AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
\( A, B, C \) and \( D \) are four coils of wires of 2,2
2 and 3 ohm resistances respectively and are arranged to form a Wheatstone bridge.The resistance which the coil 'D' must be shunted in order that the
bridge may be balanced is:
A . \( 4 \Omega \)
B. 6.
\( c .3 \Omega \)
D. \( 8 \Omega \)
Subject: Physics
A body of mass \( M \) moves in outer space
with velocity \( V . \) It is desired to break the body into two parts so that the mass of one part is one-tenth of the total mass. After the explosion, the heavier part comes to rest while the lighter part continues to move in the original
direction of motion. The velocity of the small part will be
A. \( V \)
B. \( (V / 2) \)
c. \( (V / 10) \)
D. 10V
Subject: Physics
A particle starts from origin at \( t=0 \) with velocity of \( 15 \hat{i} \) and moves in \( x \) -y plane under the action of force which produce a constant acceleration of \( 15 \hat{i}+20 \hat{j} \)
Find \( y \) -coordinate of particle when \( x \) coordinate is \( 180 \mathrm{m} \)
Subject: Physics
The quantum number corresponding to orbit of diameter \( 0.0001 \mathrm{mm} \) in
hydrogen atom will be nearly (Given that
the radius of orbit with \( n=1 \) is \( 0.51 \times \)
\( \left.\mathbf{1 0}^{-\mathbf{1 0}}\right): \)
A . 39
B. 31
\( c \cdot 9 \)
D. 49
Subject: Maths
Let \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma}, \boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}, \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{R} \) and let
\( \Delta= \)
\( \left|\begin{array}{ccc}\sin (x+\alpha) & \cos (x+\alpha) & a+x \sin \alpha \\ \sin (x+\beta) & \cos (x+\beta) & b+x \sin \beta \\ \sin (x+\gamma) & \cos (x+\gamma) & c+x \sin \gamma\end{array}\right| \)
then \( \Delta \) is
This question has multiple correct options
A. independent of \( x \)
B. dependent of \( \alpha, \beta, \),
c. dependent on \( a, b, c, c \)
D. \( a \) constant
Subject: Chemistry
What is the potential of a half cell consisting of zinc electrode in \( 0.01 \mathrm{M} \)
\( Z n S O_{4} \) solution of
\( \mathbf{2 5}^{\circ} \boldsymbol{C} ?\left[\boldsymbol{E}^{\boldsymbol{o}}=\mathbf{0 . 7 6 3} \boldsymbol{V}\right] \)
Subject: Physics
A vessel containing \( 50 k g \) of water is placed at a height \( 15 m \) above the ground. Assuming the gravitational potential energy at ground to be zero, what will be the gravitational potential energy of water in the vessel? Consider
\( \boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-2} \)
\( \mathbf{A} \cdot 5.0 k J \)
B. \( 7.5 k J \)
c. \( 10.0 k J \)
D. \( 12.5 k J \)
Subject: Maths
Two candles of the same height are lighted at the same time. The first is
consumed in 4 hours and the second in
3 hours. Assuming that each candle burns at a constant rate, in how many
hours after being lighted was the first candle twice the height of the second?
A \( \cdot \frac{3}{4} \) hr.
B. \( \frac{11}{2} \) hr.
c. \( 2 h r \)
D. \( \frac{12}{5} \) h.
E \( \cdot \frac{21}{2} \) hr.
Subject: Maths
Show that the points
\( \boldsymbol{A}(\mathbf{1}, \mathbf{2}, \mathbf{7}), \boldsymbol{B}(\mathbf{2}, \mathbf{6}, \mathbf{3}) \) and \( \boldsymbol{C}(\mathbf{3}, \mathbf{1 0},-\mathbf{1}) \)
are collinear.
Subject: Chemistry
For the redox reaction \( Z n(S)+C u^{2+}(0.1 M) \rightarrow \)
\( Z n^{2+}(1 M)+C u(s) \) taking place in a cell, \( E_{c e l l}^{0} \) is
1.10 volt. \( E_{\text {cell}} \) for the cell will be:
\( \left(2.303 \frac{R T}{F}=0.0591\right) \)
\( \mathbf{A} \cdot 2 \cdot 14 V \)
B. \( 1.80 V \)
c. \( 1.07 V \)
D. \( 0.82 V \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{3} & \mathbf{7} \\ \mathbf{2} & \mathbf{5}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{cc}-\mathbf{3} & \mathbf{2} \\ \mathbf{4} & -\mathbf{1}\end{array}\right] \) find
the \( \boldsymbol{A}+\boldsymbol{B} \)
Subject: Chemistry
When hydrogen is passed over a black solid compound \( A, \) the products are 'a colourless liquid' and 'a reddish brown
metal B'.

Substance B is divided into two parts,
each placed in separate test tubes. Dilute HCl is added to one part of
substance B and dilute \( H N O_{3} \) to the
other. What happens to substance \( A \) when it reacts with hydrogen ? Give
reasons for your answer
Subject: Maths
Find the coefficient of \( x^{50} \) in the
expression:
\( (1+x)^{1000}+2 x(1+x)^{999}+ \)
\( \mathbf{3} x^{2}(\mathbf{1}+\boldsymbol{x})^{\mathbf{9} 9 \mathbf{8}}+\ldots .+\mathbf{1 0 0} \mathbf{1} \boldsymbol{x}^{\mathbf{1 0 0 0}} \)
A \( .^{1000} \mathrm{C}_{50} \)
В. \( ^{1001} \mathrm{C}_{50} \)
\( \mathbf{c} \cdot^{1002} C_{50} \)
D. \( ^{1003} \Omega_{50} \)
Subject: Maths
\( \boldsymbol{y}=\sin ^{1}\left[\frac{\boldsymbol{2} \boldsymbol{x}}{\mathbf{1}+\boldsymbol{x}^{2}}\right], \boldsymbol{t h e n} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)
Subject: Chemistry
Explain the mechanism of the following
reaction. \( \mathbf{2} \boldsymbol{C} \boldsymbol{H}_{3}-\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{O} \boldsymbol{H} \frac{\boldsymbol{H}^{+}}{4 \mathbf{1} \mathbf{3} \boldsymbol{K}} \boldsymbol{C} \boldsymbol{H}_{3}- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{O}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{3}+\boldsymbol{H}_{2} \boldsymbol{O} \)
Subject: Physics
Two waves having same velocity enter electric and magnetic fields
respectively. If \( \lambda_{1} \) and \( \lambda_{2} \) are
their wavelengths as they move in the
fields, then
A \( \cdot \lambda_{1}, \lambda_{2} \) are constants
B. \( \lambda_{1} \) and \( \lambda_{2} \) are variable
c. \( \lambda_{1} \) is variable \( \lambda_{2} \) is constant
D. \( \lambda_{2} \) is variable, \( \lambda_{1} \) is constant
Subject: Chemistry
Give the electron configuration of the given metal (atom/ions)
\( M n O_{2} \)
A \( \cdot[A r] 3 s^{2} 3 p^{1} \)
B \( \cdot[A r] 3 d^{1} 4 s^{2} \)
c. \( [A r] 3 d^{3} \)
D. None of these
Subject: Chemistry
A 0.2 molar solution of formic acid is
\( 3.2 \% \) ionized, its ionization constant is:
A \( \cdot 9.6 \times 10^{-3} \)
B . \( 2.1 \times 10^{-4} \)
c. \( 1.25 \times 10^{-6} \)
D. \( 2.1 \times 10^{-8} \)
Subject: Chemistry
1 mole aqueous solution of \( S O_{2} C l_{2} \) is
neutralised by :
This question has multiple correct options
A \( \cdot 2 \) mol of \( C a(O H)_{2} \)
B. 1 mol of \( C a(O H)_{2} \)
c. 2 mol of \( K O H \)
D. 4 mol of \( K O H \)
Subject: Biology
Match Column-I with Column-II.
ColumnColumn-II
(a)
(i) Symbiotic association of fungi Saprophyte with plant roots
(ii) Decomposition of dead organic
(b) Parasite materials
(iii) Living on living plants or
(c) Lichens animals
(d)
(iv) Symbiotic association of algae Mycorrhiza and fungi
Choose the correct answer from the
option given.
B. (a)-(iii), (b)-(ii), (c)-(i), (d)-(iv)
C. (a)-(ii), (b)-(i), (c)-(iii), (d)-(iv)
D. (a)-(ii), (b)-(iii), (c)-(iv), (d)-(i)
Subject: Maths
Find the vertices of the triangle whose mid point of sides are (3,1),(5,6) and (-3,2)
A \( \cdot(-1,7)(-5,-3)(6,5) \)
B . (7,1)(2,3)(4,1)
c. (-1,7)(-5,-3)(11,5)
D. (1,7)(5,3)(-11,5)
Subject: Chemistry
The electronic configuration of four atoms are given in brackets:
\( \mathrm{L}:\left(1 s^{2} 2 s^{2} 2 p^{1}\right) \)
\( \mathrm{M}(: \)
\( \left.1 s^{2} 2 s^{2} 2 p^{5}\right) \)
\( Q:\left(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{1}\right) \)
\( 1 s^{2} 2 s^{2} 2 p^{2} \)
The element that would most readily
form a diatomic molecule is :
A. \( Q \)
в. м
c.
D.
Subject: Maths
If \( P(x, y, z) \) is a point on the line segment joining \( Q(2,2,4) \) and \( R(3,5,6) \) such that the projection of \( \overrightarrow{O P} \) on the axes are \( \frac{13}{5}, \frac{19}{5}, \frac{26}{5} \)
respectively, then \( P \) divides \( Q R \) in ratio
A .1: 3
B. 2: 3
c. 3: 2
D. 3: 1
Subject: Maths
If \( a>0, \) then the expression \( a x^{2}+ \)
\( b x+c \) is positive for all values of \( x \)
provided
A \( . b^{2}-4 a c>0 \)
В. \( b^{2}-4 a c<0 \)
\( \mathbf{c} \cdot b^{2}-4 a c=0 \)
D. \( b^{2}-a c<0 \)
Subject: Physics
The plane of a dip circle is set in the geographic meridian. Then the apparent
dip is \( \left(\delta_{1} \text { is the actual dip and } \delta_{2} \) is the \right. declination):
A \( \cdot \theta=\tan ^{-1}\left(\frac{\tan \delta_{1}}{\tan \delta_{2}}\right) \)
B . \( \theta=\tan ^{-1}\left(\tan \delta_{1} \cos \delta_{2}\right) \)
c. \( \theta=\tan ^{-1}\left(\frac{\tan \delta_{2}}{\cos \delta_{1}}\right) \)
D. \( \theta=\tan ^{-1}\left[\tan \delta_{1} \cos \delta_{2}\right] \)
Subject: Maths
If \( \boldsymbol{y}=\sqrt{(\boldsymbol{a}-\boldsymbol{x})(\boldsymbol{x}-\boldsymbol{b})}-(\boldsymbol{a}- \)
\( b) \tan ^{-1} \sqrt{\frac{a-x}{x-b}}(a>b) \) then \( \frac{d y}{d x}= \)
A. \( \sqrt{\frac{a-x}{x-b}} \)
B . \( \sqrt{(a-x)(x-b)} \)
c. 0
D.
Subject: Maths
\( \ln \) a \( \Delta A B C, \) if \( \angle A=53^{\circ} \) and \( \angle C=44^{\circ} \)
then the value of \( \angle B \) is
\( A \cdot 73^{\circ} \)
в. \( 83^{\circ} \)
c. \( 103^{\text {। }} \)
D. \( 46^{\circ} \)
Subject: Chemistry
Assertion
Colloidal solutions exhibits Brownian
motion.
Reason
Brownian motion is responsible for stability of solutions.
Choose the correct option about assertion and reason from the following:
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
In the figure given below, \( \boldsymbol{C D} \| \boldsymbol{E} \boldsymbol{F} \)
\( A B . \) If \( A B=22.5 \mathrm{cm}, E P=7.5 \mathrm{cm} \)
\( P C=15 \mathrm{cm} \) and \( D C=27 \)
m. Calculate \( \boldsymbol{E} \boldsymbol{F} \)
A. \( E F=14.5 \mathrm{cm} \)
3. \( E F=13.5 \mathrm{cm} \)
\( c . E F=12.5 \mathrm{cm} \)
Done of the above
Subject: Maths
The altitude of a cone is \( 20 \mathrm{cm} \) and its
semi-vertical angle is \( 30^{0} . \) If the semivertical angle is increasing at the rate
of \( 2^{0} \) per second, then the radius of the base is increasing at the rate of
A. \( 30 \mathrm{cm} / \mathrm{sec} \)
в. \( \frac{160}{3} \mathrm{cm} / \mathrm{sec} \)
c. \( 10 \mathrm{cm} / \mathrm{sec} \)
D. \( 160 \mathrm{cm} / \mathrm{sec} \)
Subject: Physics
Potentiometer wire of length \( 1 \mathrm{m} \) is connected in series with \( 490 \Omega \)
resistance and 2 V battery. If \( 0.2 \mathrm{mV} / \mathrm{cm} \) is the potential gradient, the resistance of the potentiometer wire is
\( A \cdot 4.9 \Omega \)
B. 7.9 \( \Omega \)
\( c \cdot 5.9 \Omega \)
D. \( 6.9 \Omega \)
Subject: Physics
Find the fraction of kinetic energy lost when the body of mass \( M \) is jerked into
motion
A \( \cdot \frac{M}{M+m} \)
В. \( \frac{M}{M-m} \)
c. \( \frac{2 M}{M+m} \)
D. \( \frac{M}{2(M+m)} \)
Subject: Biology
if the percentage of air pollution from different sources are given in the table.
With the help of this, answer the following questions:
Sources of air \( \quad \) Industry \( \quad \) Transportation pollution
Percentage \( \quad 52 \% \) 27\%
a) Which are the two sources to be
monitored more to control air pollution?
(b) Mention the preventive measure for each one of these two sources to control
air pollution?
Subject: Chemistry
Identify the correct statement(s) from
the following. This question has multiple correct options
A. The ion having a positive charge on it is known as electro - positive ion.
B. The ion having a negative charge on it is known as electro - negative ion.
C. Simple ion is an ion which contains one or more atoms of the same element.
D. Compound ion is an ion which contains two or more atoms of different elements forming a single unit.
Subject: Physics
A body of mass 'm' is taken from the earth's surface to the height equal to twice the radius (R) of the earth. The
change in potential energy of body will be -
A. \( \mathrm{mg} \) २R
в. \( \frac{2}{3} m g R \)
c. \( 3 \mathrm{mgR} \)
D. \( \frac{1}{3} m g R \)
Subject: Chemistry
The ether when treated with \( H \)
produces
\( \bigcirc\rangle-_{0}-\mathrm{cH}_{2}-\langle\bigcirc\rangle \)
\( \bigcirc\rangle-\mathrm{c} \mathrm{H}_{2} \)
\( \bigcirc\rangle-\mathrm{cH}_{2} \mathrm{o} \)
\( \bigcirc\rangle \)
\( \sqrt{0}-0 \)
Subject: Physics
In Rutherford experiment, a 5.3 MeV
\( \alpha- \) particle moves towards the gold nucleus \( (Z=79) . \) How close does the
\( \alpha- \) particle to get the centre of the nucleus,before it comes momentarily to
rest and reverses its motion? \( \left(\boldsymbol{E}_{\mathbf{0}}=\right. \) \( \left.\mathbf{8 . 0} \times \mathbf{1 0}^{-\mathbf{1 2}} \mathbf{F} / \boldsymbol{m}\right) \)
A \( \cdot 3.4 \times 10^{-15} \mathrm{m} \)
B. \( 8.6 \times 10^{-14} \) m
c. \( 4.3 \times 10^{-14} \) и
D. \( 1.6 \times 10^{-14} \mathrm{m} \)
Subject: Maths
Sum of \( \frac{\mathbf{8}}{\mathbf{4}}, \frac{\mathbf{9}}{\mathbf{6}}, 1, \frac{\mathbf{3}}{\mathbf{5}} \) is equal to
A \( \cdot \frac{152}{30} \)
в. \( 5 \frac{3}{30} \)
c. \( 5 \frac{2}{30} \)
D. \( _{5} \frac{1}{30} \)
Subject: Maths
If \( \vec{a}, \vec{b}, \vec{c} \) are three vectors such that \( \vec{a}, \vec{b}, \vec{c}, \) then prove that \( \vec{a} \times \vec{b}=\vec{b} \times \vec{c}= \)
\( \vec{c} \times \vec{a}, \) and hence show that \( [\overrightarrow{\boldsymbol{a}} \overrightarrow{\boldsymbol{b}} \overrightarrow{\boldsymbol{c}}]=\mathbf{0} \)
Subject: Chemistry
In the synthesis of sodium carbonate by solvay (or ammonia-soda) process, the recovery of ammonia is done by treating
\( N H_{4} C l \) with \( C a(O H)_{2} . \) The by-product obtained in this process is:
A. \( C a C l_{2} \)
в. \( N a C l \)
c. \( N a O H \)
D. \( \operatorname{NaH} \mathrm{CO}_{3} \)
Subject: Chemistry
Gas Density
\( A \)
\[
\begin{array}{l}
0,82 g L^{-1} \\
0,26 g L^{-1}
\end{array}
\]
\( 0.51 g L^{-1} \)
Pick up the correct statement/
statements.
1. Gas \( A \) will tend to lie at the bottom.
2. The number of atoms of various
\( \operatorname{gases} A, B \) and \( C \) are same.
3. The gases will diffuse to form homogeneous mixture.
4. Average kinetic energy of each gas is
same.
\( \mathbf{A} \cdot 2,3 \)
в. 1,4
\( c \cdot 1 \)
D. 3,4
Subject: Maths
The eccentricity of the conic
represented by the equation \( x^{2}+ \)
\( 2 y^{2}-2 x+3 y+2=0 \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{1}{2} \)
c. \( \frac{1}{\sqrt{2}} \)
D. \( \sqrt{2} \)
Subject: Maths
A focus of an ellipse is at the origin. The directrix is the line \( \mathbf{x}=\mathbf{4} \) and the eccentricity is \( \frac{1}{2} . \) Then the length of the semi major axis is
A \( \cdot \frac{5}{3} \)
B. \( \frac{8}{3} \)
\( c \cdot \frac{2}{3} \)
D. \( \frac{4}{3} \)
Subject: Physics
The electric field of an electromagnetic wave traveling through the vacuum is given by the equation \( \boldsymbol{E}= \)
\( \boldsymbol{E}_{0} \sin (\boldsymbol{K} \boldsymbol{x}-\boldsymbol{\omega} \boldsymbol{t}) . \) The quantity that is
independent of wavelength is:
A . \( k \omega \)
в. \( \frac{k}{\omega} \)
\( \mathbf{c} \cdot k^{2} \omega \)
\( D \)
Subject: Physics
A rectangular loop with a slide wire of
length \( l \) is kept in a uniform magnetic
field as shown in figure (a). The
resistance of slider is \( \boldsymbol{R} \). Neglecting self
inductance of the loop find the current
in the connector during its motion with
a velocity \( \boldsymbol{v} \)
\( (b) \)
A \( \cdot \frac{B l v}{R_{1}+R_{2}+R} \)
B. \( \frac{B l v\left(R_{1}+R_{2}\right)}{R\left(R_{1}+R_{2}\right)} \)
c. \( \frac{B l v\left(R_{1}+R_{2}\right)}{R R_{1}+R R_{2}+R_{1} R_{2}} \)
D \( \cdot \operatorname{Blv}\left(\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}\right) \)
Subject: Physics
A cube has sides of length \( 1.2 \times \)
\( 10^{-2} m . \) Calculate the volume.
A \( .1 .7 \times 10^{-6} m^{3} \)
В. \( 1.73 \times 10^{-6} m^{3} \)
C. \( 1.70 \times 10^{-6} m^{3} \)
D. \( 1.732 \times 10^{-6} \mathrm{m}^{3} \)
Subject: Physics
An ideal gas is enclosed in a container of volume \( V \) at a pressure \( P . \) It is being
pumped out of the container by using a pump with stroke volume \( v \). What is
final pressure in container after \( n- \)
strokes of the pump? (assume
temperature remains same).
\( ^{\mathbf{A}} \cdot P\left(\frac{V}{V+v}\right)^{n} \)
B. \( \frac{P V}{(V-v)^{n}} \)
c. \( P \frac{V^{n}}{v^{n}} \)
\( P\left(\frac{V}{V-v}\right)^{n} \)
Subject: Maths
The amplitude of \( \frac{1+\sqrt{3 i}}{\sqrt{3}+1} \) is
\( ^{A} \cdot \frac{\pi}{3} \)
в. \( -\frac{\pi}{3} \)
\( c \cdot \frac{\pi}{6} \)
D. \( -\frac{\pi}{6} \)
Subject: Chemistry
Number of water molecules in one litre
of pure water is :
A. \( 6.023 \times 10^{23} \)
3 \( 3.02 \times 10^{3} \times 10^{-63} \)
B. \( 3.45 \times 10^{25} \)
c. \( 55.4 \times 10^{23} \)
D. \( 18 \times 10^{23} \)
Subject: Maths
If \( f(x)=\frac{x+1}{x-1}, \) what is the value of
\( \boldsymbol{f}\left(\boldsymbol{f}\left(\boldsymbol{f}\left(\boldsymbol{f}\left(\left(\frac{3}{5}\right)\right)\right)\right)\right) ? \)
A . -
B.
\( c .0 .6 \)
D. 1.3
E. 7
Subject: Maths
The coefficient of \( x \) in the expansion of \( (1-a x)^{-1}(1-b x)^{-1}(1-c x)^{-1} \) is?
A \( . a+b+c \)
B. \( a-b-c \)
c. \( -a+b+c \)
D. \( a-b+c \)
Subject: Physics
A parallel plate capacitor (fig.) made of circular plates each of radius \( \boldsymbol{R}= \) \( 6.0 \mathrm{cm} \) has a capacitance \( C=100 \mu \mathrm{F} \)
The capacitor is connected to a \( 230 V \) ac supply with a (angular) frequency of
300 rad \( s^{-1} \)
Is the conduction current equal to the
displacement current?
Subject: Biology
Assertion
Plants lack excretory organs.
Reason
Plant usually absorb essential nutrients
and lead a passive life.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but the reason is correct.
Subject: Physics
Two parallel wires carrying currents \( \boldsymbol{I}_{1} \)
and \( I_{2} \) in opposite directions and
separated by a distance \( d \) experience a
A . Replusive force \( \mu_{0} I_{1} I_{2} / 2 \pi d \)
B. Attractive force \( \mu_{0} I_{1} I_{2} / 2 \pi d \)
C. Repulsive force \( \mu_{0} I_{1} I_{2} / 2 \pi d^{2} \)
D. Attractive force \( \mu_{0} I_{1} I_{2} / 2 \pi d^{2} \)
Subject: Physics
The earth's magnetic field at a certain place has a horizontal component of \( 0.3 G \) and total strength \( 0.5 G . \) Find
angle of dip in \( \tan ^{-1} \)
A \( \cdot \delta=\tan ^{-1} \frac{4}{3} \)
B. \( \delta=\tan ^{-1} \frac{3}{4} \)
c. \( \delta=\tan ^{-1} \frac{5}{3} \)
D. \( \delta=\tan ^{-1} \frac{3}{5} \)
Subject: Physics
A ball is bouncing elastically with a
speed \( 1 \mathrm{m} / \mathrm{s} \) between walls of a railway
compartment of size \( 10 m \) in a direction
perpendicular to walls. The train is
moving at a constant velocity of \( 10 \mathrm{m} / \mathrm{s} \)
parallel to the direction of motion of the ball. As seen from the ground.
This question has multiple correct options
A. The direction of motion of the ball changes every 10
B. Speed of ball changes every 10
C. Average speed of ball over any 20 interval is fixed.
D. The acceleration of ball is the same as from the train
Subject: Maths
In the given figure \( \boldsymbol{\alpha} \) and \( \boldsymbol{\beta} \) are
measured in degrees. Which one of the
following statements is not correct?
\( \mathbf{A} \cdot \beta>\alpha \)
\( \mathbf{B} \cdot \sec \beta=2 \)
\( \mathbf{C} \cdot \tan 3 \alpha=\sqrt{3} \)
D \( \cdot \sin (\beta-\alpha)=\frac{1}{\sqrt{2}} \)
Subject: Physics
A metal rod \( 40 \mathrm{cm} \) long is dropped on to a wooden floor and rebounds into air.
Compressional waves of many frequencies are thereby set up in the rod. If the speed of compressional waves in the rod in \( 5500 \mathrm{m} / \mathrm{s} \), what is the lowest frequency of compressional waves to which the rod resonated as it
rebounds?
A . 675 \( \mathrm{H} \)
в. 6875 Н
c. \( 16875 \mathrm{Hz} \)
D. о нz
Subject: Physics
The moment of inertia of a solid cylinder
about its own axis is the same at its
moment of inertia about an axis
passing through its cenre of gravity and perpendicular to its length. The relation between its length \( L \) and radius \( R \) is
В. \( L=\sqrt{3} R \)
c. \( L=3 R \)
D. \( L=R \)
Subject: Maths
Let \( u, v \) and \( w \) be such that \( |u|= \)
\( \mathbf{1},|\boldsymbol{v}|=\mathbf{3} \) and \( |\boldsymbol{w}|=2 . \) If the projection
of \( v \) along \( u \) is equal to that of \( w \) along \( u \) and vectors \( v \) and \( w \) are perpendicular
to each other, then \( |\boldsymbol{u}-\boldsymbol{v}+\boldsymbol{w}| \) equals
A . 2
B. \( \sqrt{7} \)
c. \( \sqrt{14} \)
D. 14
Subject: Maths
The area of the region bounded by the curves \( \mathbf{y}=\sqrt{\boldsymbol{x}} \) and \( \boldsymbol{y}=\sqrt{\mathbf{4}-\mathbf{3} \boldsymbol{x}} \) and
\( \mathbf{y}=\mathbf{0} \) is:
A . \( 4 / 9 \)
B. 16/9
\( c \cdot 8 / 9 \)
D. 9/2
Subject: Chemistry
Assertion
Atomic size increases down the group.
Reason

Since there are more filled energy levels
so the valence electrons are found
farther from the nucleus increasing the
atomic size.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
An isosceles right-angled prism and a
convex lens (focal length \( =40 \mathrm{cm} \) ) are
placed as shown in the above figure,
and a \( 5 \mathrm{cm} \) wide strip with the letter
LIGHT' written on it placed as indicated.
What is the nature and position of the
image formed after refraction through the prism and the lens?
[Given the critical angle of the glass
used for the prism and the lens is \( 42^{\circ} . \)
Subject: Maths
f \( x=3 t, y=1 / 2(t+1), \) then the value
of \( t \) for which \( x=2 y \) is
\( A \cdot 1 \)
B. \( 1 / 2 \)
\( c .-1 \)
D. \( 2 / 3 \)
Subject: Maths
The probability of a man hitting the \( \operatorname{target} \) is \( \frac{1}{4} . \) If he fires 7 times, the probability of hitting the target exactly six times is
\( ^{\mathrm{A}} \cdot_{^{7}} C_{5}\left(\frac{1}{4}\right)^{6}\left(\frac{3}{4}\right) \)
\( ^{\mathrm{B} \cdot}^{7} C_{6}\left(\frac{3}{4}\right)^{6}\left(\frac{1}{4}\right) \)
\( ^{\mathbf{c}} \cdot_{7} C_{6}\left(\frac{1}{4}\right)^{6}\left(\frac{3}{4}\right) \)
\( ^{\mathrm{D} \cdot}^{7} C_{6}\left(\frac{1}{2}\right)^{6}\left(\frac{1}{2}\right) \)
Subject: Physics
Two coils \( A \) and \( B \) have mutual
inductance \( 2 \times 10^{-2} \) henry. If the
current in the primary is \( i= \) \( 5 \sin (10 \pi t) \) then the maximum value of
e.m.f. induced in coil B is:
A . \pivolt
в. \( \frac{\pi}{2} \) volt
c. \( \frac{\pi}{3} \) volt
D. \( \frac{\pi}{4} \) volt
Subject: Biology
arranged at the equatorial plate (see Fig. 1 ). When these cells are treated with colchicine, cell division is arrested and
the cells never enter anaphase. If we were to compare a colchicine treated
cell at metaphase and an untreated cell
in the same phase, we notice that
chromosomes are more dispersed and do not arrange themselves on the
equatorial plate in the treated cells (see Fig \( 2 .) \) Using this information, which of the
following will be affected by colchicine?
A . Centromere
B. Spindle fiber
c. Centriole
D. Arms of chromosomes
Subject: Chemistry
The phosphate of a certain metal M is
\( M_{3}\left(P O_{4}\right)_{2} . \) The correct formula of metal sulphate would be:
\( \mathbf{A} \cdot M_{2}\left(S O_{4}\right)_{3} \)
в. \( M S O_{4} \)
c. \( M_{3}\left(S O_{4}\right)_{2} \)
D. \( M_{2} S O_{4} \)
Subject: Physics
In the electric field of an point charge \( q \)
a certain charge is carried from point \( \mathbf{A} \)
to \( \mathrm{B}, \mathrm{C}, \mathrm{D} \) and \( \mathrm{E} \). Then the work done
during movement along each path is:
A. least along the path AB
B. least along the path AD
C. zero along any one of the path \( A B, A C, A D \) and \( A E \)
D. least along AE