A travelling microscope is used to determine the refractive index of a glass slab. If 40 divisions are there in
$1\, cm$ on main scale and $50$ Vernier scale divisions are equal to $49$ main scale divisions, then least count of the
travelling microscope is _____ $\times 10^{-6}\,m$ .
✓ Accepted Answer:5
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Q2mcq
Arrange the four graphs in descending order of total work done; where $W_{1},W_{2},W_{3}$ and $W_{4}$ are the work done
corresponding to figure $a,b,c$ and $d$ respectively.
a.
$W_{3} >W_{2} >W_{1} >W_{4}$
Correct Answer
b.
$W_{3} >W_{2} >W_{4} >W_{1}$
c.
$W_{2} >W_{3} >W_{4} >W_{1}$
d.
$W_{2} >W_{3} >W_{1} >W_{4}$
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Q3mcq
Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A:If we move from poles to equator, the direction of acceleration due to gravity of earth always
points towards the center of earth without any variation in its magnitude.
Reason R: At equator, the direction of acceleration due to the gravity is towards the center of earth.
In the light of above statements, choose the correct answer from the options given below
a.
Assertion and reason both are correct and reason
is correct explanation of assertion.
b.
Assertion and reason both are correct but reason
is not correct explanation of assertion.
c.
Assertion is true but reason is false
d.
Assertion is false but reason is true
Correct Answer
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Q4mcq
A radioactive nucleus can decay by two different processes. Half-life for the first process is $3. 0$ hours while it
is $4. 5$ hours for the second process. The effective halflife of the nucleus will be
a.
$3. 75$ hours
b.
$0. 56$ hours
c.
$0. 26$ hours
d.
$1. 80$ hours
Correct Answer
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Q5nat
A ball is projected vertically upward with an initial velocity of $50\,m\,s^{-1}$ at $t= 0\,s$ . At $t= 2\,s$ , another ball is
projected vertically upward with same velocity. At $t=$ ____ $s$ , second ball will meet the first ball
$(g = 10\,m\,s^{-2})$ .
✓ Accepted Answer:6
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Q6mcq
If $p$ is the density and $\eta$ is coefficient of viscosity of fluid which flows with a speed $v$ in the pipe of diameter $d$ ,
the correct formula for Reynolds number $R_{e}$ is
a.
$R_{e} = \frac{\pi d}{\rho v}$
b.
$R_{e} = \frac{\rho v}{\eta d}$
c.
$R_{e} = \frac{\rho vd}{\eta}$
Correct Answer
d.
$R_{e} = \frac{\eta}{\rho νd}$
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Q7mcq
A sinusoidal wave $y(t) = 40 sin(10 \times 10^{6}\pi t)$ is amplitude modulated by another sinusoidal wave
$x(t) = 20 sin(1000\pi t)$ . The amplitude of minimum frequency component of modulated signal is
a.
$0. 5$
b.
$0. 25$
c.
$20$
d.
$10$
Correct Answer
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Q8mcq
Two coils of self inductance $L_{1}$ and $L_{2}$ are connected in series combination having mutual inductance of the
coils as $M$ . The equivalent self inductance of the combination will be
a.
$\frac{1}{L_{1}} + \frac{1}{L_{2}} + \frac{1}{M}$
b.
$L_{1}+L_{2}-2M$
Correct Answer
c.
$L_{1}+L_{2}+M$
d.
$L_{1}+L_{2}+ 2M$
No explanation saved for this question yet.
Q9mcq
The charge on capacitor of capacitance $15\mu F$ in the figure given below is
a.
$60\,$ $\mu$ $C$
Correct Answer
b.
$130\,$ $\mu$ $C$
c.
$260\,$ $\mu$ $C$
d.
$585\,$ $\mu$ $C$
No explanation saved for this question yet.
Q10mcq
Find the equivalent resistance between point $A$ and $B$
a.
$65\,\Omega$
b.
$20\,\Omega$
c.
$5\,\Omega$
Correct Answer
d.
$2\,\Omega$
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A solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of
rotational kinetic energy of the ball to its total kinetic energy is
a.
$\frac{1}{5}$
b.
$\frac{2}{5}$
c.
$\frac{2}{7}$
d.
$\frac{7}{10}$
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A flask contains argon and oxygen in the ratio of $3 : 2$ in mass and the mixture is kept at $27^{\circ}C$ . The ratio of their
average kinetic energy per molecule respectively
a.
$3 : 5$
b.
$9 : 4$
c.
$2 : 3$
d.
$1 : 1$
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A batsman hits back a ball of mass $0. 4\, kg$ straight in the direction of the bowler without changing its initial
speed of $15\,m\,s^{-1}$ . The impulse imparted to the ball is _____ $N\,s$ .
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A bar magnet having a magnetic moment of $2. 0 \times 10^{5}\,J\,T^{-1}$ , is placed along the direction of uniform
magnetic field of magnitude $B= 14 \times 10^{-5}\,T$ . The work done in rotating the magnet slowly through $60^{\circ}$
from the direction of field is
a.
$14\,J$
b.
$8\,J$
c.
$4\,J$
d.
$1. 4\,J$
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For a specific wavelength $670\, nm$ of light coming from a galaxy moving with velocity $v$ , the observed
wavelength is $670. 7\, nm$ . The value of $v$ is
a.
$3 \times 10^{8}\,m\,s^{-1}$
b.
$3. 13 \times 10^{5}\,m\,s^{-1}$
c.
$3 \times 10^{10}\,m\,s^{-1}$
d.
$4. 48 \times 10^{5}\,m\,s^{-1}$
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A geyser heats water flowing at a rate of $2. 0\, kg$ per minute from $30^{\circ}C$ to $70^{\circ}C$ . If geyser operates on a gas
burner, the rate of combustion of fuel will be _____ $g\, min^{-1}$ .
[Heat of combustion $= 8 \times 10^{3} Jg^{-1}$ , Specific heat of water $= 4. 2 Jg^{-1}^{\circ }C^{-1}$ ]
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In the arrangement shown in figure $a_{1},a_{2},a_{3}$ and $a_{4}$ are the accelerations of masses $m_{1},m_{2},m_{3}$ and $m_{4}$
respectively. Which of the following relation is true for this arrangement?
a.
$4a_{1}+ 2a_{2}+a_{3}+a_{4} = 0$
b.
$a_{1}+ 4a_{2}+ 3a_{3}+a_{4} = 0$
c.
$a_{1}+ 4a_{2}+ 3a_{3}+ 2a_{4} = 0$
d.
$2a_{1}+ 2a_{2}+ 3a_{3}+a_{4} = 0$
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A set of $20$ tuning forks is arranged in a series of increasing frequencies. If each fork gives $4$ beats with respect
to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of
last fork is _____ $Hz$ .
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A system to $10$ balls each of mass $2\, kg$ are connected via massless and unstretchable string. The system is
allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the $7^{th \,}$ and
$8^{th \,}$ ball is _____ $N$ when $6^{th \,}$ ball just leaves the table.
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The stopping potential for photoelectrons emitted from a surface illuminated by light of wavelength $6630$ Åis
$0. 42\,V$ . If the threshold frequency is $x\times 10^{13}\,s$ , where $x$ is (nearest integer): (Given, speed light
$= 3 \times 10^{8}\,m\,s^{-1}$ . Planck's constant $= 6. 63 \times 10^{-34}\,J\,s$ )
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A heat engine operates with the cold reservoir at temperature $324\,K$ . The minimum temperature of the hot
reservoir, if the heat engine takes $300\,J$ heat from the hot reservoir and delivers $180\,J$ heat to the cold reservoir
per cycle, is _____ $K$ .
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A parallel plate capacitor with plate area $A$ and plate separation $d= 2\,m$ has a capacitance of $4\,$ $\mu$ $F$ . The new
capacitance of the system if half of the space between them is filled with a dielectric material of dielectric
constant $K = 3$ (as shown in figure) will be
a.
$2\,$ $\mu$ $F$
b.
$32\,$ $\mu$ $F$
c.
$6\,$ $\mu$ $F$
d.
$8\,$ $\mu$ $F$
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A metal surface is illuminated by a radiation of wavelength $4500\,A^{\circ }$ . The ejected photo-electron enters a
constant magnetic field of $2\, mT$ making an angle of $90^{\circ}$ with the magnetic field. If it starts revolving in a
circular path of radius $2\, mm$ , the work function of the metal is approximately
a.
$1. 36\, eV$
b.
$1. 69\, eV$
c.
$2. 78\, eV$
d.
$2. 23\, eV$
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Two $10\, cm$ long, straight wires, each carrying a current of $5\,A$ are kept parallel to each other. If each wire
experienced a force of $10^{-5}\,N$ , then separation between the wires is _____ $cm.$
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A metallic conductor of length $1\,m$ rotates in a vertical plane parallel to east-west direction about one of its
end with angular velocity $5\, rad \,s^{-1}$ . If the horizontal component of earth's magnetic field is $0. 2 \times 10^{-4}\,T$ ,
then emf induced between the two ends of the conductor is
a.
$5\mu V$
b.
$50\mu V$
c.
$5\,mV$
d.
$50\,mV$
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A small bulb is placed at the bottom of a tank containing water to a depth of $\sqrt{7}\,m$ . The refractive index of
water is $\frac{4}{3}$ . The area of the surface of water through which light from the bulb can emerge out is $x\pi \,m^{2}$ . The
value of $x$ is _____ .
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Sixty four conducting drops each of radius $0. 02\,m$ and each carrying a charge of $5\,\mu C$ are combined to form a
bigger drop. The ratio of surface density of bigger drop to the smaller drop will be
a.
$1 : 4$
b.
$4 : 1$
c.
$1 : 8$
d.
$8 : 1$
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The osmotic pressure exerted by a solution prepared by dissolving $2. 0\,g$ of protein of molar mass
$60\, kg \, mol^{-1}$ in $200\, mL$ of water at $27\,^{\circ}C$ is____ $Pa$ . [integer value] (use $R = 0. 083\,L$ bar $mol^{-1} \,K^{-1}$ )
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In a solid $AB, A$ atoms are in $ccp$ arrangement and $B$ atoms occupy all the octahedral sites. If two atoms from
the opposite faces are removed, then the resultant stoichiometry of the compound is $A_{x}B_{y}$ . The value of $x$ is
[nearest integer]
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Reaction of $[Co (H_{2}O)_{6}]^{2+}$ with excess ammonia and in the presence of oxygen results into a diamagnetic
product. Number of electrons present in $t_{2g}$ -orbitals of the product is
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The measured $BOD$ values tor four difterent water samples $(A -D)$ are as tollows: $A = 3$ ppm; $B = 18$ ppm;
$C = 21$ ppm; $D = 4$ ppm. The water samples which can be called as highly polluted with organic wastes, are
a.
$A&B$
b.
$A&D$
c.
$B&C$
d.
$B&D$
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$A$ fish swimming in water body when taken out from the water body is covered with a film of water of weight
$36\,g$ . When it is subjected to cooking at $100\,^{\circ}C$ , then the internal energy for vaporization in $kJmol^{-1}$ is
integer]
[Assume steam to be an ideal gas. Given $\Delta _{vap}H^{\ominus }$ for water at $373\,K$ and $1$ bar is
$41. 1\, kJ \, mol^{-1} : R = 8. 31\,J\,K^{-1}\, mol^{-1}$ ]
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Match List I with List II.
List-I List-II
Enzyme Conversion of
A. Invertase I. Starch into maltose
B. Zymase II. Maltose into glucose
C. Diastase III. Glucose into ethanol
D. Maltase IV. Cane sugar into glucose
Choose the most appropriate answer from the options given below
a.
$\,A -III, B -IV, C -II, D -I$
b.
$A -III, B -II, C -I, D -IV$
c.
$A -IV, B -III, C -I, D -II$
d.
$A -IV, B -II, C -III, D -I$
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$CNG$ is an important transportation fuel. When $100\, gCNG$ is mixed with $208\,g$ oxygen in vehicles, it leads to
the formation of $CO_{2}$ and $H_{2}O$ and produces large quantity of heat during this combustion, then the amount of
carbon dioxide, produced in grams is [nearest integer] [Assume CNG to be methane]
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Catalyst A reduces the activation energy for a reaction by $10\, kJ \, mol^{-1}$ at $300\,K$ . The ratio of rate constants,
$\frac{k_{T},\, Catalysed}{k_{T},\, Uncatalysed}$ is $e^{x}$ . The value of $x$ is____[nearest integer] [Assume that the pre-exponential factor is same in
both the cases. Given $R = 8. 31\,J\,K^{-1}\, mol^{-1}$ ]
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If the inverse trigonometric functions take principal values, then
$cos^{-1}(\frac{3}{10}cos(tan^{-1}(\frac{4}{3}))+ \frac{2}{5}sin(tan^{-1}(\frac{4}{3} )))$ is equal to
a.
$0$
b.
$\frac{\pi}{4}$
c.
$\frac{\pi}{3}$
d.
$\frac{\pi}{6}$
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$||$
If $a_{1}(> 0),a_{2},a_{3},a_{4},a_{5}$ are in a G.P. , $a_{2}+a_{4} = 2a_{3}+ 1$ and $3a_{2}+a_{3} = 2a_{4}$ , then $a_{2}+a_{4}+ 2a_{5}$ is equal
to _____.
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If $y=y(x)$ is the solution of the differential equation $x\frac{dy}{dx} + 2y=xe^{x},y(1) = 0$ then the local maximum
value of the function $z(x) =x^{2}y(x)- e^{x},x\in R$ is
a.
$1 - e$
b.
$0$
c.
$\frac{1}{2}$
d.
$\frac{4}{e} - e$
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Let $f(x) = min{1, 1 +xsinx}, 0 \leq x\leq 2\pi$ . If $m$ is the number of points, where $f$ is not differentiable and $n$
is the number of points, where $f$ is not continuous, then the ordered pair $(m,n)$ is equal to
a.
$(2, 0)$
b.
$(1, 0)$
c.
$(1, 1)$
d.
$(2, 1)$
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Consider a cuboid of sides $2x, 4x$ and $5x$ and a closed hemisphere of radius $r$ . If the sum of their surface areas
is constant $k$ , then the ratio $x:r$ , for which the sum of their volumes is maximum, is
a.
$2 : 5$
b.
$19 : 45$
c.
$3 : 8$
d.
$19 : 15$
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If the system of equations $\alpha x+y+z= 5,x+ 2y+ 3z= 4,x+ 3y+ 5z=\beta$ . Has infinitely many solutions,
then the ordered pair $(\alpha ,\beta )$ is equal to
a.
$(1, -3)$
b.
$(-1, 3)$
c.
$(1, 3)$
d.
$(-1, -3)$
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Let the mean of $50$ observations is $15$ and the standard deviation is $2$ . However, one observation was wrongly
recorded. The sum of the correct and incorrect observations is $70$ . If the mean of the correct set of observations
is $16$ , then the variance of the correct set is equal to
a.
$10$
b.
$36$
c.
$43$
d.
$60$
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Let $\vec{a}= ˆi+ ˆj+ 2ˆk, \vec{b}= 2ˆi-3ˆj+ ˆk$ and $\vec{c}= ˆi-ˆj+ˆk$ be the three given vectors. Let $\vec{v}$ be a vector in the
plane of $\vec{a}$ and $\vec{b}$ whose projection on $\vec{c}$ is $\frac{2}{\sqrt{3}}$ . If $\vec{v},ˆj= 7$ , then $\vec{v}\cdot (ˆi+ˆk)$ is equal to
a.
$6$
b.
$7$
c.
$8$
d.
$9$
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The locus of the mid-point of the line segment joining the point $(4, 3)$ and the points on the ellipse
$x^{2} + 2y^{2} = 4$ is an ellipse with eccentricity
a.
$\frac{\sqrt{3}}{2}$
b.
$\frac{1}{2\sqrt{2}}$
c.
$\frac{1}{\sqrt{2}}$
d.
$\frac{1}{2}$
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If $A=\sum ^{\infty }_{n=1} \frac{1}{(3+(-1)^{n})^{n}}$ and $B=\sum ^{\infty }_{n=1} \frac{(-1)^{n}}{(3+(-1)^{n})^{n}}$ , then $\frac{A}{B}$ is equal to
a.
$\frac{11}{9}$
b.
$1$
c.
$-\frac{11}{9}$
d.
$- \frac{11}{3}$
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If the probability that a randomly chosen $6$ -digit number formed by using digits $1$ and $8$ only is a multiple of
$21$ is $p$ , then $96p$ is equal to _____.
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If the lines $\vec{r}=(ˆi-ˆj+ˆk)+\lambda (3ˆj- ˆk)$ and $\vec{r}=(\alpha ˆi-ˆj)+\mu (2ˆi-3ˆk)$ are co-planar, the the distance of
the plane containing these two lines from the point $(\alpha , 0, 0)$ is
a.
$\frac{2}{9}$
b.
$\frac{2}{11}$
c.
$\frac{4}{11}$
d.
$2$
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Let a line $L_{1}$ be tangent to the hyperbola $\frac{x^{2}}{16} - \frac{y^{2}}{4} = 1$ and let $L_{2}$ be the line passing through the origin and
perpendicular to $L_{1}$ . If the locus of the point of intersection of $L_{1}$ and $L_{2}$ is $(x^{2} +y^{2})^{2} =\alpha x^{2} +\beta y^{2}$ , then
$\alpha +\beta$ is equal to ______.
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If the plane $2x+y-5z= 0$ is rotated about its line of intersection with the plane $3x- y+ 4z-7 = 0$ by an
angle of $\frac{\pi}{2}$ , then the plane after the rotation passes through the point
a.
$(2, -2, 0)$
b.
$(-2, 2, 0)$
c.
$(1, 0, 2)$
d.
$(-1, 0, -2)$
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Let $f :R R$ be defined as $f(x) =x-1$ and $g:R\rightarrow {1, -1} \rightarrow \rightarrow \rightarrow R$ be defined as $g(x) = \frac{x^{2}}{x^{2}-1}$ . Then the
function $f\vec{o}g$ is:
a.
One-one but not onto
b.
onto but not one-one
c.
Both one-one and onto
d.
Neither one-one nor onto
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