A gas mixture consists of $3$ moles of oxygen and $5$ moles of argon at temperature $T$ . Assuming the gases to be
ideal and the oxygen bond to be rigid, the total internal energy (in units of $RT$ ) of the mixutre is :
a.
$15$
Correct Answer
b.
$13$
c.
$20$
d.
$11$
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Q2mcq
Shown in the figure is rigid and uniform one meter long rod $AB$ held in horizontal position by two strings tied
to its ends and attached to the ceiling. The rod is off mass $'m'$ and has another weight of mass $2\,m$ hung at a
distance of $75\, cm$ from $A$ . The tension in the string at $A$ is:
a.
$0. 5\,mg$
b.
$2\,mg$
c.
$0. 75\,mg$
d.
$1\,mg$
Correct Answer
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Q3nat
A circular coil of radius $10\, cm$ is placed in a uniform magnetic field of $3. 0 \times 10^{-5}\,T$ with its plane
perpendicular to the field initially. It is rotated at constant angular speed about an axis along the diameter of
coil and perpendicular to magnetic field so that it undergoes half of rotation in $0. 2\,s$ . The maximum value of
EMF induced (in $\mu$ $V$ ) in the coil will be close to the integer....
✓ Accepted Answer:15
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Q4mcq
If speed $V$ , area $A$ and force $F$ are chosen as fundamental units, then the dimension of Young's modulus will be
:
a.
$FA^{2} V^{-1}$
b.
$FA^{2} V^{-3}$
c.
$FA^{2} V^{-2}$
d.
$FA^{-1} V^{0}$
Correct Answer
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Q5mcq
A uniform cylinder of mass $M$ and radius $R$ is to be pulled over a step of height a $(a\, < R)$ by applying a force
$F$ at its centre $'O'$ perpendicular to the plane through the axes of the cylinder on the edge of the step (see
figure). The minimum value of $F$ required is :
A charged particle (mass $m$ and charge $q$ ) moves along $X$ axis with velocity $V_{0}$ . When it passes through the
origin it enters a region having uniform electric field $\vec{E}= -Eˆj$ which extends upto $x = d$ . Equation of path of
electron in the region $x > d$ is:
When radiation of wavelength $A$ is used to illuminate a metallic surface, the stopping potential is $V$ . When the
same surface is illuminated with radiation of wavelength $3A$ , the stopping potential is $\frac{V}{4}$ . If the threshold
wavelength for the metallic surface is $n$ $\lambda$then value of $n$ will be :
✓ Accepted Answer:9
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Q8mcq
A spherical mirror is obtained as shown in the figure from a hollow glass sphere, if an object is positioned in
front of the mirror, what will be the nature and magnification of the image of the object? (Figure down as
schematic and not to scale)
a.
Inverted, real and magnified
b.
Erect, virtual and magnified
c.
Erect, virutual and unmagnified
d.
Inverted, real and unmagnified
Correct Answer
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Q9nat
An engine takes in $5$ moles of air at $20\,^{\circ}C$ and $1\, atm$ , and compresses it adiabatically to $1/10^{th}$ of the original
volume. Assuming air to be a diatomic ideal gas made up of rigid molecules, the change in its internal energy
during this process comes out to be $XkJ$ . The value of $X$ to the nearest integer is:
✓ Accepted Answer:46
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Q10mcq
Interference fringes are observed on a screen by illuminating two thin slits $1\, mm$ apart with a light source
$($ $\lambda$ $= 632. 8\, nm)$ . The distance between the screen and the slits is $100\, cm$ . If a bright fringe is observed on a
screen at distance of $1. 27\, mm$ from the central bright fringe, then the path difference between the waves,
which are reaching this point from the slits is close to :
a.
$1. 27\mu m$
Correct Answer
b.
$2\,. 87 nm$
c.
$2\, nm$
d.
$2. 05\,$ $\mu$ $m$
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Consider four conducing materials copper, tungsten, mercury and aluminum with resistivity $\rho$ $_{C}, \,$ $\rho$ $_{T}, \,$ $\rho$ $_{M}$ and
$\rho$ $_{A}$ respectively. Then :
a.
$\rho$ $_{C} >$ $\rho$ $_{A} >$ $\rho$ $_{T}$
b.
$\rho$ $_{M} >$ $\rho$ $_{A} >$ $\rho$ $_{C}$
c.
$\rho$ $_{A} >$ $\rho$ $_{T} >$ $\rho$ $_{C}$
d.
$\rho$ $_{A} >$ $\rho$ $_{M} >$ $\rho$ $_{C}$
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Train $A$ and train $B$ are running on parallel tracks in the opposite directions with speed of $36\, km \, hour^{-1}$ and
$72\, km \, hour^{-1}$ , respectively. A person is walking in train $A$ in the direction opposite to its motion with a speed
of $1. 8\, km \, hour^{-1}$ . Speed $(in \,m\,s^{-1})$ of this person as observed from train $B$ will be close to: (take the
distance between the tracks as negligible)
a.
$29. 5\,m\,s^{-1}$
b.
$28. 5\,m\,s^{-1}$
c.
$31. 5\,m\,s^{-1}$
d.
$30. 5\,m\,s^{-1}$
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The least count of the main scale of a vernier calipers is $1\, mm$ . Its vernier scale is divided into $10$ divisions
and coincide with $9$ divisions of the main scale. When jaws are touching each other, the $7^{th}$ division of the
vernier scale coincides with a division of the main scale and the zero of vernier scale is lying right side of the
zero of the main scale. When this vernier is used to measure the length of the cylinder the zero of the vernier
scale between $3. 1\, cm$ and $3. 2\, cm$ and $4^{th}$ VSD coincides with the main scale division. The length of the
cylinder is (VSD is vernier scale division)
a.
$3. 2 cm$
b.
$3. 21 cm$
c.
$3. 07 cm$
d.
$2. 99 cm$
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A bead of mass $m$ stays at point $P(a, \,b)$ on a wire bent in the shape of a parabola $y= 4Cx^{2}$ and rotating with
angular speed $\omega$(see figure). The value of $\omega$ is (neglect friction)
a.
$2\sqrt{2gC}$
b.
$\sqrt{2gC}$
c.
$\sqrt{\frac{2gC}{ab}}$
d.
$\frac{\sqrt{2g}}{C}$
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A beam of protons with speed $4 \times 10^{5}\,m\,s^{-1}$ enters a uniform magnetic field of $0. 3\,T$ at an angle $60^{\circ}$ to the
magnetic field, the pitch of the resulting helical path of protons is close to : (Mass of the proton
$= 1. 67 \times 10^{-27}\, kg$ , charge of the proton $= 1. 69 \times 10^{-19}C$ )
a.
$2\, cm$
b.
$5 cm$
c.
$12\, cm$
d.
$4\, cm$
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A plane electromagnetic wave, has frequency of $2. 0 \times 10^{10}\, Hz$ and its energy density is $1. 02 \times 10^{-8}\,J\,m^{-3}$
in vacuum. The amplitude of the magnetic field of the wave is close to $( \frac{1}{4$\pi$$\epsilon$_{0}} = 9 \times 10^{9} \frac{Nm^{2}}{C^{2}})$ and speed of
light $= 3 \times 10^{8}\,m\,s^{-1}$ .
a.
$150\, nT$
b.
$160\, nT$
c.
$180\, nT$
d.
$190\, nT$
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A $5\,$ $\mu$ $F$ capacitor is charged fully by a $220\,V$ supply. It is then disconnected from the supply and is connected
in series to another uncharged $2. 5\,$ $\mu$ $F$ capacitor. If the energy change during the charge redistribution is $\frac{X}{100}\,J$
then value of $X$ to the nearest integer is :
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In a reactor, $2\, kg$ of $_{92}U^{235}$ fuel is fully used up in $30$ days. The energy released fission is $200\, MeV$ . Given that
the Avogadro number, $N = 6. 023 \times 10^{26}$ per kilo mole and $1\,eV = 1. 6 \times 10^{-19}\,J$ . The power output of the
reactor is close to:
a.
$35\, MW$
b.
$60\, MW$
c.
$125\, MW$
d.
$54\, MW$
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A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in
the figure. The radius of vessel is $5\, cm$ and the angular speed of rotation is $\omega$ $\, rad \,s^{-1}$ . The difference in the
height, $h\,(in \, cm)$ of liquid at the Centre of vessel and at the sides of the vessel will be :
a.
$\frac{2$\omega$^{2}}{25g}$
b.
$\frac{5$\omega$^{2}}{2g}$
c.
$\frac{25$\omega$^{2}}{2g}$
d.
$\frac{2$\omega$^{2}}{5g}$
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A particle of mass $m$ with an initial velocity $uˆi$ collides perfectly elastically with a mass $3\,m$ at rest. It moves
with a velocity $vˆj$ after collision, then, $v$ is given by
a.
$v = \sqrt{\frac{2}{3}}u$
b.
$v = \frac{u}{\sqrt{3}}$
c.
$v = \frac{u}{\sqrt{2}}$
d.
$v = \frac{1}{\sqrt{6}}u$
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A small block starts slipping down from a point $B$ on an inclined plane $AB$ , which is making an angle $\theta$with
the horizontal section $BC$ is smooth and the remaining section $CA$ is rough with a coefficient of friction $\mu$ . It
is found that the block comes to rest as it reaches the bottom (point A) of the inclined plane. If $BC = 2AC$ ,
the coefficient of friction is given by $\mu$ $= k\,tan$ $\theta$. The value of $k$ is .......
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Two identical strings $X$ and $Z$ made of same material have tension $T_{X}$ and $T_{Z}$ in then if their fundamental
frequencies are $450\, Hz$ and $300\, Hz$ , respectively, then the ratio $T_{X}/T_{Z}$ is :
a.
$2. 25$
b.
$0. 44$
c.
$1. 25$
d.
$1. 5$
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The mass density of a spherical galaxy varies as $\frac{K}{r}$ over a large distance $r$ from its center. In that region, a small
star is in a circular orbit of radius $R$ . Then the period of revolution, $T$ depends on $R$ as:
a.
$T^{2} \propto \,R$
b.
$T^{2} \propto \,R^{3}$
c.
$T^{2} \propto \frac{1}{R^{3}}$
d.
$T\, \propto R$
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Magnetic materials used for making permanent magnets $(P)$ and magnets in a transformer $(T)$ have different
properties of the following, which property best matches for the type of magnet required?
a.
$T\, :$ Large retentivity, small coercivity
b.
$P\, :$ small retentivity, large coercivity
c.
$T\, :$ Large retentivity, large coercivity
d.
$P :$ large retentivity, large coercivity
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An amplitude modulated waves is represented by expression $v_{m} = 5(1 + 0. 6\, cos \,6280t)\, sin(211 \times 10^{4}t)\,V$ .
The minimum and maximum amplitudes of the amplitudes modulated wave are, respectively:
a.
$\frac{3}{2}V, 5V$
b.
$\frac{5}{2}V, \,8V$
c.
$5V, 8V$
d.
$3V, 5V$
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On heating compound $(A)$ gives a gas $(B)$ which is constituent of air. This gas when treated with $H_{2}$ in the
presence of a catalyst gives another gas $(C)$ which is basic in nature. $(A)$ should not be :
a.
$NaN_{3}$
b.
$Pb (NO_{3})_{2}$
c.
$(NH_{4})_{2}Cr_{2}O_{7}$
d.
$NH_{4}NO_{2}$
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For octahedral $Mn(II)$ and tetrahedral $Ni(II)$ complexes, consider the following statements :
$(I)$ both the complexes can be high spin.
$(II) Ni(II)$ complex can very rarely be of low spin.
$(III)$ with strong field ligands, $Mn(II)$ complexes can be low spin.
$(IV)$ aqueous solution of $Mn(II)\, ions$ is yellow in color.
The correct statements are :
a.
$(I)$ and $(II)$ only
b.
$(I)$ , $(II)$ and $(IV)$ only
c.
$(I)$ , $(II)$ and $(III)$ only
d.
$(II)$ , $(III)$ and $(IV)$ only
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The oxidation states of iron atoms in compounds $(A)$ , $(B)$ and $(C)$ , respectively, are $x, \,y$ and $z$ . Then sum of
$x, \,y$ and $z$ is ........... $Na_{4}[Fe (CN)_{5}(NOS)] Na_{4}[FeO_{4}] [Fe_{2}(CO)_{9}]$
$(A) (B) (C)$
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An open beaker of water in equilibrium with water vapour is in a sealed container. When a few grams of
glucose are added to the beaker of water, the rate at which water molecules :
a.
leaves the vapour increases
b.
leaves the solution increases
c.
leaves the solution decreases
d.
leaves the vapour decreases
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Consider that $d^{6}$ metal ion $(M^{2+})$ forms a complex with aqua ligands, and the spin only magnetic moment of
the complex is $4 .90 BM$ . The geometry and the crystal field stabilization energy of the complex is :
a.
$\,octahedral and\, -2. 4\Delta _{0}+ 2P$
b.
tetrahedral and $-0 .6 \Delta _{t}$
c.
$\,octahedral and\, -1. 6\Delta _{0}$
d.
$\,tetrahedral and\, -1. 6\Delta _{t}+ 1P$
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The mass of gas adsorbed, $x$ , per unit mass of adsorbate, $m$ , was measured at various pressures, $p. \,$ A graph
between $log \,\frac{x}{m}$ and $log \,p$ gives a straight line with slope equal to $2$ and the intercept equal to $0. 4771$ . The
value of $\frac{x}{m}$ at a pressure of $4\, atm$ is :
(Given $log \,3 = 0. 4771$ )
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For the following Assertion and Reason, the correct option is
Assertion (A) : When $Cu$ (II) and sulphide ions are mixed, they react together extremely quickly to give a
solid.
Reason (R) : The equilibrium constant of $Cu^{2+}(aq) + S^{2-}(aq) \rightleftharpoons Cus(s)$ is high because the solubility
product is low.
a.
(A) is false and (R) is true.
b.
Both (A) and (R) are false.
c.
Both (A) and (R) are true but (R) is not the
explanation for (A).
d.
Both (A) and (R) are true and (R) is the
explanation for (A).
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The internal energy change (in $J$ ) when $90\,g$ of water undergoes complete evaporation at $100^{\circ}C$ is ..............
(Given : $\Delta H_{vap}$ for water at $373\,K = 41\, kJ / mol$ , $R = 8. 314\, JK^{-1} \, mol^{-1}$ )
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In Carius method of estimation of halogen, $0. 172\,g$ of an organic compound showed presence of $0. 08\,g$ of
bromine. Which of these is the correct structure of the compound ?
a.
$CH_{3}CHBr_{2}$
d.
$H_{3}C -CH_{2}-Br$
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The Gibbs energy change (in $J$ ) for the given reaction at $[Cu^{2+}]=[Sn^{2}+]= 1 M$ and $298\,K$ is :
$Cu(s) + Sn^{2+}(aq. ) Cu^{2+}(aq. ) + Sn(s)$ ;
$(E^{0}_{Sn^{2+}|Sn} = -0 .16 \vec{V}, E^{0}_{Cu^{2+}}_{Cu} = 0 .34 V,$ Take $F = 96500 C mol^{-1})$
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Let $X = {x\in N\, : \,1 \leq x\leq 17}$ and $Y = {ax+b\, : \,x\in X\, and \,a, \,b\in R, \,a> 0}$ . If mean and variance of
elements of $Y$ are $17$ and $216$ respectively then $a+b$ is equal to
a.
$7$
b.
$-7$
c.
$-27$
d.
$9$
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Let $S$ be the set of all $\lambda \in R$ for which the system of linear equations
$2x- y+ 2z= 2$
$x-2y+\lambda z= -4$
$x+\lambda y+z= 4$
has no solution. Then the set $S$
a.
Contains more than two elements
b.
Is an empty set
c.
Is a singleton
d.
Contains exactly two elements
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Let $y=y(x)$ be the solution of the differential equation, $\frac{2+sinx}{y+1}. \frac{dy}{dx} = -cosx$ , $y> 0, \,y(0) = 1$ . If $y($ $\pi$ $) =a$
and $\frac{dy}{dx}$ at $x=$ $\pi$is $b$ , then the ordered pair $(a, \,b)$ is equal to
a.
$(2, \frac{3}{2})$
b.
$(1, -1)$
c.
$(1, \,1)$
d.
$(2, \,1)$
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Box $1$ contains $30$ cards numbered $1$ to $30$ and Box $2$ contains $20$ cards numbered $31$ to $50$ . A box is selected at
random and a card is drawn from it. The number on the card is found to be a non-prime number. The
probability that the card was drawn from Box $1$ is
a.
$\frac{2}{3}$
b.
$\frac{8}{17}$
c.
$\frac{4}{17}$
d.
$\frac{2}{5}$
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$\{ae^{x} +be^{-x}, -1 \leq x< 1$
If a function $f(x)$ defined by $f(x) = cx^{2}, 1 \leq x\leq 3$ be continuous for some $a,b,c\in R$ and
$\{_{2}$
$ax + 2cx, 3 <x\leq 4$
$f'(0) +f'(2) =e$ , then the value of $a$ is
a.
$\frac{1}{e^{2}-3e+13}$
b.
$\frac{e}{e^{2}-3e-13}$
c.
$\frac{e}{e^{2}+3e+13}$
d.
$\frac{e}{e^{2}-3e+13}$
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If $|x| < 1, \,|y| < 1$ and $x\neq 1$ , then the sum to infinity of the following series
$(x+y) +(x^{2} +xy+y^{2})+(x^{3} +x^{2}y+xy^{2} +y^{3})+. . . . .$ is
a.
$\frac{x+y-xy}{(1+x)(1+y)}$
b.
$\frac{x+y+xy}{(1+x)(1+y)}$
c.
$\frac{x+y-xy}{(1-x)(1-y)}$
d.
$\frac{x+y+xy}{(1-x)(1-y)}$
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If the letters of the word $'MOTHER'$ be permuted and all the words so formed (with or without meaning) be
listed as in a dictionary, then the position of the word $'MOTHER'$ is.....
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$||| |||$
Let $\vec{a}, \,\vec{b}$ and $\vec{c}$ be three unit vectors such that $\vec{a}- \vec{b}^{2} + \vec{a}- \vec{c}^{2} = 8$ . Then $\vec{a}+ 2\vec{b}^{2} + \vec{a}+ 2\vec{c}^{2}$ is equal to
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Let $A$ be a $2 \times 2$ real matrix with entries from ${0, \,1}$ and $|A| \neq 0$ . Consider the following two statements;
$(P)$ If $A\neq l_{2}$ , then $|A| = -1$
$(Q)$ If $|A| = 1$ , then $tr(A) = 2$
Where $l_{2}$ denotes $2 \times 2$ identity matrix and $tr(A)$ denotes the sum of the diagonal entries of $A$ . Then
a.
$(P)$ is false and $(Q)$ is true
b.
Both $(P)$ and $(Q)$ are false
c.
$(P)$ is true and $(Q)$ is false
d.
Both $(P)$ and $(Q)$ are true
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Let $\alpha > 0,\beta > 0$ be such that $\alpha ^{3} +\beta ^{2} = 4$ . If the maximum value of the term independent of $x$ in the
binomial expansion of $(\alpha x \frac{1}{9} +\beta x^{-}\frac{1}{6})^{10}$ is $10k$ , then $k$ is equal to
a.
$336$
b.
$352$
c.
$84$
d.
$176$
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A line parallel to the straight line $2x- y= 0$ is tangent to the hyperbola $\frac{x^{2}}{4} - \frac{y^{2}}{2} = 1$ at the point $(x_{1}, \,y_{1})$ .
Then $x^{2}_{1} + 5y^{2}_{1}$ is equal to
a.
$6$
b.
$8$
c.
$10$
d.
$5$
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