AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If \( \int_{0}^{1} \frac{\tan ^{-1} x}{x} d x \) is equal to
A \( \cdot \int_{0}^{\frac{\pi}{2}} \frac{\sin x}{x} d x \)
B \( \cdot \int_{0}^{\frac{\pi}{2}} \frac{x}{\sin x} d x \)
\( ^{\mathbf{C}} \cdot \frac{1}{2} \int_{0}^{\frac{\pi}{2}} \frac{\sin x}{x} d x \)
\( ^{\mathrm{D}} \cdot \frac{1}{2} \int_{0}^{\frac{\pi}{2}} \frac{x}{\sin x} d x \)
Subject: Physics
The Sl unit of electric flux is
\( \begin{array}{ll}\text { A. } N & C^{-1} m^{2} \\ \end{array} \)
\( \begin{array}{lll}\text { В. } N & C & m^{-2}\end{array} \)
\begin{tabular}{ll} 
c. \( N \) & \( C^{-2} m^{2} \) \\
\hline
\end{tabular}
D. \( N \quad C^{-1} m^{-2} \)
Subject: Chemistry
For a gaseous reaction \( \boldsymbol{A} \rightarrow \boldsymbol{B}+\mathbf{2} \boldsymbol{C} \)
at \( 250^{\circ} \mathrm{C}, \) following data were observed.
The partial pressure of the gases at 100th min will be (in 100x mm)
Time
20 \( \quad 40 \)
\[
(\min )
\]
Total pressure
\( (\mathrm{mm} \mathrm{Hg}) \) 587.6
Subject: Maths
The set of angles between \( 0 \& 2 \pi \)
satisfying the equation \( 4 \cos ^{2} \theta \) \( 2 \sqrt{2} \cos \theta-1=0 \) is -
A \( \cdot\left\{\frac{\pi}{12}, \frac{5 \pi}{12}, \frac{19 \pi}{12}, \frac{23 \pi}{12}\right\} \)
В \( \cdot\left\{\frac{\pi}{12}, \frac{7 \pi}{12}, \frac{17 \pi}{12}, \frac{23 \pi}{12}\right\} \)
c. \( \left\{\frac{5 \pi}{12}, \frac{13 \pi}{12}, \frac{19 \pi}{12}\right\} \)
D. \( \left\{\frac{\pi}{12}, \frac{7 \pi}{12}, \frac{19 \pi}{12}, \frac{23 \pi}{12}\right\} \)
Subject: Maths
For three numbers \( a, b, c \) product of the
average of the numbers, \( a^{2}, b^{2}, c^{2} \) and \( \frac{1}{a^{2}}, \frac{1}{b^{2}}, \frac{1}{c^{2}} \) cannot be less than
A . 1
B. 3
\( c .9 \)
D. none of these
Subject: Physics
If we want to maximise the magnitude
of the magnetic force acting on a charged particle moving in a magnetic field. By which of the following statements we can maximise it.
I. Maximize the strength of the
magnetic field
Il. Minimize the velocity of particle.
III. Ensure that the particle is moving in the same direction as the magnetic field lines
A. I only
B. I and II only
c. I and III only
D. II and III only
E . ।, II, and III
Subject: Chemistry
IUPAC name of the Wiilkinson's catalyst
\( \left[\boldsymbol{R h C l}\left(\boldsymbol{P} \quad \boldsymbol{P h}_{3}\right)_{3}\right] \)
A. Chlorotris (triphenylphosphine) rhodium (I)
B. Chlorotris (triphenylphosphine) rhodium (IV)
C. Chlorotris (triphenylphosphine) rhodium (0)
D. Chlorotris (triphenylphosphine) rhodium (VI)
Subject: Physics
The Universal gas constant may be
expressed as:
a) \( 8.31 \mathrm{J} / \mathrm{mole}-\mathrm{K} \)
c) \( 2.00 \mathrm{J} / \mathrm{mole}-\mathrm{K} \)
b) 8.31 cal/mole-K
d) 2.00 cal/mole-K
A . a,
в. а,
\( c \cdot b, c \)
D. b,
Subject: Maths
\( \mathbf{f} \mathbf{A}=\left[\begin{array}{lll}\mathbf{1} & \mathbf{- 3} & \mathbf{- 4} \\ \mathbf{- 1} & \mathbf{3} & \mathbf{4} \\ \mathbf{1} & \mathbf{- 3} & \mathbf{- 4}\end{array}\right], \) then \( \mathbf{A}^{2}= \)
\( A \cdot A \)
в. -4
c. Null matrix
D. \( 2 A \)
Subject: Maths
Given the sequence of numbers
\( \boldsymbol{x}_{1}, \boldsymbol{x}_{2}, \boldsymbol{x}_{3}, \ldots \ldots . . \boldsymbol{x}_{2013} \) which satisfies
\( \frac{\boldsymbol{x}_{\mathbf{1}}}{\boldsymbol{x}_{\mathbf{1}}+\mathbf{1}}=\frac{\boldsymbol{x}_{\mathbf{2}}}{\boldsymbol{x}_{\mathbf{2}}+\mathbf{3}}=\frac{\boldsymbol{x}_{\mathbf{3}}}{\boldsymbol{x}_{\mathbf{3}}+\mathbf{5}}=\dots \dots \)
\( \frac{x_{2013}}{x_{2013}+4025}, \) nature of the sequence is
A . A.P
в. \( G . P \)
c. \( H . P \)
D. A.G.P
Subject: Maths
Which of the following quantities is/are positive?
This question has multiple correct options
A \( \cdot \cos \left(\tan ^{-1}(\tan 4)\right) \)
B. \( \sin \left(\cot ^{-1}(\cot 4)\right) \)
c. \( \tan \left(\cos ^{-1}(\cos 5)\right) \)
D. \( \cot \left(\sin ^{-1}(\sin 4)\right) \)
Subject: Physics
A body cools from \( 70^{\circ} \mathrm{C} \) to \( 50^{\circ} \mathrm{C} \) in 5
minutes. Temperature of surroundings
is \( 20^{\circ} \mathrm{C} . \) Its temperature after next 10 minutes is
A \( \cdot 26^{\circ} \mathrm{C} \)
В. \( 30^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 35^{\circ} C \)
D. \( 45^{\circ} \mathrm{C} \)
Subject: Maths
If \( 27 a+9 b+3 c+d=0, \) then the
equation \( 4 a x^{3}+3 b x^{2}+2 c x+d=0 \)
has atleast one real root lying between
A. 0 and 1
B. 1 and 3
c. 0 and 3
D. None
Subject: Physics
A system of springs with their springs constants are as shown in figure. The
frequency of oscillation of the mass \( m \)
will be (assuming the springs to be massless
A \( \cdot \frac{1}{2 \pi} \sqrt{\frac{k_{1} k_{2}\left(k_{3}+k_{4}\right)}{\left[\left(k_{1}+k_{2}\right)+\left(k_{3}+k_{4}\right)+k_{1} k_{4}\right] m}} \)
B \( \cdot \frac{I}{2 \pi} \sqrt{\frac{k_{1} k_{2}\left(k_{3}+k_{4}\right)}{\left[\left(k_{1}+k_{2}\right)+\left(k_{3}+k_{4}\right)+k_{1} k_{2}\right] m}} \)
c. \( \frac{1}{2 \pi} \sqrt{\frac{k_{1} k_{2}\left(k_{3}+k_{4}\right)}{\left[\left(k_{1}+k_{2}\right)+\left(k_{3}+k_{4}\right)+k_{1} k_{2}\right] m}} \)
D \( \frac{1}{2 \pi} \sqrt{\frac{\left(k_{1}+k_{2}\right)+\left(k_{3}+k_{4}\right)+k_{1} k_{2}}{\left[\left(k_{1}+k_{2}\right)+\left(k_{3}+k_{4}\right)+k_{1} k_{2}\right] m}} \)
Subject: Physics
Two uniform rods of equal length but different masses are rigidly joined to
form an \( L \) shaped body, which is then
smoothly pivoted about \( O \) as shown.
If the body is in equilibrium in the
shown configuration, ratio \( M: m \) will
be :
\( A \)
B.
\( c \cdot \sqrt{2} \)
D. \( \sqrt{3} \)
Subject: Maths
The area of parallelogram whose two
sides are \( \boldsymbol{y}=\boldsymbol{x}+\mathbf{3}, \mathbf{2} \boldsymbol{x}-\boldsymbol{y}+\mathbf{1}=\mathbf{0} \)
and remaining two sides are passing through (0,0) is?
A. 2 sq. unit
B. 3 sq. unit
c. \( \frac{5}{2} \) sq. unit
D. \( \frac{7}{2} \) sq. unit
Subject: Physics
If a disc slides from top to bottom of an
inclined plane, it takes time \( t_{1} \). If it rolls, it takes time \( t_{2} . \) Now, \( \frac{t_{2}^{2}}{t_{1}^{2}} \) is
A \( \cdot \frac{1}{2} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{3}{2} \)
D. \( \frac{2}{5} \)
Subject: Chemistry
\( 0.216 g \) of an organic compound gives
\( 28.8 c m^{3} \) of moist nitrogen measured at 288K and 732.7mm pressure.
The percentage of nitrogen in the substance is approximately:
tension at \( 288 \mathrm{K}=12.7 \mathrm{mm} \)
A . 15
B. 20
c. 25
D. 30
Subject: Biology
Assertion
In pigeons, females are heterogametic and males are homogametic.
Reason
In pigeons, females have \( z \) W sex chromosomes and males have \( \mathrm{ZZ} \) sex
chromosomes.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
If \( x=2, y=1 \) and \( z=-3, \) then \( x^{3}+ \)
\( y^{3}+z^{3}-3 x y z \) is equal to
\( \mathbf{A} \cdot \mathbf{6} \)
B.
\( c \cdot 2 \)
D.
Subject: Physics
If a vector \( \vec{A} \) makes an angles \( \alpha, \beta \) and
\( Y \) respectively with the \( x, y \) and \( z \) axes
respectively. Then \( \sin ^{2} \alpha+\sin ^{2} \beta \)
\( +\sin ^{2} \gamma \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. 1
c. 2
D. 3
Subject: Physics
Imagine a light planet revolving around a very massive star in a circular orbit of
radius R with a speed of revolution T. If the gravitational force of attraction between the planet and the star is proportional to \( \boldsymbol{R}^{-5 / 2}, \) then
A \( \cdot T^{2} \) is proportional to \( R^{2} \)
B . \( T^{2} \) is proportional to \( R^{7 / 2} \)
c. \( T^{2} \) is proportional to \( R^{3 / 2} / 2 \) proportional
D. \( T^{2} \) is proportional to \( R^{3.75} \)
Subject: Physics
A light ray is incident perpendicularly to
one face of a \( 90^{\circ} \) prism and is totally
internally reflected at the glass-air
interface. If the angle of reflection is \( 45^{\circ} \)
we conclude that the refractive index \( n \)
A \( \cdot n>\frac{1}{\sqrt{2}} \)
В . \( n>\sqrt{2} \)
c. \( _{n<\frac{1}{\sqrt{2}}} \)
D. \( n<\sqrt{2} \)
Subject: Physics
The equation of a progressive wave is \( \boldsymbol{y}=\mathbf{0 . 0 5} \sin \left(\mathbf{2 0 0} \boldsymbol{t}-\frac{\boldsymbol{x}}{\mathbf{2}}\right) \) where \( \boldsymbol{x}, \boldsymbol{y} \) are
in metres and \( t \) in seconds, then
a ) velocity of wave is \( 100 m s^{-1} \)
b) maximum velocity of particle in the wave is \( 10 m s^{-1} \)
c) wavelength of wave is \( 4 \pi m \)
A. only a and c are true
B. only b and c are true
c. only a and b are true
D. a,b,c are true
Subject: Maths
\( \lim _{x \rightarrow a} \frac{x^{m}-a^{m}}{x^{n}-a^{n}} \) is equal to.
A \( . m n a^{m-n} \)
в. \( \frac{m}{n} a^{m-n} \)
c. \( \frac{n}{m} a^{m-n} \)
D. \( m n a^{m+n} \)
Subject: Chemistry
For \( B F_{3} \) molecule, which of the
following is/are true?

This question has multiple correct options
\( A \cdot B \) -atom is \( s p^{2} \) hybridised.
B. There is a \( p \pi-p \pi \) back bonding in this molecule.
C. Observed B-F bond length is found to be less than the expected bond length.
D. There is a \( p \pi-d \pi \) back bonding in this molecule.
Subject: Chemistry
Write expressions for \( \boldsymbol{K}_{\boldsymbol{p}} \) for the
following equilibria:
(a) \( 4 N H_{3(g)}+5 O_{2(g)} \rightleftharpoons 4 N O(g)+ \)
\( \mathbf{6} \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O}(\boldsymbol{g}) \)
(b) \( \boldsymbol{N} \boldsymbol{H}_{\boldsymbol{3}(\boldsymbol{g})}+\boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{C l}(\boldsymbol{g}) \)
\( (c) 2 C l_{2(g)}+2 N O_{2(g)} \rightleftharpoons 2 N O_{2} C l_{2(g)} \)
Subject: Maths
If \( \boldsymbol{y}=\sec \sqrt{\boldsymbol{a}+\boldsymbol{b} \boldsymbol{x}} \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) equals-
A \( \cdot \frac{b}{b \sqrt{a+b x}} \sec \sqrt{a+b x} \tan \sqrt{a+b x} \)
в. \( \frac{b}{2 \sqrt{a+b x}} \sec \sqrt{a+b x} \tan \sqrt{a+b x} \)
c. \( 2 b \sqrt{a+b x} \sec \sqrt{a+b x} \tan \sqrt{a+b x} \)
D. None of these
Subject: Physics
A bike accelerates uniformly from rest to a speed of \( 7.10 \mathrm{m} / \mathrm{s} \) over a distance of
\( 35.4 m . \) Determine the acceleration of
the bike. \( \left(\operatorname{in} m / s^{2}\right) \)
\( \mathbf{A} \cdot 0.712 \)
в. 0.71
\( c .0 .7 \)
D. 7.71
Subject: Maths
The value of the integer \( \int_{0}^{\pi} e^{\cos ^{2} x} \cdot \cos ^{3}(2 n+1) x d x, n \) integer
is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. \( 2 \pi \)
D. none of these
Subject: Physics
When \( 4 V \) DC is connected across an
inductor, current is \( 0.2 A . \) When \( A C \) of
\( 4 V \) is applied the current is \( 0.1 A \) Then self inductance of the coil is:
\( \left[\text { Given } \omega=1000 \text { rads}^{-1}\right] \)
A \( .20 \mathrm{mH} \)
в. \( 40 \mathrm{mH} \)
c. \( 20 \sqrt{3} \mathrm{mH} \)
D. none of these
Subject: Physics
Two identical pith balls are charged by rubbing against each other. They are suspended from a horizontal rod
through two strings of length \( 20 \mathrm{cm} \) each, the separation between the suspension points being \( 5 \mathrm{cm} . \) In
equilibrium, the separation between
the balls is \( 3 \mathrm{cm} \). Find the mass of each
ball and the tension in the strings. (The
charge on each ball has a magnitude
\( \left.2.0 \times 10^{-8} C\right) \)
Subject: Biology
Show the pathway of electric impulse.
A. Dendrite \( \rightarrow \) Cell body \( \rightarrow \) Axon \( \rightarrow \) to its end
B. Cell body \( \rightarrow \) Dendrite \( \rightarrow \) Axon \( \rightarrow \) to its end
C . Axon \( \rightarrow \) Cell body \( \rightarrow \) Dendrite \( \rightarrow \) to its end
D. Dendrite \( \rightarrow \) Axon \( \rightarrow \) Cell body \( \rightarrow \) to its end
Subject: Chemistry
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{B r} \frac{A l \operatorname{co.KOH}}{\Delta} \boldsymbol{B} \stackrel{\boldsymbol{H B r}}{\longrightarrow} \)
\( C \stackrel{N a / \text {ether}}{ } D \) the compound D is
A. ethane
B. propane
c. n-butane
D. n-pentane
Subject: Maths
If the squares of the lengths of the tangents from a point \( P \) to the circles \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}=\boldsymbol{a}^{2}, \boldsymbol{x}^{2}+\boldsymbol{y}^{2}=\boldsymbol{b}^{2} \) and \( \boldsymbol{x}^{2}+ \)
\( y^{2}=c^{2} \operatorname{are} \) in A.P., then
This question has multiple correct options
A \( \cdot a^{2}, b^{2}, c^{2} \) are in A.P
B. \( \frac{1}{a^{2}}, \frac{1}{b^{2}}, \frac{1}{c^{2}} \) are in \( \mathrm{H.P} \)
c. \( a^{2}, b^{2}, c^{2} \) are in G.P
D. \( \frac{1}{a^{2}}, \frac{1}{b^{2}}, \frac{1}{c^{2}} \) are in A.F.
Subject: Physics
\( n \) charged drops, each of radius \( r \) and
charge \( q, \) coalesce to form a big drop of
radius \( R \) and charge \( Q . \) If \( V \) is
the electric potential and \( \boldsymbol{E} \) is the electric field at the surface of a drop,
then :
A \( \cdot E_{\text {big}}=n^{2 / 3} E_{\text {small}} \)
B. \( V_{\text {big}}=n^{1 / 3} V_{\text {small}} \)
C. \( E_{\text {small}}=n^{2 / 3} E_{\text {big}} \)
D. \( V_{\text {big}}=n^{2 / 3} V_{\text {small}} \)
Subject: Physics
An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. The piston and the cylinder have equal cross sectional area A. When the piston is in
equilibrium the volume of the gas \( V_{0} \)
and its pressure is \( P_{0} \). The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency:
A \( \cdot \frac{1}{2 \pi} \sqrt{\frac{M V_{0}}{A \gamma P_{0}}} \)
c. \( \frac{1}{2 \pi} \frac{V_{0} M P_{0}}{A^{2}} \)
D. \( \frac{1}{2 \pi} \sqrt{\frac{A^{2} \gamma P_{0}}{M V_{0}}} \)
Subject: Maths
The value of \( \lim _{x \rightarrow 0} \frac{(1-\cos 2 x) \sin 5 x}{x^{2} \sin 3 x} \)
equal to
A \( \cdot \frac{10}{3} \)
в. \( \frac{3}{10} \)
\( c \cdot \frac{6}{5} \)
D.
Subject: Maths
Factorise the following: \( y^{6}+32 y^{3}-64 \)
A \( \cdot(y+2)\left(y^{4}-2 y^{3}+8 y^{3}+8 y+16\right) \)
B . \( \left(y^{2}+2 y-4\right)\left(y^{4}-2 y^{3}+8 y^{2}+8 y+16\right) \)
C \( \cdot\left(y^{2}+2 y-4\right)\left(y^{4}-2 y^{3}+8 y^{2}\right) \)
D. \( (y+2)\left(y^{4}-2 y^{3}+8 y^{2}+8 y\right) \)
Subject: Physics
A \( 1 \mathrm{kg} \) ball is suspended in a uniform electric field with the help of a string fixed to a point. The ball is given a charge \( \sqrt{5} \) coulomb and the string
makes an angle \( 37^{0} \) with the vertical in
the equilibrium position. In the equilibrium position the tension is double the weight of the ball. Find the magnitude of the electric field in \( \mathrm{N} / \mathrm{C} \)
\( A \cdot 6 \)
B. 3
\( c \cdot 2 \)
D. 5
Subject: Chemistry
A solution of urea (mol. mass 56
\( \left.g m o l^{-1}\right) \) boils at \( 100.18^{\circ} C \) at the
atmospheric pressure. If \( \boldsymbol{K}_{f} \) and \( \boldsymbol{K}_{\boldsymbol{b}} \) for
water are 1.86 and 0.52 Kkg.mol\( ^{-1} \)
respectively, the above solution will freeze at:
A. \( -6.54^{\circ} \)
B. \( 6.54^{\circ} \mathrm{C} \)
\( c \cdot 0.654^{\circ} C \)
D. \( -0.654^{\circ} \mathrm{C} \)
Subject: Chemistry
Following reaction is spontaneous at \( 300 K \)
\( 2 C u O(s) \longrightarrow C u_{2} O(s)+I / 2 O_{2}(g) \)
\( \boldsymbol{\Delta} \boldsymbol{H}=-\mathbf{1 4 4 . 6 k} \boldsymbol{J m o l}^{-1} ; \boldsymbol{\Delta} \boldsymbol{S}= \)
\( 0.116 k J m o l^{-1} \) if true enter 1 else 0
\( A \)
Subject: Maths
Find the angle between the two lines
whose direction cosines are given by
equations \( l+m+n=0 \) and \( l^{2}+ \)
\( \boldsymbol{m}^{2}-\boldsymbol{n}^{2}=\mathbf{0} \)
A \( \cdot \frac{\pi}{6} \)
в.
\( c \cdot \frac{\pi}{2} \)
D.
Subject: Physics
A particle of mass \( 10 \mathrm{gm} \) is placed in a potential field given by \( V=\left(50 x^{2}+\right. \)
100) \( J / k g . \) The frequency of oscillation
in cycles/sec is:
A \( \cdot \frac{10}{\pi} \)
в. \( \frac{5}{\pi} \)
c. \( \frac{100}{\pi} \)
D. \( \frac{50}{\pi} \)
Subject: Maths
If \( [\boldsymbol{x} \quad \boldsymbol{y}]=\left[\begin{array}{ll}1 & 5\end{array}\right], \) then \( 2 \boldsymbol{x}+\mathbf{5} \boldsymbol{y}= \)
A . 26
B. 27
c. 29
D. None of these
Subject: Chemistry
A colourless salt (X) has \( 50 \% N a_{2} S O_{3} \)
and \( 50 \% H_{2} O . \) Then (a)The formula of
\( (X) \) is
(b)The amount of \( S O_{2} \) at NTP obtained
when 2.52 g of \( (X) \) reacts with excess of
dil. \( \boldsymbol{H}_{2} \boldsymbol{S O}_{4} \) is
A \( \cdot N a_{2} S O_{3} \cdot 7 H_{2} O, 0.224 \mathrm{L} \) at \( \mathrm{NTP} \) from \( 2.52 \mathrm{g} \) of \( (\mathrm{X}) \)
B. \( N a_{2} S O_{3} \cdot 6 H_{2} O, 0.224 \mathrm{L} \) at \( \mathrm{NTP} \) from \( 2.52 \mathrm{g} \) of \( (\mathrm{X}) \)
C. \( N a_{2} S O_{3} \cdot 7 H_{2} O, 2.24 \mathrm{L} \) at NTP from 2.52 g of \( (x) \)
D. \( N a_{2} S O_{3} \cdot 6 H_{2} O, 2.24 \mathrm{L} \) at NTP from \( 2.52 \mathrm{g} \) of \( (\mathrm{X}) \)
Subject: Maths
Prove that:
\( \left|\begin{array}{ccc}\mathbf{0} & \boldsymbol{a} & -\boldsymbol{b} \\ -\boldsymbol{a} & \boldsymbol{0} & -\boldsymbol{c} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{0}\end{array}\right|=\mathbf{0} \)
Subject: Maths
Discuss the commutativity and associativity of binary operation \( * \)
defined on \( A=Q-\{1\} \) by the rule \( a * \)
\( \boldsymbol{b}=\boldsymbol{a}-\boldsymbol{b}+\boldsymbol{a} \boldsymbol{b} \) fo all \( \boldsymbol{a}, \boldsymbol{b} \in \boldsymbol{A} . \) Also find
the identity element of \( * \) in \( A \) and hence
find the invertible elements of \( \boldsymbol{A} \)
Subject: Physics
A solid conducting sphere of radius \( ^{\prime} a^{\prime} \)
having charge \( q \) is surrounded by a
concentric conducting spherical shell of
inner radius \( 2 a \) and outer radius \( 3 a \) as
shown in figure. If the amount of heat
produced when switch is closed is \( \alpha\left(\frac{K q^{2}}{24 a}\right) . \) Fill the value of \( \alpha \)
Subject: Physics
A point charge q is kept on the vertex of the cone of base radius \( r \) and height \( r \)
The electric flux through the curved surface will be
\( ^{A} \cdot \frac{q}{2 \varepsilon_{0}}\left(1-\frac{1}{\sqrt{2}}\right) \)
В \( \cdot \frac{q}{\varepsilon_{0}}\left(\frac{1}{2 \sqrt{2}}\right) \)
\( c . \) zer
D. \( \frac{q}{\varepsilon_{0} \sqrt{2}} \)
Subject: Maths
The perpendicular distance from the point of intersection of the lines \( 3 x+ \) \( 2 y+4=0,2 x+5 y-1=0 \) to the line
\( 7 x+24 y-15=0 \) is
A \( \cdot \frac{2}{3} \)
B.
\( c \cdot \frac{1}{5} \)
D.
Subject: Physics
A uniform pressure p is exerted on all
sides of a solid cube at temperature
\( t^{0} C . \) By what amount should the
temperature of the cube be raised in
order to bring its volume back to the value it had before the pressure was applied? The coefficient of volume expansion of the cube y and the bulk modulus is B.
\( \mathbf{A} \cdot \frac{p}{\sqrt{2 y} B} \)
B. \( \frac{p}{2 y B} \)
c. \( \frac{2 p}{y B} \)
D. \( \frac{p}{y B} \)
Subject: Maths
\( \frac{1}{(x+1)\left(x^{2}+2 x+2\right)}=\frac{A}{x+1}+ \)
\( \frac{B x+C}{(x+1)^{2}+1} \Rightarrow A+B= \)
\( A \cdot 2 \)
B. -
\( c \)
\( D \)
Subject: Chemistry
Which of the following is a suitable example for illustrating the law of conservation of mass? (Atomic mass of
\( 0=16 ; H=1) \)
A. \( 18 g \) of water is formed by the combination of \( 16 g \) oxygen with \( 2 g \) of hydrogen
B. 18g of water in liquid state is obtained by heating 18 g of ice
c. \( 18 g \) of water is completely converted into vapour state on heating
D. \( 18 g \) of water freezes at \( 4^{\circ} C \) to give same mass of ice.
Subject: Physics
Water drops fall from a tap on to the floor \( 5.0 \mathrm{m} \) below at regular intervals of time. The first drop strikes the floor
when the fifth drop beings to fall. The height at which the third drop will be from ground, at the instant when the first drop strikes the ground is (Take \( \boldsymbol{g}=\mathbf{1 0 m s}^{-2} \mathbf{j} \)
A . \( 1.25 m \)
B. \( 2.15 m \)
c. \( 2.75 m \)
D. \( 3.75 m \)
Subject: Maths
One angle of a triangle is \( \frac{2 x}{3} \) grad, another is \( \frac{3 x}{2} \) degrees, whilst the third is \( \frac{\pi x}{75} \) radians. Express all angles in
degress.
A. Hence three angles of the triangle are \( 43^{\circ}, 30^{\circ}, 30^{\circ} \)
B. Hence three angles of the triangle are \( 24^{\circ}, 60^{\circ}, 96^{\circ} \)
C. Hence three angles of the triangle are \( 74^{\circ}, 27^{\circ}, 98^{\circ} \)
D. Hence three angles of the triangle are \( 30^{\circ}, 60^{\circ}, 90^{\circ} \)
Subject: Maths
Find matrix \( \boldsymbol{A} \) such that
\( \left[\begin{array}{cc}2 & -1 \\ 1 & 0 \\ -3 & 4\end{array}\right] A=\left[\begin{array}{cc}-1 & -8 \\ 1 & -2 \\ 9 & 22\end{array}\right] \)
Subject: Chemistry
At constant temperature \( N_{2} \) gas of 200
\( \mathrm{cm} \) at \( 720 \mathrm{mm} \) pressure and \( O_{2} \) gas of
\( 400 \mathrm{cm}^{3} \) at \( 750 \mathrm{mm} \) pressure. These are
mixed in 1 ltr capacity flask, than what will be the final pressure.
\( A \cdot 111 \mathrm{mm} \)
B. 222 mm
c. \( 333 \mathrm{mm} \)
D. 444 mm
Subject: Chemistry
In the following reaction, how is the rate
of appearance of \( B r_{2} \) related to the rate
of disappearance of the \( B r^{-} ? \)
\( \boldsymbol{B} \boldsymbol{r} \boldsymbol{O}^{3-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{5} \boldsymbol{B} \boldsymbol{r}^{-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{6} \boldsymbol{H}^{+} \rightarrow \)
\( \mathbf{3} \boldsymbol{B} \boldsymbol{r}_{2}(\boldsymbol{l})+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \)
A \( \cdot \frac{\left.d B r_{2}\right]}{d t}=-\frac{d\left[B r^{-}\right]}{d t} \)
B. \( \frac{d\left[B r_{2}\right]}{d t}=+\frac{3}{5} \frac{d\left[B r^{-}\right]}{d t} \)
C. \( \frac{\left.d B r_{2}\right]}{d t}=-\frac{3}{5} \frac{d B r-1}{d t} \)
D. \( \frac{d\left[B r_{2}\right]}{d t}=-\frac{5}{3} \frac{d\left[B r^{-}\right]}{d t} \)
Subject: Maths
Which statement represents the inverse of the statement "lf it is snowing, then
Skeeter wears a sweater."?
A. If Skeeter wears a sweater, then it is snowing
B. If Skeeter does not wear a sweater, then it is not snowing.
C. If it is not snowing, then Skeeter does not wear a sweater
D. If it is not snowing, then Skeeter wears a sweater
Subject: Biology
Assertion
Except sciophyte and plants of dense forest, light is rarely a limiting factor in
nature.
Reason
Light saturation occurs at 10 percent of full summer sunlight.
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 parallel beam of white light is
incident on a thin film of air of uniform
thickness. Wavelengths \( 7200 \dot{A} \) and \( \mathbf{5 4 0 0} \dot{\boldsymbol{A}} \) are observed to be missing from the spectrum of reflected light viewed normally. The other wavelength in the visible region missing in the reflected spectrum is
В. 4320 А
c. \( 5500 \dot{h} \)
Subject: Chemistry
Enthalpy change for the reaction
\( \mathbf{4} \boldsymbol{H}_{(g)} \rightarrow \mathbf{2} \boldsymbol{H}_{\mathbf{2}(\boldsymbol{g})} \) is \( -\mathbf{8 6 9 . 6 k J . T h e} \)
dissociation energy of \( \boldsymbol{H}-\boldsymbol{H} \) bond is?
Subject: Physics
Two moles of a monoatomic gas at 300 Kis kept in a non-conducting container
enclosed by a piston. Gas is now compressed to increase the temperature from \( 300 \mathrm{K} \) to \( 400 \mathrm{K} \). Find work done by the gas \( (\boldsymbol{R}= \) \( \left.\frac{\mathbf{2 5}}{\mathbf{3}} \boldsymbol{J} / \boldsymbol{m o l} \boldsymbol{K}\right) \)
Subject: Chemistry
Which of the following complex will give
white precipitate with \( \mathrm{BaCl}_{2}(\mathrm{aq}) \) ?
\( A \cdot\left[\cos \left(N H_{2}\right)_{4} S O_{4}\right] N O_{2} \)
B. \( \left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{5} S O_{4}\right] \mathrm{C} \)
\( \mathbf{c} \cdot\left[\operatorname{cr}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}\right] \mathrm{SO}_{4} \)
D. Both \( B \) and \( C \)