Thermodynamic process is shown below on a $P - V$ diagram for one mole of an ideal gas. If $V_{2} = 2V_{1}$ , then
the ratio of temperature $\frac{T_{2}}{T_{1}}$ is :
a.
$\sqrt{2}$
Correct Answer
b.
$\frac{1}{\sqrt{2}}$
c.
$\frac{1}{2}$
d.
$2$
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Q2nat
Two identical conducting spheres with negligible volume have $2. 1\, nC$ and $-0. 1\, nC$ charges, respectively.
They are brought into contact and then separated by a distance of $0. 5\,m$ . The electrostatic force acting
between the spheres is ___ $\times 10^{-9}\,N$ .
[Given : $4\pi \epsilon _{0} = \frac{1}{9\times 10^{9}}$ SI unit]
✓ Accepted Answer:36
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Q3nat
A reversible heat engine converts one-fourth of the heat input into work. When the temperature of the sink is
reduced by $52\,K,$ its efficiency is doubled. The temperature in Kelvin of the source will be ___ .
✓ Accepted Answer:208
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Q4mcq
An $L.C.R.$ circuit contains resistance of $110\,\Omega$ and a supply of $220\,V$ at $300\, rad \,s^{-1}$ angular frequency. If
only capacitance is removed from the circuit, current lags behind the voltage by $45^{\circ}$ . If on the other hand, the
only the inductor is removed the current leads by $45^{\circ}$ with the applied voltage. The $R.M.S.$ current flowing
in the circuit will be:
a.
$2. 5\,A$
b.
$2\,A$
Correct Answer
c.
$1\,A$
d.
$1. 5\,A$
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Q5mcq
A stone is dropped from the top of a building. When it crosses a point $5\,m$ below the top, another stone starts to
fall from a point $25\,m$ below the top. Both stones reach the bottom of building simultaneously. The height of the
building is :
a.
$25\,m$
b.
$45\,m$
Correct Answer
c.
$35\,m$
d.
$50\,m$
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Q6mcq
Match List I with List II.
List I List II
(a) Rectifier (i) Used either for stepping up or stepping down the A.C. voltage
(b)Stabilizer (ii) Used to convert A.C. voltage into D.C. voltage
(c) Transformer(iii)Used to remove any ripple in the rectified output voltage
Used for constant output voltage even when the input voltage
(iv)
(d)Filter
or load current change
Choose the correct answer from the options given below:
The wavelength of an X-ray beam is $10\,$ ā«. The mass of a fictitious particle having the same energy as that of
the X-ray photons is $\frac{x}{3} h\, kg.$ The value of $x$ is ___ . ( $h=$ Planck's constant)
✓ Accepted Answer:10
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Q8mcq
Given below are two statements:
Statement I: In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution.
Statement II : In a diatomic molecule, the rotational energy at a given temperature equals the translational
kinetic energy for each molecule.
In the light of the above statements, choose the correct answer from the options given below:
a.
Statement $I$ is false but Statement $II$ is true.
b.
Statement $I$ is true but Statement $II$ is false.
Correct Answer
c.
Both Statement $I$ and Statement $II$ are true.
d.
Both Statement $I$ and Statement $II$ are false.
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Q9mcq
The point $A$ moves with a uniform speed along the circumference of a circle of radius $0. 36\,m$ and covers $30^{\circ}$ in
$0. 1\,s$ . The perpendicular projection $P$ from $A$ on the diameter $MN$ represents the simple harmonic motion of $P$
. The restoration force per unit mass when $P$ touches $M$ will be :
a.
$0. 49\,N$
b.
$9. 87\,N$
Correct Answer
c.
$50\,N$
d.
$100\,N$
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Q10mcq
$Y =Asin(\omega t+\phi _{0})$ is the time-displacement equation of a $SHM.$ At $t= 0$ the displacement of the particle is
$Y = \frac{A}{2}$ and it is moving along negative $x$ -direction. Then the initial phase angle $\phi _{0}$ will be:
a.
$\frac{2\pi}{3}$
b.
$\frac{\pi}{6}$
c.
$\frac{5\pi}{6}$
Correct Answer
d.
$\frac{\pi}{3}$
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Two identical springs of spring constant $2k$ are attached to a block of mass $m$ and to fixed support (see figure).
When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The
time period of oscillations of this system is :
a.
$\pi \sqrt{\frac{m}{k}}$
b.
$2\pi \sqrt{\frac{m}{2k}}$
c.
$\pi \sqrt{\frac{m}{2k}}$
d.
$2\pi \sqrt{\frac{m}{k}}$
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If $e$ is the electronic charge, $c$ is the speed of light in free space and $h$ is Planck's constant, the quantity $_{4\pi \epsilon _{0}}_{hc}$
has dimensions of :
a.
$[MLT^{0}]$
b.
$[M^{0}\,L^{0}\,T^{0}]$
c.
$[MLT^{-1}]$
d.
$[LC^{-1}]$
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Two small spheres each of mass $10\, mg$ are suspended from a point by threads $0. 5\,m$ long. They are equally
charged and repel each other to a distance of $0. 20\,m$ . The charge on each of the sphere is $\frac{a}{21} \times 10^{-8}\,C.$ The
value of $a$ will be ___.[Given $g= 10\,m\,s^{-2}$ ]
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The peak electric field produced by the radiation coming from the $8\,W$ bulb at a distance of $10\,m$ is
$\frac{x}{10}\sqrt{\,} \frac{\mu _{0}c}{\pi} \,V\,m^{-1}$ . The efficiency of the bulb is $10%$ and it is a point source. The value of $x$ is,
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If a message signal of frequency $f_{m}$ is amplitude modulated with a carrier signal of frequency $f_{c}$ and radiated
through an antenna, the wavelength of the corresponding signal in air is
a.
$\frac{c}{f_{c}-f_{m}}$
b.
$\frac{c}{f_{m}}$
c.
$\frac{c}{f_{c}}$
d.
$\frac{c}{f_{c}+f_{m}}$
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For extrinsic semiconductors; when doping level is increased;
a.
Fermi-level of $p$ and $n$ - type semiconductors will not be affected.
b.
Fermi-level of $p$ -type semiconductor will go upward and Fermi-level of $n$ -type semiconductors will go
downward.
c.
Fermi-level of both p-type and n-type semiconductors will go upward for $T >T_{F}\,K$ and downward for
$T <T_{F}\,K,$ where $T_{F}$ is Fermi temperature.
d.
Fermi-level of $p$ - type semiconductors will go downward and Fermi-level of $n$ - type semiconductor will go
upward.
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An electron with kinetic energy $K_{1}$ enters between parallel plates of a capacitor at an angle $\alpha$ with the plates.
It leaves the plates at angle $\beta$ with kinetic energy $K_{2}.$ Then the ratio of kinetic energies $K_{1} :K_{2}$ will be :
a.
$\frac{sin^{2}\beta}{cos^{2}\alpha}$
b.
$\frac{cos\beta}{sin\alpha}$
c.
$\frac{cos\beta}{cos\alpha}$
d.
$\frac{cos^{2}\beta}{cos^{2}\alpha}$
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Consider the diffraction pattern obtained from the sunlight incident on a pinhole of diameter $0. 1\,\mu m.$ If the
diameter of the pinhole is slightly increased, it will affect the diffraction pattern such that
a.
its size increases, and intensity increases
b.
its size decreases, and intensity decreases
c.
its size decreases, but intensity increases
d.
its size increases, but intensity decreases
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A current of $6\,A$ enters one corner $P$ of an equilateral triangle $PQR$ having $3$ wires of resistance $2\,\Omega$ each and
leaves by the corner $R.$ The currents $i_{1}$ in ampere is
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The stopping potential for electrons emitted from a photosensitive surface illuminated by light of wavelength
$491\, nm$ is $0. 710\,V.$ When the incident wavelength is changed to a new value, the stopping potential is
$1. 43\,V.$ The new wavelength is :
a.
$382\, nm$
b.
$309\, nm$
c.
$329\, nm$
d.
$400\, nm$
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The initial velocity $v_{i}$ required to project a body vertically upward from the surface of the earth to reach a
height of $10R$ , where $R$ is the radius of the earth, may be described in terms of escape velocity $v_{e}$ such that
$v_{i} =\sqrt{\frac{x}{y}} \times v_{e}$ . The value of $x$ will be
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Two particles having masses $4\,g$ and $16\,g$ respectively are moving with equal kinetic energies. The ratio of the
magnitudes of their linear momentum is $n: 2$ . The value of $n$ will be ___.
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A sphere of radius $a$ and mass $m$ rolls along a horizontal plane with constant speed $v_{0}$ . It encounters an inclined
plane at angle $\theta$ and climbs upward. Assuming that it rolls without slipping, how far up the sphere will travel?
a.
$\frac{2}{5} \frac{v^{2}_{0}}{gsin\theta}$
b.
$\frac{7v^{2}_{0}}{10\,gsin\theta}$
c.
$\frac{v^{2}_{0}}{5gsin\theta}$
d.
$\frac{v^{2}_{0}}{2gsin\theta}$
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An electron of mass $m_{e}$ and a proton of mass $m_{p} = 1836\,m_{e}$ are moving with the same speed. The ratio of
their de Broglie wavelength $\frac{\lambda _{electron}}{\lambda _{proton}}$ will be :
a.
$1836$
b.
$\frac{1}{1836}$
c.
$918$
d.
$1$
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If $\vec{P} \times \vec{Q}= \vec{Q}\times \vec{P}$ , the angle between $\vec{P}$ and $\vec{Q}$ is $\theta (0^{\circ}<\theta < 360^{\circ})$ . The value of $\theta$ will be ___ $^{\circ}$ .
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The unit cell of copper corresponds to a face centered cube of edge length $3. 596\,$ Ć with one copper atom at
each lattice point. The calculated density of copper in $kg /m^{3}$ is ___ . [Molar mass of $Cu : 63. 54\,g;$ Avogadro
Number $= 6. 022 \times 10^{23}\,J$ ]
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Given below are two statements:
Statement I: The $pH$ of rain water is normally $~5. 6$ .
Statement II : If the $pH$ of rain water drops below $5. 6$ , it is called acid rain.
In the light of the above statements, choose the correct answer from the options given below:
a.
Both Statement $I$ and Statement $II$ are true.
b.
Statement $I$ is false but Statement $II$ is true.
c.
Statement $I$ is true but Statement $II$ is false.
d.
Both Statement $I$ and Statement $II$ are false.
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Given below are two statements:
Statement I : $\alpha$ and $\beta$ forms of sulphur can change reversibly between themselves with slow heating or slow
cooling.
Statement II : At room temperature the stable crystalline form of sulphur is monoclinic sulphur.
In the light of the above statements, choose the correct answer from the options given below:
a.
Both Statement $I$ and Statement $II$ are true.
b.
Statement $I$ is true but Statement $II$ is false.
c.
Statement $I$ is false but Statement $II$ is true.
d.
Both Statement $I$ and Statement $II$ are false.
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Five moles of an ideal gas at $293\,K$ is expanded isothermally from an initial pressure of $2. 1\, MPa$ to $1. 3\, MPa$
against at constant external pressure $4. 3\, MPa$ . The heat transferred in this process is ___ $kJmol^{-1}$ .
(Rounded-off to the nearest integer)
[ Use $R= 8. 314\,J\, mol^{-1} \,K^{-1}$ ]
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Given below are two statements:
Statement I : The identification of $Ni^{2+}$ is carried out by dimethyl glyoxime in the presence of $NH_{4}OH$ .
Statement II :The dimethyl glyoxime is a bidentate neutral ligand.
In the light of the above statements, choose the correct answer from the options given below:
a.
Statement $I$ is false but Statement $II$ is true.
b.
Statement $I$ is true but Statement $II$ is false.
c.
Both Statement $I$ and Statement $II$ are true.
d.
Both Statement $I$ and Statement $II$ are false.
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Electromagnetic radiation of wavelength $663\, nm$ is just sufficient to ionise the atom of metal $A$ . The
ionization energy of metal $A$ in $kJ \, mol^{-1}$ is ___. (Rounded-off to the nearest integer)
$[h = 6. 63 \times 10^{-34} Js, c = 3. 00 \times 10^{8}\, ms^{-1}, \,N_{A} = 6. 02 \times 10^{23}\, mol^{-1}]$
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Consider titration of $NaOH$ solution versus $1. 25\,M$ oxalic acid solution. At the end point following burette
readings were obtained.
(i) $4. 5\, mL$
(ii) $4. 5\, mL$
(iii) $4. 4\, mL$
(iv) $4. 4\, mL$
(v) $4. 4\, mL$
If the volume of oxalic acid taken was $10. 0\, mL$ then the molarity of the $NaOH$ solution is ___ $M$ . (Rounded-
off to the nearest integer)
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Among the following, number of metal/s which can be used as electrodes in the photoelectric cell is ___
. (Integer answer)
(A) $Li$
(B) $Na$
(C) $Rb$
(D) $Cs$
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In which of the following order the given complex ions are arranged correctly with respect to their decreasing
spin only magnetic moment?
(i) $[FeF_{6}]^{3-}$
(ii) $[Co (NH_{3})_{6}]^{3+}$
(iii) $[NiCl_{4}]^{2-}$
(iv) $[Cu (NH_{3})_{4}]^{2+}$
a.
$(ii) > (i) > (iii) > (iv)$
b.
$(iii) > (iv) > (ii) > (i)$
c.
$(i) > (iii) > (iv) > (ii)$
d.
$(ii) > (iii) > (i) > (iv)$
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Copper reduces $NO^{-}_{3}$ into $NO$ and $NO_{2}$ depending upon the concentration of $HNO_{3}$ in solution. (Assuming
fixed $[Cu^{2+}]$ and $P_{NO} = P_{NO_{2}}$ ), the $HNO_{3}$ concentration at which the thermodynamic tendency for reduction
of $NO^{-}_{3}$ into $NO$ and $NO_{2}$ by copper is same is $10^{x}\,M$ . The value of $2x$ is ___. (Rounded-off to the nearest
integer)
[Given, $E^{o}_{Cu^{2+}/ Cu} = 0. 34\,V, E^{o}_{NO^{-}_{3}}_{/ NO} = 0. 96\,V, E^{o}_{NO^{-}_{3}}_{/ NO_{2}} = 0. 79\,V$ and at $298\,K$ , $\frac{RT}{F}(2. 303) = 0. 059$ ]
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The rate constant of a reaction increases by five times on increase in temperature from $27^{\circ}C$ to $52^{\circ}C$ . The
value of activation energy in $kJmol^{-1}$ is ___ .(Rounded-off to the nearest integer) $[R= 8. 314\,J\,K^{-1}\, mol^{-1}]$
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Carbylamine test is used to detect the presence of primary amino group in an organic compound. Which of the
following compound is formed when this test is performed with aniline?
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If a compound $AB$ dissociates to the extent of $75%$ in an aqueous solution, the molality of the solution which
shows a $2. 5\,K$ rise in the boiling point of the solution is ___ molal. (Rounded-off to the nearest integer)
$[K_{b} = 0. 52K\, kg \, mol^{-1}]$ .
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The number of compound/s given below which contain/s $-COOH$ group is ___ . (Integer answer)
(A) Sulphanilic acid
(B) Picric acid
(C) Aspirin
(D) Ascorbic acid
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If the curve $x^{2} + 2y^{2} = 2$ intersects the line $x+y= 1$ at two points $P$ and $Q$ , then the angle subtended by the
line segment $PQ$ at the origin is
a.
$\frac{\pi}{2} -tan^{-1}(\frac{1}{3})$
b.
$\frac{\pi}{2} + tan^{-1}(\frac{1}{3} )$
c.
$\frac{\pi}{2} + tan^{-1}(\frac{1}{4})$
d.
$\frac{\pi}{2} -tan^{-1}(\frac{1}{4} )$
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In a group of $400$ people, $160$ are smokers and non-vegetarian; $100$ are smokers and vegetarian and the
remaining $140$ are non-smokers and vegetarian. Their chances of getting a particular chest disorder are
$35%, 20%$ and $10%$ respectively. A person is chosen from the group at random and is found to be suffering
from the chest disorder. The probability that the selected person is a smoker and non-vegetarian is :
a.
$\frac{14}{45}$
b.
$\frac{7}{45}$
c.
$\frac{8}{45}$
d.
$\frac{28}{45}$
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A plane passes through the points $A(1, 2, 3),B(2, 3, 1)$ and $C(2, 4, 2)$ . If $O$ is the origin and $P$ is $(2, -1, 1)$
$-$
, then the projection of $O\vec{P}$ on this plane is of length:
a.
$\sqrt{\frac{2}{5}}$
b.
$\sqrt{\frac{2}{7}}$
c.
$\sqrt{\frac{2}{3}}$
d.
$\sqrt{\frac{2}{11}}$
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Let $A$ be a set of all $4$ -digit natural numbers whose exactly one digit is $7$ . Then the probability that a randomly
chosen element of $A$ leaves remainder $2$ when divided by $5$ is:
a.
$\frac{1}{5}$
b.
$\frac{122}{297}$
c.
$\frac{97}{297}$
d.
$\frac{2}{9}$
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Let $A$ be a $3 \times 3$ matrix with $det (A) = 4$ . Let $R_{i}$ denote the $i^{th}$ row of $A$ . If a matrix $B$ is obtained by
performing the operation $R_{2} \rightarrow 2\rightarrow R_{2}+ 5R_{3}$ on $2\,A$ , then $det (B)$ is equal to :
a.
$64$
b.
$16$
c.
$128$
d.
$80$
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$|$
$||$
A line $l$ passing through origin is perpendicular to the lines
$l_{1} : \vec{r}= (3 +t)Ėi + (-1 + 2t)Ėj + (4 + 2t)Ėk$
$l_{2} : \vec{r}= (3 + 2s)Ėi + (3 + 2s)Ėj + (2 +s)Ėk$
If the co-ordinates of the point in the first octant on $l_{2}$ at a distance of $\sqrt{17}$ from the point of intersection of $l$
and $l_{1}$ are $(a, \,b, \,c)$ , then $18(a+b+c)$ is equal to ___ .
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A function $f$ is defined on $[-3, 3]$ as
$min{ x , 2 - x^{2}}, -2 \leq x\leq 2$
$f(x) ={$
$[|x|]\,\,, \,\,2 < |x| \leq 3$
where $[x]$ denotes the greatest integer $\leq x$ . The number of points, where $f$ is not differentiable in $(-3, 3)$ is
___ .
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A hyperbola passes through the foci of the ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1$ and its transverse and conjugate axes coincide
with major and minor axes of the ellipse, respectively. If the product of their eccentricities is one, then the
equation of the hyperbola is:
a.
$\frac{x^{2}}{9} - \frac{y^{2}}{16} = 1$
b.
$x^{2} - y^{2} = 9$
c.
$\frac{x^{2}}{9} - \frac{y^{2}}{25} = 1$
d.
$\frac{x^{2}}{9} - \frac{y^{2}}{4} = 1$
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Let $\vec{a}= Ėi +\alpha Ėj + 3Ėk$ and $\vec{b}= 3Ėi - \alpha Ėj + Ėk$ . If the area of the parallelogram whose adjacent sides are represented
by the vectors $\vec{a}$ and $\vec{b}$ is $8\sqrt{3}$ square units, then $\vec{a}\cdot \vec{b}$ is equal to ___ .
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The integral $\int \frac{e^{3 log}^{e}^{2}^{x}+5e^{2 log}^{e}^{2}^{x}}{e^{4 log}^{e x}+5e^{3 log}^{e x}-7e^{2 log}^{e x}} dx, \,x> 0$ , is equal to
(where $c$ is a constant of integration)
a.
$log_{e} x^{2} + 5x-7 + c$
b.
$4 log_{e} x^{2} + 5x-7 + c$
c.
$\frac{1}{4}log_{e} x^{2}+ 5x-7 + c$
d.
$log_{e} \sqrt{x^{2}+ 5x-7}+c$
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A function $f(x)$ is given by $f(x) = \frac{5^{x}}{5^{x}+5}$ , then the sum of the series
$f(\frac{1}{20})+f(\frac{2}{20})+f(\frac{3}{20})+ ā¦ +f( \frac{39}{20} )$
is equal to:
a.
$\frac{19}{2}$
b.
$\frac{49}{2}$
c.
$\frac{39}{2}$
d.
$\frac{29}{2}$
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If the curve, $y=y(x)$ represented by the solution of the differential equation $(2xy^{2} - y)dx+x dy= 0$ ,
passes through the intersection of the lines, $2x-3y= 1$ and $3x+ 2y= 8$ , then $|y(1)|$ is equal to ___ .
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Let $x$ denote the total number of one-one functions from a set $A$ with $3$ elements to a set $B$ with $5$ elements
and $y$ denote the total number of one-one functions from the set $A$ to the set $A\times B$ . Then :
a.
$y= 273x$
b.
$2y= 273x$
c.
$2y= 91x$
d.
$y= 91x$
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$|| ||$
$||$
A line is a common tangent to the circle $(x-3)^{2} +y^{2} = 9$ and the parabola $y^{2} = 4x$ . If the two points of
contact $(a,b)$ and $(c,d)$ are distinct and lie in the first quadrant, then $2(a+c)$ is equal to ___ .
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