AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
As you have learnt in the text, a
geostationary satellite orbits the earth at a height of nearly \( 36,000 \mathrm{km} \) from the
surface of the earth. What is the
potential due to earth's gravity at the site of this satellite? (Take the potential energy at infinity to be zero). Mass of the earth \( =6.0 \times 10^{24} k g, \) radius \( =6400 \)
\( \mathbf{k m} \)
Subject: Chemistry
Assertion: \( C a C l_{2} \) can't be used for
drying ethyl alcohol
Reason: Calcium chloride can form an
addition compound with ethyl alcohol
A. Both Assertion and Reason are true and Reason is the correct explanation to Assertion
B. Both Assertion and Reason are true and Reason is not the correct explanation to Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
Subject: Physics
A hammer weighing of \( 1 \mathrm{kg} \) moving with the speed of \( 10 \mathrm{m} \mathrm{s}^{-1} \) strikes the head
of a nail driving it \( 10 \mathrm{cm} \) into a wall.
Neglecting the mass of the nail, calculate the acceleration during the
impact
A. \( 400 \mathrm{m} \mathrm{s}^{-2} \)
B. \( 500 \mathrm{m} \mathrm{s}^{-2} \)
c. \( 600 \mathrm{m} \mathrm{s}^{-2} \)
D. \( 700 \mathrm{m} \mathrm{s}^{-2} \)
Subject: Physics
Two equal electric currents are flowing perpendicular to each other as shown in figure. AB and CD are perpendicular to each other and symmetrically placed with respect to the currents. Where do
we expect the resultant magnetic field to be zero?
\( A \cdot \) on \( A B \)
B. on CD
\( c \). on both \( A B \& \) CD
D. on both OD \& BO
Subject: Physics
A wire of density \( \rho \) is stretched between
the clamps at a distance \( L \) apart, while
being subjected to an extension \( l(l<< \)
\( L), Y \) is the Young's modulus of the
wire. The lowest resonant frequency of transverse vibration of the wire is
approximately given by :
A \( \cdot f=\frac{1}{2 L} \sqrt{\frac{Y L}{l \rho}} \)
B. \( f=\frac{1}{2 L} \sqrt{\frac{Y \rho L}{l^{2}}} \)
\( ^{\mathrm{c}} \cdot f=\frac{1}{2 L} \sqrt{\frac{Y l}{L \rho}} \)
D \( f=\frac{1}{2 L} \sqrt{\frac{L \rho}{Y l}} \)
Subject: Physics
The free-body diagram will be identical
to the one we drew in the example of the
frictionless plane, except we will have a vector for the force of friction in the
negative \( x \) direction. What is the work
done on the box by the force of kinetic
friction?
A \( . \) \mumgh \( \sin 30^{\circ} \)
B. \( \mu \) mgh tan30 \( ^{\text {0 }} \)
c. \( \mu m g h \cot 30^{\circ} \)
D. \( \mu \) mgh \( \cos 30^{\circ} \)
Subject: Maths
Verify Lagrange's mean value theorem for the following function on the indicated interval. In each case find a
point \( ^{\prime} c^{\prime} \) in the indicated interval as stated by the Lagrange's mean value theorem:
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}-\mathbf{1} \) on \( [\mathbf{2}, \boldsymbol{3}] \)
Subject: Chemistry
Match the following substances with types of inter molecular forces:
List-I List-II
a) \( C H_{4} \)
i) London, dipole-dipole
\( b \)
ii) London
\[
C H C l_{3}
\]
\( c \)
iii) London, dipole-dipole, hydrogen
\[
C_{4} H_{9} O H \quad \text { bonding. }
\]
A . a-ii, b-i, c-iii
B. a-i, b-ii, c-iii
c. a-iii, b-i, c-ii
D. a-iii, b-ii, c-
Subject: Maths
One hundred identical coins, each with probability, \( p, \) of showing up heads are
tossed once. If \( 0<p<1 \) and the
probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of \( p \) is:
\( A \cdot \frac{1}{2} \)
в. \( \frac{49}{101} \)
c. \( \frac{50}{101} \)
D. \( \frac{51}{101} \)
Subject: Maths
If \( P(1) \) be the probability of an event \( A \)
then
A. \( -1 \leq P(1) \leq 1 \)
B. \( 0 \leq P(1)<0.5 \)
c. \( 0 \leq P(1) \leq 1 \)
D. None of these
Subject: Physics
Initially car \( A \) is \( 21 \mathrm{m} \) ahead of car \( B \).
Both start moving at time \( t=0 \) in same direction along straight line. if \( A \) is moving with constant velocity \( 20 \mathrm{m} / \mathrm{s} \) and B starts from rest with an
acceleration \( 2 m / s^{2} \) towards \( A, \) then the
time when car \( B \) will catch the car \( A \) is
A . \( 21 s \)
в. \( 22 s \)
\( c .10 s \)
D. Can never catch \( A \)
Subject: Maths
The value of \( x \) satisfying the equation \( \tan ^{-1} x+\tan ^{-1}\left(\frac{2}{3}\right)=\tan ^{-1}\left(\frac{7}{4}\right) \)
equal to
\( A \cdot \frac{1}{2} \)
в. \( -\frac{1}{2} \)
\( c \cdot \frac{3}{2} \)
D. \( -\frac{1}{3} \)
E
Subject: Physics
In an inductance coil the current
increases from zero to \( 6 A \) in 0.3 second
by which an induced e.m.f. of \( 60 \mathrm{V} \) is produced in it. The value of coefficient of self-induction of coil is :
A. \( 1 H \)
в. \( 0.5 H \)
\( c .2 H \)
D. \( 3 H \)
Subject: Physics
The terminal velocity \( \left(V_{c}\right) \) of a small
sphere falling under gravity in a viscous liquid is related to its radius as
A. \( V_{c} \propto r \)
B. \( V_{c} \propto \frac{1}{r} \)
c. \( V_{c} \propto r^{2} \)
D. \( V_{c} \propto r^{3} \)
Subject: Chemistry
What is the activation energy for the reverse of this reaction?
\( N_{2} O_{4}(g) \longrightarrow 2 N O_{2}(g) \)
Data for the given reaction is: \( \Delta \boldsymbol{H}= \)
\( +54 k J \) and \( E_{f}=+57.2 k J \)
A \( .-54 k J \)
в. \( +3.2 k J \)
\( \mathbf{c} .+60.2 k J \)
D. \( +111.2 k J \)
Subject: Physics
A laser lamp is of \( 9 m W \) diameter \( = \)
\( 2 m m . \) Then what is the amplitude of
magnetic field associated with it?
A \( .49 \mu T \)
B. \( 98 \mu T \)
c. \( 9.8 \mu T \)
D. \( 4.9 \mu T \)
Subject: Physics
Find the height from the earth's surface where \( g \) will be \( 25 \% \) of its value on the
surface of earth \( (\mathrm{R}=\mathbf{6 4 0 0} \mathrm{km}) . \) (b) Find
the percentage increase in the value of \( \mathrm{g} \) at a depth h from the surface of earth.
Subject: Physics
Spherical balls of radius \( \mathbf{R} \) are falling in a viscous fluid of viscosity \( \eta \) with a velocity v. The retarding viscous force acting on the spherical ball is:
A. directly proportional to R but inversely proportional to
B. directly proportional to both radius R and velocity v
C. inversely proportional to both radius R and velocity
D. inversely proportional to R but directly proportional to velocity v
Subject: Physics
A metal disc of radius R rotates with an
angular velocity, \( \omega=1 r a d / s \) about an
axis perpendicular to its plane passing through its centre in a magnetic field of induction B acting perpendicular to the plane of the disc. The induced e.m.f. between the rim and axis of the disc is:
A \( . B R^{2} \)
B \( \cdot 2 B^{2} R^{2} \)
\( c \cdot B R^{3} \)
D. \( B R^{2} / 2 \)
Subject: Chemistry
When \( H_{2} O_{2} \) reacts with ozone, and
forms \( H_{2} O \) and \( O_{2} . \) In this reaction \( O_{2} \)
is released by:
This question has multiple correct options
A \( . H_{2} O \)
в. \( O_{3} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O}_{2} \)
D. \( O_{2} \)
Subject: Chemistry
Assertion
Chemicals added to foods for
increasing their life are called preservatives.
Reason
Natural sweeteners like sucrose and
artificial sweeteners like saccharin are
commonly used as food preservatives.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Biology
The correct lists of the phylogenic
hierarchy is
A. Domain, kingdom, phylum, family, class, order, genus, species
B. Phylum, family, order, domain, class, kingdom, species, genus
C. Kingdom, domain, family, order, class, phylum, genus, species
D. Domain, kingdom, phylum, class, order, family, genus, species
E. Family, kingdom, order, domain, phylum, genus, class, species
Subject: Physics
An open pipe of length \( 33 \mathrm{cm} \) resonates with frequency of \( 1000 H z \). If the speed
of sound is \( 330 m s^{-1}, \) then this
frequency is
A. The fundamental frequency of the pipe
B. The first harmonic of the pipe
c. The second harmonic of the pipe
D. The forth harmonic of the pipe
Subject: Maths
\( \boldsymbol{f}(\boldsymbol{x}+\mathbf{1})=(-1)^{x+1} \boldsymbol{x}-\boldsymbol{2} \boldsymbol{f}(\boldsymbol{x}) \) for \( \boldsymbol{x} \in \mathbb{N} \)
and \( f(1)=f(1986) . \) Then sum of digits
of \( (\boldsymbol{f}(\mathbf{1})+\boldsymbol{f}(\mathbf{2})+\ldots .+\boldsymbol{f}(\mathbf{1 9 8 5}))= \)
\( \mathbf{A} \cdot \mathbf{4} \)
B. 3
\( c \cdot 7 \)
D. 1
Subject: Chemistry
The sugar moiety present in \( \boldsymbol{R} \boldsymbol{N} \boldsymbol{A} \)
molecule is:
A. \( \beta-D-2 \) - deoxyribose
B. \( \beta-D- \) galactose
c. \( \beta-D \) - fructofuranose
D. \( \beta-D- \) ribose
E. \( \beta-D-3- \) ribose
Subject: Maths
Assertion
The order of the differential equation of
all conics whose centre lies at (0,0) is 3
Reason
The order of differential equation.is
same as the number of arbitrary unknowns (constants) in the given
curve.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
If the MP is \( 30 \% \) above \( \mathrm{CP} \) and a
discount of \( 10 \% \) is given for cash payments, what is the profit?
A . \( 10 \% \)
B. \( 15.5 \% \)
c. \( 17 \% \)
D. \( 18.5 \% \)
Subject: Physics
Shown in the figure here is a convergent
lens placed inside a cell filled with a liquid. The lens has focal length +20
\( \mathrm{cm} \) when in air and its material has
refractive index \( 1.50 . \) If the liquid has
refractive index \( 1.60, \) the focal length of
the system is
\( A \cdot+80 \mathrm{cm} \)
B. - 80 cm
C. \( -24 \mathrm{cm} \)
\( D .-100 \mathrm{cm} \)
Subject: Chemistry
The balanced equation in acidic
medium is :
\( \boldsymbol{S}_{2} \boldsymbol{O}_{3}^{2-}+\boldsymbol{S} \boldsymbol{b}_{2} \boldsymbol{O}_{5} \stackrel{\boldsymbol{H}^{+}}{\rightarrow} \boldsymbol{S b} \boldsymbol{O}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{3} \)
A \( \cdot 3 S_{2} O_{3}^{2-}+2 S b_{2} O_{5}+6 H^{+} 3 H_{2} O \rightarrow 4 S b O+6 H_{2} S O_{3} \)
B . \( 2 S_{2} O_{3}^{2-}+2 S b_{2} O_{5}+6 H^{+} 3 H_{2} O \rightarrow 4 S b O+4 H_{2} S O_{3} \)
\( \mathrm{c} \cdot 3 S_{2} O_{3}^{2-}+2 S b_{2} O_{5}+4 H^{+} 2 H_{2} O \rightarrow 4 S b O+2 H_{2} S O_{3} \)
D. none of these
Subject: Maths
State true or false:
If \( u(x) \) and \( v(x) \) are differentiable functions such that \( \frac{u}{v}(x)=7 \) \( \frac{\boldsymbol{u}^{\prime}(\boldsymbol{x})}{\boldsymbol{v}^{\prime}(\boldsymbol{x})}=\boldsymbol{p} \) and \( \left(\frac{\boldsymbol{u}(\boldsymbol{x})}{\boldsymbol{v}(\boldsymbol{x})}\right)^{\prime}=\boldsymbol{q}, \) then
\( \frac{\boldsymbol{p}+\boldsymbol{q}}{\boldsymbol{p}-\boldsymbol{q}}=\mathbf{1} \)
A. True
B. False
Subject: Chemistry
Assertion
Argon does not react.
Reason
Noble gases have complete octet so
they dont have tendency to pair with
other elements and they show zero
valency.
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
\( \mathbf{A} \)
\( 2.0 V \) potentiometer used for the
determination of internal resistance of
a \( 1.5 V \) cell. The balance point of the cell
in open circuit is \( 76 \mathrm{cm} \). When a resistor
of \( 9.5 \Omega \) is used in the external circuit of
the cell, the balance point shifts to \( 57 \mathrm{cm} \) length of the potentiometer wire. Determine the internal resistance of the
cell
A \( .1 .7 \Omega \)
В. \( 2.5 \Omega \)
c. \( 1.5 \Omega \)
D. \( 0.5 \Omega \)
Subject: Physics
A domain in ferromagnetic iron is in the
form of a cube of side length \( 2 \mu m \) then
the number of iron atoms in the domain
are (Molecular mass of iron \( =\mathbf{5 5 g} \)
\( m o l^{-1} \) and density \( =7.92 g c m^{-3} \) )
A \( \cdot 6.92 \times 10^{12} \) atoms
B. \( 6.92 \times 10^{11} \) atoms
c. \( 6.92 \times 10^{10} \) atoms
D. \( 6.92 \times 10^{13} \) atoms
Subject: Physics
Statement -1: Kinetic energy can be divided by volume and
Statement -2: Dimensions of kinetic
energy and volumeare different
A. Statement- -1 is True Statement-2 is True
Statement-2 is a correct explanation for Statement-
B. Statement- - - is True Statement-2 is True:
Statement-2 is NOT a correct explanation for Statement-1
c. statement - - is True Statement - - 2 is False.
D. Statement-1 is False Statement- -2 is True
Subject: Physics
When a current of \( 2 \mathrm{A} \) flows in a battery
from negative to positive terminal, the potential difference across it is 12 V. If a
current of 3 A flowing in the opposite direction produces a potential difference of \( 15 V \), the emf of the battery is?
A . \( 54 v \)
B. \( 13.2 \mathrm{V} \)
c. \( 65 v \)
D. \( 50 v \)
Subject: Physics
Three charges \( Q,+q \) and \( +q \) are placed
at the vertices of a right angle triangle (isosceles triangle) as shown. If the net electrostatic potential energy of the
configuration is zero, value of \( Q \) is:
A \( \cdot \frac{+q}{2+\sqrt{2}} \)
B. \( \frac{-q}{2+\sqrt{2}} \)
c. \( \frac{+2 q}{2+\sqrt{2}} \)
D. \( \frac{-2 q}{2+\sqrt{2}} \)
Subject: Maths
\( \int(2+\log x)(e x)^{x} d x=\dots .+C ; x>1 \)
\( \mathbf{A} \cdot(e x)^{x} \)
B . \( x^{x} \)
c. \( (e x)^{-x} \)
D. \( e^{x^{x}} \)
Subject: Physics
A particle moves along a straight line such that it's displacement x changes with time \( t \) as \( x=\sqrt{a t^{2}+2 b t+c} \)
A \( \cdot \frac{1}{x} \)
B. \( \frac{1}{x^{2}} \)
c. \( \frac{1}{x^{3}} \)
D. \( \frac{1}{x^{4}} \)
Subject: Maths
Find the min. value of \( \frac{\boldsymbol{a}^{2}}{\cos ^{2} \boldsymbol{x}}+\frac{\boldsymbol{b}^{2}}{\sin ^{2} \boldsymbol{x}} \)
A. \( (a+b)^{2} \)
2) \( a+b+b^{-2} b+b^{-2} \)
B . \( (a-b)^{2} \)
\( \mathbf{c} \cdot a^{2}+b^{2} \)
D. \( a^{2}-b^{2} \)
Subject: Physics
Refractive indices of 2 different media
with separating boundary at the
diagonal of rectangular glass slab are
shown. Total angle of deviation of the ray
as shown in the figure, when it emerges
in air is :
air
A \( \cdot 120^{\circ} \)
B. 90
\( c \cdot 60^{\circ} \)
D \( .45^{\circ} \)
\( E \cdot 30 \)
Subject: Physics
Two particles are executing \( S . H . M \) of same amplitude and frequency along the same straight line path. They pass each other when going in opposite directions, each time their displacement is half of their amplitude. What is the phase difference between
them?
A \( .5 \pi / 6 \)
в. \( 2 \pi / 3 \)
c. \( \pi / 3 \)
D. \( \pi / 6 \)
Subject: Biology
Assertion
Many plants are propagated vegetatively even though they bear
seeds.
Reason
Potatoes multiply by tubers and apple by grafting etc.
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
Let circles \( C_{1} \) and \( C_{2} \) an Argand plane
be given by \( |z+1|=3 \) and \( |z-2|=7 \)
respectively. If a variable circle
\( \left|z-z_{0}\right|=r \quad \) be inside circle \( C_{2} \) such
that it touches \( C_{1} \) externally and \( C_{2} \)
internally then locus of \( z_{0} \) describes a
conic \( \boldsymbol{E} \) whose eccentricity is equal to
A \( \cdot \frac{1}{10} \)
B. \( \frac{3}{10} \)
c. \( \frac{5}{10} \)
D. \( \frac{7}{10} \)
Subject: Physics
Let a steel bar of length \( ' l \) ', breadth 'b' and depth 'd' be loaded at the centre by a load 'W'. Then the sag of bending of beam is (Y = Young's modulus of material of steel)
A \( \frac{W l^{3}}{2 b d^{3} Y} \)
в. \( \frac{W l^{3}}{4 b d^{3} Y} \)
c. \( \frac{W l^{2}}{2 b d^{3} Y} \)
D. \( \frac{W l^{3}}{4 b d^{2} Y} \)
Subject: Maths
A purse contains 4 copper coins and 3
silver coins. A second purse contains 6 copper coins and 4 silver coins. A purse is chosen randomly and a coin is taken out of it. What is the probability that it is a copper coin?
A \( \cdot \frac{41}{70} \)
B. \( \frac{31}{70} \)
c. \( \frac{27}{70} \)
D.
Subject: Physics
A gas undergoes a process in which its pressure \( P \) and volume \( V \) are related as
\( \boldsymbol{V} \boldsymbol{P}^{n}= \) constant. The bulk modulus for
the gas in this process is:
A . np
B. \( p^{1 / n} \)
c. \( \frac{p}{n} \)
D. \( p^{n} \)
Subject: Physics
Assertion
The presence of large magnetic flux through a coil maintains a current in
the coil if the circuit is continuous.
Reason
Magnetic flux is essential to maintain
an Induced current in the coil.
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: Chemistry
Which of the following order(s) is/are
incorrect?
This question has multiple correct options
\( \mathbf{A} \cdot H_{2} P O_{4}>H_{3} P O_{3}>H_{3} P O_{2} \) (reducing character)
B. \( N_{2} O<N O<N_{2} O_{5} \) (oxidation state on nitrogen
atom)
\( \mathbf{C} \cdot N H_{3}>P H_{3}>A s H_{3}>S b H_{3}(\text { basicity }) \)
D \( \cdot S b H_{3}>N H_{3}>A s H_{3}>P H_{3} \) (reducing character)
Subject: Chemistry
Calculate the depression in the freezing
point of water when \( 10 g \) of
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H C l C O O H} \) is added to
\( 250 g \) of water
\( \left[\boldsymbol{K} \boldsymbol{a}=\mathbf{1 . 4} \times \mathbf{1 0}^{-\mathbf{3}}, \boldsymbol{K}_{\boldsymbol{f}}=\right. \)
1.86 \( \left.\boldsymbol{K} \boldsymbol{k g} \boldsymbol{m o l}^{-1}\right] \)
Subject: Maths
If \( N \) is the number of positive integral
solutions of \( \boldsymbol{x}_{1} \times \boldsymbol{x}_{2} \times \boldsymbol{x}_{3} \times \boldsymbol{x}_{4}=\mathbf{7 7 0} \)
then:
This question has multiple correct options
A. \( N \) is divisible by 4 district primes
B. \( N \) is a perfect square
C. \( N \) is a perfect fourth power
D. \( N \) is a perfect \( 8^{t h} \) power
Subject: Maths
The solution of \( \frac{d y}{d x}=x \log x \)
A \( \cdot 2 y=x^{2}\left[\log x+\frac{1}{2}\right]+c \)
B. \( 2 y=x^{2}\left[\log x-\frac{1}{2}\right]+c \)
c. \( _{y}=\frac{x^{2}}{2}(\log 2-x)+c \)
D. \( y^{2}=x^{2} \log x+x+c \)
Subject: Chemistry
Write the IUPAC Name of the following
structure
\[
\begin{array}{rl}
\mathbf{C H}_{3}-\underset{\mathbf{U}}{\mathbf{O}} \mathbf{H}-\mathbf{C} \mathbf{H}-\mathbf{C} \mathbf{H}-\mathbf{C} \mathbf{H}_{3} \\
\mathbf{O} \mathbf{H} & \mathbf{O} \mathbf{H}
\end{array}
\]
Subject: Chemistry
When two isomeric aromatic liquid compounds \( A \) and \( B \) having hydrogen bond, are heated. Compound A boils at a lower temperature than B.
Which statement is correct?
This question has multiple correct options
A. Intermolecular H bonding present in A
B. Intramolecular H bonding present in A and B both
c. Intramolecular H bonding present in B
D. Intramolecular H bonding present in A
Subject: Physics
A ray of monochromatic light is incident on one refracting face of a prism of
angle \( 75^{\circ} . \) It passes through the prism and is incident on the other face at the
critical angle. If the refractive index of the material of the prism is \( \sqrt{2} \), the angle of incidence on the first face of
the prism is:
A . \( 30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 0^{\circ} \)
Subject: Maths
The probability that at least one of the events \( A \) and \( B \) occurs is \( \frac{3}{5} . \) If \( A \) and \( B \) occur simultaneously with probability \( \frac{1}{5} \operatorname{then} P\left(A^{\prime}\right)+P\left(B^{\prime}\right) \) is
A \( \cdot \frac{2}{5} \)
B. \( \frac{4}{5} \)
\( c \cdot \frac{6}{5} \)
D.
Subject: Physics
A long cylindrical wire carries a linear charge density of \( 3 \times 10^{-8} \mathrm{Cm}^{-1} . \) An
electron revolve around it in a circular
path under the influence of the
attractive force. \( K E \) of the electron is :
A . \( 1.44 \times 10^{-7} J \)
В . \( 2.88 \times 10^{-17} J \)
D. \( 8.64 \times 10^{-17} J \)
Subject: Maths
\( \int e^{x / 2} \sin \left(\frac{\pi}{4}+\frac{x}{2}\right) d x= \)
A \( \cdot \sqrt{2} e^{x / 2} \sin \frac{x}{2}+c \)
B . \( \sqrt{2} e^{x / 2} \cos \frac{x}{2}+c \)
C \( \cdot-\sqrt{2} e^{x / 2} \sin \frac{x}{2}+c \)
D. \( -\sqrt{2} e^{x / 2} \cos \frac{x}{2}+c \)
Subject: Physics
Which of the following is an implication of the zeroth law of thermodynamics?
A. Energy in the universe can neither be created nor destroyed
B. A pure crystal kept at \( -273.15^{\circ} \mathrm{C} \) has a very low entropy
C. If systems A and B are in thermal equilibrium with system C , then systems A, B,C are in thermal equilibrium with each other
D. Entropy of the universe is always increasing
Subject: Maths
If
\( (1-p)\left(1+3 x+9 x^{2}+27 x^{3}+81 x^{4}+\right. \)
\( 1-p^{6}, p \neq 1 \) then the value of \( \frac{p}{x} \) is
A \( \cdot \frac{1}{3} \)
B. 3
\( c \cdot \frac{1}{2} \)
D. 2
Subject: Chemistry
Match the following
Column - I Column - II
a) A nearly ideal solution
p) \( H_{2} O+ \)
\[
C_{2} H_{5} O H
\]
b) A solution
q) \( C_{6} H_{6}+ \) showing positive deviation \( \quad C_{6} H_{5} C H_{3} \)
c) A solution
r) \( C_{6} H_{6}+C H C l_{3} \)
showing negative deviation
s) \( C H_{3} C O C H_{3}+ \)
d) An azeotropic mixture
\[
C_{2} H_{5} O H
\]
\( t \)
\( \Delta H \) and \( \Delta V \) are
positive
and \( \Delta V \)
\( \Delta H \)
u) are negative
\( \mathbf{A} \cdot \mathrm{A}-\mathrm{q} ; \mathrm{B}-\mathrm{s}, \mathrm{t} ; \mathrm{C}-\mathrm{r}, \mathrm{u} ; \mathrm{D}-\mathrm{p} \)
B. \( A-s ; B-s, t ; C-r ; D-q, p \)
\( \mathbf{C} \cdot A-q ; B-s ; C-r ; D-p, t \)
D. \( A-r ; B-p ; C-s, t ; D-q \)
Subject: Maths
If \( y^{2}+b^{2}=2 x y, \) then \( \frac{d y}{d x} \) equals
This question has multiple correct options
A \( \cdot \frac{1}{x y-b^{2}} \)
в. \( \frac{y}{y-x} \)
c. \( \frac{x y-b^{2}}{(y-x)^{2}} \)
\( \frac{x y-b^{2}}{y} \)
Subject: Maths
. If \( A, B, C \) are angles of angle and \( \mid \begin{array}{ccc}\mathbf{1} & \mathbf{1} \\ \mathbf{1}+\boldsymbol{s} \mathbf{i} \boldsymbol{n} \boldsymbol{A} & \mathbf{1}+\boldsymbol{\operatorname { s i n }} \boldsymbol{B} & \mathbf{1}+ \\ \boldsymbol{s i n} \boldsymbol{A}+\boldsymbol{s i n}^{2} \boldsymbol{A} & \boldsymbol{s i n} \boldsymbol{B}+\boldsymbol{s i n}^{2} \boldsymbol{B} & \boldsymbol{s i n} \boldsymbol{C}\end{array} \)
\( =0 \) then triangle is isosceles
II. If \( \boldsymbol{a}=\mathbf{1}+\mathbf{2}+\mathbf{4}+--- \) upto \( \mathbf{n} \)
terms \( \boldsymbol{b}=\mathbf{1}+\mathbf{3}+\mathbf{9}+--- \) up to \( \mathbf{n} \)
terms \( c=1+5+25+---- \) up to \( n \) terms then \( \Delta\left|\begin{array}{ccc}a & 2 b & 4 c \\ 2 & 2 & 2 \\ 2^{n} & 3^{n} & 5^{n}\end{array}\right|=0 \)
A. I, II both are true
B. only lis true
c. only I I is true
D. neither of them are true
Subject: Chemistry
Calculate the cell EMF in mV for:
\( \boldsymbol{P t}\left|\boldsymbol{H}_{2}(\boldsymbol{1} \boldsymbol{a} \boldsymbol{t m})\right| \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{0} . \boldsymbol{0} \boldsymbol{1} \boldsymbol{M})|\boldsymbol{A} \boldsymbol{g} C l(s)| \boldsymbol{A} \)
if \( \Delta G_{t}^{o} \) values are at \( 25^{\circ} \mathrm{C} \) \( -109.56 \frac{k J}{m o l} \) for \( A g C l(s) \) and
\( -130.79 \frac{k J}{m o l} \) for \( \left(H^{+}+C l^{-}\right)(a q) \)
A \( .456 m V \)
в. \( 654 m V \)
c. \( 546 m V \)
D. None of these
Subject: Maths
\( \int \sqrt{1-\sin x} d x= \)
A. \( 2 \sqrt{1+\sin x}+C \)
B . \( 2 \sqrt{1-\sin x}+C \)
c. \( 2 \sqrt{1-2 \sin x}+C \)
D. \( 2 \sqrt{1-\sin 2 x}+C \)
Subject: Physics
The radius of sphere is measured to be
\( (2.1 \pm 0.5) \mathrm{cm} \)
Calculate its surface area with error
limits.
\( \mathbf{A} \cdot S=(55.4 \pm 26.4) \mathrm{cm}^{2} \)
B . \( S=(55.4 \pm 26.4) \mathrm{mm}^{2} \)
\( \mathbf{c} \cdot S=(55.4 \pm 13.2) \mathrm{cm}^{2} \)
D. None of these