A capillary tube made of glass of radius $0. 15\, mm$ is dipped vertically in a beaker filled with methylene iodide
(surface tension $= \,0. 05\,N\,m^{-1}$ , density $= \,667\, kg \,m^{-3}$ ) which rises to height $h$ in the tube. It is observed that
the two tangents drawn from observed that the two tangents drawn from liquid-glass interfaces (from opp. sides
of the capillary) make an angle of $60$ ΒΊwith one another. Then $h$ is close to ( $g = 10\,m\,s^{-2}$ )
a.
$0. 049\,m$
b.
$0. 087\,m$
Correct Answer
c.
$0. 137\,m$
d.
$0. 172\,m$
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Q2mcq
If momentum $(P)$ , area $(A)$ and time $(T)$ are taken to be the fundamental quantities then the dimensional
formula for energy is :
a.
$[P^{2}\, AT^{-2}]$
b.
$[PA^{-1} T^{-1}]$
c.
$[PA^{1/2} T^{-1}]$
Correct Answer
d.
$[P^{1/2} AT^{-1}]$
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Q3mcq
A charge Q is distributed over two concentric conducting thin spherical shells radii $r$ and $R\,(R > r)$ . If the
surface charge densities on the two shells are equal, the electric potential at the common centre is :
In a hydrogen atom the electron makes a transition from $(n\, + \,1)^{th}$ level to the $n^{th}$ level. If $n >> 1$ , the
frequency of radiation emitted is proportional to :
a.
$\frac{1}{n}$
b.
$\frac{1}{n^{3}}$
Correct Answer
c.
$\frac{1}{n^{2}}$
d.
$\frac{1}{n^{4}}$
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Q5mcq
A heat engine is involved with exchange of heat of $1915\,J, \,-40\,J, \, + 125\,J$ and $-Q\,J$ , during one cycle
achieving and efficiency of $50. 0%$ . The value of $Q$ is:
a.
$640\,J$
b.
$40\,J$
c.
$980\,J$
Correct Answer
d.
$400\,J$
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Q6nat
A light ray enters a solid glass sphere of refractive index $\mu$ $= \sqrt{3}$ at an angle of incidence $60^{\circ}$ . The ray is both
reflected and refracted at the farther surface of the sphere. The angle (in degrees) between the reflected and
refracted rays at this surface is _____________.
✓ Accepted Answer:90
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Q7mcq
In a plane electromagnetic wave, the directions of electric field and magnetic field are represented by $Λk$ and
$2Λi -2Λj$ , respectively. What is the unit vector along direction of propagation of the wave.
a.
$\frac{1}{\sqrt{2}}(Λi +Λj)$
Correct Answer
b.
$\frac{1}{\sqrt{2}}(Λj + k)$
c.
$\frac{1}{\sqrt{5}}(Λi + 2Λj)$
d.
$\frac{1}{\sqrt{5}}(2Λi +Λj)$
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Q8mcq
An ideal gas in a closed container is slowly heated. As its temperature increases, which of the following
statements are true ?
(A) the mean free path of the molecules decreases
(B) the mean collision time between the molecules decreases.
(C) the mean free path remains unchanged.
(D) the mean collision time relations unchanged.
a.
$(B)$ and $(C)$
Correct Answer
b.
$(A)$ and $(B)$
c.
$(C)$ and $(D)$
d.
$(A)$ and $(D)$
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Q9mcq
Two uniform circular discs are rotating independently in the same direction around their common axis passing
through their centres. The moment of inertia and angular velocity of the first disc are $0. 1\,kg -m^{2}$ and
$10\,rad\,s^{-1}$ respectively while those for the second one are $0. 2\,kg -m^{2}$ and $5\, rad \,s^{-1}$ respectively. At some
instant they get stuck together and start rotating as a single system about their common axis with some angular
speed. The kinetic energy of the combined system is :
a.
$\frac{10}{3}J$
b.
$\frac{20}{3}J$
Correct Answer
c.
$\frac{5}{3}J$
d.
$\frac{2}{3}J$
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Q10mcq
A wire carrying current $I$ is bent in the shape $ABCDEFA$ as shown, where rectangle $ABCDA$ and $ADEFA$
are perpendicular to each other. If the sides of the rectangles are of lengths $a$ and $b$ , then the magnitude and
direction of magnetic moment of the loop $ABCDEFA$ is :
a.
$\sqrt{2}abI\, along \,( \frac{Λj}{\sqrt{2}} + \frac{Λk}{\sqrt{2}})$
Correct Answer
b.
$abI$ along $( \frac{Λj}{\sqrt{2}} + \frac{Λk}{\sqrt{2}})$
c.
$\sqrt{2}abI$ along $(\frac{Λj}{\sqrt{5}} + \frac{2Λk}{\sqrt{5}})$
d.
$abI$ along $( \frac{Λj}{\sqrt{5}} + \frac{Λk}{\sqrt{5}})$
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A particle is moving $5$ times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that
of the electron is $1. 878 \times 10^{-4}$ . The mass of the particle is close to :
a.
$4. 8 \times 10^{-27}\, kg$
b.
$9. 1 \times 10^{-31\,} kg$
c.
$1. 2 \times 10^{-28}\, kg$
d.
$9. 7 \times 10^{-28}\, kg$
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A $10\,$ $\mu$ $F$ capacitor is fully charged to a potential difference of $50\,V$ After removing the source voltage it is
connected to an uncharged capacitor in parallel. Now the potential difference across them becomes $20\,V$ . The
capacitance of the second capacitor is :
a.
$15\,$ $\mu$ $F$
b.
$30\,$ $\mu$ $F$
c.
$20\,$ $\mu$ $F$
d.
$10\,$ $\mu$ $F$
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The figure shows a region of length 'π' with a uniform magnetic field of $0. 3\,T$ in it and a proton entering the
region with velocity $4 \times 10^{5}\,m\,s^{-1}$ making an angle $60^{\circ}$ with the field. If the proton completes $10$ revolution
by the time it cross the region shown, 'π' is close to (mass of proton $= \,1. 67 \times 10^{-27}\, kg$ , charge of the proton
$= \,1. 6 \times 10^{-19}\,C$ )
a.
$0. 11\,m$
b.
$0. 88\,m$
c.
$0. 44\,m$
d.
$0. 22\,m$
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When the temperature of a metal wire is increased from $0$ ΒΊ $C\, to \,10$ ΒΊ $C$ , its length increases by $0. 02%$ .The
percentage change in its mass density will be closed to:
a.
$0. 06$
b.
$2. 3$
c.
$0. 008$
d.
$0. 8$
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An inductance coil has a reactance of $100\,\Omega$ . When an AC signal of frequency $1000\, Hz$ is applied to the coil,
the applied voltage leads the current by $45^{\circ}$ . The self-inductance of the coil is
a.
$1. 1 \times 10^{-2}\,H$
b.
$1. 1 \times 10^{-1}\,H$
c.
$5. 5 \times 10^{-5}\,H$
d.
$6. 7 \times 10^{-7}\,H$
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In a Young's double slit experiment, $16$ fringes are observed in a certain segment of the screen when light of
wavelength $700\, nm$ is used. If the wavelength of light is changed to $400\, nm$ , the number of fringes observed
in the same segment of the screen would be :
a.
$24$
b.
$30$
c.
$18$
d.
$28$
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A small point mass carrying some positive charge on it, is released from the edge of a table. There is a uniform
electric field in this region in the horizontal direction. Which of the following options then correctly describe
the trajectory of the mass ? (Curves are drawn schematically and are not to scale)
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An ideal cell of emf $10V$ is connected in circuit shown in figure. Each resistance is $2\Omega$ . The potential
difference (in $V$ ) across the capacitor when it is fully charged is _____________
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A square shaped hole of side $l= \,\frac{a}{2}$ is carved out at a distance $d = \frac{a}{2}$ from the centre ' $O$ ' of a uniform circular
disk of radius a. If the distance of the centre of mass of the remaining portion from $O$ is $-\frac{a}{x}$ , value of $X$ (to the
nearest integer) is :
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A potentiometer wire $PQ$ of $1m$ length is connected to a standard cell $E_{1}$ . Another cell $E_{2}$ of emf $1. 02\,V$ is
connected with a resistance ' $r$ ' and switch $S$ (as shown in figure). With switch $S$ open, the null position is
obtained at a distance of $49\, cm$ from $Q$ . The potential gradient in the potentiometer wire is :
a.
$0. 02\,V/ cm$
b.
$0. 01\,V/ cm$
c.
$0. 03\,V/ cm$
d.
$0. 04\,V/ cm$
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A wire of density $9 \times 10^{-3}\, kg \, cm^{-3}$ is stretched between two clamps $1\,m$ apart. The resulting strain in the
wire is $4. 9\, \times \,10^{-4}$ . The lowest frequency of the transverse vibrations in the wire (Young's modulus of wire
$Y\, = \,9 \times 10^{10}\, Nm^{-2}$ ), (to the nearest integer),_______
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The height β $h$ β at which the weight of a body will be the same as that at the same depth βhβ from the surface of
the earth is (Radius of the earth is $R$ and effect of the rotation of the earth is neglected)
a.
$\frac{\sqrt{5}}{2}R -R$
b.
$\frac{R}{2}$
c.
$\frac{\sqrt{5}R-R}{2}$
d.
$\frac{\sqrt{3}R-R}{2}$
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The displacement time graph of a particle executing SHM is given in figure: (sketch is schematic and not to
scale)
Which of the following statements is/are true for this motion?
(A) The force is zero at $t= \frac{3T}{4}$
(B) The magnitude of acceleration is maximum at $t=T$
(C) The speed is maximum at $t= \frac{T}{4}$
(D) The $P.E.$ is equal to $K.E.$ of the oscillation at $t= \frac{T}{2}$
a.
$(A), (B)$ and $(C)$
b.
$(B), (C)$ and $(D)$
c.
$(A), (B)$ and $(D)$
d.
$(A)\, and \,(D)$
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A particle of mass $m$ is moving along the $x$ -axis with initial velocity $uΛi$ . It collides elastically with a particle of
mass $10m$ at rest and then moves with half its initial kinetic energy (see figure). If $sin \,$ $\theta$ $_{1} = sin \,\sqrt{n}$ $\theta$ $_{2}$ then
value of n is ________.
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The results given in the below table were obtained during kinetic studies of the following reaction:
$2A + B \rightarrow C + D\rightarrow$
Experiment $[A]/ molL^{-1} [B]/ molL^{-1}$ Initial rate/ $molL^{-1} min^{-1}$
I $0. 1 0. 1 6. 00 \times 10^{-3}$
II $0. 1 0. 2 2. 40 \times 10^{-2}$
III $0. 2 0. 1 1. 20 \times 10^{-2}$
IV X $0. 2 7. 20 \times 10^{-2}$
V $0. 3$ Y $2. 88 \times 10^{-1}$
X and Y in the given table are respectively :
a.
$\,0. 4, \,0. 4$
b.
$0. 4, \,0. 3$
c.
$\,0. 3, \,0. 4$
d.
$\,0. 3, \,0. 3$
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Match the type of interaction in column $A$ with the distance dependence of their interaction energy in column
$B :$
A B
(i) ion - ion (a) $\frac{1}{r}$
(ii) Dipole - dipole (b) $\frac{1}{r^{2}}$
(iii) London dispersion (c) $\frac{1}{r^{3}}$
(iv) $\frac{1}{r^{6}}$
a.
(i) - (b); (ii) - (d); (iii) - (c)
b.
(i) - (a); (ii) - (b); (iii) - (d)
c.
(i) - (a); (ii) - (b); (iii) - (c)
d.
(i) - (a); (ii) - (c); (iii) - (d)
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Two compounds $A$ and $B$ with same molecular formula $(C_{3}H_{6}O)$ undergo Grignard reaction with
methylmagnesium bromide to give products $C$ and $D$ . Products $C$ and $D$ show following chemical tests.
Test C D
Ceric
Positive Positive
ammonium nitrate Test
Turbidity obtained after Turbidity obtained
Lucas Test
five minutes Immediately
Iodoform Test Positive Negative
$C$ and $D$ respectively are
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Amongst the following statements regarding adsorption, those that are valid are:
(a) $\Delta H$ becomes less negative as adsorption proceeds.
(b) On a given adsorbent, ammonia is adsorbed more than nitrogen gas.
(c) On adsorption, the residual force acting along the surface of the adsorbent increases
(d) With increase in temperature, the equilibrium concentration of adsorbate increases.
a.
(d) and (a)
b.
(b) and (c)
c.
(a) and (b)
d.
(c) and (d)
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The ratio of the mass percentages of ' $C$ & $H$ ' and ' $C$ & $O$ ' of a saturated acyclic organic compound ' $X$ ' are
$4 : 1$ and $3 : 4$ respectively. Then, the moles of oxygen gas required for complete combustion of two moles of
organic compound ' $X$ ' is_______
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Simplified absorption spectra of three complexes ((i) and (ii) and (iii)) of $M^{+n}$ ion are provided below; their
$\lambda _{max}$ values are marked as $A, \,B$ and $C$ respectively. The correct match between the complexes and their $\lambda _{max}$
values is:
(i) $[M(NCS)_{6}]^{(-6+n)}$
(ii) $[MF_{6}]^{(-6+n)}$
(iii) $[M(NH_{3})_{6}]^{n+}$
a.
$A -(iii), \,(B) -(i), \,C -(ii)$
b.
$A -(ii), \,(B) -(i), \,C -(iii)$
c.
$A -(ii), \,(B) -(iii), \,C -(i)$
d.
$\,A -(i), \,(B) -(ii), \,C -(iii)$
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For the disproportionation reaction $2 Cu^{+}(aq) \rightleftharpoons Cu(s) + Cu^{2+}(aq)$ at $298K,ln \,K$ (where $K$ is
the equilibrium constant) is _______ $\times 10^{-1}$
Given $:(E^{\circ}_{Cu^{2+}/ Cu^{+}}= 0. 16V E^{\circ}_{Cu}+_{/ Cu}= 0. 52V\frac{RT}{F} = 0. 025)$
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The correct observation in the following reaction is:
$--Sucrose^{Gly \, cosidic \, bond} A + B^{Seliw \, anoff}?$
$Cleavage \,(Hydrolys\vec{i}s) Reagen\vec{t}$
a.
Formation of blue colour
b.
Gives no colour
c.
Formation of red colour
d.
Formation of violet colour
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The work function of sodium metal is $4. 41 \times 10^{-19}J.$ If photons of wavelength $300\, nm$ are incident on the
metal, the kinetics energy of the ejected electrons will be $(h = 6. 63 \times 10^{-34}J\,s; \,c = 3 \times 10^{8}\,\,m\,s^{-1})$
__________ $\times 10^{-21}J$
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Three elements $X, Y$ and $Z$ are in the $3^{rd\,}$ period of the periodic table. The oxides of $X, Y$ and $Z$ , respectively,
are basic, amphoteric and acidic. The correct order of the atomic numbers of $X, \,Y$ and $Z$ is:
a.
$Z\, < \,Y\, < \,X$
b.
$\,X < \,Y\, < \,Z$
c.
$\,X\, < \,Z\, < \,Y$
d.
$Y\, < \,X\, < \,Z$
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The oxidation states of transition metal atoms in $K_{2}Cr_{2}O_{7}, \, KMnO_{4}$ and $K_{2}FeO_{4},$ respectively, are $x, y$ and
$z$ . The sum of $x, \,y$ and $z$ is______
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The heat of combustion of ethanol into carbon dioxides and water is $-327$ Kcal at constant pressure. The heat
evolved (in cal) at constant volume at $27^{\circ}\,C$ (if all gases behave ideally) is $(R = 2\, calmol^{-1} K^{-1})$ ________
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Two elements $A$ and $B$ have similar chemical properties. They don't form solid hydrogencarbonates, but react
with nitrogen to form nitrides. $A$ and $B$ , respectively, are :
a.
$Na$ and $Rb$
b.
$\, Na \,$ and $Ca$
c.
$Cs$ and $Ba$
d.
$Li$ and $Mg$
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Let $E^{C}$ denote the complement of an event $E$ . Let $E_{1},E_{2}$ and $E_{3}$ be any pairwise independent events with
$P(E_{1}) > 0$ and $P(E_{1}\cap E_{2}\cap E_{3}) = 0$ then $P((E_{2}^{C} \cap E^{C}_{3} )/E_{1})$ is equal to
a.
$P(E_{2}^{C})+P(E_{3})$
b.
$P(E_{3}^{C})- P(E^{C}_{2} )$
c.
$P(E_{3}) - P(E_{2}^{C})$
d.
$P(E_{3}^{C})- P(E_{2})$
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Let $n> 2$ be an integer. Suppose that there are $n$ Metro stations in a city located around a circular path. Each
pair of the nearest stations is connected by a straight track only. Further, each pair of the nearest station is
connected by blue line, whereas all remaining pairs of stations are connected by red line. If number of red lines
is $99$ times the number of blue lines, then the value of $n$ is
a.
$201$
b.
$200$
c.
$101$
d.
$199$
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If a curve $y=f(x)$ , passing through the point $(1, \,2)$ , is the solution of the differential equation
$2x^{2}dy=(2xy+y^{2})dx$ , then $f(\frac{1}{2})$ is equal to
a.
$\frac{1}{1+log_{e}2}$
b.
$\frac{1}{1-log_{e}2}$
c.
$1 + log_{e}2$
d.
$\frac{-1}{1+log_{e}2}$
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A plane passing through the point $(3, 1, 1)$ contains two lines whose direction ratios are $\,1, \,-\,2, \,2\,$ and $\,2, \,3, -1$
respectively. If, this plane also passes through the point $(\alpha , -3, 5)$ , then $\alpha$ is equal to
a.
$5$
b.
$-10$
c.
$10$
d.
$-5$
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For a positive integer $n, \,(1 + \frac{1}{x})^{n}$ is expanded in increasing powers of $x$ . If three consecutive coefficients in
this expansion are in the ratio, $2 : \,5 : \,12,$ then $n$ is equal to
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$a b c$
$[ ]$
Let $a, \,b, \,c\in R$ be all non-zero and satisfies $a^{3} +b^{3} +c^{3} = 2$ . If the matrix $A= b c a$ satisfies
$[c a b]$
$A^{T}A=I,$ then a value of $abc$ can be
a.
$-\frac{1}{3}$
b.
$\frac{1}{3}$
c.
$3$
d.
$\frac{2}{3}$
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If the sum of first $11$ terms of an A.P. , $a_{1},a_{2},a_{3}β¦ β¦$ is $0(a_{1} \neq 0)$ then the sum of the A.P
$a_{1},a_{3},a_{5}, β¦ . .a_{23}$ is $ka_{1}$ where $k$ is equal to
a.
$-\frac{121}{10}$
b.
$\frac{121}{10}$
c.
$\frac{72}{5}$
d.
$-\frac{72}{5}$
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The set of all possible values of $\theta$ in the interval $(0,\pi )$ for which the points $(1, \,2)$ and $(sin\theta , \, cos\theta )$ lie on the
same side of the line $x+y= 1$ is?
a.
$(0, \frac{\pi}{2})$
b.
$(\frac{\pi}{4} , \frac{3\pi}{4})$
c.
$(0, \frac{3\pi}{4})$
d.
$(0, \frac{\pi}{4} )$
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Consider a region $R={(x, \,y) \in R^{2} :x^{2} \leq y\leq 2x}$ . If a line $y=\alpha$ divides the area of region $R$ into two
equal parts, then which of the following is true ?
a.
$\alpha ^{3} -6\alpha ^{2} + 16 = 0$
b.
$3\alpha ^{2} -8\alpha ^{3/2} + 8 = 0$
c.
$3\alpha ^{2} -8\alpha + 8 = 0$
d.
$\alpha ^{3} -6\alpha ^{3/2} -16 = 0$
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For some $\theta \in (0, \frac{\pi}{2}),$ if the eccentricity of the hyperbola, $x^{2} - y^{2} sec^{2} \theta = 10$ is $\sqrt{5}$ times the eccentricity of
the ellipse, $x^{2} sec^{2} \theta +y^{2} = 5,$ then the length of the latus rectum of the ellipse, is
a.
$2\sqrt{6}$
b.
$\sqrt{30}$
c.
$\frac{2\sqrt{5}}{3}$
d.
$\frac{4\sqrt{5}}{3}$
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Let $S$ be the sum of the first $9$ term of the series :
${x+ka} +{x^{2} + (k+ 2)a}+{x^{3} + (k+ 4)a}+{x^{4} + (k+ 6)a}+ β¦$ where $a\neq 0$ and $x\, \neq \,1$ . If
$S = \frac{x^{10}-x+45a(x-1)}{x-1}$ , then $k$ is equal to
a.
$-5$
b.
$1$
c.
$-3$
d.
$3$
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$| |$
Let the position vectors of points ' $A$ ' and ' $B$ ' be $Λi +Λj +Λk$ and $2Λi +Λj + 3Λk,$ respectively. A point $'P'$ divides the
$----^{2}$
line segment $AB$ internally in the ratio $\lambda : 1(\lambda > 0)$ . If $O$ is the origin and $O\vec{B}\cdot O\vec{P}-3 O\vec{A}\times O\vec{P} = 6$ then
$\lambda$ is equal to
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Let $f :R R$ be a function which satisfies $f(x+y) =f(x) +f(y), \,\,\forall x, \,y\in R$ . If $f(1) = 2$ and
$g(n) =\sum ^{(}_{k}^{\vec{n}}_{=1}^{-1)} f(k),\,n\in N$ then the value of $n$ , for which $g(n) = 20$ , is
a.
$5$
b.
$20$
c.
$4$
d.
$9$
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