Consider two uniform discs of the same thickness and different radii $R_{1} =R$ and $R_{2} =\alpha R$ made of the same
material. If the ratio of their moments of inertia $I_{1}$ and $I_{2}$ , respectively, about their axes is $I_{1} :I_{2} = 1 : 16$ then
the value of $\alpha$ is :
a.
$2\sqrt{2}$
b.
$\sqrt{2}$
c.
$2$
Correct Answer
d.
$4$
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Q2mcq
Match the thermodynamics processes taking place in a system with the correct conditions. In the table : $\Delta Q$ is
the heat supplied, $\Delta W$ is the work done and $\Delta U$ is change in internal energy of the system.
Process Condition
(I) Adiabatic (A) $\Delta W = 0$
(II) Isothermal (B) $\Delta Q= 0$
(III) Isochoric (C) $\Delta U \neq 0, \Delta W \neq 0, \Delta Q\neq 0$
(IV) Isobaric (D) $\Delta U = 0$
The value of current $i_{1}$ flowing from $A$ to $C$ in the circuit diagram is :
a.
$5\,A$
b.
$2. 25\,A$
c.
$0. 75\,A$
d.
$1\,A$
Correct Answer
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Q4mcq
A small ball of mass $m$ is thrown upward with velocity $u$ from the ground. The ball experiences a resistive
force $mkv^{2}$ where $v$ is it speed. The maximum height attained by the ball is :
In a photoelectric effect experiment, the graph of stopping potential $V$ versus reciprocal of wavelength
obtained is shown in the figure. As the intensity of incident radiation is increased :
a.
Straight line shifts to right
b.
Slope of the straight line get more steep
c.
Straight line shifts to left
d.
Graph does not change
Correct Answer
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Q6nat
The speed verses time graph for a particle is shown in the figure. The distance travelled (in $m$ ) by the particle
during the time interval $t = 0$ to $t = 5s$ will be __________
✓ Accepted Answer:20
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Q7mcq
For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes
perpendicular to the sheet and passing through $O$ (the centre of mass) and $O$ ' (corner point) is:
a.
$2/3$
b.
$1/4$
Correct Answer
c.
$1/8$
d.
$1/2$
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Q8mcq
A paramagnetic sample shows a net magnetisation of $6\,A/m$ when it is placed in an external magnetic field of
$0. 4\,T$ at a temperature of $4\,K$ . When the sample is placed in an external magnetic field of $0. 3\,T$ at a
temperature of $24\,K$ , then the magnetisation will be :
a.
$1\,A/m$
b.
$4\,A/m$
c.
$2. 25\,A/m$
d.
$0. 75\,A/m$
Correct Answer
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Q9nat
The change in the magnitude of the volume of an ideal gas when a small additional pressure $\Delta P$ is applied at a
constant temperature, is the same as the change when the temperature is reduced by a small quantity $\Delta T$ at
constant pressure. The initial temperature and pressure of the gas were $300\,K\,$ and $2\, atm$ respectively. If
$|\Delta T| = C|\Delta P|$ then value of $C$ in $(K/ atm)$ is __________
✓ Accepted Answer:150
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Q10mcq
The driver of bus approaching a big wall notices that the frequency of his bus's horn changes from $420\, Hz$ to
$490\, Hz$ when he hears it after it gets reflected from the wall. Find the speed of the bus if speed of the sound is
$330\, ms^{-1}$ :
a.
$91\, kmh^{-1}$
Correct Answer
b.
$81\, kmh^{-1}$
c.
$61\, kmh^{-1}$
d.
$71\, kmh^{-1}$
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A circular coil has moment of inertia $0. 8\, kg \,m^{2}$ around any diameter and is carrying current to produce a
magnetic moment of $20\, Am^{2}$ . The coil is kept initially in a vertical position and it can rotate freely around a
horizontal diameter. When a uniform magnetic field of $4\,T$ is applied along the vertical, it starts rotating
around its horizontal diameter. The angular speed the coil acquires after rotating by $60^{o}$ will be :
a.
$10\, rad \,s^{-1}$
b.
$10$ $\pi$ $\,rad\,s^{-1}$
c.
$20$ $\pi$ $\,rad\,s^{-1}$
d.
$20\, rad \,s^{-1}$
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Four resistance $40\,\Omega , 60\,\Omega , 90\,\Omega 110\,\Omega$ and make the arms of a quadrilateral $ABCD$ . Across $AC$ is a battery
of emf $40\,V$ and internal resistance negligible. The potential difference across $BD$ in $V$ is __________
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A capacitor $C$ is fully charged with voltage $V_{0}$ . After disconnecting the voltage source, it is connected in
parallel with another uncharged capacitor of capacitance $\frac{C}{2}$ . The energy loss in the process after the charge is
distributed between the two capacitors is :
a.
$\frac{1}{2}CV_{0}^{2}$
b.
$\frac{1}{3}CV_{0}^{2}$
c.
$\frac{1}{4}CV_{0}^{2}$
d.
$\frac{1}{6}CV_{0}^{2}$
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A quantity $x$ is given by $(1Fv /WL )$ in terms of moment of inertia $I$ , force $F$ , velocity $v$ , work $W$ and length
$L$ . The dimensional formula for $x$ is same as that of :
a.
planck's constant
b.
force constant
c.
energy density
d.
coefficient of viscosity
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A body is moving in a low circular orbit about a planet of mass $M$ and radius $R$ . The radius of the orbit can be
taken to be $R$ itself. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is:
a.
$\frac{1}{\sqrt{2}}$
b.
$2$
c.
$1$
d.
$\sqrt{2}$
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Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density $d$ . The area
of the base of both vessels is $S$ but the height of liquid in one vessel is $x_{1}$ and in the other $x_{2}$ . When both
cylinders are connected through a pipe of negligible volume very close to the bottom, the liquid flows from one
vessel to the other until it comes to equilibrium at a new height. The change in energy of the system in the
process is :
a.
$gdS(x^{2}_{2} +x^{2}_{1})$
b.
$gdS(x_{2}+x_{1})^{2}$
c.
$\frac{3}{4}gdS(x_{2}- x_{1})^{2}$
d.
$\frac{1}{4}gdS(x_{2}- x_{1})^{2}$
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A person pushes a box on a rough horizontal plateform surface. He applies a force of $200\,N$ over a distance of
$15\,m$ . Thereafter, he gets progressively tired and his applied force reduces linearly with distance to $100\,N$ . The
total distance through which the box has been moved is $30\,m$ . What is the work done by the person during the
total movement of the box?
a.
$3280\,J$
b.
$2780\,J$
c.
$5690\,J$
d.
$5250\,J$
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A particle of charge $q$ and mass $m$ is subjected to an electric field $E =E_{0}(1-ax^{2})$ in the $x-$ direction, where a
and $E_{0}$ are constants. Initially the particle was at rest at $x= 0$ . Other than the initial position the kinetic energy
of the particle becomes zero when the distance of the particle from the origin is :
a.
$a$
b.
$\sqrt{\frac{2}{a}}$
c.
$\sqrt{\frac{3}{a}}$
d.
$\sqrt{\frac{1}{a}}$
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The distance between an object and a screen is $100\, cm$ . A lens can produce real image of the object on the
screen for two different positions between the screen and the object. The distance between these two positions
is $40\, cm$ . If the power of the lens is close to $( \frac{N}{100} )D$ where $N$ is an integer, the value of $N$ is _________
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Find the Binding energy per nucleon for $^{120}_{50}Sn$ . Mass of proton $m_{p} = 1. 00783\,U$ , mass of neutron
$m_{n} = 1. 00867\,U$ and mass of tin nucleus $m_{sn} = 119. 902199\,U$ . (take $1U\, = \,931\,MeV$ )
a.
$7 .5MeV$
b.
$9. 0MeV$
c.
$\,8.0MeV$
d.
$8 .5MeV$
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A series $L- R$ circuit is connected to a battery of emf $V$ . If the circuit is switched on at $t= 0$ , then the time at
which the energy stored in the inductor reaches $( \frac{1}{n})$ times of its maximum value, is :
a.
$\frac{L}{R}ln( \frac{\sqrt{n}}{\sqrt{n}-1} )$
b.
$\frac{L}{R} ln(\frac{\sqrt{n}+1}{\sqrt{n}-1})$
c.
$\frac{L}{R}ln( \frac{\sqrt{n}}{\sqrt{n}+1} )$
d.
$\frac{L}{R} ln(\frac{\sqrt{n}-1}{\sqrt{n}})$
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Orange light of wavelength $6000 \times 10^{-10} m$ illuminates a single slit of width $0. 6 \times 10^{-4} m$ . The maximum
possible number of diffraction minima produced on both sides of the central maximum is __________
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A cube of metal is subjected to a hydrostatic pressure $4\,GPa$ . The percentage change in the length of the side of
the cube is close to : (Given bulk modulus of metal, $B= 8 \times 10^{10} Pa$ )
a.
$5$
b.
$0. 6$
c.
$20$
d.
$1. 67$
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A $100\, mL$ solution was made by adding $1. 43\,g$ of $Na_{2}CO_{3}. xH_{2}O.$ The normality of the solution is $0. 1\,N$ .
The value of $x$ is _______
(The atomic mass of $Na$ is $23g/ mol$ )
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The incorrect statement(s) among (a) - (c) is (are) :
(a) $W(VI)$ is more stable than $Cr(VI)$ .
(b) in the presence of $HCl$ , permanganate titrations provide satisfactory results.
(c) some lanthanoid oxides can be used as phosphors
a.
(b) and (c) only
b.
(a) and (b) only
c.
(b) only
d.
(a) only
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Consider the following equations :
$2 Fe^{2+} + H_{2}O_{2} \rightarrow xA + yB\rightarrow$
(in basic medium)
$2 MnO^{-}_{4} + 6H^{+}+ 5H_{2}O_{2} \rightarrow x\rightarrow'C + y'D + z'E$
(in acidic medium)
The sum of the stoichiometric coefficients $x, y, x', y'$ and $z'$ for products $A, B, C, D$ and $E$ respectively, is
_______
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The number of molecules with energy greater than the threshold energy for a reaction increases five fold by a
rise of temperature from $27^{o}C$ to $42^{o}C$ . Its energy of activation in $J/ mol$ is _________ (Take
$ln \,5 = 1. 6094; \,R = 8. 314\,J\, mol^{-1}$ )
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A sample of red ink (a colloidal suspension) is prepared by mixing eosine dye, egg white, $HCHO$ and water.
The component which ensures stability of the ink sample is :
a.
Egg white
b.
Water
c.
$HCHO$
d.
Eosin dye
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$250\, mL$ of a waste solution obtained from the workshop of a goldsmith contains $0. 1\,M\, AgNO_{3}$ and
$0. 1M\, AuCl$ . The solution was electrolyzed at $2\,V$ by passing a current of $1\,A$ for $15$ minutes. The
metal/metals electrodeposited will be : $(E^{0}_{Ag^{+}/Ag} = 0. 80V, E^{0}_{Au^{+}/Au} = 1. 69V)$
a.
only gold
b.
silver and gold in proportion to their atomic weights
c.
only silver
d.
silver and gold in equal mass proportion
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If the equilibrium constant for $A \rightleftharpoons B + C$ is $K^{(1)}_{eq}$ and that of $B + C \rightleftharpoons P$ is $K^{(2)}_{eq} ,$ the equilibrium constant for
$A \rightleftharpoons P$ is :
a.
$K^{(1)}_{eq} /K^{(2)}_{eq}$
b.
$K^{(2)}_{eq} -K^{(1)}_{eq}$
c.
$K^{(1)}_{eq} + K^{(2)}_{eq}$
d.
$K^{(1)}_{eq} K^{(2)}_{eq}$
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The osmotic pressure of a solution of $NaCl$ is $0. 10$ atm and that of a glucose solution is $0. 20$ atm. The
osmotic pressure of a solution formed by mixing $1\,L$ of the sodium chloride solution with $2\,L$ of the glucose
solution is $x \times 10^{-3}$ atm. $x$ is ________ (nearest integer)
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An alkaline earth metal ' $M$ ' readily forms water soluble sulphate and water insoluble hydroxide. Its oxide $MO$
is very stable to heat and does not have rock-salt structure. $M$ is
a.
$Sr$
b.
$Ca$
c.
$Mg$
d.
$Be$
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Suppose the vectors $x_{1},x_{2}$ and $x_{3}$ are the solutions of the system of linear equations, $Ax=b$ when the vector
$1 0 0$
$[ ] [ ] [ ]$
$b$ on the right side is equal to $b_{1},b_{2}$ and $b_{3}$ respectively. If $x_{1} = 1 , \,x_{2} = 2 , \,x_{3} = 0$ ;
$[ ] [ ] [ ]$
$1 1 1$
$1 0 0$
$[ ] [ ] [ ]$
$b_{1} = 0 , \,b_{2} = 2 , \,b_{3} = 0$ , then the determinant of $A$ is equal to
$[ ] [ ] [ ]$
$0 0 2$
a.
$4$
b.
$2$
c.
$\frac{1}{2}$
d.
$\frac{3}{2}$
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Let ${x}$ and $[x]$ denote the fractional part of $x$ and the greatest integer $\leq x$ respectively of a real number $x$ . if
$\int _{0}^{n}{x}dx, \,\int _{0}^{n}[x]dx$ and $10(n^{2} - n),(n\in N,n> 1)$ are three consecutive terms of a G.P. then $n$ is equal
to__
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The circle passing through the intersection of the circles, $x^{2} +y^{2} -6x= 0$ and $x^{2} +y^{2} -4y= 0$ having its
centre on the line, $2x-3y+ 12 = 0$ , also passes through the point :
a.
$(-1, 3)$
b.
$(-3, 6)$
c.
$(-3, 1)$
d.
$(1, -3)$
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Let $a_{1},a_{2}, … ,a_{n}$ be a given A.P. whose common difference is an integer and $S_{n} =a_{1}+a_{2}+ … +a_{n}$ . If
$a_{1} = 1,a_{n} = 300$ and $15 \leq n\leq 50,$ then the ordered pair $(S_{n-4},a_{n-4})$ is equal to:
a.
$(2490, 249)$
b.
$(2480, 249)$
c.
$(2480, 248)$
d.
$(2490, 248)$
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If the variance of the following frequency distribution:
Class: $10 -20\,\,\,\,\,\,\,\,20 -30\,\,\,\,\,\,\,\,30 -40$
Frequency: $2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2$
is $50,$ then $x$ is equal to _______
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Let $f : (0, \infty ) (0, \infty )$ be a differentiable function such that $f(1) =e$ and $lim_{t\rightarrow \rightarrow x} \frac{t^{2}f^{2}(x)-x^{2}f^{2}(t)}{t-x} = 0.$ If
$f(x) = 1$ , then $\vec{x}$ is equal to:
a.
$\frac{1}{e}$
b.
$2e$
c.
$\frac{1}{2e}$
d.
$e$
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If for some positive integer $n$ , the coefficients of three consecutive terms in the binomial expansion of
$(1 +x)^{n+5}$ are in the ratio $5 : 10 : 14$ , then the largest coefficient in the expansion is :
a.
$462$
b.
$330$
c.
$792$
d.
$252$
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The area (in sq. units) of the largest rectangle $ABCD$ whose vertices $A$ and $B$ lie on the $x$ -axis and vertices $C$
and $D$ lie on the parabola, $y=x^{2} -1$ below the $x$ -axis, is :
a.
$\frac{2}{3\sqrt{3}}$
b.
$\frac{1}{3\sqrt{3}}$
c.
$\frac{4}{3}$
d.
$\frac{4}{3\sqrt{3}}$
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Let $PQ$ be a diameter of the circle $x^{2} +y^{2} = 9$ . If $\alpha$ and $\beta$ are the lengths of the perpendiculars from $P$ and $Q$
on the straight line, $x+y= 2$ respectively, then the maximum value of $\alpha \beta$ is _______
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The angle of elevation of a cloud $C$ from a point $P, 200\,m$ above a still take is $30^{o}$ . If the angle of depression
of the image of $C$ in the lake from the point $P$ is $60^{o}$ , then $PC$ (in $m$ ) is equal to
a.
$100$
b.
$200\sqrt{3}$
c.
$400$
d.
$400\sqrt{3}$
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A test consists of $6$ multiple choice questions, each having $4$ alternative answers of which only one is correct.
The number of ways, in which a candidate answers all six questions such that exactly four of the answers are
correct, is ___________
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$||||$
If $\vec{a}= 2ˆi+ ˆj+ 2ˆk$ , then, the value of $ˆi\times (\vec{a}\times ˆi)^{2} + ˆj\times (\vec{a}\times ˆj)^{2} + ˆk\times (\vec{a}\times ˆk)^{2}$ , is equal to :
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If the perpendicular bisector of the line segment joining the points $P(1, 4)$ and $Q(k, 3)$ has $y$ -intercept equal to
$-4$ , then a value of $k$ is;
a.
$-2$
b.
$-4$
c.
$\sqrt{14}$
d.
$\sqrt{15}$
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Let $_{i}^{50}\cup _{=1}X_{i} =_{i}\cup _{=1}^{n} Y_{i} =T$ , where each $X_{i}$ contains $10$ elements and each $Y_{i}$ contains $5$ elements. If each element
of the set $T$ is an element of exactly $20$ of sets $X_{i}$ 's and exactly $6$ of sets $Y_{i}$ 's then $n$ is equal to :
a.
$15$
b.
$50$
c.
$45$
d.
$30$
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In a game two players $A$ and $B$ take turns in throwing a pair of fair dice starting with player $A$ and total of
scores on the two dice, in each throw is noted. $A$ wins the game if he throws a total of $6$ before $B$ throws a
total of $7$ and $B$ wins the game if he throws a total of $7$ before $A$ throws a total of six. The game stops as soon
as either of the players wins. The probability of $A$ winning the game is :
a.
$\frac{5}{31}$
b.
$\frac{31}{61}$
c.
$\frac{5}{6}$
d.
$\frac{30}{61}$
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Let $\lambda \neq 0$ be in $R$ . If $\alpha$ and $\beta$ are the roots of the equation, $x^{2} - x+ 2\lambda = 0$ and $\alpha$ and $\gamma$ are the roots of the
equation, $3x^{2} -10x+ 27\lambda = 0,$ then $\frac{\beta \gamma}{\lambda}$ is equal to:
a.
$27$
b.
$18$
c.
$9$
d.
$36$
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Let $x= 4$ be a directrix to an ellipse whose centre is at the origin and its eccentricity is $\frac{1}{2}.$ If $P(1,\beta ),\beta > 0$ is
a point on this ellipse, then the equation of the normal to it at $P$ is
a.
$4x-3y= 2$
b.
$8x-2y= 5$
c.
$7x-4y= 1$
d.
$4x-2y= 1$
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