question_answer 1) Solar spectrum is an example for
A)
line emission spectrum
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B)
continuous emission spectrum
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C)
band absorption spectrum
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D)
line absorption spectrum
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question_answer 2) When a piece of metal is illuminated by a monochromatic light of wavelength \[\lambda \], then stopping potential is \[3{{V}_{s}}\]. When same surface is illuminated by light of wavelength \[2\lambda \], then stopping potential becomes \[{{V}_{s}}\]. The value of threshold wavelength for photoelectric emission will be
A)
\[4\lambda \]
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B)
\[8\lambda \]
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C)
\[\frac{4}{3}\lambda \]
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D)
\[6\lambda \]
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question_answer 3) The maximum kinetic energy of emitted electrons in a photoelectric effect does not depend upon
A)
wavelength
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B)
frequency
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C)
intensity
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D)
work function
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question_answer 4) The ratio of minimum wavelengths of Lyman and Balmer series will be
A)
1.25
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B)
0.25
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C)
5
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D)
10
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question_answer 5) Hydrogen atom does not emit X-rays because
A)
it contains only a single electron
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B)
energy levels in it are far apart
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C)
its size is very small
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D)
energy levels in it are very close to each other
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question_answer 6)
The potential difference between A and B in the following figure is
A)
32 V
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B)
48 V
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C)
24 V
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D)
14 V
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question_answer 7) The magnetic field at the centre of a circular current carrying conductor of radius r is \[{{B}_{c}}\]. The magnetic field on its axis at a distance r from the centre is \[{{B}_{a}}\]. The value of \[{{B}_{c}}:{{B}_{a}}\] will be
A)
\[1:\sqrt{2}\]
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B)
\[1:2\sqrt{2}\]
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C)
\[2\sqrt{2}:1\]
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D)
\[\sqrt{2}:1\]
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question_answer 8)
Current \[I\] is flowing in conductor shaped as shown in the figure. The radius of the curved part is r and the length of straight portion is very large. The value of the magnetic field at the centre O will be
A)
\[\frac{{{\mu }_{0}}I}{4\pi r}\left( \frac{3\pi }{2}+1 \right)\]
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B)
\[\frac{{{\mu }_{0}}I}{4\pi r}\left( \frac{3\pi }{2}-1 \right)\]
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C)
\[\frac{{{\mu }_{0}}I}{4\pi r}\left( \frac{\pi }{2}+1 \right)\]
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D)
\[\frac{{{\mu }_{0}}I}{4\pi r}\left( \frac{\pi }{2}-1 \right)\]
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question_answer 9) Two tangent galvanometers A and B are identical except in their number of rums. They are connected in series. On passing a current through them, deflections of \[{{60}^{o}}\] and \[{{30}^{o}}\] are produced. The ratio of the number of rums in A and B is
A)
\[1:3\]
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B)
\[3:1\]
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C)
\[1:2\]
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D)
\[2:1\]
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question_answer 10)
The resultant force on the current loop PQRS due to a long current carrying conductor will be
A)
\[{{10}^{-4}}N\]
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B)
\[3.6\times {{10}^{-4}}N\]
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C)
\[1.8\times {{10}^{-4}}N\]
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D)
\[5\times {{10}^{-4}}N\]
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question_answer 11) How many \[6\mu F\], 200 V condensers are needed to make a condenser of \[18\mu F\], 600 V?
A)
9
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B)
18
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C)
3
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D)
27
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question_answer 12)
The total energy stored in the condenser system shown in the figure will be
A)
\[2\mu J\]
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B)
\[4\mu J\]
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C)
\[8\mu J\]
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D)
\[16\mu J\]
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question_answer 13) A metal wire is subjected to a constant potential difference. When the temperature of the metal wire increases, the drift velocity of the electron in it
A)
increases, thermal velocity of the electron decreases
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B)
decreases, thermal velocity of the electron decreases
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C)
increases, thermal velocity of the electron increases
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D)
decreases, thermal velocity of the electron increases
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question_answer 14)
The equivalent resistance between the points A and B will be (each resistance is \[10\sqrt{3}\,kgwt\])
A)
\[30\,\Omega \]
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B)
\[8\,\Omega \]
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C)
\[10\,\Omega \]
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D)
\[40\,\Omega \]
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question_answer 15) In the Bohr model of hydrogen atom, the electron is pictured to rotate in a circular orbit of radius \[5\times {{10}^{-11}}m\], at a speed \[2.2\times {{10}^{6}}m/s\]. What is the current associated with electron motion?
A)
1.12 mA
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B)
3 mA
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C)
0.75 mA
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D)
2.25 mA
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question_answer 16) A certain current on passing through a galvanometer produces a deflection of 100 divisions. When a shunt of one ohm is connected, the deflection reduces to 1 division. The galvanometer resistance is
A)
\[100\,\Omega \]
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B)
\[99\,\Omega \]
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C)
\[10\,\Omega \]
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D)
\[9.9\,\Omega \]
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question_answer 17) Two similar circular loops carry equal current in the same direction. On moving coils further apart, the electric current will
A)
increase in both
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B)
decrease in both
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C)
remain unaltered
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D)
increases in one and decreases in the second
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question_answer 18)
The value of alternating emf E in the given circuit will be
A)
220 V
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B)
140 V
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C)
100 V
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D)
20 V
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question_answer 19) A current of 5 A is flowing at 220 V in the primary coil of a transformer. If the voltage produced in the secondary coil is 2200 V and 50% of power is lost, then the current secondary will be
A)
2.5 A
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B)
5 A
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C)
0.25 A
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D)
0.5 A
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question_answer 20) For a series LCR circuit at resonance, the statement which is not true is
A)
Peak energy stored by a capacitor = peak energy stored by an inductor.
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B)
Average power = apparent power.
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C)
Watt less current is zero.
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D)
Power factor is zero.
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question_answer 21) If \[{{\mu }_{0}}\] is permeability of free space and \[{{\varepsilon }_{0}}\] is permittivity of free space, the speed of light in vacuum is given by
A)
\[\sqrt{{{\mu }_{0}}{{\varepsilon }_{0}}}\]
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B)
\[\sqrt{\frac{{{\mu }_{0}}}{{{\varepsilon }_{0}}}}\]
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C)
\[\sqrt{\frac{1}{{{\varepsilon }_{0}}{{\mu }_{0}}}}\]
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D)
\[\sqrt{\frac{{{\varepsilon }_{0}}}{{{\mu }_{0}}}}\]
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question_answer 22) In Young's double slit experiment, a third slit is made in between the double slits. Then
A)
intensity of fringes totally disappears
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B)
only bright light is observed on the screen
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C)
fringes of unequal width are formed
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D)
contrast between bright and dark fringes is reduced
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question_answer 23) In a two slit experiment with monochromatic light fringes are obtained on a screen placed at some distance from the slits. If the screen is moved by \[5\times {{10}^{-2}}m\] towards the slits, the change in fringe width is \[3\times {{10}^{-5}}m\]. If separation between the slits is \[{{10}^{-3}}m\], the wavelength of light used is
A)
\[6000\,\,\overset{o}{\mathop{A}}\,\]
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B)
\[5000\,\,\overset{o}{\mathop{A}}\,\]
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C)
\[3000\,\,\overset{o}{\mathop{A}}\,\]
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D)
\[4500\,\,\overset{o}{\mathop{A}}\,\]
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question_answer 24) In a Fraunhofer diffraction experiment at a single slit using a light of wavelength 400 nm, the first minimum is formed at an angle of \[{{30}^{o}}\]. The direction 6 of the first secondary maximum is given by
A)
\[{{\sin }^{-1}}\left( \frac{2}{3} \right)\]
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B)
\[{{\sin }^{-1}}\left( \frac{3}{4} \right)\]
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C)
\[{{\sin }^{-1}}\left( \frac{1}{4} \right)\]
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D)
\[ta{{n}^{-1}}\left( \frac{2}{3} \right)\]
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question_answer 25) Maximum diffraction takes place in a given slit for
A)
\[\gamma \]-rays
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B)
ultraviolet light
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C)
infrared light
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D)
radio waves
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question_answer 26) If an electron and a proton have the same de Broglie wavelength, then the kinetic energy of the electron is
A)
zero
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B)
less than that of a proton
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C)
more than that of a proton
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D)
equal to that of a proton
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question_answer 27) Two protons are kept at a separation of 40 \[{{A}^{o}}\] is the nuclear force and \[{{F}_{e}}\] is the electrostatic force between them. Then
A)
\[{{F}_{n}}>>{{F}_{e}}\]
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B)
\[{{F}_{n}}={{F}_{e}}\]
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C)
\[{{F}_{n}}<<{{F}_{e}}\]
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D)
\[{{F}_{n}}\approx {{F}_{e}}\]
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question_answer 28) Blue colour of sea water is due to
A)
interference of sunlight reflected from the water surface
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B)
scattering of sunlight by the water molecules
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C)
image of sky in water
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D)
refraction of sunlight
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question_answer 29) The ratio of the nuclear radii of elements with mass numbers 216 and 125 is
A)
\[216:125\]
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B)
\[\sqrt{216}:\sqrt{125}\]
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C)
\[6:5\]
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D)
None of these
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question_answer 30) On bombarding \[{{U}^{235}}\] by slow neutron, 200 MeV energy is released, if the power output of atomic reactor is 1.6 MW, then the rate of fission will be
A)
\[5\times {{10}^{22}}/s\]
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B)
\[5\times {{10}^{16}}/s\]
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C)
\[8\times {{10}^{16}}/s\]
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D)
\[20\times {{10}^{16}}/s\]
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question_answer 31) A ray of light enters from a rarer to a denser medium. The angle of incidence is \[i\]. Then the reflected and refracted rays are mutually perpendicular to each other. The critical angle for the pair of media is
A)
\[{{\sin }^{-1}}(\tan i)\]
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B)
\[{{\tan }^{-1}}(\sin i)\]
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C)
\[{{\sin }^{-1}}(\cot i)\]
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D)
\[{{\cos }^{-1}}(\tan i)\]
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question_answer 32) A fish in water (refractive index n) looks at a bird vertically above in the air. If y is the height of the bird and \[x\] is the depth of the fish from the surface, then the distance of the bird as estimated by the fish is
A)
\[x+y\left( 1-\frac{1}{n} \right)\]
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B)
\[x+ny\]
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C)
\[x+y\left( 1+\frac{1}{n} \right)\]
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D)
\[y+x\left( 1-\frac{1}{n} \right)\]
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question_answer 33)
Figure shows a mixture of blue, green and red colored rays incident normally on a right angled prism. The critical angles of the material of the prism for red, green and blue are \[{{46}^{o}},{{44}^{o}}\] and \[{{43}^{o}}\] respectively. The arrangement will separate
A)
red colour from blue and green
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B)
blue colour from red and green
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C)
green colour from red and blue
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D)
all the three colours
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question_answer 34) A convex and a concave lens separated by distance d are then put in contact. The focal length of the combination
A)
decreases
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B)
increases
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C)
becomes
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D)
remains the same
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question_answer 35)
A convex lens is made of 3 layers of glass of 3 different materials as in the figures. A point object is placed on its axis. The number of images of the object are
A)
1
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B)
2
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C)
3
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D)
4
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question_answer 36) An unpolarised beam of intensity \[{{I}_{0}}\] falls on a polarold. The intensity of the emergent light is
A)
\[\frac{{{I}_{0}}}{2}\]
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B)
\[{{I}_{0}}\]
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C)
\[\frac{{{I}_{0}}}{4}\]
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D)
Zero
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question_answer 37) Which of the following as a dichroic crystal?
A)
Quartz
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B)
Tourmaline
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C)
Mica
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D)
Selenite
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question_answer 38) Two identical metal spheres charged with \[+12\mu F\] and \[-8\mu F\] are kept at certain distance in air. They are brought into contact and then kept at the same distance. The ratio of the magnitudes of electrostatic forces between them before and after contact is
A)
\[12:1\]
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B)
\[8:1\]
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C)
\[24:1\]
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D)
\[4:1\]
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question_answer 39) A small conducting sphere of radius r is lying concentrically inside a bigger hollow conducting sphere of radius R. The bigger and smaller spheres are charged with Q and \[q\,(Q>q)\] and are insulated from each other. The potential difference between the spheres will be
A)
\[\frac{1}{4\pi {{\varepsilon }_{0}}}\left( \frac{q}{r}-\frac{q}{R} \right)\]
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B)
\[\frac{1}{4\pi {{\varepsilon }_{0}}}\left( \frac{q}{R}-\frac{Q}{r} \right)\]
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C)
\[\frac{1}{4\pi {{\varepsilon }_{0}}}\left( \frac{q}{r}-\frac{Q}{R} \right)\]
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D)
\[\frac{1}{4\pi {{\varepsilon }_{0}}}\left( \frac{Q}{R}+\frac{q}{r} \right)\]
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question_answer 40) The charges Q, +q and +q are placed at the vertices of an equilateral triangle of side \[l\]. If the net electrostatic potential energy of the system is zero, then Q is equal to
A)
\[-\frac{q}{2}\]
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B)
\[-q\]
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C)
\[\frac{+q}{2}\]
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D)
Zero
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question_answer 41) Dimensional formula for the universal gravitational constant G is
A)
\[[{{M}^{-1}}{{L}^{2}}{{T}^{-2}}]\]
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B)
\[[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\]
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C)
\[[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}]\]
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D)
\[[{{M}^{-1}}{{L}^{3}}{{T}^{-1}}]\]
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question_answer 42) A body is projected vertically upwards. The times corresponding to height h while ascending and while descending are \[{{t}_{1}}\] and \[{{t}_{2}}\]respectively Then the velocity of projection is (g is acceleration due to gravity)
A)
\[g\sqrt{{{t}_{1}}{{t}_{2}}}\]
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B)
\[\frac{g{{t}_{1}}{{t}_{2}}}{{{t}_{1}}+{{t}_{2}}}\]
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C)
\[\frac{g\sqrt{{{t}_{1}}{{t}_{2}}}}{2}\]
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D)
\[\frac{g\,({{t}_{1}}+{{t}_{2}})}{2}\]
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question_answer 43) A mass of 10 kg is suspended from a spring balance. It is pulled aside by a horizontal string so that it makes an angle of \[{{60}^{o}}\] with the vertical The new reading of the balance is
A)
20 kg - wt
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B)
10 kg - wt
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C)
\[10\sqrt{3}\,kgwt\]
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D)
\[20\sqrt{3}\,kg-wt\]
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question_answer 44) A body weighs 50 gin air and 40 gin water. How much would it weigh in a liquid of specific gravity 1.5?
A)
30 g
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B)
35 g
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C)
65 g
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D)
45 g
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question_answer 45) A body of mass 4 kg is accelerated upon b constant force, travels a distance of 5 m in the first second and a distance of 2 m in the third second. The force acting on the body is
A)
2 N
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B)
4 N
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C)
6 N
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D)
8 N
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question_answer 46) A simple pendulum is suspended from the ceiling of a lift. When the lift is at rest its time period is T. With what acceleration should lift be accelerated upwards in order to reduce its period to T/2? (g is acceleration due to gravity).
A)
2 g
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B)
3 g
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C)
4 g
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D)
g
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question_answer 47) If y is the ratio of specific heats and R is the universal gas constant, then the molar specific heat at constant volume C is given by
A)
\[\gamma R\]
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B)
\[\frac{(\gamma -1)R}{\gamma }\]
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C)
\[\frac{R}{\gamma -1}\]
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D)
\[\frac{\gamma R}{\gamma -1}\]
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question_answer 48)
An ideal gas is taken via path ABCA as shown in figure. The net work done in the whole cycle is
A)
\[3{{p}_{1}}{{V}_{1}}\]
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B)
\[-3{{p}_{1}}{{V}_{1}}\]
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C)
\[6{{p}_{1}}{{V}_{1}}\]
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D)
Zero
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question_answer 49) In which of the processes, does the internal energy of the system remain constant?
A)
Adiabatic
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B)
Isochoric
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C)
Isobaric
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D)
Isothermal
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question_answer 50)
The coefficient of thermal conductivity of copper is 9 times that of steel. In the composite cylindrical bar shown in the figure, what will be the temperature at the junction of copper and steel?
A)
\[{{75}^{o}}C\]
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B)
\[{{67}^{o}}C\]
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C)
\[{{25}^{o}}C\]
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D)
\[{{33}^{o}}C\]
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question_answer 51) The equation of a simple harmonic wave is given by \[y=6\text{ }\sin \text{ }2\pi \,(2t-0.1x)\] where \[x\] and y are in mm and t is in seconds. The phase difference between two particles 2 mm apart at any instant is
A)
\[{{18}^{o}}\]
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B)
\[{{36}^{o}}\]
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C)
\[{{54}^{o}}\]
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D)
\[{{72}^{o}}\]
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question_answer 52) With what velocity should an observer approach a stationary sound source, so that the apparent frequency of sound should appear double the actual frequency? (v is velocity of sound).
A)
\[\frac{v}{2}\]
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B)
3 v
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C)
2 v
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D)
v
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question_answer 53) If a black body emits 0.5 J of energy per second when it is at \[{{27}^{o}}C\], then the amount of energy emitted by it when it is at \[{{627}^{o}}C\] will be
A)
40.5 J
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B)
162 J
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C)
13.5 J
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D)
135 J
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question_answer 54) A string vibrates with a frequency of 200 Hz. When its length is doubled and tension is altered, it begins to vibrate with a frequency of 300 Hz. The ratio of the new tension to the original tension is
A)
\[9:1\]
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B)
\[1:9\]
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C)
\[3:1\]
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D)
\[1:3\]
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question_answer 55) How many times more intense is a 60 dB sound than a 30 dB sound?
A)
1000
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B)
2
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C)
100
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D)
4
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question_answer 56) The masses of two radioactive substances are same and their half-lives are 1 yr and 2 yr respectively. The ratio of their activities after 4 yr will be
A)
\[1:4\]
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B)
\[1:2\]
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C)
\[1:3\]
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D)
\[1:6\]
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question_answer 57) \[_{92}{{U}^{235}}\] undergoes successive disintegrations with the end product of \[_{82}P{{b}_{203}}\]. The number of \[\alpha \] and \[\beta \] particles emitted are
A)
\[\alpha =6,~\beta =4\]
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B)
\[\alpha =6,~\beta =0\]
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C)
\[\alpha =8,~\beta =6\]
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D)
\[\alpha =3,~\beta =3\]
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question_answer 58) The most stable particle in Baryon group is
A)
neutron
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B)
omega-particle
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C)
proton
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D)
lambda-particle
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question_answer 59) In an unbiased p-n junction
A)
Potential at p is more than that at n
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B)
Potential at p is less than that at n
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C)
Potential at p is equal to that at n
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D)
Potential at p is +ve and that at n is -ve
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question_answer 60)
To get an output \[Y=1\] from the circuit shown, the inputs A, B and C must be respectively
A)
0, 1, 0
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B)
1, 0, 0
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C)
1, 0, 1
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D)
1, 1, 0
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question_answer 61) The number of nodal planes present in \[{{\sigma }^{*}}s\] anti bonding orbitals is
A)
1
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B)
2
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C)
0
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D)
3
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question_answer 62) Which of the following electrolytic solutions has the least specific conductance?
A)
0.02 N
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B)
0.2 N
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C)
2 N
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D)
0.002 N
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question_answer 63) The overlapping of orbitals in benzene is of the type
A)
\[sp-sp\]
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B)
\[p-p\]
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C)
\[s{{p}^{2}}-s{{p}^{2}}\]
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D)
\[s{{p}^{3}}-s{{p}^{3}}\]
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question_answer 64) The calculated bond order of superoxide ion \[(CO_{2}^{-})\] is
A)
2.5
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B)
2
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C)
1.5
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D)
1
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question_answer 65) Which of the following can be measured by the Ostwald-Walker dynamic method?
A)
Relative lowering of vapour pressure
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B)
Lowering of vapour pressure
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C)
Vapour pressure of the solvent
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D)
All of the above
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question_answer 66) Mesomeric effect involves delocalization of
A)
pi electrons
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B)
sigma electrons
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C)
protons
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D)
None of these
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question_answer 67) Which of the following has the maximum number of unpaired 'd' electrons?
A)
\[Z{{n}^{2+}}\]
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B)
\[F{{e}^{2+}}\]
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C)
\[N{{i}^{3+}}\]
done
clear
D)
\[C{{u}^{+}}\]
done
clear
View Answer play_arrow
question_answer 68) One mole of which of the following has the highest entropy?
A)
Liquid nitrogen
done
clear
B)
Hydrogen gas
done
clear
C)
Mercury
done
clear
D)
Diamond
done
clear
View Answer play_arrow
question_answer 69) Which of the following species does not exert a resonance effect?
A)
\[{{C}_{6}}{{H}_{5}}N{{H}_{2}}\]
done
clear
B)
\[{{C}_{6}}{{H}_{5}}\overset{+}{\mathop{N}}\,{{H}_{3}}\]
done
clear
C)
\[{{C}_{6}}{{H}_{5}}OH\]
done
clear
D)
\[{{C}_{6}}{{H}_{5}}Cl\]
done
clear
View Answer play_arrow
question_answer 70) A complex compound in which the oxidation number of a metal is zero is
A)
\[{{K}_{4}}[Fe{{(CN)}_{6}}]\]
done
clear
B)
\[{{K}_{3}}[Fe{{(CN)}_{6}}]\]
done
clear
C)
\[[Ni{{(CO)}_{4}}]\]
done
clear
D)
\[[Pt{{(N{{H}_{3}})}_{4}}]C{{l}_{2}}\]
done
clear
View Answer play_arrow
question_answer 71) Catalytic dehydrogenation of a primary alcohol gives a
A)
secondary alcohol
done
clear
B)
aldehyde
done
clear
C)
ketone
done
clear
D)
ester
done
clear
View Answer play_arrow
question_answer 72) Excess of \[PC{{l}_{5}}\] reacts with cone \[{{H}_{2}}S{{O}_{4}}\] giving
A)
chlorosulphonic acid
done
clear
B)
thionyl chloride
done
clear
C)
sulphuryl chloride
done
clear
D)
sulphurous acid
done
clear
View Answer play_arrow
question_answer 73) If one mole of ammonia and one mole of hydrogen chloride are mixed in a closed container to form ammonium chloride gas, then
A)
\[\Delta H>\Delta U\]
done
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B)
\[\Delta H=\Delta U\]
done
clear
C)
\[\Delta H<\Delta U\]
done
clear
D)
there is no relationship
done
clear
View Answer play_arrow
question_answer 74) The compound on dehydrogenation gives a ketone. The original compound is
A)
primary alcohol
done
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B)
secondary alcohol
done
clear
C)
tertiary alcohol
done
clear
D)
carboxylic acid
done
clear
View Answer play_arrow
question_answer 75) Which is the most easily liquifiable rare gas?
A)
Xe
done
clear
B)
Kr
done
clear
C)
Ar
done
clear
D)
Ne
done
clear
View Answer play_arrow
question_answer 76) Three moles of \[PC{{l}_{5}}\], three moles of \[PC{{l}_{3}}\]and two moles of \[C{{l}_{2}}\] are taken in a closed vessel. If at equilibrium the vessel has 1.5 moles of\[PC{{l}_{5}}\], the number of moles of \[PC{{l}_{3}}\] present in it is
A)
5
done
clear
B)
3
done
clear
C)
6
done
clear
D)
4.5
done
clear
View Answer play_arrow
question_answer 77) How many optically active stereomers are possible for butan-2,3-diol?
A)
1
done
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B)
2
done
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C)
3
done
clear
D)
4
done
clear
View Answer play_arrow
question_answer 78) An octahedral complex is formed when hybrid orbitals of the following type are involved
A)
\[s{{p}^{3}}\]
done
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B)
\[ds{{p}^{2}}\]
done
clear
C)
\[{{d}^{2}}s{{p}^{3}}\]
done
clear
D)
\[s{{p}^{2}}{{d}^{2}}\]
done
clear
View Answer play_arrow
question_answer 79) For the reaction\[2HI(g)\rightleftarrows {{H}_{2}}(g)+{{I}_{2}}(g)-Q\,\,kJ\],the equilibrium constant depends upon
A)
temperature
done
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B)
pressure
done
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C)
catalyst
done
clear
D)
volume
done
clear
View Answer play_arrow
question_answer 80) The angle strain in cyclobutane is
A)
\[{{24}^{o}}44'\]
done
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B)
\[{{29}^{o}}16'\]
done
clear
C)
\[{{19}^{o}}22'\]
done
clear
D)
\[{{9}^{o}}44'\]
done
clear
View Answer play_arrow
question_answer 81) Methoxy methane and ethanol are
A)
position isomers
done
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B)
chain isomers
done
clear
C)
functional isomers
done
clear
D)
optical isomers
done
clear
View Answer play_arrow
question_answer 82) When the azimuthal quantum number has the value of 2, the number of orbitals possible are
A)
7
done
clear
B)
5
done
clear
C)
3
done
clear
D)
0
done
clear
View Answer play_arrow
question_answer 83) For the reaction \[F{{e}_{2}}{{O}_{3}}+3CO\xrightarrow{{}}2Fe+3C{{O}_{2}}\] the volume of carbon monoxide required to reduce one mole of ferric oxide is
A)
\[22.4\,\,d{{m}^{3}}\]
done
clear
B)
\[44.8\,\,d{{m}^{3}}\]
done
clear
C)
\[67.2\,\,d{{m}^{3}}\]
done
clear
D)
\[11.2\,\,d{{m}^{3}}\]
done
clear
View Answer play_arrow
question_answer 84) The monomers of buna-S rubber are
A)
vinyl chloride and sulphur
done
clear
B)
butadiene
done
clear
C)
styrene and butadiene
done
clear
D)
isoprene and butadiene
done
clear
View Answer play_arrow
question_answer 85) An element with atomic number 21 is a
A)
halogen
done
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B)
representative element
done
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C)
transition element
done
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D)
alkali metal
done
clear
View Answer play_arrow
question_answer 86) n-propyl bromide on treating with alcoholic KOH produces
A)
propane
done
clear
B)
propene
done
clear
C)
propyne
done
clear
D)
propanol
done
clear
View Answer play_arrow
question_answer 87) Mercury is a liquid metal because
A)
it has a completely filled s orbital
done
clear
B)
it has a small atomic size
done
clear
C)
it has a completely filled d orbital that prevents d-d overlapping of orbitals
done
clear
D)
it has a completely filled d orbital that causes d-d overlapping
done
clear
View Answer play_arrow
question_answer 88) A compound is formed by elements A and B. This crystallizes in the cubic structure where the A atoms are at the corners of the cube and B atoms are at the body centres. The simplest formula of the compound is
A)
AB
done
clear
B)
\[{{A}_{6}}B\]
done
clear
C)
\[{{A}_{8}}{{B}_{4}}\]
done
clear
D)
\[A{{B}_{6}}\]
done
clear
View Answer play_arrow
question_answer 89) Anisole can be prepared by the action of methyl iodide on sodium phenate. The reaction is called
A)
Wurtz's reaction
done
clear
B)
Williamson's reaction
done
clear
C)
Fittig's reaction
done
clear
D)
Etard's reaction
done
clear
View Answer play_arrow
question_answer 90) Malleability and ductility of metals can be accounted due to
A)
the presence of electrostatic force
done
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B)
the crystalline structure in metal
done
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C)
the capacity of layers of metal ions to slide over the other
done
clear
D)
the interaction of electrons with metal ions in the lattice
done
clear
View Answer play_arrow
question_answer 91) The correct order in which the first ionization potential increases is
A)
Na, K, Be
done
clear
B)
K, Na, Be
done
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C)
K, Be, Na
done
clear
D)
Be, Na, K
done
clear
View Answer play_arrow
question_answer 92) \[10\,\,c{{m}^{3}}\] of 0.1 N monobasic acid requires \[15\,\,c{{m}^{3}}\] of sodium hydroxide solution whose normality is
A)
1.5 N
done
clear
B)
0.15 N
done
clear
C)
0.066 N
done
clear
D)
0.66 N
done
clear
View Answer play_arrow
question_answer 93) The IUPAC name for tertiary butyl iodide is
A)
4-iodo butane
done
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B)
2-iodo butane
done
clear
C)
1-iodo-3-methyl propane
done
clear
D)
2-iodo-2-methyl propane
done
clear
View Answer play_arrow
question_answer 94) When sulphur dioxide is passed in an acidified\[{{K}_{2}}C{{r}_{2}}{{O}_{7}}\] solution, the oxidation state of sulphur is changed from
A)
+ 4 to 0
done
clear
B)
+ 4 to +2
done
clear
C)
+ 4 to +6
done
clear
D)
+6 to +4
done
clear
View Answer play_arrow
question_answer 95) Mass of 0.1 mole of methane is
A)
1g
done
clear
B)
16 g
done
clear
C)
1.6 g
done
clear
D)
0.1 g
done
clear
View Answer play_arrow
question_answer 96) The maximum number of hydrogen bonds that a molecule of water can have is
A)
1
done
clear
B)
2
done
clear
C)
3
done
clear
D)
4
done
clear
View Answer play_arrow
question_answer 97) A gas deviates from ideal behaviour at a high pressure because its molecules
A)
attract one another
done
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B)
show the Tyndall effect
done
clear
C)
have kinetic energy
done
clear
D)
are bound by covalent bonds
done
clear
View Answer play_arrow
question_answer 98) The reagent used to convert an alkyne to alkene is
A)
\[Zn/HCl\]
done
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B)
\[Sn/HCl\]
done
clear
C)
\[Zn-Hg/HCl\]
done
clear
D)
\[Pd-{{H}_{2}}\]
done
clear
View Answer play_arrow
question_answer 99) When compared to \[\Delta {{G}^{o}}\] for the formation of \[A{{l}_{2}}{{O}_{3}}\], the \[\Delta {{G}^{o}}\] for the formation of \[C{{r}_{2}}{{O}_{3}}\] is
A)
higher
done
clear
B)
lower
done
clear
C)
same
done
clear
D)
unpredicted
done
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View Answer play_arrow
question_answer 100) In order to increase the volume of a gas by 10%, the pressure of the gas should be
A)
increased by 10%
done
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B)
increased by 1%
done
clear
C)
decreased by 10%
done
clear
D)
decreased by 1%
done
clear
View Answer play_arrow
question_answer 101) Helium is used in balloons in place of hydrogen because it is
A)
incombustible
done
clear
B)
lighter than hydrogen
done
clear
C)
radioactive
done
clear
D)
more abundant than hydrogen
done
clear
View Answer play_arrow
question_answer 102) The basic principle of Cottnell?s precipitator is
A)
Le-Chatelier's principle
done
clear
B)
peptisation
done
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C)
neutralization of charge on colloidal particles
done
clear
D)
scattering of light'
done
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View Answer play_arrow
question_answer 103) When carbon monoxide is passed over solid caustic soda heated to \[{{200}^{o}}C\], it forms
A)
\[N{{a}_{2}}C{{O}_{3}}\]
done
clear
B)
\[NaHC{{O}_{3}}\]
done
clear
C)
\[HCOONa\]
done
clear
D)
\[C{{H}_{3}}COONa\]
done
clear
View Answer play_arrow
question_answer 104) \[{{N}_{2}}+3{{H}_{2}}\rightleftarrows 2N{{H}_{3}}\]heat. What is the effect of the increase of temperature on the equilibrium of the reaction?
A)
Equilibrium is shifted to the left
done
clear
B)
Equilibrium is shifted to the right
done
clear
C)
Equilibrium is unaltered
done
clear
D)
Reaction rate does not change
done
clear
View Answer play_arrow
question_answer 105) Hydrogen gas is not liberated when the following metal is added to dil \[HCl\]
A)
Ag
done
clear
B)
Zn
done
clear
C)
Mg
done
clear
D)
Sn
done
clear
View Answer play_arrow
question_answer 106)
Consider the Bom-Haber cycle for the formation of an ionic compound given below and identify the compound (Z) formed.
A)
\[{{M}^{+}}{{X}^{-}}\]
done
clear
B)
\[{{M}^{+}}{{X}^{-}}(s)\]
done
clear
C)
\[MX\]
done
clear
D)
\[{{M}^{+}}{{X}^{-}}(g)\]
done
clear
View Answer play_arrow
question_answer 107) In the brown ring test, the brown colour of the ring is due to
A)
ferrous nitrate
done
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B)
ferric nitrate
done
clear
C)
a mixture of NO and \[N{{O}_{2}}\]
done
clear
D)
nitrosoferrous sulphate
done
clear
View Answer play_arrow
question_answer 108) Amines behave as
A)
Lewis acid
done
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B)
Lewis base
done
clear
C)
aprotic acid
done
clear
D)
neutral compound
done
clear
View Answer play_arrow
question_answer 109) Dalda is prepared from oils by
A)
oxidation
done
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B)
reduction
done
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C)
hydrolysis
done
clear
D)
distillation
done
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View Answer play_arrow
question_answer 110) The chemical name of anisole is
A)
ethanoic acid
done
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B)
methoxy benzene
done
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C)
propanone
done
clear
D)
acetone
done
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View Answer play_arrow
question_answer 111) The number of disulphide linkages present in insulin are
A)
1
done
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B)
2
done
clear
C)
3
done
clear
D)
4
done
clear
View Answer play_arrow
question_answer 112) 80 g of oxygen contains as many atoms as in
A)
80 g of hydrogen
done
clear
B)
1 g of hydrogen
done
clear
C)
10 g of hydrogen
done
clear
D)
5 g of hydrogen
done
clear
View Answer play_arrow
question_answer 113) Which metal has a greater tendency to form metal oxide?
A)
Cr
done
clear
B)
Fe
done
clear
C)
Al
done
clear
D)
Ca
done
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View Answer play_arrow
question_answer 114) Identify the reaction that does not take place in a blast furnace.
A)
\[CaC{{O}_{3}}\xrightarrow{{}}CaO+C{{O}_{2}}\]
done
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B)
\[CaO+Si{{O}_{2}}\xrightarrow{{}}CaSi{{O}_{3}}\]
done
clear
C)
\[2F{{e}_{2}}{{O}_{3}}+3C\xrightarrow{{}}4Fe+3C{{O}_{2}}\]
done
clear
D)
\[C{{O}_{2}}+C\xrightarrow{{}}2CO\]
done
clear
View Answer play_arrow
question_answer 115) Waxes are esters of
A)
glycerol
done
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B)
long chain alcohols
done
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C)
glycerol and fatty acid
done
clear
D)
long chain alcohols and long chain fatty acids
done
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View Answer play_arrow
question_answer 116) An ionic compound is expected to have tetrahedral structure if \[{{r}_{+}}/{{r}_{-}}\] lies in the range of
A)
0.414 to 0.732
done
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B)
0.225 to 0.414
done
clear
C)
0.155 to 0.225
done
clear
D)
0.732 to 1
done
clear
View Answer play_arrow
question_answer 117) Among the following, which is least acidic?
A)
phenol
done
clear
B)
o-cresol
done
clear
C)
p-nitrophenol
done
clear
D)
p-chlorophenol
done
clear
View Answer play_arrow
question_answer 118) A ligand can also be regarded as
A)
Lewis acid
done
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B)
Bronstedbase
done
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C)
Lewis base
done
clear
D)
Bronsted acid
done
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View Answer play_arrow
question_answer 119) The colour of sky is due to
A)
transmission of light
done
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B)
wavelength of scattered light
done
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C)
absorption of light by atomspheric gases
done
clear
D)
All of the above
done
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View Answer play_arrow
question_answer 120) Which of the following organic compounds answers to both iodoform test and Fehling's test?
A)
Ethanol
done
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B)
Methanal
done
clear
C)
Ethanal
done
clear
D)
Propanone
done
clear
View Answer play_arrow
question_answer 121) The locus of a point which moves such that the sum of its distances from two fixed points is a constant, is
A)
a circle
done
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B)
a parabola
done
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C)
an ellipse
done
clear
D)
a hyperbola
done
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View Answer play_arrow
question_answer 122) The centroid of the triangle ABC, where \[A\equiv (2,3),\]\[B\equiv (8,10)\] and \[C\equiv (5,5)\]is
A)
\[(5,6)\]
done
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B)
\[(6,5)\]
done
clear
C)
\[(6,6)\]
done
clear
D)
\[(15,18)\]
done
clear
View Answer play_arrow
question_answer 123) If \[3{{x}^{2}}+xy-{{y}^{2}}-3x+6y+k=0\] represents a pair of lines, then k is equal to
A)
\[0\]
done
clear
B)
\[9\]
done
clear
C)
\[1\]
done
clear
D)
\[-9\]
done
clear
View Answer play_arrow
question_answer 124) The equation of the smallest circle passing through the points \[(2,2)\] and \[(3,3)\] is
A)
\[{{x}^{2}}+{{y}^{2}}+5x+5y+12=0\]
done
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B)
\[{{x}^{2}}+{{y}^{2}}-5x-5y+12=0\]
done
clear
C)
\[{{x}^{2}}+{{y}^{2}}+5x-5y+12=0\]
done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-5x+5y-12=0\]
done
clear
View Answer play_arrow
question_answer 125) The characteristic roots of the matrix \[\left[ \begin{matrix} 1 & 0 & 0 \\ 2 & 3 & 0 \\ 4 & 5 & 6 \\ \end{matrix} \right]\] are
A)
\[1,3,6\]
done
clear
B)
\[1,2,4\]
done
clear
C)
\[4,5,6\]
done
clear
D)
\[2,4,6\]
done
clear
View Answer play_arrow
question_answer 126) If \[{{e}_{1}}\] and \[{{e}_{2}}\] are the eccentricities of a hyperbola \[3{{x}^{2}}-3{{y}^{2}}=25\] and its conjugate, then
A)
\[e_{1}^{2}+e_{2}^{2}=2\]
done
clear
B)
\[e_{1}^{2}+e_{2}^{2}=4\]
done
clear
C)
\[{{e}_{1}}+{{e}_{2}}=4\]
done
clear
D)
\[{{e}_{1}}+{{e}_{2}}=\sqrt{2}\]
done
clear
View Answer play_arrow
question_answer 127) If p and q are prime numbers satisfying the condition \[{{p}^{2}}-2{{q}^{2}}=1,\] then the value of \[{{p}^{2}}+2{{q}^{2}}\]is
A)
\[5\]
done
clear
B)
\[15\]
done
clear
C)
\[16\]
done
clear
D)
\[17\]
done
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View Answer play_arrow
question_answer 128) If \[A(adj\,A)=5I\] where \[I\] is the identity matrix of order 3, then \[|adj\,\,A|\] is equal to
A)
\[125\]
done
clear
B)
\[25\]
done
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C)
\[5\]
done
clear
D)
\[10\]
done
clear
View Answer play_arrow
question_answer 129) The number of solutions for the equation \[\sin 2x+\cos 4x=2\] is
A)
\[0\]
done
clear
B)
\[1\]
done
clear
C)
\[2\]
done
clear
D)
\[\infty \]
done
clear
View Answer play_arrow
question_answer 130) \[\int{{{e}^{x}}.{{x}^{5}}\,dx}\] is
A)
\[{{e}^{x}}[{{x}^{5}}+5{{x}^{4}}+20{{x}^{3}}+60{{x}^{2}}+120x+120]+C\]
done
clear
B)
\[{{e}^{x}}[{{x}^{5}}-5{{x}^{4}}-20{{x}^{3}}-60{{x}^{2}}-120x-120]+C\]
done
clear
C)
\[{{e}^{x}}[{{x}^{5}}-5{{x}^{4}}+20{{x}^{3}}-60{{x}^{2}}+120x-120]+C\]
done
clear
D)
\[{{e}^{x}}[{{x}^{5}}-5{{x}^{4}}+20{{x}^{3}}-60{{x}^{2}}-120x+120]+C\]
done
clear
View Answer play_arrow
question_answer 131) The equation \[\frac{{{x}^{2}}}{2-\lambda }-\frac{{{y}^{2}}}{\lambda -5}-1=0\] represents an ellipse, if
A)
\[\lambda >5\]
done
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B)
\[\lambda <2\]
done
clear
C)
\[2<\lambda <5\]
done
clear
D)
\[2>\lambda >5\]
done
clear
View Answer play_arrow
question_answer 132) The equation of the normal to the hyperbola \[\frac{{{x}^{2}}}{16}-\frac{{{y}^{2}}}{9}=1\] at \[(-4,0)\]is
A)
\[2x-3y=1\]
done
clear
B)
\[x=0\]
done
clear
C)
\[x=1\]
done
clear
D)
\[y=0\]
done
clear
View Answer play_arrow
question_answer 133) The converse of the contrapositive of the conditional \[p\to \tilde{\ }q\]is
A)
\[p\to q\]
done
clear
B)
\[\tilde{\ }p\to \tilde{\ }q\]
done
clear
C)
\[\tilde{\ }q\to p\]
done
clear
D)
\[\tilde{\ }p\to q\]
done
clear
View Answer play_arrow
question_answer 134) The perimeter of a certain sector of a circle is equal to the length of the arc of the semicircle. Then, the angle at the centre of the sector in radians is
A)
\[\pi -2\]
done
clear
B)
\[\pi +2\]
done
clear
C)
\[\frac{\pi }{3}\]
done
clear
D)
\[\frac{2\pi }{3}\]
done
clear
View Answer play_arrow
question_answer 135) The value of \[\tan \,67\frac{{{1}^{o}}}{2}+\cos 67\frac{{{1}^{o}}}{2}\] is
A)
\[\sqrt{2}\]
done
clear
B)
\[3\sqrt{2}\]
done
clear
C)
\[2\sqrt{2}\]
done
clear
D)
\[2-\sqrt{2}\]
done
clear
View Answer play_arrow
question_answer 136) If \[f(x)\] is an even function and \[f'(x)\] exists, then \[f'(e)+f'(-e)\]is
A)
\[>0\]
done
clear
B)
\[0\]
done
clear
C)
\[\ge 0\]
done
clear
D)
\[<0\]
done
clear
View Answer play_arrow
question_answer 137) If a is a complex number satisfying the equation \[{{a}^{2}}+a+1=0,\]then \[{{\alpha }^{31}}\]is equal to
A)
\[\alpha \]
done
clear
B)
\[{{\alpha }^{2}}\]
done
clear
C)
\[1\]
done
clear
D)
\[i\]
done
clear
View Answer play_arrow
question_answer 138) The derivative of \[\sin ({{x}^{3}})\] w.r.t. \[cos({{x}^{3}})\] is
A)
\[-\tan ({{x}^{3}})\]
done
clear
B)
\[\tan ({{x}^{3}})\]
done
clear
C)
\[-cot({{x}^{3}})\]
done
clear
D)
\[cot({{x}^{3}})\]
done
clear
View Answer play_arrow
question_answer 139) A unit vector perpendicular to both the vectors \[\hat{i}+\hat{j}\]and \[\hat{j}+\hat{k}\]
A)
\[\frac{-\hat{i}-\hat{j}+\hat{k}}{\sqrt{3}}\]
done
clear
B)
\[\frac{\hat{i}+\hat{j}-\hat{k}}{3}\]
done
clear
C)
\[\frac{\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}}\]
done
clear
D)
\[\frac{\hat{i}-\hat{j}+\hat{k}}{\sqrt{3}}\]
done
clear
View Answer play_arrow
question_answer 140) If \[A=\left| \begin{matrix} {{a}_{1}} & {{b}_{1}} & {{c}_{1}} \\ {{a}_{2}} & {{b}_{2}} & {{c}_{2}} \\ {{a}_{3}} & {{b}_{3}} & {{c}_{3}} \\ \end{matrix} \right|\] and \[B=\left| \begin{matrix} {{c}_{1}} & {{c}_{2}} & {{c}_{3}} \\ {{a}_{1}} & {{a}_{2}} & {{a}_{3}} \\ {{b}_{1}} & {{b}_{2}} & {{b}_{3}} \\ \end{matrix} \right|,\] then
A)
\[A=-B\]
done
clear
B)
\[A=B\]
done
clear
C)
\[B=0\]
done
clear
D)
\[B={{A}^{2}}\]
done
clear
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question_answer 141) On the set Z of all integers * is defined by \[a*b=a+b-5,\] if \[2*(x*3)=5,\]then x is equal to
A)
\[0\]
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B)
\[3\]
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C)
\[5\]
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D)
\[10\]
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question_answer 142) Which of the following is false?
A)
Addition is commutative in N
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B)
Multiplication is associative in N
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C)
If \[a*b={{a}^{b}}\] for all a, \[b\in N\] then * is commutative in N
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D)
Addition is associative in N
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question_answer 143) If \[\vec{a}.\hat{i}=\vec{a}.\left( \hat{i}+\hat{j} \right)=\vec{a}.\left( \hat{i}+\hat{j}+\hat{k} \right)=1\] then \[\vec{a}\] is equal to
A)
\[\hat{i}+\hat{j}\]
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B)
\[\hat{i}-\hat{k}\]
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C)
\[\hat{i}\]
done
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D)
\[\hat{i}+\hat{j}-\hat{k}\]
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question_answer 144) If a and b are unit vectors and \[|\vec{a}+\vec{b}|=1,\] then\[|\vec{a}-\vec{b}|=1,\] is equal to
A)
\[\sqrt{2}\]
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B)
\[1\]
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C)
\[\sqrt{5}\]
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D)
\[\sqrt{3}\]
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question_answer 145) The projection of \[\vec{a}=3\hat{i}-\hat{j}+5\hat{k}\] on \[\vec{b}=2\hat{i}+3\hat{j}+\hat{k}\]is
A)
\[\frac{8}{\sqrt{35}}\]
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B)
\[\frac{8}{\sqrt{39}}\]
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C)
\[\frac{8}{\sqrt{14}}\]
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D)
\[\sqrt{14}\]
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question_answer 146) If \[A\left[ \begin{matrix} 1 & 2 \\ 3 & 4 \\ \end{matrix} \right],\]then \[{{A}^{-1}}\] is equal to
A)
\[-\frac{1}{2}\left[ \begin{matrix} 4 & -2 \\ -3 & 1 \\ \end{matrix} \right]\]
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B)
\[\frac{1}{2}\left[ \begin{matrix} 4 & -2 \\ -3 & 1 \\ \end{matrix} \right]\]
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C)
\[\left[ \begin{matrix} -2 & 4 \\ 1 & 3 \\ \end{matrix} \right]\]
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D)
\[\left[ \begin{matrix} 2 & 4 \\ 1 & 3 \\ \end{matrix} \right]\]
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question_answer 147) The set \[\{-1,0,1\}\] is not a multiplicative group because of the failure of
A)
closure law
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B)
associative law
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C)
identity law
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D)
inverse law
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question_answer 148) The angle of elevation of the top of a TV tower from three points A, B and C in a straight line through the foot of the tower are \[\alpha ,2\alpha \] and \[3\alpha \]respectively. If \[AB=a,\] then height of the tower is
A)
\[a\text{ }tan\text{ }\alpha \]
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B)
\[a\text{ }sin\text{ }\alpha \]
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C)
\[a\text{ }sin\text{ 2}\alpha \]
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D)
\[a\text{ }sin\text{ 3}\alpha \]
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question_answer 149) The angles A, B and C of a triangle ABC are in AP. If \[b:c=\sqrt{3}:\sqrt{2},\] then the angle A is
A)
\[{{30}^{o}}\]
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B)
\[{{15}^{o}}\]
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C)
\[{{75}^{o}}\]
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D)
\[{{45}^{o}}\]
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question_answer 150) \[\sin \left( 2{{\sin }^{-1}}\sqrt{\frac{63}{65}} \right)\] is equal to
A)
\[\frac{2\sqrt{126}}{65}\]
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B)
\[\frac{4\sqrt{65}}{65}\]
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C)
\[\frac{8\sqrt{63}}{65}\]
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D)
\[\frac{\sqrt{63}}{65}\]
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question_answer 151) A variable line \[\frac{x}{a}+\frac{y}{b}=1\] is such that \[a+b=4\] The locus of the mid point of the portion of the line intercepted between the axes is
A)
\[x+y=4\]
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B)
\[x+y=8\]
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C)
\[x+y=1\]
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D)
\[x+y=2\]
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question_answer 152) The point \[(5,-7)\] lies outside the circle
A)
\[{{x}^{2}}+{{y}^{2}}-8x=0\]
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B)
\[{{x}^{2}}+{{y}^{2}}-5x+7y=0\]
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C)
\[{{x}^{2}}+{{y}^{2}}-5x+7y-1=0\]
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D)
\[{{x}^{2}}+{{y}^{2}}-8x+7y-2=0\]
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question_answer 153) If the circles \[{{x}^{2}}+{{y}^{2}}=9\]and \[{{x}^{2}}+{{y}^{2}}+2\alpha x+2y+1=0\]touch each other internally, then a is equal to
A)
\[\pm \frac{4}{3}\]
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B)
\[1\]
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C)
\[\frac{4}{3}\]
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D)
\[-\frac{4}{3}\]
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question_answer 154) The locus of the mid point of the line joining the focus and any point on the parabola \[{{y}^{2}}=4ax\] is a parabola with the equation of directrix as
A)
\[x+a=0\]
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B)
\[2x+a=0\]
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C)
\[x=0\]
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D)
\[x=\frac{a}{2}\]
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question_answer 155) The tangents drawn at the extremities of a focal chord of the parabola \[{{y}^{2}}=16x\]
A)
intersect on \[x=0\]
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B)
intersect on the line \[x+4=0\]
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C)
intersect at an angle of \[{{60}^{o}}\]
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D)
intersect at an angle of \[{{45}^{o}}\]
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question_answer 156) If \[f:R\to R\] is defined by \[f(x)={{x}^{3}},\] then \[{{f}^{-1}}(8)\]is equal to
A)
\[\{2\}\]
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B)
\[\{2,2\omega ,2{{\omega }^{2}}\}\]
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C)
\[\{2,-2\}\]
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D)
\[\{2,2\}\]
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question_answer 157) R is a relation on. N given by \[R=\{(x,y):4x+3y=20\}\]. Which of the following belongs to R?
A)
\[(-4,12)\]
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B)
\[(5,0)\]
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C)
\[(3,4)\]
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D)
\[(2,4)\]
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question_answer 158) If \[{{\log }_{10}}7=0.8451,\]then the position of the first significant figure of \[{{7}^{-20}}\]is
A)
\[16\]
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B)
\[17\]
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C)
\[20\]
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D)
\[15\]
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question_answer 159) \[\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+.....\]upto n terms is equal to
A)
\[\frac{n}{4n+6}\]
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B)
\[\frac{1}{6n+4}\]
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C)
\[\frac{n}{6n+4}\]
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D)
\[\frac{n}{3n+7}\]
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question_answer 160) The ten's digit in \[1!4!+7!+10!+12!+13!+15!+16!+17!\]is divisible by
A)
\[4\]
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B)
\[3!\]
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C)
\[5\]
done
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D)
\[7\]
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question_answer 161) The value of \[\int_{-2}^{2}{(a{{x}^{3}}+bx+c)}dx\] depends on the
A)
value of b
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B)
value of c
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C)
value of a
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D)
values of a and b
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question_answer 162) The area of the region bounded by \[y=2x-{{x}^{2}}\]and the x -axis is
A)
\[\frac{8}{3}sq\,unit\]
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B)
\[\frac{4}{3}sq\,unit\]
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C)
\[\frac{7}{3}sq\,unit\]
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D)
\[\frac{2}{3}sq\,unit\]
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question_answer 163) The differential equation \[y\,\frac{dy}{dx}+x=\]represents
A)
a family of hyperbolas
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B)
a family of circles whose centres are on the y-axis
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C)
a family of parabolas
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D)
a family of circles whose centres are on the x-axis
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question_answer 164) If \[f({{x}^{5}})=5{{x}^{3}},\]then \[f'(x)\] is equal to
A)
\[\frac{3}{\sqrt[5]{{{x}^{2}}}}\]
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B)
\[\frac{3}{\sqrt[5]{x}}\]
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C)
\[\frac{3}{x}\]
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D)
\[\sqrt[5]{x}\]
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question_answer 165) \[f(x)=\left\{ \begin{matrix} 2a-x & in & -a<x<a \\ 3x-2a & in & a\le x \\ \end{matrix} \right.\] Then, which of the following is true?
A)
\[f(x)\] is discontinuous at \[x=a\]
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B)
\[f(x)\] is not differentiable at \[x=a\]
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C)
\[f(x)\] is differentiable at \[x\ge a\]
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D)
\[f(x)\] is continuous at all \[x<a\]
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question_answer 166) The maximum area of a rectangle that can be inscribed in a circle of radius 2 unit is (in square unit)
A)
\[4\]
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B)
\[8\pi \]
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C)
\[8\]
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D)
\[5\]
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question_answer 167) If z is a complex number such that \[z=-\bar{z},\] then
A)
z is purely real
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B)
z is purely imaginary
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C)
z is any complex number
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D)
real part of z is the same as its imaginary part
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question_answer 168) The value of \[\underset{k=1}{\mathop{\overset{6}{\mathop{\Sigma }}\,}}\,\left( \sin \frac{2k\pi }{7}-i\cos \frac{2k\pi }{7} \right)\]is
A)
\[i\]
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B)
\[0\]
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C)
\[-i\]
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D)
\[-1\]
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question_answer 169) \[\underset{x\to \infty }{\mathop{\lim }}\,\,x\,\sin \left( \frac{2}{x} \right)\] is equal to
A)
\[\infty \]
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B)
\[0\]
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C)
\[2\]
done
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D)
\[\frac{1}{2}\]
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question_answer 170) A stone is thrown vertically upwards and the height x ft reached by the stone in t seconds is given by\[x=80t-16{{t}^{2}}\]. The stone reaches the maximum height in
A)
\[2s\]
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B)
\[2.5s\]
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C)
\[3s\]
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D)
\[1.5s\]
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question_answer 171) The maximum value of \[\frac{\log x}{x}\] in \[(2,\infty )\] is
A)
\[1\]
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B)
\[\frac{2}{e}\]
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C)
\[e\]
done
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D)
\[\frac{1}{e}\]
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question_answer 172) If \[f(x)=b{{e}^{ax}}+a{{e}^{bx}},\] then \[f'(0)\] is equal to
A)
\[0\]
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B)
\[2ab\]
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C)
\[ab(a+b)\]
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D)
\[ab\]
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question_answer 173) If \[\sqrt{\frac{1+\cos A}{1-csoA}}=\frac{x}{y},\] then the value of tan A is is equal is
A)
\[\frac{{{x}^{2}}+{{y}^{2}}}{{{x}^{2}}-{{y}^{2}}}\]
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B)
\[\frac{2xy}{{{x}^{2}}+{{y}^{2}}}\]
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C)
\[\frac{{{x}^{2}}+{{y}^{2}}}{{{x}^{2}}-{{y}^{2}}}\]
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D)
\[\frac{2xy}{{{y}^{2}}-{{x}^{2}}}\]
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question_answer 174) \[\int{\frac{\sec \,x}{\sec \,x+\tan x}}dx\]is equal to
A)
\[\tan \,x-\sec x+C\]
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B)
\[\log (1+\sec x)+C\]
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C)
\[\sec x+\tan \,x+C\]
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D)
\[\log \sin x+\log \cos x+C\]
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question_answer 175) If \[\int{f(x)\,dx=g(x),}\] then \[\int{f(x)\,g=g(x)\,dx}\] is equal to
A)
\[\frac{1}{2}{{f}^{2}}(x)\]
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B)
\[\frac{1}{2}{{g}^{2}}(x)\]
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C)
\[\frac{1}{2}{{[g'(x)]}^{2}}\]
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D)
\[f'(x)g(x)\]
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question_answer 176) The general solution of \[|\sin x|=\cos x\]is (when\[n\,\in \,I\]) given by
A)
\[n\pi +\frac{\pi }{4}\]
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B)
\[2n\,\,\pi \pm \frac{\pi }{4}\]
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C)
\[n\,\,\pi \pm \frac{\pi }{4}\]
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D)
\[n\,\,\pi -\frac{\pi }{4}\]
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question_answer 177) The real root of the equation \[{{x}^{3}}-6x+9=0\] is
A)
\[-6\]
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B)
\[-9\]
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C)
\[6\]
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D)
\[-3\]
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question_answer 178) The digit in the unit?s place of \[{{5}^{834}}\] is
A)
\[0\]
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B)
\[1\]
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C)
\[3\]
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D)
\[5\]
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question_answer 179) The remainder when \[{{3}^{100}}\times {{2}^{50}}\]is divided by 5 is
A)
\[1\]
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B)
\[2\]
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C)
\[3\]
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D)
\[4\]
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question_answer 180) \[\int{\frac{\sin x\,\cos x}{\sqrt{1-{{\sin }^{4}}x}}}dx\] is equal to
A)
\[\frac{1}{2}{{\sin }^{-1}}({{\sin }^{2}}x)+C\]
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B)
\[\frac{1}{2}{{\cos }^{-1}}({{\sin }^{2}}x)+C\]
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C)
\[{{\tan }^{-1}}({{\sin }^{2}}x)+C\]
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D)
\[{{\tan }^{-1}}(2{{\sin }^{2}}x)+C\]
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