Given figure shows few data points in a photo-electric effect experiment for a certain metal. The minimum
energy for ejection of electrons from its surface is: (Planck's constant $h = 6.62 \times 10^{-34}\,J.s$ )
a.
$2.27\,eV$
Correct Answer
b.
$2.59\,eV$
c.
$1.93\,eV$
d.
$2.10\,eV$
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Q2mcq
Blocks of masses $m, \,2m, \,4m$ and $8m$ are arranged in a line of a frictionless floor. Another block of mass $m$ ,
moving with speed $υ$ along the same line (see figure) collides with mass $m$ in perfectly inelastic manner. All the
subsequent collisions are also perfectly inelastic. By the time the last block of mass $8m$ starts moving the total
energy loss is $p%$ of the original energy. Value of ‘ $p$ ’ is close to:
a.
$77$
b.
$94$
Correct Answer
c.
$37$
d.
$87$
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Q3mcq
A wire $A$ , bent in the shape of an arc of a circle, carrying a current of $2\,A$ and having radius $2\, cm$ and another
wire $B$ , also bent in the shape of an arc of a circle, carrying a current of $3\,A$ and having radius of $4\,cm$ , are
placed as shown in the figure. The ratio of the magnetic fields due to the wires $A$ and $B$ at the common centre
$O$ is:
a.
$4 : 6$
b.
$6 : 4$
c.
$2 : 5$
d.
$6 : 5$
Correct Answer
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Q4mcq
Two charged thin infinite plane sheets of uniform charge density $\sigma _{+}$ and $\sigma _{-}$ , where $|\sigma _{+}| > |\sigma _{-}|$ , intersect at
the right angle. Which of the following best represents the electric field lines for the system:
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Q5mcq
On the $x$ -axis and at a distance $x$ from the origin, the gravitational field due to a mass distribution is given by
$\frac{Ax}{(x^{2}+a^{2})^{3/2}}$ in the $x$ -direction. The magnitude of the gravitational potential on the $x$ -axis at a distance $x$ , taking its
value to be zero at infinity is:
a.
$\frac{A}{(x^{2}+a^{2})^{1/2}}$
Correct Answer
b.
$\frac{A}{(x^{2}+a^{2})^{3/2}}$
c.
$A(x^{2} +a^{2})^{1/2}$
d.
$A(x^{2} +a^{2})^{3/2}$
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Q6nat
A closed vessel contains $0.1$ mole of a monoatomic ideal gas at $200\,K$ . If $0.05$ mole of the same gas at $400\,K$
is added to it, the final equilibrium temperature (in $K$ ) of the gas in the vessel will be close to ______
✓ Accepted Answer:267
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Q7mcq
A battery of $3.0\,V$ is connected to a resistor dissipating $0.5\,W$ of power. If the terminal voltage of the battery
is $2.5\,V$ , the power dissipated within the internal resistance is:
a.
$0.50\,W$
b.
$0.072\,W$
c.
$0.10\,W$
Correct Answer
d.
$0.125\,W$
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Q8mcq
A small bar magnet is placed with its axis at $30^{o}$ with an external magnetic field of $0. 06\,T$ experiences a
torque of $0. 018\, Nm$ . The minimum work required to rotate it from its stable to unstable equilibrium position
is:
a.
$6. 4 \times 10^{-2}\,J$
b.
$9. 2 \times 10^{-3}\,J$
c.
$7. 2 \times 10^{-2}\,J$
Correct Answer
d.
$11. 7 \times 10^{-3}\,J$
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Q9nat
$ABC$ is a plane lamina of the shape of an equilateral triangle. $D, \,E$ are mid-points of $AB, \,AC$ and $G$ is the
centroid of the lamina. Moment of inertia of the lamina about an axis passing through $G$ and perpendicular to
the plane $ABC$ is $I_{0}$ . If part $ADE$ is removed, the moment of inertia of the remaining part about the same axis
is $\frac{NI_{0}}{16}$ where $N$ is an integer. Value of $N$ is:
✓ Accepted Answer:11
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Q10mcq
Match the $\frac{C_{p}}{C_{v}}$ ratio for ideal gases with different type of molecules:
Molecule Type $C_{p}/C_{v}$
(A) Monoatomic (I) $7/5$
(B) Diatomic rigid molecules (II) $9/7$
(C) Diatomic non-rigid molecules (III) $4/3$
(D) Triatomic rigid molecules (IV) $5/3$
For a transvers wave travelling, along a straight line, the distance between two peaks (crests) is $5\,m$ , while the
distance between one crest and one trough is $1. 5\,m$ . The possible wavelengths (in $m$ ) of the waves are:
A circular disc of mass $M$ and radius $R$ is rotating about its axis with angular speed $\omega _{1}$ . If another stationary
disc having radius $\frac{R}{2}$ and same mass $M$ is dropped co-axially on to the rotating disc. Gradually both discs
attain constant angular speed $\omega _{2}$ . The energy lost in the process is $p%$ of the initial energy. Value of $p$ is
______
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A air bubble of radius $1\,cm$ in water has an upward acceleration of $9.8\,cms^{-2}$ . The density of water is
$1\,gm\,cm^{-3}$ and water offers negligible drag force on the bubble. The mass of the bubble is $(g\, = \,980\,cm/s^{2})$ .
a.
$4.51\,gm$
b.
$3. 15\,gm$
c.
$4.15\,gm$
d.
$1.52\,gm$
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A beam of plane polarized light of large cross-sectional area and uniform intensity of $3 .3 \,W\,m^{-2}$ falls
normally on a polarizer (cross-sectional area $3 \times 10^{-4}\,m^{2}$ ), which rotates about its axis with an angular speed
of $31 .4 \, rad \,s^{-1}$ . The energy of light passing through the polarizer per revolution, is close to:
a.
$1 .0 \times 10^{-5}\,J$
b.
$1. 0 \times 10^{-4}\,J$
c.
$1. 5 \times 10^{-4}\,J$
d.
$5. 0 \times 10^{-4}\,J$
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A two point charges $4q$ and $-q$ are fixed on the $x$ -axis at $x= \frac{-d}{2}$ and $x= \frac{d}{2}$ , respectively. If the third point
charge ‘ $q$ ’ is taken from the origin to $x=d$ along the semicircle as shown in the figure, the energy of the
charge will:
a.
Increase by $\frac{3q^{2}}{4\pi \in _{0}d}$
b.
Increase by $\frac{2q^{2}}{3\pi \in _{0}d}$
c.
decrease by $\frac{q^{2}}{4\pi \in _{0}d}$
d.
decrease by $\frac{4q^{2}}{3\pi \in _{0}d}$
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Take the breakdown voltage of the zener diode used in the given circuit as $6V$ . For the input voltage shown in
the figure below, the time variation of the output voltage is: (Graphs drawn are schematic and not to the scale)
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$⌢$
Starting from the origin at time $t = 0$ , with initial velocity $5\, j \,ms^{-1}$ , a particle moves in the $x$ - $y$ plane with a
$⌢ ⌢$
constant acceleration of $(10 i + 4 j)ms^{-2}$ . At time $t$ , its coordinates are $(20\,m,\,y_{0}\,m)$ . The values of $t$ and $y_{0}$
are, respectively:
a.
$2\,s$ and $18\,m$
b.
$4\,s$ and $52\,m$
c.
$2\,s$ and $24\,m$
d.
$5\,s$ and $25\,m$
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In the line spectra of hydrogen atom, difference between the largest and the shortest wavelengths of the Lyman
series is $305\,A^{\circ }$ . The corresponding difference for the Paschan series in $A^{\circ }$ is:________
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A tennis ball is released from a height $h$ and after freely falling on a wooden floor it rebounds and reaches
height $h/2$ . The velocity versus height of the ball during its motion may be represented graphically by: (graphs
are drawn schematically and on not to scale)
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The specific heat of water $= 4200\,J kg^{-1}\,K^{-1}$ and the latent heat of ice $= 3.4 \times 10^{5}\,J$ k $g^{-1}$ . $100$ grams of ice at
$0\,^{o}C$ is placed in $200\,g$ of water at $25\,^{o}C$ . The amount of ice that will melt as the temperature of water reaches
$0\,^{o}C$ is close to (in grams)
a.
$61.7$
b.
$63. 8$
c.
$69. 3$
d.
$64. 6$
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A small bar magnet is moved through a coil at constant speed from one end to the other. Which of the
following series of observations will be seen on the galvanometer $G$ attached across the coil?
Three positions shown describe: (a) the magnet's entry (b) magnet is completely inside and (c) magnet's exit.
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Particle $A$ of mass $m_{A} = \frac{m}{2}$ moving along the $x$ -axis with velocity $v_{0}$ collides elastically with another
particle $B$ at rest having mass $m_{B} = \frac{m}{3}$ . If both the particles move along the $x$ -axis after the collision, the
change $\Delta \lambda$ in the wavelength of the particle $A$ , in terms of its de-Broglie wavelength $(\lambda _{0})$ before the collision
is:
a.
$\Delta \lambda = \frac{3}{2}\lambda _{0}$
b.
$\Delta \lambda = \frac{5}{2}\lambda _{0}$
c.
$\Delta \lambda = 2\lambda _{0}$
d.
$\Delta \lambda = 4\lambda _{0}$
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In a compound microscope, the magnified virtual image is formed at a distance of $25\,cm$ from the eye-piece.
The focal length of its objective lens is $1\,cm$ . If the magnification is $100$ and the tube length of the microscope
is $20\,cm$ , then the focal length of the eye-piece lens (in $cm$ ) is ______
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Among statements (a) - (d), the correct ones are :
(a) Lime stone is decomposed to $CaO$ during the extraction of iron from its oxides.
(b) In the extraction of silver, silver is extracted as an anionic complex.
(c) Nickel is purified by Mond’s process.
(d) $Zr$ and $Ti$ are purified by Van Arkel method.
a.
(a), (b), (c) and (d)
b.
(a), (c) and (d) only
c.
(b), (c) and (d) only
d.
(c) and (d) only
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An organic compound (A) (molecular formula $C_{6}H_{12}O_{2}$ ) was hydrolysed with dil. $H_{2}SO_{4}$ to give a
carboxylic acid (B) and an alcohol (C). ‘ $C$ ’ gives white turbidity immediately when treated with anhydrous
$ZnCl_{2}$ and conc. $HCl$ . The organic compound (A) is:
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$[P]$ on treatment with $Br_{2}/ FeBr_{3}$ in $CCl_{4}$ produced a single isomer $C_{8}H_{7}O_{2}Br$ wile heating $[P]$ with
sodalime gives toluene. The compound $[P]$ is:
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On heating, lead (ll) nitrate gives a brown gas (A). The gas (A) on cooling changes to a colourless solid/liquid
(B). (B) on heating with NO changes to ablue solid (C). The oxidation number of nitrogen in solid (C) is:
a.
$+5$
b.
$+2$
c.
$+3$
d.
$+4$
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If $75%$ of a first order reaction was completed in $90$ minutes, $60%$ of the same reaction would be completed in
approximately (in minutes) _____
(Take: $log 2 = 0.30\,; log 2.5 = 0.40$ )
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For one mole of an ideal gas, which of these statements must be true?
(a) Internal energy $(U)$ and enthalpy $(H)$ each depends on temperature.
(b) Compressibility factor $Z$ is not equal to 1
(c) $C_{P,\,m}\,-C_{V,\,m} = R$
(d) $dU = C_{v}dT$ for any process
a.
(a) and (c)
b.
(b), (c) and (d)
c.
(c) and (d)
d.
(a), (c) and (d)
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At $300\,K$ , the vapour pressure of a solution containing $1$ mole of $n$ -hexane and $3$ moles of $n$ -heptane is
$550\, mm$ of $Hg$ . At the same temperature, if one more mole of $n$ -heptane is added to this solution, the vapour
pressure of the solution increases by $10\, mm$ of $Hg$ . What is the vapour pressure in $mmHg$ of $n$ - heptane in its
pure state______?
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A $20. 0\, mL$ solution containing $0. 2\,g$ impure $H_{2}O_{2}$ reacts completely with $0. 316\,g$ of $KMnO_{4}$ in acid
solution. The purity of $H_{2}O_{2}$ (in $%$ ) is______ (mol. wt. of $H_{2}O_{2} = 34$ ; mol. wt. of $KMnO_{4} = 158$ )
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The mean and variance of $8$ observations are $10$ and $13. 5,$ respectively. If $6$ of these observations are
$5, 7, 10, 12, 14, 15,$ then the absolute difference of the remaining two observations is :
a.
$9$
b.
$5$
c.
$3$
d.
$7$
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Let $f$ be a twice differentiable function on $(1, 6)$ , If $f(2) = 8, \,f'(2) = 5, \,f'(x) \geq 1$ and $f''(x) \geq 4,$ for all
$x\in (1, 6)$ , then :
a.
$f(5) +f'(5) \leq 26$
b.
$f(5) +f'(5) \geq 28$
c.
$f'(5) +f''(5) \leq 20$
d.
$f(5) \leq 10$
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Suppose a differentiable function $f(x)$ satisfies the identity $f(x+y) =f(x) +f(y) +xy^{2} +x^{2}y,$ for all real
$x$ and $y$ . If $_{x}lim_{\rightarrow 0\rightarrow } \frac{f(x)}{x} = 1,$ then $f'(3)$ is equal to :
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The probability of a man hitting a target is $\frac{1}{10}.$ The least number of shots required, so that the probability of his
hitting the target at least once is greater than $\frac{1}{4},$ is....
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Let $y=y(x)$ be the solution of the differential equation, $xy' - y=x^{2}(xcosx+ sinx)$ , $x> 0$ . If $y(\pi ) =\pi ,$
then $y''(\frac{\pi}{2})+y(\frac{\pi}{2} )$ is equal to :
a.
$2 + \frac{\pi}{2}$
b.
$1 + \frac{\pi}{2} + \frac{\pi ^{2}}{4}$
c.
$2 + \frac{\pi}{2} + \frac{\pi ^{2}}{4}$
d.
$1 + \frac{\pi}{2}$
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Let $P(3, 3)$ be a point on the hyperbola, $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1.$ If the normal to it at $P$ intersects the $x$ -axis at $(9, 0)$
and $e$ is its eccentricity, then the ordered pair $(a^{2},e^{2})$ is equal to:
a.
$( \frac{9}{2}, 3)$
b.
$(\frac{3}{2}, 2)$
c.
$( \frac{9}{2}, 2)$
d.
$(9, 3)$
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Let $u= \frac{2z+i}{z-ki} ,z=x+iy$ and $k> 0$ . If the curve represented by $Re (u)+ Im (u) = 1$ intersects the $y$ -axis at
points $P$ and $Q$ where $PQ = 5$ then the value of $k$ is
a.
$\frac{3}{2}$
b.
$\frac{1}{2}$
c.
$4$
d.
$2$
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Two vertical poles $AB= 15\,m$ and $CD= 10\,m$ are standing apart on a horizontal ground with points $A$ and
$C$ on the ground. If $P$ is the point of intersection of $BC$ and $AD,$ then the height of $P$ (in $m$ ) above the line
$AC$ is :
a.
$20/3$
b.
$5$
c.
$10/3$
d.
$6$
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A survey shows that $63%$ of the people in a city read newspaper $A$ whereas $76%$ read news paper $B$ . If $x%$ of
the people read both the newspapers, then a possible value of $x$ can be:
a.
$29$
b.
$37$
c.
$65$
d.
$55$
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If the equation of a plane $P$ , passing through the intersection of the planes, $x+ 4y- z+ 7 = 0$ and
$3x+y+ 5z= 8$ is $ax+by+ 6z= 15$ for some $a,b\in R,$ then the distance of the point $(3, 2, -1)$ from the
plane $P$ is $… …$
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Let $x_{0}$ be the point of local maxima of $f(x) = \vec{a}\cdot (\vec{b}\times \vec{c}),$ where $\vec{a}=xˆi-2ˆj+ 3ˆk, \,\,\vec{b}= -2ˆi+xˆj- ˆk$ and
$\vec{c}= 7ˆi-2ˆj+xˆk.$ Then the value of $\vec{a}\cdot \vec{b}+ \vec{b}\cdot \vec{c}+ \vec{c}\cdot \vec{a}$ at $x=x_{0}$ is:
a.
$-4$
b.
$-30$
c.
$14$
d.
$-22$
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Let $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1(a>b)$ be a given ellipse, length of whose latus rectum is $10$ . If its eccentricity is
the maximum value of the function, $\phi (t) = \frac{5}{12} +t- t^{2}$ , then $a^{2} +b^{2}$ is equal to :
a.
$145$
b.
$116$
c.
$126$
d.
$135$
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$cos\theta \,isin\theta a b$
If $A=[ ], \,\,(\theta = \frac{\pi}{24} )$ and $A^{5} =[ ],$ where $i= \sqrt{-1}$ , then which one of the following is not
$isin\theta cos\theta c d$
true?
a.
$0 \leq a^{2} +b^{2} \leq 1$
b.
$a^{2} - d^{2} = 0$
c.
$a^{2} - c^{2} = 1$
d.
$a^{2} - b^{2} = \frac{1}{2}$
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A triangle $ABC$ lying in the first quadrant has two vertices as $A(1, 2)$ and $B(3, 1)$ . If $\angle BAC = 90^{o},$ and
$ar (\Delta ABC) = 5\sqrt{5}$ sq. units, then the abscissa of the vertex $C$ is :
a.
$1 + \sqrt{5}$
b.
$1 + 2\sqrt{5}$
c.
$2 + \sqrt{5}$
d.
$2 -1\sqrt{5}$
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Given the following two statements:
$(S_{1}) : (q \vee p) \rightarrow (p \leftrightarrow ~q)\rightarrow$ is a tautology
$(S_{2}) : ~q \wedge (~p \leftrightarrow q)$ is a fallacy. Then :
a.
both $(S_{1})$ and $(S_{2})$ are not correct.
b.
only $(S_{1})$ is correct.
c.
only $(S_{2})$ is correct.
d.
both $(S_{1})$ and $(S_{2})$ are correct.
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Let $\alpha$ and $\beta$ be the roots of $x^{2} -3x+p= 0$ and $\gamma$ and $\delta$ be the roots of $x^{2} -6x+q= 0.$ If $\alpha ,\beta ,\gamma ,\delta$ from a
geometric progression. Then ratio $(2\,q+p) : (2\,q- p)$ is
a.
$3 : 1$
b.
$9 : 7$
c.
$5 : 3$
d.
$33 : 31$
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