AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The acceleration of a particle is given by \( \vec{a}=\left\lfloor 2 \hat{i}+6 t \hat{j}+\frac{2 \pi^{2}}{9} \cos \frac{\pi t}{3} \hat{k}\right\rfloor m / s^{2} \)
\( \mathbf{A t} t=\mathbf{0}, \overrightarrow{\boldsymbol{r}}=\mathbf{0} \) and \( \overrightarrow{\boldsymbol{v}}=(\mathbf{2} \overrightarrow{\mathbf{i}}+\hat{\boldsymbol{j}}) \boldsymbol{m} \boldsymbol{s}^{1} \)
The position vector at \( t=2 s \) is
\( \mathbf{A} \cdot(8 \hat{i}+10 \hat{j}+\hat{k}) m \)
B . \( (8 \hat{i}+10 \hat{j}+3 \hat{k}) m \)
c. \( (3 \hat{i}+8 \hat{j}+10 \hat{k}) m \)
D. \( (10 \hat{i}+3 \hat{j}+8 \hat{k}) m \)
Subject: Chemistry
Which of the following in relation to the energy of sublevels in H atom is incorrect?
A. \( 4 s<4 p<4 d<4 f \)
B. \( 3 s<4 s<5 s<6 s \)
c. \( 4 s=4 p<5 s<6 p \)
D. \( 2 s<3 s=3 p<4 d \)
Subject: Maths
\( \int \frac{d t}{(6 t-1)} \) is equal to:
A \( \cdot \frac{1}{6} \ln (6 t-1)+C \)
B. \( \ln (6 t-1)+C \)
\( c \cdot-\frac{1}{6} \ln (6 t-1)+C \)
D. None of these
Subject: Physics
An electric field of \( 1500 V / m \) and \( a \)
magnetic field of \( 0.04 W b / m^{2} \) act on a moving electron. The minimum uniform speed along a straight line the electron could have is.
A \( \cdot 1.6 \times 10^{15} \mathrm{m} / \mathrm{s} \)
в. \( 6 \times 10^{-16} \mathrm{m} / \mathrm{s} \)
C \( .3 .75 \times 10^{4} \mathrm{m} / \mathrm{s} \)
D. \( 3.75 \times 10^{2} \mathrm{m} / \mathrm{s} \)
Subject: Physics
Let \( S \) be the set of all points in a plane. Let \( R \) be a relation on \( S \) such that for any
two points a and \( b, \) aRb iff b is within 1 \( \mathrm{cm} \) from a. Then R is
A. Equivalence relation
B. Reflexive and symmetric not transitive
C. Reflexive and transitive not symmetric
D. Symmetric and transitive not reflexive
Subject: Maths
Consider three points \( \boldsymbol{P}=(-\sin (\boldsymbol{\beta}- \)
\( \boldsymbol{\alpha}),-\cos \beta), \boldsymbol{Q}=(\cos (\beta-\boldsymbol{\alpha}), \sin \beta) \)
and \( \boldsymbol{R}=(\cos (\boldsymbol{\beta}-\boldsymbol{\alpha}+\boldsymbol{\theta}), \sin (\boldsymbol{\beta}-\boldsymbol{\theta})) \)
where \( 0<\alpha, \beta, \theta<\frac{\pi}{4} . \) Then
A. \( P \) lies on the line segment \( R Q \)
B. \( Q \) lies on the line segment \( P R \)
c. \( R \) lies on the line segment \( Q P \)
D. \( P, Q, R \) are non-collinear
Subject: Biology
Identify the given diagrams and mark
the correct option.
\( A \cdot A, D \) are compound while \( B, C \) are simple leaves
B. \( A, D \) are simple while \( B, C \) are compound leaves
\( \mathrm{C} \cdot \mathrm{A}, \mathrm{B} \) are simple while \( \mathrm{C}, \mathrm{D} \) are compound leaves
D. \( A, B \) are compound while \( C, D \) are simple leaves
Subject: Physics
The depth at which the value of acceleration due to gravity becomes \( \frac{1}{n} \) times the value at the surface is (R be
the radius of the earth):
A \( \cdot \frac{R}{n} \)
в. \( \frac{R}{n^{2}} \)
c. \( \frac{R(n-1)}{n} \)
D. \( \frac{R n}{(n-1)} \)
Subject: Maths
If \( r, s, t \) are prime numbers and \( p, q \) are the positive integers such that LCM of \( \boldsymbol{p} \) \( q \) is \( r^{2} t^{4} s^{2}, \) then the number of ordered
pair \( (\boldsymbol{p}, \boldsymbol{q}) \) is
A . 252
в. 254
c. 225
D . 224
Subject: Physics
When a \( 4 k g \) mass is hung vertically on a light spring that obeys Hooke's law,
the spring stretches by 2 cms. The work required to be done by an external agent in stretching this spring by \( 5 c m s \) will
be \( \left(\boldsymbol{g}=\mathbf{9 . 8 m} / \boldsymbol{s e c}^{2}\right) \)
A. 4.900 joule
B . 2.450 joule
c. 0.495 joule
D. 0.245 joule
Subject: Physics
A light ray is incident normally on a plane mirror.
(a) What is the angle of incidence?
(b) What is the path of reflected ray?
A \( \cdot(a) 180^{\circ},(b) \) same as incident ray
в. \( (a) 180^{\circ} \)
\( (b) \) opposite to incident ray
(b) opposite to incident ray
\( \mathbf{c} \cdot(a) 0^{\circ} \)
D. \( (a) 0^{\circ},(b) \) same as incident ray
Subject: Biology
Which of the following is incorrect
about the given graph?
A. The curve, is called oxygen dissociation curve
B. The part'A' represents percentage saturation of haemoglobin with oxygen
c. The part'B' represents partial pressure of carbon dioxide
D. This curve is highly useful in studying the effect of factors like \( P C O_{2} \), H+ concentration, etc. on binding
\( C O_{2} \) with haemoglobin
Subject: Physics
At a certain location in Africa, compass
points \( 12^{\circ} \) west of geographic north. The north tip of magnetic needle of a dip circle placed in the plane of magnetic
meridian points \( 60^{\circ} \) above the horizontal. The horizontal component of earth's field is measured to be \( 0.16 \mathrm{G} \)
The magnitude of earth's field at the
location is?
A. 0.32 G
B. 0.42 G
c. \( 4.2 \mathrm{G} \)
D. 3.2G
Subject: Chemistry
Explain why
(a) Two bodies at different
temperatures \( T_{1} \) and \( T_{2} \) if brought in thermal contact do not necessarily
settle to the mean temperature \( \left(T_{1}+T_{2}\right. \) 12
(b) The coolant in a chemical or a
nuclear plant (i.e. the liquid used to
prevent the different parts of a plant from getting too hot) should have high specific heat
(c) Air pressure in a car tyre increases during driving
(d) The climate of a harbour town is
more temperate than that of a town in a
desert at the same latitude
Subject: Physics
Two persons pull a rope towards themselves. Each person exerts a force
of \( 100 \mathrm{N} \) on the rope. Find the Young
modulus of the material of the rope if it
extends in length by 1cm. (Original length of the rope \( =2 \mathrm{m} \) and the area of
\( \operatorname{cross} \operatorname{section}=2 c m^{2} \)
Subject: Maths
Which of the following is a polynomial
with only one zero?
\( \mathbf{A} \cdot p(x)=2 x^{2}-3 x+4 \)
B \( \cdot p(x)=x^{2}-2 x+1 \)
C \( . p(x)=2 x+3 \)
D \( . p(x)=5 \)
Subject: Physics
A metal string is fixed between rigid supports. It is initially at negligible tension. Its Young's modulus is \( Y \) density is \( \rho \) and coefficient of linear
expansion is \( \alpha \). It is now cooled
through a temperature \( t, \) transverse
waves will move along it with a speed of
A \( \cdot \sqrt{\frac{Y \alpha t}{\rho}} \)
B \( \cdot Y \sqrt{\frac{\alpha t}{\rho}} \)
c. \( \alpha \sqrt{\frac{Y t}{\rho}} \)
D \( \cdot t \sqrt{\frac{\rho}{Y \alpha}} \)
Subject: Maths
The mean deviation from mean of the
observation \( \boldsymbol{a}, \boldsymbol{a}+\boldsymbol{d}, \boldsymbol{a}+\boldsymbol{2} \boldsymbol{d}, \ldots . . \boldsymbol{a}+ \)
2nd is
A \( \cdot \frac{n(n+1) d^{2}}{3} \)
в. \( \frac{n(n+1)}{2} d^{2} \)
c. \( _{a+\frac{n(n+1) d^{2}}{2}} \)
D. \( \frac{n(n+1) d}{(2 n+1)} \)
Subject: Physics
At a given place on earth's surface the horizontal component of earths magnetic field is \( 2 \times 10^{-5} \mathrm{T} \) and
resultant magnetic field is \( 4 \times 10^{-5} \mathrm{T} \)
The angle of dip at this place is?
A . \( 30^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 45^{\circ} \)
Subject: Physics
A gas mixture contain \( 1 g H_{2} \) and \( 1 g H_{e} \) temperature of gas mixture is
increased from \( 0^{\circ} \) to \( 100^{\circ} C \) at isobaric
process. Then find given heat of gas mixture
\( \left[\gamma_{H e}=\mathbf{5} / 3, \gamma_{H e}=\mathbf{7} / \mathbf{5}, R=2 c a l / m o l\right. \)
A . 124 call
в. 327 cal
c. 218 cal
D. 475 cal
Subject: Chemistry
I. \( P b O_{2} \rightarrow P b O \Delta G_{298}<0 \)
\( \| S n O_{2} \rightarrow S n O \Delta G_{298}>0 \)
Which of the above is/are true?
\( A \)
B. I
\( c . \) both (a) \& (b)
D. none of these
Subject: Physics
A toroid has a core (non -ferromagnetic) of inner radius \( 25 \mathrm{cm} \) and outer radius
\( 26 \mathrm{cm}, \) around which 3500 turns of a
wire are wound. If the current in the wire
is \( 11 A, \) what is the magnetic field (a) outside the toroid,
(b) inside the core of
the toroid, and
(c) in the empty space surrounded by the toroid.
Subject: Physics
Figure shows a three arm tube in which
a liquid is filled upto levels of height I. It
is now rotated at an angular frequency
\( \omega \) about an axis passing through arm B.
The angular frequency \( \omega \) at which level
of liquid in arm B becomes zero.
\( \mathbf{A} \cdot \sqrt{\frac{2 g}{3 l}} \)
B. \( \sqrt{\frac{g}{l}} \)
c. \( \sqrt{\frac{3 g}{l}} \)
D. \( \sqrt{\frac{3 g}{2 l}} \)
Subject: Physics
Which table correctly matches the numbered equations below with the correct nuclear process?
1) \( \frac{1}{1} \boldsymbol{H}+_{1}^{2} \boldsymbol{H} \rightarrow_{2}^{3} \boldsymbol{H} \boldsymbol{e}+\boldsymbol{\gamma} \)
2) \( 241 A m \rightarrow_{93}^{237} N p+_{2}^{4} H e \)
\( 95^{1} A m^{2} e^{23} \)
3) \( _{92}^{235} \boldsymbol{U}+_{0}^{1} \boldsymbol{n} \rightarrow_{56}^{139} \boldsymbol{B} \boldsymbol{a}+_{36}^{94} \boldsymbol{K} \boldsymbol{r}+\boldsymbol{3}_{0}^{1} \boldsymbol{n} \)
4) \( \begin{array}{l}138 \\ 53\end{array} \boldsymbol{I} \rightarrow_{54}^{138} \boldsymbol{X} \boldsymbol{e}+_{-1}^{0} \boldsymbol{e}+\overline{\boldsymbol{v}} \)
A. 1 alpha decay 2 nuclear fission 3 beta decay 4 nuclear fusion
B. 1 nuclear fission 2 alpha decay 3 nuclear fusion 4 beta decay
c. 1 nuclear fusion 2 alpha decay 3 nuclear fission
4 beta decay
D. 1 Nuclear fusion 2 beta decay 3nuclear fission 4 alpha decay
E. 1 beta decay 2alpha decay ear fusion
ear fission
Subject: Maths
Find the projection of \( \vec{b}+\vec{c} \) on \( \vec{a}, \) where \( \vec{a}=2 \hat{i}-2 \hat{j}+\hat{k}, \vec{b}=\hat{i}+2 \hat{j}-2 \hat{k} \) and
\( \vec{c}=2 \hat{i}-\hat{j}+4 \hat{k} \)
Subject: Maths
Find \( x, \) if the angles of a triangle have
measures \( \left(x+40^{0}\right),\left(2 x+20^{0}\right) \) and \( 3 x \)
also state which type of triangle is this.
A . \( x=60^{\circ} \) and Equilateral triangle
B. \( x=20^{\circ} \) and Scalene triangle
C . \( x=20^{\circ} \) and Equilateral triangle
D. \( x=40^{\circ} \) and Scalene triangle
Subject: Maths
If \( \alpha=\cos \theta+i \sin \theta, \) then \( \frac{1+\alpha}{1-\alpha} \) is
equal to
A \( \cdot \cot \frac{\theta}{2} \)
B. \( \cot \theta \)
\( \mathrm{c} \cdot_{i \cot \frac{\theta}{2}} \)
D. \( i \tan \frac{\theta}{2} \)
Subject: Chemistry
At \( 30^{\circ} C, \) the solubility of \( A g_{2} C O_{3} \)
\( \left(K_{s p}=8 \times 10^{-12}\right) \) would be greatest in
one litre of:
A. \( 0.05 M \) Na\( _{2} \) CO \( _{3} \)
B. \( 0.05 M A g N O_{3} \)
c. Pure water
D. \( 0.05 M N H_{3} \)
Subject: Maths
Find the area of the closed figure bounded by the following curve
\( \boldsymbol{y}=\boldsymbol{x}^{2}-\boldsymbol{2} \boldsymbol{x}+\boldsymbol{2}, \boldsymbol{y}=\boldsymbol{2}+\boldsymbol{4} \boldsymbol{x}-\boldsymbol{x}^{2} \)
Subject: Chemistry
The specmc conductances in oh \( m^{-1} c m^{-1} \) of four electrolytes
\( P, Q, R \) and \( S \) are given in brackets:
\( P\left(5.0 \times 10^{-5}\right) \)
\( Q\left(7.0 \times 10^{-8}\right) \)
\( \boldsymbol{R}\left(\mathbf{1} . \mathbf{0} \times \mathbf{1 0}^{-\mathbf{1 0}}\right) \)
\( \boldsymbol{S}\left(\boldsymbol{9} \cdot \boldsymbol{2} \times \mathbf{1} \boldsymbol{0}^{\boldsymbol{3}}\right) \)
The one that offers highest resistance to the passage of electric current is:
A . \( P \)
в. \( Q \)
\( c . s \)
D. \( R \)
Subject: Biology
If the egg of an organism has 40 pg of DNA in its nucleus, how much DNA
would a diploid cell of same organism have in pachytene(X), diakinesis(Y) and anaphase-I(Z)?
A. \( x=160 \) pg, \( Y=160 \) pg, \( z=160 p g \)
B. \( \mathrm{x}=80 \mathrm{pg}, \mathrm{Y}=80 \mathrm{pg}, \mathrm{Z}=160 \mathrm{pg} \)
c. \( x=160 p g, Y=80 \) pg, \( z=160 p g \)
D. \( x=80 \) pg, \( Y=160 p g, z=80 \) pg
Subject: Chemistry
How many molecules of methane are
present in a sample that contains \( 1.0 \times 10^{10} \) moles of methane?
A. \( 6.0 \times 10^{23} \)
В. \( 1.0 \times 10^{33} \)
c. \( 6.0 \times 10^{33} \)
D. \( 6.0 \times 10^{24} \)
Subject: Physics
The angle turned by a body undergoing circular motion depends on time as
\( \boldsymbol{\theta}=\boldsymbol{\theta}_{0}+\boldsymbol{\theta}_{1} \boldsymbol{t}+\boldsymbol{\theta}_{2} \boldsymbol{t}^{2} . \) Then the angular
acceleration of the body is
\( A \cdot \theta_{1} \)
в. \( \theta_{2} \)
\( c \cdot 2 \theta_{1} \)
D. \( 2 \theta_{2} \)
Subject: Physics
A man of mass \( m \) moves on a plank of
mass \( M \) with a constant velocity \( u \) with
respect to the plank. as shown in Fig.
a) If the plank rests on a smooth
horizontal surface, determine the
velocity of the plank.
b) If the man travels a distance \( L \) with
respect to the plank, find the distance
travelled by the plank with respect to the ground.
Subject: Maths
A circular park has a path of uniform width around it. The difference between
outer and inner circumference of the
circular path is \( 132 m \). Its width is: Take \( \left(\boldsymbol{\pi}=\frac{22}{7}\right) \)
\( A \cdot 22 m \)
B. \( 20 m \)
\( \mathbf{c} \cdot 21 m \)
\( \mathbf{D} \cdot 24 m \)
Subject: Chemistry
Which of the following is the decreasing order of their dipole moments?
A. \( N H_{3}>B F_{3}>N F_{3} \)
B. \( N H_{3}>N F_{3}>B F_{3} \)
c. \( B F_{3}>N H_{3}>N F_{3} \)
D. \( B F_{3}>N F_{3}>N H_{3} \)
Subject: Physics
A hydrogen atom of mass ' \( m^{\prime} \) being at
rest, makes a transition from its first
excited state to ground state. As a
result a photon of wavelength \( ^{\prime} \lambda^{\prime} \) is
emitted and the hydrogen atom recoils.
If \( ^{\prime} \boldsymbol{E}_{0}^{\prime} \) is the ionization energy of \( \mathbf{a} \) hydrogen atom, the Planck's constant is \( h \) and \( c \) is the speed of light in vacuum,
the recoil speed is This question has multiple correct options
A \( \cdot \frac{3 E_{0}}{4 m_{c}} \)
в. \( \frac{3 E_{0}}{m c} \)
c. \( \frac{h}{2 m \lambda} \)
D. \( \frac{h}{m \lambda} \)
Subject: Physics
Two short electric dipoles are placed as
shown. The energy of electric interaction
between these dipoles will be:
A \( \cdot \frac{2 k P_{1} P_{2} \cos \theta}{r^{3}} \)
B. \( \frac{-2 k P_{1} P_{2} \cos \theta}{r^{3}} \)
c. \( \frac{-2 k P_{1} P_{2} \sin \theta}{r^{3}} \)
D. \( \frac{-4 k P_{1} P_{2} \cos \theta}{r^{3}} \)
Subject: Chemistry
Consider the following statements;
(I) Rutherford name was associated
with the development of periodic table.
(II) A metal M having electronic configuration \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 2 p^{6}, 3 d^{10}, 4 s^{1} \) is d-
block element.
(III) Diamond is not an element.
(IV) The electronic configuration of the
most electronegative element is \( 1 s^{2}, 2 s^{2}, 2 p^{5}, \) Select the correct option
from the given codes.
A . ।, ॥।, IV
B. I, II, III, IV
c. ॥, IV
D. I, III, IV
Subject: Physics
A coil of resistance \( 400 \Omega \) is placed in a magnetic field. If the magnetic flux \( \phi(W b) \) linked with the coil varies with time \( t(\sec ) \) as \( \Phi=50 t^{2}+4 \)
The current in the coil at \( t=2 \sec \) is
A. 2A
B. 1A
\( c .0 .5 A \)
D. 0.1A
Subject: Maths
Find the adjoint of matrix \( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right]= \)
\( \left[\begin{array}{ccc}1 & 1 & 1 \\ 2 & 1 & -3 \\ -1 & 2 & 3\end{array}\right] \) and evaluate the answer
Subject: Chemistry
Assertion
The isothermal curves intersect each
other at a certain point
Reason
The isothermal change takes place slowly so, the isothermal curves have
very little slope.
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. Reason is correct but Assertion is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
Using properties of deteminants, prove
\[
\operatorname{that}\left|\begin{array}{ccc}
\frac{(\boldsymbol{a}+\boldsymbol{b})^{2}}{\boldsymbol{c}} & \boldsymbol{c} & \boldsymbol{c} \\
\boldsymbol{a} & \frac{(\boldsymbol{b}+\boldsymbol{c})^{2}}{\boldsymbol{a}} & \boldsymbol{a} \\
\boldsymbol{b} & \boldsymbol{b} & \frac{(\boldsymbol{c}+\boldsymbol{a})^{2}}{\boldsymbol{b}}
\end{array}\right|
\]
\( 2(a+b+c)^{3} \)
Subject: Physics
\( 1300 J \) of heat energy is supplied to
raise the temperature of \( 0.5 k g \) of lead
from \( 20^{\circ} C \) to \( 40^{\circ} C . \) Calculate the
specific heat capacity of lead.
A \( \cdot 65 \mathrm{J} k g^{-1} K^{-1} \)
B \( \cdot 260 J k g^{-1} K^{-1} \)
c. \( 130 \mathrm{Jkg}^{-1} \mathrm{K}^{-1} \)
D. \( 1300 \mathrm{Jkg}^{-1} \mathrm{K}^{-1} \)
Subject: Chemistry
In a first order reaction, the initial conc.
of the reactant was \( M / 10 . \) After 8 minutes 20 seconds the conc. becomes
\( M / 100 \)
What is the rate constant?
A. \( 5 \times 10^{-3} \) second \( ^{-1} \)
B. \( 2.303 \times 10^{-5} \) second\( ^{-1} \)
c. \( 2.303 \times 10^{-4} \) second\( ^{-1} \)
D. \( 4.606 \times 10^{-3} \) second \( ^{-1} \)
Subject: Chemistry
The correct statement for the following
reaction is:
\( \boldsymbol{N} \boldsymbol{H}_{3}+\boldsymbol{H}^{+} \rightarrow \boldsymbol{N} \boldsymbol{H}_{4}^{+} \)
A. the state of hybridisation changes
B. bond angle increases
C. \( N H_{3} \) act as a Lewis acid
D. regular geometry changes
Subject: Maths
The internal centre of similitude of two
circles \( (x-3)^{2}+(y-2)^{2}= \)
\( \mathbf{9},(\boldsymbol{x}+\mathbf{5})^{2}+(\boldsymbol{y}+\mathbf{6})^{2}=\mathbf{9} \) is
A \( \cdot(-1,-2) \)
B. (-2,-1)
c. (3,2)
(年. (3,2)
D. (-5,-6)
Subject: Maths
If \( P(A)=\frac{1}{4}, P(\bar{B})=\frac{1}{2} \) and \( P(A \cup \)
B) \( =\frac{5}{9}, \) then \( P(A / B) \) is
\( ^{A} \cdot \frac{7}{36} \)
в.
c. \( \frac{7}{18} \)
D. \( \frac{7}{72} \)
Subject: Physics
On a linear escalator running between
two points \( A \) and \( B, \) a boy takes time \( t_{1} \)
to move from \( A \) to \( B \), if the boy runs with a constant speed on the escalator. If the
boy runs from \( \mathrm{B} \) to \( \mathrm{A} \), he takes time \( t_{2} \) to
reach B from A. What is the time taken
by the boy to move from \( A \) to \( B \) if he stands still on the escalator?
[The escalator moves from A to B]
Subject: Maths
Let \( A \) and \( B \) be the remainders when the
polynomials \( y^{3}+2 y^{2}-5 a y-7 \) and
\( y^{3}+a y^{2}-12 y+6 \) are divided by \( y+ \)
1 and \( y-2 \) respectively. If \( 2 A+B=6 \)
find the value of \( a \)
Subject: Maths
If \( \frac{1}{2}\left(e^{y}-e^{-y}\right)=x, \) prove that
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{1}{\sqrt{\boldsymbol{x}^{2}+\mathbf{1}}} \)
Subject: Chemistry
Which of the following is not a redox reaction?
A \( \cdot 2 N O+O_{2} \rightarrow 2 N O_{2} \)
в. \( C l_{2}+H_{2} O \rightarrow H C l+H C l O \)
\( \mathrm{c} \cdot 2 \mathrm{Cr} \mathrm{O}_{4}^{2-}+2 \mathrm{H}^{+} \rightarrow \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}+\mathrm{H}_{2} \mathrm{O} \)
D. \( M n O_{4}^{-}+8 H^{+} \rightarrow M n^{2+}+4 H_{2} O \)
Subject: Chemistry
At \( 100^{\circ} \mathrm{C} \), benzene \( \& \) toluene have
vapour pressure of \( 1375 \& 558 \) Torr
respectively. Assuming these two form an ideal binary solution, calculate the composition of Ithe solution that boils
at 1 atm \( \& 100^{\circ} \mathrm{C} \). What is the
composition of vapour issuing at these conditions?
A . \( x_{b}=0.2472, Y_{b}=0.4473 \)
B. \( x_{b}=0.4473, Y_{b}=0.2472 \)
c. \( x_{b}=0.362, Y_{b}=0.321 \)
D. None of these
Subject: Maths
\( \int \frac{\cos ^{2} x}{\sin ^{4} x} d x \)
A. \( -\frac{1}{3} \tan ^{3} x \)
B. \( \frac{1}{3} \cot ^{3} x \)
C. \( -\frac{1}{3} \cot ^{3} x \)
D. \( \frac{1}{3} \tan ^{3} x \)
Subject: Maths
Find the differential equation of the
family of curves \( \boldsymbol{y}=\boldsymbol{A} \boldsymbol{e}^{2 \boldsymbol{x}}+\boldsymbol{B} \boldsymbol{e}^{-\boldsymbol{2 x}} \)
where \( A \) and \( B \) are arbitrary constants.
Subject: Physics
A step-down transformer is connected to 2400 volts line and 80 amperes of current is found to flow in output load.
The ratio of the turns in primary and secondary coil is \( 20: 1 . \) If transformer efficiency is \( 100 \% \), then the current flowing in primary coil will be :
\( A \cdot 8 A \)
в. \( 4 A \)
\( c .5 A \)
D. \( 9 A \)
Subject: Biology
Match the hominids with their correct
brain size:
(a) Homo habilis
(i) 900 cc
(b) Homo neanderthalensis
(ii) 1350 сс
(c) Homo erectus
(iii) \( 650-800 \) сс
(d) Homo sapiens
(iv) \( 1400 \mathrm{cc} \)
Select the correct option.
\( A \cdot(a)-(i i i),(b)-(i),(c)-(i v),(d)-(i i) \)
B. (a)-(iii), (b)-(ii), (c)-(i), (d)-(iv)
c. (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
D. (a)-(iv), (b)-(iii), (c)-(i), (d)-(ii)
Subject: Physics
A body dropped from a height \( h \) with initial velocity zero, strikes the ground with a velocity \( 3 m / s \). Another body of same mass dropped from the same height \( h \) with an initial velocity of \( 4 m / s \) The final velocity of second mass, with which it strikes the ground is
A. \( 5 m / s \)
в. \( 12 \mathrm{m} / \mathrm{s} \)
\( \mathrm{c} \cdot 3 \mathrm{m} / \mathrm{s} \)
D. \( 4 m / s \)
Subject: Physics
Assertion: Substances which at room
temperature retain their ferromagnetic
property for a long period of time are
called permanent magnets.

Reason: Permanent magnet can be
made by placing a ferromagnetic rod in
a solenoid and passing current through
¡t.
A. If both assertion and reason are true and reason is the
correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If both assertion and reason are false.
Subject: Physics
A point charge \( 50 \mu C \) is located in the
\( x-y \) plane at the position vector \( \vec{r}_{0}= \) \( (2 \hat{i}+3 \hat{j}) m . \) The electric field at the
point of position vector \( \vec{r}= \) \( (8 \hat{i}-5 \hat{j}) m, \) in vector from is equal to:
A \( \cdot 900(-3 \hat{i}+4 \hat{j}) V / m \)
B \( \cdot 90(3 \hat{i}-4 \hat{j}) V / m \)
c. \( 9(-3 \hat{i}+4 \hat{j}) V / m \)
D. \( 900(3 \hat{i}-4 \hat{j}) V / m \)
Subject: Chemistry
What is the order of reactivity of the following compounds towards nucleophilic substitution?
\( \langle-\mathbf{C l} \leqslant-\mathbf{C l}(-\mathbf{l})-\mathbf{C l} \)
(I)
\( (\mathbf{I I}) \)
\( (\mathrm{III}) \)
\( (\mathbf{I V}) \)
A. \( I<I I<I I I<I V \)
в. \( I V<I I I<I I<I \)
c. \( I V<I<I I<I I I \)
D. \( I V<I I<I<I I I \)
Subject: Maths
The value of \( \int_{0}^{\frac{\pi}{4}}(\sqrt{\tan x}+\sqrt{\cot x}) d x \)
is equal to
A \( \cdot \frac{\pi}{2} \)
B. \( -\frac{\pi}{2} \)
c. \( \frac{\pi}{\sqrt{2}} \)
D. \( -\frac{\pi}{\sqrt{2}} \)
Subject: Physics
The speed of electromagnetic waves in
air is
A \( \cdot 2 \times 10^{5} \mathrm{km} / \mathrm{s} \)
B . \( 2 \times 10^{6} \mathrm{km} / \mathrm{s} \)
\( c \cdot 2 \times 10^{7} \mathrm{km} / \mathrm{s} \)
D. \( 2 \times 10^{8} \mathrm{km} / \mathrm{s} \)
Subject: Physics
A block of mass \( 3 m \) and base \( ^{\prime} a^{\prime}, \) height
\( b^{\prime}, \) is resting on the smooth horizontal
surface. A man of mass \( m \) goes from \( \mathrm{P} \) to \( Q \) on the wedge. Find the
displacement of the centre of mass of \( (\text { man }+\text { block }) \) system.
Subject: Maths
The length of the shortest chord of the circles \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}+\boldsymbol{2} \boldsymbol{g} \boldsymbol{x}+\boldsymbol{2} \boldsymbol{f} \boldsymbol{y}+\boldsymbol{c}=\boldsymbol{0} \)
which passes through the point \( (a, b) \) inside the circle
Subject: Maths
The value of \( \lim _{x \rightarrow 2} \frac{\sqrt{1+\sqrt{2+x}}-\sqrt{3}}{x-2} \) is
equal to?
A. \( \frac{1}{8 \sqrt{3}} \)
в. \( \frac{1}{\sqrt{3}} \)
c. \( 8 \sqrt{3} \)
D. \( \sqrt{3} \)
Subject: Physics
Two charged particles moving with
velocities \( v_{1} \) and \( v_{2} \) have some
separation between them. The ratio of magnetic force to the Colombian force between them is (c is speed of light)
A. \( \frac{v_{1} v_{2}}{c^{2}} \)
в. \( \frac{c^{2}}{v_{i} v_{2}} \)
c. \( \frac{c}{v_{1}} \)
D. \( \frac{c}{v_{2}} \)
Subject: Physics
The Poisson's ratio of a material is \( 0.8 . \) If
a force is applied to a wire of this material decreases its cross-sectional
area by \( 4 \%, \) then the percentage increase in its length will be.
A . \( 1 \% \)
B. 2\%
\( c .2 .5 \% \)
D. \( 4 \% \)