question_answer 1)
Two springs of spring constants \[{{k}_{1}}\] and \[{{k}_{2}}\] are joined in series and a mass m is attached to them as shown in figure. The time-period of oscillations of the springs is
A)
\[T=\pi \sqrt{\frac{m({{k}_{1}}+{{k}_{2}})}{{{k}_{1}}{{k}_{2}}}}\]
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B)
\[T=2\pi \sqrt{\frac{m({{k}_{1}}+{{k}_{2}})}{{{k}_{1}}{{k}_{2}}}}\]
done
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C)
\[T=2\pi \sqrt{\frac{m}{{{k}_{1}}+{{k}_{2}}}}\]
done
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D)
\[T=2\pi \sqrt{\frac{m({{k}_{1}}+{{k}_{2}})}{2{{k}_{1}}{{k}_{2}}}}\]
done
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question_answer 2) A hot body at temperature T losses heat to the surrounding temperature \[{{T}_{S}}\] by radiation. If the difference in temperature is small then, the rate of loss of heat by the hot body is proportional to
A)
\[(T-{{T}_{S}})\]
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B)
\[{{(T-{{T}_{S}})}^{2}}\]
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C)
\[{{(T-{{T}_{S}})}^{1/2}}\]
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D)
\[{{(T-{{T}_{S}})}^{4}}\]
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question_answer 3) Which one of the following statement is not correct in the case of light emitting diodes?
A)
It is a heavily doped p-n junction
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B)
It emits light only when it is forward biased
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C)
It emits light only when it is reverse biased
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D)
The energy of the light emitted is less than the energy of the semiconductor used
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question_answer 4) Which one of the following cannot be used as a moderator in a nuclear reactor?
A)
Water
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B)
Heavy water
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C)
Molten sodium
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D)
Graphite
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question_answer 5) The fraction of a sample of radioactive nuclei that remains undecayed after one mean life is
A)
\[\frac{1}{e}\]
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B)
\[1-\frac{1}{e}\]
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C)
\[\frac{1}{{{e}^{2}}}\]
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D)
\[1-\frac{1}{{{e}^{2}}}\]
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question_answer 6) If the radius of a nucleus of mass number 3 is R, ,then the radius of a nucleus of mass number 81 is
A)
\[3\,R\]
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B)
\[9\,R\]
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C)
\[{{(27)}^{1/2}}\,R\]
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D)
\[27\text{ }R\]
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question_answer 7) In hydrogen atom, which one of the following transitions is most energetic?
A)
\[{{n}_{1}}=2\to {{n}_{2}}=1\]
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B)
\[{{n}_{1}}=3\to {{n}_{2}}=1\]
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C)
\[{{n}_{1}}=10\to {{n}_{2}}=2\]
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D)
\[{{n}_{1}}=100\to {{n}_{2}}=3\]
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question_answer 8) A common example of \[{{\beta }^{-}}\] decay is \[_{15}{{P}^{32}}{{\to }_{17}}{{S}^{32}}+x+y\]. Then x and y stand for
A)
electron and neutrino
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B)
positron and neutrino
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C)
electron and antineutrino
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D)
positron and antineutrino
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question_answer 9) Based on the energy band description, a solid can be classified as insulator the energy gap between the valance band and conduction band is
A)
\[3\,\,eV<{{E}_{g}}<6\,eV\]
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B)
\[{{E}_{g}}>6\,eV\]
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C)
\[{{E}_{g}}<3\,eV\]
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D)
\[{{E}_{g}}=0\,eV\]
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question_answer 10)
In the diagram, a system of two metals of equal lengths and of same cross-sectional area are joined together. The coefficient of thermal conductivities of the metals are K and \[2K\]respectively. If the furnace temperature at one end is \[{{300}^{o}}C\]and ice box temperature at the other end is \[{{0}^{o}}C,\] then the junction temperature is
A)
\[{{100}^{o}}C\]
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B)
\[{{125}^{o}}C\]
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C)
\[{{150}^{o}}C\]
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D)
\[{{200}^{o}}C\]
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question_answer 11) A Carnot cycle has the reversible processes in the following order
A)
isothermal expansion, adiabatic expansion, isothermal compression and adiabatic compression
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B)
isothermal compression, adiabatic expansion, isothermal expansion and adiabatic compression
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C)
isothermal expansion, adiabatic compression, isothermal compression and adiabatic expansion
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D)
adiabatic expansion, isothermal expansion, adiabatic compression and isothermal compression
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question_answer 12) Through which mode of propagation, the radio waves can be sent from one place to another
A)
ground wave propagation
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B)
sky wave propagation
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C)
space wave propagation
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D)
All of them
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question_answer 13)
The logic operation carried out by the circuit below is that of
A)
AND gate
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B)
OR gate
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C)
NOT gate
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D)
NAND gate
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question_answer 14) If \[\beta ,{{R}_{L}}\] and r are the AC current gain, load resistance and the input resistance of a transistor respectively in CE configuration, the voltage and the power gains respectively are
A)
\[\beta \frac{{{R}_{L}}}{r}\] and \[{{\beta }^{3}}\frac{{{R}_{L}}}{r}\]
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B)
\[\beta \frac{r}{{{R}_{L}}}\] and \[{{\beta }^{2}}\frac{r}{{{R}_{L}}}\]
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C)
\[\beta \frac{{{R}_{L}}}{r}\] and \[\beta {{\left( \frac{{{R}_{L}}}{r} \right)}^{2}}\]
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D)
\[\beta \frac{r}{{{R}_{L}}}\] and \[\beta {{\left( \frac{r}{{{R}_{L}}} \right)}^{2}}\]
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question_answer 15) A message signal of frequency \[5\text{ }kHz\]and peak voltage \[10\text{ }V\]is used to amplify modulate a carrier wave with frequency \[1\text{ }MHz\]and peak voltage 20 V. The side bands produced are
A)
\[(1000\pm 5)kHz\]
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B)
\[(1000\pm 7.5)kHz\]
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C)
\[(1000\pm 10)kHz\]
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D)
\[(1000\pm 15)kHz\]
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question_answer 16) The volume of one mole of an ideal gas changes from V to \[2\text{ }V\]at temperature\[{{327}^{o}}C\] If R is the universal gas constant, then the work done in this process is
A)
\[300\text{ }R\]In 2
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B)
\[600\text{ }R\]In 2
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C)
\[300\]In 2
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D)
\[600\] In 2
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question_answer 17) A wooden piece can float both in mercury (of density\[13.6\text{ }g/cc\]) and in water (of density\[1\text{ }g/cc\]). The ratio of mass of mercury displaced to the mass of water displaced is
A)
\[1\]
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B)
\[13.6\]
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C)
\[\frac{1}{13.6}\]
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D)
\[\frac{12.6}{13.6}\]
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question_answer 18) A container of height 10 m which is open at the top, has water to its full height. Two small openings are made on the wall of the container .one exactly at the middle and the other at the bottom. The ratio of the velocities with which water comes out from the middle and the bottom region respectively is
A)
\[2\]
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B)
\[\frac{1}{2}\]
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C)
\[\sqrt{2}\]
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D)
\[\frac{1}{\sqrt{2}}\]
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question_answer 19) If the radius of a spherical liquid (of surface tension S) drop increases from r to \[r+Ar,\]the corresponding increase in the surface energy is
A)
\[8\pi \,r\,\Delta rS\]
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B)
\[4\pi \,r\,\Delta rS\]
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C)
\[16\pi \,r\,\Delta rS\]
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D)
\[2\pi \,r\,\Delta rS\]
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question_answer 20) Which one of the following is not an assumption in the kinetic theory of gases?
A)
The volume occupied by the molecules of the gas is negligible
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B)
The force of attraction between the molecules is negligible
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C)
The collision between molecules are elastic
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D)
All molecules have some speed
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question_answer 21) The crystal structure can be studied using
A)
UV rays
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B)
X-rays
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C)
IR radiation
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D)
Microwave
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question_answer 22) The number of turns of the primary and the secondary coils of a transformer are 10 and 100 respectively. The primary voltage and the current are given as \[2\text{ }V\]and\[1\text{ }A\]. Assuming the efficiency of the transformer as \[90%,\] the secondary voltage and the current respectively are
A)
\[20\text{ }V\]and\[0.1\text{ }A\]
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B)
\[0.2\text{ }V\]and \[1\text{ }A\]
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C)
\[20\,\,V\]and \[0.09\text{ }A\]
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D)
\[0.2\,\,V\]and \[0.9\text{ }A\]
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question_answer 23) Which one of the following units is not that of mutual inductance?
A)
Henry
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B)
Weber
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C)
Ohm-second
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D)
Volt-second-\[{{(ampere)}^{-1}}\]
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question_answer 24) In an L-C-R series AC circuit at resonance
A)
the capacitive reactance is more than the inductive reactance
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B)
the capacitive reactance equals the inductive reactance
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C)
the capacitive reactance is less than the inductive reactance
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D)
the power dissipated is minimum
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question_answer 25) In an L-C-R serries resonant circuit which one of the following cannot be the expression for the Q-factor
A)
\[\frac{\omega L}{R}\]
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B)
\[\frac{1}{\omega \,\,CR}\]
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C)
\[\sqrt{\frac{L}{C}}\frac{1}{R}\]
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D)
\[\frac{R}{LC}\]
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question_answer 26) If the eighth bright band due to light of wavelength \[{{\lambda }_{1}}\] coincides with ninth bright band from light of wavelength \[{{\lambda }_{2}}\]in Young's double slit experiment, then the possible wavelengths of visible light are
A)
\[400\,\,nm\]and \[450\,\,nm\]
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B)
\[425\text{ }nm\] and \[400\text{ }nm\]
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C)
\[400\,\,nm\] and \[425\text{ }nm\]
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D)
\[450\,\,nm\] and \[400\,\,nm\]
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question_answer 27) The elastic energy stored per unit volume in a stretched wire is
A)
\[\frac{1}{2}\] (Young modulus) \[{{(Strain)}^{2}}\]
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B)
\[\frac{1}{2}\] (Stress) \[{{(Strain)}^{2}}\]
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C)
\[\frac{1}{2}\frac{Stress}{Strain}\]
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D)
\[\frac{1}{2}\] (Young modulus) (Stress)
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question_answer 28) The electromagnetic waves of frequency \[~2\text{ }MHz\]to \[30\text{ }MHz\]are used
A)
in ground wave propagation
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B)
in sky wave propagation
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C)
in microwave propagation
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D)
in satellite communication
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question_answer 29) Assuming that the earth is a sphere of radius \[{{R}_{E}}\]with uniform density, the distance from its centre at which the acceleration due to gravity is equal to \[\frac{g}{3}\] (g = the acceleration due to gravity on the surface of earth) is
A)
\[\frac{{{R}_{E}}}{3}\]
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B)
\[2\,\,\frac{{{R}_{E}}}{3}\]
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C)
\[\frac{{{R}_{E}}}{3}\]
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D)
\[\frac{{{R}_{E}}}{4}\]
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question_answer 30) The terminal velocity of a rain drop of radius r Is \[2\text{ }cm\,\,\,{{s}^{-1}}\]. If eight such identical drops combine to form a single large drop, the terminal velocity would be
A)
\[1\,cm\,\,\,{{s}^{-1}}\]
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B)
\[2\,cm\,\,\,{{s}^{-1}}\]
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C)
\[4\,cm\,\,\,{{s}^{-1}}\]
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D)
\[8\,cm\,\,\,{{s}^{-1}}\]
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question_answer 31) The maximum kinetic energy of photoelectrons
A)
varies linearly with the frequency of the incident radiation
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B)
, varies linearly with the wavelength of incident light
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C)
proportional to the frequency of the incident radiation
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D)
proportional to the square of the frequency of incident radiation
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question_answer 32) Which one of the following is not associated with the total internal reflection?
A)
The mirage formation
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B)
Optical fibre communication
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C)
The glittering of diamond
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D)
Dispersion of light
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question_answer 33) The angular width of the central maximum of the diffraction pattern in a single slit (of width a) experiment, with \[\lambda \] as the wavelength of light, is
A)
\[\frac{3\lambda }{2a}\]
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B)
\[\frac{\lambda }{2a}\]
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C)
\[\frac{2\lambda }{a}\]
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D)
\[\frac{\lambda }{a}\]
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question_answer 34) The Brewster angle for the glass-air interface is \[{{54.74}^{o}}\]. if a ray of light going from air to glass strikes at an angle of incidence \[{{45}^{o}},\] then the angle of refraction is (Given, tan\[{{54.74}^{o}}=\sqrt{2}\])
A)
\[{{60}^{o}}\]
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B)
\[{{30}^{o}}\]
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C)
\[{{25}^{o}}\]
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D)
\[{{54.74}^{o}}\]
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question_answer 35) When sun light is scattered by minute particles of atmosphere, the intensity of light scattered away is proportional to
A)
\[{{(wavelength\text{ }of\text{ }light)}^{4}}\]
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B)
\[{{(frequency\text{ }of\text{ }light)}^{4}}\]
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C)
\[{{(wavelength\text{ }of\text{ }light)}^{2}}\]
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D)
\[{{(frequency\text{ }of\text{ }light)}^{2}}\]
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question_answer 36) If K be the kinetic energy and m the mass of a moving particle, then the de-Broglie wavelength of the particle is
A)
\[\lambda =\frac{h}{\sqrt{mK}}\]
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B)
\[\lambda =\frac{2h}{\sqrt{mK}}\]
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C)
\[\lambda =\frac{h}{2\sqrt{mK}}\]
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D)
\[\lambda =\frac{h}{\sqrt{2\,mK}}\]
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question_answer 37) The radius of gyration of a thin uniform circular disc (of radius R) about an axis passing through its centre and lying in its plane is
A)
\[R\]
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B)
\[\frac{R}{\sqrt{2}}\]
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C)
\[\frac{R}{4}\]
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D)
\[\frac{R}{2}\]
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question_answer 38) Two particles of masses \[1\text{ }kg\]and \[\text{2 }kg\] are located at \[{{x}_{1}}=0,\] \[{{y}_{1}}=0\] and \[{{x}_{2}}=1,\]\[{{y}_{2}}=0\] respectively. The centre of mass of the system is at.
A)
\[x=1;\,\,y=2\]
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B)
\[x=2;\,\,y=1\]
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C)
\[x=\frac{1}{3};\,\,y=\frac{2}{3}\]
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D)
\[x=\frac{2}{3};\,\,y=\frac{1}{3}\]
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E)
None of these
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question_answer 39) The energy that is associated with one gram of mass is
A)
\[9\times {{10}^{-13}}\,J\]
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B)
\[9\times {{10}^{-16}}\,J\]
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C)
\[9\times {{10}^{13}}\,J\]
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D)
\[9\times {{10}^{16}}\,J\]
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question_answer 40) If the polar ice caps were to -melt suddenly
A)
the length of the day will be more than \[24\text{ }h\]
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B)
the length of the day will be less than \[24\text{ }h\]
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C)
the length of the day will remain as \[24\text{ }h\] the length of the day will become more
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D)
than \[24\text{ }h\] initially and then becomes equal to \[24\text{ }h\]
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question_answer 41) The work done in taking an object of mass m from the surface of earth to a height \[h=R,\] where R is the radius of the earth, is
A)
\[mgR\]
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B)
\[\frac{1}{2}mgR\]
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C)
\[\frac{1}{3}mgR\]
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D)
\[\frac{2}{3}mgR\]
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question_answer 42) The inversion temperature of a copper-iron thermocouple is \[{{540}^{o}}C\]when the cold junction temperature is \[{{0}^{o}}C\]. If the cold junction temperature is increased by\[{{10}^{o}}C,\] then the inversion temperature and the neutral temperature of the thermocouple respectively are
A)
\[{{270}^{o}}C\]and \[{{530}^{o}}C\]
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B)
\[{{270}^{o}}C\] and \[{{550}^{o}}C\]
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C)
\[{{280}^{o}}C\]and \[{{530}^{o}}C\]
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D)
\[{{280}^{o}}C\]and \[{{550}^{o}}C\]
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question_answer 43) Two bulbs marked \[60\text{ }W,\] \[220\text{ }V\] and \[100\text{ }W\]\[220\text{ }V\] are connected in series and the series combination is now connected across a \[220\text{ }V\] mains supply. The power dissipated in the circuit is
A)
\[37.5\text{ }W\]
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B)
\[75\text{ }W\]
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C)
\[80\text{ }W\]
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D)
\[40\text{ }W\]
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question_answer 44)
The steady state current through the battery in the circuit given below is
A)
\[17\,A\]
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B)
\[7\,A\]
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C)
zero
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D)
\[\frac{10}{7}A\]
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question_answer 45) Two concentric circular loops of radii R and 2R carry currents of 2i and i respectively in opposite sense (ie, clockwise in one coil and counter-clockwise in the other coil). The resultant magnetic field at their common centre is
A)
\[{{\mu }_{0}}\frac{i}{4R}\]
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B)
\[{{\mu }_{0}}\frac{5i}{4R}\]
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C)
\[{{\mu }_{0}}\frac{3i}{4R}\]
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D)
\[{{\mu }_{0}}\frac{i}{2R}\]
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question_answer 46)
Three identical spherical balls A, B and C are placed on a table as shown in the figure along a straight line. B and C are at rest initially. The ball A hits B head on with a speed of \[10\,m{{s}^{-1}}\]. Then after all collisions (assumed to be elastic) A and B are brought to rest and C takes off with a velocity of
A)
\[5\,m{{s}^{-1}}\]
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B)
\[10\,m{{s}^{-1}}\]
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C)
\[2.5\,m{{s}^{-1}}\]
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D)
\[7.5\,m{{s}^{-1}}\]
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question_answer 47) An object placed on an inclined plane starts sliding when the angle of incline becomes\[{{30}^{o}}\]. The coefficient of static friction between the object and the plane is
A)
\[\frac{1}{\sqrt{3}}\]
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B)
\[\sqrt{3}\]
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C)
\[\frac{1}{2}\]
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D)
\[\frac{\sqrt{3}}{2}\]
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question_answer 48)
Given below is a graph between a variable force (F) (along y-axis) and the displacement (x) (along x-axis) of a particle in one dimension. The work done by the force in the displacement interval between \[0\text{ }m\]and \[30\text{ }m\]is
A)
\[275\text{ }J\]
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B)
\[375\text{ }J\]
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C)
\[400\text{ }J\]
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D)
\[300\text{ }J\]
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question_answer 49) The mobility of free electrons (charge = e, mass = -m and relaxation time = \[\tau \].) in a metal is proportional to
A)
\[\frac{e}{m}\tau \]
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B)
\[\frac{m}{e}\tau \]
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C)
\[\frac{e}{m\tau }\]
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D)
\[\frac{m}{e\tau }\]
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question_answer 50) n identical capacitors each of capacitance C when connected in parallel give the effective capacitance \[90\text{ }\mu F\]and when connected in series give \[\text{2}\text{.5 }\mu F\]. Then the values of n and C respectively are
A)
\[6\] and \[15\,\mu F\]
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B)
\[5\] and \[18\,\mu F\]
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C)
\[15\] and \[6\,\mu ,F\]
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D)
\[18\] and \[5\,\mu ,F\]
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question_answer 51) A capacitor is charged by a battery and the energy stored is U. The battery is now removed and the separation distance between the plates. is doubled. The energy stored now is
A)
\[\frac{U}{2}\]
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B)
\[U\]
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C)
\[2\,\,U\]
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D)
\[4\,\,U\]
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question_answer 52) The number of ways one can arrange three identical capacitors to obtain distinct effective capacitances is
A)
\[8\]
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B)
\[6\]
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C)
\[4\]
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D)
\[3\]
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question_answer 53) When a uniform wire of resistance R is stretched uniformly to increase its length by \[10%,\]the new resistance value would
A)
remain as R
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B)
become \[1.21R\]
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C)
become \[1.10\text{ }R\]
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D)
become \[1.20\text{ }R\]
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question_answer 54) Rocket propulsion is associated with
A)
the conservation of angular momentum
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B)
the conservation of mass
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C)
the conservation of mechanical energy
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D)
Newton's third law of motion
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question_answer 55) Which one of the following statements is not correct in uniform circular motion?
A)
The speed of the particle remains constant
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B)
The acceleration always points towards the centre
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C)
The angular speed remains constant
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D)
The velocity remains constant
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question_answer 56) If a car is to travel with a speed v along a frictionless, banked circular track of radius r, the required angle of banking so that the car does skid, is
A)
\[\theta ={{\tan }^{-1}}\,\left( \frac{{{v}^{2}}}{rg} \right)\]
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B)
\[\theta ={{\tan }^{-1}}\,\left( \frac{v}{rg} \right)\]
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C)
\[\theta ={{\tan }^{-1}}\,\left( \frac{{{r}^{2}}}{vg} \right)\]
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D)
\[\theta <{{\tan }^{-1}}\,\left( \frac{{{v}^{2}}}{rg} \right)\]
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question_answer 57) Three forces \[{{F}_{1}},{{F}_{2}}\] and \[{{F}_{3}}\] together keep a body in equilibrium. If \[{{F}_{1}}=3N\]along the positive x-axis, \[{{F}_{2}}=4N\] along the positive y-axis, then the third force \[{{F}_{3}}\] is
A)
\[5\text{ }N\]making an angle \[\theta ={{\tan }^{-1}}\left( \frac{3}{4} \right)\] with the negative y-axis
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B)
\[5\text{ }N\]making an angle \[\theta ={{\tan }^{-1}}\left( \frac{4}{3} \right)\] with the negative y-axis
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C)
\[7\text{ }N\]making an angle \[\theta ={{\tan }^{-1}}\left( \frac{3}{4} \right)\] with the negative y-axis
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D)
\[7\text{ }N\] making an angle \[\theta ={{\tan }^{-1}}\left( \frac{4}{3} \right)\] with the negative y-axis
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question_answer 58) The electrostatic potential of a uniformly charged thin spherical shell of charge Q and radius R at a distance r from the centre is
A)
\[\frac{Q}{4\,\pi \,{{\varepsilon }_{0}}r}\]for points outside and \[\frac{Q}{4\,\pi \,{{\varepsilon }_{0}}R}\] for points inside the shell
done
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B)
\[\frac{Q}{4\,\pi \,{{\varepsilon }_{0}}r}\] for both points inside and outside the shell
done
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C)
zero for points outside and \[\frac{Q}{4\,\pi \,{{\varepsilon }_{0}}r}\] for points inside the shell
done
clear
D)
zero for both points inside and outside the shell
done
clear
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question_answer 59) The electric field and the potential of an electric dipole vary with distance r as
A)
\[\frac{1}{r}\]and \[\frac{1}{{{r}^{2}}}\]
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B)
\[\frac{1}{{{r}^{2}}}\] and \[\frac{1}{r}\]
done
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C)
\[\frac{1}{{{r}^{2}}}\] and \[\frac{1}{{{r}^{3}}}\]
done
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D)
\[\frac{1}{{{r}^{3}}}\] and \[\frac{1}{{{r}^{2}}}\]
done
clear
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question_answer 60) A point charge Q is placed at one of the vertices of a cubical block. The electric flux flowing through this cube is
A)
\[\frac{Q}{6{{\varepsilon }_{0}}}\]
done
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B)
\[\frac{Q}{4{{\varepsilon }_{0}}}\]
done
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C)
\[\frac{Q}{8{{\varepsilon }_{0}}}\]
done
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D)
\[\frac{Q}{{{\varepsilon }_{0}}}\]
done
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question_answer 61) Two parallel infinite line charges \[+\lambda \] and \[-\lambda \] are placed with a separation distance R in free space. The net electric field exactly mid-way between the two line charges is
A)
\[\frac{Q}{6\,{{\varepsilon }_{0}}}\]
done
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B)
\[\frac{Q}{4\,{{\varepsilon }_{0}}}\]
done
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C)
\[\frac{Q}{8\,{{\varepsilon }_{0}}}\]
done
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D)
\[\frac{Q}{\,{{\varepsilon }_{0}}}\]
done
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question_answer 62) A particle is thrown vertically up with a certain velocity. Assuming the air resistance to be negligible, which one of the following represents the velocity (along y-axis) time (along x-axis) graph for the entire motion of the particle till it reaches back to the ground
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 63) The dimensions of .the coefficient of viscosity are
A)
\[[M{{L}^{-1}}{{T}^{-3}}]\]
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B)
\[[M{{L}^{-1}}{{T}^{-1}}]\]
done
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C)
\[[M{{L}^{-2}}{{T}^{-1}}]\]
done
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D)
\[[ML{{T}^{-1}}]\]
done
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question_answer 64) The components of the sum of two vectors \[2\hat{i}+3\hat{j}\] and \[2\hat{j}+3\hat{k}\]along x and y directions respectively are
A)
\[2\] and \[5\]
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B)
\[4\]and \[6\]
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C)
\[2\] and \[6\]
done
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D)
\[4\]and \[3\]
done
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question_answer 65) An object is projected so that its horizontal range R is maximum. If the maximum height attained by the object is H, then the ratio of R/H is
A)
\[4\]
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B)
\[1/4\]
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C)
\[2\]
done
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D)
\[1/2\]
done
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question_answer 66) Which one of the following is not a characteristics of diamagnetism?
A)
The diamagnetic materials are repelled by a bar magnet
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B)
The magnetic susceptibility of the materials is small and negative
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C)
The origin of diamagnetism is the spin of electrons
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D)
The material move from a region of strong magnetic field to weak magnetic field
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question_answer 67) When the number of turns of the coil is doubled, the current sensitivity of a moving coil galvanometer is doubled whereas, the voltage sensitivity of the galvanometer
A)
remains the same
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B)
is halved
done
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C)
is doubled
done
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D)
is quadrupled
done
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question_answer 68) Ampere's circuital law is equivalent to
A)
Biot-Savart law
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B)
Coulomb's law
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C)
Faraday's law
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D)
Kirchhoff?s law
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question_answer 69) A proton, a deuteron and an alpha particle all having same momenta enter a uniform magnetic field and describe circular paths. The respective radii of their paths are in the ratio
A)
\[4:2:1\]
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B)
\[2:2:1\]
done
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C)
\[1:2:4\]
done
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D)
\[1:1:1\]
done
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question_answer 70) If the horizontal component of the earth's magnetic field is \[0.30\text{ }G,\] and the dip angle is \[60{}^\circ \] at a given place, then the value of earth's total magnetic field is
A)
\[0.15\text{ }G\]
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B)
\[0.15\,\sqrt{3}G\]
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C)
\[0.15\,\sqrt{2}G\]
done
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D)
\[~0.60\text{ }G\]
done
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question_answer 71) If a current of \[5\text{ }A\]in a coil of self inductance \[2\text{ }mH\]is cut-off in time \[0.1\text{ }s,\]the induced emf in the coil is
A)
\[0.1\,\,V\]
done
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B)
\[0.01\text{ }V\]
done
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C)
\[0.2V\]
done
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D)
\[0.02V\]
done
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question_answer 72) A source of sound is approaching an observer with speed of \[30\text{ }m{{s}^{-1}}\]and the observer is approaching the source with a speed of\[60\,\,m{{s}^{-1}}\]. Then the fractional change in the frequency of sound (speed of sound in air \[=330\,\,m{{s}^{-1}}\]) is
A)
\[\frac{1}{3}\]
done
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B)
\[\frac{3}{10}\]
done
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C)
\[\frac{2}{5}\]
done
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D)
\[\frac{2}{3}\]
done
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question_answer 73) A wave motion is described by \[y(x,t)=a\,\sin (kx-\omega t)\]. Then the ratio of the maximum particle velocity to the wave velocity is
A)
\[\omega a\]
done
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B)
\[\frac{1}{ka}\]
done
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C)
\[\frac{\omega }{k}\]
done
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D)
\[ka\]
done
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question_answer 74) The equation of a damped simple harmonic motion is \[m\frac{{{d}^{2}}x}{d{{t}^{2}}}+\frac{dx}{dt}+kx=0\]. Then the angular frequency of oscillation is
A)
\[\omega ={{\left( \frac{k}{m}-\frac{{{b}^{2}}}{4{{m}^{2}}} \right)}^{1/2}}\]
done
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B)
\[\omega ={{\left( \frac{k}{m}-\frac{b}{4m} \right)}^{1/2}}\]
done
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C)
\[\omega ={{\left( \frac{k}{m}-\frac{{{b}^{2}}}{4m} \right)}^{1/2}}\]
done
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D)
\[\omega ={{\left( \frac{k}{m}-\frac{{{b}^{2}}}{4{{m}^{2}}} \right)}^{1/2}}\]
done
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question_answer 75) The fundamental frequencies of an open and a closed tube, each of same length L with v as the speed of sound in air, respectively are
A)
\[\frac{v}{2L}\] and \[\frac{v}{L}\]
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B)
\[\frac{v}{L}\] and \[\frac{v}{2L}\]
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C)
\[\frac{v}{2L}\] and \[\frac{v}{4L}\]
done
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D)
\[\frac{v}{4L}\] and \[\frac{v}{2L}\]
done
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question_answer 76) For the reaction, \[{{N}_{2}}(g)+3{{H}_{2}}(g)\rightleftharpoons 2N{{H}_{3}}(g)\] at \[400\text{ }K,{{K}_{p}}=41.\] Find the value for the following reaction \[\frac{1}{2}{{N}_{2}}(g)+\frac{3}{2}{{H}_{2}}(g)\rightleftharpoons N{{H}_{3}}(g)\]
A)
6.4
done
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B)
0.02
done
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C)
50
done
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D)
4.6
done
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question_answer 77) What will be the resultant pH when 200 mL of, an aqueous solution of \[HCl(pH=2.0)\]is mixed with 300 mL of an aqueous solution of \[NaOH(pH=12)?\]
A)
2.699
done
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B)
13.30
done
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C)
11.3010
done
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D)
1.330
done
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question_answer 78) Why do most chemical reaction rates increases rapidly as the temperature rises?
A)
The fraction of the molecules with kinetic energy greater than the activation energy increases rapidly with temperature
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B)
The average kinetic energy increases as temperature rises
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C)
The activation energy decreases as the temperature rises
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D)
More collision take place between particles so that the reaction can occur
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question_answer 79) To an equilibrium mixture of \[2S{{O}_{2}}(g)+{{O}_{2}}(g)\rightleftharpoons 2S{{O}_{3}}(g),\] some helium, an inert gas, is added at constant volume. The addition of helium causes the total pressure to double, which of the following is true?
A)
The concentration of all three gases is unchanged
done
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B)
The concentration of sulphur trioxide increases
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C)
The number of moles of sulphur trioxide increases
done
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D)
The concentration of sulphur dioxide increases
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question_answer 80) Identify the substance whose 0.1 M solution is basic?
A)
Ammonium chloride
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B)
Ammonium acetate
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C)
Ammonium sulphate
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D)
Sodium acetate
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question_answer 81) The vapour pressure of pure liquid solvent is 0.80 arm. When a non-volatile substance B is added to the solvent, its vapour pressure drops to 0.6 arm. What is the mole fraction of component B in this solution?
A)
0.75
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B)
0.25
done
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C)
0.48
done
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D)
0.3
done
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question_answer 82) The standard enthalpy of formation of\[{{\text{H}}_{\text{2}}}\text{(g)}\] and\[C{{l}_{2}}(g)\]and\[HCl(g)\]are \[218\text{ }kJ/mol,\]\[\text{ }121.68\text{ }kJ/mol\]and\[92.31\text{ }kJ/mol\]respectively. Calculate standard enthalpy change in kJ for \[\frac{1}{2}{{H}_{2}}(g)\frac{1}{2}C{{l}_{2}}(g)\xrightarrow{{}}HCl(g)\]
A)
\[+\,\,431.99\]
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B)
\[-246.37\]
done
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C)
\[-431.99\]
done
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D)
\[+\,247.37\]
done
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E)
None of these
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question_answer 83) In which of the following pair the enthalpy of neutralization does not remain constant?
A)
\[\text{HN}{{\text{O}}_{\text{3}}}\]and\[\text{ }\!\!~\!\!\text{ NaOH}\]
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B)
\[HCl\]and \[NaOH\]
done
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C)
\[HCN\]and \[NaOH\]
done
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D)
\[{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\] and \[NaOH\]
done
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question_answer 84) A system is changed from an initial state to a final state by a manner such that \[\Delta H=q.\]If the change from the initial state to the final state were made by a different manner then \[\Delta H\]remains same but q changes because
A)
\[\Delta H\] is a path function and q is a state function
done
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B)
\[\Delta H\]is a state function and q is a path function
done
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C)
Both \[\Delta H\]and q are state function
done
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D)
Both \[\Delta H\]and q are path function
done
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question_answer 85) When water is cooled to ice, its entropy
A)
increases
done
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B)
decreases
done
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C)
remains same
done
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D)
becomes zero
done
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question_answer 86) The charge on \[\text{Fe(OH}{{\text{)}}_{\text{3}}}\]sol is due to
A)
adsorption of hydroxyl ion
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B)
adsorption of hydrogen ion
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C)
adsorption of ferric ion
done
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D)
absorption of ferric ion
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question_answer 87) Which of the following statement is true?
A)
Chemisorption forms multimolecular layer
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B)
Chemisorption is a reversible process
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C)
Chemisorption is independent of the pressure
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D)
Chemisorption has low enthalpy change
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question_answer 88) Identify the incorrect statement out of the following.
A)
Isoelectronic species have dissimilar ionic radii
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B)
Be and Al does not show diagonal relationship
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C)
Outer electronic configuration of halogen is \[n{{s}^{2}}.n{{p}^{7}}\]
done
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D)
In any period atomic radius of noble gas is the highest
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question_answer 89) According to VSEPR theory, the molecule that has T-shape is
A)
\[Cl{{F}_{3}}\]
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B)
\[N{{H}_{3}}\]
done
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C)
\[B{{F}_{3}}\]
done
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D)
\[{{H}_{2}}O\]
done
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question_answer 90) Bakelite is the polymer of
A)
benzaldehyde and phenol
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B)
formaldehyde and phenol
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C)
formaldehyde and benzyl alcohol
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D)
acetaldehyde and phenol
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question_answer 91) Which of these elements is expected to have the lowest first ionisation potential?
A)
Sr
done
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B)
As
done
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C)
Xe
done
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D)
S
done
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question_answer 92) Which is false statement about LCAO?
A)
Addition of atomic orbital results in molecular orbital
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B)
Atomic orbital of nearly same energy combine to molecular orbital
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C)
Bonding molecular orbital occupies higher energy than the atomic orbitals
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D)
Each molecular orbital accommodate maximum of two electrons
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question_answer 93) Which one among the following statement about transition elements is incorrect?
A)
They show variable oxidation state
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B)
All the ions are coloured
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C)
They exhibit diamagnetic and paramagnetic properties
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D)
They exhibit catalytic properties
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question_answer 94) German silver is an alloy of
A)
copper, zinc and silver
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B)
copper, zinc and nickel
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C)
copper, zinc and tin
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D)
manganese, chromium and nickel
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question_answer 95) The metal-carbon bond in metal carbonyls possess
A)
only s character
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B)
only p character
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C)
both s and p character
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D)
only d character
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question_answer 96) Irregular trend in the standard reduction potential value of first row transition elements is due to
A)
regular variation of first and second ionisation enthalpies
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B)
irregular variation of sublimation enthalpies
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C)
regular variation of sublimation enthalpies
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D)
increase in the number of unpaired electrons
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question_answer 97) Which of the following lanthanoid ion is paramagnetic?
A)
\[C{{e}^{4+}}\]
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B)
\[Y{{b}^{2+}}\]
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C)
\[L{{u}^{3+}}\]
done
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D)
\[E{{u}^{2+}}\]
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question_answer 98) The complex \[{{[Co{{F}_{6}}]}^{4-}}\] is
A)
outer orbital and diamagnetic
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B)
inner orbital and paramagnetic
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C)
inner orbital and diamagnetic
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D)
outer orbital and paramagnetic
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question_answer 99) The oxidation number, d-orbital occupation and coordination number of Cr in the complex \[cis[Cr{{(en)}_{2}}C{{l}_{2}}]Cl\]are respectively
A)
\[+\,3,\text{ }3d\]and 4
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B)
\[~+\,3,\text{ }4d\] and 6
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C)
\[+\,3,\text{ }3d\]and 6
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D)
\[~+\,2,\text{ }3d\] and 6
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question_answer 100) Which is a non-aromatic compound?
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 101) The number of isomers including stereoisomers possible for the compound having molecular formula \[{{\text{C}}_{\text{4}}}{{\text{H}}_{\text{8}}}\]is
A)
one
done
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B)
two
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C)
three
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D)
four
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question_answer 102) The correct order of decreasing acidic nature of \[Hp,\text{ }ROH,CH\equiv CH\]and\[N{{H}_{3}}\] is
A)
\[CH\equiv CH>{{H}_{2}}O>ROH>N{{H}_{3}}\]
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B)
\[{{H}_{2}}O\,>ROH>CH\equiv CH>N{{H}_{3}}\]
done
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C)
\[ROH>N{{H}_{3}}>CH\equiv CH>{{H}_{2}}O\]
done
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D)
\[{{H}_{2}}O>ROH>N{{H}_{3}}>CH\equiv CH\]
done
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question_answer 103) Reaction between propene and hydrochloric acid to form \[iso-\]propyl chloride takes place through
A)
nucleophilic addition reaction
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B)
electrophilic substitution reaction
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C)
nucleophilic substitution reaction
done
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D)
electrophilic addition reaction
done
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question_answer 104) Stability of\[iso-\]butylene can be best explained by
A)
inductive effect
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B)
mesomeric effect
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C)
hyperconjugative effect
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D)
steric effect
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question_answer 105) The d and I enantiomers of an optically active compound differ in
A)
their boiling and melting point
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B)
their rotation of plane polarized light
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C)
their solubility
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D)
their refractive index
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question_answer 106) Cannizaro reaction is not given by
A)
methanal
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B)
phenyl methanal
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C)
2, 2-dimethyl butanal
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D)
phenyl ethanol
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question_answer 107) Which of the following compound will have the smallest \[\text{p}{{\text{K}}_{\text{a}}}\]value?
A)
Benzoic acid
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B)
Formic acid
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C)
Acetic acid
done
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D)
Phenyl acetic acid
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question_answer 108) Ethyl alcohol cannot be used as a solvent for methyl magnesium iodide because
A)
methyl magnesium iodide reacts with alcohol-giving methane
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B)
the reaction between them is explosive in nature
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C)
methyl magnesium iodide is converted to ethyl magnesium iodide
done
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D)
alcohol is immiscible with methyl magnesium iodide
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question_answer 109) Which is not true about acetophenone?
A)
It reacts with alkaline potassium permanganate followed by acid hydrolysis and forms benzoic acid
done
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B)
It reacts with iodine and sodium hydroxide to form tri-iodomethane
done
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C)
It is prepared by the reaction of benzene with benzoyl chloride in presence of anhydrous aluminium chloride
done
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D)
It does not react with freshly prepared ammoniacal silver nitrate solution
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question_answer 110) Formation of methyl tertiary butyl ether by the reaction of sodium tertiary butoxide and methyl bromide involves
A)
elimination reaction
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B)
electrophilic addition reaction
done
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C)
nucleophilic substitution unimolecular reaction
done
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D)
nucleophilic substitution bimolecular reaction
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question_answer 111) 10 g of a radioisotope is reduced to 1.25 g of . active material after 12 yr. Therefore, the half-life of the isotope (in yr) is
A)
24
done
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B)
4
done
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C)
2
done
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D)
8
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question_answer 112) Out of the following, which is the correct set of quantum number for the outermost electron of potassium atom (Z = 19)?
A)
\[n-4\] \[l-3\] \[m-2\] \[s-\,\,\,\,\,\text{-1/2}\]
done
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B)
\[n-4\] \[l-2\] \[m-0\] \[s-\,\,\,\,\,\text{-1/2}\]
done
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C)
\[n-4\] \[l-1\] \[m-0\] \[s-\,\,\,\,\,+\text{1/2}\]
done
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D)
\[n-4\] \[l-0\] \[m-0\] \[s-\,\,\,\,\,\text{-1/2}\]
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question_answer 113) The molecules present in 5.6 L of sulphur dioxide at STP is
A)
\[1.5\times {{10}^{23}}\]
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B)
\[1.5\times {{10}^{-23}}\]
done
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C)
\[4\times {{10}^{23}}\]
done
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D)
\[0.15\times {{10}^{23}}\]
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question_answer 114) What is the relationship between the parent and daughter nuclei, when a nucleus of an atom undergoes beta emission?
A)
Isobars
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B)
Isotopes
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C)
Isotones
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D)
Isomers
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question_answer 115) In photoelectric effect, the kinetic energy of the photoelectron increases linearly with the
A)
wavelength of the incident light
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B)
frequency of the incident light
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C)
velocity of the incident light
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D)
atomic mass of an element
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question_answer 116) Dual behaviour of matter was proposed by
A)
Niels Bohr
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B)
Erwin Schrodinger
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C)
Louis de-Broglie
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D)
Max Planck
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question_answer 117) What is the maximum number of emission lines obtained when the excited electron of a hydrogen atom in \[n=5\]drops to the ground state?
A)
10
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B)
5
done
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C)
12
done
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D)
15
done
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question_answer 118) For a reaction\[[R]\xrightarrow{{}}P\]a graph of [R] against time is found to be a straight line. What is the order of this reaction?
A)
Second order
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B)
Third order
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C)
First order
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D)
Zero order
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question_answer 119) For getting accurate value of molar mass of a solute by osmotic pressure measurement
A)
the solute must be volatile
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B)
the solution concentration must be high
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C)
the solute should undergo dissociation
done
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D)
the solute must be non-volatile
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question_answer 120) In a catalytic experiment involving the Haber process, \[{{N}_{2}}(g)+3{{H}_{2}}(g)\xrightarrow{{}}2N{{H}_{3}}(g),\] the rate of reaction was measured as Rate \[=[N{{H}_{3}}]=2.0\times {{10}^{-4}}M{{s}^{-1}}\] If there were no side reactions what was the rate of reaction expressed in terms of \[{{N}_{2}}?\]
A)
\[1\times {{10}^{-4}}M{{s}^{-1}}\]
done
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B)
\[4\times {{10}^{-4}}M{{s}^{-1}}\]
done
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C)
\[5\times {{10}^{-3}}M{{s}^{-1}}\]
done
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D)
\[1\times {{10}^{-3}}M{{s}^{-1}}\]
done
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question_answer 121) For a dilute solution, Raoulfs law states that
A)
lowering of vapour pressure is equal to the mole fraction of the solute
done
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B)
relative lowering of vapour pressure is equal to the mole fraction of the solvent
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C)
relative lowering of vapour pressure of the solvent is equal to the mole fraction of the solute
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D)
vapour pressure of the solution is equal to the vapour pressure of the solvent
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question_answer 122) 36 g of glucose (molar mass\[=180\text{ }g/mol\]) if present in 500 g of water, the molality of the solution is
A)
0.2
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B)
0.4
done
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C)
0.8
done
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D)
1.0
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clear
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question_answer 123) A certain current liberates 0.504 g hydrogen is 2 h. How many gram of oxygen can be liberated by the same current in the same time?
A)
2.0 g
done
clear
B)
0.4 g
done
clear
C)
4.0 g
done
clear
D)
8.0 g
done
clear
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question_answer 124) The reduction potential values of X, Y and Z are \[-3.05\,V,-0.44\,V\]and\[~-0.83\,V\] respectively. Which of the following order is correct with respect to their reducing property?
A)
\[X>Y>Z\]
done
clear
B)
\[X>Z>Y\]
done
clear
C)
\[Y>Z>X\]
done
clear
D)
\[~Z>Y>X\]
done
clear
View Answer play_arrow
question_answer 125) Relationship between atomic radius r and the edge length a of a body centred cubic unit cell is
A)
\[r=\frac{a}{2}\]
done
clear
B)
\[r=\sqrt{\frac{a}{2}}\]
done
clear
C)
\[r=\frac{\sqrt{3}}{4}a\]
done
clear
D)
\[r=\frac{3a}{2}\]
done
clear
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question_answer 126) Calculate the reduction potential of a half-cell containing of platinum electrode immersed in \[\text{2}\text{.0}\,\text{M}\,\text{F}{{\text{e}}^{\text{2+}}}\]and \[\text{0}\text{.02 M F}{{\text{e}}^{\text{3+}}}\text{.}\] Given \[\text{E}_{F{{e}^{3+}}/F{{e}^{2+}}}^{o}=0.771\,V,\] \[F{{e}^{3+}}+{{e}^{-}}\xrightarrow{{}}F{{e}^{2+}}\]
A)
0.653 V
done
clear
B)
0.889 V
done
clear
C)
0.0653V
done
clear
D)
2.771V
done
clear
View Answer play_arrow
question_answer 127) Faraday constant is defined as
A)
charge carried by one electron
done
clear
B)
charge carried by one mole of electron
done
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C)
charge required depositing one mole of substance
done
clear
D)
charge carried by two moles of electron
done
clear
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question_answer 128) If 300mL of a gas weighs 0.368 g at STP. What is its molecular weight?
A)
30.16
done
clear
B)
2.55
done
clear
C)
27.5
done
clear
D)
37.5
done
clear
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question_answer 129) Which one of the following compound exhibit both Schottky and Frenkel defects?
A)
\[~NaCl\]
done
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B)
\[~AgCl\]
done
clear
C)
\[AgBr\]
done
clear
D)
\[Agl\]
done
clear
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question_answer 130) Identify the molecule that has zero dipole moment.
A)
\[C{{H}_{3}}Cl\]
done
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B)
\[CHC{{l}_{3}}\]
done
clear
C)
\[C{{H}_{2}}C{{l}_{2}}\]
done
clear
D)
\[CC{{l}_{4}}\]
done
clear
View Answer play_arrow
question_answer 131) Which one statement about sulphur dioxide gas is incorrect?
A)
It has an angular shape
done
clear
B)
lt decolourises acidified potassium permanganate solution
done
clear
C)
Two S?O bonds are equal
done
clear
D)
It is a dehydrating agent
done
clear
View Answer play_arrow
question_answer 132) In which of the following arrangement, the order is not according to the property indicated against it?
A)
\[{{F}_{2}}>C{{l}_{2}}>B{{r}_{2}}>{{I}_{2}}-\]Oxidising agent
done
clear
B)
\[N{{H}_{3}}>P{{H}_{3}}>As{{H}_{3}}>Sb{{H}_{3}}>Bi{{H}_{3}}-\]Basic property
done
clear
C)
\[F>Cl>Br>I-\]Electron gain enthalpy
done
clear
D)
\[C>Si>Ge>Sn-\]Ability to form p-p bond
done
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View Answer play_arrow
question_answer 133) In \[\text{C}{{\text{O}}_{\text{2}}}\text{,C}{{\text{H}}_{\text{4}}}\]and\[\text{CH}_{\text{3}}^{\text{+}}\]the hybridisation of carbon atom are
A)
\[s{{p}^{2}},s{{p}^{3}}\]and \[s{{p}^{2}}\]respectively
done
clear
B)
\[~sp,s{{p}^{3}}\] and \[s{{p}^{2}}\]respectively
done
clear
C)
\[~sp,\text{ }s{{p}^{3}}\] and \[sp\]respectively
done
clear
D)
\[s{{p}^{2}},\text{ }s{{p}^{3}}\]and \[sp\]respectively
done
clear
View Answer play_arrow
question_answer 134) Why calcium ion makes water hard but sodium ion does not?
A)
Calcium forms insoluble compound with stearate ion present in soap
done
clear
B)
Sodium forms insoluble compound with stearate ion present in soap
done
clear
C)
Calcium forms soluble compound with stearate ion present in soap
done
clear
D)
Both calcium and sodium forms insoluble compound with stearate ion present in soap
done
clear
View Answer play_arrow
question_answer 135) The colourless gas that turns brown in air is
A)
\[NO\]
done
clear
B)
\[N{{O}_{2}}\]
done
clear
C)
\[{{N}_{2}}{{O}_{4}}\]
done
clear
D)
\[{{N}_{2}}{{O}_{5}}\]
done
clear
View Answer play_arrow
question_answer 136) IUPAC name of the complex \[{{K}_{3}}[Al{{({{C}_{2}}{{O}_{4}})}_{3}}]\]is
A)
potassium tris(oxalato)aluminate(III)
done
clear
B)
potassium tri(oxalato)aluminate(III)
done
clear
C)
potassium tris(oxalato)aluminium(III)
done
clear
D)
potassium tri(oxalato)alumimum(III)
done
clear
View Answer play_arrow
question_answer 137) The depressant used to separate lead sulphide and zinc sulphide ores is
A)
potassium cyanide
done
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B)
sodium cyanide
done
clear
C)
silver cyanide
done
clear
D)
sodium sulphide
done
clear
View Answer play_arrow
question_answer 138)
IUPAC name of the compound
A)
1-fluoro-4-methyl-2-nitrobenzene
done
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B)
4-fluoro-1-methyl-3-nitrobenzene
done
clear
C)
4-methyl-1-fluoro-2-nitrobenzene
done
clear
D)
5-methyl-2-fluoro-1-nitrobenzene
done
clear
View Answer play_arrow
question_answer 139) In the extraction of copper, the copper matte is a mixture of
A)
copper(II) sulphide and iron(II) sulphide
done
clear
B)
copperd (II) sulphide and iron(III) sulphide
done
clear
C)
copper(I) sulphide and iron(II) sulphide
done
clear
D)
copper(I) sulphide and iron(III) sulphide
done
clear
View Answer play_arrow
question_answer 140) Silver halide which is readily soluble m ammonium chloride is
A)
silver chloride
done
clear
B)
silver bromide
done
clear
C)
silver fluoride
done
clear
D)
silver iodide
done
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question_answer 141) Which of the following reagent can be used to convert ethanamide to methanamme?
A)
\[{{P}_{2}}{{O}_{5}}\]
done
clear
B)
\[NaOBr\]
done
clear
C)
\[LiAl{{H}_{4}}/{{H}_{2}}O\]
done
clear
D)
\[Na(Hg)/{{C}_{2}}{{H}_{5}}OH\]
done
clear
View Answer play_arrow
question_answer 142) Identify the product ?C? in the series \[{{C}_{6}}{{H}_{5}}N{{O}_{2}}\xrightarrow{Fe/HCl}A\xrightarrow[273\,K]{NaN{{O}_{2}}+HCl}\]\[B\xrightarrow[283\,K]{{{H}_{2}}O}C\]
A)
\[{{\text{C}}_{\text{6}}}{{\text{H}}_{\text{5}}}\text{OH}\]
done
clear
B)
\[{{\text{C}}_{\text{6}}}{{\text{H}}_{\text{5}}}\text{C}{{\text{H}}_{\text{2}}}\text{OH}\]
done
clear
C)
\[{{\text{C}}_{\text{6}}}{{\text{H}}_{\text{5}}}\text{CHO}\]
done
clear
D)
\[{{\text{C}}_{\text{6}}}{{\text{H}}_{\text{5}}}\text{N}{{\text{H}}_{\text{2}}}\]
done
clear
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question_answer 143) The class of drug used for the treatment of stress is
A)
analgesics
done
clear
B)
antiseptic
done
clear
C)
antihistamine
done
clear
D)
tranquilizers
done
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View Answer play_arrow
question_answer 144) Compound that has smell of bitter almonds is
A)
aniline
done
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B)
benzonitnie
done
clear
C)
phenylisocyanide
done
clear
D)
nitrobenzene
done
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View Answer play_arrow
question_answer 145) Which of the following is the correct increasing order of basicity of amines in gaseous phase?
A)
\[{{(C{{H}_{3}})}_{2}}NH>C{{H}_{3}}N{{H}_{2}}>{{(C{{H}_{3}})}_{3}}N>N{{H}_{3}}\]
done
clear
B)
\[{{(C{{H}_{3}})}_{3}}N>{{(C{{H}_{3}})}_{2}}NH>C{{H}_{3}}N{{H}_{2}}>N{{H}_{3}}\]
done
clear
C)
\[{{(C{{H}_{3}})}_{2}}NH>{{(C{{H}_{3}})}_{3}}N>C{{H}_{3}}N{{H}_{2}}>N{{H}_{3}}\]
done
clear
D)
\[{{(C{{H}_{3}})}_{3}}N>C{{H}_{3}}N{{H}_{2}}>{{(C{{H}_{3}})}_{2}}NH>N{{H}_{3}}\]
done
clear
View Answer play_arrow
question_answer 146) Nitrogenous base that found in RNA but absent in DNA is
A)
uracil
done
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B)
thymine
done
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C)
cytosine
done
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D)
adenine
done
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View Answer play_arrow
question_answer 147) Glycerol when reacts with potassium hydrogen sulphate at \[473\text{ }K-503\text{ }K\]forms
A)
allyl iodide
done
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B)
allyl alcohol
done
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C)
glycericacid
done
clear
D)
acrolein
done
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View Answer play_arrow
question_answer 148) Phenol reacts with bromine in chloroform at low temperature to give
A)
\[m-\]bromophenol
done
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B)
mixture of ortho and para bromophenol
done
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C)
\[~p-\] bromophenol
done
clear
D)
2, 4, 6-tribromophenol
done
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View Answer play_arrow
question_answer 149)
Identify the compound 'X' in the following reaction
A)
done
clear
B)
done
clear
C)
done
clear
D)
done
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question_answer 150) Alkyl halides undergoing substitution nucleophilic bimolecular reaction involves
A)
formation of carbocation
done
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B)
racemic mixture
done
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C)
inversion of configuration
done
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D)
retention of configuration
done
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question_answer 151) The radius of the sphere \[|\,3\,\vec{r}+2\hat{i}-\hat{j}-4\hat{k}|=3\] is
A)
\[2\]
done
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B)
\[3\]
done
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C)
\[1\]
done
clear
D)
\[9\]
done
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View Answer play_arrow
question_answer 152) The foot of the perpendicular drawn from the origin to a plane is \[(1,-1,5)\]. The equation of the plane is
A)
\[\vec{r}.(\hat{i}-\hat{j}+5\hat{k})=27\]
done
clear
B)
\[\vec{r}.(\hat{i}-\hat{j}+5\hat{k})=\sqrt{27}\]
done
clear
C)
\[\vec{r}.(5\hat{i}-\hat{j}+\hat{k})=\frac{1}{\sqrt{27}}\]
done
clear
D)
\[x-y-5z-27=0\]
done
clear
View Answer play_arrow
question_answer 153) The dual of the statement \[(\tilde{\ }p)\wedge [(\tilde{\ }q)\wedge (p\vee q)\wedge (\tilde{\ }r)]\]is
A)
\[p\wedge [q\vee (p\wedge q)\vee r]\]
done
clear
B)
\[(\tilde{\ }p)\vee [(\tilde{\ }q)\vee (p\wedge q)\vee (\tilde{\ }r)]\]
done
clear
C)
\[(\tilde{\ }p)\wedge [(\tilde{\ }q)\vee (p\vee q)\vee r]\]
done
clear
D)
\[(\tilde{\ }p)\vee [(\tilde{\ }q)\vee (p\wedge q)\vee r]\]
done
clear
View Answer play_arrow
question_answer 154) The vector equation of the straight line \[6x-8=2y-7=3z\]is
A)
\[\vec{r}=\left( \frac{8}{6}\hat{i}+\frac{7}{2}\hat{j} \right)+t\left( \frac{1}{6}\hat{i}+\frac{1}{2}\hat{j}-\frac{1}{3}\hat{k} \right)\]
done
clear
B)
\[\vec{r}=\left( \frac{8}{6}\hat{i}+\frac{7}{2}\hat{j} \right)+s\left( \frac{1}{6}\hat{i}+\frac{1}{2}\hat{j}-\frac{1}{3}\hat{k} \right)\]
done
clear
C)
\[\vec{r}=\left( -\frac{8}{6}\hat{i}-\frac{7}{2}\hat{j} \right)+t\left( \frac{1}{6}\hat{i}+\frac{1}{2}\hat{j}-\frac{1}{3}\hat{k} \right)\]
done
clear
D)
\[\vec{r}=\left( -\frac{8}{6}\hat{i}-\frac{7}{2}\hat{j} \right)+s\left( \frac{1}{6}\hat{i}-\frac{1}{2}\hat{j}-\frac{1}{3}\hat{k} \right)\]
done
clear
View Answer play_arrow
question_answer 155) The unit normal vector to the plane \[3x+2y-2z=8\sqrt{17}\] is
A)
\[\frac{1}{\sqrt{3}}\,(\hat{i}+\hat{j}-\hat{k})\]
done
clear
B)
\[\frac{1}{\sqrt{17}}\,(3\hat{i}+2\hat{j}-2\hat{k})\]
done
clear
C)
\[\frac{1}{\sqrt{13}}\,(3\hat{i}+2\hat{j}+2\hat{k})\]
done
clear
D)
\[\frac{1}{\sqrt{11}}\,(3\hat{i}+\hat{j}+\hat{k})\]
done
clear
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question_answer 156) The centroid of the triangle formed by joining the mid points of the sides of a triangle with vertices \[(-1,-1),(2,4)\] and \[(-5,-6)\] is
A)
\[\left( -\frac{2}{3},1 \right)\]
done
clear
B)
\[\left( -\frac{4}{3},-1 \right)\]
done
clear
C)
\[\left( -\frac{1}{3},\frac{1}{2} \right)\]
done
clear
D)
\[\left( -\frac{1}{4},\frac{1}{4} \right)\]
done
clear
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question_answer 157) if the straight lines \[2x+5ay-1=0\] and \[3x+7y+7=0\] are mutually perpendicular, then value of \[\alpha \] is
A)
\[\frac{6}{37}\]
done
clear
B)
\[\frac{-6}{31}\]
done
clear
C)
\[\frac{-6}{37}\]
done
clear
D)
\[\frac{-6}{35}\]
done
clear
View Answer play_arrow
question_answer 158) The pair of straight lines \[{{x}^{2}}-3{{y}^{2}}=0\]and the line \[x=1\]form a triangle which is
A)
right angled
done
clear
B)
isosceles
done
clear
C)
scalene
done
clear
D)
equilateral
done
clear
View Answer play_arrow
question_answer 159) If the straight lines \[2x-3y+1=0\] and \[4x-6y+5=0\] are tangents to the same circle, then the radius of the circle is
A)
\[\frac{3}{2\sqrt{13}}\]
done
clear
B)
\[\frac{3}{4\sqrt{13}}\]
done
clear
C)
\[\frac{3}{8\sqrt{13}}\]
done
clear
D)
\[2\]
done
clear
View Answer play_arrow
question_answer 160) If \[A\,(5,-1)\] and \[B\,(-3,7)\] are two points on a circle and if \[P(x,y)\] is any point on the circle such that s\[\angle APB=\frac{\pi }{2},\] then the equation of the circle is
A)
\[{{x}^{2}}+{{y}^{2}}-2x+6y-22=0\]
done
clear
B)
\[{{x}^{2}}+{{y}^{2}}+2x+6y-11=0\]
done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-2x+6y+22=0\]
done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-2x-6y-22=0\]
done
clear
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question_answer 161) The angle between the pair of straight lines represented by the equation \[12{{x}^{2}}+7xy-12{{y}^{2}}-x-7y-1=0\]is
A)
\[\frac{\pi }{3}\]
done
clear
B)
\[\frac{\pi }{4}\]
done
clear
C)
\[\frac{\pi }{2}\]
done
clear
D)
\[\frac{\pi }{6}\]
done
clear
View Answer play_arrow
question_answer 162) The equation of a straight line which is parallel to \[x-2y+8=0\]and passes through \[(0,4)\] is
A)
\[x-2y+8=0~~~\]
done
clear
B)
\[x-2y+7=0\]
done
clear
C)
\[x-2y+4=0\]
done
clear
D)
\[2x+2y-13=0\]
done
clear
View Answer play_arrow
question_answer 163) The algebraic sum of the moments of the forces, forming a couple, about any point in their plane is
A)
proportional to the sum of the magnitudes of the forces
done
clear
B)
inversely proportional to the magnitudes of the forces
done
clear
C)
constant and is equal to the moment of the couple
done
clear
D)
constant and is equal to one-third of the moment of the couple
done
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View Answer play_arrow
question_answer 164) At time t, the distance x cm of a moving particle in a horizontal line is given by\[x=12\,{{t}^{3}}-7\,{{t}^{2}}+14t+2.\]. The acceleration when \[t=1\text{ }s\]is
A)
\[48\,\,cm/{{s}^{2}}\]
done
clear
B)
\[68\text{ }cm/{{s}^{2}}\]
done
clear
C)
\[58\text{ }cm/{{s}^{2}}\]
done
clear
D)
\[56\text{ }cm/{{s}^{2}}\]
done
clear
View Answer play_arrow
question_answer 165) The horizontal range of a projectile is \[\frac{4}{\sqrt{3}}\] times its maximum height. The angle of projection is
A)
\[{{30}^{o}}\]
done
clear
B)
\[{{60}^{o}}\]
done
clear
C)
\[{{45}^{o}}\]
done
clear
D)
\[{{\tan }^{-1}}\,(2)\]
done
clear
View Answer play_arrow
question_answer 166) A particle with uniform acceleration reaches \[100\text{ }m\]in the 5th second and \[151\text{ }m\]in the 8th second. The acceleration is
A)
\[15m/{{s}^{2}}\]
done
clear
B)
\[~16m/{{s}^{2}}\]
done
clear
C)
\[17\text{ }m/{{s}^{2}}\]
done
clear
D)
\[20\text{ }m/{{s}^{2}}\]
done
clear
View Answer play_arrow
question_answer 167) Let \[\vec{u}\] and \[\vec{v}\] be the velocity vectors of a particle at a point O. If \[\vec{u}\] and \[\vec{v}\] are in opposite directions and if \[u>v,\] then the magnitude of the resultant velocity vector \[\vec{v}\] is
A)
\[u+v\]
done
clear
B)
\[2\,u+v\]
done
clear
C)
\[u-v\]
done
clear
D)
\[u-\frac{1}{2}v\]
done
clear
View Answer play_arrow
question_answer 168) The forces of magnitude \[9\text{ }N\]and \[11\text{ }N\]act at a point and are inclined to each other at an angle of\[{{45}^{o}}\]. The magnitude of the resultant force is
A)
\[\sqrt{301}\,N\]
done
clear
B)
\[\sqrt{202+99\sqrt{2}}\,N\]
done
clear
C)
\[\sqrt{{{9}^{2}}+{{11}^{2}}}\,\,N\]
done
clear
D)
\[202\,N\]
done
clear
View Answer play_arrow
question_answer 169) If X and Y are two non-singular matrices such that \[XY{{X}^{-1}}=\left( \begin{matrix} 3 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & -7 \\ \end{matrix} \right),\] then \[X{{Y}^{-1}}{{X}^{-1}}\] is equal to
A)
\[\left( \begin{matrix} \frac{1}{3} & 0 & 0 \\ 0 & \frac{1}{2} & 0 \\ 0 & 0 & -\frac{1}{7} \\ \end{matrix} \right)\]
done
clear
B)
\[\left( \begin{matrix} -\frac{1}{3} & 0 & 0 \\ 0 & \frac{1}{2} & 0 \\ 0 & 0 & -7 \\ \end{matrix} \right)\]
done
clear
C)
\[\left( \begin{matrix} \frac{1}{3} & 0 & 0 \\ 0 & \frac{1}{2} & 0 \\ 0 & 0 & 7 \\ \end{matrix} \right)\]
done
clear
D)
\[\left( \begin{matrix} \frac{1}{3} & 0 & 0 \\ 0 & -\frac{1}{2} & 0 \\ 0 & 0 & 7 \\ \end{matrix} \right)\]
done
clear
View Answer play_arrow
question_answer 170) Let \[\vec{a}\,-\,2\vec{b}\] and \[2\vec{a}\,-\vec{b}\] be position vectors of the points A and B respectively. The position vector of the point which divides AB in the ratio \[3:2\]externally is
A)
\[\frac{8}{5}\,\vec{a}-\frac{7}{5}\vec{b}\]
done
clear
B)
\[4\,\vec{a}+\vec{b}\]
done
clear
C)
\[\,\vec{a}+4\vec{b}\]
done
clear
D)
\[\frac{7}{5}\vec{b}-\frac{8}{5}\vec{a}\]
done
clear
View Answer play_arrow
question_answer 171) If \[|\vec{a}|=2,\,|\vec{b}|=5,\] and \[\vec{a}\,.\,\vec{b}=5\sqrt{2},\]then \[|\vec{a}\times \vec{b}|\] is equal to
A)
\[5\sqrt{2}\]
done
clear
B)
\[\sqrt{2}\]
done
clear
C)
\[4\sqrt{2}\]
done
clear
D)
\[2\]
done
clear
View Answer play_arrow
question_answer 172) Let \[\vec{a}-2\vec{b}+3\vec{c},\,\,\,\,\,-2\vec{a}+3\vec{b}-\vec{c}\]and \[4\vec{a}-7\vec{b}+7\vec{c}\]be position vectors of the points A, B and C respectively. Then, the points A, B and Care
A)
vertices of an equilateral triangle
done
clear
B)
vertices of a right angled triangle
done
clear
C)
vertices of an isosceles triangle
done
clear
D)
collinear points
done
clear
View Answer play_arrow
question_answer 173) If \[\left| \begin{matrix} {{a}_{1}} & {{b}_{1}} & {{c}_{1}} \\ {{a}_{2}} & {{b}_{2}} & {{c}_{2}} \\ {{a}_{3}} & {{b}_{3}} & {{c}_{3}} \\ \end{matrix} \right|=3,\] then \[\left| \begin{matrix} 3\,{{a}_{1}} & 9\,{{b}_{1}} & 3\,{{c}_{1}} \\ {{a}_{2}} & 3\,{{b}_{2}} & {{c}_{2}} \\ 3\,{{a}_{3}} & 9\,{{b}_{3}} & 3\,{{c}_{3}} \\ \end{matrix} \right|\] is equal to
A)
\[51\]
done
clear
B)
\[27\]
done
clear
C)
\[81\]
done
clear
D)
\[91\]
done
clear
View Answer play_arrow
question_answer 174) The domain of the function \[f(x)=\frac{1}{{{\log }_{10}}\,(1-x)}\]is
A)
\[(-\infty ,\,1]\,-\{0\}\]
done
clear
B)
\[(-\infty ,\,1)\,-\{0\}\]
done
clear
C)
\[(-\infty ,\,\,2)\,\]
done
clear
D)
\[(0,\,-\infty )\,\]
done
clear
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question_answer 175) If \[\omega \] is a complex cube root of unity, then \[\frac{a+b\omega +c{{\omega }^{2}}}{a{{\omega }^{2}}+b+c\omega }+\frac{a{{\omega }^{2}}+b\omega +c}{a+b{{\omega }^{2}}+c\omega }\] is equal to
A)
\[1\]
done
clear
B)
\[2\,\omega \]
done
clear
C)
\[2\,{{\omega }^{2}}\]
done
clear
D)
\[-1\]
done
clear
View Answer play_arrow
question_answer 176) If 19 times 12th term of an AP and 18 times 11 th term of an AP are equal, then the 30th term of the AP is
A)
\[0\]
done
clear
B)
\[2\]
done
clear
C)
\[11\]
done
clear
D)
\[29\]
done
clear
View Answer play_arrow
question_answer 177) Sum ton terms of the series \[1+11+111+....\]is
A)
\[\frac{10}{81}\,\,({{10}^{n}}-1)-\frac{n}{81}\]
done
clear
B)
\[\frac{10}{81}\,\,({{10}^{n}}-1)-\frac{n}{9}\]
done
clear
C)
\[\frac{10}{81}\,\,({{10}^{n}}-1)+\frac{n}{9}\]
done
clear
D)
\[\frac{10}{81}\,\,({{10}^{n}}-1)+\frac{n}{81}\]
done
clear
View Answer play_arrow
question_answer 178) If one root of the equation \[{{x}^{2}}-(3\sqrt{2}-2i)\,x-6\,\sqrt{2}i=0\] is \[-2i,\] then the other root of the equation is
A)
\[2i\]
done
clear
B)
\[3\,\sqrt{2}\]
done
clear
C)
\[-3\,\sqrt{2}\]
done
clear
D)
\[5\,\sqrt{2}\]
done
clear
View Answer play_arrow
question_answer 179) If \[{{z}_{1}}\] and \[{{z}_{2}}\] are non-zero complex numbers such that arg \[\left( \frac{{{z}_{1}}}{{{z}_{2}}} \right)=\frac{\pi }{2},\] then \[\left| \frac{3{{z}_{1}}-5{{z}_{2}}}{3{{z}_{1}}+5{{z}_{2}}} \right|\] equal to
A)
\[\sqrt{2}\]
done
clear
B)
\[\sqrt{34}\]
done
clear
C)
\[1\]
done
clear
D)
\[\frac{2}{\sqrt{34}}\]
done
clear
View Answer play_arrow
question_answer 180) Which one of the following is not true for the function \[f(x)={{x}^{2}}-x+1,\,0\le x\le 1\]?
A)
Increases on \[\left[ \frac{1}{2},1 \right]\]
done
clear
B)
Decreases on \[\left[ 0,\frac{1}{2} \right]\]
done
clear
C)
Increases on \[\left[ 0,\frac{1}{2} \right]\]
done
clear
D)
Neither increases nor decreases on \[[0,\,\,1]\]
done
clear
View Answer play_arrow
question_answer 181) The value of the integral \[\int{{{({{x}^{4}}+3{{x}^{3}}+9{{x}^{2}}+8x-6)}^{12}}}\] \[(4{{x}^{3}}+9{{x}^{2}}+18x+8)\,dx\] is equal to
A)
\[\frac{{{({{x}^{4}}+3{{x}^{3}}+9{{x}^{2}}+8x-6)}^{12}}}{12}+c\]
done
clear
B)
\[\frac{{{(4{{x}^{3}}+9{{x}^{2}}+18x+8)}^{13}}}{13}+c\]
done
clear
C)
\[\frac{{{({{x}^{4}}+3{{x}^{2}}+9{{x}^{2}}+8x-6)}^{13}}}{13}+c\]
done
clear
D)
\[\frac{{{({{x}^{4}}+3{{x}^{2}}+9{{x}^{2}}+8x-6)}^{11}}}{11}+c\]
done
clear
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question_answer 182) \[\int{{{x}^{2}}\,{{7}^{x}}\,\,dx}\] is equal to
A)
\[\frac{{{x}^{2}}{{7}^{x}}}{\log \,7}+2x\frac{{{7}^{x}}}{{{(\log \,7)}^{2}}}+2\frac{{{7}^{x}}}{{{(\log \,7)}^{3}}}+c\]
done
clear
B)
\[\frac{{{x}^{2}}{{7}^{x}}}{\log \,7}-2x\frac{{{7}^{x}}}{{{(\log \,7)}^{2}}}+2\frac{{{7}^{x}}}{{{(\log \,7)}^{3}}}+c\]
done
clear
C)
\[{{x}^{2}}{{7}^{x}}-2x\,\frac{7x}{\log \,7}+2\,\frac{7x}{{{(\log \,7)}^{2}}}+c\]
done
clear
D)
\[\frac{{{x}^{2}}{{7}^{x}}}{{{(\log \,7)}^{2}}}-2x\,\frac{{{7}^{x}}}{{{(\log \,7)}^{3}}}+2\frac{{{7}^{x}}}{{{(\log \,7)}^{4}}}+c\]
done
clear
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question_answer 183) If \[y=\cos \,(m\,\,{{\sin }^{-1}}\,x),\] then \[(1-{{x}^{2}})\,\frac{{{d}^{2}}y}{d{{x}^{2}}}-x\frac{dy}{dx}+{{m}^{2}}y\] is equal to
A)
\[1\]
done
clear
B)
\[7\]
done
clear
C)
\[-1\]
done
clear
D)
\[0\]
done
clear
View Answer play_arrow
question_answer 184) \[{{\cos }^{2}}\,B+{{\cos }^{2}}\,(A-B)\,-2\cos \,A\,\cos \,B\,\cos \,(A-B)\]is equal to
A)
\[co{{s}^{2}}\text{ }A\]
done
clear
B)
\[co{{s}^{2}}\text{ }A-1\]
done
clear
C)
\[si{{n}^{2}}\text{ }A\]
done
clear
D)
\[1\]
done
clear
View Answer play_arrow
question_answer 185) If \[A+B+C=\pi ,\]then \[\tan \frac{A}{2}.\tan \frac{B}{2}+\tan \frac{B}{2}.\tan \frac{C}{2}+\tan \frac{C}{2}+\tan \frac{C}{2}.\tan \frac{A}{2}\]is equal to
A)
\[3\]
done
clear
B)
\[2\]
done
clear
C)
\[1\]
done
clear
D)
\[0\]
done
clear
View Answer play_arrow
question_answer 186) If \[{{\tan }^{-1}}\,(1-x),\,\,{{\tan }^{-1}}\,(x)\] and \[{{\tan }^{-1}}\,(1+x)\] are in AP, then the value of \[{{x}^{3}}+{{x}^{2}}\]is equal to
A)
\[2\]
done
clear
B)
\[-1\]
done
clear
C)
\[1\]
done
clear
D)
\[-2\]
done
clear
View Answer play_arrow
question_answer 187) \[{{\sin }^{-1}}x+{{\sec }^{-1}}x+{{\cot }^{-1}}x+{{\cos }^{-1}}x\]\[+\text{cose}{{\text{c}}^{-1}}\,x+{{\tan }^{-1}}x\] is equal to
A)
\[\pi \]
done
clear
B)
\[2\pi \]
done
clear
C)
\[\frac{\pi }{2}\]
done
clear
D)
\[\frac{3\pi }{2}\]
done
clear
View Answer play_arrow
question_answer 188) The general solution of the equation\[sin\text{ }x+cos\text{ }x=2\]is
A)
\[x=n\pi \,+{{(-1)}^{n}}\,\frac{\pi }{4},\,n=....,-3,\,-2,\,\] \[-1,\,0,1,\,2,\,3,...\]
done
clear
B)
\[x=n\pi +{{(-1)}^{n}}\frac{\pi }{6},n=....,-3,-2,-1,\] \[0,\,1,\,2,\,3,....\]
done
clear
C)
\[x=n\pi +{{(-1)}^{n+1}}\frac{\pi }{4},n=...,-3,-2,\] \[-1,0,1,2,3,...\]
done
clear
D)
does not exist
done
clear
View Answer play_arrow
question_answer 189) If a \[\sin \theta +b\,\cos \theta =4\] and a \[\sin \theta -b\,\cos \theta =3,\]then the value of \[\sin 2\,\theta \] is
A)
\[\frac{7}{{{a}^{2}}+{{b}^{2}}}\]
done
clear
B)
\[\frac{5}{{{a}^{2}}+{{b}^{2}}}\]
done
clear
C)
\[\frac{7}{{{a}^{2}}-{{b}^{2}}}\]
done
clear
D)
\[\frac{7}{2ab}\]
done
clear
View Answer play_arrow
question_answer 190) \[(1-\tan A)\,(\cot \,A+1)\] is equal to
A)
\[(1-\tan A)\,(1+tanA)\]
done
clear
B)
\[(1+\tan A)\,(cot\,A-1)\]
done
clear
C)
\[(1+\tan A)\,(1-cot\,A)\]
done
clear
D)
\[(\tan \,A-1)\,(\cot \,A-1)\]
done
clear
View Answer play_arrow
question_answer 191) \[\int{{{\sec }^{2}}x\,\,\text{cose}{{\text{c}}^{2}}x\,\,dx}\]is equal to
A)
\[\tan x-\cot \,x+c\]
done
clear
B)
\[\tan x+\cot \,x+c\]
done
clear
C)
\[\tan x+\operatorname{cosec}\,x+c\]
done
clear
D)
\[\cot x+\operatorname{cosec}\,+c\]
done
clear
View Answer play_arrow
question_answer 192) The area of the region bounded by the curve \[x=2\,\cos \,\theta ,\,\,y=2\,\sin \theta ,\,x=0,\,x=2\] and the x-axis is (in sq unit)
A)
\[4\pi \]
done
clear
B)
\[2\pi \]
done
clear
C)
\[\pi \]
done
clear
D)
\[\frac{\pi }{2}\]
done
clear
View Answer play_arrow
question_answer 193) The solution of the differential equation \[\frac{dy}{dx}=5+5x+10y+10xy\]is
A)
\[\log \,(5+10y)=x+\frac{{{x}^{2}}}{2}+c\]
done
clear
B)
\[\frac{1}{10}\log \,(5+10y)=x+\frac{{{x}^{2}}}{2}+c\]
done
clear
C)
\[\frac{1}{5}\log \,(5+10y)=x+\frac{{{x}^{2}}}{2}+c\]
done
clear
D)
\[\frac{1}{10}\log \,(5+10y)=x+{{x}^{2}}+c\]
done
clear
View Answer play_arrow
question_answer 194) The order and degree of the differential equation \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+y+{{\left( \frac{dy}{dx}+\frac{{{d}^{3}}y}{d{{x}^{3}}} \right)}^{5/2}}=0\] are respectively
A)
\[3,\,\,\,2\]
done
clear
B)
\[2,\,\,3\]
done
clear
C)
\[3,\,\,1\]
done
clear
D)
\[3,\,\,5\]
done
clear
View Answer play_arrow
question_answer 195) \[\int_{0}^{\pi /2}{\frac{{{\sin }^{100}}x}{{{\sin }^{100}}x+{{\cos }^{100}}x}\,\,dx}\]is equal to
A)
\[\frac{\pi }{2}\]
done
clear
B)
\[\frac{\pi }{12}\]
done
clear
C)
\[\frac{\pi }{4}\]
done
clear
D)
\[\frac{\pi }{8}\]
done
clear
View Answer play_arrow
question_answer 196) If \[(\vec{a}\times \vec{b})\times \vec{c}=\vec{a}\times (\vec{b}\times \vec{c})\]and \[\vec{a},\vec{b}\] and \[\vec{c}\] are not mutually perpendicular vectors, then
A)
\[\vec{a}\] and \[\vec{c}\] are parallel
done
clear
B)
\[\vec{a}\] and \[\vec{b}\] are parallel
done
clear
C)
\[\vec{b}\]and \[\vec{c}\] are parallel
done
clear
D)
\[\vec{a}\] and \[\vec{c}\]are perpendicular
done
clear
View Answer play_arrow
question_answer 197) Which me of the following is a point on the straight line \[\vec{r}=(-5\hat{i}+2\hat{j}+3\hat{k})\,+\,t\,(9\hat{i}-5\hat{j}+3\hat{k})\]?
A)
\[(13,-8,\,7)\]
done
clear
B)
\[(4,-3,\,5)\]
done
clear
C)
\[(-14,7,\,6)\]
done
clear
D)
\[(22,-13,12)\]
done
clear
View Answer play_arrow
question_answer 198) \[\vec{r}=(1-t)\,(3\hat{i}-4\hat{j}+7\hat{k})+t(\hat{i}+\hat{j}-\hat{k})\]\[+s(-2\hat{i}+\hat{j}-\hat{k})\] is the equation of a plane in vector form when it
A)
passes through three given non-collinear points
done
clear
B)
passes through one point and parallel to two vectors
done
clear
C)
passes through two points and parallel to one vector
done
clear
D)
passes through one point and perpendicular to one vector
done
clear
View Answer play_arrow
question_answer 199) The point of intersection of the lines \[\frac{x-1}{3}=\frac{y-1}{-1}=\frac{z+1}{0}\] and \[\frac{x-4}{2}=\frac{y}{0}=\frac{z+1}{3}\]is
A)
\[(4,0,1)\]
done
clear
B)
\[(4,0,-1)\]
done
clear
C)
\[(1,1,1)\]
done
clear
D)
\[(1,1,-1)\]
done
clear
View Answer play_arrow
question_answer 200) If \[3\hat{i}+\hat{j}-2\hat{k}\]and \[\hat{i}-3\hat{j}+4\hat{k}\] are the diagonals of a parallelogram, then the area of the parallelogram is
A)
\[10\sqrt{3}\] sq unit
done
clear
B)
\[5\sqrt{3}\] sq unit
done
clear
C)
\[5\sqrt{2}\]sq unit
done
clear
D)
\[10\sqrt{2}\]sq unit
done
clear
View Answer play_arrow
question_answer 201) \[\vec{a}=\hat{i}+2\hat{j}+3\hat{k},\,\,\,\,\,\vec{b}=-\hat{i}+2\hat{j}+3\hat{k}\] and \[\vec{c}=2\hat{i}-2\hat{j}-3\hat{k},\]then \[(\vec{b}+\vec{c}).\vec{a}\times \{(\vec{b}+\vec{c})\times \vec{a}\}\] is equal to
A)
\[9\]
done
clear
B)
\[21\]
done
clear
C)
\[13\]
done
clear
D)
\[7\]
done
clear
View Answer play_arrow
question_answer 202) The coefficient of \[{{x}^{4}}\]in the expansion of \[{{(1+x)}^{-2}},\]where \[|x|<1,\] is
A)
\[-5\]
done
clear
B)
\[5\]
done
clear
C)
\[4\]
done
clear
D)
\[-3\]
done
clear
View Answer play_arrow
question_answer 203) If \[m{{=}^{n}}{{C}_{2}},\] then \[^{m}{{C}_{2}}\] is equal to
A)
\[^{n+1}{{C}_{4}}\]
done
clear
B)
\[{{2}^{n+1}}{{C}_{4}}\]
done
clear
C)
\[{{3}^{n+1}}{{C}_{4}}\]
done
clear
D)
\[{{4}^{n+1}}{{C}_{4}}\]
done
clear
View Answer play_arrow
question_answer 204) \[\frac{1+\frac{1}{2!}+\frac{1}{4!}+\frac{1}{6!}+...}{\frac{1}{1!}+\frac{1}{3!}+\frac{1}{5!}+....}\] is equal to
A)
\[\frac{{{e}^{2}}-1}{{{e}^{2}}+1}\]
done
clear
B)
\[\frac{{{e}^{2}}+1}{{{e}^{2}}-1}\]
done
clear
C)
\[\frac{e+1}{e-1}\]
done
clear
D)
\[\frac{1-{{e}^{2}}}{e+{{e}^{2}}}\]
done
clear
View Answer play_arrow
question_answer 205) Four arithmetic means between -10 and 25 are inserted. Then, the 5th term in the series is
A)
\[11\]
done
clear
B)
\[19\]
done
clear
C)
\[17\]
done
clear
D)
\[18\]
done
clear
View Answer play_arrow
question_answer 206) The mean deviation about the mean for the values 18, 20, 12, 14, 19, 22, 26, 16, 19, 24 is
A)
\[3.1\]
done
clear
B)
\[3.4\]
done
clear
C)
\[3.2\]
done
clear
D)
\[3.3\]
done
clear
View Answer play_arrow
question_answer 207) \[3\,{{\log }_{e}}2+\frac{1}{4}-\frac{1}{2}.\frac{1}{{{4}^{2}}}+\frac{1}{3}.\frac{1}{{{4}^{3}}}-....\]is equal to
A)
\[{{\log }_{e}}10\]
done
clear
B)
\[3\,\,{{\log }_{e}}4\]
done
clear
C)
\[2\,{{\log }_{e}}5\]
done
clear
D)
\[{{\log }_{e}}\,8\]
done
clear
View Answer play_arrow
question_answer 208) The number of ways of selecting a boy and a girl from a class consisting of 20 boys and 30 girls is
A)
\[50\]
done
clear
B)
\[10\]
done
clear
C)
\[600\]
done
clear
D)
\[1300\]
done
clear
View Answer play_arrow
question_answer 209) The sum of the coefficients in the expansion of \[{{(1+x-3x)}^{143}}\] is
A)
\[-1\]
done
clear
B)
\[1\]
done
clear
C)
\[-3\]
done
clear
D)
\[-7\]
done
clear
View Answer play_arrow
question_answer 210) If \[f(x)={{\cot }^{-1}}\left[ \sqrt{\frac{1+\sin x}{1-\sin x}} \right],\,0\le x\le \frac{\pi }{4},\]then \[f'\left( \frac{\pi }{4} \right)\] is equal to
A)
\[\frac{1}{2}\]
done
clear
B)
\[\frac{-1}{2}\]
done
clear
C)
\[\frac{1-{{x}^{2}}}{1+{{x}^{2}}}\]
done
clear
D)
\[\frac{x}{1-{{x}^{2}}}\]
done
clear
View Answer play_arrow
question_answer 211) For the function \[f(x)=|x-8|,\,0\le x\le 16,\] the Rollers theorem is not applicable as
A)
the function is not continuous at\[x=8\]
done
clear
B)
\[f(0)\ne f(16)\]
done
clear
C)
the function is not differentiable at \[x=8\]
done
clear
D)
the function is not differentiable at all points in \[(0,\,16)\]
done
clear
View Answer play_arrow
question_answer 212) If the tangent at \[x=c\] to the curve \[y={{x}^{3}}-5{{x}^{2}}-3x,\,1\le x\le 3,\]is parallel to the chord joining the points \[(1,-7)\] and \[(3,-27),\] then the value of c is equal to
A)
\[1\]
done
clear
B)
\[\frac{5}{3}\]
done
clear
C)
\[\frac{7}{3}\]
done
clear
D)
\[\frac{2}{3}\]
done
clear
View Answer play_arrow
question_answer 213) If \[x=2\,\left[ \cos \theta +\log \,\left( \tan \frac{\theta }{2} \right) \right],y=2\,\,\sin \theta ,\]then \[\frac{dy}{dx}\]is
A)
\[\cot \theta \]
done
clear
B)
\[\cos \theta \]
done
clear
C)
\[\tan \theta \]
done
clear
D)
\[\sin \theta \]
done
clear
View Answer play_arrow
question_answer 214) If \[y=6\,\,\sin x\,{{\log }_{10}}x+{{e}^{{{x}^{2}}}},\] then \[\frac{dy}{dx}\] is equal to
A)
\[\frac{6\,\,\sin x}{x}+6\,\cos \,x\,{{\log }_{10}}\,x+2x{{e}^{{{x}^{2}}}}\]
done
clear
B)
\[\frac{6\,\,\sin x}{x}\,{{\log }_{10}}\,e+6\,\cos \,x\,{{\log }_{10}}x+2x{{e}^{{{x}^{2}}}}\]
done
clear
C)
\[6\,\cos \,x\,{{\log }_{10}}x+6\,\sin x.\frac{10}{x}+2x{{e}^{{{x}^{2}}}}\]
done
clear
D)
\[\frac{6\,\sin \,x}{x}+6\,\cos \,x\,{{\log }_{10}}x+x{{e}^{{{x}^{2}}}}\]
done
clear
View Answer play_arrow
question_answer 215) Two events A and 5 have probabilities \[0.3\] and \[0.4\] respectively. The probability that both A and B occur simultaneously is \[0.1\]. The probability that neither A nor B occur is
A)
\[0.2\]
done
clear
B)
\[0.3\]
done
clear
C)
\[0.4\]
done
clear
D)
\[0.1\]
done
clear
View Answer play_arrow
question_answer 216) \[\underset{n\to \infty }{\mathop{\lim }}\,\,\,\frac{{{2}^{n+1}}+{{3}^{n+1}}}{{{2}^{n}}+{{3}^{n}}}\]is equal to
A)
\[0\]
done
clear
B)
\[1\]
done
clear
C)
\[2\]
done
clear
D)
\[3\]
done
clear
View Answer play_arrow
question_answer 217) The value of n such that \[\underset{x\to 3}{\mathop{\lim }}\,\,\frac{{{x}^{n}}-{{3}^{n}}}{x-3}=108\]is
A)
\[3\]
done
clear
B)
\[7\]
done
clear
C)
\[6\]
done
clear
D)
\[4\]
done
clear
View Answer play_arrow
question_answer 218) If the function \[f(x)=\left\{ \begin{matrix} \frac{{{x}^{3}}-8}{{{x}^{2}}-4}, & if & x\ne 2 \\ k, & if & x=2 \\ \end{matrix} \right.\] is continuous at \[x=2,\]then the value of k is
A)
\[2\]
done
clear
B)
\[0\]
done
clear
C)
\[3\]
done
clear
D)
\[4\]
done
clear
View Answer play_arrow
question_answer 219)
The probability distribution of a random variable X is \[x=x\] \[-1\] \[0\] \[1\] \[2\] \[P(X=X)\] \[0.2\] \[0.1\] \[0.4\] \[\lambda \]
Then, \[P(0<X\le 2)\] is equal to
A)
\[0.8\]
done
clear
B)
\[0.6\]
done
clear
C)
\[0.5\]
done
clear
D)
\[0.7\]
done
clear
View Answer play_arrow
question_answer 220) The general solution of \[{{\cot }^{2}}\theta =3\] is
A)
\[2n\pi \pm \frac{\pi }{3},n\in Z\]
done
clear
B)
\[n\pi \pm \frac{\pi }{6},n\in Z\]
done
clear
C)
\[n\pi \pm \frac{\pi }{2},n\in Z\]
done
clear
D)
\[2n\pi \pm \frac{\pi }{6},n\in Z\]
done
clear
View Answer play_arrow
question_answer 221) If A and B are square matrices such that \[AB\text{ }=A\]and \[BA=B,\]then \[{{A}^{2}}+{{B}^{2}}\]is equal to
A)
\[AB\]
done
clear
B)
\[A+B\]
done
clear
C)
\[BA+B\]
done
clear
D)
\[AB+A\]
done
clear
View Answer play_arrow
question_answer 222) If A is a square matrix of order 3 and if \[\det \,(A)=3,\] then \[\det \,[adj\,\,\{adj\,(adj\,A)\}]\] is equal to
A)
\[{{81}^{2}}\]
done
clear
B)
\[81\]
done
clear
C)
\[729\]
done
clear
D)
\[27\]
done
clear
View Answer play_arrow
question_answer 223) The value of the determinant \[\left| \begin{matrix} 1+\log \,a & \log \,b & \log \,c \\ \log \,a & 1+\log \,b & \log \,c \\ \log \,a & \log \,b & 1+\log \,c \\ \end{matrix} \right|\]is equal to
A)
\[\log \,(abc)\]
done
clear
B)
\[1-\log \,\,abc\]
done
clear
C)
\[\log \,(a+b+c)\]
done
clear
D)
\[1+\,\log \,abc\]
done
clear
View Answer play_arrow
question_answer 224) If A and Bare square matrices of order 3 such that \[det\text{ }A=1\] and \[det\text{ }B=-1~\]then \[det\text{ (-10}\,\text{AB)}\] is equal to
A)
\[10\]
done
clear
B)
\[-10\]
done
clear
C)
\[-1000\]
done
clear
D)
\[1000\]
done
clear
View Answer play_arrow
question_answer 225) \[{{\sin }^{2}}\,\frac{\pi }{8}+{{\sin }^{2}}\,\frac{3\pi }{8}+{{\sin }^{2}}\frac{5\pi }{8}+{{\sin }^{2}}\frac{7\pi }{8}\]is equal to
A)
\[1\]
done
clear
B)
\[\frac{3}{2}\]
done
clear
C)
2
done
clear
D)
\[\frac{5}{2}\]
done
clear
View Answer play_arrow