An electric field is given by $(6ˆi + 5ˆj + 3ˆk)\,N\,C^{-1}$ . The electric flux through a surface area $30ˆi\,m^{2}$ lying in
YZ-plane(in SI unit) is:
a.
$90$
b.
$150$
c.
$180$
Correct Answer
d.
$60$
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Q2mcq
In an a.c. circuit, voltage and current are given by: $V = 100 sin(100t)\,V$ and $I = 100 sin(100t+ \frac{\pi}{3})\, mA$
respectively. The average power dissipated in one cycle is :
a.
$5\,W$
b.
$10\,W$
c.
$2. 5\,W$
Correct Answer
d.
$25\,W$
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Q3mcq
A small liquid drop of radius $R$ is divided into $27$ identical liquid drops. If the surface tension is $T$ , then the
work done in the process will be :
a.
$8\pi R^{2}T$
Correct Answer
b.
$3\pi R^{2}T$
c.
$\frac{1}{8}\pi R^{2}T$
d.
$4\pi R^{2}T$
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Q4nat
Hydrogen atom is bombarded with electrons accelerated through a potential different of $V$ , which causes
excitation of hydrogen atoms. If the experiment is being formed at $T = 0\,K$ . The minimum potential
difference needed to observe any Balmer series lines in the emission spectra will be $\frac{\alpha}{10} \,V$ , where $\alpha =$
_________.(Write the value to the nearest integer)
✓ Accepted Answer:121
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Q5nat
A charge of $4. 0\,\mu C$ is moving with a velocity of $4. 0 \times 10^{6}\,m\,s^{-1}$ along the positive $y$ -axis under a magnetic
field $B$ of strength $(2ˆk)\,T$ . The force acting on the charge is $xˆi\,N$ . The value of $x$ is ______.
✓ Accepted Answer:32
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Q6mcq
The truth table for this given circuit is:
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Q7nat
In the given figure, the charge stored in $6\mu F$ capacitor, when points $A$ and $B$ are joined by a connecting wire is
_______ $\mu C$ .
✓ Accepted Answer:36
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Q8mcq
A stone of mass $900\,g$ is tied to a string and moved in a vertical circle of radius $1\,m$ making $10\, rpm$ . The
tension in the string, when the stone is at the lowest point is (if $\pi ^{2} = 9. 8$ and $g= 9. 8\,m\,s^{-2}$ )
a.
$97\,N$
b.
$9. 8\,N$
Correct Answer
c.
$8. 82\,N$
d.
$17. 8\,N$
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Q9mcq
$N$ moles of a polyatomic gas $(f = 6)$ must be mixed with two moles of a monoatomic gas so that the mixture
behaves as a diatomic gas. The value of $N$ is:
a.
$6$
b.
$3$
c.
$4$
Correct Answer
d.
$2$
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Q10mcq
A particle is moving in a straight line. The variation of position $x$ as a function of time $t$ is given as
$x=(t^{3} -6t^{2} + 20t+ 15)\,m$ . The velocity of the body when its acceleration becomes zero is:
a.
$4\,m\,s^{-1}$
b.
$8\,m\,s^{-1}$
Correct Answer
c.
$10\,m\,s^{-1}$
d.
$6\,m\,s^{-1}$
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Two metallic wires $P$ and $Q$ have same volume and are made up of same material. If their area of cross
sections are in the ratio $4 : \,1$ and force $F_{1}$ is applied to $P$ , an extension of $\Delta l$ is produced. The force which is
required to produce same extension in $Q$ is $F_{2}$ . The value of $\frac{F_{1}}{F_{2}}$ is ______.
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A plane electromagnetic wave of frequency $35\, MHz$ travels in free space along the $X$ -direction. At a
particular point (in space and time) $\vec{E} = 9. 6ˆj\,V\,m^{-1}$ . The value of magnetic field at this point is:
a.
$3. 2 \times 10^{-8}ˆk\,T$
b.
$3. 2 \times 10^{-8}ˆi$
c.
$9. 6ˆj\,T$
d.
$9. 6 \times 10^{-8}ˆk\,T$
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A simple harmonic oscillator has an amplitude $A$ and time period $6\pi$ second. Assuming the oscillation starts
from its mean position, the time required by it to travel from $x=A$ to $x= \frac{\sqrt{3}}{2}A$ will be $\frac{\pi}{x}\,s$ , where
$x=_______.$
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If the distance between object and its two times magnified virtual image produced by a curved mirror is $15\, cm$
, the focal length of the mirror must be :
a.
$15\, cm$
b.
$-12\, cm$
c.
$-10\, cm$
d.
$\frac{10}{3}\, cm$
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A body of mass $5\, kg$ moving with a uniform speed $3\,m\,s\sqrt{2}^{-1}$ in $X- Y$ plane along the line $y=x+ 4$ . The
angular momentum of the particle about the origin will be _______ $kg \,m^{2}\,s^{-1}$ .
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In the given circuit, the current flowing through the resistance $20\,\Omega$ is $0. 3\,A$ , while the ammeter reads $0. 9\,A$ .
The value of $R_{1}$ is _____ $\Omega$ .
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The bob of a pendulum was released from a horizontal position. The length of the pendulum is $10\,m$ . If it
dissipates $10%$ of its initial energy against air resistance, the speed with which the bob arrives at the lowest
point is: [Use, $g= 10\,m\,s^{-2}$ ]
a.
$6\,m\,s\sqrt{5}^{-1}$
b.
$5\,m\,s\sqrt{6}^{-1}$
c.
$5\,m\,s\sqrt{5}^{-1}$
d.
$2\,m\,s\sqrt{5}^{-1}$
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Two particles $X$ and $Y$ having equal charges are being accelerated through the same potential difference.
Thereafter, they enter normally in a region of uniform magnetic field and describes circular paths of radii $R_{1}$
and $R_{2}$ respectively. The mass ratio of $X$ and $Y$ is :
a.
$2$
$( \frac{R_{2}}{R_{1}})$
b.
$2$
$(\frac{R_{1}}{R_{2}})$
c.
$( \frac{R_{1}}{R_{2}})$
d.
$(\frac{R_{2}}{R_{1}})$
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A particle is moving in a circle of radius $50\, cm$ in such a way that at any instant the normal and tangential
components of its acceleration are equal. If its speed at $t = 0$ is $4\,m\,s^{-1}$ , the time taken to complete the first
revolution will be $\frac{1}{\alpha}[1 -e^{-2\pi }]\,s$ , where $\alpha =$ ______.
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Given below are two statements:
Statement I: Most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus and the
electrons revolve around it, is Rutherford's model.
Statement II: An atom is a spherical cloud of positive charges with electrons embedded in it, is a special case
of Rutherford's model.
In the light of the above statements, choose the most appropriate from the options given below.
a.
Both statement I and statement II are false
b.
Statement I is false but statement II is true
c.
Statement I is true but statement II is false
d.
Both statement I and statement II are true
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A planet takes $200$ days to complete one revolution around the Sun. If the distance of the planet from Sun is
reduced to one fourth of the original distance, how many days will it take to complete one revolution?
a.
$25$
b.
$50$
c.
$100$
d.
$20$
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In Young's double slit experiment, light from two identical sources are superimposing on a screen. The path
difference between the two lights reaching at a point on the screen is $\frac{7\lambda}{4}$ . The ratio of intensity of fringe at this
point with respect to the maximum intensity of the fringe is:
a.
$\frac{1}{2}$
b.
$\frac{3}{4}$
c.
$\frac{1}{3}$
d.
$\frac{1}{4}$
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A physical quantity $Q$ is found to depend on quantities $a, \,b, \,c$ by the relation $Q=_{c^{2}}$ . The percentage error in
$a, \,b$ and $c$ are $3%, \,4%$ and $5%$ respectively. Then, the percentage error in $Q$ is:
a.
$66%$
b.
$43%$
c.
$34%$
d.
$14%$
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$o$
In a single slit diffraction pattern, a light of wavelength $6000\,A$ is used. The distance between the first and
third minima in the diffraction pattern is found to be $3\, mm$ when the screen is placed $50\, cm$ away from slits.
The width of the slit is ____ $\times 10^{-4}\,m$ .
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A bob of mass $m$ is suspended by a light string of length $L$ . It is imparted a minimum horizontal velocity at the
lowest point $A$ such that it just completes half circle reaching the top most position $B$ . The ratio of kinetic
energies $\frac{(\,K.E.\,)_{A}}{(\,K.E.\,)_{B}}$ is :
a.
$3 : 2$
b.
$5 : 1$
c.
$2 : 5$
d.
$1 : 5$
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Two sources of light emit with a power of $200\,W$ . The ratio of number of photons of visible light emitted by
each source having wavelengths $300\, nm$ and $500\, nm$ respectively, will be :
a.
$1 : 5$
b.
$1 : 3$
c.
$5 : 3$
d.
$3 : 5$
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A wire of length $L$ and radius $r$ is clamped at one end. If its other end is pulled by a force $F$ , its length increases
by $l$ . If the radius of the wire and the applied force both are reduced to half of their original values keeping
original length constant, the increase in length will become:
a.
$3$ times
b.
$\frac{3}{2}$ times
c.
$4$ times
d.
$2$ times
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A horizontal straight wire $5\,m$ long extending from east to west falling freely at right angle to horizontal
component of earth's magnetic field $0. 60 \times 10^{-4}\, Wb \,m^{-2}$ . The instantaneous value of emf induced in the
wire when its velocity is $10\,m\,s^{-1}$ is _______ $\times 10^{-3}\,V$ .
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The half-life of radioisotopic bromine - $82$ is $36$ hours. The fraction which remains after one day is _________
$\times 10^{-2}$ .
(Given antilog $0. 2006 = 1. 587)$
Round off to the nearest integer
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Chromatographic technique/s based on the principle of differential adsorption is/are
A. Column chromatography B. Thin layer chromatography C. Paper chromatography
Choose the most appropriate answer from the options given below:
a.
$B$ only
b.
$A$ only
c.
$A\,&\,B$ only
d.
$C$ only
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Molality of $0. 8M\,H_{2}SO_{4}$ solution (density $1. 06\,g\, cm^{-3}$ ) is _______ $\times 10^{-3}\,m$ .
Round off your answer to the nearest integer.
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Which of the following statements are correct about $Zn, Cd$ and $Hg$ ?
A. They exhibit high enthalpy of atomization as the d-subshell is full.
B. $Zn$ and $Cd$ do not show variable oxidation state while $Hg$ shows $+I$ and $+ II$ .
C. Compounds of $Zn, Cd$ and $Hg$ are paramagnetic in nature.
D. $Zn, Cd$ and $Hg$ are called soft metals.
Choose the most appropriate from the options given below:
a.
B, D only
b.
B, C only
c.
A, D only
d.
C, D only
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Standard enthalpy of vapourisation for $CCl_{4}$ is $30. 5\, kJ \, mol^{-1}$ . Heat required for vapourisation of $284\,g$ of
$CCl_{4}$ at constant temperature is __________ $kJ$ . (Given molar mass in $gmol^{-1}; C = 12, Cl = 35. 5$ )
Round off your answer to the nearest integer.
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Given below are two statements:
Statement I: Fluorine has most negative electron gain enthalpy in its group.
Statement II: Oxygen has least negative electron gain enthalpy in its group.
In the light of the above statements, choose the most appropriate from the options given below.
a.
Both Statement I and Statement II are true
b.
Statement I is true but Statement II is false
c.
Both Statement I and Statement II are false
d.
Statement I is false but Statement II is true
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If $50\, mL$ of $0. 5M$ oxalic acid is required to neutralise $25\, mL$ of $NaOH$ solution, the amount of $NaOH$ in
$50\, mL$ of given $NaOH$ solution is_______g.
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A constant current was passed through a solution of $AuCl^{-}_{4}$ ion between gold electrodes. After a period of
$10. 0$ minutes, the increase in mass of cathode was $1. 314\,g$ . The total charge passed through the solution is ___
$\times 10^{-2}\,F$ . (Given atomic mass of $Au = 197)$
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The following concentrations were observed at $500\,K$ for the formation of $NH_{3}$ from $N_{2}$ and $H_{2}$ . At
equilibrium : $[N_{2}] = 2 \times 10^{-2}M, [H_{2}] = 3 \times 10^{-2}M$ and $[NH_{3}] = 1. 5 \times 10^{-2}M$ . Equilibrium constant for the
reaction is ______.
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Let $x= \frac{m}{n}(m,n$ are co-prime natural numbers) be a solution of the equation $cos(2 sin^{-1} x)= \frac{1}{9}$ and let
$\alpha ,\beta (\alpha >\beta )$ be the roots of the equation $mx^{2} - nx- m+n= 0$ . Then the point $(\alpha ,\beta )$ lies on the line
a.
$3x+ 2y= 2$
b.
$5x-8y= -9$
c.
$3x-2y= -2$
d.
$5x+ 8y= 9$
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Let the slope of the line $45x+ 5y+ 3 = 0$ be $27r_{1}+ \frac{9r_{2}}{2}$ for some $r_{1}, \,\,r_{2} \in R$ . Then
$_{x}lim_{\rightarrow 3\rightarrow } (\int _{3}^{x} \frac{8t^{2}}{^{3}^{r}^{2}^{x}-rx^{2}-rx^{3}-3x}_{2}_{2}_{1} dt)$ is equal to ______.
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Let $\alpha ,\beta$ be the roots of the equation $x^{2} - \sqrt{6}x+ 3 = 0$ such that $Im (\alpha ) >Im (\beta )$ . Let $a, \,b$ be integers not
divisible by $3\,$ and $n$ be a natural number such that $\frac{\alpha ^{99}}{\beta} +\alpha ^{98} = 3^{n}(a+ib), \,i= \sqrt{-1}$ . Then $n+a+b$ is
equal to ___________.
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$|$
Let for any three distinct consecutive terms $a, \,b, \,c$ of an A.P, the lines $ax+by+c= 0$ be concurrent at the
point $P$ and $Q(\alpha ,\beta )$ be a point such that the system of equations $x+y+z= 6$ , $2x+ 5y+\alpha z=\beta$ and
$x+ 2\,y+ 3\,z= 4$ , has infinitely many solutions. Then $(PQ)^{2}$ is equal to _______.
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Let $O$ be the origin, and $M$ and $N$ be the points on the lines $\frac{x-5}{4} = \frac{y-4}{1} = \frac{z-5}{3}$ and $\frac{x+8}{12} = \frac{y+2}{5} = \frac{z+11}{9}$
$--$
respectively such that $MN$ is the shortest distance between the given lines. Then $O\vec{M} \cdot O\vec{N}$ is equal to
_________.
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$---$
Let $O\vec{A}= \vec{a}, O\vec{B}= 12\vec{a}+ 4\vec{b}$ and $O\vec{C}= \vec{b}$ , where $O$ is the origin. If $S$ is the parallelogram with adjacent sides
$OA$ and $OC$ , then $\frac{area \, of \, the \, quadrilateral \, OABC}{area \, of \,S}$ is equal to _____
a.
$6$
b.
$10$
c.
$7$
d.
$8$
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Let a unit vector $uˆ=xˆi+yˆj+zˆk$ make angles $\frac{\pi}{2}, \frac{\pi}{3}$ and $\frac{2\pi}{3}$ with the vectors $\frac{1}{\sqrt{2}}ˆi+ \frac{1}{\sqrt{2}}ˆk, \frac{1}{\sqrt{2}}ˆj+ \frac{1}{\sqrt{2}}ˆk$ and
$\frac{1}{\sqrt{2}}ˆi+ \frac{1}{\sqrt{2}}ˆj$ respectively. If $\vec{v}= \frac{1}{\sqrt{2}}ˆi+ \frac{1}{\sqrt{2}}ˆj+ \frac{1}{\sqrt{2}}ˆk$ , then $|\hat{u}- \vec{v}|^{2}$ is equal to
a.
$\frac{11}{2}$
b.
$\frac{5}{2}$
c.
$9$
d.
$7$
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If $sin(\frac{y}{x})= log_{e} x + \frac{\alpha}{2}$ is the solution of the differential equation $xcos( \frac{y}{x})\frac{dy}{dx} =ycos(\frac{y}{x})+x$ and
$y(1)= \frac{\pi}{3}$ , then $\alpha ^{2}$ is equal to
a.
$3$
b.
$12$
c.
$4$
d.
$9$
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If $\int _{6}\frac{\pi}{\pi 3} \sqrt{1 -sin 2x}dx=\alpha +\beta \sqrt{2}+\gamma \sqrt{3}$ , where $\alpha ,\beta$ and $\gamma$ are rational numbers, then $3\alpha + 4\beta - \gamma$ is equal
to _____.
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If each term of a geometric progression $a_{1}, a_{2}, a_{3}, …$ with $a_{1} = \frac{1}{8}$ and $a_{2} \neq a_{1}$ , is the arithmetic mean of the
next two terms and $S_{n} = a_{1}+ a_{2}+ … + a_{n}$ , then $S_{20}-S_{18}$ is equal to
a.
$2^{15}$
b.
$-2^{18}$
c.
$2^{18}$
d.
$-2^{15}$
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Let $P(\alpha ,\beta )$ be a point on the parabola $y^{2} = 4x$ . If $P$ also lies on the chord of the parabola $x^{2} = 8y$ whose mid
point is $(1, \frac{5}{4})$ , then $(\alpha -28)(\beta -8)$ is equal to _______.
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$||$
If $\int \frac{sinx+cosx}{\sqrt{sin^{3}xcos3xsin(x-\theta )}}\frac{3}{2} \frac{3}{2} dx=A\sqrt{cos\theta tanx-sin\theta}+B\sqrt{cos\theta -sin\theta cotx}+C,$ where $C$ is the integration
constant, then $AB$ is equal to
a.
$4 cosec (2\theta )$
b.
$4 sec\theta$
c.
$2 sec\theta$
d.
$8 cosec (2\theta )$
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If $log_{e}a, log_{e}b, log_{e}c$ are in an $A.P.$ and $log_{e}a-log_{e}2b, log_{e}2b-log_{e}3c, log_{e}3c-log_{e}a$ are also in an
$A.P.$ , then $a:b:c$ is equal to
a.
$9 : \,6 : \,4$
b.
$16 : \,4 : \,1$
c.
$25 : \,10 : \,4$
d.
$6 : \,3 : \,2$
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An integer is chosen at random from the integers $1\,, \,2, 3, \,. . . . . , \,50$ . The probability that the chosen integer is
a multiple of atleast one of $4, 6$ and $7$ is
a.
$\frac{8}{25}$
b.
$\frac{21}{50}$
c.
$\frac{9}{50}$
d.
$\frac{14}{25}$
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If $R$ is the smallest equivalence relation on the set ${1, 2, 3, 4}$ such that ${(1, 2), (1, 3)} \subset R$ , then the number
of elements in $R$ is ______.
a.
$10$
b.
$12$
c.
$8$
d.
$15$
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If the mean and variance of five observations are $\frac{24}{5}$ and $\frac{194}{25}$ respectively and the mean of first four
observations is $\frac{7}{2}$ , then the variance of the first four observations in equal to
a.
$\frac{4}{5}$
b.
$\frac{77}{12}$
c.
$\frac{5}{4}$
d.
$\frac{105}{4}$
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Let $f(x) =\sqrt{\,} _{r}lim_{\rightarrow \rightarrow x}{\frac{2r^{2}[(f(r))^{2}-f(x)f(r)]}{r^{2}-x^{2}} - r^{3}e\frac{f(r)}{r} }$ be differentiable in $(-\infty , 0) \cup (0, \infty )$ and $f(1) = 1$ . Then
the value of $ae$ , such that $f(a) = 0$ , is equal to ______.
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Let $A$ be the point of intersection of the lines $3x+ 2\,y= 14, 5\,x- y= 6$ and $B$ be the point of intersection of
the lines $4\,x+ 3\,y= 8, \,6\,x+y= 5$ . The distance of the point $P(5, -2)$ from the line $AB$ is
a.
$\frac{13}{2}$
b.
$8$
c.
$\frac{5}{2}$
d.
$6$
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