AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Biology
What is the correct sequence of the
following in a heart attack?
1. Narrowing of the inner orifice of the vessel
2. 'Plaque' from fibrous tissue and high cholesterol
3. Inadequate supply of blood and
oxygen
4. Clots of blood carried Into the
coronary arteries
A .2,3,1,4
B. 2, 4, 1, 3
\( c \cdot 1,2,3,4 \)
D. 4,2,1,3
Subject: Physics
The energy band diagrams for three
semiconductor sample of silicon are
shown. It follows that.
A. Sample X is undoped while samples Y and Z have been doped with a third group and a fifth group impurity respectively
B. Sample X is undoped while both samples Y and Z have been doped with a fifth group impurity
c. Sample X has been doped with equal amounts of third and fifth group impurities while samples \( Y \) and \( z \) are undoped
D. Sample X is undoped while samples Y and Z have been doped with a fifth group and a third group impurity respectively
Subject: Chemistry
An electron in \( H \) -atom in ground state
absorbs 1.5 times as much energy as the minimum required for its escape (i.e., \( 13.6 e V) \) from the atom. Calculate
the wavelength of emitted electron.
A . \( \lambda=4.70 \times 10^{-10} \mathrm{m} \)
В. \( \lambda=61 \times 10^{-9} m \)
c. \( \lambda=4.70 \times 10^{-14} \mathrm{m} \)
D. \( \lambda=2.7 \times 10^{-10} \mathrm{m} \)
Subject: Physics
The acceleration of Particle starting
from rest and moving along a straight
line is as shown. Other than at \( t=0 \)
when is the velocity of the object equal
to zero?
A. At \( t=3.5 s \)
B. During the interval from \( 1 s \) to 3 s
C. At \( t=5 s \)
D. At no other time on this graph
Subject: Physics
Draw a circuit diagram of an electric circuit containing a cell, a key, an ammeter, a resistor of \( 4 \Omega \) in series with
a combination of two resistors \( (8 \Omega \)
each ) in parallel and a voltmeter across parallel combination. Each of them dissipate maximum energy and canwithstand a maximum power of
\( 16 W \) without melting. Find the
maximum current that can flow
through the three resistors.
Subject: Maths
If \( \boldsymbol{y}^{2}=\boldsymbol{x}^{2}-\boldsymbol{x}+\mathbf{1} \) and \( \quad \boldsymbol{I}_{\boldsymbol{n}}=\int \frac{\boldsymbol{x}^{\boldsymbol{n}}}{\boldsymbol{y}} \boldsymbol{d} \boldsymbol{x} \)
and \( \boldsymbol{A I}_{3}+\boldsymbol{B I}_{2}+\boldsymbol{C I}_{1}=\boldsymbol{x}^{2} \boldsymbol{y} \) then
ordered triplet \( A, B, C \) is
\( ^{A} \cdot\left(\frac{1}{2},-\frac{1}{2}, 1\right) \)
В . (3,1,0)
\( \mathbf{c} \cdot(1,-1,2) \)
D. \( \left(3,-\frac{5}{2}, 2\right) \)
Subject: Chemistry
In the system, \( C a F_{2}(s) \rightleftharpoons \)
\( C a^{+2}(a q)+2 F^{-} \) increasing the
concentration of \( C a^{2+} \) ions four times
will cause the equilibrium
concentration of \( \boldsymbol{F}^{-} \) ions to change to
times the initial value.
A . 4
B. \( \frac{1}{2} \)
\( c \cdot 2 \)
D.
Subject: Physics
A coil and a magnet moves with their constant speeds \( 5 m / \)sec and \( 3 m / \)sec
respectively, towards each other, then induced emf in coil is \( 16 m V . \) If both
moves in the same direction, then
induced emf in the coil:
\( \mathbf{A} \cdot 15 m V \)
в. \( 4 m V \)
c. \( 64 m V \)
D. zero
Subject: Maths
\( \operatorname{Let} \overrightarrow{\boldsymbol{A}}=\hat{\boldsymbol{i}}+2 \hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{B}}=\boldsymbol{4} \hat{\boldsymbol{i}}+2 \hat{\boldsymbol{j}}, \overrightarrow{\boldsymbol{C}}= \)
\( \mathbf{2} \hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{j}}+\mathbf{2} \hat{k} . \) Then the ratio in which \( \boldsymbol{C} \)
divides \( A B \) is
A . 3: 4
B. 1: 3
c. 1: 2
D. 1: 1
Subject: Maths
In a class of 75 students, 15 are above
average, 45 are average and the rest below average achievers. The probability that an above average achieving student fails is \( 0.005, \) that an average achieving student fails is 0.05
and the probability of a below average achieving student failing is \( 0.15 . \) If \( a \) student is know to have passed, what is
the probability that he is a below average achiever?
Subject: Chemistry
Which of the following compound has
three \( 1^{\circ} \), one \( 2^{\circ} \) and one \( 3^{\circ} \) carbon?
A \( \cdot C H_{3}\left(C H_{2}\right)_{4} C H_{3} \)
в. \( C H_{3} C H\left(C H_{3}\right) C H_{3} \)
c. \( C H_{3}\left(C H_{2}\right)_{3} C H_{3} \)
D. \( C H_{3} C H\left(C H_{3}\right) C H_{2} C H_{3} \)
Subject: Maths
In the given isosceles trapezium ABCD,
\( \boldsymbol{A B} \| \boldsymbol{D C} \) and \( \boldsymbol{A D}=\boldsymbol{B C} \). If \( \angle \boldsymbol{D}= \)
\( 60^{\circ}, A B=18 c m \) and \( A D=12 c m, \) find
the length of DC
A . \( 60^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 90 \)
D. \( 20^{\circ} \)
Subject: Physics
The resultant of two forces \( P \) and \( q \) is
right angle to \( P \), the resultant of \( P \) and
\( Q \) acting at the same angle is at right
angle to \( Q \). Prove that \( P \) is the
geometric mean of \( Q \) and \( Q \) (i.e. \( P= \)
\( \sqrt{\boldsymbol{Q} \boldsymbol{q}} ? \)
Subject: Maths
If \( \tan (x+y)=33 \) and \( x=\tan ^{-1} 3, \) then \( y \)
will be
A. 0.3
B \( \cdot \tan ^{-1}(1.3) \)
\( \mathbf{c} \cdot \tan ^{-1}(0.3) \)
D. \( \tan ^{-1}\left(\frac{1}{18}\right) \)
Subject: Chemistry
The unit of molar conductivity is
A \( \cdot \operatorname{scm}^{2} s^{-1} \)
B . \( \mathrm{S} l^{2} \mathrm{mol}^{-1} \)
c. \( \operatorname{scm}^{2} m o l^{-1} \)
D. None of these
Subject: Physics
The potential at a point due to a charge
of \( 5 \times 10^{-7} \) C located \( 10 \mathrm{cm} \) away is:
A. \( 3.5 \times 10^{5} \mathrm{V} \)
B. 3.5 \( \times 10^{4} \mathrm{v} \)
c. \( 4.5 \times 10^{4} v \)
D. \( 4.5 \times 10^{5} \mathrm{v} \)
Subject: Maths
\( \int \frac{(\boldsymbol{x}+\mathbf{1})}{\boldsymbol{x}\left(\mathbf{1}+\boldsymbol{x} \boldsymbol{e}^{\boldsymbol{x}}\right)} \boldsymbol{d} \boldsymbol{x}= \)
\( \mathbf{A} \cdot \log \left|\frac{e^{x}}{1+x e^{x}}\right|+c \)
в. \( -\log \left|\frac{e^{x}}{1+x e^{x}}\right|+c \)
c. \( \log \left|\frac{x e^{x}}{1+x e^{x}}\right|+c \)
D. \( -\log \left|\frac{e^{x}}{1-x e^{x}}\right|+c \)
Subject: Physics
A current carrying loop of radius \( 2 \mathrm{cm} \)
has \( 4 A \) current flowing in an anti-
clockwise direction. The plane of the loop makes an angle of \( \theta \) with the direction of the magnetic field which is in an upward direction. the value of the
magnetic field is 0.7 Tesla.if potential
energy of loop in magnetic field is \( \approx \) \( 0.01 J, \) then value of \( \theta \) is:
A \( \cdot 45^{\circ} \)
B . \( 60^{\circ} \)
\( c .30^{\circ} \)
D. None of these
Subject: Physics
If the change in the value of \( g \) at height
\( h \) above earth surface is the same as
that at depth \( x\left(x \quad \text { or } \quad h<R_{e}\right), \) then
A \( \cdot x=h^{2} \)
в. \( x=h \)
c. \( _{x}=\frac{h}{2} \)
D. \( x=2 h \)
Subject: Maths
If \( \omega \neq 1 \) is a cube root of unity and
\( (\omega+x)^{n}=1+12 \omega+69 \omega+\ldots . \) then
values of \( 4 n \) and \( \omega \) respectively are
A . 36,1
в. 12,2
c. \( 24,1 / 2 \)
D. \( 18,1 / 3 \)
Subject: Physics
The magnetic field at center \( O \) of the
\( \operatorname{arcin} \) figure is
A \( \cdot \frac{\mu_{0} I}{4 \pi \times r}[\sqrt{2}+\pi] \)
\( ^{\mathbf{B}} \cdot \frac{\mu I}{2 \pi r}\left[\frac{\pi}{4}+(\sqrt{2}-1)\right] \)
C \( \frac{\mu_{0}}{4 \pi} \times \frac{I}{r}[(\sqrt{2}-\pi)] \)
\( ^{\mathrm{D}} \cdot \frac{\mu_{0}}{4 \pi} \times \frac{I}{r}\left[\left(\sqrt{2}+\frac{\pi}{4}\right)\right] \)
Subject: Physics
The amplitude of a particle executing
SHM about O is 10 cm. Then:
This question has multiple correct options
A. When the K.E. is 0.64 of its max. K.E. its displacement is \( 6 \mathrm{cm} \) from 0 .
B. When the displacement is 5 cm from 0 its K.E. is 0.75 of its max.P.E.
C. Its total energy at any point is equal to its maximum
K.E.
D. Its velocity is half the maximum velocity when its displacement is half the maximum displacement.
Subject: Biology
The presence of checkpoint during
mitosis ensures the attachment of all
chromosomal kinetochore proteins to
the spindle fibres. The absence of
attachment of kinetochore proteins produces a signal preventing mitosis to
proceed to next stage. The occurrence of
this check point is responsible for transition from
A. Anaphase to telophase
B. Prophase to metaphase
C. Metaphase to telophase
D. Prophase to anaphase
E. Metaphase to anaphase
Subject: Maths
Find \( a \) and \( b \) for the ellipse \( b^{2} x^{2}+ \) \( a^{2} y^{2}=a^{2} b^{2} \) if the distance between the
directrices is \( 5 \sqrt{5} \) and the distance
between the foci is \( 4 \sqrt{5} \). Give answer to
the nearest integer
Subject: Maths
In \( \triangle \boldsymbol{L} M \boldsymbol{N}, \triangle \boldsymbol{L}=\boldsymbol{6} \boldsymbol{0}^{\circ}, \angle \boldsymbol{M}=\mathbf{5 0}^{\circ} \) If
\( \angle L M N \sim \triangle P Q R \) then the value of \( \angle R \)
is
A \( .40^{\circ} \)
B . \( 60^{\circ} \)
\( c \cdot 70^{\circ} \)
D. \( 110^{\circ} \)
Subject: Chemistry
In the extraction of copper, the smelt
formed in the blast furnace contains:
A. \( C u_{2} S+ \) little \( F e S \)
в. \( C u_{2} S+ \) little \( F e O \)
c. \( C u_{2} O+ \) little \( F e S \)
D. \( C u_{2} O+ \) little \( F e O \)
Subject: Maths
Consider the following two statements:
\( P: \) If 7 is an odd number, then 7 is
divisible by 2.
Q: If 7 is a prime number, then 7 is an odd number
If \( V_{1} \) is the truth value of the
contrapositive of \( \mathrm{P} \) and \( V_{2} \) is the truth value of contrapositive of \( Q, \) then the ordered pair \( \left(V_{1}, V_{2}\right) \) equals:
A. \( (F, F) \)
в. \( (T, T) \)
c. \( (T, F) \)
D. \( (F, T) \)
Subject: Physics
A small quantity, mass \( m \), of water at a
temperature \( \theta\left(\text { in }^{\circ} C\right) \) is poured on to a large mass \( M \) of ice which is at its
melting point. If \( c \) is specific heat capacity of water and \( L \) the latent heat
of fusion of ice, then the mass of ice
melted is given by
A \( \cdot \frac{M L}{m c \theta} \)
в. \( \frac{m c \theta}{M L} \)
с. \( \frac{M c \theta}{L} \)
D. \( \frac{m c \theta}{L} \)
Subject: Maths
Assertion \( (A): \) If \( f(x)=|x|, \) then \( f \) has
minimum value at \( x=0 \)
Reason (R): A function f(x) has
minimum value at \( x=a \) if \( f^{\prime}(a)=0 \) and
\( \mathbf{f}^{\prime \prime}(\mathbf{a})>\mathbf{0} \)
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. A is true and R is false
D. A is false and R is true
Subject: Physics
A particle of charge \( q \) and mass \( m \) is moving through a region of space at right angles to an electric field and a
magnetic field, where the crossed magnetic and electric fields produce a zero net force on the charge. If the speed of the charge is doubled, which of the following changes will again produce a zero net force on the charge? This question has multiple correct options
A \( \cdot \) Reducing the Electric field to \( \frac{1}{2} E \)
B. Increasing the Electric field to \( 2 E \)
c. Reducing the Magnetic field to \( \frac{1}{2} B \)
D. Increasing the Magnetic field to \( 2 B \)
E. Doubling both the Magnetic and Electric Fields
Subject: Physics
A mercury barometer is known to be defective. It contains a small quantity of air in the space above the mercury. When an accurate barometer reads 770
\( \mathrm{mm}, \) the defective one reads \( 760 \mathrm{mm} \)
and when the accurate one reads 750
\( \mathrm{mm}, \) the defective one reads \( 742 \mathrm{mm} \)
The true atmospheric pressure when the defective barometer reads \( 750 \mathrm{mm} \)
is
A. \( 68 \mathrm{cm} \) of \( \mathrm{Hg} \)
в. \( 79.88 \mathrm{cm} \) of \( \mathrm{Hg} \)
\( c .75 .88 \mathrm{cm} \) of \( \mathrm{Hg} \)
D. 72.15 cm of Hg
Subject: Chemistry
Define mixtures.
(a) \( \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}(l) \)
\[
\boldsymbol{\Delta} \boldsymbol{H}_{298 K}^{o}=-285.9 \boldsymbol{k J m o l}^{-1}
\]
(b) \( \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \)
\[
\boldsymbol{\Delta} \boldsymbol{H}_{298 K}^{o}=-241.8 \boldsymbol{k J m o l}^{-1}
\]
The molar enthalpy of vapourisation of water will be:
B. 22.0 kJ mol-
c. \( 44.1 \mathrm{kJ} \mathrm{mol}^{-} \)
D. \( 527.7 k J \) mol\( ^{-} \)
Subject: Physics
Calculate the heat energy required to convert completely \( 10 \mathrm{kg} \) of water at \( 50^{\circ} \mathrm{C} \) into steam at \( 100^{\circ} \mathrm{C} \), given that the
specific heat capacity of water is \( 4200 J /\left(k g^{\circ} C\right) \) and the specific latent heat of vaporisation of water is
\( 2260 k J / k g \)
A. 30451 KJ
B. 60562 KJ
c. 72103 KJ
D. 24700 KJ
Subject: Physics
Mass of the earth is 81 times the mass
of the moon and distance between the
earth and moon is 60 times the radius
of the earth. If \( R \) is radius of the earth,
then the distance between moon and
the point on the line joining the moon and the earth where the gravitation force becomes zero is
A. 30R
в. 15R
\( c \cdot 6 R \)
D. 5R
Subject: Physics
Assertion
For small deformations, the stress and
strain are proportional to each other
Reason
A class of solids called elastomers does
not obey Hooke's law.
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
In a certain region of space, the
potential is given by \( \boldsymbol{V}=\boldsymbol{k}\left[\mathbf{2} \boldsymbol{x}^{2}-\boldsymbol{y}^{2}+\boldsymbol{z}^{2}\right] . \) The electric field
at the point (1,1,1) has magnitude \( = \)
A \( . k \sqrt{6} \)
в. \( 2 k \sqrt{6} \)
c. \( 2 \sqrt{3} k \)
D. \( 4 k \sqrt{3} \)
is
Subject: Maths
\( \left|\begin{array}{cc}\mathbf{1} & \log _{\boldsymbol{b}} \boldsymbol{a} \\ \log _{\boldsymbol{a}} \boldsymbol{b} & \mathbf{1}\end{array}\right|= \)
A \( . a b \)
B. ba
\( c \cdot a b \)
\( D \)
Subject: Maths
f \( \boldsymbol{A}=\{\mathbf{2}, \boldsymbol{4}, \boldsymbol{5}\}, \boldsymbol{B}=\{\boldsymbol{7}, \boldsymbol{8}, \boldsymbol{9}\} \) then
\( n(A \times B) \) is equal to-
\( A \cdot 6 \)
B. 9
\( c .3 \)
\( D \)
Subject: Chemistry
A mixture of chlorobenzene and wate
(immiscible) boils at \( 90.3^{\circ} \mathrm{C} \) at an
external pressure of \( 740.2 \mathrm{mm} . \) The vapour pressure of pure water at
\( 90.3^{\circ} \mathrm{C} \) is \( 530.1 \mathrm{mm} \). Calculate the \( \% \)
composition of distillate:
A. \( H_{2} O=35 \% \)
в. \( H_{2} O= \) 22\%
c. \( H_{2} O= \) २९\% \( \%= \)
D. \( H_{2} O=71 \% \)
Subject: Chemistry
For the hypothetical reactions, the
equilibrium constant \( \boldsymbol{K}_{\boldsymbol{p}} \) values are
given:
\( \boldsymbol{A} \rightleftharpoons \boldsymbol{B} ; \boldsymbol{K}_{\mathbf{1}}=\mathbf{2} ; \boldsymbol{B} \rightleftharpoons \boldsymbol{C} ; \boldsymbol{K}_{2}=\mathbf{4} ; \boldsymbol{C} \rightleftharpoons \)
\( \boldsymbol{D} ; \boldsymbol{K}_{3}=\boldsymbol{3} \)
The equilibrium constant \( (K) \) for the
reaction \( \boldsymbol{A} \rightleftharpoons \boldsymbol{D} \) is:
A .48
B. 6
\( c \cdot 24 \)
D. 12
Subject: Physics
If the potential energy between electron and proton at a distance \( r \) is given by \( U=-\left(\frac{k e^{2}}{3 r^{3}}\right) . \) The force is :
A \( \cdot_{F}=\frac{k e^{2}}{r^{2}} \)
B. \( _{F}=-\frac{3}{4} \frac{k e^{2}}{r^{4}} \)
\( ^{\mathrm{c}} \cdot_{F}=\frac{k e^{2}}{r^{4}} \)
D. \( _{F}=\frac{k e^{2}}{r} \)
Subject: Physics
A ray of light travelling in air is incident on the plane of a transparent medium.
The angle of incident is \( 45^{0} \) and that of
refraction is \( 30^{0} . \) The refractive index of
the medium with respect to air is:
A .2
в. \( \frac{1}{\sqrt{2}} \)
c. \( 2 \sqrt{2} \)
D. \( \sqrt{2} \)
Subject: Maths
The probability that a man will live 10 more years, is \( \frac{1}{4} \) and the probability that his wife will live 10 more years, is
\( \mathbf{1} \)
- Then, what is the probability that
\( \overline{\mathbf{3}} \)
neither will be alive in 10 years?
A \( \cdot \frac{1}{2} \)
в. \( \frac{3}{7} \)
\( c \cdot \frac{2}{3} \)
D.
Subject: Physics
A cart \( A \) of mass \( 50 k g \) moving at a
speed of \( 20 k m / h \) hits a lighter cart \( B \)
of mass \( 20 \mathrm{kg} \) moving towards it at a speed of \( 10 \mathrm{km} / \mathrm{h} \). The two carts cling to
each other. Find the change of
momentum of cart A.
Subject: Physics
Electric field at a distance \( x \) from the
origin its given as \( \boldsymbol{E}=\frac{\mathbf{1 0 0 N}-\boldsymbol{m}^{2} / \boldsymbol{C}}{\boldsymbol{x}^{2}} \)
Then potential difference between the
points situated at \( x=10 m \) and \( x= \)
\( 20 m \) is:
\( A \cdot 5 V \)
B. \( 10 V \)
\( c .15 V \)
D. \( 4 V \)
Subject: Maths
The distance between the two parallel chords of length \( 8 \mathrm{cm} \) and \( 6 \mathrm{cm} \) in a circle of diameter \( 10 \mathrm{cm} \) if the chords lic
on the same side of the centre is
A. \( 1 \mathrm{cm} \)
B. 2 \( \mathrm{cm} \)
\( c \cdot 3 \mathrm{cm} \)
D. \( 4 \mathrm{cm} \)
Subject: Chemistry
I ne properties IIKe Ionızatıon potentıal, electronegativity, electron affinity and power of the catenation of the member
in a group depend on many factors. For example, the smaller the size of the
atom greater will be the ionization
potential. At the same time symmetry in the electronic configuration of the
elements also play a part in their ionization energy. Smaller the atomic
size, greater will be the mutual electronic repulsion and lesser will be
electron affinity. Similarly,
the catenation which is a direct result
of \( \mathbf{M}-\mathbf{M} \) bond strength is also affected by similar considerations.
The correct decreasing order of catenation among group 16 elements is
A. \( O>S>S e>T e \)
в. \( S>O>S e>T e \)
\( \mathbf{c} \cdot S>S e>T e>O \)
D. \( S>S e>O>T e \)
Subject: Physics
A charged particle is moving in a uniform magnetic field in a circular
path. The energy of the particle is doubled. If the initial radius of the
circular path was \( R, \) the radius of the new circular path after the energy is doubled will be:
A. \( 0.5 R \)
в. \( \sqrt{2} R \)
\( c .2 R \)
D. \( \frac{R}{\sqrt{2}} \)
Subject: Physics
A circular loop of mass \( \mathrm{m} \) and \( \mathrm{R} \) rests
flat on a horizontal frictionless
surface.A bullet also of mass \( \mathrm{m} \), and
moving with a velocity v, strikes the loop and gets embedded in it. The thickness of the hoop is much smaller than R. The anguler velocity with system rotates after the bullet strikes the hoop is
Subject: Chemistry
The molar conductivity of a solution of a weak acid \( \boldsymbol{H} \boldsymbol{X}(\mathbf{0 . 0 1} \boldsymbol{M}) \) is \( \mathbf{1 0} \) times
smaller than the molar conductivity of a
solution of a weak acid \( \boldsymbol{H} \boldsymbol{Y}(\mathbf{0 . 1} \boldsymbol{M}) . \) If
\( \boldsymbol{\lambda}_{\boldsymbol{X}^{-}}^{\circ} \approx \boldsymbol{\lambda}_{\boldsymbol{Y}^{-}}^{\circ}, \) the difference in their \( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}} \)
values, \( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}}(\boldsymbol{H} \boldsymbol{X})-\boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}}(\boldsymbol{H} \boldsymbol{Y}), \) is
(consider degree of ionization of both
acids to be \( <<1 \) )
Subject: Chemistry
Conversion of sulphur to \( \boldsymbol{S O}_{3} \) has
\( \triangle H=2 x K c a l \) and conversion of \( S O_{2} \)
to \( S O_{3} \) involves \( \triangle H=-y k c a l \). The
correct thermochemical equation for
formation of \( \boldsymbol{S} \boldsymbol{O}_{2} \) is:
A \( . S+O_{2} \rightarrow S O_{2} \triangle H=(y-2 x) \)
B. \( S+O_{2} \rightarrow S O_{2} \triangle H=-(y-2 x) \)
c. \( S+O_{2} \rightarrow S O_{2} \triangle H=(x+y) \)
D. \( S+O_{2} \rightarrow S O_{2} \triangle H=2 y-3 x \)
Subject: Maths
The domain of \( \mathbf{f}(\mathbf{x})=\log _{\mathbf{x}}\left(\mathbf{9}-\mathbf{x}^{2}\right) \) is
A. (-3,3)
B. \( (0, \infty) \)
c. (0,1)\( \cup(1, \infty) \)
D. (0,1)\( \cup(1,3) \)
Subject: Chemistry
Soaps do not work with hard water
containing calcium and magnesium
ions because:
A \( \cdot C a^{2+} \) and \( M g^{2+} \) ions form insoluble calcium and magnesium salts in the form of scum
B. \( N a^{+} \) and \( K^{+} \) present in soap react with \( C a^{2+} \) and hinder the cleansing process
C . a large amount of soap is to be used in presence of \( C a^{2+} \) and \( M g^{2+} \)
D. scum formed by the combination of \( N a^{+}, C a^{2+} \) and \( M g^{2+} \) stick to the cloth and are not removed on agitation
Subject: Physics
Two coils \( X \) and \( Y \) are placed in a
circuit such that a current changes by
\( 3 A \) in coil \( X \) and magnetic flux changes of \( 1.2 ~ W b \) occurs in \( Y \). The
value of mutual inductance of the coils
is :
\( \mathbf{A} \cdot 0.2 H \)
в. \( 0.4 \mathrm{H} \)
c. \( 0.6 H \)
D. \( 3.6 H \)
Subject: Chemistry
In the following reaction:
\( \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g}) \rightarrow \boldsymbol{3} \boldsymbol{S}(\boldsymbol{s})+ \)
\( 2 H_{2} O(l), \) the number of moles sulphur
formed by 2 moles each of \( S O_{2} \) and
\( \boldsymbol{H}_{2} \boldsymbol{S} \) is :
Subject: Physics
A bullet of mass \( 10 g \) and speed
\( 500 m / s \) is fired into a door and gets embedded exactly at the center of the door. The door is \( 1.0 m \) wide and weighs \( 12 k g . \) It is hinged at one end and rotates about a vertical axis practically without friction. Find the angular speed of the door just after the bullet embeds
into it.
Subject: Maths
The perimeter of a rhombus is \( 40 \mathrm{cm} \) and the length of one of its diagonals is 12 cm then the area of the rhombus is
\( \mathbf{A} \cdot 95 \mathrm{cm}^{2} \)
B. \( 96 \mathrm{cm}^{2} \)
c. \( 97 \mathrm{cm}^{2} \)
D. \( 98 \mathrm{cm}^{2} \)
Subject: Maths
If \( \cos ^{-1} x-\cos ^{-1} \frac{y}{2}=\alpha \) where -1
\( 1 \leq x \leq 1,-2 \leq y \leq 2, x \leq \frac{y}{2} \) then for
all \( 4 x^{2}-4 x y \cos \alpha+y^{2} \) is equal to
A \( \cdot 4 \sin ^{2} \alpha-2 x^{2} y^{2} \)
B. \( 4 \cos ^{2} \alpha+2 x^{2} y^{2} \)
\( \mathbf{c} \cdot 4 \sin ^{2} \alpha \)
\( D \cdot 2 \sin ^{2} \alpha \)
Subject: Physics
A student initially at rest on a frictionless frozen pond throws a \( 2 \mathrm{kg} \) hammer in one direction. After the
throw, the hammer moves off in one
direction while the student moves in the
other direction.Then:
A. the hammer will have the momentum with greater magnitude
B. the student will have the momentum with greater magnitude
c. the hammer will have the greater kinetic energy
D. the student will have the greater kinetic energy
Subject: Maths
The sides of an equilateral triangle are increasing at the rate of \( 2 \mathrm{cm} / \mathrm{s} \). The rate at which the area increases when
the side is \( 10 \mathrm{cm} \), is
\( \mathbf{A} \cdot \sqrt{3} c m^{2} / s \)
B. \( 10 \mathrm{cm}^{2} / \mathrm{s} \)
c. \( 10 \sqrt{3} \mathrm{cm}^{2} / \mathrm{s} \)
D. \( \frac{10}{\sqrt{3}} c m^{2} / s \)
Subject: Chemistry
A student takes about \( 4 \mathrm{ml} \) of distilled
water in four test tubes marked \( P, Q, R \)
and \( S . \) He then dissolves in each test
tube, an equal amount of various salts,
viz. sodium sulphate in \( P, \) potassium
sulphate in \( Q, \) calcium sulphate in \( R \)
and magnesium sulphate in \( S \). After that, he adds an equal amount of soap solution in each test tube. On shaking each of these test tubes well, he
observes a good amount of lather
(foam) in the test tube marked:
A. \( P \) and \( Q \)
B. \( Q \) and \( R \)
c. \( P, Q \) and \( S \)
D. \( P, R \) and \( S \)
Subject: Chemistry
Which of the following reactions is not correct for the formation of acid rain?
A. \( N_{2}+O_{2} \rightarrow 2 N O \)
в. \( 2 N O+O_{2} \rightarrow 2 N O_{2} \)
c. \( H_{2} O+2 N O_{2} \rightarrow H N O_{2}+H N O_{3} \)
D. \( N O+O_{2} \rightarrow N O_{2} \)