A biconvex lens of refractive index $1. 5$ has a focal length of $20\, cm$ in air. Its focal length when immersed in a
liquid of refractive index $1. 6$ will be:
a.
$-16\, cm$
b.
$-160\, cm$
Correct Answer
c.
$+160\, cm$
d.
$+16\, cm$
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Q2nat
When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to
the kinetic energy is $\frac{x}{8}$ , where $x=$ _________.
✓ Accepted Answer:9
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Q3mcq
Given below are two statements:
Statement I : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise
will be smaller in hot water.
Statement II : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise
will be smaller in cold water.
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.
Both Statement I and Statement II are false
c.
Statement I is true but Statement II is false
Correct Answer
d.
Statement I is false but Statement II is true
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Q4mcq
Match List I with List II
Chose the correct answer from the options given below
a.
$A -IV, \,B -I, \,C -III, \,D -II$
b.
$A -II, \,B -III, \,C -I, \,D -IV$
c.
$A -IV, \,B -III, \,C -I, \,D -II$
Correct Answer
d.
$\,A -I, \,B -II, \,C -III, \,D -IV$
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Q5mcq
A convex mirror of radius of curvature $30\, cm$ forms an image that is half the size of the object. The object
distance is :
a.
$-45\, cm$
b.
$45\, cm$
c.
$-15\, cm$
Correct Answer
d.
$15\, cm$
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Q6mcq
The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is $25%$ of the
velocity of light, then the ratio of K.E. of electron and K.E. of photon will be:
a.
$\frac{1}{1}$
b.
$\frac{1}{8}$
Correct Answer
c.
$\frac{8}{1}$
d.
$\frac{1}{4}$
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Q7nat
The magnetic potential due to a magnetic dipole at a point on its axis situated at a distance of $20\, cm$ from its
center is $1. 5 \times 10^{-5}\,T\,m$ . The magnetic moment of the dipole is _______ $A\,m^{2}$ . (Given :
$\frac{\mu _{0}}{4\pi} = 10^{-7\,}T\,m\,A^{-1}$ )
✓ Accepted Answer:6
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Q8nat
When a hydrogen atom going from $n= 2$ to $n= 1$ emits a photon, its recoil speed is $\frac{x}{5}\,m\,s^{-1}$ . Where $x=$
_______. (Use: mass of hydrogen atom $= 1. 6 \times 10^{-27}\, kg$ , charge of electron $e= 1. 6 \times 10^{-19}\,C)$
✓ Accepted Answer:17
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Q9nat
A square loop of side $10\, cm$ and resistance $0. 7\,\Omega$ is placed vertically in the east-west plane. A uniform
magnetic field of $0. 20\,T$ is set up across the plane in the north-east direction. The magnetic field is decreased
to zero in $1\,s$ at a steady rate. Then, the magnitude of induced emf is $\sqrt{x}\times 10^{-3}\,V$ . The value of $x$ is _______.
✓ Accepted Answer:2
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Q10nat
In a double slit experiment shown in figure, when light of wavelength $400\, nm$ is used, dark fringe is observed
at $P$ . If $D= 0. 2\,m$ , the minimum distance between the slits $S_{1}$ and $S_{2}$ is $\alpha \, mm$ . Write the value of $10\alpha$ to the
nearest integer.
✓ Accepted Answer:2
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The explosive in a Hydrogen bomb is a mixture of $_{1}H^{2},_{1}H^{3}$ and $_{3}Li^{6}$ in some condensed form. The chain
reaction is given by $_{3}Li^{6}+_{0}n^{1}_{2}He^{4}+_{1}H^{3}$ ; $_{1}H^{2}+_{1}H^{3}_{2}He^{4}+_{0}n^{1}$
During the explosion the energy released is approximately [Given :
$M(Li)= 6. 01690\, amu, M(_{1}\vec{H}^{2})= 2. 01471\, amu, \,M(_{2}\vec{H}e^{4})= 4. 00388\, amu$ and $1\,amu = 931. 5\, MeV$ ]
a.
$28. 12 MeV$
b.
$12. 64 MeV$
c.
$16. 48 MeV$
d.
$22. 22 MeV$
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A galvanometer having coil resistance $10\,\Omega$ shows a full scale deflection for a current of $3\, mA$ . For it to
measure a current of $8\,A$ , the value of the shunt should be:
a.
$3 \times 10^{-3}\Omega$
b.
$4. 85 \times 10^{-3}\Omega$
c.
$3. 75 \times 10^{-3}\Omega$
d.
$2. 75 \times 10^{-3}\Omega$
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Two vessels $A$ and $B$ are of the same size and are at same temperature. $A$ contains $1\,g$ of hydrogen and $B$
contains $1\,g$ of oxygen. $P_{A}$ and $P_{B}$ are the pressures of the gases in $A$ and $B$ respectively, then $\frac{P_{A}}{P_{B}}$ is :
a.
$16$
b.
$8$
c.
$4$
d.
$32$
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Two charges of $5Q$ and $-2Q$ are situated at the points $(3a, \,0)$ and $(-5a, \,0)$ respectively. The electric flux
through a sphere of radius $4a$ having centre at origin is:
a.
$\frac{2Q}{\epsilon _{0}}$
b.
$\frac{5Q}{\epsilon _{0}}$
c.
$\frac{7Q}{\epsilon _{0}}$
d.
$\frac{3Q}{\epsilon _{0}}$
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In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of
the wings are $70\,m\,s^{-1}$ and $65\,m\,s^{-1}$ respectively. If the wing area is $2\,m^{2}$ , the lift of the wing is _______ $N$ .
(Given density of air $= 1. 2\, kg \,m^{-3}$ )
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A thermodynamic system is taken from an original state $A$ to an intermediate state $B$ by a linear process as
shown in the figure. Its volume is then reduced to the original value from $B$ to $C$ by an isobaric process. The
total work done by the gas from $A$ to $B$ and $B$ to $C$ would be :
a.
$33800\,J$
b.
$2200\,J$
c.
$600\,J$
d.
$800\,J$
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A ball rolls off the top of a stairway with horizontal velocity $u$ . The steps are $0. 1\,m$ high and $0. 1\,m$ wide. The
minimum velocity $u$ with which that ball just hits the step $5$ of the stairway will be $\sqrt{x}\,m\,s^{-1}$ , where $x=$
_______ [use $g= 10\,m\,s^{-2}$ ].
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The potential energy function (in $J$ ) of a particle in a region of space is given as $U =(2x^{2} + 3y^{3} + 2z)$ . Here
$x, \,y$ and $z$ are in meter. The magnitude of $x$ - component of force (in $N$ ) acting on the particle at point
$P(1, \,2, \,3)\,m$ is:
a.
$2$
b.
$6$
c.
$4$
d.
$8$
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A $16\,\Omega$ wire is bend to form a square loop. A $9\,V$ battery with internal resistance $1\,\Omega$ is connected across one
of its sides. If a $4\,$ $\mu$ $F$ capacitor is connected across one of its diagonals, the energy stored by the capacitor will
be $\frac{x}{2}$ $\mu$ $J$ , where $x=$ ______.
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A block of mass $100\, kg$ slides over a distance of $10\,m$ on a horizontal surface. If the co-efficient of friction
between the surfaces is $0. 4$ , then the work done against friction (in $J$ ) is:
a.
$4200$
b.
$3900$
c.
$4000$
d.
$4500$
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An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet $S$
having surface charge density $+\sigma$ . The electron at $t= 0$ is at a distance of $1\,m$ from $S$ and has a speed of
$1\,m\,s^{-1}$ . The maximum value of $\sigma$ , if the electron strikes $S$ at $t= 1\,s$ is $\alpha [\frac{m\epsilon _{0}}{e} ] \frac{C}{m^{2}}$ . The value of $\alpha$ is _____.
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A cylinder is rolling down on an inclined plane of inclination $60^{\circ}$ . Its acceleration during rolling down will be
$\frac{x}{\sqrt{3}}\,m\,s^{-2}$ , where $x =$ _______(use $g= 10\,m\,s^{-2}$ ).
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The electric current through a wire varies with time as $I =I_{0}+\beta t$ , where $I_{0} = 20\,A$ and $\beta = 3\,A\,s^{-1}$ . The
amount of electric charge crossed through a section of the wire in $20\,s$ is:
a.
$80\,C$
b.
$1000\,C$
c.
$800\,C$
d.
$1600\,C$
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A capacitor of capacitance $100\,$ $\mu$ $F$ is charged to a potential of $12\,V$ and connected to a $6. 4\, mH$ inductor to
produce oscillations. The maximum current in the circuit would be :
a.
$3. 2\,A$
b.
$1. 5\,A$
c.
$2. 0\,A$
d.
$1. 2\,A$
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The deflection in moving coil galvanometer falls from $25$ divisions to $5$ division when a shunt of $24\,\Omega$ is
applied. The resistance of galvanometer coil will be:
a.
$12\,\Omega$
b.
$96\,\Omega$
c.
$48\,\Omega$
d.
$100\,\Omega$
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If the radius of curvature of the path of two particles of same mass are in the ratio $3 : \,4$ , then in order to have
constant centripetal force, their velocities will be in the ratio of:
a.
$\sqrt{3}: 2$
b.
$1 : \sqrt{3}$
c.
$\sqrt{3}: 1$
d.
$2 : \sqrt{3}$
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A body starts moving from rest with constant acceleration covers displacement $S_{1}$ in first $(p-1)$ seconds and
$S_{2}$ in first $p$ seconds. The displacement $S_{1}+S_{2}$ will be made in time :
a.
$(2p+ 1)\,s$
b.
$\sqrt{(2p^{2}-2p+ 1)}\,s$
c.
$(2p-1)\,s$
d.
$(2p^{2} -2p+ 1)\,s$
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From the compounds given below, number of compounds which give positive Fehling's test is
Benzaldehyde, Acetaldehyde, Acetone, Acetophenone,Methanal, 4-nitrobenzaldehyde, cyclohexane
carbaldehyde.
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Appearance of blood red colour, on treatment of the sodium fusion extract of an organic compound with
$FeSO_{4}$ in presence of concentrated $H_{2}SO_{4}$ indicates the presence of element/s
a.
$Br$
b.
$N$
c.
$N$ and $S$
d.
$S$
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Given below are two statements :
Statement I : The electronegativity of group $14$ elements from $Si$ to $Pb$ gradually decreases.
Statement II : Group $14$ contains non-metallic, metallic, as well as metalloid elements.
In the light of the above statements, choose the most appropriate from the options given below :
a.
Statement I is false but Statement II is true
b.
Statement I is true but Statement II is false
c.
Both Statement I and Statement II are true
d.
Both Statement I and Statement II are false
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The mass of zinc produced by the electrolysis of zinc sulphate solution with a steady current of $0. 015\,A$ for $15$
minutes is $____\times 10^{-4}\,g$ . (Atomic mass of zinc $= 65. 4 amu)$
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For the reaction $N_{2}O_{4}(\,g) \rightleftharpoons 2 NO_{2}(\,g)$ , $K_{p} = 0. 492\, atm$ at $300\,K. K_{c}$ for the reaction at same temperature
is $______\times 10^{-2}$ . (Given : $R = 0. 082\,L\, atm \, mol^{-1} \,K^{-1}$ )
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Chlorine undergoes disproportionation in alkaline medium as shown below :
$aCl_{2}(\,g)+ bOH^{-}(aq)\rightarrow cClO\rightarrow^{-}(aq)+ dCl^{-}(aq)+ eH_{2}O(l)$
The values of $a, \,b, \,c$ and $d$ in a balanced redox reaction are respectively :
a.
$1, \,2, \,1\,and\,1$
b.
$2, \,2, \,1\,and\,3$
c.
$3, 4, \,4\,and\,2$
d.
$2, \,4, \,1\,and\,3$
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For a reaction taking place in three steps at same temperature, overall rate constant $K = \frac{K_{1}K_{2}}{K_{3}}$ . If $Ea_{1}, Ea_{2}$ and
$Ea_{3}$ are $40, 50$ and $60\, kJ / mol$ respectively, the overall $Ea$ is _________ $kJ / mol$ .
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Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R :
Assertion A : Aryl halides cannot be prepared by replacement of hydroxyl group of phenol by halogen atom.
Reason R : Phenols react with halogen acids violently.
In the light of the above statements, choose the most appropriate from the options given below:
a.
Both A and R are true but R is NOT the correct
explanation of A
b.
A is false but R is true
c.
A is true but R is false
d.
Both A and R are true and R is the correct
explanation of A
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In chromyl chloride test for confirmation of $Cl^{-}$ ion, a yellow solution is obtained. Acidification of the solution
and addition of amyl alcohol and $10%\,H_{2}O_{2}$ turns organic layer blue indicating formation of chromium
pentoxide. The oxidation state of chromium in that is
a.
$+6$
b.
$+5$
c.
$+10$
d.
$+3$
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The osmotic pressure of a dilute solution is $7 \times 10^{5}\, Pa$ at $273\,K$ . Osmotic pressure of the same solution at
$283\,K$ is $_______\times 10^{4} Nm^{-2}$ .(Nearest integer)
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Match List I with List I
List I (Substances) List II (Element Present)
A. Ziegler catalyst I. Rhodium
B. Blood Pigment II. Cobalt
C. Wilkinson catalyst III. Iron
D. Vitamin B12 IV. Titanium
Choose the correct answer from the options given below:
a.
A-II, B-IV, C-I, D-III
b.
A-II, B-III, C-IV, D-I
c.
A-III, B-II, C-IV, D-I
d.
A-IV, B-III, C-I, D-II
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The number of species from the following which are paramagnetic and with bond order equal to one is
$H_{2}, He^{+}_{2} , O^{+}_{2} , N^{2-}_{2} , O^{2-}_{2} , F_{2}, Ne^{+}_{2} , B_{2}$
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Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R:
Assertion A: The first ionisation enthalpy decreases across a period.
Reason R: The increasing nuclear charge outweighs the shielding across the period.
In the light of the above statements, choose the most appropriate from the options given below:
a.
Both A and R are true and R is the correct
explanation of A
b.
A is true but R is false
c.
A is false but R is true
d.
Both A and R are true but R is NOT the correct
explanation of A
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A solution of $H_{2}SO_{4}$ is $31. 4%\,H_{2}SO_{4}$ by mass and has a density of $1. 25\,g/ mL$ . The molarity of the $H_{2}SO_{4}$
solution is $M$ (nearest integer) [Given molar mass of $H_{2}SO_{4} = 98\,g\, mol^{-1}$ ]
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Let $f(x) = 2^{x} -x^{2}, \,x \in R$ . If $m$ and $n$ are respectively the number of points at which the curves $y = f(x)$ and
$y = f'(x)$ intersects the $x-$ axis, then the value of $m + n$ is
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For $x\in (-\frac{\pi}{2}, \frac{\pi}{2})$ , if $y(x) =\int \frac{cosecx+sinx}{cosecxsecx+tanxsin^{2}x}dx$ and $lim_{-} y(x) = 0$ then $y(\frac{\pi}{4})$ is equal to
$x (\frac{\pi}{2})$
Let $\vec{a}, \,\vec{b}$ and $\vec{c}$ be three non-zero vectors such that $\vec{b}$ and $\vec{c}$ are non-collinear if $\vec{a}+ 5\vec{b}$ is collinear with
$\rightarrow \rightarrow$
$\vec{c}, \vec{b}+ 6\vec{c}$ is collinear with $\vec{a}$ and $\vec{a}+$ $\alpha$ $\vec{b}+$ $\beta$ $\vec{c}= 0$ , then $\alpha$ $+$ $\beta$is equal to
a.
$35$
b.
$30$
c.
$-30$
d.
$-25$
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If the mean and variance of the data $65, 68, 58, 44$ , $48, 45, 60,\alpha ,\beta , 60$ where $\alpha >\beta$ are $56$ and $66. 2$
respectively, then $\alpha ^{2} +\beta ^{2}$ is equal to
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Let $PQR$ be a triangle with $R(-1, 4, 2)$ . Suppose $M(2, 1, 2)$ is the mid point of $PQ$ . The distance of the
centroid of $\Delta PQR$ from the point of intersection of the line $\frac{x-2}{0} = \frac{y}{2} = \frac{z+3}{-1}$ and $\frac{x-1}{1} = \frac{y+3}{-3} = \frac{z+1}{1}$ is
a.
$69$
b.
$9$
c.
$\sqrt{69}$
d.
$\sqrt{99}$
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If the solution curve $y=y(x)$ of the differential equation $(1 +y^{2})(1 + log_{e}x)dx+xdy= 0,x> 0$ passes
through the point $(1, 1)$ and $y(e) = \frac{\alpha -tan()}{\beta +tan(^{3})}\frac{3}{2}$ , then $\alpha + 2\beta$ is
$2$
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Let $O$ be the origin and the position vector of $A$ and $B$ be $2ˆi+ 2ˆj+ ˆk$ and $2ˆi+ 4ˆj+ 4ˆk$ respectively. If the
internal bisector of $\angle AOB$ meets the line $AB$ at $C$ , then the length of $OC$ is
a.
$\frac{2}{3}\sqrt{31}$
b.
$\frac{2}{3}\sqrt{34}$
c.
$\frac{3}{4}\sqrt{34}$
d.
$\frac{3}{2}\sqrt{31}$
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In a $\Delta ABC$ , suppose $y = x$ is the equation of the bisector of the angle $B$ and the equation of the side $AC$ is
$2x- y= 2$ . If $2\,AB=BC$ and the point $A$ and $B$ are respectively $(4, 6)$ and $(\alpha ,\beta )$ , then $\alpha + 2\beta$ is equal to
a.
$-4$
b.
$42$
c.
$2$
d.
$-1$
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The area (in sq. units) of the part of circle $x^{2} +y^{2} = 169$ which is below the line $5x- y= 13$ is
$\frac{\pi \alpha}{2\beta} - \frac{65}{2} + \frac{\alpha}{\beta}sin^{-1}(\frac{12}{13} )$ where $\alpha ,\beta$ are coprime numbers. Then $\alpha +\beta$ is equal to
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$||$
Let $(5, \frac{a}{4} )$ , be the circumcenter of a triangle with vertices $A(a, -2), \,B(a, \,6)$ and $C( \frac{a}{4}, -2)$ . Let $\alpha$ denote the
circumradius, $\beta$ denote the area and $\gamma$ denote the perimeter of the triangle. Then $\alpha +\beta +\gamma$ is
a.
$60$
b.
$53$
c.
$62$
d.
$30$
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$|$
If the value of the integral $\int _{-}\frac{\pi}{2\pi}_{2} (\frac{x2cosx}{1+\pi ^{x}} + \frac{1+sin^{2}x}{1+e^{(sin}^{x}^{)2023}})dx= \frac{\pi}{4} (\pi +a) -2,$ then the value of $a$ is
a.
$3$
b.
$-\frac{3}{2}$
c.
$2$
d.
$\frac{3}{2}$
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Equations of two diameters of a circle are $2x-3y= 5$ and $3x-4y= 7$ . The line joining the points
$(-\frac{22}{7} , -4)$ and $(- \frac{1}{7}, 3)$ intersects the circle at only one point $P(\alpha ,\beta )$ . Then $17\beta - \alpha$ is equal to
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Let $\alpha ,\beta$ be the roots of the equation $x^{2} - x+ 2 = 0$ with $Im (\alpha ) >Im (\beta )$ . Then $\alpha ^{6} +\alpha ^{4} +\beta ^{4} -5\alpha ^{2}$ is equal
to
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All the letters of the word $GTWENTY$ are written in all possible ways with or without meaning and these
words are written as in a dictionary. The serial number of the word $GTWENTY$ IS
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A line with direction ratio $2, 1, 2$ meets the lines $x = y + 2 = z$ and $x + 2 = 2y = 2z$ respectively at the point
$P$ and $Q$ . if the length of the perpendicular from the point $(1, 2, 12)$ to the line $PQ$ is $l$ , then $l^{2}$ is
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If the points of intersection of two distinct conics $x^{2} +y^{2} = 4b$ and $\frac{x^{2}}{16} + \frac{y^{2}}{b^{2}} = 1$ lie on the curve $y^{2} = 3x^{2}$ ,
then $3\sqrt{3}$ times the area of the rectangle formed by the intersection points is _______.
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Consider the function $f :[\frac{1}{2} , 1]\rightarrow R\rightarrow$ defined by $f(x) = 4\sqrt{2}x^{3} -3\sqrt{2}x-1$ . Consider the statements
(I) The curve $y=f(x)$ intersects the $x$ -axis exactly at one point
(II) The curve $y=f(x)$ intersects the $x$ -axis at $x= cos \frac{\pi}{12}$
Then
a.
Only (II) is correct
b.
Both (I) and (II) are incorrect
c.
Only (I) is correct
d.
Both (I) and (II) are correct
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