AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
An organic compound \( A \) with molecular
formula \( C_{3} H_{6} O \) is resistant to
oxidation but forms compound \( \boldsymbol{B} \)
\( C_{3} H_{8} O \) on reduction, compound \( B \)
reacts with \( H B r \) from \( C \) and \( C \) reacts
with \( M g \) from Grignard reagent. \( D \)
reacts with \( A \) to form a product which
on hydrolysis gives \( E \). Identify
\( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C}, \boldsymbol{D}, \boldsymbol{E} \)
Subject: Maths
If \( \boldsymbol{x}=\boldsymbol{m}+\mathbf{1} \) and \( \frac{\mathbf{1}}{\mathbf{3}}(\mathbf{6} \boldsymbol{x}-\mathbf{3})-(\mathbf{8}- \)
\( \mathbf{3} \boldsymbol{x})=\mathbf{1 1} ; \) find the value of \( \mathbf{m} \)
A \( . m=2 \)
в. \( m=3 \)
c. \( m=7 \)
D. \( m=5 \)
Subject: Physics
A and B are two points on the axis and
the perpendicular bisector, respectively
of an electric dipole. A and B are far
away from the dipole and at equal
distances from it. The fields at \( A \) and \( B \)
\( \operatorname{are} \vec{E}_{A} \) and \( \vec{E}_{B} . \) Then:
\( \mathbf{A} \cdot \vec{E}_{A}=\vec{E}_{B} \)
B \( \cdot \vec{E}_{A}=2 \vec{E}_{B} \)
\( \mathbf{c} \cdot \vec{E}_{A}=-2 \vec{E}_{B} \)
D \( \cdot\left|\vec{E}_{B}\right|=\frac{1}{2}\left|\vec{E}_{A}\right| \), and \( \left|\vec{E}_{A}\right| \) is perpendicular to \( \vec{E}_{B} \)
Subject: Chemistry
When electrolysis of \( K C l \) is done in
alkaline medium, 10 g of \( K C l O_{3} \) is produced as follows:
\( \boldsymbol{C l}^{\ominus}+\mathbf{6} \stackrel{\ominus}{\boldsymbol{O}} \boldsymbol{H} \rightarrow \boldsymbol{C l} \boldsymbol{O}_{3}^{\ominus}+\mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{6} \boldsymbol{e}^{-} \)
A current of 2 A is passed for 10.941 hours. The current efficiency (in \%) used in the process is ( \( M w t o f K C l O_{3}= \) 122.5
Subject: Physics
with horizontal floor. \( \mu_{s} \) and \( \mu_{k} \) are
coefficients of static and kinetic
frictions between the wiper and the floor. The wiper can not be used to wipe
the floor for \( \boldsymbol{\theta}<\boldsymbol{\theta}_{0} \) even if a large force
directed along the handle aiming
towards the centre is applied. Angle \( \theta_{0} \)
is given by:-
\( \mathbf{A} \cdot \cos ^{-1} \mu_{k} \)
\( \mathbf{B} \cdot \tan ^{-1} \mu_{s} \)
\( \mathbf{c} \cdot \tan -1 \mu_{k} \)
D. \( \cot ^{-1} \mu_{s} \)
Subject: Maths
The values of constants a and b so that \( \lim _{x \rightarrow \infty}\left(\frac{x^{2}+1}{x+1}-a x-b\right)=\frac{1}{2}, \) are
A \( a=1, b=-\frac{3}{2} \)
в. \( a=-1, b=\frac{3}{2} \)
c. \( a=0, b=0 \)
Subject: Chemistry
The correct increasing order of
strengths of following acids is:
\( \mathbf{A} \cdot H_{2} S O_{4}, C H_{3} C O O H, H_{2} C O_{3} \)
B. \( C H_{3} C O O H, H_{2} S O_{4}, H_{2} C O_{3} \)
\( \mathbf{c} \cdot H_{2} C O_{3}, C H_{3} C O O H, H_{2} S O_{4} \)
D. \( C H_{3} C O O H, H_{2} C O_{3}, H_{2} S O_{4} \)
Subject: Physics
Two men of equal masses stand at
opposite ends of the diameter of a
turntable disc of a certain mass,
moving with constant angular velocity.
The two men make their way to the
middle of the turntable at equal rates. In
doing so will
A. kinetic energy of rotation has increased while angular momentum remains same.
B. kinetic energy of rotation has decreased while angular momentum remains same.
C. kinetic energy of rotation has decreased but angular momentum has increased.
D. both, kinetic energy of rotation and angular momentum have decreased.
Subject: Chemistry
Assertion
Every collision of reactant molecule is
not successful.
Reason
Every collision of reactant molecule
with proper orientation is successful
one.
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. Assertion is incorrect but Reason is correct
Subject: Physics
When the left arm of a mercury manometer is connected to a cylinder filled with a gas, the level of the mercury in the right arm rises by \( 2 \mathrm{cm} \). If the pressure of the gas in the container \( 110160 \mathrm{Pa}, \) the atmospheric pressure is
cm of Hg. ( take \( g= \)
\( \left.10 m s^{-2}\right) \)
A . 79
B. 85 5
c. 76
D. 81
Subject: Physics
Choose the only correct statement from
the following
A. The pressure of a gas is equal to the total kinetic energy of the molecules in a unit volume of the gas.
B. The product of pressure and volume of a gas is always constant.
C. The average kinetic energy of molecules of a gas is proportional to its absolute temperature.
D. The average kinetic energy of molecules of a gas is proportional to the square root of its absolute temperature.
Subject: Chemistry
The rate constant, the activation energy
and the frequency factor of a chemical
reaction at \( 25^{\circ} \mathrm{C} \) are \( 3.0 \times 10^{-4} s^{-1} \)
\( 104.4 \mathrm{KJ} \) mol\( ^{-1} \) and \( 6.0 \times 10^{14} s^{-1} \)
respectively. The value of the rate constant as \( \boldsymbol{T} \rightarrow \infty \) is:
A . \( 2.0 \times 10^{18} s^{-1} \)
B. \( 6.0 \times 10^{14} s^{-1} \)
\( c \cdot \alpha \)
D. 3.6 \( \times 10^{20} s^{-1} \)
Subject: Physics
A rigid ball of mass m strikes a rigid
wall at \( 60^{\circ} \) and gets reflected without
loss of speed as shown in the figure
below. The value of impulse imparted by
the wall on the ball will be :
A \( \cdot \frac{m V}{3} \)
B. \( m V \)
\( \mathbf{c} \cdot 2 m V \)
D. \( \frac{m V}{2} \)
Subject: Physics
A proton of mass 'm' moving with a
speed \( v(<<c, \) velocity of light in vacuum) completes a circular orbit in time 'T' in a uniform magnetic field. If
the speed of the proton is increased to \( \sqrt{2} v, \) what will be time needed to
complete the circular orbit?
A \( \cdot \sqrt{2} T \)
в. T
c. \( \frac{T}{\sqrt{2}} \)
D. \( \frac{T}{2} \)
Subject: Chemistry
Assertion: Amphoteric species acts as either an acid or a base.

Reason: It contains both hydrophobic and hydrophilic regions.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false
Subject: Maths
If \( \sin ^{-1} x-\sin ^{-1} y=\frac{\pi}{2}, \) then
A \( \cdot x^{2}+y^{2}=1 \)
в. \( y=-\sqrt{1-x^{2}}, 0 \leq x \leq 1,-1 \leq y \leq 0 \)
C \( \cdot y=\sqrt{1-x^{2}},|x|<1 \)
D. None of these
Subject: Chemistry
(I) \( \quad \mathrm{H}_{2} \mathrm{O}_{2}+\mathrm{O}_{3} \rightarrow \mathrm{H}_{2} \mathrm{O}+2 \mathrm{O}_{2} \)
(II) \( \mathrm{H}_{2} \mathrm{O}_{2}+\mathrm{Ag}_{2} \mathrm{O} \rightarrow 2 \mathrm{Ag}+\mathrm{H}_{2} \mathrm{O}+\mathrm{O} \)
Role of hydrogen peroxide in the above reactions is:
A. oxidizing agent in (I) and reducing agent in (II)
B. reducing agent in (I) and oxidizing agent in (II)
c. reducing agent in both (I) and (II)
D. oxidizing agent in both (I) and (II)
Subject: Maths
The value of \( \int_{\pi^{3} / 27}^{\pi^{3} / 8} \sin x d t, \) where \( t=x^{3} \)
is
A \( \cdot \frac{\pi^{2}}{6}+(3-\sqrt{3}) \pi-3 \)
B. \( \cos \frac{\pi^{3}}{27}-\cos \frac{\pi^{3}}{8} \)
c. \( \frac{\pi^{2}}{6} \)
D. none of these
Subject: Chemistry
What is the apparent oxidation state of
\( \boldsymbol{K} \) element in the compound \( \boldsymbol{K} \boldsymbol{H} \boldsymbol{C} \boldsymbol{O}_{3} ? \)
A \( .+1 \)
B. +2
\( c \cdot+3 \)
D. +4
\( \mathrm{E} \cdot+5 \)
Subject: Physics
The speed of a homogenous solid sphere after rolling down an inclined plane of vertical height \( h \) from rest
without sliding is
A \( \cdot \sqrt{\left(\frac{g}{5}\right) g h} \)
в. \( \sqrt{g h} \)
c. \( \sqrt{\left(\frac{4}{3}\right) g h} \)
D. \( \sqrt{\left(\frac{10}{7}\right) g h} \)
Subject: Maths
Line \( 3 x-4 y=k \) will cut the circle
\( x^{2}+y^{2}-2 x+4 y-11=0 \) at distinct
points, if
A \( \cdot k>\frac{25}{7} \)
в. \( 15<k<30 \)
c. \( -9<k<31 \)
D. None of these
Subject: Physics
In the circuit shown in Figure the heat
produced in resistance R1 can be measured by
A. connecting both voltmeter and an ammeter in parallel to R1
B. both voltmeter in series with \( \mathrm{R} 1 \) and voltmeter in parallel to both R1 and R2
C. connecting ammeter in parallel to R1 and voltmeter in series with R1
D. connecting voltmeter in parallel to R1 and ammeter in series with R1
Subject: Chemistry
The equilibrium constant for the reaction
\( \boldsymbol{P C l}_{5(g)} \rightleftharpoons \boldsymbol{P} C l_{3(g)}+\boldsymbol{C l}_{2(g)} \) is \( 2.4 \times \)
\( 10^{-3} . \) Determine the equilibrium
constant for the reverse reaction at
same temperature
Subject: Chemistry
Number of \( \sigma \) and \( \pi \) -bonds in
\( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{C O O H} \) is:
A \( .13 \sigma, 4 \pi \)
В. \( 14 \sigma, 4 \pi \)
\( \mathrm{c} \cdot 15 \sigma, 4 \pi \)
D. \( 16 \sigma, 4 \pi \)
Subject: Maths
Let \( M \) be the set of all \( 2 \times 2 \) matrices
with entries from the set \( \boldsymbol{R} \) of real
numbers. Then the function \( \boldsymbol{f}: \boldsymbol{M} \rightarrow \boldsymbol{R} \)
defined by \( \boldsymbol{f}(\boldsymbol{A})=|\boldsymbol{A}| \) for every \( \boldsymbol{A} \in \boldsymbol{M} \)
is
A. one-one and onto
B. neither one-one nor onto
c. one-one but not onto
D. onto but not one-one
Subject: Maths
The probability that Dhoni will hit
century in every ODI matches he plays is \( \frac{1}{5} \). If he plays 6 matches in World Cup \( 2011, \) the probability that he will score 2 centuries is:
A \( \cdot \frac{768}{3125} \)
в. \( \frac{2357}{3125} \)
c. \( \frac{2178}{3125} \)
D. \( \frac{412}{3125} \)
Subject: Maths
A researcher wanted to know if there is
an association between exercise and
sleep for the population of 16 -year-olds in the United States. She obtained
survey responses from a random sample of 2,000 United States 16 -year-
olds and found convincing evidence of a positive association between exercise
and sleep. Which of the following
conclusions is well supported by the
data?
A. There is a positive association between exercise and sleep for 16 -year-olds in the United States
B. There is a positive association between exercise and sleep for 16 -year-olds in the world
c. Using exercise and sleep as defined by the study, an increase in sleep is caused by an increase of exercise for 16 -year-olds in the United States
D. Using exercise and sleep as defined by the study, an increase in sleep is caused by an increase of exercise for 16 -year-olds in the world.
Subject: Biology
Correct sequence of plants in a
hydrosere is
\( \mathbf{A} \cdot \) Pistia \( \rightarrow \) Volvox \( \rightarrow \) Scirpus \( \rightarrow \) Hydrilla \( \rightarrow \) Oak \( \rightarrow \) Lantana
B. Oak \( \rightarrow \) Lantana \( \rightarrow \) Volvox \( \rightarrow \) Hydrilla \( \rightarrow \) Pistia \( \rightarrow \) Scirpus
C. Oak \( \rightarrow \) Lantana \( \rightarrow \) Scirpus \( \rightarrow \) Pistia \( \rightarrow \) Hydrilla \( \rightarrow \) Volvox
D. Volvox \( \rightarrow \) Hydrilla \( \rightarrow \) Pistia \( \rightarrow \) Scirpus \( \rightarrow \) Lantana \( \rightarrow \) Oak
Subject: Chemistry
For the equilibrium \( S r C l_{2} \)
\( 6 H_{2} O(s) \rightleftharpoons S r C l_{2} \cdot 2 H_{2} O(s)+ \)
\( 4 H_{2} O(g) \) the equilibrium constant
\( K_{P}=16 \times 10^{-12} a t m^{4} \) at \( 1^{\circ} C . \) If one
litre of air saturated with water vapour
at \( 1^{\circ} \mathrm{C} \) is exposed to a large quantity of
\( \boldsymbol{S} \boldsymbol{r} \boldsymbol{C l}_{2} \cdot \boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O}(s), \) what weight of water
vapour will be absorbed? Saturated
vapour pressure of water at \( 1^{\circ} \boldsymbol{C}= \)
7.6 torr.
A \( .7 .2 \mathrm{mg} \)
B . \( 3.25 \mathrm{mg} \)
c. \( 2.3 \mathrm{mg} \)
D. \( 8.5 \mathrm{mg} \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{cc}\boldsymbol{4} & \boldsymbol{3} \\ \boldsymbol{1} & \boldsymbol{2}\end{array}\right] \boldsymbol{B}=\left[\begin{array}{ll}\boldsymbol{2} & \boldsymbol{1} \\ \boldsymbol{1} & \boldsymbol{2}\end{array}\right] \)
Verify \( (\boldsymbol{A} \boldsymbol{B})^{\prime}=\boldsymbol{B}^{\prime} \boldsymbol{A}^{\prime} \)
Subject: Physics
Assertion
Many great rivers flow towards the equator. The sediments that they carry
increase the time of rotation of the
earth about its own axis.
Reason
The angular momentum of the earth about its rotation axis is conserved.
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. Assertion is incorrect but Reason is correct
Subject: Physics
If in the formula \( \boldsymbol{X}=\mathbf{3} \boldsymbol{Y} \boldsymbol{Z}^{2}, \) the
dimensions of \( X \) and \( Z \) are those of the
capacitance and magnetic induction, then the dimensions of Y are:
A . \( M^{-3} L^{-2} T^{8} A^{4} \)
B. \( M^{-3} L^{-2} T^{4} A^{4} \)
\( \mathbf{c} \cdot M^{-3} L^{-2} T^{-4} A^{-4} \)
D. \( M^{-3} V^{-2} T^{-8} A^{-4} \)
Subject: Maths
If
\( f(x) \) be an increasing function defined
on
\( [a, b] \) then \( \max \{f(t) \text { such that } a \leq t \leq x, a \leq x \leq \)
\( b\}=f(x) \)
\( \& \min \{\mathrm{f}(\mathrm{t}), a \leq t \leq x, a \leq x \leq \)
\( b\}=f(a) \) and if \( f(x) \) be decreasing
function defined on \( [a, b] \) then \( \max \{f(t), a \leq t \leq x, a \leq x \leq b\}=f(a) \)
\( \min \{f(t), a \leq t \leq x, a \leq x \leq b\}=f(x) \)
On the basis of above information
answer the following questions. \( \int_{0}^{\pi / 2} \min \{\sin x, \cos x\} d x \) equals
\( \mathbf{A} \cdot 2(\sqrt{3}-1) \)
B . \( \sqrt{2}(\sqrt{2}-1) \)
\( \mathbf{c} \cdot(\sqrt{3}-1) \)
D \cdot \( \sqrt{2}(\sqrt{2}+1) \)
Subject: Chemistry
A student burns \( 2.0 g \) magnesium metal over a flame which reacts with excess
oxygen. A white cyrstalline solid begins to form on the piece of magnesium.
\( \mathbf{2} \boldsymbol{M} \boldsymbol{g}_{(s)}+\boldsymbol{O}_{2(\boldsymbol{g})} \rightarrow \mathbf{2} \boldsymbol{M} \boldsymbol{g} \boldsymbol{O}_{(s)} \)
How could you determine the reaction
obeyed the law of conservation of mass?
A. Mass the sample after the reaction is complete and compare it to the mass before the reaction begins
B. Mass the sample as the reaction is run
C. Run the reaction by filtration
D. Run the reaction in an open system
Subject: Physics
A solenoid \( 1.5 \mathrm{m} \) long and \( 4.0 \mathrm{cm} \) in diameter possesses 10 turns/cm. current of 5 A is flowing through it. Then the magnetic induction (i) inside and
(ii) at one end on the axis of solenoid
are respectively
A \( \cdot 2 \pi \times 10^{-3} T, \pi \times 10^{-3} T \)
В . \( 3 \pi \times 10^{3} T, 1.5 \pi \times 10^{3} T \)
c. \( 0.5 \pi \times 10^{3} 10^{3} T, 4 \pi \times 10^{3} T \)
D. \( 4 \pi \times 10^{3} T, 2 \pi \times 10^{3} \)
Subject: Maths
Let \( f \) be differentiable for all \( x \). If
\( \boldsymbol{f}(1)=-2 \) and \( \boldsymbol{f}^{\prime}(\boldsymbol{x}) \geq 2 \) for \( \boldsymbol{x} \in[\mathbf{1}, \boldsymbol{6}] \)
This question has multiple correct options
A. \( f(6)<8 \)
B. \( f(6) \geq 8 \)
D. \( f(6) \leq 5 \)
Subject: Chemistry
Which of the following reactions does not take place during leaching for concentration of bauxite?
A \( \cdot A l_{2} O_{3}+2 N a O H+3 H_{2} O \rightarrow 2 N a\left[A l(O H)_{4}\right. \)
B . \( 2 \mathrm{Na}\left[\mathrm{Al}(\mathrm{OH})_{4}\right]+\mathrm{CO}_{2} \rightarrow \mathrm{Al}_{2} \mathrm{O}_{3} . \mathrm{xH}_{2} \mathrm{O}+2 \mathrm{NaHCO}_{3} \)
c. \( A l_{2} O_{3} .2 H_{2} O \stackrel{\Delta}{\longrightarrow} A l_{2} O_{3}+2 H_{2} O \)
D. \( A l_{2} O_{3} \cdot x H_{2} O \stackrel{\Delta}{\longrightarrow} A l_{2} O_{3}+x H_{2} O \)
Subject: Chemistry
An amorphous solid (X) burns in air to form a gas (Y) which turns lime water milky. This gas decolourises aqueous solution of acidified \( K M n O_{4} . \) Gas \( (Y) \)
reacts with oxygen to give another gas
(z) which is responsible for acid rain. \( \mathbf{X} \)
\( Y, \) and \( z \) are:
A \( \cdot C(X), C O(Y), C O_{2}(Z) \)
B. \( S(X), S O_{2}(Y), S O_{3}(Z) \)
c. \( P(X), P_{2} O_{3}(Y), P_{2} O_{5}(Z) \)
D. \( S(X), S O_{3}(Y), C O_{2}(Z) \)
Subject: Chemistry
Write the cell reaction and calculate \( \boldsymbol{E}^{o} \)
cell of the following electrochemical
cell:
\( \boldsymbol{A} \boldsymbol{l}\left|\boldsymbol{A} \boldsymbol{l}^{3+} \| \boldsymbol{Z} \boldsymbol{n}^{2+}\right| \boldsymbol{Z} \boldsymbol{n} \)
\( (\boldsymbol{s})(\boldsymbol{a q} \cdot) \)
\[
\begin{array}{c}
(\mathbf{1} \boldsymbol{M})(\mathbf{1} \boldsymbol{M}) \\
\boldsymbol{E}_{\boldsymbol{A} l}^{o}=-\mathbf{1 . 6 6 V} \\
\boldsymbol{E}_{Z n}^{o}=-\mathbf{0 . 7 6 V}
\end{array}
\]
Subject: Biology
In EMP pathway,ATP is directly formed in the conversion of
I)Fructose 1,6 -bisphosphate to glyceraldehyde -3-phosphate II)Phosphoenolpyruvate to pyruvate acid
III)1 \( , 3 \) -bisphosphoglyceric acid to 3 phosphoglyceric acid IV)3-phosphoglyceric acid to 2phosphoglyceric acid The correct combination is
A . IV,
B. ॥ , Iv
c. ॥ा,॥
D. ।."|
Subject: Maths
If \( a x^{3}+b x^{2}+c \) is divided by \( (x-3) \)
then the remainder is:
A. \( -27 a+9 b+c \)
B . \( -27 a-9 b \)
c. \( 27 a+9 b+c \)
D. \( 27 a+9 b \)
E \( .-27 a+9 b \)
Subject: Maths
Consider quadratic equation \( a x^{2}+ \) \( (2-a) x-2=0, \) where \( a \in R \)
If exactly one root is negative, then the
range of \( a^{2}+2 a+5 \) is
\( A \cdot[4, \infty) \)
B \( \cdot[-2, \infty) \)
c. \( (-\infty, 4] \)
\( D \cdot(5, \infty) \)
Subject: Physics
The initial and final temperatures are
recorded as \( (40.6 \pm 0.3)^{0} C \) and
\( (50.7 \pm 0.2)^{0} C . \) The rise in temperature
is:
A \( \cdot 10.1^{0} C \)
B \( \cdot(10.1 \pm 0.3)^{0} C \)
c. \( (10.1 \pm 0.5)^{0} C \)
D. \( (10.1 \pm 0.1)^{0} C \)
Subject: Physics
In the given situation it is known that
when released the blocks slide. Find the
time(in second) when the small block
will fall off from the larger block. (The
size of \( m \) is very -very small then \( M, \) see
figure). If \( \boldsymbol{m}=\mathbf{1} \mathbf{k g}, \boldsymbol{M}=\mathbf{4 k g}, \boldsymbol{l}=\mathbf{4 m} \)
\( \boldsymbol{\theta}=\mathbf{3 7}^{o}, \boldsymbol{\mu}=\mathbf{0 . 4} \)
Subject: Chemistry
For the cell :
\[
\begin{array}{l}
\boldsymbol{Z} \boldsymbol{n}\left|\boldsymbol{Z} \boldsymbol{n}^{2+} \| \boldsymbol{C} \boldsymbol{u}^{2+}\right| \boldsymbol{C} \boldsymbol{u} \\
\boldsymbol{E}_{\boldsymbol{z n}}^{\ominus}=\boldsymbol{0 . 7 3 6} \boldsymbol{V} ; \boldsymbol{E}_{(c u)}^{\ominus}=-\boldsymbol{0 . 3 5} \boldsymbol{V}
\end{array}
\]
Calculate the cell EMF.
Subject: Physics
A wheel rotating at 12 rev/s is brought
to rest in \( 6 s . \) The average angular
deceleration in \( r a d / s^{2} \) of the wheel during this process is?
A . \( 4 \pi \)
в. 4
\( c \cdot 72 \)
D. \( \frac{1}{\pi} \)
\( E . \pi \)
Subject: Maths
Evaluate \( \int \frac{\boldsymbol{d x}}{\sqrt{(\boldsymbol{x}-\boldsymbol{a})(\boldsymbol{b}-\boldsymbol{x})}} \)
A \( \cdot I=2 \sin ^{-1} \sqrt{\frac{x-a}{(b-a)}}+C \)
в. \( I=2 \cos ^{-1} \sqrt{\frac{x-a}{(b-a)}}+C \)
\( ^{\mathrm{c}} \cdot_{I=\sin ^{-1}} \sqrt{\frac{x-a}{(b-a)}}+C \)
D. \( _{I}=2 \sin ^{-1} \sqrt{\frac{x-b}{(a-b)}}+C \)
Subject: Physics
Spheres \( P \) and \( Q \) are uniformly
constructed from the same material
which is a good conductor of heat and the
radius of \( Q \) is thrice the radius of \( P \). The
rate of fall of temperature of \( P \) is \( x \) times
that of \( Q . \) When both are at the same surface temperature, the value of \( x \) is :
A \( \cdot \frac{1}{4} \)
B. \( \frac{1}{3} \)
\( c .3 \)
D.
Subject: Chemistry
Sodium bicarbonate is less soluble in
water than potassium bicarbonate, it is
due to:
A. low molecular weight of \( N a H C O_{3} \) as compared to \( K H C O_{3} \)
B. hydrogen bonding, sodium bicarbonate contains a dimeric anionic structure in potassium bicarbonate, anions forman infinite chain
C. hydrogen bonding, potassium bicarbonate contains a dimeric anionic structure while in sodium bicarbonate, anions form an infinite chain
D. \( K H C O_{3} \) is thermally less stable than \( N a H C O_{3} \)
Subject: Maths
If \( A \) and \( B \) are two events such that
\( \boldsymbol{A} \subset \boldsymbol{B} \) and \( \boldsymbol{P}(\boldsymbol{B}) \neq 0, \) then which of the
following is correct? This question has multiple correct options
\( ^{\mathbf{A}} \cdot p(A \mid B)=\frac{P(B)}{P(A)} \)
B \cdot \( P(A \mid B)<P(A) \)
C \( \cdot P(A \mid B) \geq P(A) \)
D. None of these
Subject: Physics
In Young's double slit experiment the distance between two slits is \( 2 m m \) and
screen is at a distance of \( 120 \mathrm{cm} \) from
the plane of slits. The smallest distance from the central maxima where the
bright fringe due to light of wavelength
\( 6500 A^{\circ} \) and \( 5200 A^{\circ} \) would coincide?
A \( .0 .156 \mathrm{cm} \)
B. \( 0.186 \mathrm{cm} \)
c. \( 0.486 \mathrm{cm} \)
D. \( 0.456 \mathrm{cm} \)
Subject: Chemistry
Amongst the following, which is correct
about the metal sulphide sols?
A. The sol particles are positively charged due to preferential adsorption of metal ions
B. The sol particles are negatively charged due to preferential adsorption of sulphide ions
C. The anion of added electrolytes are effective in causing the coagulation of the sol
D. The sol is unstabilized due to both the electric charge and hydration of the particles
Subject: Chemistry
What is the ratio of the enthalpy yield on combustion of hydrogen atoms to steam to the yield on combustion of an equal mass of hydrogen molecules to steam? Given \( : \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}), \boldsymbol{\Delta} \boldsymbol{H}=-\boldsymbol{2} \mathbf{4} 2 \) kJ,Bond energy
\( (\boldsymbol{H}-\boldsymbol{H})=\mathbf{4 3 6} \mathbf{k J} \)
A . 0.80:
B. 1: 0.80
c. 1.80: 1
D. 2.80:
Subject: Physics
There is a uniform magnetic field \( B \) in a
circular region of radius \( R \) as shown in
figure, whose magnitude changes at
the rate of \( d B / d t . \) The emf induced
across the ends of a circular concentric
conducting arc of radius \( \boldsymbol{R}_{1} \) having
angle \( \theta \) as shown \( \left(-O A O^{\prime}=\theta\right) \) is
\( ^{\mathrm{A}} \cdot \frac{\theta}{2 \pi} R_{1}^{2} \frac{d B}{d t} \)
\( ^{\text {В }} \cdot \frac{\theta}{2}^{R^{2}} \frac{d B}{d t} \)
\( c . \theta 2 \pi R \)
D. None of these
Subject: Maths
Let \( X=\{-3,-2,-1,0,1,2\} \) and \( Y= \)
\( \{x: x \text { is an integer and }-3 \leq x<2\} \)
(i) Is \( X \) a subset of \( Y ? \)
(ii) Is \( Y \) a subset of \( X ? \)
Subject: Chemistry
The Bohr orbit radius for the hydrogen \( \operatorname{atom}(\boldsymbol{n}=\mathbf{1}) \) is approximately \( \mathbf{0 . 5 3 0} \boldsymbol{A} \)
The radius for the first excited state
\( (n=2) \) will be:
в. 1.06
c. 4.77 ,
D. \( 2.12 \dot{A} \)
Subject: Chemistry
Assertion
The percentage weight of a compound \( A \) in a solution is given by
\( \% \boldsymbol{o} \boldsymbol{f} \boldsymbol{A}= \)
\[
\frac{\text {Mass } \boldsymbol{A}}{\text {Total mass of solution}} \times \mathbf{1 0 0}
\]
Because
Reason
The mole fraction of a component \( A \) is given by, Mole fraction of \( \boldsymbol{A}= \)
Numberof moles of \( \boldsymbol{A} \) Total number of moles of all compo
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. Assertion is incorrect but Reason is correct
Subject: Chemistry
\( \mathrm{Cu}(s)+\mathrm{NO}_{3}^{-}(a q)+\mathrm{H}^{+}(a q) \rightarrow \mathrm{Cu}^{2+}(a q) \)
\( +\mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(1) \)
If the above equation is balanced with lowest whole number coefficients, find
the coefficient for \( \mathrm{H}+(\mathrm{aq}) \)
A
B. 2
\( c \cdot 3 \)
D. 4
E. 5