A stationary observer receives sound from two identical tuning forks, one of which approaches and the other
one recedes with the same speed (much less than the speed of sound). The observer hears $2\,beats/sec$ . The
oscillation frequency of each tuning fork is $v_{0} = 1400\,Hz$ and the velocity of sound in air is $350\,m/s$ . The
speed of each tuning fork is close to:
a.
$\frac{1}{2}m/s$
b.
$1m/s$
c.
$\frac{1}{4}m/s$
Correct Answer
d.
$\frac{1}{8}m/s$
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Q2mcq
An emf of $20\,V$ is applied at time $t= 0$ to a circuit containing in series $10\,mH$ inductor and $5\,\Omega$ resistor. The
ratio of the currents at time $t= \infty$ and at $t= 40\,s$ is close to: (Take $e^{2} = 7.389$ )
a.
$1.06$
Correct Answer
b.
$1.15$
c.
$1.46$
d.
$0.84$
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Q3mcq
In a building there are $15$ bulbs of $45W$ , $15$ bulbs of $100W, 15$ small fans of $10W$ and $2$ heaters of $1kW$ . The
voltage of electric main supply is $220V$ . The minimum fuse capacity (rated value) of the building will be:
a.
$5A$
b.
$25A$
c.
$15A$
d.
$20A$
Correct Answer
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Q4nat
$M$ grams of steam at $100^{o}C$ is mixed with $200g$ of ice at its melting point in a thermally insulated container. If
it produces liquid water at $40^{o}C$ [heat of vaporization of water is $540cal/g$ and heat of fusion of ice is $80cal/g$
], the value of $M$ is ________
✓ Accepted Answer:40
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Q5nat
The balancing length for a cell is $560cm$ in a potentiometer experiment. When an external resistance of $10\Omega$ is
connected in parallel to the cell, the balancing length changes by $60cm$ . If the internal resistance of the cell is
$\frac{n}{10}\Omega$ , where n is an integer then value of n is ________
✓ Accepted Answer:12
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Q6mcq
A thin lens made of glass (refractive index $= 1.5$ ) of focal length $f = 16cm$ is immersed in a liquid of
refractive index $1.42$ . If its focal length in liquid is $f_{l}$ , then the ratio $f_{l}/f$ is closest to the integer:
a.
$1$
b.
$9$
Correct Answer
c.
$5$
d.
$17$
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Q7mcq
In the figure, potential difference between $A$ and $B$ is:
a.
$10\,V$
Correct Answer
b.
$5\,V$
c.
$15\,V$
d.
$0 V$
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Q8nat
A $60pF$ capacitor is fully charged by a $20V$ supply. It is then disconnected from the supply and is connected to
another uncharged $60pF$ capacitor in parallel. The electrostatic energy that is lost in this process by the time
the charge is redistributed between them is (in $nJ$ ) ________
✓ Accepted Answer:6
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Q9mcq
An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum
diameters of the pipes are $6.4cm$ and $4.8cm$ , respectively. The ratio of the minimum and the maximum
velocities of fluid in this pipe is:
a.
$\frac{9}{16}$
Correct Answer
b.
$\frac{\sqrt{3}}{2}$
c.
$\frac{3}{4}$
d.
$\frac{81}{256}$
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Q10mcq
An elevator in a building can carry a maximum of $10$ persons, with the average mass of each person being $68\,kg$
. The mass of the elevator itself is $920\,kg$ and it moves with a constant speed of $3\,m/s$ . The frictional force
opposing the motion is $6000\,N$ . If the elevator is moving up with its full capacity, the power delivered by the
motor to the elevator $(g = 10m/s^{2})$ must be at least:
a.
$56300W$
b.
$62360W$
c.
$48000W$
d.
$66000W$
Correct Answer
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The figure gives experimentally measured $B$ vs. $H$ variation in a ferromagnetic material. The retentivity,
coercivity and saturation, respectively, of the material are:
a.
$1.5T, 50A/m$ and $1.0T$
b.
$1.5T, 50A/m$ and $1.0T$
c.
$150A/m, 1.0T$ and $1.5T$
d.
$1.0T, 50A/m$ and $1.5T$
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The sum of two forces $\vec{P}$ and $\vec{Q}$ is $\vec{R}$ such that $\vec{R} = \vec{P}$ . Find the angle between resultant of $2\vec{P}$ and $\vec{Q}$ and $\vec{Q}$
, ________
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An electron (of mass $m$ ) and a photon have the same energy $E$ in the range of a few $eV$ . The ratio of the de-
Broglie wavelength associated with the electron and the wavelength of the photon is ( $c =$ speed of light in
vacuum)
a.
$\frac{1}{c}(\frac{2E}{m})^{1/2}$
b.
$c(2mE)^{1/2}$
c.
$\frac{1}{c}(\frac{E}{2m})^{1/2}$
d.
$(\frac{E}{2m})^{1/2}$
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Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to
produce work) between temperatures, $T_{1}$ and $T_{2}$ . The temperature of the hot reservoir of the first engine is $T_{1}$
and the temperature of the cold reservoir of the second engine is $T_{2}$ . $T$ is temperature of the sink of first engine
which is also the source for the second engine. How is $T$ related to $T_{1}$ and $T_{2}$ , if both the engines perform
equal amount of work?
a.
$T = \frac{2T_{1}T_{2}}{T_{1}+T_{2}}$
b.
$T = \frac{T_{1}+T_{2}}{2}$
c.
$T = \sqrt{TT}_{1}_{2}$
d.
$T = 0$
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Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently, the mean collision time
between the gas molecule changes from $τ_{1}$ to $τ_{2}$ . If $\frac{C}{C_{v}}^{P} =\gamma$ for this gas then a good estimate for $\frac{τ}{τ_{1}}^{2}$ is given by
a.
$2$
b.
$\frac{1}{2}$
c.
$(\frac{1}{2})^{\gamma }$
d.
$( \frac{1}{2})\frac{\gamma +1}{2}$
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The electric field of a plane electromagnetic wave is given by $\vec{E} =E_{0} \frac{ˆi+ˆj}{\sqrt{2}}cos(kz+\omega t)$ . At $t= 0$ , a positively
charged particle is at the point $(x,y,z) =(0, 0, \frac{\pi}{k} )$ . If its instantaneous velocity at $(t= 0)$ is $v_{0}ˆk$ , the force
acting on it due to the wave is:
a.
parallel to $\frac{ˆi+ˆj}{\sqrt{2}}$
b.
zero
c.
antiparallel to $\frac{ˆi+ˆj}{\sqrt{2}}$
d.
parallel to $ˆk$
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In a Young’s double slit experiment, the separation between the slits is $0.15mm$ . In the experiment, a source
of light of wavelength $589nm$ is used and the interference pattern is observed on a screen kept $1.5m$ away. The
separation between the successive bright fringes on the screen is:
a.
$6.9mm$
b.
$3.9mm$
c.
$5.9mm$
d.
$4.9mm$
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Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible
force $F$ at a point $b$ above its centre of mass (see figure). If the coefficient of friction is $\mu = 0.4$ , the
maximum possible value of $100 \times \frac{b}{a}$ for a box not to topple before moving is ________
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A box weighs $196N$ on a spring balance at the north pole. Its weight recorded on the same balance if it is shifted
to the equator is close to (Take $g = 10ms^{-2}$ at the north pole and the radius of the earth $= 6400km$ ):
a.
$195.66N$
b.
$194.32N$
c.
$194.66N$
d.
$195.32N$
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A mass of $10\,kg$ is suspended by a rope of length $4\,m$ , from the ceiling. A force $F$ is applied horizontally at the
mid-point of the rope such that the top half of the rope makes an angle of $45^{\circ}$ with the vertical. Then $F$ equals:
(Take $g = 10\,m\,s^{-2}$ and the rope to be massless)
a.
$100N$
b.
$90N$
c.
$70N$
d.
$75N$
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A particle of mass $m$ and charge $q$ has an initial velocity $\vec{v}=v_{0}ˆj$ . If an electric field $\vec{E} =E_{0}ˆi$ and magnetic
field $\vec{B}=B_{0}ˆi$ act on the particle, its speed will double after a time
a.
$\frac{2mv_{0}}{qE_{0}}$
b.
$\frac{3mv_{0}}{qE_{0}}$
c.
$\frac{\sqrt{3}mv_{0}}{qE_{0}}$
d.
$\frac{\sqrt{2}mv_{0}}{qE_{0}}$
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A planar loop of wire rotates in a uniform magnetic field. Initially, at $t= 0$ , the plane of the loop is
perpendicular to the magnetic field. If it rotates with a period of $10s$ about an axis in its plane then the
magnitude of induced emf will be maximum and minimum, respectively at:
a.
$2.5\,s$ and $7.5\,s$
b.
$2.5\,s$ and $5.0\,s$
c.
$5.0\,s$ and $7.5\,s$
d.
$5.0\,s$ and $10. 0\,s$
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Mass per unit area of a circular disc of radius a depends on the distance $r$ from its centre as $\sigma (r) =A+Br$ .
The moment of inertia of the disc about the axis, perpendicular to the plane and passing through its centre is:
a.
$2\pi a^{4}( \frac{A}{4} + \frac{aB}{5})$
b.
$2\pi a^{4}( \frac{aA}{4} + \frac{B}{5})$
c.
$\pi a^{4}(\frac{A}{4} + \frac{aB}{5} )$
d.
$2\pi a^{4}(\frac{A}{4} + \frac{B}{5} )$
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Identify the correct labels of $A, B$ and $C$ in the following graph from the options given below:
Root mean square speed $(V_{rms});$ most proable speed $(V_{mp});$ Average speed $(V_{av})$
a.
$A -V_{mp}; B -V_{rms}; C -V_{av}$
b.
$A -V_{av}; B -V_{rms}; C -V_{mp}$
c.
$A -V_{rms}; B -V_{mp}; C -V_{av}$
d.
$A -V_{mp}; B -V_{av}; C -V_{rms}$
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For the following reactions
where,
$k_{s}$ and $k_{e}$ , are respectively, the rate constants for substitution and elimination, and $\mu$ $= \frac{k_{s}}{k_{e}}$ , the correct option
is ________
a.
$\mu$ $_{B} >$ $\mu$ $_{A}$ and $k_{e}(A) > k_{e}(B)$
b.
$\mu$ $_{A} >$ $\mu$ $_{B}$ and $k_{e}(B) > k_{e}(A)$
c.
$\mu$ $_{B} >$ $\mu$ $_{A}$ and $k_{e}(B) > k_{e}(A)$
d.
$\mu$ $_{A} >$ $\mu$ $_{B}$ and $k_{e}(A) > k_{e}(B)$
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Two open beakers one containing a solvent and the other containing a mixture of that solvent with a non
volatile solute are together sealed in a container. Over time:
a.
the volume of the solution increases and the
volume of the solvent decreases
b.
the volume of the solution decreases and the
volume of the solvent increases
c.
the volume of the solution and the solvent does
not change the volume of the solution does not
d.
change and the volume of the solvent decreases
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The number of possible optical isomers for the complexes $MA_{2}B_{2}$ with $sp^{3}$ and $dsp^{2}$ hybridized metal atom,
respectively, is:
Note: $A$ and $B$ are unidentate neutral and unidentate monoanionic ligands, respectively.
a.
$0$ and $2$
b.
$2$ and $2$
c.
$0$ and $0$
d.
$0$ and $1$
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Consider the following reactions:
$NaCl + K_{2}Cr_{2}O_{7}+ H_{2}SO_{4} \rightarrow (A)+\rightarrow$ side products
$(Conc.)$
$(A) + NaOH \rightarrow (B)+\rightarrow$ side products
$(B) + H_{2}SO_{4} + H_{2}O_{2} \rightarrow (C)+\rightarrow$ side products
$(dilute)$
The sum of the total number of atoms in one molecule each of $(A), (B)$ and $(C)$ is ________
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For the reaction $2H_{2}(g) + 2NO(g) \rightarrow N\rightarrow_{2}(g) + 2H_{2}O(g)$ the observed rate expression is, rate $= k_{f}[NO]^{2}[H_{2}]$ .
The rate expression for the reverse reaction is:
a.
$k_{b}[N_{2}][H_{2}O]^{2}$
b.
$k_{b}[N_{2}][H_{2}O]^{2}/[NO]$
c.
$k_{b}[N_{2}][H_{2}O]$
d.
$k_{b}[N_{2}][H_{2}O]^{2}/[H_{2}]$
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The standard heat of formation $(\Delta _{f}H_{298}^{0} )$ of ethane (in $kJ/mol$ ), if the heat of combustion of ethane,
hydrogen and graphite are $-1560, -393.5$ and $-286\,kJ/mol$ , respectively is ________
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Among statements $(a) -(d)$ , the correct ones are:
$(a)$ Decomposition of hydrogen peroxide gives di-oxygen.
$(b)$ Like hydrogen peroxide, compounds, such as $KClO_{3}, Pb(NO_{3})$ and $NaNO_{3}$ When heated liberate di-
oxygen.
$(c) 2$ -Ethylanthraquinone is useful for the industrial preparation of hydrogen peroxide.
$(d)$ Hydrogen peroxide is used for the manufacture of sodium perborate.
a.
$(a), (b), (c)$ and $(d)$
b.
$(a), (b),$ and $(c)$ only
c.
$(a), (c),$ and $(d)$ only
d.
$(a)$ and $(c)$ only
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Among the statements $(a) -(d)$ , the incorrect ones are:
$(a)$ Octahedral $Co(III)$ complexes with strong field ligands have very high magnetic moments
$(b)$ When $\Delta _{0} <P$ , the d-electron configuration of $Co(III)$ in an octahedral complex is $t^{4}_{eg}e^{2}_{g}$
$(c)$ Wavelength of light absorbed by $[Co(en)_{3}]^{3+}$ is lower than that of $[CoF_{6}]^{3-}$
$(d)$ If the $\Delta _{0}$ for an octahedral complex of $Co(III)$ is $18,000cm^{-1}$ , the $\Delta _{t}$ for its tetrahedral complex with the
same ligand will be $16,000cm^{-1}$ .
a.
$(a)$ and $(d)$ only
b.
$(c)$ and $(d)$ only
c.
$(a)$ and $(b)$ only
d.
$(b)$ and $(c)$ only
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The flocculation value of $HCl$ for arsenic sulphide $sol$ is $30\,mmolL^{-1}$ . If $H_{2}SO_{4}$ is used for the flocculation of
arsenic sulphide, the amount, in grams, of $H_{2}SO_{4}$ in $250ml$ required for the above purpose is ________
(molecular mass of $H_{2}SO_{4} = 98\,g/mol$
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Within each pair of elements $F$ and $Cl$ , $S$ and $Se$ , and $Li$ and $Na$ , respectively, the elements that release more
energy upon an electron gain are
a.
$Cl, Se$ and $Na$
b.
$Cl, S$ and $Li$
c.
$F, S$ and $Li$
d.
$F, Se$ and $Na$
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$3\,g$ of acetic acid is added to $250\,mL$ of $0.1\,M\,HCl$ and the solution made up to $500\,mL$ . To $20\,mL$ of this
solution $\frac{1}{2\,}mL$ of $5M\,NaOH$ is added. The $pH$ of the solution is ________
[Given: $pKa$ of acetic acid $= 4.75,$ molar mass of acetic acid $60\,g/mol, log 3 = 0.4771$ , Neglect any changes
in volume]
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A chromatography column, packed with silica gel as stationary phase, was used to separate a mixture of
compounds consisting of $(A)$ benzanilide $(B)$ aniline and $(C)$ acetophenone. When the column is eluted with a
mixture of solvents, hexane:ethyl acetate $(20 : 80)$ , the sequence of obtained compounds is:
a.
$(B), (C)$ and $(A)$
b.
$(B), (A)$ and $(C)$
c.
$(C), (A)$ and $(B)$
d.
$(A), (B)$ and $(C)$
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If the system of linear equations,
$x+y+z= 6$
$x+ 2y+ 3z= 10$
$3x+ 2y+\lambda z=\mu$
has more than two solutions, then $\mu - \lambda ^{2}$ , is equal to.
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Let $y=y(x)$ be a function of $x$ satisfying $y\sqrt{1 -x^{2}} =k- x\sqrt{1 -y^{2}}$ where $k$ is a constant and $y(\frac{1}{2} )= -\frac{1}{4}$
.Then $\frac{dy}{dx}$ at $x= \frac{1}{2}$ , is equal to
a.
$-\frac{\sqrt{5}}{4}$
b.
$-\frac{\sqrt{5}}{2}$
c.
$\frac{2}{\sqrt{5}}$
d.
$\frac{\sqrt{5}}{2}$
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If $\theta _{1}$ and $\theta _{2}$ be respectively the smallest and the largest values of $\theta$ in $(0, 2\pi ) -{\pi }$ which satisfy the equation,
$2cot^{2}\theta - \frac{5}{sin\theta} + 4 = 0$ , then $\int ^{\theta _{2}} cos^{2}3\theta d\theta$ is equal to:
$\theta _{1}$
a.
$\frac{\pi}{3}$
b.
$\frac{2\pi}{3}$
c.
$\frac{\pi}{3} + \frac{1}{6}$
d.
$\frac{\pi}{9}$
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$\frac{1}{x}log_{e}(\frac{1+3x}{1-2x}), when\,x\neq 0$
If the function $f$ defined on $(-\frac{1}{3}, 1/3)$ by $f(x) ={$ , is continuous, then $k$ is
$k , when\,x= 0$
equal to.
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If the foot of the perpendicular drawn from the point $(1, 0, 3)$ on a line passing through $(\alpha , 7,1)$ is $(\frac{5}{3} , \frac{7}{3}, \frac{17}{3} )$ ,
then $\alpha$ is equal to
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If $3x+ 4y= 12\sqrt{2}$ is a tangent o the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{9} = 1$ for some $a\in R,$ then the distance between the foci
of the ellipse is
a.
$2\sqrt{7}$
b.
$4$
c.
$2\sqrt{5}$
d.
$2\sqrt{2}$
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Let $a_{1},a_{2},a_{3}, …$ , be a $G. P.$ such that $a_{1} < 0,a_{1}+a_{2} = 4$ and $a_{3}+a_{4} = 16$ . If $\sum ^{9}_{i=1} a_{i} = 4\lambda$ , then $\lambda$ , is
equal to.
a.
$-513$
b.
$-171$
c.
$171$
d.
$\frac{511}{3}$
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In a workshop, there are five machines and the probability of any one of them to be out of service on a day is
$\frac{1}{4}$ . If the probability that at most two machines will be out of service on the same day is $(\frac{3}{4} )^{3}k,$ then $k$ is
equal to
a.
$\frac{17}{8}$
b.
$\frac{17}{4}$
c.
$\frac{17}{2}$
d.
$4$
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Let $\alpha$ and $\beta$ be the roots of the equation $x^{2} - x-1 = 0$ . If $p_{k} = (\alpha )^{k} + (\beta )^{k},k\geq 1,$ then which one of the
following statements is not true?
a.
$p_{3} =p_{5}- p_{4}$
b.
$p_{5} = 11$
c.
$(p_{1}+p_{2}+p_{3}+p_{4}+p_{5}) = 26$
d.
$p_{5} =p_{2}\cdot p_{3}$
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Let $X = {n\in N : 1 \leq n\leq 50}$ . If $A= {n\in X : \,n\,is\,a\,multiple\,of\,2}$ and
$B = {n\in X : \,n\,is\,a\,multiple\,of\,7}$ , then the number of elements in the smallest subset of $X$ , containing both
$A$ and $B$ , is.
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Let $y=y(x)$ be the solution curve of the differential equation, $(y^{2} - x)\frac{dy}{dx} = 1$ , satisfying $y(0) = 1$ . This
curve intersects the $X-$ axis at a point whose abscissa is
a.
$2 - e$
b.
$-e$
c.
$2$
d.
$2 +e$
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Let $A = [a_{ij}]$ and $B = [b_{ij}]$ be two $3 \times 3$ real matrices such that $b_{ij} = (3)^{(i+j-2)}a_{ij}$ , where $i,j= 1,2, 3$ . If the
determinant of $B$ is $81$ , then determinant of $A$ is
a.
$\frac{1}{3}$
b.
$3$
c.
$\frac{1}{81}$
d.
$\frac{1}{9}$
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Let $f(x)$ be a polynomial of degree $5$ such that $x= \pm 1$ are its critical points. If $_{x}lim_{\rightarrow 0\rightarrow } (2 + \frac{f(x)}{x^{3}})= 4,$ then
which one of the following is not true?
a.
$f$ is an odd function
b.
$f(1) -4f(-1) = 4$ . $x= 1$ is a point of
maximum and $x= -1$
c.
$x= 1$ is a point of local minimum and $x= -1$ is
a point of local maximum
d.
$x= 1$ is a point of local maxima of $f$
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$\rightarrow \rightarrow$
Let $\vec{a}, \vec{b}$ and $\vec{c}$ , be three unit vectors such that $\vec{a}+ \vec{b}+ \vec{c}= 0$ . If $\lambda = \vec{a}\cdot \vec{b}+ \vec{b}\cdot \vec{c}+ \vec{c}\cdot \vec{a}$ and
$\vec{d}= \vec{a}\times \vec{b}+ \vec{b}\times \vec{c}+ \vec{c}\times \vec{a}$ , then the order pair, $(\lambda , \vec{d})$ , is equal to.
a.
$( \frac{3}{2}, 3\vec{a}\times \vec{c})$
b.
$(-\frac{3}{2}, 3\vec{c}\times \vec{b})$
c.
$(\frac{3}{2}, 3\vec{b}\times \vec{c})$
d.
$(-\frac{3}{2}, 3\vec{a}\times \vec{b})$
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