A $15\,g$ mass of nitrogen gas is enclosed in a vessel at a temperature, $27^{o}C$ . The amount of heat transferred to
the gas, so that $R.M.S.$ velocity of molecules is doubled, is about.
$[R= 8 .3 \,J\,(K\, mole)^{-1}]$
a.
$14\, kJ$
b.
$10\, kJ$
Correct Answer
c.
$6\, kJ$
d.
$0 .9 \, kJ$
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Q2mcq
In a young's double slit experiment, the slits are placed $0.320\,mm$ apart. Light of wavelength $\lambda = 500\,nm$ is
incident on the slits. The total number of bright fringes that are observed in the angular range $-30^{o} \leq \theta \leq 30^{o}$
is:
a.
$321$
b.
641
Correct Answer
c.
320
d.
$640$
No explanation saved for this question yet.
Q3mcq
A particle is executing simple harmonic motion $(SHM)$ of amplitude $A,$ along the $x$ -axis, about $x= 0.$ When
its potential Energy $(PE)$ equal kinetic energy $(KE),$ the position of the particle will be:
a.
$A$
b.
$\frac{A}{2}$
c.
$\frac{A}{2\sqrt{2}}$
d.
$\frac{A}{\sqrt{2}}$
Correct Answer
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Q4mcq
A force acts on a $2\, kg$ object so that its position is given as a function of time as $x= 3t^{2} + 5.$ What is the work
done by this force in first $5$ seconds?
a.
$875\,J$
b.
$850\,J$
c.
$950\,J$
d.
$900\,J$
Correct Answer
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Q5mcq
$Ge$ and $Si$ diodes start conducting at $0.3\,V$ and $0.7\,V$ respectively. In the following figure if $Ge$ diode
connection are reversed, the value of $V_{0}$ changes by: (assume that the Ge diode has large breakdown voltage)
a.
$0.8\,V$
b.
$0.4\,V$
Correct Answer
c.
$0.2\,V$
d.
$0.6\,V$
No explanation saved for this question yet.
Q6mcq
The magnetic field associated with a light wave is given, at the origin, by
$B=B_{0} [sin(3.14 \times 10^{7})ct+ sin(6.28 \times 10^{7})ct].$ If this light falls on a silver plate having a work function of
$4 .7 eV,$ what will be the maximum kinetic energy of the photoelectrons?
$(c= 3 \times 10^{8} m s^{-1},h= 6 .6 \times 10^{-34} J s)$
a.
$6 .82 \, eV$
b.
$7 .72 \, eV$
Correct Answer
c.
$12 .5 \, eV$
d.
$8 .52 \, eV$
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Q7mcq
The energy required to take a satellite to a height $h$ above the Earth surface (radius of Earth $= 6.4 \times 10^{3}\, km$ )
is $E_{1}$ , and the kinetic energy required for the satellite to be in a circular orbit at this height is $E_{2}.$ The value of $h$
for which $E_{1}$ and $E_{2}$ are equal, is
a.
$1.28 \times 10^{4}km$
b.
$6.4 \times 10^{3}km$
c.
$3.2 \times 10^{3}km$
Correct Answer
d.
$1.6 \times 10^{3}km$
No explanation saved for this question yet.
Q8mcq
A mass of $10\, kg$ is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope
at some point, the rope deviated at an angle of $45^{\circ}$ at the roof point. If the suspended mass is at equilibrium, the
magnitude of the force applied is $(g= 10\,m\,s^{-2})$
a.
$100\,N$
Correct Answer
b.
$200\,N$
c.
$140\,N$
d.
$70\,N$
No explanation saved for this question yet.
Q9mcq
The pitch and the number of divisions, on the circular scale, for a given screw gauge are $0. 5\, mm$ and $100$
respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies $3$
divisions below the mean line.
The readings of the main scale and the circular scale, for a thin sheet, are $5 .5 \, mm$ and $48$ respectively, the
thickness of this sheet is:
a.
$5.755\,mm$
b.
$5.740\,mm$
c.
$5.725\,mm$
Correct Answer
d.
$5.950\,mm$
No explanation saved for this question yet.
Q10mcq
A particle having the same charge as of electron moves in a circular path of radius $0.5\,cm$ under the influence
of a magnetic field of $0.5\,T.$ If an electric field of 100 V/mmakes it to move in a straight path, then the mass
of the particle is (Given charge of electron $= 1.6 \times 10^{-19}C$ )
a.
$9.1 \times 10^{-31} kg$
b.
$1.6 \times 10^{-27} kg$
c.
$2.0 \times 10^{-24} kg$
Correct Answer
d.
$1.6 \times 10^{-19} kg$
No explanation saved for this question yet.
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A power transmission line feeds input power at $2300\,V$ to a step down transformer with its primary windings
having $4000$ turns. The output power is delivered at $230\,V$ by the transformer. If the current in the primary of
the transformer is $5\,A$ and its efficiency is $90\,%$ , the output current would be:
a.
$35\,A$
b.
$25\,A$
c.
$50\,A$
d.
$45\,A$
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Two point charges $q_{1}(\sqrt{10}\,$ $\mu$ $C)$ and $q_{2}(-25\,$ $\mu$ $C)$ are placed on the $x$ -axis at $x= 1\,m$ and $x= 4\,m$
respectively. The electric field $(in\,V/m)$ at a point $y= 3\,m$ on $y$ -axis is,
$[Take\,\frac{1}{4\pi \epsilon _{0}} = 9 \times 10^{9}\,N\,m^{2}C^{-2}]$
a.
$(-81\,ˆi + 81\,ˆj)\times 10^{2}$
b.
$(81\,ˆi -81\,ˆj)\times 10^{2}$
c.
$(-63\,ˆi + 27\,ˆj)\times 10^{2}$
d.
$(63ˆi -27ˆj)\times 10^{2}$
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A series $AC$ circuit containing an inductor $(20\, mH),$ a capacitor $(120\,$ $\mu$ $F)$ and a resistor $(60\,\Omega )$ is driven by
an $AC$ source of $24\,V/50\, Hz.$ The energy dissipated in the circuit in $60\,s$ is:
a.
$5.17 \times 10^{2}\,J$
b.
$3.39 \times 10^{3}\,J$
c.
$2.26 \times 10^{3}\,J$
d.
$5.65 \times 10^{2}\,J$
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At a given instant, say $t= 0,$ two radioactive substance $A$ and $B$ have equal activities. The ratio $\frac{R_{B}}{R_{A}}$ of their
activities after time $t$ itself decays with time $t$ as $e^{-3t}.$ If the half-life of $A$ is $ln2,$ the half-life of $B$ is:
a.
$2ln2$
b.
$4ln2$
c.
$\frac{ln2}{4}$
d.
$\frac{ln2}{2}$
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One of the two identical conducting wires of length $L$ is bent in the form of a circular loop and the other one
into a circular coil of $N$ identical turns. If the same current is passed in both, the ratio of the magnetic field at
the centre of the loop $(B_{L})$ to that at the centre of the coil $(B_{C}),$ i.e. $\frac{B_{L}}{B_{C}}$ will be
a.
$\frac{1}{N^{2}}$
b.
$\frac{1}{N}$
c.
$N$
d.
$N^{2}$
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In the given circuit the internal resistance of the $18V$ cell is negligible. If $R_{1} = 400\,\Omega , \,R_{3} = 100\,\Omega$ and
$R_{4} = 500\,\Omega$ and the reading of an ideal voltmeter across $R_{4}$ is $5\,V,$ then the value of $R_{2}$ will be:
a.
$550\,\Omega$
b.
$300\,\Omega$
c.
$450\,\Omega$
d.
$230\,\Omega$
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The top of a water tank is open to air and its water level is maintained. It is giving out $0.74\,m^{3}$ water per minute
through a circular opening of $2\, cm$ radius in its wall. The depth of the centre of the opening from the level of
water in the tank is close to:
a.
$2.9\,m$
b.
$4.8\,m$
c.
$6.0\,m$
d.
$9.6\,m$
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A rod of length $50\,cm$ is pivoted at one end. It is raised such that it makes an angle of $30^{o}$ from the horizontal as
shown and released from rest. Its angular speed when it passes through the horizontal (in $rad s^{-1}$ ) will be
$(g= 10\,ms^{-2})$
a.
$\frac{\sqrt{20}}{3}$
b.
$\sqrt{30}$
c.
$\sqrt{\frac{30}{2}}$
d.
$\frac{\sqrt{30}}{2}$
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In a communication system operating at wavelength $800\,nm,$ only one percent of source frequency is available
as signal bandwidth. The number of channels accommodated for transmitting $TV$ signals of band width
$6\,MHz$ are (Take velocity of light $c= 3 \times 10^{8} m/s, \,h= 6.6 \times 10^{-34} J-s$ )
a.
$6.25 \times 10^{5}$
b.
$4.87 \times 10^{5}$
c.
$3.75 \times 10^{6}$
d.
$3.86 \times 10^{6}$
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A musician using an open flute of length $50\, cm$ produces second harmonic sound waves. A person runs
towards the musician from another end of a hall at a speed of $10\, km \,h^{-1}$ . If the wave speed is $330\,m\,s^{-1}$ , the
frequency heard by the running person shall be close to
a.
$333\, Hz$
b.
$500\, Hz$
c.
$666\, Hz$
d.
$753\, Hz$
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Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror $(M_{1})$ and
parallel to the second mirror $(M_{2})$ is finally reflected from the second mirror $(M_{2})$ and parallel to the first
mirror $(M_{1}).$ The angle between the two mirrors will be:
a.
$60^{o}$
b.
$45^{o}$
c.
$90^{o}$
d.
$75^{o}$
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Two carnot engines $A$ and $B$ are operated in series. The first one, $A,$ receives heat at $T_{1}(= 600K)$ and rejects to
a reservoir at temperature $T_{2}.$ The second engine $B$ receives heat rejected by the first engine and, in turn, rejects
to a heat reservoir at $T_{3}(= 400K).$ Calculate the temperature $T_{2}$ if the work outputs of the two engines are
equal:
a.
$500\,K$
b.
$400\,K$
c.
$300\,K$
d.
$600\,K$
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A rod of mass $M$ and length $2L$ is suspended at its middle by a wire. It exhibits torsional oscillations. If two
masses, each of mass $m$ , are attached at a distance $L/2$ from its centre on both sides, it reduces the oscillation
frequency by $20%$ . The value of ratio $m/M$ is close to
a.
$0.17$
b.
$0.77$
c.
$0.57$
d.
$0.37$
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In a car race on straight road, car $A$ takes a time $t$ less than car $B$ at the finish and passes finishing point with a
speed $v$ more than that of car $B.$ Both the cars start from rest and travel with constant acceleration $a_{1}$ and $a_{2}$
respectively. Then $v$ is equal to:
a.
$\frac{2a_{1}a_{2}}{a_{1}+a_{2}}t$
b.
$\frac{a_{1}+a_{2}}{2}t$
c.
$\sqrt{a_{1}a_{2}}t$
d.
$\sqrt{2aa}_{1}_{2}t$
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Charge is distributed within a sphere of radius $R$ with a volume charge density $\rho (r) = \frac{A}{r^{2}}e^{-}\frac{2r}{a} ,$ where $A$ and $a$
are constants. If $Q$ is the total charge of this charge distribution, the radius $R$ is:
a.
$\frac{a}{2}log(\frac{1}{1-^{Q}})$
$2\pi aA$
b.
$alog(\frac{1}{1-^{Q}})$
$2\pi aA$
c.
$alog(1 - \frac{Q}{2\pi aA} )$
d.
$\frac{a}{2} log(1 - \frac{Q}{2\pi aA})$
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A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants
$K_{1}, \,K_{2}, \,K_{3}, \,K_{4}$ arranged as shown in the figure. The effective dielectric constant $K$ will be:
The position co-ordinates of a particle moving in a $3D$ coordinate system is given by
$x=acos$ $\omega$ $t$
$y=asin\omega t$
and $z=a\omega t$
The speed of the particle is:
a.
$\sqrt{2}\,a\omega$
b.
$a\omega$
c.
$2a$ $\omega$
d.
$\sqrt{3}\,a\omega$
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For the following reaction, the mass of water produced from $445\,g\,$ of $C_{57}H_{110}O_{6}$ is:
$2\,C_{57}H_{110}O_{6}(s) + 163O_{2}(g) \rightarrow 114\, CO\rightarrow_{2}(g) + 110H_{2}O(l)$
a.
$490\,g$
b.
$890\,g$
c.
$445\,g$
d.
$495\,g$
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A solution containing $62\,g$ ethylene glycol in $250\,g$ water is cooled to $-10^{o}C$ . If $K_{f}$ for water is
$1.86\,K\, kg \, mol^{-1}$ , the amount of water (in $g$ ) separated as ice is:
a.
$48$
b.
$64$
c.
$16$
d.
$32$
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Homoleptic octahedral complexes of a metal ion $'M^{3+}'$ with three monodentate ligands $L_{1}, \,L_{2}\,and\,L_{3}$ absorb
wavelengths in the region of green, blue and red respectively. The increasing order of the ligand strength is:
a.
$L_{3} >L_{1} >L_{2}$ .
b.
$L_{1} >L_{2} >L_{3}$ .
c.
$L_{2} >L_{1} >L_{3}$ .
d.
$L_{3} >L_{2} >L_{1}$ .
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For the reaction, $2A+B\rightarrow \rightarrow$ products, when the concentration of $A$ and $B$ both were doubled, the rate of the
reaction increased from $0.3\,mol L^{-1}s^{-1}$ to $2.4\,mol L^{-1}s^{-1}. \,$ When the concentration of $A$ alone is doubled,
the rate increased from $0.3\,mol L^{-1}s^{-1}$ to $0.6\,mol L^{-1}s^{-1}.$
Which one of the following statements is correct?
a.
Order of the reaction with respect to $B$ is $2$
b.
Total order of the reaction is $4$
c.
Order of the reaction with respect to $A$ is $2$
d.
Order of the reaction with respect to $B$ is $1$
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At $100^{o}C, \,$ copper $(Cu)$ has $FCC$ unit cell structure with cell edge length of $x$ Å. What is the approximate
density of $Cu$ (in $g cm^{-3}$ ) at this temperature?
$[Atomic\,Mass\,of\,Cu= 63.55\,u]$
a.
$\frac{105}{x^{3}}$
b.
$\frac{205}{x^{3}}$
c.
$\frac{422}{x^{3}}$
d.
$\frac{211}{x^{3}}$
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The entropy change associated with the conversion of $1\,kg$ of ice at $273\,K$ to water vapours at $383\,K$ is:
(Specific heat of water liquid and water vapour are $4.2\,kJ K^{-}$ and $2.0\,kJ K^{-1}kg^{-1}$ ; heat of liquid fusion and
vaporization of water are $334\,kJ kg^{-1}$ and $2491\,kJ kg^{-1}$ , respectively). ( $log$
$273 = 2.436, log 373 = 2.572, log 383 = 2.583$ )
a.
$9.26\,kJ kg^{-1}K^{-1}$
b.
$2.64\,kJ kg^{-1}K^{-1}$
c.
$8.49\,kJ kg^{-1}K^{-1}$
d.
$7.90\,kJ kg^{-1}K^{-1}$
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Which of the following combination of statements is true regarding the interpretation of the atomic orbitals?
$(A)$ An electron in an orbital of high angular momentum stays away from the nucleus than an electron in the
orbital of lower angular momentum.
$(B)$ For a given value of the principal quantum number, the size of the orbit is inversely proportional to the
azimuthal quantum number.
$(C)$ According to wave mechanics, the ground state angular momentum is equal to $\frac{h}{2\pi}$ .
$(D)$ The plot of $ψ$ Vs $r$ for various azimuthal quantum numbers, shows peak shifting towards higher $r$ value.
a.
$(B), \,(C)$
b.
$(A), \,(B)$
c.
$(A), \,(C)$
d.
$(A), \,(D)$
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The test performed on compound $x$ and their inferences are:
Test Inference
$(a) 2, \,4$ - $DNP$ test Coloured precipitate yellow
$(b)$ Iodoform test Yellow precipitate
$(c)$ Azo-dye test No dye formation
Compound $'x'$ is:
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The correct match between Item I and Item II is:
Item I Item II
$(A)$ Benzaldehyde $(P)$ Mobile phase
$(B)$ Alumina $(Q)$ Adsorbent
$(C)$ Acetonitrile $(R)$ Adsorbate
If the standard electrode potential for a cell is $2\,V$ at $300\,K,$ the equilibrium constant $(K)$ for the reaction.
$Zn(s) +Cu^{2+}(aq) \rightleftharpoons Zn^{2+}(aq) +Cu(s)\,$
at $300\,K$ is approximately:
$(R= 8\,JK^{-1}mol^{-1}, \,F = 96000\,C mol^{-1})$
a.
$e^{-160}$
b.
$e^{-80}$
c.
$e^{160}$
d.
$e^{320}$
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Consider the following reversible chemical reactions:
$A_{2}(g) +B_{2}(g) \rightleftharpoons 2^{k_{1}} AB(g)$ .....(1)
$6AB(g) \rightleftharpoons 3^{k_{2}} A_{2}(g) + 3B_{2}(g)$ .....(2)
The relation between $K_{1}$ and $K_{2}$ is:
a.
$K_{2} =K_{1}^{-3}$
b.
$K_{1}K_{2} = \frac{1}{3}$
c.
$K_{2} =K_{1}^{3}$
d.
$K_{1}K_{2} = 3$
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Let $S$ be the set of all triangles in the $xy$ -plane, each having one vertex at the origin and the other two vertices
lie on coordinate axes with integral coordinates. If each triangle in $S$ has area $50$ sq. units, then the number of
elements in the set $S$ is:
a.
$36$
b.
$32$
c.
$9$
d.
$18$
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Let $f$ be a differentiable function from $R$ to $R$ such that $|f(x) - f(y)| \leq 2|x- y|^{3/2},$ for all $x,y\in R.\,$ If
$1$
$f(0) = 1$ then $\int f^{2}(x)dx$ is equal to
$0$
a.
$0$
b.
$1$
c.
$2$
d.
$\frac{1}{2}$
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Let the equations of two sides of a triangle be $3x-2y+ 6 = 0$ and $4x+ 5y-20 = 0.$ If the orthocenter of
this triangle is at $(1, \,1)$ then the equation of it's third side is:
a.
$122y+ 26x+ 1675 = 0$
b.
$26x-122y-1675 = 0$
c.
$26x+ 61y+ 1675 = 0$
d.
$122y-26x-1675 = 0$
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$e^{t} e^{-t}cos\,t e^{-t} sin \,t$
$[ ]$
If $A= e^{t} -e^{-t} cost- e^{-t} sint -e^{-t} sint+e^{-t} cost ,$ then $A$ is:
$[_{t}_{-t}_{-t} ]$
$e 2e sint -2e cost$
a.
Invertible only if $t=\pi$
b.
Not invertible for any $t\in R$
c.
Invertible only if $t= \frac{\pi}{2}$
d.
Invertible for all $t\in R$
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Let $\vec{a}= ˆi +ˆj + \sqrt{2}ˆk, \vec{b}=b_{1}ˆi +b_{2}ˆj + \sqrt{2}ˆk$ and $\vec{c}= 5ˆi +ˆj + \sqrt{2}ˆk$ be three vectors such that the projection
vector of $\vec{b}$ on $\vec{a}$ is $\vec{a}$ . If $\vec{a}+ \vec{b}$ is perpendicular to $\vec{c}$ , then $\vec{b}$ is equal to:
a.
$\sqrt{22}$
b.
$\sqrt{32}$
c.
$6$
d.
$4$
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The number of natural numbers less than $7000$ which can be formed by using the digits $0, \,1, \,3, \,7, \,9$
(repetition of digits allowed) is equal to:
a.
$375$
b.
$250$
c.
$374$
d.
$372$
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$| |$
An urn contains $5$ red and $2$ green balls. A ball is drawn at random from the urn. If the drawn ball is green,
then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original
ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second
ball is red, is:
a.
$\frac{21}{49}$
b.
$\frac{26}{49}$
c.
$\frac{32}{49}$
d.
$\frac{27}{49}$
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The number of all possible positive integral value of $\alpha$ for which the roots of the quadratic equation
$6x^{2} -11x+\alpha = 0$ are rational numbers is:
a.
$5$
b.
$3$
c.
$4$
d.
$2$
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The equation of the plane containing the straight line $\frac{x}{2} = \frac{y}{3} = \frac{z}{4}$ and perpendicular to the plane containing
the straight lines $\frac{x}{3} = \frac{y}{4} = \frac{z}{2}$ and $\frac{x}{4} = \frac{y}{2} = \frac{z}{3}$ is:
a.
$3x+ 2y-3z= 0$
b.
$x+ 2y-2z= 0$
c.
$x-2y+z= 0$
d.
$5x+ 2y-4z= 0$
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For each $x\in R$ , let $[x]$ be the greatest integer less than or equal to $x$ . Then $_{x}lim_{\rightarrow 0\rightarrow }_{-} \frac{x([x]+|x|) sin[x]}{|x|}$ is equal to
a.
$1$
b.
$0$
c.
$-sin 1$
d.
$sin 1$
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Let $A(4, -4)$ and $B(9, 6)$ be points on the parabola, $y^{2} = 4x.$ Let $C$ be chosen on the arc $AOB$ of the
parabola, where $O$ is the origin, such that the area of $\Delta ACB$ is maximum. Then, the area (in sq. units) of
$\Delta ACB$ , is:
a.
$32$
b.
$31\frac{3}{4}$
c.
$30\frac{1}{2}$
d.
$31\frac{1}{4}$
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The sum of the following series $1 + 6 + \frac{9(1^{2}+2^{2}+3^{2})}{7} + \frac{12(1^{2}+2^{2}+3^{2}+4^{2})}{9} + \frac{15(1^{2}+2^{2}+…+5^{2})}{11}+. . . .$ up to $15$ terms,
is:
a.
$7520$
b.
$7510$
c.
$7830$
d.
$7820$
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A data consists of $n$ observations: $x_{1}, \,x_{2}, \, … \,, \,x_{n}.$ If $\sum ^{n}_{i=1} (x_{i}+ 1)^{2} = 9n$ and $\sum ^{n}_{i=1} (x_{i}-1)^{2} = 5n$ , then
the standard deviation of this data is
a.
$5$
b.
$\sqrt{7}$
c.
$\sqrt{5}$
d.
$2$
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Let $a, \,b$ and $c$ be the $7^{th}, \,11^{th}$ and $13^{th}$ terms respectively of a non-constant A.P. . If these are also the three
consecutive terms of a G.P. , then $\frac{a}{c}$ is equal to:
a.
$2$
b.
$\frac{7}{13}$
c.
$\frac{1}{2}$
d.
$4$
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A hyperbola has its centre at the origin, passes through the point $(4, \,2)$ and has transverse axis of length $4$
along the $x-axis.$ Then the eccentricity of the hyperbola is:
a.
$\sqrt{3}$
b.
$\frac{3}{2}$
c.
$\frac{2}{\sqrt{3}}$
d.
$2$
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Let $f : [0,1] \rightarrow \rightarrow R$ be such that $f(xy) =f(x).f(y),$ for all $x,y\in [0,1], \,$ and $f(0) \neq 0.$ If $y=y(x)$ satisfies
the differential equation, $\frac{dy}{dx} =f(x)$ with $y(0) = 1$ then $y(\frac{1}{4})+y(\frac{3}{4})$ is equal to:
a.
$5$
b.
$2$
c.
$3$
d.
$4$
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If both the roots of the quadratic equation $x^{2} - mx+ 4 = 0$ are real and distinct and they lie in the interval
$(1, \,5),$ then $m$ lies in the interval:
Note: In the actual JEE paper interval was $[1, \,5]$
a.
$(-5, -4)$
b.
$(3, \,4)$
c.
$(5, \,6)$
d.
$(4, \,5)$
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