In a double - slit experiment, at a certain point on the screen the path difference between the two interfering
waves is $\frac{1}{8}th$ of a wavelength. The ratio of the intensity of light at that point to that at the center of a bright
fringe is:
a.
$0.853$
Correct Answer
b.
$0.672$
c.
$0.568$
d.
$0.760$
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Q2mcq
A capacitor is made of two square plates each of side ‘ $a$ ’ making a very small angle $\alpha$ between them, as
shown in figure. The capacitance will be close to:
A very long wire ABDMNDC is shown in figure carrying current I. AB and BC parts are straight, long and at
right angle. At D wire forms a circular turn DMND of radius R. AB, BC parts are tangential to circular turn at
N and D. Magnetic filed at the center of circle is:
A transverse wave travels on a taut steel wire with a velocity of $v$ when tension in it is $2.06 \times 10^{4}N.$ When the
tension is changed to $T,$ the velocity changed to $\frac{v}{2}.$ The value of $T$ is close to:
a.
$2.50 \times 10^{4}N$
b.
$5.15 \times 10^{3} N$
Correct Answer
c.
$30.5 \times 10^{4} N$
d.
$10.2 \times 10^{2} N$
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Q5nat
The first member of the Balmer series of hydrogen atom has a wavelength of $6561\,A^{\circ }$ . The wavelength of the
second member of the Balmer series (in nm) is_____________
✓ Accepted Answer:486
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Q6mcq
A galvanometer having a coil resistance $100 \Omega$ gives a full scale deflection when a current of $1mA$ is passed
through it. What is the value of the resistance which can convert this galvanometer into a voltmeter given full
scale deflection for a potential difference of $10V?$
a.
$10k\Omega$
b.
$8.9 k\Omega$
c.
$7.9 k\Omega$
d.
$9.9 k\Omega$
Correct Answer
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Q7mcq
A uniform sphere of mass $500\,g$ rolls without slipping on a plane horizontal surface with its centre moving at a
speed of $5.00\, cm \,s^{-1}$ . Its kinetic energy is:
a.
$8.75 \times 10^{-4} J$
Correct Answer
b.
$8.75 \times 10^{-3} J$
c.
$6.25 \times 10^{-4} J$
d.
$1.13 \times 10^{-3} J$
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Q8mcq
An electron (mass $m$ ) with initial velocity $\vec{v}=v_{0}ˆi+v_{0}ˆj$ is in an electric filed $\vec{E} = -E_{0}ˆk.$ If $\lambda _{0}$ is initial de-
Broglie wavelength of electron, its de-Broglie wave length at time $t$ is given by:
A particle of mass $m$ is dropped from a height $h$ above the ground. At the same time another particle of the
same mass is thrown vertically upwards from the ground with a speed of $\sqrt{2gh}.$ If they collide head-on
completely inelastically, the time taken for the combined mass to reach the ground, in units of $\sqrt{\frac{h}{g}}$ is:
a.
$\sqrt{\frac{1}{2}}$
b.
$\sqrt{\frac{3}{4}}$
c.
$\frac{1}{2}$
d.
$\sqrt{\frac{3}{2}}$
Correct Answer
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Q10mcq
In the given circuit, value of $Y$ is:
a.
$0$
Correct Answer
b.
toggles between $0$ and $1$
c.
will not execute
d.
$1$
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An object is gradually moving away from the focal point of a concave mirror along the axis of the mirror. The
graphical representation of the magnitude of linear magnification $(m)$ versus distance of the object from the
mirror $(x)$ is correctly given by
(Graphs are drawn schematically and are not to scale)
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Two liquids of densities $\rho _{1}$ and $\rho _{2}(\rho _{2} = 2\rho _{1})$ are filled up behind a square wall of side $10m$ as shown in figure.
Each liquid has a height of $5m.$ The ratio of the forces due to these liquids exerted on upper part MN to that at
the lower part NO is (Assume that the liquids are not mixing):
a.
$\frac{1}{3}$
b.
$\frac{2}{3}$
c.
$\frac{1}{2}$
d.
$\frac{1}{4}$
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A particle of mass $m$ and charge $q$ is released from rest in a uniform electric field. If there is no other force on
the particle, the dependence of its speed $v$ on the distance $x$ travelled by it is correctly given by (graphs are
schematic and not drawn to scale)
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A particle moves such that its position vector $\vec{r}(t) = cos\omega tˆi+ sin\omega tˆj$ where $\omega$ is a constant and $t$ is time. Then
which of the following statements is true for the velocity $\vec{v}(t)$ and acceleration $\vec{a}(t)$ of the particle:
a.
$\vec{v}$ is perpendicular to $\vec{r}$ and $\vec{a}$ is directed away
from the origin
b.
$\vec{v}$ and $\vec{a}$ both are perpendicular to $\vec{r}$
c.
$\vec{v}$ and $\vec{a}$ both are parallel to $\vec{r}$
d.
$\vec{v}$ is perpendicular to $\vec{r}$ and $\vec{a}$ is directed towards
the origin
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A Carnot engine having an efficiency of $\frac{1}{10}$ is being used as a refrigerator. If the work done on the refrigerator
is $10\,J,$ the amount of heat absorbed from the reservoir at a lower temperature is
a.
$99\,J$
b.
$100\,J$
c.
$1\,J$
d.
$90\,J$
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As shown in figure. When a spherical cavity (centred at $O$ ) of radius $1$ is cut out of a uniform sphere of radius
$R$ (centred at $C$ ), the centre of mass of remaining (shaded part of sphere is at $G,$ i.e., on the surface of the
cavity. $R$ can be determined by the equation:
a.
$(R^{2} +R+ 1)(2 - R) = 1$
b.
$(R^{2} - R-1)(2 - R) = 1$
c.
$(R^{2} - R+ 1)(2 - R) = 1$
d.
$(R^{2} +R-1)(2 - R) = 1$
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A plane electromagnetic wave of frequency $25GHz$ is propagating in vacuum along the z-direction. At a
particular point in space and time, the magnetic filed is given by $^{-8}ˆ$ The corresponding electric
$\vec{B}= 5 \times 10 j T.$
field $\vec{E}$ is (speed of light $= 3 \times 10^{8} m\,s^{-1}$ )
a.
$1.66 \times 10^{-16}ˆi \frac{V}{m}$
b.
$-1.66 \times 10^{-16}ˆi \frac{V}{m}$
c.
$-15ˆi\frac{V}{m}$
d.
$15ˆi\frac{V}{m}$
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A simple pendulum is being used to determine the value of gravitational acceleration $g$ at a certain place. The
length of the pendulum is $25.0\,cm$ and a stopwatch with $1\,s$ resolution measures the time taken for $40$
oscillations to be $50\,s$ . The accuracy in $g$ is:
a.
$5.40%$
b.
$3.40%$
c.
$4.40%$
d.
$2.40%$
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An asteroid is moving directly towards the centre of the earth. When at a distance of $10R$ ( $R$ is the radius of
the earth) from the centre of the earth, it has a speed of $12\, km \,s^{-1}.$ Neglecting the effect of earth's
atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from
the earth is $11.2\,km\,s^{-1})$ ? Give your answer to the nearest integer in $km \,s^{-1}$ __________.
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The series combination of two batteries, both of the same emf $10V,$ but different internal resistance of $20 \Omega$
and $5 \Omega ,$ is connected to the parallel combination of two resistors $30 \Omega$ and $x \Omega .$ The voltage difference across
the battery of internal resistance $20 \Omega$ is zero, the value of $x$ (in $\Omega )$ is____
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Consider a mixture of $n$ moles of helium gas and $2n$ moles of oxygen gas (molecules taken to be rigid) as an
ideal gas. Its $\frac{C_{P}}{C_{V}}$ value will be:
a.
$\frac{19}{13}$
b.
$\frac{67}{45}$
c.
$\frac{40}{27}$
d.
$\frac{23}{15}$
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As shown in the figure, a battery of emf $\in$ is connected to an inductor $L$ and resistance $R$ in series. The switch
is closed at $t= 0.$ The total charge that flows from the battery, between $t= 0$ and $t=t_{c}$ ( $t_{c}$ is the time
constant of the circuit) is:
a.
$\frac{\in L}{eR^{2}}$
b.
$\frac{\in L}{R^{2}}(1 - \frac{1}{e})$
c.
$\frac{\in L}{R^{2}}$
d.
$\frac{\in R}{eL^{2}}$
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Three containers $C_{1},C_{2}$ and $C_{3}$ have water at different temperatures. The table below shows the final
temperature $T$ when different amounts of water (given in liters) are taken from each container and mixed
(assume no loss of heat during the process)
$C_{1} C_{2} C_{3} T$
$1l 2l -- 60^{o}C$
$-- 1l 2l 30^{o}C$
$2l -- 1l 60^{o}C$
$1l 1l 1l \theta$
The value of $\theta$ (in $^{o}C$ to the nearest integer) is___________
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Consider two charged metallic spheres $S_{1}$ and $S_{2}$ of radii $R_{1}$ and $R_{2},$ respectively. The electric fields $E_{1}$ (on
$S_{1}$ ) and $E_{2}$ (on $S_{2}$ ) on their surfaces are such that $\frac{E_{1}}{E_{2}} = \frac{R_{1}}{R_{2}} .$ Then the ratio $V_{1}$ (on $S_{1}$ ) $/V_{2}$ (on $S_{2}$ ) of the
electrostatic potentials on each sphere is:
a.
$\frac{R}{R_{2}}^{1}$
b.
$2$
$(\frac{R_{1}}{R_{2}})$
c.
$(\frac{R_{2}}{R_{1}})$
d.
$3$
$(\frac{R_{1}}{R_{2}})$
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A ball is dropped from the top of a $100\,m$ high tower on a planet. In the last $\frac{1}{2}s$ before hitting the ground, it
covers a distance of $19\,m.$ Acceleration due to gravity (in $m\,s^{-2}$ ) near the surface on that planet is______
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The correct order of the calculated spin-only magnetic moments of complexes $(A)$ to $(D)$ is:
$(A)Ni(CO)_{4}$
$(B) [Ni(H_{2}O)_{6}]Cl_{2}$
$(C)Na_{2}[Ni(CN)_{4}]$
$(D)PdCl_{2}(PPh_{3})_{2}$
a.
$(A) ≈(C) < (B) ≈(D)$
b.
$(C) < (D) < (B) < (A)$
c.
$(C) ≈(D) < (B) < (A)$
d.
$(A) ≈(C) ≈(D) < (B)$
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Among the reactions $(a) -(d),$ the reaction(s) that does/do not occur in the blast furnace during the extraction
of iron is/are:
$(a)CaO+SiO_{2} \rightarrow \rightarrow CaSiO_{3}$
$(b) 3Fe_{2}O_{3}+CO\rightarrow 2\rightarrow Fe_{3}O_{4}+CO_{2}$
$(c)FeO+SiO_{2} \rightarrow \rightarrow FeSiO_{3}$
$(d)FeO Fe+ \frac{1}{2} O_{2}$
a.
$a$
b.
$a$ and $d$
c.
$c$ and $\vec{d}$
d.
$d$
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Among the compounds $A$ and $B$ with molecular formula $C_{9}H_{18}O_{3}, A$ is having higher boiling point than $B.$
The possible structures of $A$ and $B$ are:
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A metal $(A)$ on heating in nitrogen gas gives compound $B.$ on treatment with $B H_{2}O$ gives a colourless gas
which when passed through $CuSO_{4}$ solution gives a dark blue-violet coloured solution. $A$ and $B$ respectively,
are:
a.
$Na$ and $NaNO_{3}$
b.
$Na$ and $Mg_{3}N_{2}$
c.
$Mg$ and $Mg_{3}N_{2}$
d.
$Mg$ and $Mg(NO_{3})_{2}$
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In the following sequence of reactions the maximum number of atoms present in molecule ‘ $C$ ’ in one plane
is_______
$--A^{Red}_{Cu tu}^{hot}_{\vec{b}e} B_{Anhydrous A}^{CH_{3}Cl(1.eq)}_{\vec{l}Cl_{3}} C$
(A is a lowest molecular weight alkyne)
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Among $(a) -(d),$ the complexes that can show geometrical isomerism are:
$(a) [Pt(NH_{3})_{3}Cl]^{+}$
$(b) [Pt(NH_{3})Cl_{5}]^{-}$
$(c) [Pt(NH_{3})_{2}Cl(NO_{2})]$
$(d) [Pt(NH_{3})_{4}ClBr]^{2+}$
a.
$b$ and $c$
b.
$d$ and $a$
c.
$c$ and $d$
d.
$a$ and $b$
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Hydrogen has three isotopes $(A), \,(B)$ and $(C).$ If the number of neutron(s) in $(A), \,(B)$ and $(C)$ respectively,
are $(x), \,(y)$ and $(z),$ the sum of $(x), \,(y)$ and $(z)$ is
a.
$3$
b.
$2$
c.
$4$
d.
$1$
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An unsaturated hydrocarbon $X$ absorbs two hydrogen molecules on catalytic hydrogenation, and also gives
following reaction:
$--X^{(i)O_{3}} A^{[Ag (NH_{3})}\rightarrow \rightarrow^{_{2}]^{+}} B^{(3-oxo-hexanedicarboxylic acid)}X^{will be:}$
$\frac{(ii)\vec{Z}n}{H2O}$
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For the following Assertion and Reason, the correct option is:
Assertion: The $pH$ of water increases with increase in temperature.
Reason: The dissociation of water into $H^{+}$ and $OH^{-}$ is an exothermic reaction.
a.
Both assertion and reason are true, and the reason
is the correct explanation for the assertion.
b.
Both assertion and reason are false.
c.
Both assertion and reason are true, but the reason
is not the correct explanation for the assertion.
d.
Assertion is not true, but reason is true.
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White phosphorus on reaction with concentrated $NaOH$ solution in an inert atmosphere of $CO_{2}$ gives
phosphine and compound $(X). (X)$ on acidification with $HCl$ gives compound $(Y).$ The basicity of compound
$(Y)$ is:
a.
$2$
b.
$1$
c.
$4$
d.
$3$
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Complexes $(ML_{5})$ of metals $Ni$ and $Fe$ have ideal square pyramidal and trigonal bipyramidal geometries,
respectively. The sum of the $90^{o}, 120^{o}$ and $180^{o} L -M -L$ angles in the two complexes is_______
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For the following Assertion and Reason, the correct option is:
Assertion: For hydrogenation reactions, the catalytic activity increases from Group $5$ to Group $11$ metals with
maximum activity shown by Group $7 -9$ elements.
Reason: The reactants are most strongly adsorbed on group $7 -9$ elements.
a.
The assertion is true, but the reason is false
b.
Both assertion and reason are false
c.
Both assertion and reason are true and the reason
is the correct explanation for the assertion
d.
Both assertion and reason are true but the reason
is not the correct explanation for the assertion
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Consider the following plots of rate constant versus $\frac{1}{T}$ for four different reactions. Which of the following
orders is correct for the activation energies of these reactions?
a.
$E_{b} >E_{a} >E_{d} >E_{c}$
b.
$E_{a} >E_{c} >E_{d} >E_{b}$
c.
$E_{c} >E_{a} >E_{d} >E_{b}$
d.
$E_{b} >E_{d} >E_{c} >E_{a}$
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$NaClO_{3}$ is used, even in spacecrafts, to produce $O_{2}.$ The daily consumption of pure $O_{2}$ by a person in $492\,L$
at $1$ atm, $300K.$ How much amount of $NaClO_{3},$ in grams, is required to produce $O_{2}$ for the daily consumption
of a person at $1$ atm, $300K$ ? _____
$NaClO_{3}(s) + Fe(s) O_{2}(g) + NaCl(s) + FeO(s)$
$R = 0 .082 \,L\, atm \, \vec{m}ol^{-1} \,K^{-1}$
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At constant volume, $4\,mol$ of an ideal gas when heated from $300K$ to $500K$ changes its internal energy by
$5000J.$ The molar heat capacity at constant volume is ________
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Let $\alpha = \frac{-1+i\sqrt{3}}{2}$ . If $a= (1 +\alpha )\sum ^{100}_{k=0} \alpha ^{2k}$ and $b=\sum ^{100}_{k=0} \alpha ^{3k}$ , then $a$ and $b$ , are the roots of the quadratic
equation.
a.
$x^{2} + 101x+ 100 = 0$
b.
$x^{2} -102x+ 101 = 0$
c.
$x^{2} -101x+ 100 = 0$
d.
$x^{2} + 102x+ 101 = 0$
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The mirror image of the point $(1, 2, 3)$ , in a plane is $(- \frac{7}{3}, -\frac{4}{3}, -\frac{1}{3} ).$ Which of the following points lies on this
plane?
a.
$(1, \,1, \,1)$
b.
$(1, -1, \,1)$
c.
$(-1, -1, \,1)$
d.
$(-1, -1, -1)$
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Let $S$ , be the set of all functions $f : [0, 1] \rightarrow \rightarrow R$ , which are continuous on $[0, 1]$ , and differentiable on $(0, 1)$ .
Then for every $f$ in $S$ , there exists $c\in (0, 1)$ , depending on $f$ , such that.
a.
$|f(c) - f(1)| < (1 - c) f'(c)$
b.
$\frac{f(1)-f(c)}{1-c} =f'(c)$
c.
$|f(c) +f(1)| < (1 +c) f'(c)$
d.
$|f(c) - f(1)| < f'(c)$
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Let $f : (1, 3) \rightarrow \rightarrow R$ , be a function defined by $f(x) = \frac{x[x]}{1+x^{2}},$ where $[x]$ , denotes the greatest integer $\leq x.$ Then
the range of $f$ , is
Let $\vec{a}= ˆi-2ˆj+ˆk$ and $\vec{b}= ˆi- ˆj+ ˆk$ , be two vectors. If $\vec{c}$ , is a vector such that $\vec{b}\times \vec{c}= \vec{b}\times \vec{a}$ and $\vec{c}\cdot \vec{a}= 0,$
then $\vec{c}\cdot \vec{b}$ , is equal to.
a.
$-\frac{3}{2}$
b.
$\frac{1}{2}$
c.
$-\frac{1}{2}$
d.
$-1$
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If $\frac{\sqrt{2}sin\alpha}{\sqrt{1+cos2\alpha}} = \frac{1}{7}$ and $\sqrt{\frac{1-cos2\beta}{2}} = \frac{1}{\sqrt{10}}, \,\alpha , \beta \in (0, \frac{\pi}{2})$ , then $tan(\alpha + 2\beta )$ , is equal to
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The mean and variance of $20$ observations are found to be $10$ and $4,$ respectively. On rechecking, it was found
that an observation $9$ was incorrect and the correct observation was $11,$ then the correct variance is
a.
$3.99$
b.
$4.01$
c.
$4.02$
d.
$3.98$
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If a line $y=mx+c$ , is a tangent to the circle $(x-3)^{2} +y^{2} = 1$ , and it is perpendicular to a line $L_{1},$ where
$L_{1}$ is the tangent to the circle $x^{2} +y^{2} = 1$ , at the point $(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}})$ , then
a.
$c^{2} -7c+ 6 = 0$
b.
$c^{2} + 7c+ 6 = 0$
c.
$c^{2} + 6c+ 7 = 0$
d.
$c^{2} -6c+ 7 = 0$
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If $\alpha$ and $\beta$ , be the coefficients of $x^{4}$ and $x^{2}$ , respectively in the expansion of
$(x+ \sqrt{x^{2}-1})^{6} +(x- \sqrt{x^{2}-1})^{6}$ , then
a.
$\alpha +\beta = 60$
b.
$\alpha +\beta = -30$
c.
$\alpha - \beta = 60$
d.
$\alpha - \beta = -132$
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Let $f(x)$ , be a polynomial of degree $3$ , such that $f(-1) = 10, f(1) = -6, f(x)$ , has a critical point at $x= -1$
and $f'(x)$ , has a critical point at $x= 1.$ Then $f(x)$ , has local minima at $x=$
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Let $A$ and $B$ , be two events such that the probability that exactly one of them occurs is $\frac{2}{5}$ , and the probability
that $A$ or $B$ , occurs is $\frac{1}{2}$ , then the probability of both of them occur together is.
a.
$0.02$
b.
$0.20$
c.
$0.01$
d.
$0.10$
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Let a line $y=mx(m> 0)$ , intersect the parabola, $y^{2} =x$ , at a point $P,$ other than the origin. Let the tangent
to it a $P$ , meet the $x$ -axis at the point $Q.$ If area $(\Delta OPQ) = 4$ square unit, then $m$ is equal to
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