AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The radius of a sphere is measured to be \( 5.3 \pm 0.1 \mathrm{cm} . \) Calculate the
percentage error in the measurement of
its volume.
A . \( 3.45 \% \)
B . \( 5.66 \% \) \%
c. \( 2.4 \% \)
D. 1.05\%\%\%\%
Subject: Maths
Construct following quadrilaterals
(i) Quadrilateral \( L I F T \)
\( \boldsymbol{L} \boldsymbol{I}=\boldsymbol{4} \boldsymbol{c m} \)
\( \boldsymbol{I} \boldsymbol{F}=\mathbf{3} \boldsymbol{c m} \)
\( \boldsymbol{T} \boldsymbol{L}=\mathbf{2 . 5} \boldsymbol{c m} \)
\( \boldsymbol{L} \boldsymbol{F}=\mathbf{4 . 5} \boldsymbol{c m} \)
\( \boldsymbol{I} \boldsymbol{T}=\boldsymbol{4} \boldsymbol{c m} \)
(ii) Quadrilateral \( G O L D \)
\( \boldsymbol{O} \boldsymbol{L}=\mathbf{7 . 5} \boldsymbol{c m} \)
\( G L=6 \mathrm{cm} \)
\( G D=6 \mathrm{cm} \)
\( \boldsymbol{L} \boldsymbol{D}=\mathbf{5} \boldsymbol{c m} \)
\( O D=10 \mathrm{cm} \)
(iii) Rhombus \( B E N D \)
\( \boldsymbol{B} \boldsymbol{N}=\mathbf{5} . \boldsymbol{6} \boldsymbol{c m} \)
\( D E=6.5 \mathrm{cm} \)
Subject: Physics
Two beams of red and violet colours are
made to pass separately through prism
(angle of the prism is \( 60^{\circ} \) ). In the position of minimum deviation, the angle of refraction will be:
\( A \cdot 30^{\circ} \) for both the colours
B. greater for the violet colour
c. greater for the red colour
D. equal but not \( 30^{\circ} \) for both the colours
Subject: Maths
The condition that the chord \( x \cos \alpha+ \)
\( \boldsymbol{y} \sin \boldsymbol{\alpha}-\boldsymbol{p}=\mathbf{0} \) of \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}-\boldsymbol{a}^{2}=\mathbf{0} \) may
subtend a right angle at the centre of the circle is
A \( \cdot a^{2}=2 p^{2} \)
B \( \cdot p^{2}=2 a^{2} \)
c. \( a=2 p \)
D. \( p=2 a \)
Subject: Physics
A transverse progressive wave on a stretched string has a velocity of
\( 10 m s^{-1} \) and frequency of \( 100 H z . \) The phase difference between two particles
of the string which nbare \( 2.5 \mathrm{cm} \) apart will be :
A \( \cdot \frac{\pi}{8} \)
в.
c. \( \frac{3 \pi}{8} \)
D. \( \frac{\pi}{2} \)
Subject: Maths
Let \( \vec{a} \) and \( \vec{b} \) two unit vectors such that \( |\vec{a}+\vec{b}|=\sqrt{3} \cdot \operatorname{lf} \vec{c}=\vec{a}+2 \vec{b}+ \)
\( 3(\vec{a} \times \vec{b}), \) then \( 2 \vec{c} \) is equal to
A . \( \sqrt{55} \)
B. \( \sqrt{37} \)
c. \( \sqrt{51} \)
D. \( \sqrt{43} \)
Subject: Maths
The cost of \( 2 \mathrm{kg} \) of apples and \( 1 \mathrm{kg} \) of grapes on the day was found to be Rs.
160. After a month the cost of \( 4 \mathrm{kg} \) of
apples \( 2 \mathrm{kg} \) of grapes is \( \mathrm{Rs} .300 \) Represent the situation algebraically.
Subject: Chemistry
The approximate radius of polonium nucleus of mass number 210 is:
\( \mathbf{A} \cdot 8 \times 10^{-6} m \)
B. \( 8 \times 10^{-5} m \)
\( \mathbf{c} \cdot 4 \times 10^{-6} m \)
D. none of these
Subject: Maths
The integral of \( \int e^{x}(\sin x+\cos x) d x \) is
\( \mathbf{A} \cdot e^{x} \cos x+c \)
B \( \cdot e^{x} \sin x+c \)
\( \mathbf{c} \cdot e^{x} \sec x+c \)
D. none of this
Subject: Chemistry
The electronic configuration of
potassium is :
\( \mathbf{A} \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{3} 4 s^{2} 3 d^{2} \)
B \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{5} 4 s^{2} \)
\( \mathbf{C} \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{1} \)
D. \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{1} \)
Subject: Physics
Calculate the average molecular kinetic
energy :
(a) per kilomole,
(b) per kilogram,
of oxygen at \( 27^{\circ} \mathrm{C} \)
\( (R=8320 J / K m o l e K, \) Avogadro's
number \( =\mathbf{6 . 0 3} \times \)
\( 10^{26} \) molecules \( / \) Kmole
Subject: Physics
A person places his ear at the end of a long steel pipe. He hears two distinct sounds at an interval of 0.5 s when
another person hammers at the other end of the pipe. If the speed of the sound in metal and air are \( 3630 \mathrm{ms}^{-1} \) and 330
\( \mathrm{m} s^{-1} \) respectively, then the distance between the two persons is
A. \( 90.75 \mathrm{m} \)
в. 181.5 \( \mathrm{m} \)
c. \( 363 \mathrm{m} \)
D. 1650 \( \mathrm{m} \)
Subject: Physics
If a ray of light incident on a plane mirror is such that it makes an angle of
\( 30^{\circ} \) with the mirror, then the angle of
reflection is:
A . \( 30^{\circ} \)
B . \( 4.5^{\circ} \)
\( \mathrm{c} .55^{\circ} \)
D. \( 60^{\circ} \)
Subject: Maths
Identify the equation of a straight line passing through the point of intersection of \( \boldsymbol{x}-\boldsymbol{y}+\mathbf{1}=\mathbf{0} \) and \( \mathbf{3} \boldsymbol{x}+ \)
\( \boldsymbol{y}-\mathbf{5}=\mathbf{0} \) and perpendicular to one of
them.
A. \( x+y+3=0 \)
в. \( x+y-3=0 \)
c. \( x-3 y-5=0 \)
D. \( x-3 y+5=0 \)
Subject: Maths
If \( A=(a, b, c, d), B=(p, q, r, s) . \) then which
of the following are relations from \( A \) to
B? Give reasons for your answer:
This question has multiple correct options
A. \( R_{1}=\{(a, p),(b, r),(c, s)\} \)
B. \( R_{2}=\{(q, b),(c, s),(d, r)\} \)
C. \( R_{3}=\{(a, p),(a, q),(d, p),(c, r),(b, r)\} \)
D. \( R_{4}=\{(a, p),(a, q),(b, s),(s, b)\} \)
Subject: Physics
The acceleration due to gravity \( g \) and density of the earth \( p \) are related by which of the following relations? (Here \( G \) is the gravitational constant and \( R \) is the radius of the earth)
A \( \cdot p=\frac{4 \pi}{3 G R d} \)
в. \( _{p}=\frac{3 g}{4 \pi G R} \)
c. \( _{p}=\frac{3 G}{4 \pi G R} \)
D. \( p=\frac{4 \pi G R}{3 G} \)
Subject: Chemistry
Select correct statement about stability
of cations.
\( \mathbf{A} \cdot G e^{4+}>S n^{4+}>P b^{4} \)
B. \( G e^{2+}<S n^{2+}<P b^{2+} \)
c. \( P b^{2+}>P b^{4+}, S n^{4+}>S n^{2+} \)
D. All the above are correct statements
Subject: Physics
Three particles \( A, B \) and \( C \) of equal
mass move with equal speed \( V \) along the medians of an equilateral triangles as shown in the figure. They collide at
the centroid \( G \) of the triangle. After the
collision, \( A \) comes to rest, \( B \) retraces
its path with the speed \( V \). What is the velocity of \( C ? \)
Subject: Physics
The capacitance of a parallel plate
capacitor with air as medium is \( 3 \mu \mathrm{F} \) As a dielectric is introduced between
the plates, the capacitance becomes 15
\( \mu \mathrm{F} . \) The permittivity of the medium in
\( C^{2} N^{-1} m^{-2} \) is
A . \( 8.15 \times 10^{-11} \)
В. \( 0.44 \times 10^{-10} \)
C . \( 15.2 \times 10^{12} \)
D. \( 1.6 \times 10^{-14} \)
Subject: Chemistry
The molecular orbital configuration of
\( C N^{+} \) is :
\( \mathbf{A} \cdot K K \sigma(2 s)^{2}, \sigma^{*}(2 s)^{2}, \pi\left(2 p_{x}\right)^{2}, \pi\left(2 p_{y}\right)^{2} \)
B . \( K K \sigma(2 s)^{2}, \sigma^{*}(2 s)^{2}, \sigma\left(2 p_{z}\right)^{2}, \pi\left(2 p_{x}\right)^{1}, \pi\left(2 p_{y}\right)^{1} \)
C \( \cdot K K \sigma(2 s)^{2}, \sigma^{*}(2 s)^{2}, \sigma\left(2 p_{z}\right)^{2}, \pi\left(2 p_{x}\right)^{2}, \pi\left(2 p_{y}\right)^{1} \)
D. \( K K \sigma(2 s)^{2} \sigma^{*}(2 s)^{2}, \sigma\left(2 p_{z}\right)^{2} \pi\left(2 p_{x}\right)^{2}, \pi\left(2 p_{y}\right)^{2} \)
Subject: Chemistry
Sodium fusion extract, obtained from
aniline, on treatment with iron (II)
sulphate and \( H_{2} S O_{4} \) in presence of air
gives a prussian blue precipitate. The blue colour is due to the formation of:
\( \mathbf{A} \cdot F e_{4}\left[F e(C N)_{6}\right]_{3} \)
B. \( F e_{3}\left[F e(C N)_{6}\right]_{2} \)
\( \mathbf{c} \cdot F e_{4}\left[F e(C N)_{6}\right]_{2} \)
D. \( F e_{3}\left[F e(C N)_{6}\right]_{3} \)
Subject: Physics
A flat circular coil of \( n \) turns, area \( A \) and resistance \( \boldsymbol{R} \) is placed in a uniform
magnetic field \( B \). The plane of coil is
initially perpendicular to \( B \). When the
coil is rotated through an angle of \( 180^{\circ} \)
about one of its diameter, a charge \( Q_{1} \)
flows through the coil. When the same
coil after being brought to its initial position, is rotated through an angle of
\( 360^{\circ} \) about the same axis a charge \( Q_{2} \)
flows through it. Then \( Q_{2} / Q_{1} \)
A . 1
B . 2
c. \( 1 / 2 \)
D.
Subject: Chemistry
The correct order of volalitity is:
\( \mathbf{A} \cdot N H_{3}<H_{2} O \)
B. p-nitro phenol < o-nitro phenol
\( \mathbf{c} \cdot C H_{3} O H>C H_{3}-O-C H_{3} \)
D. \( H F>H C l \)
Subject: Physics
The angular velocity of the earth with
which it has to rotate so that the
acceleration due to gravity on \( 60^{\circ} \)
latitude becomes zero is
A . \( 2.5 \times 10^{-3} r a d / s \)
В. \( 1.5 \times 10^{-3} r a d / s \)
C \( .4 .5 \times 10^{-3} \mathrm{rad} / \mathrm{s} \)
D. \( 0.5 \times 10^{-3} \mathrm{rad} / \mathrm{s} \)
Subject: Physics
A steel rod of length \( 1 \mathrm{m} \) is heated from
\( 25^{\circ} \) to \( 75^{\circ} \mathrm{C} \) keeping its length constant. The longitudinal strain developed in the rod is (Given coefficient of linear expansion of stee \( \left.=12 \times 10^{-6} /^{\circ} C\right) \)
A. \( 6 \times 10^{-4} \)
В. \( -6 \times 10^{-5} \)
c. \( -6 \times 10^{-4} \)
D. zero
Subject: Chemistry
\( \mathrm{CaCl}_{2} \) is preferred over \( \mathrm{NaCl} \) for clearing ice on roads on particularly in very cold countries. This is because:
A \( \cdot C a C l_{2} \) is not soluble in \( H_{2} O \) than \( N a C l \)
B . \( C a C l_{2} \) is hygroscopic but \( N a C l \) is not
c. eutectic mixture of \( C a C l_{2} / H_{2} O \) freezes at \( -55^{\circ} C \) while that of \( N a C l / H_{2} O \) freezes at \( -18^{\circ} C \)
D. \( N a C l \) makes the road slippery but \( C a C l_{2} \) does not
Subject: Chemistry
Watch column A mame or the
Scientists) with column B (their
contributions towards the
understanding of the atomic structure).
Column A Column \( \mathbf{B} \)
A. Ernest Rutherford
1. Indivisibility of atoms
B. J.J Thompson
2. Stationary orbits
C. Dalton
3. Concept of nucleus
D. Neils Bohr
4. Discovery of electrons
E. James Chadwick
5. Atomic number
F. E Goldstein
6. Neutron
G. Moseley \( \quad \) 7. Canal rays
\( \mathbf{A} \cdot A \rightarrow 3, B \rightarrow 4, C \rightarrow 1, D \rightarrow 2, E \rightarrow 6, F \rightarrow 7, G \rightarrow 5 \)
\( \mathbf{B} \cdot A \rightarrow 3, B \rightarrow 4, C \rightarrow 6, D \rightarrow 2, E \rightarrow 1, F \rightarrow 5, G \rightarrow 5 \)
\( \mathbf{C} \cdot A \rightarrow 3, B \rightarrow 4, C \rightarrow 1, D \rightarrow 2, E \rightarrow 6, F \rightarrow 5, G \rightarrow 5 \)
\( \mathbf{D} \cdot A \rightarrow 3, B \rightarrow 4, C \rightarrow 1, D \rightarrow 2, E \rightarrow 5, F \rightarrow 7, G \rightarrow 6 \)
Subject: Chemistry
Identify the balanced chemical reaction of sodium chloride and sulphuric acid:
A \( \cdot 2 N a C l+H_{2} S O_{4} \rightarrow N a_{2} S O_{4}+2 H C l \)
в. \( 2 N a C l+H_{2} S O_{4} \rightarrow 2 N a_{2} S O_{4}+2 H C l \)
c. \( 2 N a C l+2 H_{2} S O_{4} \rightarrow N a_{2} S O_{4}+2 H C l \)
D. \( 2 \mathrm{NaCl}+\mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow 2 \mathrm{Na}_{2} \mathrm{SO}_{4}+3 \mathrm{HCl} \)
Subject: Chemistry
Which one of the following metals can not be extracted by using Al as a reducing agent
A. \( N a \) from \( N a_{2} O \)
B. \( C r \) from \( C r_{2} O_{3} \)
c. \( M n \) from \( M n O_{2} \)
D. Fe from \( F e_{2} O_{3} \)
Subject: Maths
Give examples of polynomials \( \boldsymbol{p}(\boldsymbol{x}), \boldsymbol{g}(\boldsymbol{x}), \boldsymbol{q}(\boldsymbol{x}) \) and \( \boldsymbol{r}(\boldsymbol{x}), \) which satisfy
the division algorithm and
(i) \( \operatorname{deg} p(x)=\operatorname{deg} q(x) \)
(ii) \( \operatorname{deg} \boldsymbol{q}(\boldsymbol{x})= \)
\( \operatorname{deg} r(x) \) (iii) \( \operatorname{deg} r(x)=0 \)
Subject: Physics
If a galvanometer has full scale
deflection current \( I_{G} \) and resistance \( G \)
A shunt resistance \( R_{A} \) is used to
convert it into an ammeter of range \( \boldsymbol{I}_{\mathbf{0}} \)
and a resistance \( R_{V} \) is connected in series to convert it into a voltmeter of
range \( V_{0} \) such that \( V_{0}=I_{0} G \) then
\( R_{A} R_{V} \) and \( \frac{R_{A}}{R_{V}} \) respectively are
\( ^{\mathbf{A}} \cdot G^{2} \) and \( \frac{I_{G}^{2}}{\left(I_{0}-I_{G}\right)^{2}} \)
в. \( G^{2} \) and \( \frac{I_{0}^{2}}{\left(I_{0}-I_{G}\right)^{2}} \)
\( ^{\mathrm{c}} \cdot G^{2} \) and \( \frac{I_{G}}{\left(I_{0}-I_{G}\right)^{2}} \)
D. \( G^{2} \) and \( \frac{I_{G}^{2}}{\left(I_{0}+I_{G}\right)^{2}} \)
Subject: Maths
Find the shortest distance between the
line \( \boldsymbol{x}=\mathbf{1}+\boldsymbol{t}, \boldsymbol{y}=\mathbf{1}+\boldsymbol{6} \boldsymbol{t}, \boldsymbol{z}=\boldsymbol{2} \boldsymbol{t}, \boldsymbol{t} \in \boldsymbol{R} \)
and \( \boldsymbol{x}=\mathbf{1}+\mathbf{2 k}, \boldsymbol{y}=\mathbf{5}+\mathbf{1 5 k}, \boldsymbol{z}= \)
\( -2+6 k, k \in R \)
Subject: Maths
Let \( f(x) \) be a continuous function which satisfies \( \boldsymbol{f}\left(\boldsymbol{x}^{2}+\mathbf{1}\right)=\frac{\mathbf{2}}{\boldsymbol{f}\left(\mathbf{2}^{x}\right)-\mathbf{1}} \boldsymbol{\&} \)
\( \boldsymbol{f}(\boldsymbol{x})>\mathbf{0} \forall \boldsymbol{x} \varepsilon \boldsymbol{R} \) Then \( \lim _{\boldsymbol{x} \rightarrow \mathbf{1}} \boldsymbol{f}(\boldsymbol{x}) \) is
\( A \cdot 4 \)
B. 2
\( c \)
D. does not exist
Subject: Physics
An object of radius 'R' and mas 'M' is rolling horizontally without slipping with speed 'V'. It the rolls up the hill to a
maximum height \( \boldsymbol{h}=\mathbf{3} \boldsymbol{v}^{2} / \mathbf{4} \boldsymbol{g} \). The
moment of inertia of the object is:
(ge eceleration due to gravity)
\( ^{\mathbf{A}} \cdot \frac{2}{5} M R^{2} \)
в. \( \frac{M R^{2}}{2} \)
c. \( M R^{2} \)
D. \( \frac{3}{2} M R^{2} \)
Subject: Maths
At an extreme point of a function \( \boldsymbol{f}(\boldsymbol{x}) \)
the tangent to the curve is
A. Parallel to the \( x \) -axis
B. Perpendicular to the \( x \) -axis
c. Inclined at an angle \( 45^{\circ} \) to the \( x \) -axis
D. Inclined at an angle \( 60^{\circ} \) to the \( x \) -axis
Subject: Maths
Let \( S \) be the set of all real numbers
except -1 and let \( ^{\prime} *^{\prime} \) be an operation defined by \( a * b=a+b+a b \) for al
\( a, b \in S . \) Determine whether \( ^{\prime} *^{\prime} \) is a
binary operation on \( S . \) If yes, check its commutativity and associativity. Also, solve the equation \( (2 * x) * 3=7 \)
Subject: Physics
What are the individual currents
through the resistor in the circuit
pictured above?
A \( \cdot I_{1}=5 A, I_{2}=4.4 A \) and \( I_{3}=6 A \)
B . \( I_{1}=2 A, I_{2}=2.4 A \) and \( I_{3}=3 A \)
\( \mathrm{c} \cdot I_{1}=4 A, I_{2}=2.4 \mathrm{A} \) and \( I_{3}=6 \mathrm{A} \)
D. \( I_{1}=2.4 A, I_{2}=4 A \) and \( I_{3}=6 A \)
\( A \)
Subject: Chemistry
Which has the highest freezing point?
A \( \cdot \operatorname{lm} K_{4}\left[F e(C N)_{6}\right] \quad \) solution
B. \( 1 m C_{6} H_{12} O_{6} \) solution
c. \( 1 m K C l \) solution
D. \( 1 m \) rock salt solution
Subject: Maths
Consider \( \boldsymbol{f}: \boldsymbol{N} \rightarrow \boldsymbol{N}, \boldsymbol{g}: \boldsymbol{N} \rightarrow \boldsymbol{N} \)
defined as \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{2} \boldsymbol{x}, \boldsymbol{g}(\boldsymbol{x})=\mathbf{3} \boldsymbol{x}+\boldsymbol{4} \)
find \( \boldsymbol{f} \boldsymbol{o} \boldsymbol{g}(\boldsymbol{x}) \)
Subject: Chemistry
Water exists both as solid and liquid at:
A \( \cdot 100^{\circ} \mathrm{C} \)
В. \( 50^{\circ} \) С
c. \( 2.5^{\circ} \mathrm{C} \)
D. \( 0^{\circ} \mathrm{C} \)
E \( .-10^{\circ} \mathrm{C} \)
Subject: Physics
One end of a uniform rod having mass \( \mathrm{m} \) and length \( l \) is hinged. The rod is
placed on a smooth horizontal surface and rotates on it about the hinged end
at a uniform angular velocity \( \omega . \) The
force exerted by the hinge on the rod has a horizontal component equal to:
\( \mathbf{A} \cdot m \omega^{2} l \)
B. Zero
\( \mathrm{c} \cdot \mathrm{mg} \)
D \( \cdot \frac{1}{2} m \omega^{2} \)
Subject: Chemistry
Assertion
Aqueous solution of \( N a O X \) is alkaline.
Reason
It is a salt of weak acid \( (\boldsymbol{H} \boldsymbol{O} \boldsymbol{X}) \) are
strong base \( (N a O H) \)
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
A body of mass \( M \) (figure shown above)
with a small disc of mass \( m \) placed on it rests on a smooth horizontal plane. The disc is set in motion in the
horizontal direction with velocity \( v . \) The
height (relative to the initial level) to
which the disc rise after breaking off
the body \( M \) is given as \( h= \) \( \frac{M v^{2}}{x g(M+m)} . \) The friction is assumed to
be absent. Find ' \( x \) '.
Subject: Physics
A projectile is launched vertically upward. It explodes into two pieces at the top point of its trajectory. One piece has twice the mass of the other.
Immediately after the explosion,
the more massive piece has
kinetic energy \( \boldsymbol{E} \). What is the total
kinetic energy of both pieces immediately after the explosion?
\( \mathbf{A} \cdot 1.5 E \)
B. \( 2 E \)
\( c .3 E \)
D. not enough information to answer
E. Answer required
Subject: Maths
One factor of \( \Delta= \)
\( \left|\begin{array}{ccc}a^{2}+\lambda & a b & a c \\ a b & b^{2}+\lambda & c b \\ c a & c b & c^{2}+\lambda\end{array}\right| \)
\( A \cdot \lambda^{2} \)
B. \( 1 / \lambda \)
c. \( \left(a^{2}+\lambda\right)\left(b^{2}+\lambda\right)\left(c^{2}+\lambda\right) \)
D. none
Subject: Maths
\( 5 \% \) income of \( A \) is equal to \( 15 \% \) income of \( \mathrm{B} \) and \( 10 \% \) income of \( \mathrm{B} \) is equal to \( 20 \% \) income of \( C . \) If the income of \( C \) is
Rs.2000, then find the total income of \( A \)
B and C.
Subject: Biology
Bucket handle movements is seen in
\( \mathbf{A} \cdot 1^{s t} \) rib
B. \( 3^{r d} \) rib to \( 5^{t h} \) rib
c. \( 6^{t h} \) rib to \( 10^{t h} \) rib
D. \( 11^{t h} \) and \( 12^{t h} \) rib
Subject: Maths
If \( S_{n}=n P+\frac{n(n-1) Q}{2}, \) where \( S n \)
denotes the sum of the first \( n \) terms of
an \( A P, \) then the common difference is
\( \mathbf{A} \cdot P+Q \)
в. \( 2 P+3 Q \)
c. \( 2 Q \)
D. \( Q \)
Subject: Chemistry
An ideal gas is filled in a closed rigid and thermally insulated container. A
coil of \( 100 \Omega \) resistor carrying current
1 A for 5 min supplies heat to the gas.
The change in internal energy of the gas is
A. \( 10 k J \)
B. \( 30 k J \)
c. \( 20 k J \)
D. \( 0 k J \)
Subject: Maths
Assertion \( \operatorname{Let} \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{0} & \boldsymbol{c} & -\boldsymbol{b} \\ -\boldsymbol{c} & \boldsymbol{0} & \boldsymbol{a} \\ \boldsymbol{b} & \boldsymbol{-} \boldsymbol{a} & \boldsymbol{0}\end{array}\right] \) and \( \boldsymbol{t} \in \boldsymbol{C} \)
\( \boldsymbol{a} \boldsymbol{d} \boldsymbol{j}(\boldsymbol{t} \boldsymbol{I}-\boldsymbol{A})=\boldsymbol{t}^{2} \boldsymbol{I}+\boldsymbol{t} \boldsymbol{A}+\boldsymbol{A}^{2}+\left(\boldsymbol{a}^{2}+\right. \)
\( \left.b^{2}+c^{2}\right) I \)
Reason
\( \boldsymbol{a} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A}=\boldsymbol{A}^{2}+\left(\boldsymbol{a}^{2}+\boldsymbol{b}^{2}+\boldsymbol{c}^{2}\right) \boldsymbol{I} \)
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
Given \( A \) -B-C the co-ordinate of point \( A \) is the smallest.lf \( \mathrm{d}(\mathrm{A}, \mathrm{B})=7.5, \mathrm{d}(\mathrm{B}, \mathrm{C}):=13,8 \)
and the coordinate of point \( \mathrm{B} \) is \( 8.5, \) then find the coordinates of points \( A \) and \( C \)
\( A \cdot A \leftrightarrow 0, C \leftrightarrow 63.2 \)
B. \( A \leftrightarrow 5, C \leftrightarrow 40 \)
\( \mathrm{c} \cdot \mathrm{A} \leftrightarrow 1, \mathrm{C} \leftrightarrow 22.3 \)
D. \( A \leftrightarrow 3, C \leftrightarrow 18 \)
Subject: Chemistry
For the Daniel cell involving the cell reaction \( Z n_{(s)}+C u_{(a q)}^{+2} \rightleftharpoons \)
\( Z n^{+2}_{(a q)}+C u_{(s)} \) the standard free
energies of formation of \( Z n_{(s)}, C u_{(s)} \) \( C u_{(a q)}^{+2} \) and \( Z n_{(a q)}^{+2} \) are 0,0,64.4
KJ/Mole and -154.0 KJ/Mole,
respectively. Calculate the standard
EMF of the cell?
A. 2.13 Volts
B. 1.13 Volts
c. \( 2.26 \mathrm{Volts} \)
D. 3.42Volts
Subject: Physics
(a) Write the principle of working of a metre bridge.
(b) In a metre bridge, the balance point
is found at a distance \( l_{1} \) with
resistances \( \mathrm{R} \) and \( \mathrm{S} \) as shown in the
figure. An unknown resistance X is now
connected in parallel to the resistance
and the balance point is found at a
distance \( l_{2} . \) Obtain a formula for \( X \) is
terms of \( l_{1}, l_{2} \) and \( s \)
Subject: Physics
Select and write the most appropriate answer from the given alternatives for the following:A particle rotates in U.C.M. with tangential velocity \( v \) along a horizontal circle of diameter \( D \). Total
angular displacement of the particle in
time 't' is
A. \( v t \)
B. \( \left(\frac{v}{D}\right)-t \)
c. \( \frac{v t}{2 D} \)
D. \( \frac{2 v t}{D} \)
Subject: Physics
A resistance of \( 2 \Omega \) is connected across
one gap of a metre-bridge (the length of the wire is \( 100 \mathrm{cm} \) ) and an unknown
resistance, greater than \( 2 \Omega \), is connected across the other gap. When these resistance are interchanged, the balance point shifts by \( 20 \mathrm{cm} \) Neglecting any corrections, the unknown resistance is
A. \( 3 \Omega \)
в. \( 4 \Omega \)
\( c \cdot 5 \Omega \)
D. \( 6 \Omega \)
Subject: Biology
The leaves are modified into tendrils,
hooks, pitcher and bladder in the following plants respectively.
A. Sweet pea, cat's nail, Nepenthes, Utricularia
B. Sweet pea, cat's nail, Utricularia, Nepenthes
c. Nepenthes, cat's nail, sweet pea, Utricularia
D. Nepenthes, sweet pea, cat's nail, Utricularia
E. Utricularia, Nepenthes, cat's nail, sweet pea
Subject: Chemistry
The compound B formed in the sequence of reaction, \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{O H} \stackrel{\boldsymbol{P C l}_{5}}{\longrightarrow} \boldsymbol{A} \frac{\text {alcoholic}}{\boldsymbol{K O H}} \boldsymbol{B} \)
is:
A. Propene
B. Propyne
C. Propane
D. Propanol
Subject: Maths
\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{- 5} & \mathbf{7} \\ \mathbf{0} & \mathbf{7} & \mathbf{9} \\ \mathbf{1 1} & \mathbf{8} & \mathbf{9}\end{array}\right], \) then trace of
matrix A is.
A . 17
B. 25
\( c .3 \)
D. 12
Subject: Physics
1 kg of water is converted into steam at
the same temperature and at 1 atm (100
kPa). The density of water and steam
are \( 1000 \mathrm{kgm}^{-3} \) and \( 0.6 \mathrm{kgm}^{-3} \)
respectively. The latent heat of
vaporisation of water is \( 2.25 \times \) \( 10^{6} J k g^{-1} . \) What will be increase in
energy?
A \( .3 \times 10^{5} J \)
В . \( 4 \times 10^{6} J \)
c. \( 2.08 \times 10^{6} J \)
D. None of these
Subject: Maths
Evaluate: \( \int \frac{x^{2}+1}{x^{4}+1} d x \) equals
A. \( \frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{x^{2}-1}{\sqrt{2} x}\right)+C \)
B. \( \frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{1-x^{2}}{\sqrt{2} x}\right)+C \)
c. \( \frac{1}{2} \tan ^{-1}\left(\frac{x^{2}-1}{\sqrt{2} x}\right)+C \)
D. \( \frac{1}{2} \tan ^{-1}\left(\frac{1-x^{2}}{\sqrt{2} x}\right)+C \)
Subject: Chemistry
\( S^{-2} \) is isoelectronics with \( x^{+2} . \) If an
atom of \( x \) contain \( (z+2) \) neutrons then
find no. of \( e^{-}, p \) and \( n \) in \( x \) and \( x^{+2} .(z= \)
Atomic no)
Subject: Physics
A thin wire of length \( 2 m \) is
perpendicular to the \( x-y \) plane. It is
moved with velocity \( \overrightarrow{\boldsymbol{v}}=(2 \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}+ \)
\( \hat{k}) m / s \) through a region of magnetic induction \( \vec{B}=(\hat{i}+2 \hat{j}) W b / m^{2} . \) Then
potential difference induced between the ends of the wire is
A . \( 2 V \)
B. \( 4 V \)
\( c .0 V \)
D. none of these