A compound microscope consists of an objective lens of focal length $1\, cm$ and an eye piece of focal length
$5\, cm$ with a separation of $10\, cm.$ The distance between an object and the objective lens, at which the strain on
the eye is minimum is $\frac{n}{40}cm.$ The value of is....... $n$
✓ Accepted Answer:50
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Q2mcq
Activities of three radioactive substances $A, \,B$ and are represented by the curves $C A, \,B$ and $C,$ in the figure.
Then their half-lives $T\frac{1}{2}(A) :T\frac{1}{2}(B) :T\frac{1}{2} (C)$ are in the ratio:
a.
$2 : \,1 : \,1$
b.
$3 : \,2 : \,1$
c.
$2 : \,1 : \,3$
Correct Answer
d.
$4 : \,3 : \,1$
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Q3mcq
A physical quantity zdepends on four observables $a, \,b, \,c$ and , as $d z=_{\sqrt{c}d^{3}} .$ The percentage of error in the
measurement of $a, \,b, \,c$ and are $d 2%, 1. 5%, 4%$ and $2. 5%$ respectively. The percentage of error in is : $z$
a.
$12. 25%$
b.
$16. 5%$
c.
$13. 5%$
d.
$14. 5%$
Correct Answer
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Q4mcq
A square loop of side $2a,$ and carrying current is kept in $I XZ$ plane with its centre at origin. A long wire
carrying the same current is placed parallel to the -axis and passing through the point $I z (0, \,b, \,0), (b>> \,a)$ .
The magnitude of the torque on the loop about -axis is given by. $z$
a.
$\frac{\mu _{0}I^{2}a^{2}}{2\pi b_{2}_{2}}$
b.
$\frac{\mu _{0}I^{2}a^{3}}{2\pi b_{2}^{2}_{3}}$
c.
$\frac{2\mu _{0}Ia}{\pi b}$
Correct Answer
d.
$\frac{2\mu _{0}Ia}{\pi b^{2}}$
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Q5mcq
Three different processes that can occur in an ideal monoatomic gas are shown in the $P$ vs $V$ diagram. The
paths are labelled as $A B,A\rightarrow \rightarrow C$ and $A\rightarrow \rightarrow D$ . The change in internal energies during these process are
taken as $E_{AB},E_{AC}$ and $\vec{E}_{AD}$ and the work done as $W_{AB},W_{AC}$ and $W_{AD}$ . The correct relation between these
parameters are:
Assume that the displacement (s) of air is proportional to the pressure difference $(\Delta p)$ created by a sound
wave. Displacement (s) further depends on the speed of sound (v), density of air $(\rho )$ and the frequency (f). If
$\Delta p~10 Pa,n~300 m/s,p~1 kg/m^{3} f~1000Hz$ , then s will be of the order of (take the multiplicative
constant to be 1 )
a.
$\frac{3}{100}mm$
Correct Answer
b.
$10\, mm$
c.
$\frac{1}{10}mm$
d.
$1\, mm$
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Q7nat
A beam of electrons of energy E scatters from a target having atomic spacing of $1\,$ ā«. The first maximum
intensity occurs at $\theta = 60^{\circ}.$ Then $E(in \, eV)$ is........
(Planck's constant $h= 6. 64 \times 10^{-34}\, Js, \,1\,eV = 1. 6 \times 10^{-19}J,$ electron mass $m = 9. 1 \times 10^{-31}\, kg$ )
✓ Accepted Answer:50
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Q8mcq
A hollow spherical shell at outer radius floats just submerged under the water surface. The inner radius of the $R$
shell is $r\,.$ If the specific gravity of the shell material is $\frac{27}{8}$ with respect to water, the value of is: $r$
a.
$\frac{8}{9}R$
Correct Answer
b.
$\frac{4}{9}R$
c.
$\frac{2}{3}R$
d.
$\frac{1}{3}R$
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Q9mcq
For a concave lens of focal length , the relation between object and image distance and respectively, $f u v,$
from its pole can best be represented by ( $u=v$ is the reference line):
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Q10mcq
With increasing biasing voltage of a photo diode, the photocurrent magnitude:
a.
remains constant
b.
increases initially and after attaining certain value, it decreases
c.
increases linearly
d.
increases initially and saturates finally
Correct Answer
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In a resonance tube experiment when the tube is filled with water up to a height of $17. 0\, cm ,$ from bottom, it
resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork
occurs at a height of $24. 5\, cm .$ If the velocity of sound in air is $330\,m\,s^{-1},$ the tuning fork frequency is :
a.
$2200\, Hz$
b.
$550\, Hz$
c.
$1100\, Hz$
d.
$3300\, Hz$
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A solid sphere of radius $R$ carries a charge $Q+q$ distributed uniformly over its volume. A very small point
like piece of it of mass $m$ gets detached from the bottom of the sphere and falls down vertically under gravity.
This piece carries charge . If it acquires a speed when it has fallen through a vertical height (see figure), $q Ī½ y$
then (assume the remaining portion to be spherical)
Two capacitors of capacitances and $C 2C$ are charged to potential differences and $V 2V$ , respectively. These
are then connected in parallel in such a manner that the positive terminal of one is connected to the negative
terminal of the other. The final energy of this configuration is :
a.
$\frac{25}{6}CV^{2}$
b.
$\frac{3}{2}CV^{2}$
c.
zero
d.
$\frac{9}{2}CV^{2}$
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A bullet of mass $5\, gram$ , travelling with a speed of $210\,m\,s^{-1}$ strikes a fixed wooden target. One half of its
kinetic energy is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its
material is $0. 030\,(gram \,^{\circ}C)^{-1} (1\,calorie = 4 .2 \times 10^{7}\, ergs)$ close to :
a.
$87. 5^{\circ}C$
b.
$83. 3^{\circ}C$
c.
$119. 2^{\circ}C$
d.
$38. 4^{\circ}C$
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An electrical power line, having a total resistance of $2\Omega ,$ delivers $1\, kW$ at $220\,V$ . The efficiency of the
transmission line is approximately :
a.
$72%$
b.
$91%$
c.
$85%$
d.
$96%$
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An electron is constrained to move along the -axis with a speed of $y 0. 1\,c$ (c is the speed of light) in the
presence of electromagnetic wave, whose electric field is $\vec{E}= 30Ėj sin(1. 5 \times 10^{7}t -5 \times 10^{-2}x)\,V\,m^{-1}.$
where in in seconds and $t x$ is im meters.The maximum magnetic force experienced by the electron will be:
(given $c = 3 \times 10^{8}\,m\,s^{-1}$ and electron charge $= 1. 6 \times 10^{-19}\, Coloumbs$
a.
$3. 2 \times 10^{-18}\,N$
b.
$2. 4 \times 10^{-18}\,N$
c.
$4. 8 \times 10^{-19}\,N$
d.
$1. 6 \times 10^{-19}\,N$
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The value of the acceleration due to gravity is $g_{1}$ at a height $h= \frac{R}{2}$ ( $R=$ radius of the earth) from the surface
of the earth. It is again equal to $g_{1}$ at a depth below the surface the earth. The ratio $d (\frac{d}{R})$ equals:
a.
$\frac{4}{9}$
b.
$\frac{5}{9}$
c.
$\frac{1}{3}$
d.
$\frac{7}{9}$
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A particle of mass $200\, MeV \,c^{-2}$ collides with a hydrogen atom at rest. Soon after the collision, the particle
comes to rest, and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle
(in $eV$ ) is $\frac{N}{4}.$ The value of $N$ is: (Given the mass of the hydrogen atom to be $1\, GeV \,c^{-2}$ ).........
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A force $\vec{F} =(Ėi+ 2Ėj+ 3Ėk)\,N$ acts at a point $(4Ėi+ 3Ėj- Ėk)\,m$ . Then the magnitude of torque about the point
$(Ėi+ 2Ėj+ Ėk)\,m$ will be $\sqrt{x\,}N -m.$ The value of is.......... $x$
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A galvanometer of resistance $G$ is converted into a voltameter of range $0 -1\,V$ by connecting a resistance $R$
in series with it. The additional resistance that should be connected in series with $R_{1}$ to increase the range of
the voltmeter to $0 -2V$ will be :
a.
$G$
b.
$R_{1}$
c.
$R_{1}- G$
d.
$R_{1}+G$
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A helicopter rises from rest on the ground vertically upwards with a constant acceleration g. A food packet is
dropped from the helicopter when it is at a height h. The time taken by the packet to reach the ground is close to
[ is the acceleration due to gravity]: $g$
a.
$t= \frac{2}{3}\sqrt{\,} (\frac{h}{g})$
b.
$t= 1. 8\sqrt{\,} (\frac{h}{g})$
c.
$t= 3. 4\sqrt{\,} (\frac{h}{g})$
d.
$t=\sqrt{\frac{2h}{3g}}$
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A wheel is rotating freely with an angular speed on a shaft. The moment of inertia of the wheel is and the $\omega I$
moment of inertia of the shaft is negligible. Another wheel of moment of inertia $3I$ initially at rest is suddenly
coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is:
a.
$\frac{5}{6}$
b.
$\frac{1}{4}$
c.
$0$
d.
$\frac{3}{4}$
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Number of molecules in a volume of $4\, cm^{3}$ of a perfect monoatomic gas at some temperature T and at a
pressure of $2\, cm$ of mercury is close to? (Given, mean kinetic energy of a molecule (at T) is
$4 \times 10^{-14}\, erg, \,g = 980\, cm \,s^{-2}$ density of mercury $= 13. 6\,g\, cm^{-3}$ )
a.
$4 .8 \times 10^{18}$
b.
$4. 0 \times 10^{16}$
c.
$5. 8 \times 10^{16}$
d.
$5. 8 \times 10^{18}$
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A balloon is moving up in air vertically above a point on the ground. When it is a height $A h_{1},$ a girl standing at
a distance d (point B) from A (see figure) sees it at an angle $45^{\circ}$ with respect to the vertical. When the balloon
climbs up a further height $h_{2}$ , it is seen at an angle $60^{\circ}$ with respect to the vertical if the girl moves further by a
distance $2. 464\,d$ (point C). Then the height $h_{2}$ is (given $tan 30^{\circ}= 0. 5774$ ):
a.
$1. 464\,d$
b.
$0. 732\,d$
c.
$0 .464 \,d$
d.
$d$
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Two concentric circular coils, $C_{1}$ and $C_{2}$ , are placed in the $XY$ plane. $C_{1}$ has $500$ turns, and a radius of $1\, cm$ .
$C_{2}$ has 200 turns and radius of $20\, cm .\,C_{2}$ carries a time dependent current $I(t) =(5t^{2} -2t+ 3)A$ where is $t$
in s. The emf induced in $C_{1}(in \, mV)$ at the instant $t= 1$ s is $\frac{4}{x}.$ The value of is .......... $x$
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Consider the following reaction:
$N_{2}O_{4}(g)= 2 NO_{2}(g): \,\Delta H^{0} = +58k$
For each of the following cases $(a, \,b)$ , the direction in which the equilibrium shifts is:
(a) Temperature is decreased.
(b) Pressure is increased by adding $N_{2}$ at constant T.
a.
(a) towards product, (b) towards reactant
b.
(a) towards reactant, (b) towards product
c.
(a) towards reactant, (b) no change
d.
(a) towards product, (b) no change
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The increasing order of the acidity of the -hydrogen of the following compounds is:$\alpha$
$(A)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(B)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(C)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(D)$
a.
$(D) < (C) < (A) < (B)$
b.
$(B) < (C) < (A) < (D)$
c.
$(A) < (C) < (D) < (B)$
d.
$(C) < (A) < (B) < (D)$
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The difference between the radii of $3^{rd}$ and $4^{th\,}$ orbits of $L^{2+}_{i}$ is $\Delta R_{1}$ . The difference between the radii of $3^{rd}$
and $4^{th\,}$ orbits of $He^{+} \Delta R_{2}.$ Ratio $\Delta R_{1} :\Delta R_{2}$ is :
a.
$8 : 3$
b.
$3 : 8$
c.
$2 : \,3$
d.
$3 : \,2$
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An oxidation-reduction reaction in which 3 electrons are transferred has a $\Delta G^{0}$ of $17. 37\, kJ \, mol^{-1}$ at $25^{\circ}C.$
The value of $E^{o}_{cell}$ (in V) is $_______ \times 10^{-2}$ .
$(1F = 96500\,C\, mol^{-1})$
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A flask contains a mixture of compounds and . Both compounds decompose by first-order kinetics. The $A B$
half-lives for and are $A B 300\,s$ and $180\,s$ , respectively. If the concentrations of and are equal initially, the $A B$
time required for the concentration of A to be four times that of (in s) is : $B (Use \, ln \,2 = 0. 693)$
a.
$180$
b.
$900$
c.
$300$
d.
$120$
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A soft drink was bottled with a partial pressure of $CO_{2}$ of 3 bar over the liquid at room temperature. The
partial pressure of $CO_{2}$ over the solution approaches a value of 30 bar when $44\,g$ of $CO_{2}$ is dissolved in $1\, kg$
of water at room temperature. The approximate $pH$ of the soft drink is ___________ $\times 10^{-1}$ .
(First dissociation constant of $H_{2}CO_{3} = 4. 0 \times 10^{-7}; \, log 2 = 0. 3;$ density of the soft drink $= 1\,g\, mL^{-1}$ )
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A diatomic molecule $X_{2}$ has a body-centred cubic $(bcc)$ structure with a cell edge of $300\, pm.$ The density of
the molecule is $6. 17\, gcm^{-3}.$ The number of molecules present in $200\,g$ of $X_{2}$ is :
(Avogadro constant $(N_{A}) = 6 \times 10^{23} mol^{-1}$ )
a.
$40\,N_{A}$
b.
$8\,N_{A}$
c.
$4\,N_{A}$
d.
$2\,N_{A}$
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$|$
The mean and variance of observations are and $7 8 16$ , respectively. If five observations are $2, 4, 10, 12, 14$
then the absolute difference of the remaining two observations is :
a.
$1$
b.
$4$
c.
$2$
d.
$3$
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The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters
of the word 'SYLLABUS' such that two letters are distinct and two letters are alike, is
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If the minimum and the maximum values of the function $f :[\frac{\pi}{4}, \frac{\pi}{2}]\rightarrow \rightarrow R,$ defined by
$-sin^{2} \theta -1 -sin^{2} \theta 1$
$f(\theta ) = -cos^{2} \theta -1 -cos^{2} \theta 1$ are $m$ and $M$ respectively, then the ordered pair $(m, \,M)$ is equal to :
$12 10 -2$
a.
$(0, 2\sqrt{2})$
b.
$(-4, 0)$
c.
$(-4, \,4)$
d.
$(0, 4)$
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If is the sum of the first 10 terms of the series, $S tan^{-1}(\frac{1}{3})+ tan^{-1}(\frac{1}{7})+ tan^{-1}(\frac{1}{13})+ tan^{-1}(\frac{1}{21})+ ā¦ ā¦$
then $tan(S)$ is equal to :
a.
$\frac{5}{6}$
b.
$\frac{5}{11}$
c.
$-\frac{5}{6}$
d.
$\frac{10}{11}$
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If $y=y(x)$ is the solution of the differential equation $\frac{5+e^{x}}{2+y} \cdot \frac{dy}{dx} +e^{x} = 0$ satisfying $y(0) = 1$ then value of
$y(log_{e}13)$ is
a.
$1$
b.
$-1$
c.
$0$
d.
$2$
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A survey shows that $73%$ of the persons working in an office like coffee, whereas $65%$ like tea. If denotes $x$
the percentage of them, who like both coffee and tea, then cannot be: $x$
a.
$63$
b.
$36$
c.
$54$
d.
$38$
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If is the positive root of the equation, $\alpha p(x) =x^{2} - x-2 = 0$ , then $_{x}lim_{\rightarrow \rightarrow \alpha ^{+}} \frac{\sqrt{1-cosp(x)}}{x+\alpha -4}$ is equal to
a.
$\frac{3}{2}$
b.
$\frac{3}{\sqrt{2}}$
c.
$\frac{1}{\sqrt{2}}$
d.
$\frac{1}{2}$
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$-$ If the four complex numbers $z,z,z-2 Re (z)$ and $z-2 Re (z)$ represent the vertices of a square of side $4$
units in the Argand plane, then $\bar{|}z|$ is equal to :
a.
$4\sqrt{2}$
b.
$4$
c.
$2\sqrt{2}$
d.
$2$
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If the co-ordinates of two points and are $A B (\sqrt{7}, 0)$ and $(-\sqrt{7}, 0)$ respectively and is any point on the $P$
conic, $9x^{2} + 16y^{2} = 144,$ then $PA+PB$ is equal to :
a.
$16$
b.
$8$
c.
$6$
d.
$9$
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If the line, $2\,x- y+ 3 = 0$ is at a distance $\frac{1}{\sqrt{5}}$ and $\frac{2}{\sqrt{5}}$ from the lines $4x-2y+\alpha = 0$ and $6x-3y+\beta = 0$
respectively, then the sum of all possible values of $\alpha$ and is ____________. $\beta$
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$k_{1}(x- \pi )^{2}-1, x\leq \pi$
If the function $f(x) ={$ is twice differentiable, then the ordered pair $(k_{1},k_{2})$ is equal
$k_{2}cosx, x>\pi$
to:
a.
$(\frac{1}{2}, 1)$
b.
$(1, 0)$
c.
$(\frac{1}{2}, -1)$
d.
$(1, 1)$
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$| |$
If $(a, \,b, \,c)$ is the image of the point $(1, 2, -3)$ in the line, $\frac{x+1}{2} = \frac{y-3}{-2} = \frac{z}{-1},$ then $a+b+c$ is equal to:
a.
$2$
b.
$-1$
c.
$3$
d.
$1$
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Let $f(x)=x\cdot [\frac{x}{2}],$ for $-10 <x< 10,$ where $[t]$ denotes the greatest integer function. Then the number of
points of discontinuity of $f(x)$ is equal to
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Let $\lambda \in R$ . The system of linear equations
$2x_{1}-4x_{2}+\lambda x_{3} = 1$
$x_{1}-6x_{2}+x_{3} = 2$
$\lambda x_{1}-10x_{2}+ 4x_{3} = 3$
is inconsistent for :
a.
exactly one positive value of $\lambda$
b.
exactly one negative value of $\lambda$
c.
every value of $\lambda$
d.
exactly two values of $\lambda$
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If the volume of a parallelopiped, whose coterminous edges are given by the vectors $\vec{a}= Ėi+ Ėj+nĖk$ ,
$\vec{b}= 2Ėi + \,4Ėj -\,nĖk$ and, $\vec{c}= Ėi +nĖj+ 3Ėk(n \geq 0)$ is $158$ cubic units, then :
a.
$\vec{a}\cdot \vec{c}= 17$
b.
$\vec{b}\cdot \vec{c}= 10$
c.
$n= 7$
d.
$n= 9$
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