Sound travels in a mixture of two moles of helium and $n$ moles of hydrogen. If rms speed of gas molecules in
the mixture is $\sqrt{2}$ times the speed of sound, then the value of $n$ will be
a.
$1$
b.
$2$
Correct Answer
c.
$3$
d.
$4$
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Q2mcq
Two billiard balls of mass $0. 05\, kg$ each moving in opposite directions with $10\, ms^{-1}$ collide and rebound with
the same speed. If the time duration of contact is $t= 0. 005\,s$ , then what is the force exerted on the ball due to
each other?
a.
$100\,N$
b.
$200\,N$
Correct Answer
c.
$300\,N$
d.
$400\,N$
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Q3nat
Two ideal diodes are connected in the network as shown in figure. The equivalent resistance between $A$ and $B$
is _____ $\Omega .$
✓ Accepted Answer:25
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Q4mcq
Hydrogen atom from excited state comes to the ground by emitting a photon of wavelength $\lambda$ . The value of
principal quantum number $n$ of the excited state will be :
( $R:$ Rydberg constant)
Three identical spheres each of mass $M$ are placed at the corners of a right angled triangle with mutually
perpendicular sides equal to $3\,m$ each. Taking point of intersection of mutually perpendicular sides as origin,
the magnitude of position vector of centre of mass of the system will be $\sqrt{x}\,m$ . The value of $x$ is
✓ Accepted Answer:2
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Q6mcq
For an object placed at a distance $2. 4\,m$ from a lens, a sharp focused image is observed on a screen placed at a
distance $12\, cm$ from the lens. A glass plate of refractive index $1. 5$ and thickness $1\, cm$ is introduced between
lens and screen such that the glass plate plane faces parallel to the screen. By what distance should the object
be shifted so that a sharp focused image is observed again on the screen?
a.
$0. 8\,m$
b.
$3. 2\,m$
Correct Answer
c.
$1. 2\,m$
d.
$5. 6\,m$
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Q7mcq
A current of $15\, mA$ flows in the circuit as shown in figure. The value of potential difference between the
points $A$ and $B$ will be
a.
$50V$
b.
$75V$
c.
$150V$
d.
$275V$
Correct Answer
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Q8nat
In a potentiometer arrangement, a cell of emf $1. 20\,V$ gives a balance point at $36\, cm$ length of wire. This cell
is now replaced by another cell of emf $1. 80\,V$ . The difference in balancing length of potentiometer wire in
above conditions will be _____ $cm$ .
✓ Accepted Answer:18
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Q9mcq
Light wave travelling in air along $x$ -direction is given by $E_{y} = 540 sin\pi \times 10^{4}(x- ct)\,V\,m^{-1}$ . Then, the
peak value of magnetic field of wave will be (Given $c= 3 \times 10^{8}\,m\,s^{-1}$ )
a.
$18 \times 10^{-7}\,T$
Correct Answer
b.
$54 \times 10^{-7}\,T$
c.
$54 \times 10^{-8}\,T$
d.
$18 \times 10^{-8}\,T$
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Q10mcq
A ball is projected from the ground with a speed $15\,m\,s^{-1}$ at an angle $\theta$ with horizontal so that its range and
maximum height are equal, then $tan\theta$ will be equal to
a.
$\frac{1}{4}$
b.
$\frac{1}{2}$
c.
$2$
d.
$4$
Correct Answer
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An object is taken to a height above the surface of earth at a distance $\frac{5}{4}R$ from the centre of the earth. Where
radius of earth, $R= 6400\, km$ . The percentage decrease in the weight of the object will be
a.
$36%$
b.
$50%$
c.
$64%$
d.
$25%$
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In $AM$ modulation, a signal is modulated on a carrier wave such that maximum and minimum amplitude are
found to be $6\,V$ and $2\,V$ respectively. The modulation index is
a.
$100%$
b.
$80%$
c.
$60%$
d.
$50%$
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A bag of sand of mass $9. 8\, kg$ is suspended by a rope. $A$ bullet of $200\,g$ travelling with speed $10\, ms^{-1}$ gets
embedded in it, then loss of kinetic energy will be
a.
$4. 9\,J$
b.
$9. 8\,J$
c.
$14. 7$
d.
$19. 6\,J$
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The length of a seconds pendulum at a height $h= 2R$ from earth surface will be:
(Given: $R=$ Radius of earth and acceleration due to gravity at the surface of earth $g=\pi ^{2}\,m\,s^{-2}$ )
a.
$\frac{2}{9} m$
b.
$\frac{4}{9} m$
c.
$\frac{8}{9} m$
d.
$\frac{1}{9} m$
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Two parallel plate capacitors of capacity $C$ and $3C$ are connected in parallel combination and charged to a
potential difference $18\,V$ . The battery is then disconnected and the space between the plates of the capacitor of
capacity $C$ is completely filled with a material of dielectric constant $9$ . The final potential difference across the
combination of capacitors will be _____ $V$ .
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A convex lens of focal length $20\, cm$ is placed in front of convex mirror with principal axis coinciding each
other. The distance between the lens and mirror is $10\, cm$ . A point object is placed on principal axis at a
distance of $60\, cm$ from the convex lens. The image formed by combination coincides the object itself. The
focal length of the convex mirror is _____ $cm$ .
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The ratio of wavelengths of proton and deuteron accelerated by potential $V_{p}$ and $V_{d}$ is $1 : \sqrt{2}$ . Then, the ratio
of $V_{p}$ to $V_{d}$ will be
a.
$1 : 1$
b.
$\sqrt{2}: 1$
c.
$2 : 1$
d.
$4 : 1$
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$\frac{x}{x+4}$ is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its
(i) third permitted energy level to the second level and
(ii) the highest permitted energy level to the second permitted level.
The value of $x$ will be
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Magnetic flux (in weber) in a closed circuit of resistance $20\,\Omega$ varies with time $t(s)$ as $\phi = 8t^{2} -9t+ 5$ . The
magnitude of the induced current at $t= 0. 25\,s$ will be _____ $mA$ .
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For a free body diagram shown in the figure, the four forces are applied in the ' $x$ ' and ' $y$ ' directions. What
additional force must be applied and at what angle with positive $x$ -axis so that the net acceleration of body is
zero?
a.
$\sqrt{2}\,N, 45^{\circ}$
b.
$\sqrt{2}\,N, 135^{\circ}$
c.
$\frac{2}{\sqrt{3}} \,N, 30^{\circ}$
d.
$2\,N, 45^{\circ}$
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Capacitance of an isolated conducting sphere of radius $R_{1}$ becomes $n$ times when it is enclosed by a concentric
conducting sphere of radius $R_{2}$ connected to earth. The ratio of their radii $(\frac{R_{2}}{R_{1}})$ is:
a.
$\frac{n}{n-1}$
b.
$\frac{2n}{2n+1}$
c.
$\frac{n+1}{n}$
d.
$\frac{2n+1}{n}$
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Let $\eta _{1}$ is the efficiency of an engine at $T_{1} = 447^{\circ}C$ and $T_{2} = 147^{\circ}C$ while $\eta _{2}$ is the efficiency at $T_{1} = 947^{\circ}C$
and $T_{2} = 47^{\circ}C$ . The ratio $\frac{\eta _{1}}{\eta _{2}}$ will be
a.
$0. 41$
b.
$0. 56$
c.
$0. 73$
d.
$0. 70$
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A block of ice of mass $120\,g$ at temperature $0^{\circ}C$ is put in $300\,g$ of water at $25^{\circ}C$ . The $x\,g$ of ice melts as the
temperature of the water reaches $0^{\circ}C$ . The value of $x$ is
[Use: Specific heat capacity of water $= 4200\,J\, kg^{-1} \,K^{-1}$ , Latent heat of ice $= 3. 5 \times 10^{5}\,J\, kg^{-1}$ ]
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The electric current in a circular coil of $2$ turns produces a magnetic induction $B_{1}$ at its centre. The coil is
unwound and is rewound into a circular coil of $5$ turns and the same current produces a magnetic induction $B_{2}$
at its centre.
The ratio of $\frac{B_{2}}{B_{1}}$ is:
a.
$\frac{5}{2}$
b.
$\frac{25}{4}$
c.
$\frac{5}{4}$
d.
$\frac{25}{2}$
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An electron with energy $0. 1 keV$ moves at right angle to the earth's magnetic field of $1 \times 10^{-4} Wbm^{-2}$ . The
frequency of revolution of the electron will be
(Take mass of electron $= 9. 0 \times 10^{-31}\, kg$ )
a.
$1. 6 \times 10^{5}\, Hz$
b.
$5. 6 \times 10^{5}\, Hz$
c.
$2. 8 \times 10^{6}\, Hz$
d.
$1. 8 \times 10^{6}\, Hz$
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A drop of liquid of density $\rho$ is floating half immersed in a liquid of density $\sigma$ and surface tension
$7. 5 \times 10^{-4}\,N\, cm^{-1}$ . The radius of drop in $cm$ will be : (Take : $g= 10\, ms^{-2}$ )
a.
$\frac{15}{\sqrt{2\rho -\sigma}}$
b.
$\frac{15}{\sqrt{\rho -\sigma}}$
c.
$\frac{3}{2\sqrt{\rho -\sigma}}$
d.
$\frac{3}{20\sqrt{2\rho -\sigma}}$
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A particle is moving in a straight line such that its velocity is increasing at $5\,m\,s^{-1}$ per meter. The acceleration
of the particle is _____ $m\,s^{-2}$ at a point where its velocity is $20\,m\,s^{-1}$ .
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The maximum error in the measurement of resistance, current and time for which current flows in an electrical
circuit are $1%, 2%$ and $3%$ respectively. The maximum percentage error in the detection of the dissipated heat
will be:
a.
$2$
b.
$4$
c.
$6$
d.
$8$
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Two waves executing simple harmonic motion travelling in the same direction with same amplitude and
frequency are superimposed. The resultant amplitude is equal to the $\sqrt{3}$ times of amplitude of individual
motions. The phase difference between the two motions is _____ (degree)
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While performing a thermodynamics experiment, a student made the following observations,
$HCl + NaOH NaCl + H_{2}O\Delta H = -57. 3\, kJ \, mol^{-1}$
$CH_{3}COOH + \vec{N}aOH \rightarrow CH\rightarrow_{3}COONa + H_{2}O$
$\Delta H = -55. 3\, kJ \, mol^{-1}$ .
The enthalpy of ionization of $CH_{3}COOH$ as calculated by the student is $kJ \, mol^{-1}$ .
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The correct order of energy of absorption for the following metal complexes is
$A : [Ni (en)_{3}]^{2+}, B : [Ni (NH_{3})_{6}]^{2+}, C : [Ni (H_{2}O)_{6}]^{2+}$
a.
$C < B < A$
b.
$B < C < A$
c.
$C < A < B$
d.
$A < C < B$
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The spin-only magnetic moment value of $M^{3+}$ ion (in gaseous state) from the pairs
$Cr^{3+} / Cr^{2+}, Mn^{3+} / Mn^{2}, Fe^{3+} / Fe^{2+}$ and $Co^{3+} / Co^{2+}$ that has negative standard electrode potential,
is_____ $B. M.$
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$Ka_{1}, Ka_{2}$ and $Ka_{3}$ are the respective ionization constants for the following reactions $(a), (b)$ and $(c)$ .
(a) $H_{2}C_{2}O_{4} \rightleftharpoons H^{+} + HC_{2}O^{-}_{4}$
(b) $HC_{2}O^{-}_{4} \rightleftharpoons H^{+}+ HC_{2}O^{2-}_{4}$
(c) $H_{2}C_{2}O_{4} \rightleftharpoons 2H^{+} + C_{2}O^{2-}_{4}$
The relationship between $K_{a_{1}}, \,K_{a_{2}}$ and $K_{a_{3}}$ is given as
a.
$K_{a3} = K_{a1}+ K_{a2}$
b.
$K_{a3} = \frac{K_{a1}}{K_{a2}}$
c.
$K_{a3} = K_{a1}-K_{a2}$
d.
$K_{a3} = K_{a1}\times K_{a2}$
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Match List I with List II
List-I List-II
A $XeO_{3}$ I $sp^{3} \,d$ ; linear
B $XeF_{2}$ II $sp^{3}$ ; pyramidal
C $XeOF_{4}$ III $sp^{3} d^{3}$ ; distorted octahedral
D $XeF_{6}$ IV $sp^{3} d^{2}$ ; square pyramidal
Choose the correct answer from the options given below
a.
$A -II, B -IV, C -III, D -I$
b.
$A -IV, B -II, C -III, D -I$
c.
$A -II, B -I, C -IV, D -III$
d.
$A -IV, B -II, C -I, D -III$
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The separation of two coloured substances was done by paper chromatography. The distances travelled by
solvent front, substance $A$ and substance $B$ from the base line are $3. 25\, cm. 2. 08\, cm$ and $1. 05\, cm$ .
respectively. The ratio of $R_{f}$ values of $A$ to $B$ is (Answer the nearest integer)
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A sample of $4. 5 mg$ of an unknown monohydric alcohol, $R -OH$ was added to methylmagnesium iodide. A
gas is evolved and is collected and its volume measured to be $3. 1\, mL$ . The molecular weight of the unknown
alcohol is $g/ mol$ .
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A sealed flask with a capacity of $2 dm^{3}$ contains $11\,g$ of propane gas. The flask is so weak that it will burst if
the pressure becomes $2 MPa$ . The minimum temperature at which the flask will burst is $^{\circ }C$ . [Nearest integer]
(Given: $R = 8. 3\,J\,K^{-1}\, mol^{-1}$ . Atomic masses of $C$ and $H$ are $12u$ and $1u$ respectively.) (Assume that
propane behaves as an ideal gas.)
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$---CH_{3}-CH_{2}-CN^{CH_{3}MgBr}\rightarrow \rightarrow A^{H_{3}O}\rightarrow \rightarrow^{+} B^{Zn-Hg} C$ . The correct structure of $C$ is
$Ether HC\vec{l}$
d.
$CH_{3}-CH_{2}-CH = CH_{2}$
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Match List-I with List-II
List-I List-II
A Nylon $6, 6$ I Buckets
Low density Non-stick
B II
polythene utensils
High density Bristles of
C III
polythene brushes
D Teflon IV Toys
Choose the correct answer from the options given below
a.
$A -III, B -I, C -IV, D -II$
b.
$A -III, B -IV, C -I, D -II$
c.
$A -II, B -I, C -IV, D -III$
d.
$A -II, B -IV, C -I, D -III$
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Given below are two statements.
Statement I : Pig iron is obtained by heating cast iron with scrap iron.
Statement II : Pig iron has a relatively lower carbon content than that of cast iron.
In the light of the above statements, choose the correct answer from the options given below.
a.
Both Statement I and Statement II are correct.
b.
Both Statement I and Statement II are not correct.
c.
Statement I is correct but Statement II is not
correct
d.
Statement I is not correct but Statement II is
correct.
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Two solutions $A$ and $B$ are prepared by dissolving $1\,g$ of non-volatile solutes $X$ and $Y$ . respectively in $1\, kg$ of
water. The ratio of depression in freezing points for $A$ and $B$ is found to be $1 : 4$ . The ratio of molar masses of
$X$ and $Y$ is
a.
$1 : 4$
b.
$1 : 0. 25$
c.
$1 : 0. 20$
d.
$1 : 5$
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For micelle formation, which of the following statements are correct?
(A) Micelle formation is an exothermic process.
(B) Micelle formation is an endothermic process.
(C) The entropy change is positive.
(D) The entropy change is negative.
a.
$A\,&\,D$ only
b.
$A\,&\,C$ only
c.
$B\,&\,C$ only
d.
$B\,&\,D$ only
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For the decomposition of azomethane. $CH_{3}\,N_{2}CH_{3}(g) \rightarrow CH\rightarrow_{3}CH_{3}(g) + N_{2}$ a first order reaction, the
variation in partial pressure with time at $600\,K$ is given as
The half life of the reaction is____ $\times 10^{-5}\,s$
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The molar conductivity of a conductivity cell filled with $10$ moles of $20\, mL \,\, NaCl$ solution is $\Lambda _{m1}$ and that
of $20$ moles another identical cell heaving $80\, mL \, NaCl$ solution is $\Lambda _{m2}$ , The conductivities exhibited by these
two cells are same.
The relationship between $\Lambda _{m2}$ and $\Lambda _{m1}$ is
a.
$\Lambda _{m2} = 2\Lambda _{m1}$
b.
$\Lambda _{m2} = \Lambda _{m1}/2$
c.
$\Lambda _{m2} = \Lambda _{m1}$
d.
$\Lambda _{m2} = 4\Lambda _{m1}$
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$56. 0\,L$ of nitrogen gas is mixed with excess of hydrogen gas and it is found that $20\,L$ of ammonia gas is
produced, The volume of unused nitrogen gas is found to be_____ $L$ .
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Match List I with List II.
List-I List-II
A Sulphate I Pesticide
B Fluoride II Bending of bones
C Nicotine III Laxative effect
D Sodium arsinite IV Herbicide
Choose the correct answer from the options given below
a.
$\,A -II, B -III, C -IV, D -I$
b.
$A -III, B -II, C -I, D -IV$
c.
$A -IV, B -III, C -II, D -I$
d.
$A -III, B -II, C -IV, D -I$
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Let a smooth curve $y=f(x)$ be such that the slope of the tangent at any point $(x,y)$ on it is directly
proportional to $( \frac{-y}{x})$ . If the curve passes through the points $(1, 2)$ and $(8, 1)$ , then $y(\frac{1}{8})$ is equal to
a.
$2 log_{e}2$
b.
$4$
c.
$1$
d.
$4 log_{e}2$
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Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx} = \frac{4y^{3}+2yx^{2}}{3xy^{2}+x^{3}} ,y(1) = 1$ . If for some
$n\in N,y(2) \in [n-1,n)$ , then $n$ is equal to _______.
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The number of real values of $\lambda$ , such that the system of linear equations
$2x-3y+ 5z= 9$
$x+ 3y- z= -18$
$3x- y+(\lambda ^{2} -|\lambda |)z= 16$ has no solutions, is
a.
$0$
b.
$1$
c.
$2$
d.
$4$
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Let $A= {1, 2, 3, 4, 5, 6, 7}$ . Define $B=$ { $T ⊆ A$ : either $1 ∉ T$ or $2 \in T$ } and $C =$ { $T ⊆ A:T$ the sum of all
the elements of $T$ is a prime number.} Then the number of elements in the set $B\cup C$ is _______.
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Let the area enclosed by the $x$ -axis, and the tangent and normal drawn to the curve
$4x^{3} -3xy^{2} + 6x^{2} -5xy-8y^{2} + 9x+ 14 = 0$ at the point $(-2, 3)$ be $A$ . Then $8A$ is equal to _______.
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$||$
Let $f(x)$ be a quadratic polynomial with leading coefficient $1$ such that $f(0) =p,p\neq 0$ , and $f(1) = \frac{1}{3}$ . If the
equations $f(x) = 0$ and $fofofof(x) = 0$ have a common real root, then $f(-3)$ is equal to ______.
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If the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ meets the line $\frac{x}{7} + \frac{y}{2\sqrt{6}} = 1$ on the $x$ -axis and the line $\frac{x}{7} - \frac{y}{2\sqrt{6}} = 1$ on the $y$ -axis,
then the eccentricity of the ellipse is
a.
$\frac{5}{7}$
b.
$\frac{2\sqrt{6}}{7}$
c.
$\frac{3}{7}$
d.
$\frac{2\sqrt{5}}{7}$
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Let $\vec{a}= ˆi-ˆj+ 2ˆk$ and let $\vec{b}$ be a vector such that $\vec{a}\times \vec{b}= 2ˆi- ˆk$ and $\vec{a}\cdot \vec{b}= 3$ . Then the projection of $\vec{b}$ on the
vector $\vec{a}- \vec{b}$ is:
a.
$\frac{2}{\sqrt{21}}$
b.
$2\sqrt{\frac{3}{7}}$
c.
$\frac{2}{3}\sqrt{\frac{7}{3}}$
d.
$\frac{2}{3}$
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The sum of the maximum and minimum values of the function $f(x) = |5x-7| +[x^{2} + 2x]$ in the interval
$[\frac{5}{4} , 2]$ , where $[t]$ is the greatest integer $\leq t$ , is ______.
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Let $[t]$ denote the greatest integer less than or equal to $t$ . Then the value of the integral
$\int _{-3}^{101}([sin(\pi x)] +e^{[cos(2\pi x)]})dx$ is equal to
a.
$\frac{52(1-e)}{e}$
b.
$\frac{52}{e}$
c.
$\frac{52(2+e)}{e}$
d.
$\frac{104}{e}$
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Let the point $P(\alpha ,\beta )$ be at a unit distance from each of the two lines $L_{1} : 3x-4y+ 12 = 0$ , and
$L_{2} : 8x+ 6y+ 11 = 0$ . If $P$ lies below $L_{1}$ and above $L_{2}$ , then $100(\alpha +\beta )$ is equal to
a.
$-14$
b.
$42$
c.
$-22$
d.
$14$
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Let $f$ be a twice differentiable function on $R$ . If $f'(0) = 4$ and $f(x) +\int _{0}^{x}(x- t)f'(t)dt$
$=(e^{2x} +e^{-2x})cos 2x+ \frac{2}{a}x$ , then $(2a+ 1)^{5}a^{2}$ is equal to _______.
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Let $a_{n} =\int _{-1}^{n} (1 + \frac{x}{2} + \frac{x^{2}}{3} + … + \frac{x^{n}^{-1}}{n})dx$ for every $n\in N$ . Then the sum of all the elements of the set
${n\in N :a_{n} \in (2, 30)}$ is _________.
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The tangents at the points $A(1, 3)$ and $B(1, -1)$ on the parabola $y^{2} -2x-2y= 1$ meet at the point $P$ . Then
the area (in $unit^{2}$ ) of the triangle $PAB$ is:
a.
$4$
b.
$6$
c.
$7$
d.
$8$
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Consider the following statements:
$P :$ Ramu is intelligent.
$Q:$ Ramu is rich.
$R:$ Ramu is not honest.
The negation of the statement "Ramu is intelligent and honest if and only if Ramu is not rich" can be expressed
as:
A plane $E$ is perpendicular to the two planes $2x-2y+z= 0$ and $x- y+ 2z= 4$ , and passes through the
point $P(1, -1, 1)$ . If the distance of the plane $E$ from the point $Q(a,a, 2)$ is $3\sqrt{2}$ , then $(PQ)^{2}$ is equal to
a.
$9$
b.
$12$
c.
$21$
d.
$33$
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Let the foci of the ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{7} = 1$ and the hyperbola $\frac{x^{2}}{144} - \frac{y^{2}}{\alpha} = \frac{1}{25}$ coincide. Then the length of the
latus rectum of the hyperbola is:
a.
$\frac{32}{9}$
b.
$\frac{18}{5}$
c.
$\frac{27}{4}$
d.
$\frac{27}{10}$
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