AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A block released from rest from the top
of a smooth inclined plane of angle \( \boldsymbol{\theta}_{\mathbf{1}} \)
reaches the bottom in time \( t_{1} . \) The same
block released from rest from the top of
another smooth inclined plane of angle
\( \theta_{2}, \) reaches the bottom in time \( t_{2} . \) If the
two inclined planes have the same
height, the relation between \( t_{1} \) and \( t_{2} \) is
\( \mathbf{A} \cdot \frac{t_{2}}{t_{1}}=\left(\frac{\sin \theta_{1}}{\sin \theta_{2}}\right)^{1 / 2} \)
B. \( \frac{t_{2}}{t_{1}}=1 \)
\( \mathbf{C} \cdot \frac{t_{2}}{t_{1}}=\frac{\sin n_{1}}{\sin \theta_{2}} \)
\( \mathbf{D} \cdot \frac{t_{2}}{t_{1}}=\frac{\sin ^{2} \theta_{1}}{\sin ^{2} \theta_{2}} \)
Subject: Maths
If \( \int \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{d} \boldsymbol{x}=\boldsymbol{f}(\boldsymbol{x}), \) then \( \int\{\boldsymbol{f}(\boldsymbol{x})\}^{2} \boldsymbol{d} \boldsymbol{x} \)
is equal to
A \( \cdot \frac{1}{2}\{f(x)\}^{2} \)
в. \( \{f(x)\}^{3} \)
c. \( \frac{|f(x)|^{3}}{3} \)
D \cdot \( \{f(x)\}^{2} \)
Subject: Maths
Assertion
If the roots of the equations \( x^{2}-b x+ \)
\( c=0 \) and \( x^{2}-c x+b=0 \) differ by the
same quantity, then \( b+c \) is equal to
-4
Reason
If \( \alpha, \beta \) are the roots of the equation \( A x^{2}+B x+C=0, \) then \( \alpha-\beta= \)
\( \frac{\sqrt{\boldsymbol{B}^{2}-\boldsymbol{4} \boldsymbol{A} \boldsymbol{C}}}{\boldsymbol{A}} \)
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: Maths
The distance between the parallel lines \( \boldsymbol{y}=\mathbf{2} \boldsymbol{x}+\mathbf{4} \) and \( \mathbf{6} \boldsymbol{x}=\mathbf{3} \boldsymbol{y}+\mathbf{5} \) is
A \( \cdot \frac{17}{\sqrt{3}} \)
B.
c. \( \frac{3}{\sqrt{5}} \)
D. \( \frac{17 \sqrt{5}}{15} \)
Subject: Maths
For any two complex numbers \( z_{1} \) and \( z_{2} \) with \( \left|z_{1}\right| \neq\left|z_{2}\right|,\left|\sqrt{2} z_{1}+i \sqrt{3} \overline{z_{2}}\right|^{2}+ \)
\( \left|\sqrt{3} \overline{z_{1}}+i \sqrt{2} z_{2}\right|^{2} \) is
A \( \cdot \) Less than \( 5\left(\left|z_{1}\right|^{2}+\left|z_{2}\right|^{2}\right) \)
B \cdot Greater than \( 10 \mid z_{1} z_{2} \)
c. Equal to \( \left(2\left|z_{1}\right|^{2}+3\left|z_{2}\right|^{2}\right) \)
D. zero
Subject: Physics
A conducting rod of length \( l \) is moving in a transverse magnetic field of strength \( B \) with velocity \( v \). The resistance of the rod is \( R \). The current in
the rod is
A \( \cdot \frac{B l v}{R} \)
в. \( B l v \)
c. \( Z e r o \)
D. \( \frac{B^{2} v^{2} l^{2}}{R} \)
Subject: Maths
The value of \( f(0), \) so that the function
\( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{\sqrt{a^{2}-a x+x^{2}}-\sqrt{a^{2}+a x+x^{2}}}{\sqrt{a+x}-\sqrt{a-x}} \)
becomes continuous for all \( x, \) is given
by
\( \mathbf{A} \cdot a^{3 / 2} \)
B. \( a^{1 / 2} \)
c. \( -a^{1 / 2} \)
D. \( -a^{3 / 2} \)
Subject: Physics
When Boron nucleus \( \left(_{5}^{10} B\right) \) is
bombarded by neutrons, \( \boldsymbol{\alpha}- \) particles
are emitted. The resulting nucleus is of the element and has the
mass number
A. \( L i, 7 . \)
B. \( L i, 8 . \)
c. \( N a, 7 \)
D. \( L i, 9 . \)
Subject: Physics
A rectangular tank is placed on a horizontal ground end is filled with water to a height \( H \) above the base. \( A \)
small hole is made on one vertical side
at a depth \( D \) below the level of water in
the tank. The distance \( x \) from the
bottom of the tank, at which the water jet from the tank will hit the ground is,
\( \mathbf{A} \cdot 2[D(H-D)]]^{1 / 2} \)
в. \( 2(g D)^{\frac{1}{2}} \)
C \( \cdot 2[D(H+D)]]^{1 / 2} \)
D \( \frac{1}{2}(D H)^{\frac{1}{2}} \)
Subject: Chemistry
A hydrogen electrode is immersed in a
solution with \( \mathrm{pH}=0 \) (HCl). By how much will the potential (reduction) change if an equivalent amount of NaOH is added
to the solution? (Take \( p_{H_{2}}=1 \) atm, \( T= \) \( 298 \mathrm{K} \)
A. Increase by \( 0.41 \mathrm{v} \)
B. Increase by 59 mv
c. Decrease by \( 0.41 \mathrm{v} \)
D. Decrease by 59 mv
Subject: Physics
Assertion
The magnetic poles of earth do not coincide with the geographic poles.
Reason
The discrepancy between the orientation of a compass and true north-south direction is known as
magnetic declination.
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
Heat of \( 20 \mathrm{Kcal} \) is supplied to the
system and \( 8400 J \) of external work is
done on the system so that its volume decreases at constant pressure. The change in internal energy is \( (J= \) \( 4200 J / k c a l) \)
A \( .9 .24 \times 10^{4} J \)
B. \( 7.56 \times 10^{4} J \)
c. \( 8.4 \times 10^{4} J \)
D. \( 10.5 \times 10^{4} J \)
Subject: Maths
Find \( \frac{1}{2}\left(A+A^{T}\right) \) and \( \frac{1}{2}\left(A-A^{T}\right) \)
when \( A=\left[\begin{array}{ccc}0 & a b \\ -a & 0 & c \\ -b-c 0\end{array}\right] \)
Subject: Physics
Assertion
Water kept in an open vessel will quickly evaporate on the surface of the
moon.
Reason
The temperature at the surface of the moon is much higher than the boiling point of water
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
Na \( C N \) is sometimes added in the froth
floatation process as a depressant when \( Z n S \) and \( P b S \) minerals are
expected because:
A \( \cdot Z n S \) forms soluble complex \( N a_{2}\left[Z n(C N)_{4}\right] \) while \( P b S \)
form froth
B . \( P b(C N)_{2} \) is precipitated while no effect on \( Z n S \) form froth
C . \( P b S \) forms soluble complex \( N a_{2}\left[Z n(P b)_{4}\right] \) while \( Z n S \)
form froth
D. \( N a C N \) is never added in froth floatation process
Subject: Physics
In a string the speed of wave is \( 10 \mathrm{m} / \mathrm{s} \)
and its frequency is 100 Hz. The value of
the phase difference at a distance 2.5
cm will be :
\( \mathbf{A} \cdot \pi / 2 \)
в. \( \pi / 8 \)
c. \( 3 \pi / 2 \)
D. \( 4 \pi \)
Subject: Maths
Evaluate \( \boldsymbol{I}=\int_{\boldsymbol{\pi} / \mathbf{6}}^{\boldsymbol{\pi} / \mathbf{3}} \sin \boldsymbol{x} \boldsymbol{d} \boldsymbol{x} \)
A \( \cdot \frac{1-\sqrt{3}}{2} \)
в. \( \frac{\sqrt{3}+1}{2} \)
c. \( \frac{\sqrt{3}-1}{2 \sqrt{3}} \)
D. None of these
Subject: Chemistry
Assertion
Activity of an enzyme is \( p H \) dependent.
Reason

Changes in \( p H \) affect the solubility of the enzyme in water.
A. If both (A) and (R) are true and (R) is the correct explanation of (A).
B. If both (A) and (R) are true, but (R) is not the correct explanation of \( (A) \)
c. If (A) is correct, but (R) is incorrect.
D. If (A) and (R) are both incorrect
Subject: Chemistry
If \( 0.1 \mathrm{M} H C I \) is mixed in the solution
containing only \( 0.1 M C d^{2+} \) ions and
saturated with \( \boldsymbol{H}_{2} \boldsymbol{S}, \) then \( \left[\boldsymbol{C} \boldsymbol{d}^{2+}\right] \)
remaining in the solution after \( C d S \)
stops to precipitate is
A \( \cdot 10^{-8} \)
B. \( 8.2 \times 10^{-9} \)
c. \( 5.6 \times 10^{-6} \)
D. \( 5.6 \times 10^{-10} \)
Subject: Chemistry
A constant electric current flows for 4
hours through two electrolytic cells connected in series. One contains
\( A g N O_{3} \) solution and second contains
\( C u C l_{2} \) solution. During this time, 4 grams of \( A g \) is deposited in the first cell. How many grams of Cu is deposited in the second cell?
A . 2.176 g
в. \( 0.176 \mathrm{g} \)
c. \( 1.176 \mathrm{g} \)
D. None of the above
Subject: Maths
If \( f(x)=\frac{1}{1-x}, x \neq 0,1 \) then the graph
of the function \( \boldsymbol{y}=\boldsymbol{f}\{\boldsymbol{f}(\boldsymbol{f}(\boldsymbol{x}))\}, \boldsymbol{x}>1 \)
is
A . a circle
B. an ellipse
c. a straight line
D. a pair of straight lines
Subject: Physics
An object of mass \( 1 \mathrm{kg} \) has a PE of 1 relative to the ground when it is at a height of:
A. \( 0.102 \mathrm{m} \)
B. \( 1 \mathrm{m} \)
c. \( 9.8 \mathrm{m} \)
D. 32 \( m \)
Subject: Physics
Wavelength of gamma rays are:
\( \mathbf{A} \cdot 10^{-10} m \) to less than \( 10^{-14} m \)
B. \( 10^{-14} \mathrm{m} \) to less than \( 10^{-10} \mathrm{m} \)
C \( \cdot 10^{-11} \mathrm{m} \) to less than \( 10^{-14} \mathrm{m} \)
D. \( 10^{-14} \mathrm{m} \) to less than \( 10^{-6} \mathrm{m} \)
Subject: Chemistry
Determine \( \Delta H \) for the following
reaction at \( 500 \mathrm{K} \) and constant pressure
\[
\boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightarrow \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g})
\]
use the following data:
\begin{tabular}{lll} 
Substance & \( C_{P}(\mathrm{J} / \) \( \operatorname{mol} \mathrm{K}) \) & \( \Delta_{f} H(298 \mathrm{K})( \) \( \mathrm{kJ} / \mathrm{mol}) \) \\
\hline
\end{tabular}
-110.5 \begin{tabular}{l|l} 
со & 29.12 \\
& \\
\( H_{2} O \) & 33.58 \\
& \\
\( \mathrm{CO}_{2} \) & 37.11 \\
\( \mathrm{H}_{2} \) & 29.89
\end{tabular} -241.8
-393.5 0.0
\( \mathbf{A} \cdot \Delta H=-30.3 \mathrm{k} \)
B. \( \Delta H=-50.3 \mathrm{kJ} \)
c. \( \Delta H=-40.3 \mathrm{kJ} \)
D. \( \Delta H=-20.3 \mathrm{kJ} \)
Subject: Physics
The excess pressure inside a spherical soap bubble of radius \( 1 \mathrm{cm} \) is balanced
by a column of oil (specific gravity \( = \) 0.8)\( , 2 m m \) high, the surface tension of
the bubble is :
A. \( 3.92 \mathrm{N} / \mathrm{m} \)
в. 0.0392 N / \( m \)
c. \( 0.392 \mathrm{N} / \mathrm{m} \)
D. \( 0.00392 \mathrm{N} / \mathrm{m} \)
Subject: Maths
If a \( 3 \times 3 \) matrix \( A \) has its inverse equal
to \( A, \) then \( A^{2} \) is equal to
\( \mathbf{A} \cdot\left[\begin{array}{lll}0 & 1 & 0 \\ 1 & 1 & 1 \\ 0 & 1 & 0\end{array}\right] \)
\( \mathbf{B} \cdot\left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 0 & 1\end{array}\right] \)
\( \mathbf{C} \cdot\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right] \)
\( \mathbf{D} \cdot\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\end{array}\right] \)
Subject: Maths
If \( y=e^{\sqrt{x}}+e^{-\sqrt{x}} \) then \( \frac{d y}{d x} \) equals
This question has multiple correct options
A \( \cdot \frac{e^{\sqrt{x}}-e^{-\sqrt{x}}}{2 \sqrt{x}} \)
\( \frac{e^{\sqrt{x}}-e^{-\sqrt{x}}}{2 x} \)
c. \( \frac{1}{2 \sqrt{x}} \sqrt{y^{2}-4} \)
D. \( \frac{1}{2 \sqrt{x}} \sqrt{y^{2}+4} \)
Subject: Physics
A mass \( M \) is split into two parts \( m \) and
\( (M-m) \) which are then separated by a
certain distance. The ratio \( \boldsymbol{m} / \boldsymbol{M} \) which maximizes the gravitational force between the parts is
A . 1: 4
B. 1: 3
c. 1: 2
D. 1: 1
Subject: Chemistry
Ethyl chloride \( \left(C_{2} H_{5} C l\right), \) is prepared by
reaction of ethylene with hydrogen chloride:
\( \boldsymbol{C}_{2} \boldsymbol{H}_{4}(\boldsymbol{g})+\boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g}) \longrightarrow \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{C l}(\boldsymbol{g}) ; \triangle \boldsymbol{H}=-\mathbf{7} \mathbf{2} . \mathbf{3} \boldsymbol{k} \boldsymbol{J} / \boldsymbol{m o l} \)
What is the value of \( \triangle \boldsymbol{U} \) (in \( \mathbf{k J} \) ), if \( \mathbf{7 0} \boldsymbol{g} \) of ethylene and \( 73 g \) of \( H C L \) are
allowed to react at \( 300 K ? \)
\( \mathbf{A} \cdot-69.8 \)
в. -180.75
c. -174.5
D. -139.6
Subject: Physics
The question has a paragraph followed by two statements, Statement-1 and
Statement-2. Of the given four alternatives after the statements,
choose the one that describes the
statements.
A thin air film is formed by putting the convex surface of a piano-convex lens over a plane glass plate. With monochromatic light, this film gives an interference pattern due to light reflected from the top (convex) surface and the bottom (glass plate) surface of the film.

Statement 1: When light reflects from
the air-glass plate interface, the reflected wave suffers a phase change
of \( \pi \)
Statement 2: The centre of the
interference pattern is dark.
A. Both statements 1 and 2 are true and statement 2 is the correct explanation of statement 1.
B. Both statements 1 and 2 are true but statement 2 is not the correct explanation of statement 1
c. Statement 1 is true but statement 2 is false
D. Both statements 1 and 2 are false
Subject: Chemistry
The molecular weight of \( 2.6 \mathrm{gm} \) of a gas which occupies 2.24 litres at \( 0^{\circ} C \& 760 \)
mm pressure is :
A . \( 2.6 \mathrm{gm} \)
B. 26 gm
c. \( 22.4 \mathrm{gm} \)
D. 2.24 gm
Subject: Chemistry
Assertion: At infinite dilution, both strong and weak electrolyte have degree of ionization equal to unity. Reason: At infinite dilution of an
electrolyte, the equivalent conductance
of cations and anions are
independent of each other.
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: Physics
A machine part consist of two
homogeneous solid cylinders coaxially.
Then find the distance of center of mass
from 0
\( \mathbf{A} \cdot \frac{17}{2} m m \)
\( \mathbf{B} \cdot \frac{52}{7} m m \)
\( \mathbf{c} \cdot \frac{15}{17} m m \)
\( \mathbf{D} \cdot \frac{12}{7} m m \)
Subject: Chemistry
A solution containing \( 0.122 \mathrm{kg} \) of
benzoic acid in \( 1 k g \) of benzene
(b.pt.353 K) boils at \( 354.5 K \)
Determine the apparent molar mass of benzoic acid (which dimerizes) in
the solution and the degree of
dimerization
Given: \( \Delta_{v a p} H_{1 m}(\text {benzene})= \)
\( \mathbf{3 9 4 . 5 7} \boldsymbol{J} \boldsymbol{g}^{-1} \)
A. 0.214 kg \( \mathrm{mol}^{-1}, 0.86 \)
в. 0.257 kg \( m o l^{-1}, 0.932 \)
c. \( 0.428 \mathrm{kg} \mathrm{mol}^{-1}, 0.956 \)
D. \( 0.454 \mathrm{kg} \mathrm{mol}^{-1}, 0.986 \)
Subject: Maths
The solution of \( \frac{d y}{d x}=\frac{\sqrt{x^{2}-y^{2}}+y}{x} \) is:
\( \mathbf{A} \cdot \tan ^{-1}\left(\frac{y}{x}\right)=\log (c x) \)
B・sin \( ^{-1}\left(\frac{y}{x}\right)=\log (c x) \)
c. \( \cos ^{-1}\left(\frac{y}{x}\right)=\log (c y) \)
D \( \cdot \sec ^{-1}\left(\frac{y}{x}\right)=\log (c y) \)
Subject: Chemistry
If two gases \( A B_{2} \) and \( B_{2} C \) are mixed
the following equilibria are readily
established
\( \boldsymbol{A B}_{2}(\boldsymbol{g})+\boldsymbol{B}_{2} \boldsymbol{C}(\boldsymbol{g}) \rightarrow \boldsymbol{A} \boldsymbol{B}_{3}(\boldsymbol{g})+\boldsymbol{B C}(\boldsymbol{g}) \)
\( \boldsymbol{B C}(\boldsymbol{g})+\boldsymbol{B}_{2} \boldsymbol{C}(\boldsymbol{g}) \rightarrow \boldsymbol{B}_{3} \boldsymbol{C}_{2}(\boldsymbol{g}) \)
If the reaction is started only with \( A B_{2} \)
with \( B_{2} C, \) then which of the following is
necessarily true at equilibrium:
This question has multiple correct options
\( \mathbf{A} \cdot\left[A B_{3}\right]_{e q}=[B C]_{e q} \)
\( \mathbf{B} \cdot\left[A B_{2}\right]_{e q}=\left[B_{2} C\right]_{e q} \)
\( \mathbf{c} \cdot\left[A B_{3}\right]_{e q}>\left[B_{3} C_{2}\right]_{e q} \)
\( \mathbf{D} \cdot\left[A B_{3}\right]_{e q}>[B C]_{e q} \)
Subject: Physics
A wire of resistance \( 4 \Omega \) is stretched to
twice its original length. In the process of stretching, its area of cross section gets halved. Now, the resistance of the
wire is:
\( A \cdot 8 \Omega \)
в. 16 \Omega
c. \( 1 \Omega \)
D. \( 4 \Omega \)
Subject: Chemistry
Which of the following statements are
correct?
\( \mathbf{A} \cdot \beta-\mathrm{D}(+) \) glucopyranose is more stable than \( \alpha-\mathrm{D}(+) \) glucopyranose
B. Invert sugar is laevorotatory
C. Dextrose is \( D(+) \) glucose
D. Levulose is D(-) fructose
Subject: Maths
The middle term of expansion of \( \left(\frac{10}{x}+\frac{x}{10}\right)^{10} \)
A \( \cdot^{7} C_{5} \)
в. \( ^{8} C_{5} \)
\( \mathrm{c} \cdot^{9} \mathrm{C}_{5} \)
D. \( ^{10} C_{5} \)
Subject: Physics
A cricket ball of mass \( 500 \mathrm{g} \) is moving with speed of \( 36 k m h^{-1} . \) It is reflected
back with the same speed. What is the
impulse applied on it?
A. \( 20 \mathrm{Kg} \mathrm{m} / \mathrm{s} \)
B. \( 10 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
c. \( 5 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
D. none of the above
Subject: Chemistry
For the reaction:
\( \mathbf{2} N \boldsymbol{H}_{3}(\boldsymbol{g}) \rightarrow \boldsymbol{N}_{2}(\boldsymbol{g})+\mathbf{3} \boldsymbol{H}_{2}(\boldsymbol{g}) \)
if rate of disappearance of of \( \boldsymbol{N} \boldsymbol{H}_{3} \) is
\( 1.7 g m / s e c \) then rate of appearance of
\( N_{2} \) should be:
A \( .0 .85 \mathrm{gm} / \mathrm{sec} \)
B. 3.4 gm/sec
c. \( 1.4 g m / \)sec
D. \( 0.7 \mathrm{gm} / \mathrm{sec} \)
Subject: Physics
A uniform electric field \( \boldsymbol{E}=\mathbf{2} \times \)
\( 10^{3} N C^{-1} \) is acting along the positive \( x \)
axis. The flux through the same square if the line normal to tis plane makes a
\( 60^{\circ} \) angle with the \( x \) -axis is
\( \begin{array}{lll}\text { A. } 30 N & C^{-1} m^{2}\end{array} \)
B. \( 10 N \quad C^{-1} m^{2} \)
\( \begin{array}{lll}c \cdot 20 N & C^{-1} m^{2} & ^{2}\end{array}^{C^{2}} \)
D. \( 25 N \quad C^{-1} m^{2} \)
Subject: Physics
An automobile travelling with a speed of \( 60 k m / h, \) can brake to stop within a
distance of \( 20 m . \) If the car is going
twice as fast, i.e. \( 120 k m / h \), the
stopping distance will be:
A . \( 20 m \)
в. \( 40 m \)
\( c .60 m \)
D. \( 80 m \)
Subject: Chemistry
Assertion(A): In the dissociation of
\( P C l_{5} \) at constant pressure and
temperature addition of helium at equilibrum increases the dissociation
of \( \boldsymbol{P} \boldsymbol{C l}_{5} \)
Reason(R): Helium removes \( C l_{2} \) from
the field of action.
A. Both Assertion and Reason are true and Reason is correct explanation of Assertion.
B. Both Assertion and Reason are true but Reason is not correct explanation of Assertion
c. Assertion is true but Reason is false.
D. Both Assertion and Reason are false
Subject: Chemistry
Study the figure given below and mark
the correct statement about \( K_{c} \) and
dependence of extent of reaction on it.
A. \( x \) - Reaction does not occur
Y - Reaction proceeds to completion; Z - Reaction does not occur
B. X- Reaction completes; Y - Reaction does not occur; Z Reactants and products are at equilibrium
c. \( x \) - Reaction hardly occurs;
Y - Reactants and products are at equilibrium; Z - Reaction proceeds completion
D. \( x \) - Reaction proceeds completion; \( Y \) - Reactants and products are at equilibrium; Z - Reaction hardly occurs
Subject: Chemistry
The value of \( K_{c}=4.24 \) at \( 800 K \) for the
reaction
\( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \)
Calculate equilibrium concentrations of
\( C O_{2}, H_{2}, C O \) and \( H_{2} O \) at \( 800 K, \) if only
\( C O \) and \( H_{2} O \) are present initially at concentration of \( 0.10 M \) each?
Subject: Chemistry
Pick out the correct statement(s) above
a universal indicator.
This question has multiple correct options
A. It is a mixture of some indicators.
B. It shows the change in colour at different pH with altogether different colours for a change in pH by units
C. Phenolphthalein is an universal indicator.
D. a mixture of methyl red, \( \alpha \) -naphthol, phthalein blue shows different colours between pH range 4 to 11
Subject: Maths
If \( f(x) \) is a polynomial in \( x(>0) \)
satisfying the equation \( \boldsymbol{f}(\boldsymbol{x})+ \) \( f\left(\frac{1}{x}\right)=f(x) \cdot f\left(\frac{1}{x}\right) \) and \( f(2)=-7 \)
then \( f(3) \) is equal to
A . -26
в. -27
c. -28
D. -29
Subject: Maths
The total number of matrices
\( \boldsymbol{A}= \)
\( \left(\begin{array}{ccc}0 & 2 x & 2 x \\ 2 y & y & -y \\ 1 & -1 & 1\end{array}\right),(x, y \in R, x \neq y) \) for
which \( \boldsymbol{A}^{\boldsymbol{T}} \boldsymbol{A}=\mathbf{3} \boldsymbol{I}_{3} \) is:
\( A \)
B. 2
\( c .3 \)
\( D \)
Subject: Biology
Read the following statements about
forest biome and select the correct
answer
I. Temperature is generally lower in summer and higher in winter.
Il. The days are cooler and nights are warmer than in the surroundings.
III. The floor of the forest is carpeted
with lichens and mosses.
IV. Moisture content of the soil remains
stable for longer periods because of absence of evaporation.
A. I and II are correct
B. II and III are correct
c. ।, III and IV are correct
D. All are correct
Subject: Maths
f \( y=\cos 2 x \cos 3 x, \) then \( y_{n} \) is equal to
Where, \( y_{n} \) denotes the \( n^{t h} \) derivative of
\( \boldsymbol{y} \)
A \( \cdot 6^{n} \cos \left(2 x+\frac{n \pi}{2}\right) \cos \left(3 x+\frac{n \pi}{2}\right) \)
B. \( \frac{1}{2}\left[5^{\text {n }} \cos \left(\frac{\text { n } \pi}{2}+5 x\right)+\cos \left(\frac{\text { n } \pi}{2}+x\right)\right] \)
c. \( \frac{1}{2}\left[5^{\mathrm{n}} \sin \left(5 x+\frac{\mathrm{n} \pi}{2}\right)+\sin \left(x+\frac{\pi}{2}\right)\right] \)
D.
Subject: Physics
A long solenoid has 200 turns per cm
and carries a current i.The magnetic field at its centre is \( 6.28 \times \) \( 10^{-2} W b / m^{2} . \) Another long solenoid
has 100 turns per \( \mathrm{cm} \) and it carries a
current i/3.The value of magnetic field
at its centre is:
A \( \cdot 1.05 \times 10^{-2} \mathrm{Wb} / \mathrm{m}^{2} \)
в. \( 1.05 \times 10^{-5} \mathrm{Wb} / \mathrm{m}^{2} \)
c. \( 1.05 \times 10^{-3} \mathrm{Wb} / \mathrm{m}^{2} \)
D. \( 1.05 \times 10^{-4} \mathrm{Wb} / \mathrm{m}^{2} \)
Subject: Maths
If \( A^{T}=\left[\begin{array}{cc}3 & 4 \\ -1 & 2 \\ 0 & 1\end{array}\right] \) and \( B= \)
\( \left[\begin{array}{ccc}-1 & 2 & 1 \\ 1 & 2 & 3\end{array}\right], \) then find \( A^{T}-B^{T} \)
Subject: Chemistry
The molecular formula of the
hydrocarbon (A) is:
\( (\mathrm{A}) \)
\( \mathbf{A} \cdot C_{2} H_{6} \)
\( \mathbf{B} \cdot C_{2} H_{4} \)
\( \mathbf{c} \cdot C_{3} H_{6} \)
D. \( C_{3} H_{8} \)
Subject: Chemistry
Here is another look at the reaction of
crystal violet with sodium hydroxide, a
first-order reaction \( (\ln A \mathbf{v} \text { time }) \)

What is the significance of the slope?
A. The slope represents the change in concentration over time
B. The slope represents the inverse of change in concentration over time
c. The slope represents the negative value of the rate constant
D. The slope represents the negative rate of product concentration over time
Subject: Chemistry
The density of lake water is 1.3 g/cc. and
it contains 69 g of \( N a^{+} \) ions per kg of
water. What is molality of \( N a^{+} \) ion in the lake?
\( A \cdot 1 m \)
B. 3 \( m \)
\( c \cdot 2 m \)
D. \( 4 \mathrm{m} \)
Subject: Physics
An alternating current generator has an
internal resistance \( \boldsymbol{R}_{\boldsymbol{g}} \) and an internal
reactance \( X_{g} . \) It is used to supply power to a passive load consisting of a
resistance \( \boldsymbol{R}_{g} \) and a reactance \( \boldsymbol{X}_{\boldsymbol{L}} . \) For maximum power to be delivered from the generator to the load, the value of
\( X_{L} \) is equal to
A . zero
в. \( X_{g} \)
c. \( -x_{g} \)
D. \( R_{g} \)
Subject: Physics
Two sources of equal emf are connected to an external resistance R. The internal
resistances of two sources are \( \boldsymbol{R}_{1} \) and
\( \boldsymbol{R}_{2}\left(\boldsymbol{R}_{2}>\boldsymbol{R}_{1}\right) . \) If the potential difference
across the source having internal
resistance \( R_{2} \) is zero, then;
в. \( R=R_{1} R_{2} /\left(R-R_{1}\right) \)
C. \( R=R_{2} \times\left(R_{1}+R_{2}\right) /\left(R_{2}-R_{1}\right) \)
D. \( R=R_{2}-R_{1} \)