AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Assertion
consider the determinant \( \Delta= \) \( \left|\begin{array}{lll}a_{1}+b_{1} x^{2} & a_{1} x^{2}+b_{1} & c_{1} \\ a_{2}+b_{2} x^{2} & a_{2} x^{2}+b_{2} & c_{2} \\ a_{3}+b_{3} x^{2} & a_{3} x^{2}+b_{3} & c_{3}\end{array}\right|=0, \) where
\( \boldsymbol{x}_{i}, \boldsymbol{y}_{i}, \boldsymbol{z}_{i} \in \boldsymbol{R} \quad(\boldsymbol{i}=\mathbf{1}, \boldsymbol{2}, \boldsymbol{3}), \quad \boldsymbol{x} \in \boldsymbol{R} \)
The values of \( x \) satisfying \( \Delta=0 \) are
\( \boldsymbol{x}=\mathbf{1},-\mathbf{1} \)
Reason
\( \left|\begin{array}{lll}\boldsymbol{a}_{1} & \boldsymbol{b}_{1} & \boldsymbol{c}_{1} \\ \boldsymbol{a}_{2} & \boldsymbol{b}_{2} & \boldsymbol{c}_{2} \\ \boldsymbol{a}_{3} & \boldsymbol{b}_{3} & \boldsymbol{c}_{3}\end{array}\right|=\mathbf{0}, \) then \( \boldsymbol{\Delta}=\mathbf{0} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Maths
The value of the following polynomial at the indicate value of variables:
\( \boldsymbol{q}(\boldsymbol{y})=\boldsymbol{3} \boldsymbol{y}^{2}-\boldsymbol{4} \boldsymbol{y}+\sqrt{11} \) at \( \boldsymbol{y}=\boldsymbol{2} \) is
equal to \( 4+\sqrt{11} \)
A. True
B. False
Subject: Maths
If \( \boldsymbol{A}=-\mathbf{1 2 5} \boldsymbol{m}^{\mathbf{6}} \boldsymbol{n}^{2} \boldsymbol{x}, \boldsymbol{B}=\boldsymbol{6} \boldsymbol{m}^{2} \boldsymbol{n} \boldsymbol{x}, \boldsymbol{C}= \)
\( -\boldsymbol{6} \boldsymbol{4} \boldsymbol{m}^{6} \boldsymbol{n}^{2} \boldsymbol{x} \) and \( \boldsymbol{D}=\boldsymbol{8} \boldsymbol{m}^{2} \boldsymbol{n} \boldsymbol{x} \), then
\( (\boldsymbol{A} \div \boldsymbol{B})+(\boldsymbol{C} \div \boldsymbol{D}) \) is \( _{-}-\ldots- \) - -
Subject: Physics
If a star can convert all the He nuclei
completely into oxygen nuclei, the energy released per oxygen nuclei is:
[Mass of \( H e \) nucleus is \( 4.0026 a m u \) and
mass of oxygen nucleus is \( 15.9994 a m u \)
A. \( 7.6 \mathrm{MeV} \)
B. 56.12 MeV
c. \( 10.24 \mathrm{MeV} \)
D. \( 23.9 \mathrm{MeV} \)
Subject: Physics
The equation of a progressive wave for a
wire is:
\( \boldsymbol{Y}=\mathbf{4} \sin \left[\frac{\boldsymbol{\pi}}{\mathbf{2}}\left(\boldsymbol{8} \boldsymbol{t}-\frac{\boldsymbol{x}}{\boldsymbol{8}}\right)\right] . \) If \( \boldsymbol{x} \) and \( \boldsymbol{y} \) are
measured in cm then velocity of wave is
A. \( 64 \mathrm{cm} / \mathrm{s} \) along \( -x \) direction
B. \( 32 c m / s \) along \( -x \) direction
c. \( 32 c m / s \) along \( +x \) direction
D. \( 64 \mathrm{cm} / \mathrm{s} \) along \( +x \) direction
Subject: Maths
D.E. of family of parabolas symmetrical
about the X-axis is
A \( \cdot y \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}=0 \)
B. \( y \frac{d^{2} y}{d x^{2}}-\left(\frac{d y}{d x}\right)^{2}=0 \)
\( ^{\mathbf{C}}-y \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}=1 \)
D. \( y^{2} \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}=1 \)
Subject: Chemistry
The standard enthalpies of formation of
\( C O_{2(g)}, \) and \( H C O O H(I) \) are
\( -393.7 k J / m o l \) and \( -409.2 k J / m o l \)
respectively This question has multiple correct options
A. \( -393.7 k J / \) mol is the enthalpy change for the reaction \( C_{(s)}+O_{2(g)} \rightarrow C O_{2(g)} \)
B. The enthalpy change for the reaction \( C O_{2(g)}+ \) \( H_{2(g)} \rightarrow H C O O H_{(I)} \) would be \( -15.5 k J / m o l \)
c. The enthalpy chage for the reaction \( H_{2} O+C O \rightarrow \) \( H C O O H \) is \( -409.2 k J / m o l \)
D. The enthalpy change for the reaction \( H_{2(g)}+ \) \( C O_{2(g)} \longrightarrow H_{2} O_{(I)}+C O_{(g)} \) is \( -409.2 k J / m o l \)
Subject: Physics
Consider the following two statements A and B and identify the correct answer.
A) We cannot define Young's modulus and rigidity modulus for liquids and
gases.
B) The theoretical limits of Poisson's
ratio are 1 to 0.5
A. Both A \& B are true
B. A is false but B is true
c. Both A \& B are false
D. A is true but B is false
Subject: Maths
If \( \vec{i}, \vec{j}, \vec{k} \) be the position vectors of the vertices of a triangle, then its area is
A \( \cdot \sqrt{3} \) sq. units
B. \( \frac{1}{2} \sqrt{3} \) sq. units
c. 3 sq. units
D. \( 3 \sqrt{3} \) sq. units
Subject: Chemistry
In the following sequence of reaction all stereoisomers of (X) have been taken.
Find \( Q \) and \( R \)

Here \( Q= \) Total number of stereoisomers
of \( Y \)
\( \mathrm{R}= \) Total number of stereoisomers of \( \mathrm{Z} \)
What is the sum of \( Q \) and \( R ? \)
Subject: Maths
Normal to the curve \( x^{2}=4 y \) which
passes through the point \( (\mathbf{1}, \mathbf{2}) \)
A. \( x+y=3 \)
в. \( x-y=3 \)
c. \( 2 x+y=4 \)
D. \( x+2 y=5 \)
Subject: Maths
Let \( \Delta_{\mathrm{o}}=\left[\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right] \) and let \( \Delta_{1} \)
denote the determinant formed by the
cofactors of elements of \( \Delta_{0} \) and \( \Delta_{2} \)
denote the determinant formed by the
cofactor of \( \Delta_{1}, \) similarly \( \Delta_{n} \) denotes the
determinant formed by the cofactors of
\( \Delta_{n-1} \) then the determinant value of \( \Delta_{n} \)
is
\( \mathbf{A} \cdot \Delta_{0}^{2 n} \)
B . \( \Delta_{0}^{2^{2}} \)
\( \mathbf{C} \cdot \Delta_{0}^{n^{2}} \)
D. \( \Delta^{2}_{0} \)
Subject: Maths
f \( \triangle \boldsymbol{P} \boldsymbol{Q} \boldsymbol{R} \cong \triangle \boldsymbol{C} \boldsymbol{A} \boldsymbol{B}, \boldsymbol{P} \boldsymbol{Q}=\boldsymbol{C} \boldsymbol{A} . \) If true
enter 1 else 0
Subject: Physics
A gas is compressed at constant pressure \( 50 N / m^{2} \) from a volume of
\( 0 m^{3} \) to a volume \( 4 m^{3} . \) Energy \( 100 J \) is then added to the gas by heating. Its internal energy is :
A. Increased by \( 100 \mathrm{J} \)
B. Increased by 200 J
c. Decreased by \( 100 \mathrm{J} \)
D. Increased by 400 J
Subject: Chemistry
Select the incorrect statements about
the plots of \( \ln \boldsymbol{K} \) vs \( \frac{\mathbf{1}}{\boldsymbol{T}} \)
This question has multiple correct options
A . Linear with slope equal to \( \frac{\Delta G^{o}}{R} \) and intercept \( \Delta H \)
B. Curve
c. Linear with slope \( -\frac{\Delta H^{o}}{R} \) and intercept \( \frac{\Delta S^{o}}{R} \)
D. Linear with slope \( -\frac{\Delta S^{o}}{R} \) and intercept \( \frac{\Delta H^{o}}{R} \)
Subject: Physics
A particle is an linear simple harmonic motion between two extreme point \( \mathbf{A} \) and B. \( 10 \mathrm{cm} \) apart(See figure below) If the direction from \( A \) to \( B \) is taken as
positive direction, what are signs of displacement \( x, \) velocity \( V \) and acceleration a, when the particle is at
\( \mathbf{A} ? \)
A \( . x=-v e, V=-v e, a=-v e \)
в. \( x=+v e, V=0, a=-v e \)
c. \( x=+v e, V=-v e, a=+v e \)
D. \( x=-v e, V=0, a=+v e \)
Subject: Physics
In an ideal transformer turn ratio is 2: 3
If input voltage is \( 100 \mathrm{V} / 60 \mathrm{Hz} \), then
output voltage is
A . 150 V/90 нz \( z \) z
B. 150 V/40 нZ
c. \( 150 \vee / 60 \) Н \( z \)
D. 66.6 V/60 нz
Subject: Physics
Two points of a rod move with velocities \( 3 v \) and \( v \) perpendicular to the rod and in the same direction,
separated by a distance 'r'. at Then the angular velocity of rod is :
A \( \cdot \frac{4 v}{r} \)
в. \( \frac{3 v}{r} \)
c. \( \frac{2 v}{r} \)
D. \( \frac{v}{r} \)
Subject: Chemistry
The electrolyte used in electrolytic
refining of impure aluminium is
\( \mathbf{A} \cdot A I_{2} O_{3}+C a F_{2} \)
B. \( N a_{3} A l F_{6}+C a F_{2} \)
\( \mathbf{c} \cdot A l_{2} O_{3}, N a_{3} A l F_{6} a n d C a F_{2} \)
D. Any aluminium salt is molten state
Subject: Physics
A student is weighing an object using a spring balance. The weight and mass of the object are respectively
\( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
A. \( 25 N, \) skg
в. \( 50 N, 5 k g \)
c. \( 25 N, 2.0 k g \)
D. \( 50 N, 2.5 k g \)
Subject: Chemistry
Natural rubber or raw rubber consists of
basic material latex which is a
dispersion of isoprene. During the treatment, this isoprene forms a high molecular weight polymer of isoprene. Natural rubber can be obtained from
five hundred different species of plants. In the isoprene polymer all the isoprene have:
A. trans 1, 4 configuration
B. cis 1, 4 configuration
c. both cis and trans 1,4 configuration
D. none of these
Subject: Maths
If \( \boldsymbol{x} \cos \boldsymbol{\theta}=\boldsymbol{y} \cos \left(\boldsymbol{\theta}+\frac{\boldsymbol{2} \boldsymbol{\pi}}{\boldsymbol{3}}\right)= \)
\( z \cos \left(\theta+\frac{4 \pi}{3}\right), \) then the value of \( x y+ \)
\( \boldsymbol{y} \boldsymbol{z}+\boldsymbol{z} \boldsymbol{x}= \)
\( A \)
B.
c.
D.
Subject: Chemistry
If
0.1 mol of salt is added to \( 1 L \) water,
which of these salts is expected to produce the most acidic solution?
A. \( N a C_{2} H_{3} O_{2} \)
B. \( N H_{4} N O_{3} \)
\( \mathrm{c} \cdot \mathrm{CuSO}_{4} \)
D. \( A l C l_{3} \)
Subject: Physics
One atomic mass unit is equal to:
A \( \cdot 1.66 \times 10^{-27} g \)
B . \( 1.66 \times 10^{-24} g \)
c. \( 1.66 \times 10^{-23} g \)
D. \( 1.66 \times 10^{-25} g \)
Subject: Maths
\( f \frac{\sqrt{1+\sin \frac{39 \pi}{8}}}{\sqrt{1+\sin \frac{57 \pi}{8}}}=\tan \left(\frac{k \pi}{16}\right) \) then
least positive value of \( k \) is
A . 1
B. 3
\( c .5 \)
D.
Subject: Biology
Which of the following action or activity may causes undesirable effect to our
environment?
i) Catching and keeping animals such as bird and cats at home.
ii) Feeding birds such as pigeon and crows in our neighbourhood.
iii) Burning unwanted plastic product in our neighbourhood o reduce non biodegradable rubbish.
iv) Dumping biodegradable refuse such as fruit skins and bones in our sewage
to make the water nutrients rich for
healthy growth of flowering plants.
A. iii and iv only
B. ii and iv only
c. ii, iii and daily
D. i, ii, iii and D
Subject: Chemistry
The reaction \( \boldsymbol{C}_{\mathbf{6}} \boldsymbol{H}_{\mathbf{5}} \boldsymbol{I}+\mathbf{2} \boldsymbol{N} \boldsymbol{a}+ \)
\( \boldsymbol{C H}_{3} \boldsymbol{I} \rightarrow \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{C H}_{3}+\mathbf{2} \boldsymbol{N} \boldsymbol{a} \boldsymbol{I} \) is called:
A. Wurtz reaction
B. Fittig reaction
c. Wurtz - Fittig reaction
D. Sandmeyer reaction
Subject: Maths
The sum of infinite series \( \frac{1.3}{2}+\frac{3.5}{2^{2}}+ \)
\( \frac{5.7}{2^{3}}+\frac{7.9}{2^{4}}+\ldots \infty \)
A . 21
B . 22
\( c \cdot 23 \)
D. None
Subject: Maths
Construct a \( \triangle A B C \) in which the base
\( B C=5 \mathrm{cm}, \angle B A C=40^{\circ} \) and the
median from \( \boldsymbol{A} \) to \( \boldsymbol{B} \boldsymbol{C} \) is \( \boldsymbol{6} \mathrm{cm} . \) Also
measure the length of the altitude from
\( A \)
Subject: Physics
If \( g_{E} \) and \( g_{M} \) are the accelerations due
to gravity on the surfaces of the Earth and the Moon respectively and if Millikan's oil drop experiment could be performed on the two surfaces, one will find the ratio (electronic charge on the Moon/ electronic charge on the Earth) to be:
A . 1
B.
\( \mathbf{c} \cdot g_{E} / g_{M} \)
D. \( g_{M} / g_{E} \)
Subject: Chemistry
Select correct statement(s).
A \( . \) Equivalent mass of \( X e O_{3}= \) \( \frac{\text {molar mass}}{6} \) and Equivalent mass of \( H X e O_{4}^{-}= \)
\( \frac{\text { molar mass }}{6} \)
B. As reaction I or II goes to forward side, pressure increases
C. Both are correct statements
D. None of the above is correct statement
Subject: Physics
Four solid rigid balls each of mass \( m \)
and radius \( r \) are fixed on a rigid-ring of
radius \( 2 r \) and mass \( 2 m . \) The system is
whirled about \( ^{\prime} O^{\prime} \) as shown. The radius
of gyration of the system is
\( 128 m r^{2} / 30 . \) how?
A \( \cdot \sqrt{\frac{128}{5}} \)
B.
c. \( r \sqrt{\frac{128}{3}} \)
Subject: Maths
The side of an equilateral triangle expands at the rate of \( \sqrt{3} \mathrm{cm} / \) sec.When
the side is \( 12 \mathrm{cm}, \) the rate of increase of
its area is
A \( \cdot 12 \mathrm{cm}^{2} / \mathrm{sec} \)
B. \( 18 \mathrm{cm}^{2} / \mathrm{sec} \)
c. \( 3 \sqrt{3} \mathrm{cm}^{2} / \mathrm{sec} \)
D. \( 10 \mathrm{cm}^{2} / \mathrm{sec} \)
Subject: Physics
The figure represents a displacement
time graph of a body moving in a
straight line. The instantaneous velocity
of the body at \( 3 s \) is :
A \( \cdot 4 m s^{-1} \)
B. \( 3 m s^{-1} \)
\( c \)
D. \( 1 \mathrm{ms}^{-1} \)
Subject: Maths
If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}}{1+|\boldsymbol{x}|} \cdot \) then
\( f(x) \) is
A. injective but not surjective
B. surjective but not injective
c. injective as well as surjective
D. neither injective nor surjective
Subject: Biology
Which one of the following options
correctly designate the percent contribution of gases \( (A, B, C \text { and } D) \)
responsible of global warming?
\( N_{2} O(6 \%) \)
(2)\( \quad C F C s(20 \%) \quad C O_{2}(14 \%) \quad N_{2} O(6 \%) \) (3) \( N_{2} O(20 \%) \quad C H_{4}(14 \%) \quad C F C s(6 \% \)
(4)
\( C H_{4}(20 \%) \quad N_{2} O(14 \%) \) \( C F C s\left(6^{\circ}\right. \)
\( A \cdot A \)
B. B
\( c \cdot c \)
\( D . D \)
Subject: Maths
If \( 270^{\circ}<A<360^{\circ}, 90^{\circ}<B< \)
\( 180^{\circ}, \cos A=\frac{5}{13}, \tan B=-\frac{15}{8}, \) then
\( \sin (\boldsymbol{A}+\boldsymbol{B})= \)
A \( \cdot \frac{140}{221} \)
в. \( \frac{171}{221} \)
c. \( \frac{140}{171} \)
D. \( \frac{221}{171} \)
Subject: Physics
A ball is projected horizontally from the
top of a tower with a velocity \( v_{0} \). It will be
moving at an angle of \( 60^{\circ} \) with the horizontal after time -
A. \( \frac{v_{0}}{\sqrt{3} g_{g}} \)
B. \( \frac{\sqrt{3} v_{0}}{g} \)
c. \( \frac{v_{0}}{g} \)
D. \( \frac{v_{0}}{2 g g g g g g_{0}} \)
Subject: Physics
A spring-block system is resting on a frictionless floor as shown in the figure.
The spring constant is \( 2.0 \mathrm{Nm}^{-1} \) and the mass of the block is 2.0 kg. lgnore the mass of the spring. Initially, the spring is in an unstretched condition.
Another block of mass \( 1.0 \mathrm{kg} \) moving with a speed of \( 2.0 ~ m s^{-1} \) collides elastically with the first block. The collision is such that the \( 2.0 \mathrm{kg} \) block
does not hit the wall. The distance, in
metres. between the two blocks when
the spring returns to its unstretched position for the first time after the collision is

Round off your answer to nearest integer.
Subject: Physics
Consider a spherical shell of radius \( \mathrm{R} \) with a total charge + q uniformly spread on its surface(center of the chell lies at
the origin \( x=0 \) ). Two point charges, \( +q \) and \( -q \) are brought, one after the other, from far away and placed at \( x=-a / 2 \)
and \( \boldsymbol{x}=+\boldsymbol{a} / 2(\boldsymbol{a}<\boldsymbol{R}), \) respectively
Magnitude of the work done in this
process is?
A \( \cdot(Q+q)^{2} \cdot 4 \pi \varepsilon_{0} \)
\( a \)
B. Zero
\( \mathbf{c} \cdot q^{2} / 4 \pi \varepsilon_{0} \)
D \( \cdot Q q / 4 \pi \varepsilon_{0} a \)
Subject: Physics
A car is travelling at \( 30 \mathrm{m} / \mathrm{s} \) on a circular road of radius \( 300 \mathrm{m} \). It is
increasing its speed at the rate of \( 4 m / s^{2} . \) The acceleration of the car is
A \( \cdot 3 m / s^{2} \)
B. \( 4 m / s^{2} \)
c. \( 5 m / s^{2} \)
D. \( 1 \mathrm{m} / \mathrm{s}^{2} \)
Subject: Physics
A broadcasting station transmits waves
of frequency \( 71 \times 10^{4} H z \) with speed of
\( 3 \times 10^{8} m / s . \) The wavelength of the
wave is :
A . \( 418.8 \mathrm{m} \)
B. 324.6 m
c. \( 208.4 \mathrm{m} \)
D. 422.5 m
Subject: Maths
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{\boldsymbol{x}+\mathbf{1}}{\boldsymbol{x}^{2}+\mathbf{2}}, \boldsymbol{x} \in \boldsymbol{R} \).Find \( \boldsymbol{f}(\boldsymbol{4}) \)
Subject: Chemistry
The constant of proportionality which relates energy to the frequency of electromagnetic radiation is Planck's constant and its value is :
A \( \cdot 06.62 \times 10^{-34} J s \)
B. \( 3.1 \times 10^{-31} J s \)
\( \mathbf{c} \cdot 6.67 \times 10^{23} J s \)
D. none of these
Subject: Maths
Mean deviation for \( n \) observations
\( x_{1}, x_{2}, \ldots . . x_{n} \) from their mean \( \bar{X} \) is given
by:
A \( \cdot \sum_{i=1}^{n}\left(x_{i}-\bar{X}\right) \)
B \( \cdot \frac{1}{n} \sum_{i=1}^{n}\left|x_{i}-\bar{X}\right| \)
C \( \cdot \sum_{i=1}^{n}\left(x_{i}-\bar{X}\right)^{2} \)
D \( \cdot \frac{1}{n} \sum_{i=1}^{n}\left(x_{i}-\bar{X}\right)^{2} \)
Subject: Maths
If \( \mathbf{A} \) and \( \mathbf{B} \) are two square matrices
such that \( \mathbf{B}=-\mathbf{A}^{-1} \mathbf{B} \mathbf{A} \) then \( (\mathbf{A}+ \)
\( \mathbf{B})^{2}= \)
A . 0
B. \( A^{2}+B^{2} \)
c. \( A^{2}+2 A B+B^{2} \)
D. \( A+B \)
Subject: Chemistry
A \( 6.90 M \) KOH solution in water has
\( 30 \% \) by weight of \( K O H . \) The density of
KOH solution is:
A. \( 1.288 g / m L \)
в. \( 12.88 g / m L \)
c. \( 0.1288 g / m L \)
D. none of these
Subject: Chemistry
When \( C O_{2} \) is passed through lime water, it turns milky. The milkiness is due to:
A. \( C a C O_{3} \)
в. \( C a(O H)_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. \( C O_{2} \)
Subject: Physics
By observing the diagram, answer the
following.
a) How does the pressure at A differ
from the pressure at B.?
b) The pressure at \( B \) is greater than the
pressure at D. Is it true?. Justify your
answer.
c) Compare the pressure at \( A \) and \( C \).
d) If the water is replaced with mercury,
how would this affect the pressure at \( A \)
and D?
Subject: Maths
A group of 10 observations has mean 5 and \( S . D .2 \sqrt{6} \) another group of 20 observations has mean 5 and \( \mathrm{S.D.} 3 \sqrt{2} \)
then the S.D. of combined group of 30 observations is
A \( \cdot \sqrt{5} \)
B. \( 2 \sqrt{5} \)
\( c \cdot 3 \sqrt{5} \)
D. none of these
Subject: Physics
A boy playing on the roof of a \( 10 \mathrm{m} \) high building throws a ball with a speed of \( 10 m s^{-1} \) at an angle of \( 30^{\circ} \) with the horizontal. How far from the throwing point with the ball be at the height of 10 \( \mathrm{m} \) from the ground? \( (\boldsymbol{g}= \) \( 10 m s^{-2}, \sin 30^{\circ}=1 / 2, \cos 30^{\circ}= \)
Subject: Chemistry
3.2 moles of \( H I(g) \) were heated in a sealed bulb at 444 till the equilibrium was reached. Its degree of dissociation
was found to be \( 20 \% \). Calculate the
number of moles of hydrogen iodide, hydrogen and iodine present at the equilibrium point and determine the value of equilibrium constant for the
reaction \( 2 H I(g) \rightleftharpoons H_{2}(g)+I_{2}(g) \)
Considering the volume of the container \( 1 L \)
Subject: Physics
For a constant hydraulic stress on an object, the fractional change in the object's volume \( (\Delta V / V) \) and its bulk modulus (B) are related as:
A \( \cdot \frac{\Delta V}{V} \propto B \)
B. \( \frac{\Delta V}{V} \propto \frac{1}{B} \)
c. \( \frac{\Delta V}{V} \propto B^{2} \)
D. \( \frac{\Delta V}{V} \propto B^{-2} \)
Subject: Chemistry
\( \Delta \mathrm{SOH} 2(g)=130.6 \mathrm{JK}-1 \mathrm{mol}-1 \Delta \mathrm{SH} 2(\mathrm{g}) 0=130 \)
6JK-1mol-1 is:
A . \( -163.2 \mathrm{Jmol}^{-1} \mathrm{K}^{-1} \)
B. +163.2Jmol-1K-1+163.2Jmol-1K-1
c. \( -303 J \) mol \( ^{-1} K^{-1} \)
D. \( +303 J \) mol \( ^{-1} \) K \( ^{-1} \)
Subject: Physics
A lead bullet penetrates into a solid
object and melts. Assuming that \( 50 \% \) of its kinetic energy was used to heat it,
the initial speed of the bullet is (the
initial temperature of the bullet is \( 25^{\circ} \mathrm{C} \)
and its melting point is \( 300^{\circ} \mathrm{C} \) ). Latent
heat of fusion of lead \( =2.5 \times 10^{4} J / k g \) and specific heat capacity of lead \( = \) \( \mathbf{1 2 5 J} / \boldsymbol{k g}-\boldsymbol{K} \)
A. \( 100 \mathrm{m} / \mathrm{s} \)
в. \( \simeq 490 m / s \)
\( \mathrm{c} .520 \mathrm{m} / \mathrm{s} \)
D. \( 360 \mathrm{m} / \mathrm{s} \)
Subject: Biology
Out of the seven characters of pea
studied by Mendel,gens for three were situated on chromosome number four
(flower position,pod shape and plant height.) Suppose if they were closely situated and were linked then which of
the following rule would not have been discovered or explained Mendel?
A. Law of dominance
B. Law of seggregation
c. Law of independent assortment
D. Law of purity of gametes
Subject: Chemistry
To \( A g_{2} C r O_{4} \) solution over its own precipitate, \( C r O_{4}^{2-} \) ions are added. This results in:
A . Increase in \( A g^{+} \) concentration
B. Decrease in \( A g^{+} \) concentration
c. Increase in solubility product
D. shifting of \( A g^{+} \) ions from the precipitate into the solution
Subject: Chemistry
following reaction:
\( \boldsymbol{C}_{6} \boldsymbol{H}_{6}+\boldsymbol{D}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \stackrel{D_{2} \boldsymbol{O}}{\longrightarrow} \boldsymbol{X} \)
\( A \)
B.
\( c \)
\( D \)
Subject: Physics
If the ratio of the concentration of
electrons to that of holes in a
semiconductor is \( \frac{7}{5} \) and the ratio of current is \( \frac{7}{4}, \) then what is the ratio of their drift velocities?
A \( \cdot \frac{5}{8} \)
B. \( \frac{4}{5} \)
\( c \cdot \frac{5}{4} \)
D. \( \frac{4}{7} \)
Subject: Maths
If in \( \triangle P Q R \) and \( \triangle L M N, \angle P=\angle M= \)
\( \mathbf{6 0}^{\circ}, \boldsymbol{P Q}: \boldsymbol{M} \boldsymbol{L}=\boldsymbol{P} \boldsymbol{R}: \boldsymbol{M} \boldsymbol{N} \) and \( \angle \boldsymbol{N}= \)
\( 55^{\circ}, \) then \( \angle Q \) is:
A .50
B. 55
\( c \cdot 65 \)
D. 75
Subject: Physics
In a meter bridge, the gaps are closed by resistances 2 and 3 ohms. The value
of shunt to be added to 3 ohm resistor
to shift the balancing point by \( 22.5 \mathrm{cm} \)
is.
A . \( 1 \Omega \)
B. 2\Omega
c. \( 2.5 \Omega \)
D. \( 5 \Omega \)
Subject: Physics
In a hydrogen atom, the electron moves
in an orbit of radius \( 0.5 A^{\circ} \) making \( 10^{16} \) revolution per second. The magnetic moment associated with the orbital
motion of the electron is \( A m^{2} \)
A. \( 1.602 \times 10^{-19} \)
?
В. \( 1.256 \times 10^{-22} \)
c. \( 1.67 \times 10^{-2} \)
D. \( 1.256 \times 10^{-23} \)
Subject: Physics
The time period of a particle in SHM is
12 sec. At \( t=0, \) it is at mean position. The ratio of the distance travelled in the
second and sixth second is.
A \( \cdot(\sqrt{3-1}) \)
B. \( (\sqrt{2-1}) \)
c. \( \frac{1}{(\sqrt{2}-1)} \)
D. \( \frac{1}{\sqrt{2}} \)
Subject: Chemistry
The name of compound \( (A) \) is:
A. Methyl- \( \alpha \) -D-glucofuranoside
B. Methyl- \( \beta \) -D-glucofuranoside
C . Methyl- \( \alpha \) -D-glucopyranoside
D. Methyl- \( \beta \) -D-glucopyranoside
Subject: Physics
A solid cylindrical rod of radius \( 3 m m \) gets depressed under the influence of a load through \( 8 m m . \) The depression produced in an identical hollow rod with
outer and inner radii of \( 4 m m \) and \( 2 m m \)
respectively, will be
A. 2.7mm
B. \( 1.9 \mathrm{mm} \)
c. \( 3.2 \mathrm{mm} \)
D. 7.7mm
Subject: Maths
Write a pair of linear equations which has the unique solution \( x=-1, y=3 . \) How many such pairs can you write?
A. \( x+y=2 \& x-y=-4 ; \) infinite
B. \( 2 x+y=6 \& 2 x-3 y=6 ; 3 \)
c. \( 5 x-8 y=13 \) \& \( x+3 y=7 ; 8 \)
D. Cannot be determined