AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Assertion
Chlorine gas disproportionates in hot and conc. NaOH solution
Reason
NaCl and NaOCl are formed in the above
reaction
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
If the unit vectors \( \vec{e}_{1} \) and \( \vec{e}_{2} \) are inclined
at an angle \( 2 \theta \) and \( \left|\vec{e}_{1}-\vec{e}_{2}\right|<1 \), then
for \( \boldsymbol{\theta} \in[\mathbf{0}, \boldsymbol{\pi}], \boldsymbol{\theta} \) may lie in the interval
\( \mathbf{A} \cdot\left[0, \frac{\pi}{6}\right] \)
В \( \cdot\left[\frac{\pi}{6}, \frac{\pi}{2}\right] \)
c. \( \left[\frac{5 \pi}{6}, \pi\right] \)
D. \( \left[\frac{\pi}{2}, \frac{5 \pi}{6}\right] \)
Subject: Maths
Two students Anil and Ashima
appeared in an examination. The probability that Anil will qualify the examination is 0.05 and that Ashima
will qualify the examination is 0.10 . The probability that both will quailfy the examination is 0.02 . Find the
probability that
(a) Both Anil and Ashima will not
qualify the examination. (N)
(b) Atleast one of them will not qualify the examination. (N)
(c) Only one of them will qualify the examination. (N)
Subject: Maths
If in the expansion of \( (1-x)^{2 n-1}, \) the
coefficient of \( x^{r} \) denoted by \( a_{r}, \) then :
\( \mathbf{A} \cdot a_{r-1}+a_{2 n-r}=0 \)
В \( \cdot a_{r-1}-a_{2 n-r}=0 \)
c. \( a_{r-1}+2 a_{a n-r}=0 \)
D. None of these
Subject: Maths
Sector area of a circle in radians is
A \( \cdot 2 \times \frac{\theta}{2} r^{2} \)
в. \( \frac{\theta}{2} \times r^{2} \)
c. \( _{\pi \times \frac{\theta}{2} r^{2}} \)
D. \( _{2 \times \frac{\theta}{2} \pi r} \)
Subject: Maths
Equation of plane parallel to \( 3 x+4 y+ \)
\( \mathbf{5} \boldsymbol{z}-\mathbf{6}=\mathbf{0}, \mathbf{6} \boldsymbol{x}+\mathbf{8} \boldsymbol{y}+\mathbf{1 0} \boldsymbol{z}-\mathbf{1 6}=\mathbf{0} \)
and equidistant from them is
A. \( 3 x+4 y+5 z=7 \)
B. \( 3 x+4 y+5 z=10 \)
c. \( 6 x+8 y+10 z=0 \)
D. \( 6 x+8 y+10 z=3 \)
Subject: Chemistry
The figure below shows three steps \( (A, \)
B, \( C \) ) of Polymerase Chain Reaction
(PCR). Select the option giving
correct identification together with what it represents?
DNA
A . A - Denaturation at a temperature of about \( 50^{\circ} \mathrm{C} \)
B. C - Extension in the presence of heat stable DNA polymerase
C. A - Annealing with two sets of primers
D. B - Denaturation at a temperature of about \( 98^{\circ} \mathrm{C} \) separating the two DNA strands
Subject: Chemistry
Behaviour of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) and \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) is
different Nal because:
A \( \cdot H_{2} S O_{4} \) is stronger acid than \( H_{3} P O_{4} \)
B. \( H_{2} S O_{4} \) is a strong oxidising agent and oxidises colourless gas to coloured vapour
\( \mathrm{c} \cdot H_{3} P O_{4} \) is tribasic acid
D. \( H_{2} S O_{4} \) is a dibasic acid
Subject: Chemistry
In a set of reactions of propionic acid yielded a compound \( D \) \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C O O H} \stackrel{S O C l_{2}}{\rightarrow} \boldsymbol{B} \stackrel{N H_{3}}{\longrightarrow} \boldsymbol{C} \frac{\boldsymbol{K O H}}{B r_{2}} \)
\( D \)
The structure of \( D \) would be:
A. \( C H_{3} C H_{2} C H_{2} N H_{2} \)
B. \( C H_{3} C H_{2} C O N H_{2} \)
c. \( C H_{3} C H_{2} N H C H_{3} \)
D. \( C H_{3} C H_{2} N H_{2} \)
Subject: Maths
f \( \sum_{r=1}^{n} t_{r}=\frac{1}{12} n(n+1)(n+2), \) then the
value of \( \sum_{r=1}^{n} \frac{1}{t_{r}} \) is
A \( \cdot \frac{2 n}{n+1} \)
в. \( \frac{n}{(n+1)} \)
c. \( \frac{4 n}{n+1} \)
D. \( \frac{3 n}{n+1} \)
Subject: Chemistry
A chemist is preparing to analyse samples that will contain no more than \( 0.5 \mathrm{g} \) of uranium. His procedure calls for
preparing the uranium as \( U^{4+} \) ion and
oxidizing it by \( M n O_{4}^{-} \) in acid solution:
\( \boldsymbol{U}^{4+}+\boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}^{-}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{U} \boldsymbol{O}_{2}^{2+}+ \)
\( \boldsymbol{M} \boldsymbol{n}^{2+}+\boldsymbol{H}_{3} \boldsymbol{O}^{+} \)
If he wants to react the total \( U^{4+} \)
sample with a maximum of \( 50 \mathrm{ml} \) of \( K M n O_{4} \) solution, what concentration does he choose? \( (\mathrm{U}=238) \)
A. 0.0336 M
B. 0.0168 М
c. 0.168 м
D. 0.0672 M
Subject: Maths
ff \( \boldsymbol{y}=\boldsymbol{e}^{\boldsymbol{a} \boldsymbol{x}} \) cos \( \boldsymbol{b} \boldsymbol{x}, \) then find the value of
\( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}-\boldsymbol{2} \boldsymbol{a} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\left(\boldsymbol{a}^{2}+\boldsymbol{b}^{2}\right) \boldsymbol{y} \)
A . 0
B. 1
\( \mathbf{c} \cdot e^{a x} \)
D. 3a
Subject: Physics
Figure shows a container filled with a liquid of density \( \rho . \) Four points \( A, B, C \) and D lie on the vertices of a vertical
square. Points A and C lie on a vertical
line and points \( \mathrm{B} \) and \( \mathrm{D} \) lies on a
horizontal line. Choose the correct
statement(s) about the pressure at the
four points
This question has multiple correct options
A \( \cdot P_{D}=P_{B} \)
B . \( P_{A}<P_{B}=P_{D}<P_{C} \)
\( \mathbf{c} \cdot P_{D}=P_{B}=\frac{P_{c}-P_{A}}{2} \)
D \( \cdot P_{D}=P_{B}=\frac{P_{c}+P_{A}}{2} \)
Subject: Maths
The sum of the series \( 1+2.2+3.2^{2}+ \)
\( 4.2^{3}+5.2^{4}+.+100.2^{99} \) is \( ? \)
B. \( 100.2^{100}+1 \)
c. \( \$ \$ 99.2^{\lambda}[100] \$ \$ \)
D. \( 99.2^{100}+1 \)
Subject: Physics
A girl weighing 50 kg makes a high jump of \( 1.2 \mathrm{m} . \mathrm{What} \) is her kinetic energy at the highest point? \( \left(\boldsymbol{g}=\mathbf{1 0 m s}^{-\mathbf{2}}\right) \)
A. 6000
B. 600 J
c. 60 J
D. zero
Subject: Chemistry
In pure HCOOH liquid, concentration of \( H C O O^{-}=10^{-3} M \) at \( 27^{0} C . \) What is
the self ionisation constant at \( 27^{0} C ? \)
\( \left(k=\left[\boldsymbol{H} \boldsymbol{C O O H}_{2}^{+}\right]\left[\boldsymbol{H} \boldsymbol{C O O}^{-}\right]\right) ? \)
A \( \cdot 10^{-3} \)
B . \( 10^{3} \)
\( c \cdot 10^{6} \)
D. \( 10^{-6} \)
Subject: Physics
that of copper. A \( 50 \mathrm{cm} \) length of copper
wire of diameter 2.0 mm is joined to a
\( 50 \mathrm{cm} \) length of steel wire of diameter
1.0 \( m m, \) making a combination wire of
length \( 1.0 \mathrm{m}, \) as shown. The
combination wire is stretched by a
weight added to its end. Both the copper
and the steel wires obey Hooke's
law. What is the ratio
\( A \cdot 4 \)
B. 2
\( c \cdot 1 \)
D. 0.5
Subject: Physics
\( 1 \mathrm{kg} \) of iron (specific heat \( 120 \mathrm{Cal} \mathrm{kg}^{-1} \mathrm{C} \)
-1 ) is heated by \( 1000^{\circ} \mathrm{C} \). The increase in
its mass is :
A. zero
B . \( 5.6 \times 10^{-8} \mathrm{kg} \)
\( \mathbf{c} \cdot 5.6 \times 10^{-16} \mathrm{Kg} \)
D. \( 5.6 \times 10^{-12} \mathrm{g} \)
Subject: Biology
waters off the Eastern coast of the
United States was examined by
scientists. The results are depicted in
the graph which shows the algal count at 6 different locations. The control was
also carried out without the addition of
nutrients.
The greatest increase in algae in
response to phosphorus addition is shown by location
Control Nitrogen
Phosphorus
\( A \)
\( B .2 \)
\( c \cdot 3 \)
\( D \cdot 4 \)
\( E \)
Subject: Physics
If a ship of mass \( 4 \times 10^{7} \) kg initially at
rest is pulled by a force of \( 5 \times 10^{4} \mathrm{N} \)
through a distance of 4 m, then the
speed of the ship will be (resistance due to water is negligible)
\( \mathbf{A} \cdot 5 m s^{-1} \)
B . \( 1.5 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 60 \mathrm{ms}^{-1} \)
D. \( 0.1 \mathrm{ms}^{-1} \)
Subject: Physics
A chain of length \( L \) and mass \( m \) is
allowed to fall on a table such that the
part falling on the table comes to rest simultaneously. The force acting on the
table when \( l \) part of it has lied on the
table is:
\( ^{\text {A } \cdot \frac{3 m l g}{L}} \)
\( ^{\text {в. }} \frac{2 m l g}{L} \)
c. \( \frac{m l g}{L} \)
D. \( \frac{3 m l g}{2 L} \)
Subject: Maths
Three pieces of cakes of weights \( 4 \frac{1}{2} \) lbs \( \mathbf{6} \frac{\mathbf{3}}{\mathbf{4}} \) lbs and \( \mathbf{7} \frac{\mathbf{1}}{\mathbf{5}} \) lbs respectively are to be
divided into parts of equal weights. Further each must be as heavy as possible. If one such part is served to each guest then what is the maximum number of guests that could be entertained?
Subject: Physics
The velocity with which particle strikes the plane \( \boldsymbol{O B} \)
A \( \cdot 15 \mathrm{ms}^{-1} \)
B. \( 30 m s^{-1} \)
\( c \cdot 20 m s^{-1} \)
D. \( 10 \mathrm{ms}^{-1} \)
Subject: Physics
A bullet of mass \( 20 g \) is moving with a
speed of \( 150 \mathrm{ms}^{-1} . \) It strikes a target and is brought to rest after piercing 10 \( c m \) into it. Calculate the average force
of resistance offered by the target.
A \( .2500 \mathrm{N} \)
в. 2000 J
c. \( 2250 N \)
D. 2100 J
Subject: Physics
In a series combination of two
capacitances \( C^{\prime} \) and \( C(C>C) \) (as
shown in the circuit)
A. C' stores more energy than \( C \)
B. \( C \) stores more energy than \( C^{\prime} \)
c. potential difference across \( C \) is more than that across
\( C \)
D. potential difference across \( C^{\prime} \) is less than that across \( C \)
Subject: Chemistry
At \( 80^{\circ} C, \) distilled water has hydronium
\( \operatorname{ion}\left(H_{3} O^{+}\right) \) concentration equal to \( 1 \times \)
\( 10^{-6} \) mol \( / l . \) The value of \( K_{w} \) at this
temperature would be:
A \( \cdot 1 \times 10^{-6} \)
В. \( 1 \times 10^{-12} \)
c. \( 1 \times 10^{-9} \)
D. \( 1 \times 10^{-14} \)
Subject: Maths
f \( \log _{3} 2, \log _{3}\left(2^{x}-5\right) \) and \( \log _{3}\left(2^{x}-\right. \)
\( 7 / 2) \) are in A.P, then \( x \) is equal to
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 2,3
Subject: Maths
If \( f(x)=\operatorname{sgn}\left(x^{5}\right) \) then which of the
following is/are false (where sgn denotes signum function) This question has multiple correct options
\( \mathbf{A} \cdot f^{\prime}\left(0^{+}\right)=1 \)
B. \( f^{\prime}\left(0^{-}\right)=1 \)
C. \( f \) is continuous but not differentiable at \( x=0 \)
D. fis discontinuous at \( x=0 \)
Subject: Chemistry
The following reactions are carried out:
\( \boldsymbol{A}: \) Nitrogen \( + \) metal \( \rightarrow \) compound \( \boldsymbol{X} \)
\( B: X+ \) water \( \rightarrow \) ammonia \( + \) another
compound \( C: \) Ammonia \( + \) metal oxide \( \rightarrow \) metal \( + \)
water \( +N_{2} \)

One metal that can be used for reaction
\( A \) is magnesium. Write the correctly
balanced equation for reaction \( B \), where \( X \) is the compound formed
A \( . N a N_{2}+H_{2} O \rightarrow N H_{3}+N a_{2} O \)
B. \( M g_{3} N_{2}+3 H_{2} O \rightarrow 2 N H_{3}+3 M g O \)
c. \( C a_{3} N_{2}+H_{2} O \rightarrow N H_{3}+C a O \)
D. None of these
Subject: Chemistry
If the mass of electron is \( 9.11 \times 10^{-31} \)
kg. Planck's constant is \( 6.626 \times 10^{-34} \)
J-s and uncertainty in position is \( 0.1 A \) then uncertainty in velocity is?
A \( \cdot 5.79 \times 10^{8} \mathrm{m} / \mathrm{s} \)
В. \( 5.79 \times 10^{5} \mathrm{m} / \mathrm{s} \)
c. \( 5.79 \times 10^{6} \mathrm{m} / \mathrm{s} \)
D. \( 5.79 \times 10^{7} \mathrm{m} / \mathrm{s} \)
Subject: Physics
If the particle was to start at the extreme position i.e \( x=+A \), then what will be the equation of SHM:
\( \mathbf{A} \cdot A \cos (\omega t) \)
B. \( \operatorname{Asin}(\omega t) \)
c. \( \operatorname{Acot}(\omega t) \)
D. \( \operatorname{Atan}(\omega t) \)
Subject: Physics
If \( g \) is the acceleration due to gravity at
the Earths, surface, the gain of the potential energy of an object of mass \( \mathrm{m} \)
raised from the surface of the Earth to
height equal to the radius \( \mathrm{R} \) of the Earth
is :
A \( \cdot \frac{m g R}{4} \)
в. \( \frac{m g R}{2} \)
\( \mathrm{c} \cdot m g R \)
D. \( 2 m g R \)
Subject: Physics
and \( C \) have radii \( a, b \) and \( c(a<b<c) \)
and surface charge densities on them
\( \operatorname{are} \sigma,-\sigma, \) and \( \sigma \) respectively. The
values of \( \boldsymbol{V}_{\boldsymbol{A}} \) and \( \boldsymbol{V}_{\boldsymbol{B}} \) will be:
A \( \cdot \frac{\sigma}{\epsilon_{0}}(a-b+c), \frac{\sigma}{\epsilon_{0}}\left(\frac{a^{2}}{b}-b+c\right) \)
B \( \cdot \frac{\sigma}{\epsilon_{0}}(a-b+c), \frac{\sigma}{\epsilon_{0}} \frac{a^{2}}{c} \)
c. \( \frac{\sigma}{\epsilon_{0}}(a+b-c), \frac{\sigma}{\epsilon_{0}}\left(\frac{a^{2}}{c}-b+c\right) \)
\( \stackrel{\sigma}{\epsilon_{0}}\left(\frac{a^{2}}{c}-\frac{b^{2}}{c}+c\right), \frac{\sigma}{\epsilon_{0}}(a-b+c) \)
Subject: Maths
If the determinant
\( \left|\begin{array}{ccc}\boldsymbol{b}-\boldsymbol{c} & \boldsymbol{c}-\boldsymbol{a} & \boldsymbol{a}-\boldsymbol{b} \\ \boldsymbol{b}^{\prime}-\boldsymbol{c}^{\prime} & \boldsymbol{c}^{\prime}-\boldsymbol{a}^{\prime} & \boldsymbol{a}^{\prime}-\boldsymbol{b}^{\prime} \\ \boldsymbol{b}^{\prime \prime}-\boldsymbol{c}^{\prime \prime} & \boldsymbol{c}^{\prime \prime}-\boldsymbol{a}^{\prime \prime} & \boldsymbol{a}^{\prime \prime}-\boldsymbol{b}^{\prime \prime}\end{array}\right| \)
is expressible as \( m\left|\begin{array}{lll}a & b & c \\ a^{\prime} & b^{\prime} & c^{\prime} \\ a^{\prime \prime} & b^{\prime \prime} & c^{\prime \prime}\end{array}\right|, \) then
the value of \( \mathrm{m} \) is
A . -
B.
\( c \)
\( D \)
Subject: Physics
A truck weighing 1000 kgf changes its
speed from \( 36 k m h^{-1} \) to \( 72 k m h^{-1} \) in 2
minutes. \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} \boldsymbol{s}^{-2}\right) . \) Calculate the
work done by the engine
A \( \cdot 1.5 \times 10^{4} J \)
В. \( 1 \times 10^{5} J \)
c. \( 7.2 \times 10^{5} J \)
D. \( 0 . J \)
Subject: Physics
Assertion
Displacement-time equation of two particles moving in a straight line are, \( s_{1}=2 t-4 t^{2} \) and \( s_{2}=2 t+4 t^{2} \)
Relative velocity between the two will go on increasing.
Reason
If velocity and acceleration are of same sign then speed will increase.
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 is incorrect but Reason is correct
Subject: Physics
A double concave thin lens made out of
glass \( (\mu=1.5) \) have radii of curvature
\( 500 \mathrm{cm} . \) This lens is used to rectify the defect in vision of a person. The far point of the person will be at
\( A \cdot 5 m \)
B. 2.5 \( m \)
c. \( 1.25 \mathrm{m} \)
D. \( 1 \mathrm{m} \)
Subject: Chemistry
Magnesium reacts with an element \( (\boldsymbol{X}) \)
to form an ionic compound. If the ground state electronic configuration of
\( (X) \) is \( 1 s^{2} 2 s^{2} 2 p^{3}, \) the simplest formula for this compound is:
A. \( M g_{2} X \)
в. \( M g_{2} X_{3} \)
с. \( M g_{3} X_{2} \)
D. \( M g X_{2} \)
Subject: Physics
A stone is dropped from the top of a tall cliff and \( n \) seconds later another stone
is thrown vertically downwards with velocity u. Then the second stone overtakes the first, below the top of the
cliff at a distance given by:
[Assume u sufficiently enough to overtake the first stone]
\( A \)
\( \left(\frac{g}{2}\right)\left[n \frac{\left(\frac{g n}{2}-u\right)}{g n-u}\right]^{2} \)
B.
\( \left(\frac{g}{2}\right)\left[n \frac{\left(g n-\frac{u}{2}\right)}{g n-u}\right]^{2} \)
c.
\( (g)\left[\frac{(g n-u)}{g n-(u / 2)}\right]^{2} \)
D.
\( \left(\frac{g}{5}\right)\left[\frac{(g n-u)}{g n-(u / 2)}\right]^{2} \)
Subject: Chemistry
The equilibrium of formation of phosgene is represented as:
\( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C} \boldsymbol{O} \boldsymbol{C l}_{2}(\boldsymbol{g}) \)
The reaction is carried out in a \( 500 m L \)
flask. At equilibrium 0.3 mole of
phosgene, 0.1 mole of \( C O \) and 0.1 mole
of \( C l_{2} \) are present. The equilibrium
constant of the reaction
is
A . 30
B. 15
c. 5
D. 3
Subject: Maths
f \( x+y+z=\pi \) and
\( \Delta=\left|\begin{array}{ccc}\sin 3 x & \sin 3 y & \sin 3 z \\ \sin x & \sin y & \sin z \\ \cos x & \cos y & \cos z\end{array}\right| \)
then \( \Delta \) equals
\( A \)
в.
\( c . \)
\( D \)
Subject: Maths
Find the reduced form of the expression \( \frac{20 u^{3} v^{2}-15 u^{2} v}{10 u^{4} v+30 u^{3} v^{3}} \)
A \( \cdot \frac{5 u v}{40 u^{7} v^{4}} \)
в. \( \frac{2 v-1}{u+2 u v^{2}} \)
c. \( \frac{4 u v-3}{2 u^{2}+6 u v^{2}} \)
D. \( \frac{2 u v-3 u v^{2}}{u^{2}+6} \)
Subject: Maths
The center of a circle which passes
through the points (0,0),(1,0) and touches the circles \( x^{2}+y^{2}=9 \)
\( ^{A} \cdot\left(\frac{3}{2}, \frac{1}{2}\right) \)
в. \( \left(\frac{1}{2}, \frac{3}{2}\right) \)
c. \( \left(\frac{1}{2}, \frac{1}{2}\right) \)
D. \( \left(\frac{1}{2}, \sqrt{2}\right) \)
Subject: Physics
A ray of light is incident on a prism A \( B C \) of refractive index \( \sqrt{3} \) as shown in
figure.
(a) Find the angle of incidence for which
the deviation of light ray by the prism
A \( B C \) is minimum.
(b) By what angle the second prism must be rotated, so that the final ray
suffer net minimum deviation.
A \( \cdot 30^{\circ}, 60^{\circ} \)
B . \( 60^{\circ}, 30^{\circ} \)
\( \mathbf{c} \cdot 60^{\circ}, 60^{\circ} \)
D. None of these
Subject: Physics
A wedge of mass \( M=2 \mathrm{kg} \) is placed
over a rough horizontal surface having
coefficient of friction \( \mu, \) a block of mass
\( m=1 \mathrm{kg} \) is placed over this wedge as
shown in figure. If coefficient of friction
between wedge and block is \( \mu_{1}=0.8 \)
then the minimum value of \( \mu \) so that
wedge does not slip over a horizontal
surface, is
\( A .0 .8 \)
в. 0.75
\( c .0 .5 \)
D. zero
Subject: Chemistry
Consecutive elements \( X, Y \) and \( Z \) are in
Period 3 of the Periodic Table. Element \( Y \)
has the highest first ionisation energy and the lowest melting point of these three elements.

What are the identities of \( X, Y \) and \( Z ? \)
A. Sodium, magnesium, aluminium
B. Magnesium, aluminium, silicon
c. Aluminium, silicon, phosphorus
D. silicon, phosphorous, sulfur
Subject: Maths
Evaluate: \( \lim _{x \rightarrow 1} \frac{x^{\frac{1}{3}}-1}{x^{-\frac{2}{3}}-1} \)
A \( \cdot \frac{-1}{2} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{2}{3} \)
D. \( \frac{3}{2} \)
Subject: Physics
A planet revolves round the sun in an
elliptical orbit of semi minor and major
axes \( x \) and \( y \) respectively. Then the time period of revolution is proportional to:
A. \( \quad(x+y)^{\frac{3}{2}} \)
в. \( \quad(y-x)^{\frac{3}{2}} \)
c. \( \quad_{x} \frac{3}{2} \)
D. \( \frac{3}{y^{\frac{3}{2}}} \)
Subject: Biology
The figure shows four animals (a), (b),
(c) and (d). Select the correct answer
with respect to a common characteristics of two of these animals.
(a)
(b)
(d)
A . (a) and
(d) respire mainly through body wall.
B. (b) and
(c) show radial symmetry.
\( c \cdot(a) \) and
(b) have cnidoblasts for self-defense.
D. (c) and
(d) have a true coelom.
Subject: Chemistry
Which of the following is/are correct
about critical conditions of real gas
following van der Waal's equation of
state?
This question has multiple correct options
A \( \cdot \) At \( T_{C}, \) there is no distinction between liquid and
vapour state, hence the density of liquid becomes equal to the density of vapour
B. \( A t \)
\( T_{C}, \) both \( \left[\frac{\partial P}{\partial V}\right]_{T} \) and \( \left[\frac{\partial^{2} P}{\partial V^{2}}\right]_{T} \) are equal to zero
\( \mathbf{C} \cdot Z=3 / 8 \) for every gas at \( T_{C}, \) and gases are more compressible than ideal gas
D. For temperature less than \( T_{C} \), the volume has three imaginary roots
Subject: Chemistry
When \( H_{2} O_{2} \) is added to an acidified
solution of \( K_{2} C r_{2} O_{7}, \) the solution:
A. turns green due to the formation of \( C r_{2} O_{3} \)
B. turns yellow due to the formation of \( K_{2} C r O_{4} \)
c. turns deep blue-violet due to the formation of \( \operatorname{Cr} O\left(O_{2}\right)_{2} \)
D. gives green precipitate due to the formation of \( C r(O H)_{3} \)
Subject: Biology
Which one of the following sequences shows the correct hierarchy of
classification, going from the most inclusive to the least inclusive?
A. Kingdom, Domain, Phylum, Order, Class, Family Genus, Species
B. Domain, Kingdom, Phylum, Class, order, Family Genus, Species
c. Genus, species, Kingdom, Phylum, order, Class, Family
D. species, Genus, Family, Class, order, Phylum, Kingdon
E. Domain, Phylum, Kingdom, Genus, Species, Family, Order, Class
Subject: Chemistry
Assertion
A mixture of o-nitrophenol and \( p \) nitrophenol can be separated by steam distillation.
Reason
p-nitrophenol is steam volatile whereas o-nitrophenol is not steam volatile.
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: Biology
Match the items in Column I with as
many items as possible in Column \( \begin{array}{llll} & \text { Column I } & & \text { Column II } \\ \text { (a) } & \text { Deer } & \text { (i) } & \text { Autotroph } \\ \text { (b) } & \text { Parrot } & \text { (ii) } & \text { Ecosystem } \\ \text { (c) } & \text { Cobra } & \text { (iii) } & \text { Pond } \\ \text { (d) } & \text { Pine tree } & \text { (iv) } & \begin{array}{l}\text { Deciduous } \\ \text { forests }\end{array} \\ \text { (e) } & \text { Grasshopper } & \text { (v) } & \text { Parasite } \\ & \text { (vi) } & \text { Carnivore } \\ & \text { (vii) } & \text { Producer }\end{array} \)
Subject: Physics
In Boolean algebra \( \boldsymbol{A} . \boldsymbol{B}=\boldsymbol{Y} \) implies
that:
A. product of \( A \) and \( B \) is \( Y \)
B. \( Y \) exists when \( A \) exists or \( B \) exists
c. \( Y \) exists when both \( A \) and \( B \) exist but not when only \( A \) or \( B \) exists
D. \( Y \) exists when \( A \) or \( B \) exists but not both \( A \) and \( B \) exist
Subject: Chemistry
A gas obeys the Van der Waals equation
The approximate value of the constants
a' and 'b' for this gas are:
\( \mathbf{A} \cdot 1.88 \times 10^{6} c c^{2} a t m / m o l e^{2}, 120 c c / m o l e \)
B . \( 3.16 \times 10^{6} c c^{2} a t m / \) mole \( ^{2}, 30 \mathrm{cc} / \mathrm{mole} \)
C. \( 3.16 \times 10^{6} \mathrm{cc}^{2} \) atm \( / \mathrm{mole}^{2}, 50 \mathrm{cc} / \mathrm{mol} \)
D. \( 0.86 \times 10^{5} \mathrm{cc}^{2} \) atm / mole \( ^{2}, 30 \mathrm{cc} / \mathrm{mole} \)
Subject: Chemistry
The reaction:
\[
\mathbf{2} \boldsymbol{C}+\boldsymbol{O}_{2} \rightarrow \boldsymbol{2} \boldsymbol{C} \boldsymbol{O}
\]
is carried out by taking \( 24 g \) of carbon
and \( 96 ~ g O_{2} . \) The amount of other
reactant in grams that should be taken
so that nothing is left at the end of the
reaction is :
Subject: Physics
A force acts on a \( 3 g \) particle in such a way that the position of the particle as a function of time is given by \( \boldsymbol{x}=\mathbf{3} \boldsymbol{t}- \)
\( 4 t^{2}+t^{3}, \) where \( x \) is in meters and \( t \) is in
second. The work done during the first 4 second is:
A. \( 490 m J \)
J
в. \( 450 m J \)
\( \mathrm{c} .528 \mathrm{mJ} \)
D. \( 530 m J \)
Subject: Maths
If \( \mathbf{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{0} & \mathbf{3}\end{array}\right] \) and \( \mathbf{B}=[\mathbf{3}-\mathbf{1}], \) then
\( \mathbf{B A}= \)
A. \( \left[\begin{array}{ll}3 & 0 \\ 0 & 3\end{array}\right] \)
B. \( \left[\begin{array}{ll}3 & 0\end{array}\right] \)
\( \begin{array}{ll}\text { c. }[3 & 3]\end{array} \)
D. \( [0-3] \)
Subject: Maths
The number of terms whose values
depends on \( x \) in the expansion of \( \left(x^{2}-2+\frac{1}{x^{2}}\right)^{n} \) is
\( \mathbf{A} \cdot 2 n+1 \)
B. \( 2 n \)
\( c \)
D. none of these