In the experiment to determine the galvanometer resistance by half-deflection method, the plot of $1/\theta$ vs the
resistance $(R)$ of the resistance box is shown in the figure. The figure of merit of the galvanometer is _____
$\times 10^{-1}\,A/$ division. [The source has emf 2V]
✓ Accepted Answer:5
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Q2nat
The density and breaking stress of a wire are $6 \times 10^{4}\,kg/m^{3}$ and $1.2 \times 10^{8}\,N/m^{2}$ respectively. The wire is
suspended from a rigid support on a planet where acceleration due to gravity is $\frac{1}{3}^{rd\,}$ of the value on the surface
of earth. The maximum length of the wire with breaking is _____ m (take, $g = 10\,m/s^{2}$ ).
✓ Accepted Answer:600
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Q3mcq
In the given figure $R_{1} = 10\Omega , R_{2} = 8\Omega , R_{3} = 4\Omega$ and $R_{4} = 8\Omega$ . Battery is ideal with emf $12\,V$ . Equivalent
resistant of the circuit and current supplied by battery are respectively :
a.
$10.5\Omega$ and $1.14\,A$
b.
$12\Omega$ and $1\,A$
Correct Answer
c.
$10.5\Omega$ and $1\,A$
d.
$12\Omega$ and $11.4\,A$
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Q4mcq
Following gates section is connected in a complete suitable circuit.
$\,For which of the following combination, bulb will glow (ON) :\,$
a.
$A = 0, \,B = 0, C = 0, D = 1$
b.
$A = 0, \,B = 1, C = 1, D = 1$
c.
$A = 1, \,B = 0, C = 0, D = 0$
Correct Answer
d.
$A = 1, \,B = 1, C = 1, D = 0$
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Q5mcq
Two conducting circular loops A and B are placed in the same plane with their centers coinciding as shown in
figure. The mutual inductance between them is :
a.
$\frac{\mu _{0}\pi b^{2}}{2a}$
b.
$\frac{\mu _{o}}{2\pi} \cdot \frac{b^{2}}{a}$
c.
$\frac{\mu _{0}}{2\pi} \cdot \frac{a^{2}}{b}$
d.
$\frac{\mu _{0}\pi a^{2}}{2b}$
Correct Answer
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Q6mcq
The angle between vector $Q$ and the resultant of $(2Q+ 2P)$ and $(2Q-2P)$ is :
Three blocks $M_{1},M_{2},M_{3}$ having masses $4\,kg, 6\,kg$ and $10\,kg$ respectively are hanging from a smooth pully
using rope 1,2 and 3 as shown in figure. The tension in the rope $1,T_{1}$ when they are moving upward with
acceleration of $2\,ms^{-2}$ is _____ $N ($ if $g = 10\,m/s^{2}$ ).
✓ Accepted Answer:240
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Q8nat
The electric field between the two parallel plates of a capacitor of $1.5\mu F$ capacitance drops to one third of its
initial value in $6.6\mu s$ when the plates are connected by a thin wire. The resistance of this wire is _____ $\Omega$ .
(Given, $log 3 = 1.1$ )
✓ Accepted Answer:4
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Q9mcq
A simple pendulum doing small oscillations at a place $R$ height above earth surface has time period of $T_{1} = 4\,s$ .
$T_{2}$ would be it's time period if it is brought to a point which is at a height $2R$ from earth surface. Choose the
correct relation $[R=$ radius of earth $]$ :
a.
$2\,T_{1} = T_{2}$
b.
$2\,T_{1} = 3\,T_{2}$
c.
$T_{1} = T_{2}$
d.
$3\,T_{1} = 2\,T_{2}$
Correct Answer
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Q10mcq
Given below are two statements : Statement I : When a capillary tube is dipped into a liquid, the liquid neither
rises nor falls in the capillary. The contact angle may be $0^{\circ }$ . Statement II : The contact angle between a solid
and a liquid is a property of the material of the solid and liquid as well. In the light of the above statement,
choose the correct answer from the options given below.
a.
Both Statement I and Statement II are false
b.
Both Statement I and Statement II are true
c.
Statement I is false but Statement II is true
Correct Answer
d.
Statement I is true and Statement II is false
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Given below are two statements : Statement I : Figure shows the variation of
stopping potential with frequency $(v)$ for the two photosensitive materials $M_{1}$ and $M_{2}$ . The slope gives value
of $\frac{h}{e}$ , where $h$ is Planck's constant, $e$ is the charge of electron. Statement II : $M_{2}$ will emit photoelectrons of
greater kinetic energy for the incident radiation having same frequency. In the light of the above statements,
choose the most appropriate answer from the options given below.
a.
Both Statement I and Statement II are correct
b.
Statement I is incorrect but Statement II is correct
c.
Both Statement I and Statement II are incorrect
d.
Statement I is correct and Statement II is
incorrect
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A body moves on a frictionless plane starting from rest. If $S_{n}$ is distance moved between $t=n-1$ and $t = n$
and $S_{n-1}$ is distance moved between $t = n -2$ and $t = n -1$ , then the ratio $\frac{S_{n-1}}{\,S_{n}}$ is $(1 - \frac{2}{x})$ for $n = 10$ . The
value of $x$ is ______.
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A wooden block of mass $5\,kg$ rests on a soft horizontal floor. When an iron cylinder of mass $25\,kg$ is placed on
the top of the block, the floor yields and the block and the cylinder together go down with an acceleration of
$0.1\,ms^{-2}$ . The action force of the system on the floor is equal to:
a.
$196\,N$
b.
$291\,N$
c.
$294\,N$
d.
$297\,N$
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Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia
about their diameter axis $AB$ as shown in figure is $\sqrt{8/x}$ . The value of $x$ is :
a.
$51$
b.
$34$
c.
$17$
d.
$67$
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Three capacitors of capacitances $25\mu F, 30\mu F$ and $45\mu F$ are connected in parallel to a supply of $100\,V$ . Energy
stored in the above combination is E. When these capacitors are connected in series to the same supply, the
stored energy is $\frac{9}{x}E$ . The value of $x$ is _____.
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If $G$ be the gravitational constant and $u$ be the energy density then which of the following quantity have the
dimensions as that of the $\sqrt{uG}$ :
a.
pressure gradient per unit mass
b.
Gravitational potential
c.
Energy per unit mass
d.
Force per unit mass
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A 2 A current carrying straight metal wire of resistance $1\Omega$ , resistivity $2 \times 10^{-6}\Omega m$ , area of cross-section
$10\,mm^{2}$ and mass $500\,g$ is suspended horizontally in mid air by applying a uniform magnetic field $\vec{B}$ . The
magnitude of $B$ is _____ $\times 10^{-1}\,T$ (given, $g = 10\,m/s^{2}$ ).
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A body of mass $50\,kg$ is lifted to a height of $20\,m$ from the ground in the two different ways as shown in the
figures. The ratio of work done against the gravity in both the respective cases, will be :
a.
$1 : 2$
b.
$\sqrt{3}: 2$
c.
$2 : 1$
d.
$1 : 1$
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If the collision frequency of hydrogen molecules in a closed chamber at $27^{\circ }C$ is $Z$ , then the collision frequency
of the same system at $127^{\circ }C$ is :
a.
$\frac{\sqrt{3}}{2}z$
b.
$\frac{2}{\sqrt{3}} Z$
c.
$\frac{3}{4}Z$
d.
$\frac{4}{3} Z$
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An alternating voltage of amplitude $40\,V$ and frequency $4kHz$ is applied directly across the capacitor of $12\mu F$ .
The maximum displacement current between the plates of the capacitor is nearly :
a.
$10\,A$
b.
$12\,A$
c.
$8\,A$
d.
$13\,A$
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In Young's double slit experiment, carried out with light of wavelength $5000\AA$ , the distance between the
slits is $0.3\,mm$ and the screen is at $200\,cm$ from the slits. The central maximum is at $x= 0\,cm$ . The value of $x$
for third maxima is _____ $mm$ .
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An electron rotates in a circle around a nucleus having positive charge Ze. Correct relation between total
energy (E) of electron to its potential energy (U) is :
a.
$E = U$
b.
$2E = U$
c.
$2E = 3U$
d.
$E = 2U$
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If three helium nuclei combine to form a carbon nucleus then the energy released in this reaction is _____
$\times 10^{-2}MeV$ . (Given $1u = 931MeV/c^{2}$ , atomic mass of helium $= 4.002603u$ )
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Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were
recorded as $4.62\,s, 4.632\,s, 4.6\,s$ and $4.64\,s$ . The arithmetic mean of these readings in correct significant figure
is :
a.
$5\,s$
b.
$4.623\,s$
c.
$4.6\,s$
d.
$4.62\,s$
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Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Cis form of alkene is found to be more polar than the trans form. Reason (R): Dipole moment
of trans isomer of 2-butene is zero. In the light of the above statements, choose the correct answer from the
options given below :
a.
(A) is false but (R) is true
b.
Both (A) and (R) are true and (R) is the correct
explanation of (A)
c.
(A) is true but (R) is false
d.
Both (A) and (R) are true but (R) is NOT the
correct explanation of (A)
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The heat of combustion of solid benzoic acid at constant volume is $-321.30\,kJ$ at $27^{\circ }C$ . The heat of
combustion at constant pressure is $(-321.30 - xR)kJ$ , the value of $x$ is _______.
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The number of neutrons present in the more abundant isotope of boron is ' $x$ '. Amorphous boron upon heating
with air forms a product, in which the oxidation state of boron is ' $y$ '. The value of $x+y$ is _______
a.
3
b.
9
c.
4
d.
6
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The statement(s) that are correct about the species $O^{2-}, F^{-}, Na^{+}$ and $Mg^{2+}$ . (A) All are isoelectronic (B) All
have the same nuclear charge (C) $O^{2-}$ has the largest ionic radii (D) $Mg^{2+}$ has the smallest ionic radii Choose
the most appropriate answer from the options given below :
a.
(B), (C) and (D) only
b.
(C) and (D) only
c.
(A), (C) and (D) only
d.
(A), (B), (C) and (D)
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The following reaction occurs in the Blast furnance where iron ore is reduced to iron metal
$Fe_{2}O_{3(\,s)}+ 3CO_{(g)} \rightleftharpoons Fe_{(l)}+ 3CO_{2(\,g)}$ Using the Le-chatelier's principle, predict which one of the following
will not disturb the equilibrium.
a.
Addition of $CO_{2}$
b.
Removal of $CO_{2}$
c.
Addition of $Fe_{2}O_{3}$
d.
Removal of CO
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During Kinetic study of reaction $2A+B C+D$ , the following results were obtained :
$\,A [M]\, \,B [M]\, \,initial rate of f\vec{o}rmation of D\,$
$\,I\, 0.1 0.1 6.0 \times 10^{-3}$
$\,II\, 0.3 0.2 7.20 \times 10^{-2}$ Based on above data, overall order of the reaction is
$\,III\, 0.3 0.4 2.88 \times 10^{-1}$
$\,IV\, 0.4 0.1 2.40 \times 10^{-2}$
______
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$9.3\,g$ of pure aniline is treated with bromine water at room temperature to give a white precipitate of the
product ' $P$ '. The mass of product ' $P$ ' obtaind is $26.4\,g$ . The percentage yield is _______ $%$ .
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For the Compounds : (A) $H_{3}C -CH_{2}-O -CH_{2}-CH_{2}-CH_{3}$ (B) $H_{3}C -CH^{2}_{2} -CH_{2}-CH_{2}-CH_{3}$ (C)
(D)
The increasing order of boiling point is : Choose the correct answer from the options given below :
a.
$\,(D)\, < (\,C\,) < (\,A\,) < (\,B\,)$
b.
$\,(B)\, < \,(A)\, < \,(C)\, < \,(D)\,$
c.
$\,(A)\, < \,(B)\, < \,(C)\, < \,(D)\,$
d.
$\,(B)\, < \,(A)\, < \,(D)\, < \,(C)\,$
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Given below are two statements: Statement I : Nitration of benzene involves the following step -
Statement II : Use of Lewis base promotes the electrophilic substitution of benzene. In the light of the above
statements, choose the most appropriate answer from the options given below :
(1) Statement I is correct but Statement II is incorrect(2) Statement I is incorrect but Statement II is correct
(3) Both Statement I and Statement II are correct (4) Both Statement I and Statement II are incorrect
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The spin-only magnetic moment value of the ion among $Ti^{2+}, V^{2+}, Co^{3+}$ and $Cr^{2+}$ , that acts as strong
oxidising agent in aqueous solution is _______ BM (Near integer). (Given atomic numbers :
$Ti : 22, \,V : 23, Cr : 24, Co : 27$ )
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The value of Rydberg constant $(R_{H})$ is $2.18 \times 10^{-18}\,J$ . The velocity of electron having mass $9.1 \times 10^{-31}\,kg$ in
Bohr's first orbit of hydrogen atom $=$ _______ $\times 10^{5}\,ms^{-1}$ (nearest integer).
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Given below are two statements : Statement I : In group 13, the stability of +1 oxidation state increases down
the group. Statement II : The atomic size of gallium is greater than that of aluminium. In the light of the above
statements, choose the most appropriate answer from the options given below :
a.
Both Statement I and Statement II are correct
b.
Statement I is incorrect but Statement II is correct
c.
Both Statement I and Statement II are incorrect
d.
Statement I is correct but Statement II is incorrect
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Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R)
Assertion (A) : Enthalpy of neutralisation of strong monobasic acid with strong monoacidic base is always
$-57\,kJ\,mol^{-1}$ . Reason (R) : Enthalpy of neutralisation is the amount of heat liberated when one mole of $H^{+}$
ions furnished by acid combine with one mole of $OH^{-}$ ions furnished by base to form one mole of water. In
the light of the above statements, choose the correct answer from the options given below.
a.
(A) is true but (R) is false
b.
Both (A) and (R) are true but (R) is not the
correct explanation of (A)
c.
Both (A) and (R) are true and (R) is the correct
explanation of (A)
d.
(A) is false but (R) is true
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Given below are two statement: Statements I : Bromination of phenol in solvent with low polarity such as
$CHCl_{3}$ or $CS_{2}$ requires Lewis acid catalyst. Statements II : The Lewis acid catalyst polarises the bromine to
generate $Br^{+}$ . 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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Molar ionic conductivities of divalent cation and anion are $57\,S\,cm^{2}\,mol^{-1}$ and $73\,S\,cm^{2}\,mol^{-1}$ respectively.
The molar conductivity of solution of an electrolyte with the above cation and anion will be :
a.
$187\,S\,cm^{2}\,mol^{-1}$
b.
$260\,S\,cm^{2}\,mol^{-1}$
c.
$130\,S\,cm^{2}\,mol^{-1}$
d.
$65\,S\,cm^{2}\,mol^{-1}$
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An artificial cell is made by encapsulating $0.2M$ glucose solution within a semipermeable membrane. The
osmotic pressure developed when the artificial cell is placed within a $0.05M$ solution of $NaCl$ at $300\,K$ is
_______ $\times 10^{-1}$ bar. (nearest integer). [Given : $R = 0.083\,Lbarmol^{-1}\,K^{-1}$ ] Assume complete dissociation of
$NaCl$
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In a borax bead test under hot condition, a metal salt (one from the given) is heated at point B of the flame,
resulted in green colour salt bead. The spin-only magnetic moment value of the salt is _______ BM (Nearest
integer) [Given atomic number of $Cu = 29, Ni = 28, Mn = 25, Fe = 26$ ]
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The incorrect postulates of the Dalton's atomic theory are : (A) Atoms of different elements differ in mass. (B)
Matter consists of divisible atoms. (C) Compounds are formed when atoms of different element combine in a
fixed ratio. (D) All the atoms of given element have different properties including mass. (E) Chemical reactions
involve reorganisation of atoms. Choose the correct answer from the options given below :
a.
(C), (D), (E) only
b.
(B), (D) only
c.
(A), (B), (D) only
d.
(B), (D), (E) only
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Let $f$ be a differentiable function in the interval $(0, \infty )$ such that $f(1) = 1$ and $lim_{t\rightarrow \rightarrow x} \frac{t^{2}f(x)-x^{2}f(t)}{t-x} = 1$ for
each $x> 0$ . Then $2f(2) + 3f(3)$ is equal to _______
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$||$
Let the line $2x+ 3y-k = 0, k > 0$ , intersect the $x$ -axis and $y$ -axis at the points $A$ and $B$ , respectively. If the
equation of the circle having the line segment $AB$ as a diameter is $x^{2} +y^{2} -3x-2y= 0$ and the length of the
latus rectum of the ellipse $x^{2} + 9y^{2} =k^{2}$ is $\frac{m}{n}$ , where $m$ and $n$ are coprime, then $2\,m + n$ is equal to
a.
11
b.
10
c.
12
d.
13
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Let a circle $C$ of radius 1 and closer to the origin be such that the lines passing through the point $(3, 2)$ and
parallel to the coordinate axes touch it. Then the shortest distance of the circle $C$ from the point $(5, 5)$ is :
a.
$2\sqrt{2}$
b.
$4\sqrt{2}$
c.
4
d.
5
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$| |$
If $y=y(x)$ is the solution of the differential equation $\frac{dy}{\,dx} + 2y= sin(2x),y(0) = \frac{3}{4}$ , then $y( \frac{\pi}{8})$ is equal to:
a.
$e^{\pi /8}$
b.
$e^{\pi /4}$
c.
$e^{-\pi /4}$
d.
$e^{-\pi /8}$
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For the function $f(x) = sinx+ 3x- \frac{2}{\pi} (x^{2}+x), \,where\,x\in [0, \frac{\pi}{2}],$ consider the following two statements :
(I) $f$ is increasing in $(0, \frac{\pi}{2})$ . (II) $f'$ is decreasing in $(0, \frac{\pi}{2})$ .
Between the above two statements,
a.
only (II) is true.
b.
only (I) is true.
c.
neither (I) nor (II) is true.
d.
both (I) and (II) are true
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Let $A= {1, 3, 7, 9, 11}$ and $B= {2, 4, 5, 7, 8, 10, 12}$ . Then the total number of one-one maps $f : A \rightarrow B\rightarrow$ ,
such that $f(1) +f(3) = 14$ , is :
a.
480
b.
240
c.
120
d.
180
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Let $a_{1},a_{2},a_{3}, …$ be in an arithmetic progression of positive terms. Let
$A_{k} = a^{2}_{1} -a^{2}_{2} + a^{2}_{3} -a^{2}_{4} + … + a^{2}_{2k-1} -a^{2}_{2k}$ . If $A_{3} = -153, \,A_{5} = -435$ and $a^{2}_{1} + a^{2}_{2} + a^{2}_{3} = 66$ , then
$a_{17}-A_{7}$ is equal to______
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Suppose $AB$ is a focal chord of the parabola $y^{2} = 12x$ of length $l$ and slope $m < \sqrt{3}$ . If the distance of the
chord $AB$ from the origin is $d$ , then $l\,d^{2}$ is equal to _______
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Let a rectangle $ABCD$ of sides 2 and 4 be inscribed in another rectangle $PQRS$ such that the vertices of the
rectangle $ABCD$ lie on the sides of the rectangle $PQRS$ . Let $a$ and $b$ be the sides of the rectangle $PQRS$
when its area is maximum. Then $(a+b)^{2}$ is equal to :
a.
72
b.
60
c.
64
d.
80
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The coefficients $a,b,c$ in the quadratic equation $ax^{2} +bx+c= 0$ are chosen from the set ${1, 2, 3, 4, 5, 6, 7, 8}$
. The probability of this equation having repeated roots is :
a.
$\frac{1}{128}$
b.
$\frac{1}{64}$
c.
$\frac{3}{256}$
d.
$\frac{3}{128}$
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Let $\vec{a}= \hat{i}-3\hat{j}+ 7\hat{k}, \vec{b}= 2\hat{i}- \hat{j}+ \hat{k}$ and $\vec{c}$ be a vector such that $(\vec{a}+ 2\vec{b}) \times \vec{c}= 3(\vec{c}\times \vec{a})$ . If $\vec{a}\cdot \vec{c}= 130$ , then
$\vec{b}\cdot \vec{c}$ is equal to _______
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$11x+y+\lambda z= -5$
If the system of equations $2x+ 3y+ 5z= 3$ has infinitely many solutions, then $\lambda ^{4} - \mu$ is equal to :
$8x-19y-39z=\mu$
a.
51
b.
45
c.
47
d.
49
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If $\frac{1}{\sqrt{1}+\sqrt{2}} + \frac{1}{\sqrt{2}+\sqrt{3}} + … + \frac{1}{\sqrt{99}+\sqrt{100}} =m$ and $\frac{1}{1\cdot 2} + \frac{1}{2\cdot 3} + … + \frac{1}{99\cdot 100} =n$ , then the point $(m, n)$ lies on the
line
a.
$11(x-1) -100(y-2) = 0$
b.
$11x-100y= 0$
c.
$11(x-2) -100(y-1) = 0$
d.
$11(x-1) -100y= 0$
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Let $f(x) =x^{5} + 2x^{3} + 3x+ 1,x\in R$ , and $g(x)$ be a function such that $g(f(x)) =x$ for all $x\in R$ . Then $\frac{g(7)}{g^{'}(7)}$
is equal to :
a.
14
b.
42
c.
7
d.
1
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If $S = {a\in R: |2a-1| = 3[a] + 2{a}}$ , where $[t]$ denotes the greatest integer less than or equal to $t$ and ${t}$
represents the fractional part of $t$ , then $72\sum _{a\in S}a$ is equal to ______
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If the line $\frac{2-x}{3} = \frac{3y-2}{4\lambda +1} = 4 - z$ makes a right angle with the line $\frac{x+3}{3\mu} = \frac{1-2y}{6} = \frac{5-z}{7}$ , then $4\lambda + 9\mu$ is equal
to :
a.
4
b.
13
c.
5
d.
6
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Consider the following two statements : Statement I : For any two non-zero complex numbers $z_{1},z_{2}$ ,
$(|z_{1}| + |z_{2}|) \frac{z_{1}}{|z_{1}|} + \frac{z_{2}}{|z_{2}|} \leq 2 (|z_{1}| + |z_{2}|), and\,$
Statement II : If $x,y,z$ are three distinct complex numbers and $a, b, c$ are three positive real numbers such that
$\frac{a}{|y-z|} = \frac{b}{|z-x|} = \frac{c}{|x-y|}$ , then $\frac{a^{2}}{y-z} + \frac{b^{2}}{z-x} + \frac{c^{2}}{x-y} = 1.$
Between the above two statements,
a.
Statement I is correct but Statement II is
incorrect.
b.
both Statement I and Statement II are correct.
c.
both Statement I and Statement II are incorrect.
d.
Statement I is incorrect but Statement II is
correct.
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Let two straight lines drawn from the origin $O$ intersect the line $3x+ 4y= 12$ at the points $P$ and $Q$ such that
$\triangle OPQ$ is an isosceles triangle and $\angle POQ = 90^{\circ }$ . If $l= OP^{2} + PQ^{2} + QO^{2}$ , then the greatest integer less
than or equal to $l$ is :
a.
42
b.
46
c.
44
d.
48
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Let $A$ and $B$ be two square matrices of order 3 such that $|A| = 3$ and $|B| = 2$ . Then
$A^{T}A(adj(2\,A))^{-1}(adj(4\,B))(adj(AB))^{-1}AA^{T}$ is equal to :
a.
108
b.
32
c.
81
d.
64
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Let $d$ be the distance of the point of intersection of the lines $\frac{x+6}{3} = \frac{y}{2} = \frac{z+1}{1}$ and $\frac{x-7}{4} = \frac{y-9}{3} = \frac{z-4}{2}$ from the
point $(7, 8, 9)$ . Then $d^{2} + 6$ is equal to :
a.
69
b.
78
c.
72
d.
75
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From a lot of 10 items, which include 3 defective items, a sample of 5 items is drawn at random. Let the
random variable $X$ denote the number of defective items in the sample. If the variance of $X$ is $\sigma ^{2}$ , then $96\sigma ^{2}$ is
equal to ______
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