AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Block A is hanging from a vertical spring and is at rest. Block B strikes the block A with velocity v and sticks to it. Then the value of \( v \) for which the spring just attains natural length is :
\( A \)
\[
\sqrt{\frac{60 m g^{2}}{k}}
\]
в.
\[
\sqrt{\frac{6 m g^{2}}{k}}
\]
c. \( \sqrt{\frac{10 m g^{2}}{k}} \)
D. none of these
Subject: Maths
Ram purchases a chair at \( R s .70 \) and
spent \( R s .17 \) on its repair and 50 paise
on cartage. If he sold the chair at

Rs.100 then his approximate margin of profit will be ?
A . \( 13.30 \% \)
B . \( 11.25 \% \)
c. \( 12.5 \% \)
D. 14.3\%
Subject: Physics
Charges of \( \frac{10}{3} m C \) are placed at the four vertices of a square of side \( 8 \mathrm{cm} \). The
electric potential at the centre is :
в. \( 900 \sqrt{2} M V \)
c. \( 1500 \sqrt{2} M V \)
D. \( 9000 \sqrt{2} M V \)
Subject: Biology
Assertion
Through the use of catalytic converters, unburnt hydrocarbons are changed into carbon monoxide which in turn is
changed into nitrogen oxides and water.
Reason

Motor vehicles equipped with catalytic
converters should use leaded petrol to protect the catalyst from degradation.
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
If the pressure of \( H_{2} \) gas is increased
from 1atm to 100atm keeping \( \boldsymbol{H}^{+} \) concentration constant at \( 1 M, \) the
change in reduction potential of
hydrogen half cell at \( 25^{\circ} C \) will be:
A. \( 0.059 V \)
\( V \)
B . \( 0.59 V \)
c. \( 0.0295 V \)
D. \( 0.118 V \)
Subject: Maths
Prove the following
\( 1 .\left(1-\sin ^{2} A\right) \sec ^{2} A=1 \)
\( 2 . \sec ^{4} \theta-\sec ^{2} \theta=\tan ^{4} \theta+\tan ^{2} \)
3. \( (\sec \theta-\tan \theta)^{2}=\frac{1-\sin \theta}{1+\sin \theta} \)
4. \( \frac{\tan \theta+\sec \theta-1}{\tan \theta-\sec \theta+}=\frac{1+\sin \theta}{\cos \theta} \)
Subject: Physics
Meeta's father was driving her to the school. At the traffic signal she noticed
that each traffic light was made of many tiny lights instead of a single bulb. When meeta asked this question
to her father. he explained the reason for
this.
Answer the following based on above information:
(i) What were the values displayed by meeta and her father?
(ii) What answer did meeta's father
give?
(iii) What are the tiny lights in traffic signals called and how do these
operate?
Subject: Maths
A letter is known to have come from
either \( \boldsymbol{T} \boldsymbol{A} \boldsymbol{T} \boldsymbol{A} \boldsymbol{N} \boldsymbol{A} \boldsymbol{G} \boldsymbol{A} \boldsymbol{R} \) or
CALCUTTA. On the envelope just two consecutive letters \( \boldsymbol{T} \boldsymbol{A} \) are visible. The
probability that the letter has come
from \( C \) ALCUTTA is
A \( \cdot \frac{4}{11} \)
B. \( \frac{1}{3} \)
c. \( \frac{5}{11} \)
D. \( \frac{4}{7} \)
Subject: Chemistry
Arrangement of the following group of orbitals in which they fill with electrons
\( (5 f, 6 p, 4 p, 6 s, 4 d, 4 f) \)
\( \mathbf{A} \cdot 4 p, 4 d, 6 s, 4 f, 6 p, 5 f \)
B. \( 6 s, 4 d, 4 f, 5 f, 4 p, 6 p \)
\( \mathbf{c} .6 s, 4 p, 4 d, 4 f, 5 f, 6 p \)
D. \( 4 d, 4 p, 4 f, 5 f, 6 s, 6 p \)
Subject: Biology
You have studied mitosis in onion root
tip cells. It has 14 chromosomes in each cell. Can you tell how many
chromosomes will the cell have at \( G_{1} \)
phase, after \( \mathrm{S} \) phase, and after \( \mathrm{M} \)
phase? Also, what will be the DNA
content of the cells at \( G_{1}, \) after \( S \) and at
\( G_{2}, \) if the content after M phase is \( 2 C ? \)
Subject: Maths
The greatest and least value of
\( \left(\sin ^{-1} x\right)^{2}+\left(\cos ^{-1} x\right)^{2} \) are respectively
A \( \cdot \frac{\pi^{2}}{4} a n d 0 \)
B . \( \frac{\pi}{2} a n d-\frac{\pi}{2} \)
C. \( \frac{5 \pi^{2}}{4} \) and \( \frac{\pi^{2}}{8} \)
D. \( \frac{\pi^{2}}{4} \) and \( \frac{-\pi}{4} \)
Subject: Chemistry
Co. \( C l_{3} .5 N H_{3} H_{2} O \) is a pink solid, the solution of this salt is also pink and
formed 3 mol of \( A g C l \) with silver nitrate
solution. On heating pink solid, it loses one water molecule and forms purple
solid having same ratio of \( \boldsymbol{C} \boldsymbol{o}: \boldsymbol{N} \boldsymbol{H}_{3} \)
\( C l \) as that of pink solid. The purple solid
when dissolved in water and treated
with silver nitrate forms 1 mol of \( A g C l \)
Draw the structures and name of the
pink and purple solids.
Subject: Maths
The areas of two similar triangles are
\( 121 \mathrm{cm}^{2} \) and \( 81 \mathrm{cm}^{2} \) respectively. Find the ratio of their corresponding heights.
A \( \cdot \frac{11}{9} \)
в. \( \frac{10}{9} \)
\( c \cdot \frac{9}{11} \)
D. \( \frac{9}{10} \)
Subject: Physics
A spring mass system oscillates with a
time period \( T_{1} \) when a certain mass is
attached to the spring. When a different mass is attached after removing the
first mass the time period becomes \( T_{2} \)
When both the masses are attached to
the free end of the spring with the other end fixed, the time period of oscillation is :
\( \mathbf{A} \cdot \sqrt{T_{1} T_{2}} \)
в. \( T_{1}+T_{2} \)
c. \( \frac{T_{1}+T_{2}}{2} \)
D. \( \sqrt{T_{1}^{2}+T_{2}^{2}} \)
Subject: Chemistry
The mass of photon having wavelength
1n \( m \) is:
\( \mathbf{A} \cdot 2.21 \times 10^{-35} k g \)
B . 2.21 \( \times 10^{-33} g \)
C \( .2 .21 \times 10^{-33} k g \)
D . \( 2.21 \times 10^{-26} \mathrm{kg} \)
Subject: Physics
A body falls freely for 10 sec. Its average
velocity during this journey (take \( \boldsymbol{g}= \)
\( \left.10 m s^{-2}\right) \)
A \( .100 m s^{-1} \)
B. \( 10 m s^{-1} \)
\( \mathrm{c} \cdot 50 \mathrm{ms}^{-1} \)
D. \( 5 m s^{-1} \)
Subject: Physics
A metal wire of circular cross-section
has a resistance \( \boldsymbol{R}_{1} \). The wire is now stretched without breaking so that its length is doubled and density is assumed to remain same. If the
resistance of the wire now becomes \( \boldsymbol{R}_{2} \)
then \( R_{2}: R_{1} \) is:
A .1:
B. 1: 2
\( c \cdot 4: \)
D. 1: 4
Subject: Physics
The ratio of \( d- \) Broglie wavelength of molecular of hydrogen and oxygen kept in two vessels separately at \( 27^{\circ} C \) and
\( 127^{\circ} \mathrm{C} \) respectively is:
A. \( \sqrt{\frac{4}{3}} \)
B. \( \sqrt{\frac{3}{32}} \)
c. \( \frac{8}{\sqrt{3}} \)
D.
Subject: Maths
f \( \boldsymbol{P}=(\boldsymbol{x}, \boldsymbol{y}), \boldsymbol{F}_{1}=(\boldsymbol{3}, \boldsymbol{0}) \) and \( 16 \boldsymbol{x}^{2}+ \)
\( \mathbf{2 5} \boldsymbol{y}^{2}=\mathbf{4 0 0}, \) then \( \boldsymbol{P} \boldsymbol{F}_{1}+\boldsymbol{P} \boldsymbol{F}_{2} \) equals
\( \mathbf{A} \cdot \mathbf{8} \)
B. 6
c. 10
D. 12
Subject: Physics
A radioactive nucleus undergoes a series of decays according to the scheme \( \boldsymbol{A} \stackrel{\boldsymbol{\alpha}}{\longrightarrow} \boldsymbol{A}_{1} \stackrel{\boldsymbol{\beta}}{\longrightarrow} \boldsymbol{A}_{2} \stackrel{\boldsymbol{\alpha}}{\longrightarrow} \boldsymbol{A}_{3} \stackrel{\gamma}{\longrightarrow} \boldsymbol{A}_{4} \)
If the mass number and atomic number
of \( A \) are 180 and \( 72, \) respectively, then
what are these number for \( \boldsymbol{A}_{4} \) ?
A. 172 and 69
B. 174 and 70
c. 176 and 69
D. 176 and 70
Subject: Biology
Factors responsible for the rapid spread of bread mould on slices of bread are
(i) Large number of spores.
(ii) Availability of moisture and nutrients in bread.
(iii) Presence of tubular branched
hyphae.
(iv) Formation of round shaped
sporangia.
A. (i) and (iii)
B. (ii) and iv)
c. (i) and (ii)
D. (iii) and (iv)
Subject: Physics
At a place on the surface of earth vertical component of earths field is two times that of horizontal component.
Then the latitude angle at the place is
\( \mathbf{A} \cdot \tan ^{-1}(2) \)
B \cdot \( \tan ^{-1}(1 / 2) \)
\( c \cdot 45^{\circ} \)
D. \( 0^{\circ} \)
Subject: Chemistry
Which of the following pairs is the most acidic?
\( A \cdot N_{2} O_{5}, P_{2} O_{3} \)
B. \( \mathrm{N}_{2} \mathrm{O}_{5}, \mathrm{P}_{2} \mathrm{O}_{5} \)
\( \mathbf{c} \cdot \mathbf{H}_{3} \mathbf{P} \mathbf{O}_{4}, \mathbf{H}_{3} \mathbf{P} \mathbf{O}_{3} \)
D. None of the above
Subject: Physics
Consider a huge charge reservoir at potential \( V=200 \) volts. A spherical
capacitor \( C_{1}=40 n F \) is brought in
contact with the charge reservoir and
then removed.
Afterwards, another spherical capacitor
\( C_{2}=30 n F \) is brought in contact with
\( C_{1} \) and removed. This process is
repeated many times. Assume that potential of reservoir does not change during this exercise. Then the charge in
\( (\mu C) \) on \( C_{2} \) after a very long time is :
A . 6
B. 3
\( c .9 \)
D. 12
Subject: Chemistry
\( \Delta_{f} H \) of graphite is \( 0.23 \mathrm{kJ} / \mathrm{mol} \) and
\( \Delta_{f} H \) of diamond is \( 1.896 \mathrm{kJ} / \mathrm{mol} \)
\( \boldsymbol{\Delta} \boldsymbol{H}_{t r a n s i t i o n} \) from graphite to diamond
is :
A . \( 1.66 \mathrm{kJ} / \mathrm{mol} \)
B. 2.1 kJ/mol
c. 2.33 kJ/mol
D. 1.5 kJ/mol
Subject: Maths
The length of similar components
produced by a company is approximated by a normal distribution model with a mean of \( 5 \mathrm{cm} \) and a
standard deviation of \( 0.02 \mathrm{cm} . \) If a
component is chosen at random.what
is the probability that the length of this component is between 4.98 and 5.02
\( \mathrm{cm} ? \)
\( \mathbf{A} \cdot 0.5826 \)
B . 0.6826
c. 0.6259
D. 0.6598
Subject: Maths
If \( \vec{a}, \vec{b} \) and \( \vec{c} \) are three non-coplanar vectors, then \( (\vec{a}+\vec{b}-\vec{c}) \cdot[(\vec{a}-\vec{b}) \times \)
\( (\vec{b}-\vec{c}) \) equals
A. 0
В . \( \vec{a} .(\vec{b} \times \vec{c}) \)
C \( . \vec{a} .(\vec{c} \times \vec{b}) \)
D . 3 \( \vec{a} .(\vec{b} \times \vec{c}) \)
Subject: Physics
The mid points of two small magnetic dipoles of length \( d \) in end-on positions, are separated by a distance \( \boldsymbol{x},(\boldsymbol{x}>>\boldsymbol{d}) \)
The force between them is proportional
to \( x^{-n} \) where \( n \) is :
\( A \)
в.
\( c \)
\( D \)
Subject: Maths
For \( \boldsymbol{x} \in(\mathbf{0}, \boldsymbol{\pi} / \mathbf{2}) \)
\( \sin ^{-1}(\cos x)=? \)
A. \( \pi-x \)
B \( \cdot \frac{\pi}{2}-x \)
c. \( \pi-\frac{x}{2} \)
D . \( \pi-2 x \)
Subject: Maths
The condition that \( \mathbf{f}(\mathbf{x})=\mathbf{x}^{\mathbf{3}}+\mathbf{a x}^{\mathbf{2}}+ \)
\( \mathbf{b x}+\mathbf{c} \) is an increasing function for al
real values of \( \mathbf{x} \) is
A \( \cdot a^{2}<12 b \)
B . a \( ^{2}<3 b \)
\( c \cdot a^{2}<4 b \)
D. \( a^{2}<16 b \)
Subject: Chemistry
The decreasing order of boiling points of alkyl halides is:
A. \( R F>R C l>R B r>R I \)
B. \( R B r>R C l>R I>R F \)
c. \( R I>R B r>R C l>R F \)
D. \( R C l>R F>R I>R B r \)
E \( . R I>R F>R C l>R B r \)
Subject: Maths
In a triangle \( A B C, \) a line \( P Q \) is drawn
parallel to \( B C \), points \( P \), Q being on \( A B \)
and \( A C \) respectively. If \( A B=3 A P \)
then what is the ratio of the area of
triangle \( A P Q \) to the area of triangle
\( A B C ? \)
A .1: 3
B. 1: 5
c. 1: 7
D. 1: 9
Subject: Maths
The values of \( x \epsilon[-2 \pi, 2 \pi] \) such that
\( \frac{\sin x+i \cos x}{1+i}, i=\sqrt{-1}, \) is purely
imaginary, are given by
A \( \cdot n \pi-\frac{\pi}{4} \)
в. \( n \pi+\frac{\pi}{4} \)
\( c \cdot n \pi \)
D. none of these
Subject: Physics
The graph between the resistive force
acting on a body and the position of
the body travelling in a straight line is
shown in the figure. The mass of the
body is \( 25 \mathrm{kg} \) and initial velocity is 2 m/s.When the distance covered by the
bodyi \( s 4 \mathrm{m}, \) its kinetic energy would be
A. 50
B . 40 J
c. 20
D. 10
Subject: Physics
A \( 14.5 \mathrm{kg} \) mass, fastened to the end of a steel wire of unstretched length \( 1.0 \mathrm{m} \) is whirled in a vertical circle with an
angular velocity of 2 rev/s at the bottom of the circle. The cross-sectional area of
the wire is \( 0.065 \mathrm{cm}^{2} \). Calculate the
elongation of the wire when the mass is at the lowest point of its path.
Subject: Physics
Indian style of cooling drinking water is
to keep it in a pitcher having porous walls. Water comes to the outer surface
very slowly and evaporates. Most of the energy needed for is taken from the
water itself and the water is cooled
down. Assume that a pitcher contains \( 10 k g \) of water and \( 0.2 g \) of water comes
out per second. Assuming no backward heat transfer from the atmosphere to the water, calculate the time in which
the temperature decreases by \( 5^{\circ} C \)
Specific heat capacity of water \( =4200 J k g^{-1} C^{-1} \) and latent heat of
vaporization of water \( =2 \cdot 27 \times \) \( 10^{6} J k g^{-1} \)
Subject: Maths
\( \lim _{n \rightarrow \infty} \frac{1}{n^{3}}\left[\left(1^{2}+2^{2}+\ldots+n^{2}\right)\right]=? \)
A . \( 1 / 3 \)
B. 1/16
c. \( 1 / 12 \)
D.
Subject: Chemistry
The hybridisation of \( C \) atoms in \( (C- \)
\( \boldsymbol{C}) \operatorname{single} \) -bond of \( \boldsymbol{H}-\boldsymbol{C} \equiv \boldsymbol{C}- \)
\( \boldsymbol{C H} \equiv \boldsymbol{C H}_{2} \) is
\( \mathbf{A} \cdot s p^{3}-s p^{3} \)
B \( \cdot s p^{2}-s p^{3} \)
c. \( s p-s p^{2} \)
D. \( s p^{3}-s p \)
Subject: Maths
\( f\left(a_{1}, a_{2}, a_{3} \dots, a_{n} \cdot \) are in G.P, then the \right.
determinant \( \Delta= \) \( \left|\begin{array}{ccc}\log a_{n} & \log a_{n+1} & \log a_{n+2} \\ \log a_{n+3} & \log a_{n+4} & \log a_{n+5} \\ \log a_{n+6} & \log a_{n+7} & \log a_{n+8}\end{array}\right| \) is equal
to
A . 0
B. 1
\( c \cdot 2 \)
D.
Subject: Physics
An unhappy mouse of mass \( m_{0}, \) moving on the end of a spring of spring constant p is acted upon by a damping force
\( F_{x}=-b v_{x} . \) For what value of \( b \) the
motion is critically damped?
A \( \cdot b=\sqrt{\frac{p}{m_{0}}} \)
B. \( b=2 \sqrt{p m_{0}} \)
\( ^{\mathrm{c}}_{b}=\sqrt{\frac{p^{2}}{2 m_{0}}} \)
D. \( b=\sqrt{\frac{p}{2 m_{0}}} \)
Subject: Physics
A man getting down from a running bus
falls forward:
A. as the forward movement of bus tries to pull the man forward
B. due to inertia of upper part of the body moves in the forward direction while feet come to the rest as soon
as they touch the road
C. as he leans forward as a matter of habit
D. due to the combination effect of all the three factors stated in \( (A),(B) \) and \( (C) \)
Subject: Biology
Select an option that shows the correct
sequence of the events involved in the
translation mechanism.
a. Binding of mRNA to a smaller subunit of ribosome
b. Aminoacylation of tRNA
c. Binding of initiator tRNA to the P-site
of the ribosome
d. Formation of polypeptide
e. Formation of a peptide bond between first and second amino acids at the \( A \)
site
A \( . a \rightarrow b \rightarrow c \rightarrow d \rightarrow e \)
B . \( b \rightarrow a \rightarrow e \rightarrow c \rightarrow d \)
\( \mathbf{c} \cdot b \rightarrow d \rightarrow a \rightarrow c \rightarrow e \)
D. \( b \rightarrow a \rightarrow c \rightarrow e \rightarrow d \)
Subject: Physics
Which of the following is the unit of specific heat?
\( \mathbf{A} \cdot J k g^{o} C^{-1} \)
в. \( \frac{J}{k g^{o} C} \)
c. \( \frac{k g^{o} C}{J} \)
D. \( \frac{J}{k g^{o} C^{-2}} \)
Subject: Maths
The value of \( \int_{0}^{\frac{\pi}{2}} \log \left(\frac{4+3 \sin x}{4+3 \cos x}\right) d x \)
is
\( A \cdot 2 \)
B. \( \frac{3}{4} \)
\( c \cdot 0 \)
D. -2
Subject: Physics
A body of mass \( \mathrm{m} \) is dropped from a
height h equal to the radius of the earth
(R) above the tunnel dug through the
earth as shown in the figure. Ignore the
effect of earths rotation and air
resistance, M is mass of earth. Choose
the correct alternative(s):
A. body will oscillate through the earth to a height hon both sides
B. body will execute simple harmonic motion.
c. Motion of the body is periodic.
D. body passes the center of earth with a speed \( \sqrt{\frac{2 G M}{R}} \)
Subject: Physics
A thin uniform rod of mass \( m \) and
length \( \ell \) is free to rotate about its upper end. When it is at rest it recelves an
impulse \( J \) at its lowest point, normal to
its length. Immediately after impact, This question has multiple correct options
A. The angular momentum of the rod is \( J \ell \)
B. The angular velocity of the rod is \( 3 J / m \ell \)
C. The kinetic energy of the rod is \( 3 J^{2} / 2 m \)
D. The linear velocity of the midpoint of the rod is \( 3 J / 2 M \)
Subject: Maths
The solution of the differential equation \( \frac{d y}{d x}+\frac{2 y x}{1+x^{2}}=\frac{1}{\left(1+x^{2}\right)^{2}} \)
A \( \cdot y\left(1+x^{2}\right)=c+\tan ^{-1} x \)
B. \( \frac{y}{1+x^{2}}=c+\tan ^{-1} x \)
C・ \( y \log \left(1+x^{2}\right)=c+\tan ^{-1} x \)
D \( \cdot y\left(1+x^{2}\right)=c+\sin ^{-1} x \)
Subject: Physics
Two light wires made up of the same material (Young Modulus, Y) have
length \( L \) each and radii \( R \) and \( 2 R \) respectively, They are joined together and suspended from a rigid
support. Now a weight \( W \) attached to
the free end of the joint wire as shown in the figure. Find the elastic potential energy stored in the system due to the
extension of the wire
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{3} & \boldsymbol{x} \\ \mathbf{0} & \mathbf{1}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{ll}\mathbf{9} & \mathbf{1 6} \\ \mathbf{0} & -\boldsymbol{y}\end{array}\right], \) find
\( x \) and \( y \) when \( A^{2}=B \)
Subject: Maths
Assertion
If \( a, b, c \) each greater than zero are in
A.P. then minimum value of \( b=4 \) if
\( a b c=64 \)
Reason
\( \boldsymbol{A} \cdot \boldsymbol{M} \geq \boldsymbol{G} \cdot \boldsymbol{M} \)
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
A solid compound \( X \) on heating give
\( C O_{2} \) gas and a residue. The residue
mixed with water forms \( Y . \) On passing
an excess of \( C O_{2} \) through \( Y \) in water a
clear solution \( Z \) is obtained. On boiling
\( Z, \) compound \( X \) is reformed. The
compound \( \boldsymbol{X} \) is:
A \( \cdot \operatorname{Ca}\left(\mathrm{HCO}_{3}\right)_{2} \)
в. \( C a C O_{3} \)
\( \mathbf{c} \cdot N a_{2} C O_{3} \)
D. \( K_{2} C O_{3} \)
Subject: Chemistry
reactions.
\[
\begin{array}{l}
\mathrm{CH}_{3}-\mathrm{C} \equiv \mathrm{C}-\mathrm{H}+\mathrm{D}_{2} \mathrm{O} \frac{\mathrm{Hg}^{2+}, \mathrm{H}_{2} \mathrm{SO}_{4}}{ }=[\mathrm{P}] \\
\qquad \mathrm{CH}=\mathrm{CH}_{2}+\mathrm{D}_{2} \mathrm{O} \frac{\mathrm{H}_{2} \mathrm{SO}_{4}}{ }=[\mathrm{Q}]
\end{array}
\]
\( A \)
\[
\mathrm{CH}_{3}-\underset{\mathrm{O}}{\|}-\mathrm{CHD}_{2} \text { and }
\]
\( B \)
\( c \)
\( D \)
\[
\mathrm{cH}_{3}-_{\mathrm{O}}^{\mathrm{C}-\mathrm{CH}_{3}}
\]
Subject: Physics
Same quantity of ice is filled in each of the two metal containers P and Q
having the same size, shape and wall thickness but made of different
materials. The containers are kept in
identical surroundings. The ice in \( \mathrm{P} \)
melts completely in time \( t_{1} \) whereas
that in \( Q \) takes a time \( t_{2} . \) The ratio of
thermal conductivities of the materials
of \( P \) and \( Q \) is
\( \mathbf{A} \cdot t_{2}: t_{1} \)
B . \( t_{1}: t_{2} \)
\( \mathbf{c} \cdot t_{1}^{2}: t_{2}^{2} \)
D. \( t_{2}^{2}: t_{1}^{2} \)
Subject: Physics
length \( L, \) pivoted at its centre and
balanced with a weight \( W \) at a distance
\( x \) from the left end is shown in the
figure. Two positive point charges
q and \( 2 q \) are attached at the left and
right ends of the rod. A distance \( h \)
directly below each of these charges is
a fixed positive charge \( Q \). The distance
\( x^{\prime} \) in terms of \( q, Q, L \) and \( W \) is
(Assume than \( L>>h \) and neglect
masses of the point charges)
A.
\( ^{\mathbf{B}} \cdot \frac{4 q Q L+\varepsilon_{0} h^{2} W L}{8 \pi h^{2} W} \)
\( ^{\mathbf{C}} \cdot \frac{q Q L+4 \pi \varepsilon_{0} h^{2} W L}{8 \pi \varepsilon_{0} h^{2} W} \)
D. \( \frac{q Q L+\varepsilon_{0} h^{2} W L}{h^{2} W} \)
Subject: Physics
A steel scale is correct at \( 0^{\circ} \mathrm{C} \), the
length of a brass tube measured by it at
\( 40^{\circ} \mathrm{C} \) is \( 5 \mathrm{m} . \) The correct length of the
tube at \( 0^{\circ} \mathrm{C} \) is (Coefficients of linear
expansion of steel and brass are \( 11 \times \) \( \mathbf{1 0}^{-\mathbf{6} /^{\circ} C} \) and \( \mathbf{1 9} \times \mathbf{1 0}^{-\mathbf{6} /^{\circ} \mathbf{C}} \) respectively
A. \( 4.001 \mathrm{m} \)
в. \( 5.001 m \)
\( c .4 .999 m \)
D. \( 4.501 m \)
Subject: Maths
Show that:
\[
\left|\begin{array}{ccc}
(\boldsymbol{b}+\boldsymbol{c})^{2} & \boldsymbol{b} \boldsymbol{a} & \boldsymbol{c} \boldsymbol{a} \\
\boldsymbol{a} \boldsymbol{b} & (\boldsymbol{c}+\boldsymbol{a})^{2} & \boldsymbol{c b} \\
\boldsymbol{a c} & \boldsymbol{b c} & (\boldsymbol{a}+\boldsymbol{b})^{2}
\end{array}\right|=
\]
\( 2 a b c(a+b+c)^{3} \)
Subject: Physics
Find the atomic number and mass
number of the last member in the
following series:
(a) \( _{88}^{226} R a \stackrel{-\alpha}{\longrightarrow} R n \quad-\alpha \)
\( \boldsymbol{R} \boldsymbol{a} \boldsymbol{A} \stackrel{-\boldsymbol{\alpha}}{\longrightarrow} \boldsymbol{R} \boldsymbol{a} \boldsymbol{B} \stackrel{-\boldsymbol{\beta}}{\longrightarrow} \boldsymbol{R} \boldsymbol{a} \boldsymbol{C} \)
(b) \( _{Z}^{M} A \stackrel{-\alpha}{A} B^{-\beta} C^{-\beta} \)
\( \boldsymbol{D} \stackrel{-\boldsymbol{\alpha}}{\longrightarrow} \boldsymbol{E} \)
Subject: Chemistry
The vapor pressure of water at \( 80^{\circ} \mathrm{C} \) is
355 torr. \( A \) 100 \( m l \) vessel contained
water-saturated oxygen at \( 80^{\circ} \mathrm{C} \) the
total gas pressure being 760 torr. The contents of the vessel were pumped into a \( 50.0 \mathrm{ml} \), vessel at the same
temperature, What were the partial pressure of oxygen and of water vapor
what was the total pressure in the final equilibrated state? Neglect the volume of any water which might condense.
Subject: Chemistry
In a reaction between two gaseous reactants the number of binary collisions per second (Z) is given by:
A \( \cdot Z=\pi \sigma_{A-B}^{2} \sqrt{\frac{8 K T}{\pi \mu}} n_{A} \cdot n_{B} \)
В . \( Z=\pi \sigma_{A-B} \sqrt{\frac{8 K T}{\pi \mu}} \)
c. \( Z=\sigma_{A-B}^{2} \sqrt{\frac{8 K T}{\pi \mu}} n_{A} . n_{B} \)
D \( \cdot Z=\sigma_{A-B} \sqrt{\frac{8 K T}{\pi \mu}} n_{A} \cdot n_{B} \)
Subject: Chemistry
What transition the hydrogen spectrum would have the same wavelength as the Balmer transition \( n=4 \) to \( n=2 \) of
\( \boldsymbol{H} \boldsymbol{e}^{+} \) spectrum?
A \( \cdot n_{1}=3, n_{2}=6 \)
в. \( n_{1}=2, n_{2}=4 \)
c. \( n_{1}=1, n_{2}=2 \)
D \( \cdot n_{1}=1, n_{2}=4 \)
Subject: Chemistry
A vessel of uniform cross-section of
length \( 500 \mathrm{cm} \) as shown in figure is
divided in two parts by a weightless \( \& \) frictionless piston. One part contains 5
mole of \( N_{2}(g) \) and other part contains 2
moles of \( \boldsymbol{H}_{2}(\boldsymbol{g}) \& 1 \) mole of \( \boldsymbol{H} \boldsymbol{e}(\boldsymbol{g}) \)
gaseous mixture at the same
temperature and pressure.
What is the length of \( N_{2} \) compartment? (Assume volume of piston to be engligible)
A. \( 187.5 \mathrm{cm} \)
B. 300 \( c m \)
c. \( 312.5 \mathrm{cm} \)
D. none of these
Subject: Physics
In a black box of unknown elements \( (\boldsymbol{L} \) or \( R \) or any other combination), an ac
voltage \( \boldsymbol{E}=\boldsymbol{E}_{0} \sin (\boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{\phi}) \) is applied
and current in the circuit was found to
be \( \boldsymbol{I}=\boldsymbol{I}_{0} \sin [\boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{\phi}+(\boldsymbol{\pi} / \mathbf{4})] . \) Then the
unknown elements in the box may be
A. Only capacitor
B. Inductor and resistor both
c. Either capacitor, resistor, inductor or only capacito and resistor
D. only resistor