x}{y} \right)+f(xy) \right]\] is equal to
A)
\[\cos (x-y)\]
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B)
\[\log (x-y)\]
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C)
\[\cos (x+y)\]
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D)
None of these
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question_answer 181) If\[\alpha ={{\sin }^{-1}}\frac{\sqrt{3}}{2}+{{\sin }^{-1}}\frac{1}{3}\]and\[\beta ={{\cos }^{-1}}\frac{\sqrt{3}}{2}+{{\cos }^{-1}}\frac{1}{3}\], then
A)
\[\alpha >\beta \]
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B)
\[\alpha =\beta \]
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C)
\[\alpha <\beta \]
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D)
\[\alpha +\beta =2\pi \]
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question_answer 182) If\[1+\sin \theta +{{\sin }^{2}}\theta +...\infty =4+2\sqrt{3},\,\,0<\theta <\pi \], \[\theta \ne \frac{\pi }{2}\], then
A)
\[\theta =\frac{\pi }{3}\]
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B)
\[\theta =\frac{\pi }{6}\]
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C)
\[\theta =\frac{\pi }{3}\]or\[\frac{\pi }{6}\]
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D)
\[\theta =\frac{\pi }{3}\]or\[\frac{2\pi }{3}\]
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question_answer 183) A round balloon of radius\[r\]subtends an angle \[\alpha \]at the eye of the observer, while the angle of elevation of its centre is\[\beta \]. The height of the centre of balloon is
A)
\[r\cos ec\alpha \sin \frac{\beta }{2}\]
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B)
\[r\sin \alpha \cos ec\frac{\beta }{2}\]
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C)
\[r\sin \frac{\alpha }{2}\cos ec\beta \]
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D)
\[r\cos ec\frac{\alpha }{2}\sin \beta \]
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question_answer 184) In\[\Delta ABC,\,\,{{(a-b)}^{2}}{{\cos }^{2}}\frac{C}{2}+{{(a+b)}^{2}}{{\sin }^{2}}\frac{C}{2}\]is equal to
A)
\[{{a}^{2}}\]
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B)
\[{{b}^{2}}\]
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C)
\[{{c}^{2}}\]
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D)
None of these
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question_answer 185) In a triangle\[\left( 1-\frac{{{r}_{1}}}{{{r}_{2}}} \right)\left( 1-\frac{{{r}_{1}}}{{{r}_{2}}} \right)=2\], then the triangle is
A)
right angled
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B)
isosceles
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C)
equilateral
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D)
None of these
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question_answer 186) If\[a+b+c=0\], then the roots of the equation \[4a{{x}^{2}}+3bx+2c=0\]are
A)
equal
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B)
imaginary
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C)
real
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D)
None of these
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question_answer 187)
The adjoining graph
A)
Connected
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B)
Disconnected
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C)
Neither connected nor disconnected
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D)
None of the above
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question_answer 188) The solution of\[{{\tan }^{-1}}x+2{{\cot }^{-1}}x=\frac{2\pi }{3}\]is
A)
\[-\frac{1}{\sqrt{3}}\]
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B)
\[\frac{1}{\sqrt{3}}\]
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C)
\[-\sqrt{3}\]
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D)
\[\sqrt{3}\]
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question_answer 189) The conjugate of the complex number\[\frac{{{(1+i)}^{2}}}{1-i}\]is
A)
\[1-i\]
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B)
\[1+i\]
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C)
\[-1+i\]
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D)
\[-1-i\]
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question_answer 190) A graph\[G\]has\[m\]vertices of odd degree and \[n\]vertices of even degree. Then which of the following statements is necessarily true?
A)
\[m+n\]is an odd number
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B)
\[m+n\]is an even number
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C)
\[n+1\]is an even number
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D)
\[m+1\]is an odd number
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question_answer 191) The value of\[\sin \left[ 2{{\cos }^{-1}}\frac{\sqrt{5}}{3} \right]\]is
A)
\[\frac{\sqrt{5}}{3}\]
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B)
\[\frac{2\sqrt{5}}{3}\]
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C)
\[\frac{4\sqrt{5}}{9}\]
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D)
\[\frac{2\sqrt{5}}{9}\]
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question_answer 192) In the group\[(G,{{\otimes }_{15}})\], where\[G=\{3,\,\,6,\,\,9,\,\,12\}\], \[{{\otimes }_{15}}\]is multiplication modulo 15, the identity element is
A)
3
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B)
6
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C)
12
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D)
9
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question_answer 193) A group\[(G,\,\,*)\]has 10 elements. The minimum number of elements of\[G\], which are their own inverses is
A)
2
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B)
1
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C)
9
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D)
0
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question_answer 194) \[\frac{3{{x}^{2}}+1}{{{x}^{2}}-6x+8}\]is equal to
A)
\[3+\frac{49}{2(x-4)}-\frac{13}{2(x-2)}\]
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B)
\[\frac{49}{2(x-4)}-\frac{13}{2(x-2)}\]
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C)
\[\frac{-49}{2(x-4)}+\frac{13}{2(x-2)}\]
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D)
\[\frac{49}{2(x-4)}+\frac{13}{2(x-2)}\]
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question_answer 195) The orthocentre of the triangle with vertices\[O(0,\,\,0),\,\,A\left( 0,\,\,\frac{3}{2} \right),\,\,B(-5,\,\,0)\]is
A)
\[\left( \frac{5}{2},\,\,\frac{3}{4} \right)\]
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B)
\[\left( \frac{-5}{2},\,\,\frac{3}{4} \right)\]
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C)
\[\left( -5,\,\,\frac{3}{2} \right)\]
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D)
\[(0,\,\,0)\]
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question_answer 196) The range in which\[y=-{{x}^{2}}+6x-3\]increasing, is
A)
\[x<3\]
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B)
\[x>3\]
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C)
\[7<x<8\]
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D)
\[5<x<6\]
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question_answer 197) The area bounded by the curve\[x=4-{{y}^{2}}\]and the y-axis is
A)
16 sq unit
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B)
32 sq unit
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C)
\[\frac{32}{3}\]sq unit
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D)
\[\frac{16}{3}\]sq unit
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question_answer 198) The number of positive divisors of 252 is
A)
9
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B)
5
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C)
18
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D)
10
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question_answer 199) The remainder obtained when 5124 is divided by 124 is
A)
5
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B)
0
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C)
2
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D)
1
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question_answer 200) Which of the following is not a group with respect to the given operation?
A)
The set of even integers including zero under addition
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B)
The set of odd integers under addition
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C)
{0} under addition
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D)
{1,-1} under multiplication
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question_answer 201) He is so ...... of his own idea that he will not entertain any suggestion from others.
A)
hopeful
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B)
enamoured
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C)
jealous
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D)
possessed
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question_answer 202) Undoubtedly, English is the most...... spoken language in the world today.
A)
broadly
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B)
widely
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C)
greatly
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D)
beautifully
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question_answer 203) I will be leaving for Delhi tonight and ...... to return by this weekend.
A)
waiting
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B)
plan
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C)
going
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D)
making
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question_answer 204) The vacancy ......... by the dismissal of the superintendent is expected to be filled up by the promotion of a U.D.C.
A)
made
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B)
created
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C)
caused
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D)
generated
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question_answer 205) HAGGLE
A)
Postpone
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B)
Accept
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C)
Bargain
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D)
Reject
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question_answer 206) ABSTRUSE
A)
Awful
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B)
Irrelevant
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C)
Shallow
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D)
Profound
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question_answer 207) PENCHANT
A)
Like
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B)
Eagerness
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C)
Disability
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D)
Dislike
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question_answer 208) BARTER
A)
Deal
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B)
Return
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C)
Lend
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D)
Exchange
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question_answer 209) Bringing about gentle and painless death from incurable disease
A)
Gallows
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B)
Suicide
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C)
Euphoria
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D)
Euthanasia
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question_answer 210) The act of killing ones wife
A)
Avicide
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B)
Canicide
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C)
Uxoricide
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D)
Genocide
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question_answer 211) Stage between boyhood and youth
A)
Infancy
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B)
Adolescence
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C)
Puberty
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D)
Maturity
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question_answer 212) Lack of enough blood
A)
Amnesia
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B)
Insomnia
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C)
Anaemia
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D)
Allergy
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question_answer 213) To set the people by ears
A)
To box the people
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B)
To insult and disgrace the people
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C)
To punish heavily
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D)
To excite people to a quarrel
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question_answer 214) To give chapter and verse for a thing
A)
To produce the proof of something
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B)
To eulogise the qualities of a thing
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C)
To make publicity of a thing
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D)
To attach artificial value to a thing
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question_answer 215) Dog in the manger
A)
An undersized bull almost the shape of a dog
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B)
A dog that has no kennel of its own
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C)
A person who puts himself in difficulties an account of other people
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D)
A person who prevents others from enjoying something useless to himself
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question_answer 216) To blow hot and cold
A)
Changing weather
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B)
To be untrustworthy
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C)
To change opinion often
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D)
To be rich and poor frequently
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question_answer 217) SAGACIOUS
A)
Casual
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B)
Cunning
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C)
Foolish
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D)
False
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question_answer 218) EPILOGUE
A)
Conversation
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B)
Dialogue
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C)
Dramatic
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D)
Prologue
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question_answer 219) AUSPICIOUS
A)
Spicy
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B)
Unfavorable
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C)
Conspicuous
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D)
Condemnatory
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question_answer 220) ENGULFED
A)
Encircled
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B)
Groped
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C)
Disfigured
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D)
Detached
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question_answer 221) Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group?
A)
Hill
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B)
Valley
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C)
Dam
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D)
River
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question_answer 222) In a certain code CREAM is written as NBDBQ. How in BREAD written in that code?
A)
EBFAQ
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B)
EBDAQ
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C)
BEDQA
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D)
BEFQA
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question_answer 223) If black means white, white means red, red means yellow, yellow means blue, blue means green, green means purple and purple means orange, then what is the colour of lemon?
A)
Green
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B)
Purple
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C)
Orange
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D)
Blue
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question_answer 224) Directions: In the following questions, find the word which holds the same relation with the third word as there in between the first two word. Hot: Oven : : Cold :?
A)
Ice cream
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B)
Air conditioner
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C)
Snow
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D)
Refrigerator
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question_answer 225) Directions: In the following questions, find the word which holds the same relation with the third word as there in between the first two word. Push : Pull : : Throw :?
A)
Jump
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B)
Collect
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C)
Pick
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D)
Game
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question_answer 226) Directions: In each of the following questions, one letter or a set of letter is missing, you have to understand the pattern of the series and insert the appropriate letter? R, M, ?, F, D, ?
A)
C, B
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B)
J, H
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C)
H, C
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D)
I, C
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question_answer 227) Directions: In each of the following questions, one letter or a set of letter is missing, you have to understand the pattern of the series and insert the appropriate letter? - bcc - ac - aabb - ab -cc
A)
aab ca
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B)
aba ca
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C)
ba cab
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D)
bca ca.
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question_answer 228) How many 9s are there in the following number series which are immediately preceded by 3 and followed by 6? 3 9 6 9 3 9 3 9 3 9 6 3 9 3 6 3 9 5 6 9 5 6 9 3 9 6 3 9
A)
0
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B)
3
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C)
2
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D)
4
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question_answer 229) Some boys are sitting in a row, P in sitting fourteenth from the left and Q is seventh from the right. If these are four boys between P and Q, how many boys are there in the row?
A)
25
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B)
23
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C)
21
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D)
19
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question_answer 230) Pointing to a photograph, a woman says, this mans sons sister in my mother-in-law. How is the womans husband related to the man in the photograph?
A)
Grandson
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B)
Son
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C)
Son-in-law
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D)
Nephew
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question_answer 231) The longest canal in the world is
A)
Volga Baltic
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B)
Beloye-more Baltic
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C)
Suez Canal
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D)
Grand China Canal
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question_answer 232) The oldest Hindu epic is
A)
Mahabhashya
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B)
Ramayan
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C)
Mahabharata
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D)
Ashtadhyayi
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question_answer 233) Who among the following is not associated with the Swaraj Party?
A)
C.R. Das
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B)
M.L. Kelkar
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C)
Motilal Nehru
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D)
Mahatma Gandhi
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question_answer 234) Where is the City of palaces?
A)
London
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B)
Kolkata
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C)
Patiala
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D)
Lucknow
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question_answer 235) Our National Song is
A)
Sare Jahan Se Achcha
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B)
Jana Gana Mana
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C)
Vande Mataram
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D)
All of the above
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question_answer 236) The Constitution of India was adopted by the Constituent Assembly on
A)
Dec 11, 1946
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B)
Aug 15, 1957
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C)
Nov 26, 1949
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D)
Jan 26, 1949
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question_answer 237) Gandhijis Dandi March started from
A)
Bardoli
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B)
Ahmedabad
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C)
Surat
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D)
Bombay
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question_answer 238) Who was the viceroy of India at the time of formation of the Indian National Congress?
A)
Lord Canning
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B)
Lord Dufferin
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C)
Lord Mayo
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D)
Lord Elgin
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question_answer 239) Which country was a major donor in financing the SAARC?
A)
Pakistan
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B)
Sri Lanka
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C)
India
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D)
Bangladesh
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question_answer 240) Where in the H. Q. of the European Economic Community?
A)
Bonn
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B)
Rome
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C)
Brussels
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D)
Hague
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