AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A circular plane sheet of radius \( 10 \mathrm{cm} \) is
placed in a uniform electric field of \( \mathbf{5} \times \mathbf{1 0}^{\mathbf{5}} \mathbf{N} \quad \mathbf{C}^{-1}, \) making an angle of \( \mathbf{6 0}^{\mathbf{0}} \)
with field. The electric flux through the sheet is
\( \begin{array}{lll}\text { A } \cdot 1.36 \times 10^{2} N & \text { m }^{2} & C^{-1}\end{array} \)
B . \( 1.36 \times 10^{4} N \quad m^{2} \quad C^{-1} \)
\( \begin{array}{lll}\text { С } \cdot 0.515 \times 10^{2} N & \text { m }^{2} & C^{-1}\end{array} \)
\( \begin{array}{lll}\text { D. } 0.515 \times 10^{4} N & \text { m }^{2} & C^{-1}\end{array} \)
Subject: Physics
If the forward voltage in a semiconductor diode is changed from \( 0.5 V \) to \( 0.7 V, \) then the forward current
changes by \( 1.0 m A . \) The forward resistance of diode junction will be
\( \mathbf{A} \cdot 100 \Omega \)
в. \( 120 \Omega \)
c. \( 200 \Omega \)
D. 240\Omega
Subject: Maths
A student was given a piece of rope and
told to cut it into two equal pieces, keep one piece, and pass the other piece to the next student. Each student was to
repeat this process until every student in the class had exactly one piece of rope. Which of the following could be the fraction of the original rope that one of the students had?
A \( \cdot \frac{1}{14} \)
в. \( \frac{1}{15} \)
c. \( \frac{1}{16} \)
D. \( \frac{1}{17} \)
E \( \frac{1}{18} \)
Subject: Physics
A free nucleus of mass 24 amu, intially at rest emits a gamma photon. The
energy of the photon is \( 7 M e V \). The
kinetic energy of recoiling nucleus is
approximately equal to [Take; 1 am \( u= \) \( \mathbf{9 . 3 1} \boldsymbol{M e V} \)
A . \( 3.3 k e V \)
B. 4.4keV
c. \( 1.1 k e V \)
D. 2.5keV
Subject: Maths
Assertion (A): The roots of \( (x-a)(x- \)
\( b)+(x-b)(x-c)+(x-c)(x-a)= \)
0 are real
Reason (R): A quadratic equation with non-negative discriminant has real
roots
A. Both (A) and (R) are true and (R) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not the correct explanation of \( (A) \)
\( c \cdot(A) \) is true but (R) is false
D. (A) is false but (R) is true
Subject: Physics
Science fiction films often show battles
between spaceships. Four friends were arguing what would someone in space hear if an enemy spaceship exploded? Rekha said, 'they would hear a big explosion. Renu saud,'they will not hear anything as there is no medium for sound to
travel, but they can see the explosion. Ramesh said, 'yes, they will not hear
anything and they will not be able to see the explosion. Raghav said,'the explosion produces sound of frequency above \( 20,000 \mathrm{Hz} \) hence we cannot hear it.'
Who is correct?
A. Rekha
B. Renu
C. Ramesh
D. Raghav
Subject: Physics
A train \( 100 \mathrm{m} \) long travelling at \( 40 \mathrm{m} / \mathrm{s} \) starts overtaking another train \( 200 \mathrm{m} \) long travelling at \( 30 \mathrm{m} / \mathrm{s} \). The time taken by the first train to pass the second train completely is:
A. 30
B. 40
\( c .50 \mathrm{s} \)
D. 60 s
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{3} & \mathbf{1} \\ \mathbf{7} & \mathbf{5}\end{array}\right], \) find the values of \( \boldsymbol{x} \) and
\( y \) such that \( A^{2}+x I_{2}=y A \)
Subject: Chemistry
\( \boldsymbol{S} \boldsymbol{O}_{2} \) reduces \( \boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{2-} \) to \( \boldsymbol{C r}^{2+} \). The
change in oxidation number of \( \boldsymbol{C r} \) is:
Subject: Physics
A disc of mass \( m \) and radius \( R \) moves
in the \( x \) -y plane as shown in figure. The
angular momentum of the disc about
the origin \( O \) at the instant shown is:
\( ^{\mathrm{A}} \cdot_{-}^{5}^{m R^{2} \omega \hat{k}} \)
\( ^{\mathrm{B}} \cdot \frac{7}{3}^{m R^{2} \omega \hat{k}} \)
C \( -\frac{9}{2} m R^{2} \omega \hat{k} \)
\( \stackrel{0}{2}^{m} m^{2} \omega \)
Subject: Physics
: A sphere
Il: A cube
III: A thin circular plate;
All made of the same material having the same mass are initially heated to
\( 200^{0} \mathrm{C} . \) Identify the order in which the objects cool faster when left in air
at room temperature:
A. III,II and I
B. II, I and III
c. ।, ॥ and III
D. II, III and I
Subject: Chemistry
\( \boldsymbol{P C l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \)
In above reaction, at equilibrium
condition mole fraction of \( \boldsymbol{P C l}_{5} \) is \( \mathbf{0 . 4} \)
and mole fraction of \( C l_{2} \) is \( 0.3 . \) Then
find out mole fraction of \( \boldsymbol{P} \boldsymbol{C l}_{3} \)
A . 0.3
B. 0.7
\( c .0 .4 \)
D. 0.6
Subject: Maths
Simplify \( \left(2 x+\frac{1}{3 y}\right)^{2}-\left(2 x-\frac{1}{3 y}\right)^{2} \)
A \( \cdot \frac{4 x}{3 y} \)
в. \( 2\left(4 x^{2}+\frac{1}{9 y^{2}}\right) \)
c. \( \frac{8 x}{3 y} \)
D. \( \frac{4 y}{3 x} \)
Subject: Physics
A metal sphere A of radius \( r_{1} \) charged
to a potential \( \phi_{1} \) is enveloped by a thin
walled conducting spherical shell B of
radius \( r_{2} \). Then potential \( \phi_{2} \) of the sphere \( A \) after it is connected to the
shell B by a thin conducting wire will be
A \( \cdot \phi_{1} \frac{r_{1}}{r_{2}} \)
В \( \cdot \phi_{1}\left(\frac{r_{2}}{r_{1}}\right) \)
c. \( \phi_{1}\left(1-\frac{r_{2}}{r_{1}}\right) \)
\( \mathbf{D} \cdot \mathbf{q} \phi_{1}\left(\frac{r_{1} r_{2}}{r_{1} r_{2}}\right) \)
Subject: Physics
A uniform steel rod of length 1 m and
area of cross section \( 20 \mathrm{cm}^{2} \) is hanging
from a fixed support. Find the increase in the length of the rod. \( \left(Y_{\text {steel}}=2.0 \times\right. \)
\( \mathbf{1 0}^{11} \boldsymbol{N m}^{-2}, \boldsymbol{\rho}_{\text {steel}}=\mathbf{7 . 8 5} \times \)
\( \left.10^{3} K g m^{-3}\right) \)
A \( .1 .923 \times 10^{-5} \mathrm{cm} \)
В. \( 2.923 \times 10^{-5} \mathrm{cm} \)
c. \( 1 . .123 \times 10^{-5} \mathrm{cm} \)
D. \( 3.123 \times 10^{-5} \mathrm{cm} \)
Subject: Maths
The length of a minute hand of a wall
clock is \( 8.4 \mathrm{cm} . \) Find the area swept by it in half an hour.
A \( \cdot 100 \mathrm{cm}^{2} \)
В. \( 110.88 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 120 \mathrm{cm}^{2} \)
D. \( 130 \mathrm{cm}^{2} \)
Subject: Maths
Tangent is drawn from (1,0) to \( y=e^{x} \)
then the area bounded between the
coordinate axes and the tangent is
equal to -
A \( \cdot \frac{e}{2} \)
B. \( e \)
\( ^{c} \cdot \frac{e^{2}}{2} \)
\( \mathbf{D} \cdot e^{2} \)
Subject: Physics
A ball of mass \( m \) is released from \( A \)
inside a smooth wedge of mass \( m \) as
shown in the figure. What is the speed
of the wedge when the ball reaches
point \( B ? \)
\( A \)
B \( \cdot \sqrt{2 g R} \)
\( c \)
D. \( \sqrt{\frac{3}{2} g R} \)
Subject: Maths
If the mean and variance of a binomial
distribution are 4 and 2 respectively,
then the probability of 2 successes of that binomial variate \( \boldsymbol{X}, \) is
A \( \cdot \frac{1}{2} \)
в. \( \frac{219}{256} \)
c. \( \frac{37}{256} \)
D. \( \frac{7}{64} \)
Subject: Maths
A rectangular tank containing water is \( 5 \mathrm{m} \) long, \( 3 \mathrm{m} \) broad and \( 2 \mathrm{m} \) deep. Find how much the water will rise, if a block
of lead \( 1 \mathrm{m} \times 45 \mathrm{cm} \times 30 \mathrm{cm} \) is put in the
tank?
A. \( 9 \mathrm{cm} \)
B. \( 90 \mathrm{cm} \)
\( \mathrm{c} .9 \mathrm{mm} \)
D. 9 m
Subject: Physics
If the phase difference between Alternating Voltage and Alternating
Current is \( \frac{\pi}{6} \) and the resistance in the circuit is \( \sqrt{300} \Omega, \) then the impedance of the circuit will be
A . 25\Omega
B. \( 50 \Omega \)
\( c \cdot 20 \Omega \)
D. \( 100 \Omega \)
Subject: Physics
What is the minimum energy required to launch a satellite of mass \( m \) from the
surface of a planet of mass \( M \) and radius \( R \) in a circular orbit at an
altitude of \( 2 R ? \)
A \( \cdot \frac{2 G m M}{3 R} \)
в. \( \frac{G m M}{2 R} \)
c. \( \frac{G m M}{3 R} \)
D. \( \frac{5 G m M}{6 R} \)
Subject: Physics
The periodic time of a particle doing simple harmonic motion is 4 s. The time taken for it to go from its mean position to half the maximum displacement (amplitude) is.
\( \mathbf{A} \cdot 2 s \)
B . \( 1 s \)
c. \( \frac{2}{3} s \)
D. \( \frac{1}{3} s \)
Subject: Physics
Light described at a place by the equation \( \boldsymbol{E}=(\mathbf{1 0 0} \boldsymbol{V} / \boldsymbol{M}) \times[\sin (\mathbf{5} \times \)
\( \left.\mathbf{1 0}^{\mathbf{1 5}} \boldsymbol{s}^{-\mathbf{1}}\right) \boldsymbol{t}+\boldsymbol{\operatorname { s i n }}\left(\boldsymbol{8} \times \mathbf{1 0}^{\mathbf{1 5}} \boldsymbol{s}^{-\mathbf{1}}\right) \boldsymbol{t} \)
Falls on a metal surface having work function 2.0 e.V Calculate the maximum
kinetic energy of the photoelectrons
A . 3.27 ev
B. 5 ev
c. 1.27 ev
D. 2.5 ev
Subject: Physics
A piece of metal weighs 45 g in air and \( 25 \mathrm{g} \) in a liquid of density \( 1.5 \times \) \( 10^{3} k g-m^{-3} \) kept at \( 30 C . \) When the
temperature of the liquid is raised to \( 40 C, \) the metal piece weighs 27 g. The density of liquid at \( 40 \mathrm{C} \) is \( 1.25 \times \) \( 10^{3} k g-m^{-3} . \) The coefficient of linear
expansion of metal is
A. \( 1.3 \times 10^{-3} / C \)
в. \( 5.2 \times 10^{-3} / C \)
c. \( 2.6 \times 10^{-3} / C \)
D. \( 0.26 \times 10^{-3} / C \)
Subject: Maths
\( \int \sqrt{1+x^{2}} d x \) is equal to
A \( \cdot \frac{x}{2} \sqrt{1+x^{2}}+\frac{1}{2} \log |+\sqrt{1+x^{2}}|+C \)
B. \( \frac{2}{3}\left(1+x^{2}\right)^{\frac{2}{3}}+C \)
c. \( \frac{2}{3} x\left(1+x^{2}\right)^{\frac{3}{2}}+C \)
D \( \cdot \frac{x^{2}}{2} \sqrt{1+x^{2}}+\frac{1}{2} x^{2} \log |x+\sqrt{1+x^{2}}|+C \)
Subject: Chemistry
Based on the structure shown, what is the empirical formula for this
compound?
A. \( C H O \)
в. \( C_{2} H_{3} O_{3} \)
\( \mathbf{c} \cdot C_{2} H_{3} O_{4} \)
D \( \cdot C_{3} H_{6} O_{6} \)
E \( . C_{4} H_{6} O_{6} \)
Subject: Maths
If the mean of \( x \) and \( \frac{1}{x} \) is \( M, \) then the mean of \( x^{3} \) and \( \frac{1}{x^{3}} \)
A \( \cdot \frac{M\left(M^{2}-3\right)}{2} \)
В. \( M\left(4 M^{2}-3\right) \)
\( c \cdot M^{3} \)
D. \( M^{3}+3 \)
Subject: Maths
Let \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}, \mathbf{6}\} \) and let \( \boldsymbol{R}= \)
\( \{(a, b): a, b \in A \text { and } b=a+1\} . \) Show
that \( R \) is not transitive.
Subject: Physics
Compute the electric flux through a square surface of edges \( 2 l \) due to a
charge \( +Q \) whose geometric centre is located on the \( x \) -axis at a
perpendicular distance \( l \) from the
centre of the square.
A \( \cdot \frac{Q}{\epsilon_{0}} \)
в. \( \frac{Q}{2 \epsilon_{0}} \)
c. \( \frac{Q}{4 \epsilon_{0}} \)
D. \( \frac{Q}{6 \epsilon_{0}} \)
Subject: Physics
In double slit experiment, fringes are obtained using light of wavelength
\( 4800 A^{\circ} . \) One slit is covered with a thin
glass film of refractive index 1.4 and
another slit is covered by a film of same thickness but refractive index \( 1.7 . \) By
doing so, the central fringe is shifted to fifth bright fringe in the original pattern The thickness of glass film is :
A \( \cdot 2 \times 10^{-3} m m \)
B. \( 4 \times 10^{-3} \mathrm{mm} \)
c. \( 6 \times 10^{-3} m m \)
D. \( 8 \times 10^{-3} \mathrm{mm} \)
Subject: Physics
Two fixed charges \( -2 Q \) and \( +Q \) are located at points \( (-3 a, 0) \) and \( (+3 a, 0) \) respectively, Then which of the following statement is correct?
A. Points where the electric potential due to the two charges is zero in \( x \) -y plane, lie on a circle of radius 42 and centre (5a, 0)
B. Potential is zero at \( x=a \) and \( x=9 a \)
c. Both (a) and
(b) are wrong
D. Both (a) and (b) are correct
Subject: Maths
A fair coin is tossed five times. If the out
comes are 2 heads and 3 tails (in some
order), then what is the probability that the fourth toss is a head?
A \( \cdot \frac{1}{4} \)
B. \( \frac{2}{5} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{3}{5} \)
Subject: Chemistry
For a very dilute aqueous solution of
\( \boldsymbol{K}_{4}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right], \) van't Hoff factor is :
\( \mathbf{A} \cdot i=11 \)
в. \( i=5 \)
\( c \cdot_{i}=\frac{1}{11} \)
D. \( i=10 \)
Subject: Biology
Assertion
Vocal cords consist of three pairs of mucous membrane that extend into the
lumen of the larynx.
Reason
Sound is produced by only two pairs of cords.
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
If \( 10 g \) of ice is added to \( 40 g \) of water at
\( 15^{\circ} \mathrm{C}, \) then the temperature of the
mixture is (specific heat of water= \( 4.2 \times 10^{3} J k g^{-1} K^{-1}, \) Latent heat of
fusion of ice \( =\mathbf{3 . 3 6} \times \mathbf{1 0}^{\mathbf{5}} \boldsymbol{J} \mathbf{k g}^{-\mathbf{1}} \mathbf{)} \)
A \( \cdot 15^{\circ} \mathrm{C} \)
В. \( 12^{\circ} \mathrm{C} \)
\( c \cdot 10^{\circ} C \)
D. \( 0^{\circ} \mathrm{C} \)
Subject: Physics
The volume of a gas is reduced to \( \frac{1}{4} \) of
its initial volume adiabatically at \( 27^{\circ} \)
The final temperature of the gas (if \( \gamma= \)
1.4) will be
A. \( 27 \times(4)^{0.4} K \)
B . \( 300 \times(1 / 4)^{0.4} K \)
c. \( 100 \times(4)^{\text {) } \cdot 4} K \)
D. \( 300 \times(4)^{0.4} \mathrm{K} \)
Subject: Chemistry
Which of the following elements follow Dobereiner's law of Triads?
A. \( \mathrm{Na}=23, \mathrm{Li}=7 \) and \( \mathrm{K}=39 \)
B. Cl = \( 35, \mathrm{Br}=80 \) and \( \mathrm{F}=19 \)
c. \( \mathrm{ca}=40, \mathrm{Mg}=24 \) and \( \mathrm{Sr}=88 \)
D. \( \mathrm{Na}=23, \mathrm{K}=39 \) and \( \mathrm{Rb}=85 \)
Subject: Maths
The equation of the normal to the curve \( x=a \cos ^{3} \theta, y=a \sin ^{3} \theta \) at the point
\( \boldsymbol{\theta}=\frac{\boldsymbol{\pi}}{\boldsymbol{4}} \) is
\( \mathbf{A} \cdot x=0 \)
В. \( y=0 \)
c. \( x=y \)
D. \( x+y=a \)
Subject: Maths
\( \operatorname{Det}\left[\begin{array}{ccc}\mathbf{4 3} & \mathbf{1} & \mathbf{6} \\ \mathbf{3 5} & \mathbf{7} & \mathbf{4} \\ \mathbf{1 7} & \mathbf{3} & \mathbf{2}\end{array}\right]=\dots \)
\( A \)
B. - -
\( c \cdot 0 \)
\( D \)
Subject: Chemistry
The correct geometry and hybridization
for \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{4} \) are :
A . trigonal planar, \( s p^{3} d^{3} \)
B. square planar, \( s p^{3} d^{2} \)
c. octahedral, \( s p^{3} d^{2} \)
D. trigonal bipyramidal, \( s p^{3} d \)
Subject: Chemistry
Which of the following is not a deuterolysis reaction
A. \( S O_{3}+D_{2} O \rightarrow D_{2} S O_{4} \)
в. \( C a C_{2}+2 D_{2} O \rightarrow C a(O D)_{2}+C_{2} D_{2} \)
c. \( M g_{3} N_{2}+6 D_{2} O \rightarrow 3 M g(O D)_{2}+2 N D_{3} \)
D. \( A l C l_{3} 3 D_{2} O \rightarrow A l(O D)_{3}+3 D C l \)
Subject: Biology
Assertion
Temperature and soil moisture are the important climatic factors that
regulate the process of decomposition.
Reason

Warm and moist environment favours
decomposition whereas low temperature and anaerobiosis inhibit decomposition.
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
A meteor of mass \( M \) breaks up into two
parts. The mass of one part is \( m \). For a
given separation \( r \) the mutual
gravitational force between the two parts will be maximum if
A. \( m=(M / 2) \)
в. \( m=(M / 3) \)
c. \( _{m}=\frac{M}{\sqrt{2}} \)
D. \( _{m}=\frac{M}{2 \sqrt{2}} \)
Subject: Chemistry
In a closed container at a given temperature, pressure increases from \( 100 \mathrm{mm} \) Hg to \( 160 \mathrm{mm} \) Hg in 10 sec. for
reaction.

Then the average rate of reaction in first
10 sec. will be?
A. \( 2 \mathrm{mm} / \mathrm{sec} \)
B. \( 4 \mathrm{mm} / \mathrm{sec} \)
c. \( 6 \mathrm{mm} / \mathrm{sec} \)
D. 3 mm/sec.
Subject: Physics
A student performed the experiment of
determination of focal length of a
concave mirror by u v method using an optical bench of length 1.5 meter. The focal length of the mirror used is \( 24 \mathrm{cm} \) The maximum error in the location of
the image can be \( 0.2 \mathrm{cm} . \) The 4 sets of (u, v) values recorded by the student(in
\( \mathrm{cm} \) ) are: \( (42,56),(48,48),(66,33),(78, \)
39). The data set(s) that cannot come
from experiment and is (are) incorrectly recorded, is (are):
This question has multiple correct options
A . (42, 56)
B. (48,48)
C. (66,33)
D. (78, 39)
Subject: Maths
For the following distribution function \( F(x) \) of a r.v \( X \) is given
\[
\begin{array}{ccccc}
x & 1 & 2 & 3 & 4 \\
F(x) & 0.2 & 0.37 & 0.48 & 0.62
\end{array}
\]
Then \( P(3<x \leq 5)= \)
A . 0.48
в. 0.37
c. 0.27
D. 1.47
Subject: Physics
The kinetic energy of 1 gram mole of a gas at normal temperature and pressure is \( (\mathrm{R}=8.31 \mathrm{J} / \mathrm{mole}-\mathrm{K}) \)
A \( \cdot 0.56 \times 10^{4} J \)
В. \( 1.3 \times 10^{2} J \)
c. \( 2.7 \times 10^{2} J \)
D. 3.4 \( \times 10^{3} \mathrm{J} \)
Subject: Biology
Assertion
The hierarchy includes seven obligate
categories.
Reason
Intermediate categories are used to make taxonomic position more informative.
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
The Cartesian equation of a line is
\( \frac{\boldsymbol{x}-\mathbf{5}}{\mathbf{3}}=\frac{\boldsymbol{y}+\mathbf{4}}{\mathbf{7}}=\frac{\boldsymbol{z}-\mathbf{6}}{\mathbf{2}} . \) Write its vector
form.
Subject: Physics
A solenoid has a core of a material with
relative permeability of 500. The windings of the solenoid are insulated
from the core and carry a current of \( 2 \mathrm{A} \) If the number of turns is 1000 per
meter, then magnetisation will be then
A . \( 7.78 \times 10^{5} \mathrm{Am}^{-1} \)
В. \( 8.88 \times 10^{5} \mathrm{Am}^{-1} \)
c. \( 9.98 \times 10^{5} \mathrm{Am}^{-} \)
D. \( 10.2 \times 10^{5} \mathrm{Am}^{-1} \)
Subject: Physics
Assertion
The flow of heat energy from one body to the other depends upon the amount of heat energy in them
Reason
Heat flows from lower temperature of the body to higher temperature of the body
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
On a two-lane road, car \( A \) is travelling
with a speed of \( 36 k m h^{-1} . \) Two cars \( B \)
and \( C \) approach car \( A \) in opposite
directions with a speed of \( 54 k m h^{-1} \) each. At a certain instant, when the
distance \( A B \) is equal to \( A C, \) both being
\( 1 k m, B \) decides to overtake \( A \) before \( C \)
does. What minimum acceleration of
\( \operatorname{car} B \) is required to avoid an accident?
Subject: Chemistry
The decomposition of \( N H_{3} \) on
platinum surface is zero order. What are
the rate of production of \( N_{2} \) and \( H_{2} \) in mole.lit\( ^{-1} \cdot \sec ^{-1} \) if \( K=2.5 \times \)
\( 10^{-4} \) mole.lit \( ^{-1} . \) sec \( ^{-1} ? \)
\( \begin{array}{ll}\text { A } \cdot 3.75 \times 10^{-4}, & 1.25 \times 10^{-4}\end{array} \)
B. \( 1.25 \times 10^{-4}, \quad 3.75 \times 10^{-4} \)
C . \( 2.5 \times 10^{-4}, \quad 7.5 \times 10^{-4} \)
D. \( 1.25 \times 10^{4}, \quad 3.75 \times 10^{-4} \)
Subject: Chemistry
Assertion
The complex ion \( \left[C o(e n)_{2} B r_{2}\right]^{-} \) has
three stereoisomers.
Reason
The complex ion \( \left[C o(e n)_{2} B r_{2}\right]^{-} \) has an
octahedral geometry.
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
A steel ball is dropped from a height \( h_{0} \) The collision of the ball with the floor is
inelastic with coefficient of restitution
e. Then, the height up to which the ball will rise after second collision is :
\( \mathbf{A} \cdot e^{4} h_{0} \)
B. 2eh
\( c \cdot e^{2} h_{0} \)
D. \( e^{-2} h_{0} \)
Subject: Chemistry
1 kg of water under a nitrogen pressure of 1 atmosphere dissolves 0.02 gm of nitrogen at \( 293 \mathrm{K} \) Calculate Henry's law constant.
A \( \cdot 7.2 \times 10^{-4} \) atm
B . \( 7.5 \times 10^{4} \) atm
\( c \cdot 7.4 \times 10^{4} \operatorname{atm} \)
D. \( 7.2 \times 10^{4} \) atm
Subject: Maths
A dome of a building is in the form of a hemisphere. From inside, it ws white-
washed at the cost of RS. \( 498.96 . \) If the
\( \operatorname{cost} \) of white-washing is Rs. 2.00 per
square metre, find the
(i) inside surface area of the dome,
(ii) volume of the air inside the dome.
Subject: Chemistry
Arrange the following aqueous solutions in the order of their increasing boiling points
\( (\mathrm{i}) 10^{-4} M N a C l \)
(ii) \( 10^{-4} M \) Urea
\( (\text { iii }) 10^{-3} M M g C l_{2} \)
(iv) \( 10^{-2} M N a C l \)
A \( \cdot(i)<(i i)<(i v)<(i i i) \)
B. \( (i i)<(i)<(i i i)<(i v) \)
c. \( (i i i)<(i)<(i i)<(i v) \)
D. \( (i v)<(i i i)<(i)=(i i) \)
Subject: Physics
When a metal plate is introduced
between the two plates of a charged capacitor and insulated from them,
then
This question has multiple correct options
A. the metal plate divides the capacitor into two capacitors connected in parallel to each other
B. the metal plate divides the capacitor into two capacitors connected in series with each other
C. the metal plate is equivalent to a dielectric of zero dielectric constant
D. the metal plate is equivalent to a dielectric of infinite dielectric constant
Subject: Maths
\( f(x)=\frac{a \sin x-b x+c x^{2}+x^{3}}{2 x^{2} \ell n(1+x)-2 x^{3}+x^{4}} \)
when \( x \neq 0 \) and \( f(x) \) is continuous at
\( \boldsymbol{x}=\mathbf{0}, \) find value of \( \mathbf{2 0 0} \times \boldsymbol{f}(\mathbf{0}) \)
Subject: Physics
A small cannon 'A' is mounted on a
platform (which can be rotated so that cannon can aim at any point) and is adjusted for maximum range \( R \) of
shells. It can throw shells on any point on the shown circle (dotted) on ground.
Suddenly a windstorm starts blowing in horizontal direction normal to AB with
speed \( \sqrt{2} \) times the velocity of shell. At what least distance can the shell land
from point B. (Assume that the velocity of projection. Also assume that the
platform is kept stationary while projecting the shell.)
A \( \cdot R(\sqrt{5}-1) \)
B . \( R(\sqrt{3}-1) \)
\( \mathbf{c} . R \sqrt{5} \)
D. \( R \sqrt{3} \)
Subject: Maths
A bag contains 5 red and 3 green balls. Another bag contains 4 red and 6 green balls. If one ball is drawn from each bag.
Find the probability that one ball is red and one is green?
A . \( 19 / 20 \)
B. 17/20
\( c \cdot 8 / 10 \)
D. 21/40
\( E \cdot 15 / 40 \)
Subject: Maths
Show that the minimum of \( Z \) occurs at
more than two points. Minimise and Maximise \( Z=x+2 y \)
subject to \( x+2 y \geq 100,2 x-y \leq \)
\( \mathbf{0}, \mathbf{2} \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{2 0 0} ; \boldsymbol{x}, \boldsymbol{y} \geq \mathbf{0} \)
Subject: Chemistry
Decrease in the pressure for the following equilibria: \( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{H}_{2} \boldsymbol{O}(l) \)
result in:
This question has multiple correct options
A. Formation of more \( H_{2} O(s) \)
B. Formation of more \( H_{2} O(l) \)
C . increase in melting point of \( H_{2} O(s) \)
D. decrease in melting point of \( H_{2} O(s) \)
Subject: Physics
In the circuit shown in figure cells of
emf 2,1,3 and \( 1 V \) respectively having
resistances \( 2 \Omega, 1 \Omega, 3 \Omega \) and \( 1 \Omega \) are
their internal resistances respectively.
The potential difference between D and B (in volts)
A \( \cdot \frac{5}{13} \)
в. \( \frac{2}{13} \)
c. \( \frac{10}{13} \)