AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
The equilibrium constant for the
reaction, \( \boldsymbol{H}_{2}+\boldsymbol{I}_{2} \rightarrow 2 \boldsymbol{H} \boldsymbol{I} \) at \( 700 \mathrm{K} \) is
56. If 0.5 mole of hydrogen and 1 mole of iodine are added to the system at equilibrium, the value of the
equilibrium constant will be
A . 25
B. 100
c. 56
D. 0.25
Subject: Physics
A long horizontally fixed wire carries a
current of 100 ampere. Directly above and parallel to it is a fine wire that
carries a current of 20 ampere and
weights 0.04 newton per meter. The distance between the two wires for
which the upper wire is just supported by magnetic repulsion is:
\( \mathbf{A} \cdot 10^{-2} m m \)
B. \( 10^{-2} \mathrm{cm} \)
\( \mathrm{c} \cdot 10^{-2} \mathrm{m} \)
D. \( 10^{-2} k m \)
Subject: Physics
When an additional charge of \( 2 C \) is given to a capacitor, energy stored in it is increased by \( 21 \% \). The original charge of the capacitor is :
A . \( 30 \mathrm{c} \)
B. \( 40 \mathrm{c} \)
c. \( 10 c \)
D. \( 20 \mathrm{c} \)
Subject: Chemistry
Specific conductance of \( 0.1 \mathrm{M} \) NaC solution is \( 1.01 \times 10^{-2} \) ohm \( ^{-1} \mathrm{cm}^{-1} \)
Its molar conductance in ohm \( ^{-1} \mathrm{cm}^{2} \)
\( m o l^{-1} \) is:
A \( \cdot 1.01 \times 10^{2} \)
B . \( 1.01 \times 10^{3} \)
c. \( 1.01 \times 10^{4} \)
D. 1.01
Subject: Physics
A rocket of mass \( 5700 \mathrm{kg} \) ejects mass at a constant rate of \( 15 \mathrm{kg} / \mathrm{s} \) with
constant speed of \( 12 \mathrm{km} / \mathrm{s} \). The
acceleration of the rocket 1 minute
after the blast is \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
A. \( 34.9 \mathrm{m} / \mathrm{s}^{2} \)
В. \( 27.5 \mathrm{m} / \mathrm{s}^{2} \)
\( \mathbf{c} \cdot 3.50 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 13.5 \mathrm{m} / \mathrm{s}^{2} \)
Subject: Maths
In the given figure, \( \Delta X Y Z \) is inscribed
in a circle with centre 0. If the length of chord YZ is equal to the radius of the
circle OY then \( \angle \boldsymbol{Y} \boldsymbol{X} \boldsymbol{Z}= \)
A \( \cdot 60^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 80^{\circ} \)
D. \( 100^{\circ} \)
Subject: Physics
Two cars \( A \) and \( B \) are at rest at same
point initially. If \( A \) starts with a uniform velocity of \( 40 \mathrm{m} / \mathrm{sec} \) and \( \mathrm{B} \) starts in the same direction with a constant
acceleration of \( 4 m / s^{2}, \) then \( B \) will
catch \( A \) after how much time?
A . 10 sec
B. 20 sec
c. 30 sec
D. 35 sec
Subject: Maths
Expressing \( \vec{a} \) and \( \vec{b} \) as linear combinations of \( \vec{c} \) and \( \vec{d} \) we \( \operatorname{get} \vec{a}= \) \( \boldsymbol{k} \overrightarrow{\boldsymbol{c}}+\boldsymbol{m} \overrightarrow{\boldsymbol{d}} \) and \( \overrightarrow{\boldsymbol{b}}=\boldsymbol{h} \overrightarrow{\boldsymbol{c}}+\boldsymbol{r} \overrightarrow{\boldsymbol{d}} \)
Find integer part of \( \boldsymbol{k}+\boldsymbol{m}+\boldsymbol{h}+\boldsymbol{r} ? \)
\( -\boldsymbol{a}+\boldsymbol{b}=-\boldsymbol{c} ; \mathbf{2} \boldsymbol{a}-\boldsymbol{b}=\boldsymbol{c}+\boldsymbol{d} \)
Subject: Maths
\( \operatorname{Set} \boldsymbol{U}=\{1,2, \mathbf{3}, \mathbf{4}, \mathbf{5}, \mathbf{6}, \mathbf{7}, \mathbf{8}, \mathbf{9}\}, \boldsymbol{A}= \)
\( \left\{x: x \in N, 30 \leq x^{2} \leq 70\right\}, B=\{x: x \)
is a prime number \( <10\} . \) Which of the
following does NOT belong to the set
\( (A-B)^{\prime} ? \)
\( \mathbf{A} \cdot \mathbf{4} \)
B. 5
\( c \cdot 6 \)
D.
Subject: Physics
Which of the following represents an infra-red wavelength?
A \( \cdot 10^{-4} \mathrm{cm} \)
B. \( 10^{-5} \mathrm{cm} \)
\( \mathrm{c} \cdot 10^{-6} \mathrm{cm} \)
D. \( 10^{-7} \mathrm{cm} \)
Subject: Maths
If \( f(x)=\log _{x^{2}}\left(\log _{e} x\right), \) then \( f^{\prime}(x) \) at
\( \boldsymbol{x}=\boldsymbol{e} \) is
A . 1
B.
c. \( \frac{1}{2 e} \)
D.
Subject: Chemistry
In a first order reaction, \( 75 \% \) of the reactants disappeared in 1.386 hr. What
is the rate constant?
A \( \cdot 3.6 \times 10^{-3} s^{-1} \)
В. \( 2.7 \times 10^{-4} s^{-1} \)
c. \( 72 \times 10^{-3} s^{-1} \)
D. \( 1.8 \times 10^{-3} s^{-1} \)
Subject: Physics
Two point charges \( -q \) and \( +q \) are located at points \( (0,0,-a) \) and \( (0,0, a) \) respectively. The electric potential at point \( (0,0, z) \) is :
A \( \cdot \frac{q a}{4 \pi \varepsilon_{0} z^{2}} \)
в. \( \frac{q}{4 \pi \varepsilon_{0} a} \)
c. \( \frac{2 q a}{4 \pi \varepsilon_{0}\left(z^{2}-a^{2}\right)} \)
D. \( \frac{2 q a}{4 \pi \varepsilon_{0}\left(z^{2}+a^{2}\right)} \)
Subject: Maths
The vector component of the vector \( \hat{\mathbf{i}}+ \) \( \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) perpendicular to the vector \( \boldsymbol{2} \hat{\boldsymbol{i}}- \)
\( \hat{\boldsymbol{j}}+\boldsymbol{2} \hat{\boldsymbol{k}} \) is
A \( \cdot \frac{1}{3}(\hat{i}+4 \hat{j}+\hat{k}) \)
B \( \cdot \frac{1}{4}(2 \hat{i}-2 \hat{j}-3 \hat{k}) \)
c \( \cdot \frac{1}{2}(2 \hat{i}+2 \hat{j}-\hat{k}) \)
D \( \cdot \frac{1}{4}(2 \hat{i}+2 \hat{j}-\hat{k}) \)
Subject: Chemistry
mole of \( A(g) \) is heated to \( 300^{\circ} C \) in closed one litre vessel till the following equilibrium is reached: \( \boldsymbol{A}(\boldsymbol{g}) \Leftrightarrow \boldsymbol{B}(\boldsymbol{g}) \)
The equilibrium constant for
the reaction at \( 300^{\circ} \mathrm{C} \) is \( 4 . \) What is the
concentration of \( \mathrm{B}\left(\text { in } \operatorname{mol} . l i t^{-1}\right) \) at
equilibrium?
A . 0.2
B. 0.6
\( c \cdot 0.8 \)
D. 0.1
Subject: Chemistry
Among the electrolytes
\( N a_{2} S O_{4}, C a C l_{2}, A l_{2}\left(S O_{4}\right)_{3} \) and
\( N H_{4} C l, \) the most effective coagulating
agent for \( S b_{2} S_{3} \) solution is:
A \( \cdot N a_{2} S O_{4} \)
в. \( C a C l_{2} \)
\( \mathbf{c} \cdot A l_{2}\left(S O_{4}\right) \)
D. \( N H_{4} C l \)
Subject: Physics
A cell of e.m.f. \( \boldsymbol{E} \) having an interna
resistance \( r \) is connected to an external
resistance \( R \). The potential difference \( V \)
across the resistance \( r \) varies with \( R \) as
shown in the figure by the curves
\( A \cdot A \)
8. \( B \)
\( c \)
D. \( D \)
Subject: Physics
Find the resultant magnetic moment
when \( \boldsymbol{\theta}=\mathbf{2 4 0}^{\circ} \)
\( \mathbf{A} \cdot M / 4 \pi \)
в. \( 2 M / \pi \)
c. \( 3 M / \pi \)
D. \( 3 \sqrt{3} M / 4 \pi \)
Subject: Physics
Two charges \( +5 \mu C \) and \( -5 \mu C \)
separated by \( 4 m m \) form an electric dipole. The dipole is placed in a uniform
electric field of \( 4 \times 10^{5} N / C . \) The work
done in rotating the electric dipole
through \( 180^{\circ}, \) if it starts from the
positions of \( \boldsymbol{\theta}=\mathbf{0} \) is
A. \( 4 m J \)
в. \( 8 m J \)
c. \( 12 m J \)
D. \( 16 m J \)
Subject: Chemistry
Assertion
Oxy hydrogen blow torch is used for
welding.
Reason
The temperature produced here is
above \( 2000^{0} C \)
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
If the longitudinal strain in a cubical body is three times the lateral strain then the bulk modulus \( K, \) Young's modulus \( Y \) and rigidity \( \eta \) are related by
This question has multiple correct options
A. \( K=Y \)
в. \( \eta=\frac{3 Y}{8} \)
c. \( Y=\frac{3 \eta}{8} \)
D. \( Y=\eta \)
Subject: Physics
In a transformer the number of turns of
primary coil and secondary coil are 2.5 and 2 respectively and \( 140 \mathrm{V} \) is applied on primary coil, then find the ratio of current in primary and secondary coils:
A \( \cdot I_{p}: I_{s}=4: 5 \)
B . \( I_{p}: I_{s}=5: 4 \)
\( \mathrm{c} \cdot I_{p}: I_{s}=4: 3 \)
D. \( I_{p}: I_{s}=3: 5 \)
Subject: Chemistry
Which one of the following statements
is correct?
A. Hybrid orbitals do not form \( \sigma \) bonds
B. Lateral overlap of p-orbitals or p- and d- orbitals produces \( \pi \) bonds
c. The strength of bonds follows the order
\( \sigma_{p-p}<\sigma_{s-s}<\pi_{p-p} \)
D. s-orbitals do not form \( \sigma \) bonds
Subject: Physics
A tank full of water has a small hole at
its bottom. Let \( t_{1} \) be the time taken to
empty first one thbird of the tank and \( t_{2} \) be the time taken to empty second one
third of the tank and \( t_{3} \) be the time
taken to empty rest of the tank then
\( \mathbf{A} \cdot t_{1}=t_{2}=t_{3} \)
В \( \cdot t_{1}>t_{2}>t_{3} \)
\( \mathbf{c} \cdot t_{1}<t_{2}<t_{3} \)
D. \( t_{1}>t_{2}<t_{3} \)
Subject: Maths
Draw parallelogram \( A B C D \) with the following measurements and calculate
its area
\( A B=7 \mathrm{cm}, A C=10 \mathrm{cm} \) and \( \angle \mathrm{AOB}= \)
\( 100^{\circ} \) where \( \overline{A C} \) and \( \overline{B D} \) intersect at 0
Subject: Physics
A resistance of \( R \Omega \) draws current from
a potentiometer. The potentiometer wire, \( A B, \) has a total resistance of \( R_{0} \Omega \)
A voltage \( \boldsymbol{V} \) is supplied to the
potentiometer. Derive an expression for
the voltage across \( R \) when the sliding
contact is in the middle of the
potentiometer wire.
Subject: Maths
Represent the set of real values of \( x \) on the number line satisfying \( \frac{1}{2}(2 x- \)
1) \( \leq 2 x+\frac{1}{2} \leq 5 \frac{1}{2}+x . \) Also, find the
greatest and the smallest values of \( x \)
satisfying the inequations.
\( \mathbf{A} \cdot x \epsilon[-1,4] \)
В. \( x \in[-1,5] \)
\( \mathbf{c} \cdot x \epsilon[-2,5] \)
D. \( x \epsilon[-2,7] \)
Subject: Physics
Find the magnetic field at P due to the
arrangement shown
A \( \cdot \frac{\mu_{0} i}{\sqrt{2} \pi d}\left(1-\frac{1}{\sqrt{2}}\right) \& \)
B. \( \frac{2 \mu_{0} i}{\sqrt{2} \pi d} \)
c. \( \frac{\mu_{0} i}{\sqrt{2} \pi d} \)
D. \( \frac{\mu_{0} i}{\sqrt{2} \pi d}\left(1+\frac{1}{\sqrt{2}}\right) \)
Subject: Physics
Q Type your question
fixed to a mount B of mass \( m_{2}(\text { fig }) . \) A
constant horizontal force \( F \) is applied to
the end \( \mathrm{K} \) of a light thread tightly wound on the cylinder. The friction between the
mount and the supporting horizontal plane is assumed to be absent. Find:
(a) the acceleration of the point \( K \)
(b) the kinetic energy of this system
seconds after the beginning of motion.
\( ^{\mathbf{A}} \cdot_{a_{k}}=\frac{F\left(3 m_{1}+2 m_{2}\right)}{2 m_{1}\left(m_{1}+m_{2}\right)} ; K \cdot E=\frac{1}{2} \frac{F^{2}\left(3 m_{1}+m_{2}\right)}{m_{1}\left(m_{1}+m_{2}\right)} t^{2} \)
B. \( a_{k}=\frac{F\left(3 m_{1}+2 m_{2}\right)}{m_{1}\left(m_{1}+m_{2}\right)} ; K \cdot E=\frac{1}{2} \frac{F^{2}\left(3 m_{1}+2 m_{2}\right)}{m_{1}\left(m_{1}+m_{2}\right)} t^{2} \)
\( a_{k}=\frac{F\left(3 m_{1}+2 m_{2}\right)}{2 m_{1}\left(m_{1}+m_{2}\right)} ; K \cdot E=\frac{1}{2} \frac{F^{2}\left(3 m_{1}+2 m_{2}\right)}{m_{1}\left(m_{1}+m_{2}\right)} t^{2} \)
\( ^{\mathrm{D}} a_{k}=\frac{F\left(3 m_{1}+2 m_{2}\right)}{m_{1}\left(m_{1}+m_{2}\right)} ; K \cdot E=\frac{1}{2} \frac{F^{2}\left(3 m_{1}+m_{2}\right)}{m_{1}\left(m_{1}+m_{2}\right)} t^{2} \)
Subject: Maths
If \( A \) and \( B \) are two Mutually Exclusive events in a sample space S such that
\( \boldsymbol{P}(\boldsymbol{B})=2 \boldsymbol{P}(\boldsymbol{A}) \) and \( \boldsymbol{A} \cup \boldsymbol{B}=\boldsymbol{S} \) then
\( \boldsymbol{P}(\boldsymbol{A})= \)
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{4} \)
D. 5
Subject: Maths
Let the sequence \( a_{1}, a_{2}, \ldots-\ldots--a_{n} \)
form an A.P. and let \( a_{1}=0, \) prove that
\[
\frac{\boldsymbol{a}_{\boldsymbol{3}}}{\boldsymbol{a}_{2}}+\frac{\boldsymbol{a}_{\boldsymbol{4}}}{\boldsymbol{a}_{\boldsymbol{3}}}+\frac{\boldsymbol{a}_{\boldsymbol{5}}}{\boldsymbol{a}_{\boldsymbol{4}}}+_{--------}+\frac{\boldsymbol{a}_{\boldsymbol{n}}}{\boldsymbol{a}_{\boldsymbol{n}-\boldsymbol{1}}}-
\]
\( \boldsymbol{a}_{2}\left(\frac{\mathbf{1}}{\boldsymbol{a}_{2}}+\frac{\mathbf{1}}{\boldsymbol{a}_{3}}+\ldots+\frac{\mathbf{1}}{\boldsymbol{a}_{n-2}}\right)=\frac{\boldsymbol{a}_{\boldsymbol{n}-\mathbf{1}}}{\boldsymbol{a}_{2}}+ \)
\( \frac{\boldsymbol{a}_{2}}{\boldsymbol{a}_{n-1}} \)
Subject: Chemistry
\( 100 \mathrm{ml} \) of \( 2 \mathrm{M} \) NaOH solution is diluted
by water and the final molarity becomes
0.5. The volume of water added to the
solution is:
A . \( 400 \mathrm{ml} \)
B. 300 m
c. \( 500 \mathrm{ml} \)
D. 200 m1
Subject: Physics
In a car lift, compressed air exerts a force \( F \) on a small piston having a radius of \( 5 \mathrm{cm} . \) This pressure is transmitted to a second piston of
radius \( 15 \mathrm{cm} . \) If the mass of the car to
be lifted is \( 1350 k g \), what is \( F ? \)
A . \( 1.5 \times 10^{3} N \)
В. \( 2.5 \times 10^{3} N \)
c. \( 3.5 \times 10^{3} N \)
D. \( 4.5 \times 10^{3} N \)
Subject: Physics
A spy plane is being tracked by a radar. At \( t=0, \) its position is reported as
\( (100 m, 200 m, 1000 m) .130 s \) later, its
position is reported to be
\( (2500 m, 1200 m, 1000 m) . \) Find a unit
vector in the direction of plane velocity
and the magnitude of its average
velocity.
A \( \cdot_{20 m s^{-1}} ; \frac{22 \hat{i}+5 \hat{j}}{13} \)
B. \( 20 m s^{-1} ; \frac{12 \hat{i}+5 \hat{j}}{13} \)
c. \( _{30 m s^{-1}} ; \frac{12 \hat{i}+5 \hat{j}}{13} \)
D. \( 20 m s^{-1} ; \frac{12 \hat{i}+6 \hat{j}}{13} \)
Subject: Maths
What is the rate of change of the area of
a circle with respect to its radius \( r \) at
\( \boldsymbol{r}=\boldsymbol{6} \boldsymbol{c m} \)
A . \( 12 \pi \mathrm{cm} \)
в. \( 16 \pi \mathrm{cm} \)
\( \mathrm{c} .18 \pi \mathrm{cm} \)
D. \( 24 \pi \mathrm{cm} \)
Subject: Maths
Find the sum of 100 terms of the series
\( \mathbf{1}(\mathbf{3})+\mathbf{3}(\mathbf{5})+\mathbf{5}(\mathbf{7})+\cdots \cdots \)
A. 1353300
B. 1353400
c. 1353200
D. 1353100
Subject: Chemistry
Although \( C u^{+} \) disproportionates in
aqueous solution as \( 2 C u^{+}(a q) \rightarrow \)
\( \boldsymbol{C u}(\boldsymbol{s})+\boldsymbol{C u}^{2+}(\boldsymbol{a q}) . \) Write down a
reaction in which disproportionation is reversed.
A \( \cdot C u(s)+C u^{2+}(a q)+2 C l^{-} \rightarrow C u C l(s) \)
в. \( C u(l)+C u^{2+}(a q)+2 C l^{-} \rightarrow C u C l(l) \)
c. \( C u(s)+C u^{+}(a q)+C l^{-} \rightarrow C u C l(s) \)
D. None of these
Subject: Physics
A transverse wave of amplitude \( 0.01 m \)
and frequency \( 500 H z \) is travelling
along a stretched string with a speed of \( 200 m / s . \) Find the displacement of a particle at a distance of \( 0.7 \mathrm{m} \) from the
origin after \( 0.01 s . \) Also find the phase difference between the point where
wave reaches from the origin
Subject: Maths
if \( z_{1}=3+4 i \) and \( \operatorname{Im}\left(z_{1} z_{2}\right)=0 \) Find \( z_{2} \)
A \( \cdot z_{2}=3-4 i \)
в. \( z_{2}=3+4 i \)
c. \( z_{2}=3 \pm 4 i \)
D. None of these
Subject: Chemistry
Assertion
Chlorobenzene on treatment with
\( C l_{2} / A l C l_{3} \) gives mainly \( p \)
dichlorobenzene.
Reason
Chlorine activate the ring towards an electrophile at ortho and para positions.
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
A beam of electrons accelerated by a large potential difference \( V \) is made to
strike a metal target to produce \( \boldsymbol{X} \) rays. For which of the following values of \( V, \) the resulting \( X \) -rays have the
lowest minimum wave length:
A . \( 10 \mathrm{KV} \)
в. \( 20 \mathrm{KV} \)
c. \( 30 K V \)
D. \( 40 \mathrm{KV} \)
Subject: Physics
A sounding body of negligible dimension emitting a frequency of 150 \( \mathrm{Hz} \) is dropped from a height. During its fall under gravity it passes near a balloon moving up with a constant velocity of \( 2 \mathrm{m} / \mathrm{s} \) one second after it stared to fall. The difference in the
frequency observed by the man in balloon just before and just after crossing the body will be :
(Given that - velocity of sound \( = \)
\( \mathbf{3 0 0 m / s ; g}=\mathbf{1 0 m / s ^ { 2 }} \)
A . 12
B. 6
\( c \cdot 8 \)
D. 4
Subject: Physics
The capacitors of three capacities are in
the ratio \( 1: 2: 3 . \) Their equivalent capacity when connected in parallel is \( \frac{60}{11} \mu F \) more
than that when connected in series. The
individual capacities are :
\( A \cdot 4,6,7 \)
B. 1,2,3
c. 2,3,4
D. 1,3,6
Subject: Maths
If \( \boldsymbol{y}(\boldsymbol{x}) \) satisfies the differential equation \( \cos x \frac{d y}{d x}-y \sin x=6 x \) and
\( \boldsymbol{y}\left(\frac{\boldsymbol{\pi}}{\mathbf{3}}\right)=\mathbf{0 .} \) Then value of \( \boldsymbol{y}\left(\frac{\boldsymbol{\pi}}{\boldsymbol{6}}\right) \) is
A \( \cdot \frac{\pi^{2}}{3 \sqrt{2}} \)
в. \( \frac{-\pi^{2}}{3 \sqrt{2}} \)
c. \( \frac{\pi^{2}}{2 \sqrt{3}} \)
D. \( \frac{\pi^{2}}{4} \)
Subject: Chemistry
\( 0.804 \mathrm{g} \) sample of iron ore was dissolved in acid. Iron was oxidised to
+2 state and it required \( 47.2 \mathrm{mL} \) of
\( 0.112 N K M n O_{4} \) solution for
titration. Calculate \( \% \) of \( F e_{3} O_{4} \) in ore
(as nearest integer)
Subject: Maths
(i) \( A \) lot of 20 bulbs contain 4 defective
ones. One bulb is drawn at random from
the lot. What is the probability that this bulb is defective?
(ii) Suppose the bulb drawn in
(i) is not
defective and not replaced. Now bulb is drawn at random from the rest. What is
the probability that thisbulb is not defective?
Subject: Physics
What should be lengths of steel and copper rod, so that the length of steel rod is \( 5 \mathrm{cm} \) longer than the copper rod
at all temperature? ( \( \alpha \) for copper \( = \) \( 1.7 \times 10^{-5} \circ C^{-1} \) and \( \alpha \) for steel \( = \)
\( \left.1.1 \times 10^{-5}^{\circ} C^{-1}\right) \)
Subject: Biology
List 1
A) Autotrophic nutrition
1) Leech
B) Heterotrophic nutrition
2) Paramaecium
C) Parasitic nutrition
3) Deer
D) Digestion in food vaculoes
4) Green plant
Correct match of \( A, B, C \) and \( D \) is
\( A \cdot A-4, B-3, C-2, D-1 \)
B. A- 4, B- 3, C-1, D-2
C. \( A-3, B-4, C-1, D-2 \)
D. \( A-1, B-4, C-3, D-2 \)
Subject: Physics
Assertion
The product of magnetic susceptibility and absolute temperature for a paramagnetic substance is constant
Reason

Susceptibility is positive but very small
for paramagnetic substance.
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
\( \operatorname{Let} A=\{a, b, c, d\} \) and \( B=\{x, y, z\} \)
What is the number of elements in \( \boldsymbol{A} \times \)
\( B ? \)
\( \mathbf{A} \cdot \mathbf{6} \)
B. 7
c. 12
D. 64
Subject: Physics
Two identical coherent sources of
wavelength \( \lambda \) are placed at \( (100 \lambda, 0) \) and \( (-50 \lambda, 0) \) respectively. A detector moves slowly from the origin to \( (50 \lambda, 0) \) along x-axis. The number of maxima and minima detected are, respectively [include origin and \( (50 \lambda, 0)] \)
A. 51 and 50
B. 101 and 100
c. 49 and 50
D. 50 and 49
Subject: Maths
Before Robert Norman worked on 'Dip and Field Concept', his predecessor thought that the tendency of the magnetic needle to swing towards the
poles was due to a point attractive. However, Norman showed with the help of experiment that nothing like point attractive exists. Instead, he argued that magnetic power lies is lodestone. Which one of the following is the problem on which Norman and others
worked?
A. Existence of point attractive
B. Magnetic power in lodestone
c. Magnetic power in needle
D. swinging of magnetic needle
Subject: Chemistry
Which of the following mixtures will be
buffer?
This question has multiple correct options
\( \mathbf{A} \cdot C H_{3} C O O H+C H_{3} C O O N H_{4} \)
B . \( H C l+N a C l \)
C. Borax+boric acid
D. \( C H_{3} C O O H+C H_{3} C O O N a \)
Subject: Chemistry
\( 25.6 \mathrm{g} \) of sulphur in 100 g benzene shows depression in freezing point of
\( 5.12^{\circ} \mathrm{C} . K_{f} \) for benzene is
\( 5.12^{\circ} \mathrm{Ckg} \) mol\( ^{-1} . \) The molecular
formula of sulphur in benzene is:
\( A \cdot S_{2} \)
в. \( S_{6} \)
\( \mathrm{c} \cdot S_{8} \)
D. \( S_{12} \)
Subject: Physics
The brakes of a car moving at \( 20 m / s \)
along a horizontal road are suddenly applied and it comes to rest after travelling some distance. If the coefficient of friction between the tyres and the road is 0.90 and it is assumed
that all four tyres behave identically, find the shortest distance the car would
travel before coming to a stop.
A. \( 2.22 m \)
В. \( 11.35 m \)
c. \( 22.2 m \)
D. \( 4.54 m \)
Subject: Maths
Construct a quadrilateral ABCD in which \( A B=3.8 \mathrm{cm}, \mathrm{BC}=3.4 \mathrm{cm}, \mathrm{CD}=4.5 \)
\( \mathrm{cm}, \mathrm{AD}=5 \mathrm{cm} \) and \( \angle \mathrm{B}=80^{\circ} \)
Subject: Physics
Rain is falling vertically with \( 3 m s^{-1} \) and a man is moving due North with \( 4 m s^{-1} . \) In which direction he should
hold the umbrella to protect himself from rains?
A \( \cdot 37^{\circ} \) North of vertical
B. \( 37^{\circ} \) South of vertical
C. \( 53^{\circ} \) North of vertical
D. \( 53^{\circ} \) South of vertical
Subject: Maths
Two classrooms A and B having capacity of 25 and \( (n-25) \) seats
respectively. \( A_{n} \) denotes the number of
possible seating arrangements of room
\( A^{\prime}, \) when 'n' students are to be seated
in these rooms, starting from room \( ^{\prime} \boldsymbol{A}^{\prime} \) which is to be filled up to its capacity. If \( \boldsymbol{A}_{n}-\boldsymbol{A}_{n-1}=\mathbf{2 5 !}\left(^{49} \boldsymbol{C}_{25}\right) \) then 'n' equals:
A . 50
B . 48
c. 49
D. 51
Subject: Chemistry
A balloon contains \( 14.0 L \) of air at
760 torr. What will be the volume of the
balloon when it is taken to a depth of
10 \( f t \). in a swimming pool? Assume that the temperature of the air and
water are equal (Density: \( \boldsymbol{H} \boldsymbol{g}=\mathbf{1 3 . 6} \boldsymbol{g} / \boldsymbol{m} \boldsymbol{L} .) \)
A . 11.0
в. 11.3
c. 10
D. 10.8
Subject: Chemistry
Azide ion \( \left(N_{3}^{-}\right) \) exhibits on \( N-N \)
bond order of 2 and may be represented by resonance structures I, II and III given below. \( \overline{\boldsymbol{N}}=\dot{\boldsymbol{N}}=\overline{\boldsymbol{N}}: \longleftrightarrow^{2-}: \ddot{\boldsymbol{N}}-\dot{\boldsymbol{N}} \equiv \boldsymbol{N} \)
\( \longleftrightarrow: N \equiv \vec{N}-\ddot{N}:^{2-} \)
\( \| \)
Select correct statements
A. structures land II make greater contributions than "
B. Structures II and III make smaller contributions than
c. structures land II make greater contributions than II
D. All the three structures make equal contributions
Subject: Physics
A large open top container of negligible mass and uniform cross sectional area
\( A \) has a small hole of cross sectional
area \( ^{\prime} a^{\prime} \) in its side wall near the bottom.
The container is kept over a smooth horizontal floor and contains a liquid of
density' \( \rho^{\prime} \) and mass \( ^{\prime} m^{\prime} . \) Assuming
that the liquid starts flowing through the hole the acceleration of the
container will be:
\( ^{A} \cdot \frac{2 a g}{A} \)
в. \( \frac{a g}{A} \)
c. \( \frac{2 A g}{a} \)
D. \( \frac{A g}{a} \)
Subject: Physics
The velocity of sound is \( V_{s} \) in air. If the density of air is increased to 4 times, the new velocity of sound is
A. \( \frac{V_{s}}{2} \)
в. \( \frac{V_{s}}{12} \)
c. \( 12 V_{s} \)
D. \( \frac{3}{2} V_{s}^{2} \)
Subject: Chemistry
The EMF of the cell;
\( \mathbf{M g}\left|\mathbf{M g}^{2+}(\mathbf{0 . 0 1} \mathbf{M}) \| \mathbf{S n}^{2+}(\mathbf{0 . 1} \mathbf{M})\right| \mathbf{S} \mathbf{n} \)
is:
\( \left(\text { Given: } \mathbf{E}_{\mathbf{M g}^{2+}, \mathbf{M g}}^{\circ}=-\mathbf{2 . 3 4} \mathbf{V}, \mathbf{E}_{\mathbf{S n}^{2+}, \mathbf{S n}}^{\circ}=\right. \)
\( -0.14 V) \)
\( \mathbf{A} \cdot 2 \cdot 17 V \)
в. \( 2.23 \mathrm{V} \)
c. \( 2.51 V \)
D. \( 2.45 V \)