An ideal gas at atmospheric pressure is adiabatically compressed so that its density becomes 32 times of its
initial value. If the final pressure of gas is 128 atmospheres, the value of ' $\gamma$ 'of the gas is :
a.
$1.5$
b.
$1.4$
Correct Answer
c.
$1.3$
d.
$1.6$
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Q2mcq
A dc source of emf $E_{1} = 100\,V$ and internal resistance $r= 0.5\Omega$ , a storage battery of emf $E_{2} = 90\,V$ and an
external resistance $R$ are connected as shown in figure. For what value of R no current will pass through the
battery?
a.
$5.5\Omega$
b.
$3.5\Omega$
c.
$4.5\Omega$
Correct Answer
d.
$2.5\Omega$
No explanation saved for this question yet.
Q3mcq
The change in the value of acceleration of earth towards sun, when the moon comes from the position of solar
eclipse to the position on the other side of earth in line with sun is: (mass of the moon $= 7.36 \times 10^{22}\,kg$ , radius
of the moon's orbit $= 3.8 \times 10^{8}\,m$ ).
a.
$6.73 \times 10^{-5}\,m/s^{2}$
Correct Answer
b.
$6.73 \times 10^{-3}\,m/s^{2}$
c.
$6.73 \times 10^{-2}\,m/s^{2}$
d.
$6.73 \times 10^{-4}\,m/s^{2}$
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Q4mcq
Two blocks of mass $M_{1} = 20\,kg$ and $M_{2} = 12\,kg$ are connected by a metal rod of mass $8\,kg$ . The system is
pulled vertically up by applying a force of $480\,N$ as shown. The tension at the mid-point of the rod is:
a.
$144\,N$
b.
$96\,N$
c.
$240\,N$
d.
$192\,N$
Correct Answer
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Q5mcq
A current $i$ is flowing in a straight conductor of length $L$ . The magnetic induction at a point on its axis at a
distance $\frac{L}{4}$ from its centre will be :
a.
Zero
Correct Answer
b.
$\frac{\mu _{0}i}{2\pi L}$
c.
$\frac{\mu _{0}i}{\sqrt{2}L}$
d.
$\frac{4\mu _{0}i}{\sqrt{5}\pi L}$
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Q6mcq
This question has Statement-1 and Statement-2. Of the four choices given after the Statements, choose the one
that best describes the two Statements. Statement-1: In Young's double slit experiment, the number of fringes
observed in the field of view is small with longer wavelength of light and is large with shorter wavelength of
light. Statement-2: In the double slit experiment the fringe width depends directly on the wavelength of light.
a.
Statement-1 is true, Statement-2 is true and the
Statement-2 is correct explanation of the
Statement-1.
b.
Statement-1 is false and the Statement-2 is true.
c.
Statement-1 is true Statement-2 is true and the
Statement-2 is not correct explanation of the
Statement-1.
Correct Answer
d.
Statement-1 is true and the Statement-2 is false.
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Q7mcq
The image of an illuminated square is obtained on a screen with the help of a converging lens. The distance of
the square from the lens is 40 $cm$ . The area of the image is 9 times that of the square. The focal length of the
lens is :
a.
$36\,cm$
b.
$27\,cm$
c.
$60\,cm$
d.
$30\,cm$
Correct Answer
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Q8mcq
Figure shows a circuit in which three identical diodes are used. Each diode has forward resistance of $20\Omega$ and
infinite backward resistance. Resistors $R_{1} = R_{2} = R_{3} = 50\Omega$ . Battery voltage is $6\,V$ . The current through $R_{3}$
is :
a.
$50\,mA$
Correct Answer
b.
$100\,mA$
c.
$60\,mA$
d.
$25\,mA$
No explanation saved for this question yet.
Q9mcq
Two small equal point charges of magnitude $q$ are suspended from a common point on the ceiling by insulating
mass less strings of equal lengths. They come to equilibrium with each string making angle $\theta$ from the vertical.
If the mass of each charge is $m$ , then the electrostatic potential at the centre of line joining them will be
$(\frac{1}{4\pi \in} =k).\,$
$0$
a.
$2\sqrt{kmgtan\theta}$
b.
$\sqrt{kmgtan\theta}$
c.
$4\sqrt{kmg/ tan\theta}$
Correct Answer
d.
$4\sqrt{kmg/ tan\theta}$
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Q10mcq
Given that $1\,g$ of water in liquid phase has volume $1\,cm^{3}$ and in vapour phase $1671\,cm^{3}$ at atmospheric
pressure and the latent heat of vaporization of water is $2256\,J/g$ ; the change in the internal energy in joules for
$1\,g$ of water at $373\,K$ when it changes from liquid phase to vapour phase at the same temperature is :
a.
2256
b.
167
c.
2089
Correct Answer
d.
1
No explanation saved for this question yet.
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A ball projected from ground at an angle of $45^{\circ }$ just clears a wall in front. If point of projection is $4\,m$ from the
foot of wall and ball strikes the ground at a distance of $6\,m$ on the other side of the wall, the height of the wall is
:
a.
$4.4\,m$
b.
$2.4\,m$
c.
$3.6\,m$
d.
$1.6\,m$
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A point charge of magnitude $+1\mu C$ is fixed at $(0$ , $0, 0)$ . An isolated uncharged spherical conductor, is fixed
with its center at $(4, 0, 0)$ . The potential and the induced electric field at the centre of the sphere is :
a.
$1.8 \times 10^{5}\,V$ and $-5.625 \times 10^{6}\,V/m$
b.
$0\,V$ and $0\,V/m$
c.
$2.25 \times 10^{5}\,V$ and $-5.625 \times 10^{6}\,V/m$
d.
$2.25 \times 10^{5}\,V$ and $0\,V/m$
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A plane electromagnetic wave in a non-magnetic dielectric medium is given by $\vec{E} = \vec{E}_{0}(4 \times 10^{-7}x-50t)$
with distance being in meter and time in seconds. The dielectric constant of the medium is :
a.
$2.4$
b.
$5.8$
c.
$8.2$
d.
$4.8$
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A tennis ball (treated as hollow spherical shell) starting from $O$ rolls down a hill. At point $A$ the ball becomes
air borne leaving at an angle of $30^{\circ }$ with the horizontal. The ball strikes the ground at $B$ . What is the value of
the distance $AB$ ? (Moment of inertia of a spherical shell of mass $m$ and radius $R$ about its diameter $= \frac{2}{3}mR^{2}$ )
a.
$1.87\,m$
b.
$2.08\,m$
c.
$1.57\,m$
d.
$1.77\,m$
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A and B are two sources generating sound waves. A listener is situated at $C$ . The frequency of the source at $A$
is $500\,Hz$ . A, now, moves towards $C$ with a speed $4\,m/s$ . The number of beats heard at $C$ is 6 . When $A$ moves
away from $C$ with speed $4\,m/s$ , the number of beats heard at $C$ is 18 . The speed of sound is $340\,m/s$ . The
frequency of the source at $B$ is :
a.
$500\,Hz$
b.
$506\,Hz$
c.
$512\,Hz$
d.
$494\,Hz$
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This question has Statement-1 and Statement-2. Of the four choices given after the Statements, choose the one
that best describes the two Statements. Statement-1: Short wave transmission is achieved due to the total
internal reflection of the e-m wave from an appropriate height in the ionosphere. Statement-2: Refractive index
of a plasma is independent of the frequency of e-m waves.
a.
Statement-1 is true, Statement- 2 is false.
b.
Statement-1 is false, Statement- 2 is true.
c.
Statement-1 is true, Statement- 2 is true but
Statement $-2$ is not the correct explanation of
statement-1.
d.
Statement-1 is true, Statement-2 is true and
Statement $-2$ is the correct explanation of
Statement-1.
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A certain amount of gas is taken through a cyclic process (A B C D A) that has two isobars, one isochore and
one isothermal. The cycle can be represented on a $P -V$ indicator diagram as :
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Orbits of a particle moving in a circle are such that the perimeter of the orbit equals an integer number of de-
Broglie wavelengths of the particle. For a charged particle moving in a plane perpendicular to a magnetic field,
the radius of the $n^{th\,}$ orbital will therefore be proportional to :
a.
$n^{2}$
b.
$n$
c.
$n^{1/2}$
d.
$n^{1/4}$
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A uniform wire (Young's modulus $2 \times 10^{11}Nm^{-2}$ ) is subjected to longitudinal tensile stress of $5 \times 10^{7}Nm^{-2}$ .
If the overall volume change in the wire is $0.02%$ , the fractional decrease in the radius of the wire is close to:
a.
$1.0 \times 10^{-4}$
b.
$1.5 \times 10^{-4}$
c.
$0.25 \times 10^{-4}$
d.
$5 \times 10^{-4}$
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An LCR circuit as shown in the figure is connected to a voltage source $V_{ac}$ whose frequency can be varied.
The frequency, at which the voltage across the resistor is maximum, is :
a.
$902\,Hz$
b.
$143\,Hz$
c.
$23\,Hz$
d.
$345\,Hz$
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A body starts from rest on a long inclined plane of slope $45^{\circ }$ . The coefficient of friction between the body and
the plane varies as $\mu = 0.3x$ , where $x$ is distance travelled down the plane. The body will have maximum speed
(for $g= 10\,m/s^{2}$ ) when $x=$
a.
$9.8\,m$
b.
$27\,m$
c.
$12\,m$
d.
$3.33\,m$
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To establish an instantaneous current of $2\,A$ through a $1\mu F$ capacitor ; the potential difference across the
capacitor plates should be changed at the rate of:
a.
$2 \times 10^{4}\,V/s$
b.
$4 \times 10^{6}\,V/s$
c.
$2 \times 10^{6}\,V/s$
d.
$4 \times 10^{4}\,V/s$
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A mass $m= 1.0\,kg$ is put on a flat pan attached to a vertical spring fixed on the ground. The mass of the
spring and the pan is negligible. When pressed slightly and released, the mass executes simple harmonic
motion. The spring constant is $500\,N/m$ . What is the amplitude A of the motion, so that the mass $m$ tends to
get detached from the pan ? (Take $g= 10\,m/s^{2}$ ). The spring is stiff enough so that it does not get distorted
during the motion.
a.
$A > 2.0\,cm$
b.
$A = 2.0\,cm$
c.
$A < 2.0\,cm$
d.
$A = 1.5\,cm$
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The focal length of the objective and the eyepiece of a telescope are $50\,cm$ and $5\,cm$ respectively. If the
telescope is focussed for distinct vision on a scale distant $2\,m$ from its objective, then its magnifying power
will be :
a.
$-4$
b.
$-8$
c.
$+8$
d.
$-2$
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To find the resistance of a galvanometer by the half deflection method the following circuit is used with
resistances $R_{1} = 9970\,W, R_{2} = 30\,W$ and $R_{3} = 0$ . The deflection in the galvanometer is d. With
$R_{3} = 107\,W$ the deflection changed to $\frac{d}{2}$ . The galvanometer resistance is approximately:
a.
$107\Omega$
b.
$137\Omega$
c.
$107/2\Omega$
d.
$77\Omega$
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Air of density $1.2\,kg\,m^{-3}$ is blowing across the horizontal wings of an aeroplane in such a way that its speeds
above and below the wings are $150\,ms^{-1}$ and $100\,ms^{-1}$ , respectively. The pressure difference between the
upper and lower sides of the wings, is :
a.
$60Nm^{-2}$
b.
$180Nm^{-2}$
c.
$7500Nm^{-2}$
d.
$12500Nm^{-2}$
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In a series $L -C -R$ circuit, $C = 10^{-11}$ Farad, $L = 10^{-5}$ Henry and $R = 100Ohm$ , when a constant D.C.
voltage $E$ is applied to the circuit, the capacitor acquires a charge $10^{-9}$ C. The D.C. source is replaced by a
sinusoidal voltage source in which the peak voltage $E_{0}$ is equal to the constant D.C. voltage E. At resonance
the peak value of the charge acquired by the capacitor will be :
a.
$10^{-15}C$
b.
$10^{-6}C$
c.
$10^{-10}C$
d.
$10^{-8}C$
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The half-life of a radioactive element $A$ is the same as the mean-life of another radioactive element B. Initially
both substances have the same number of atoms, then :
a.
A and B decay at the same rate always.
b.
A and $B$ decay at the same rate initially.
c.
A will decay at a faster rate than B.
d.
$B$ will decay at a faster rate than $A$ .
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The reaction $X \rightarrow Y\rightarrow$ is an exothermic reaction. Activation energy of the reaction for $X$ into $Y$ is $150\,kJ\,mol^{-1}$
. Enthalpy of reaction is $135\,kJ mol^{-1}$ . The activation energy for the reverse reaction, $Y \rightarrow X\rightarrow$ will be :
a.
$280\,kJ\,mol^{-1}$
b.
$285\,kJ\,mol^{-1}$
c.
$270\,kJ\,mol^{-1}$
d.
$15\,kJ\,mol^{-1}$
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$\,(in kJ)\,$
$Li(s) Li(g) 161$
$Li(g) \rightarrow Li\rightarrow^{+}(g) 520$
$\frac{1}{2}\,F_{2}(\,\vec{g}) \rightarrow F(g)\rightarrow 77$
Given Reaction Energy Change Based on data provided, the
$\,(Electron gain\,$
$\,F(\,g) + e^{-} \rightarrow F\rightarrow^{-}(g)$
$\,enthalpy)\,$
$Li^{+}(g) + F^{-}(g) \rightarrow LiF(s)\rightarrow -1047$
$Li(s) + \frac{1}{2} \,F_{2}(\,g) \rightarrow LiF(s)\rightarrow -617$
value of electron gain enthalpy of fluorine would be :
a.
$-300\,kJ\,mol^{-1}$
b.
$-350\,kJ\,mol^{-1}$
c.
$-328\,kJ\,mol^{-1}$
d.
$-228\,kJ\,mol^{-1}$
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A molecule $M$ associates in a given solvent according to the equation $M\rightleftharpoons (M)_{n}$ . For a certain concentration
of M, the van't Hoff factor was found to be $0.9$ and the fraction of associated molecules was $0.2$ . The value of
$n$ is:
a.
3
b.
5
c.
2
d.
4
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$\,Acid\, K_{a}$
$HCN 6.2 \times 10^{-10}$
Values of dissociation constant, $K_{a}$ are given as follows : Correct order of increasing
$HF 7.2 \times 10^{-4}$
$HNO_{2} 4.0 \times 10^{-4}$
base strength of the base $CN^{-}, F^{-}$ and $NO^{-}_{2}$ will be :
a.
$F^{-} < CN^{-} < NO^{-}_{2}$
b.
$NO^{-}_{2} < CN^{-} < F^{-}$
c.
$F^{-} < NO^{-}_{2} < CN^{-}$
d.
$NO^{-}_{2} < F^{-} < CN^{-}$
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Flocculation value of $BaCl_{2}$ is much less than that of $KCl$ for sol $A$ and flocculation value of $Na_{2}SO_{4}$ is much
less than that of $NaBr$ for sol $B$ . The correct statement among the following is :
a.
Both the sols A and B are negatively charged.
b.
Sol A is positively charged and Sol B is
negatively charged.
c.
Both the sols A and B are positively charged.
d.
Sol A is negatively charged and sol B is
positively charged.
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The density of $3M$ solution of sodium chloride is $1.252\,g\,mL^{-1}$ . The molality of the solution will be : $($ molar
mass, $NaCl = 585\,g\,mol^{-1})$
a.
$260\,m$
b.
$2.18\,m$
c.
$2.79\,m$
d.
$3.00\,m$
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Which one of the following arrangements represents the correct order of solubilities of sparingly soluble salts
$Hg_{2}Cl_{2}, Cr_{2}(SO_{4})_{3}$ , $BaSO_{4}$ and $CrCl_{3}$ respectively?
Bond order normally gives idea of stability of a molecular species. All the molecules viz. $H_{2}, Li_{2}$ and $B_{2}$ have
the same bond order yet they are not equally stable. Their stability order is :
a.
$H_{2} > B_{2} > Li_{2}$
b.
$Li_{2} > H_{2} > B_{2}$
c.
$Li_{2} > B_{2} > H_{2}$
d.
None of these
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Statement-1: The function $x^{2} (e^{x} +e^{-x})$ is increasing for all $x> 0$ . Statement-2: The functions $x^{2}e^{x}$ and
$x^{2}e^{-x}$ are increasing for all $x> 0$ and the sum of two increasing functions in any interval $(a,b)$ is an
increasing function in $(a,b)$ .
a.
Statement-1 is false; Statement-2 is true.
b.
Statement-1 is true; Statement-2 is true;
Statement-2 is not a correct explanation for
Statement-1.
c.
Statement-1 is true; Statement-2 is false.
d.
Statement-1is true; Statement-2 is true;
Statement-2 is a correct explanation for
statement-1.
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If the $x$ -intercept of some line $L$ is double as that of the line, $3x+ 4y= 12$ and the $y$ -intercept of $L$ is half as
that of the same line, then the slope of $L$ is :
a.
$-3$
b.
$-3/8$
c.
$-3/2$
d.
$-3/16$
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The acute angle between two lines such that the direction cosines $l,m,n$ , of each of them satisfy the equations
$l+m+n= 0$ and $l^{2} +m^{2} - n^{2} = 0$ is :
a.
$15^{\circ }$
b.
$30^{\circ }$
c.
$60^{\circ }$
d.
$45^{\circ }$
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$\rightarrow \rightarrow$
If $\hat{a}, \hat{b}$ and $\hat{c}$ are unit vectors satisfying $\hat{a}- \sqrt{3}\hat{b}+ \hat{c}= 0$ , then the angle between the vectors $\hat{a}$ and $\hat{c}$ is :
a.
$\frac{\pi}{4}$
b.
$\frac{\pi}{3}$
c.
$\frac{\pi}{6}$
d.
$\frac{\pi}{2}$
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If the system of linear equations :
$x_{1}+ 2x_{2}+ 3x_{3} = 6$
$x_{1}+ 3x_{2}+ 5x_{3} = 9$
$2x_{1}+ 5x_{2}+ax_{3} =b$
is consistent and has infinite number of solutions, then :
a.
$a= 8,b$ can be any real number
b.
$b= 15,a$ can be any real number
c.
$a\in R-{8}$ and $b\in R-{15}$
d.
$a= 8,b= 15$
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If a circle $C$ passing through $(4, 0)$ touches the circle $x^{2} +y^{2} + 4x-6y-12 = 0$ externally at a point $(1, -1)$
, then the radius of the circle $C$ is :
a.
5
b.
$2\sqrt{5}$
c.
4
d.
$\sqrt{57}$
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Statement-1: The line $x-2y= 2$ meets the parabola, $y^{2} + 2x= 0$ only at the point $(-2, -2)$ . Statement-2:
The line $y=mx- \frac{1}{2m}(m\neq 0)$ is tangent to the parabola, $y^{2} = -2x$ at the point $(-\frac{1}{2m^{2}}, -\frac{1}{m})$
a.
Statement-1 is true; Statement- 2 is false.
b.
Statement-1 is true; Statement-2 is true;
Statement-2 is a correct explanation for
statement-1.
c.
Statement-1 is false; Statement-2 is true.
d.
Statement-1 a true; Statement-2 is true;
Statement-2 is not a correct explanation for
statement-1.
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Let the equations of two ellipses be
$2 2 2 2$
$E_{1} : \frac{x}{3} + \frac{y}{2} = 1\,and\,E_{2} : \frac{x}{16} + \frac{y}{b^{2}} = 1,\,$
If the product of their eccentricities is $\frac{1}{2}$ , then the length of the minor axis of ellipse $E_{2}$ is :
a.
8
b.
9
c.
4
d.
2
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Statement-1: The number of common solutions of the trigonometric equations $2 sin^{2} \theta -cos 2\theta = 0$ and
$2 cos^{2} \theta -3 sin\theta = 0$ in the interval $[0, 2\pi ]$ is two. Statement-2: The number of solutions of the equation,
$2 cos^{2} \theta -3 sin\theta = 0$ in the interval $[0,\pi ]$ is two.
a.
Statement-1 is true; Statement-2 is true;
Statement-2 is a correct explanation for
statement-1.
b.
Statement-1 is true; Statement-2 is true;
Statement-2 is not a correct explanation for
statement-1.
c.
Statement-1 is false; Statement-2 is true.
d.
Statement-1 is true; Statement-2 is false.
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Given sum of the first $n$ terms of an A.P. is $2n+ 3n^{2}$ . Another A.P. is formed with the same first term and
double of the common difference, the sum of $n$ terms of the new A.P. is :
a.
$n+ 4n^{2}$
b.
$6n^{2} - n$
c.
$n^{2} + 4n$
d.
$3n+ 2n^{2}$
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Consider the differential equation :
$3$
$\frac{dy}{dx} = \frac{y}{2 (xy^{2}-x^{2})}$
Statement-1: The substitution $z=y^{2}$ transforms the above equation into a first order homogenous differential
equation. Statement-2: The solution of this differential equation is $y^{2}e^{-y^{2}}/x=C$ .
a.
Both statements are false.
b.
Statement-1 is true and statement- 2 is false.
c.
Statement-1 is false and statement-2 is true.
d.
Both statements are true.
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If $\alpha$ and $\beta$ are roots of the equation $x^{2} +px+ \frac{3p}{4} = 0$ , such that $|\alpha - \beta | = \sqrt{10}$ , then $p$ belongs to the set :
a.
${2, -5}$
b.
${-3, 2}$
c.
${-2, 5}$
d.
${3, -5}$
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Given two independent events, if the probability that exactly one of them occurs is $\frac{26}{49}$ and the probability that
none of them occurs is $\frac{15}{49}$ , then the probability of more probable of the two events is :
a.
$4/7$
b.
$6/7$
c.
3/7
d.
$5/7$
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If two vertices of an equilateral triangle are $A(-a, 0)$ and $B(a, 0),a> 0$ , and the third vertex C lies above $x$ -
axis then the equation of the circumcircle of $\triangle ABC$ is :
a.
$3x^{2} + 3y^{2} -2\sqrt{3}ay= 3a^{2}$
b.
$3x^{2} + 3y^{2} -2ay= 3a^{2}$
c.
$x^{2} +y^{2} -2ay=a^{2}$
d.
$x^{2} +y^{2} - \sqrt{3}ay=a^{2}$
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