AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Assertion: Two \( \Delta \) s are said to be
congruent if two sides and an angle of the one triangle are respectively equal to the two sides and an angle of the other triangle.

Reason: Two \( \Delta \) s are congruent if two sides and the included angle of the one
triangle are equal to the corresponding two sides and included angle of the other triangle.

Two statements A and R are given above. Which of the following statements is correct?
A. A is false and R is the correct explanation of A
B. A is true and R is the correct explanation of a A
c. \( A \) is false and \( R \) is true
D. None of these
Subject: Maths
If the integers \( m \) and \( n \) are chosen at
random from 1 to 100 then the
probability that \( 7^{m}+7^{n} \) is divisible by
5 is \( ? \)
A. \( 1 / 5 \)
B. 1/7
c. \( 1 / 4 \)
D. 1/49
Subject: Physics
In the graph below is given the variation
of force with time. Find out the net
change in momentum of the object
A. \( 24 k g m / s \)
B. \( 22 k g m / s \)
\( \mathbf{c} .6 \mathrm{kgm} / \mathrm{s} \)
D. \( 3 k g m / s \)
Subject: Physics
The angular velocity of a body changes
fro \( \omega_{1} \) to \( \omega_{2} \) without applying a torque
but by changing the moment of inertia. The ratio of corresponding radii of
gyration \( \boldsymbol{K}_{\mathbf{1}}: \boldsymbol{K}_{\mathbf{2}} \) is
\( A \cdot \omega_{1}: \omega_{2} \)
B . \( \sqrt{\omega_{1}}: \sqrt{\omega_{2}} \)
D. \( \omega_{2}: \omega_{1} \)
Subject: Maths
The radius of a circle with centre \( \boldsymbol{P} \) is
\( 25 \mathrm{cm} \) and the length of the chord is 48 \( \mathrm{cm} . \) The distance of the chord from
centre \( P \) of the circle is
\( \mathbf{A} \cdot 24 \mathrm{cm} \)
B. \( 5 \mathrm{cm} \)
\( c .7 \mathrm{cm} \)
D. \( 12 \mathrm{cm} \)
Subject: Physics
A parallel plate condenser has circular plates, each of radius \( 5 \mathrm{cm} \). It is being charged so that electric field in the gap between its plates rises steadily at the rate of \( 10^{12} V / m s . \) What is the
displacement current?
\( \mathbf{A} \cdot 0.07 A \)
B . \( 1.39 A \)
c. \( 13.9 A \)
D. \( 139 A \)
Subject: Physics
A hair dresser stand with her nose 20
\( \mathrm{cm} \) in front of a plane mirror for what distance must she focus her eyes in
order to see her nose in the mirror?
A. \( 50 \mathrm{cm} \)
B. 30 cm
\( c .60 \mathrm{cm} \)
D. \( 40 \mathrm{cm} \)
Subject: Chemistry
Sulphur trioxide can be obtained by which of the following reaction?
\( \mathbf{A} \cdot S+H_{2} S O_{4} \stackrel{\Delta}{\rightarrow} \)
в. \( H_{2} S O_{4}+P C l_{5} \) 오
\( \mathbf{c} \cdot \operatorname{CaSO}_{4}+C \triangleq \)
D. \( F e_{2}\left(S O_{4}\right)_{3} \Delta \)
Subject: Chemistry
1 L sample of impure water containing sulphide ion is made ammonial and is
titrated with \( 300 \mathrm{mL} \) of \( 0.1 M A g N O_{3} \) solution. Which of the following statements is/are correct about the
above reaction?
This question has multiple correct options
A. The strength of \( H_{2} S \) in water is \( 0.51 \mathrm{g} / \mathrm{L} \)
B. The strength of \( H_{2} S \) in water is \( 5.1 \mathrm{g} / \mathrm{L} \)
C. The concentration of \( H_{2} \) S in water in ppm is 510
D. The concentration of \( H_{2} S \) in water in ppm is 51
Subject: Physics
Two long thin wires \( A B C \) and \( D E F \) are
arranged as shown in figure. They carry
equal current \( I \) as shown. The
magnitude of the magnetic field at \( O \) is
A. zero
в. \( \mu_{0} I / 4 \pi a \)
c. \( \mu_{0} I / 2 \pi a \)
D. \( \mu_{0} I / 2 \sqrt{2} \pi a \)
Subject: Maths
\( \int_{0}^{2 x} \sqrt{1+\sin x} d x \)
A \( \cdot \sin \frac{x}{2}-\cos \frac{x}{2}-\frac{\pi}{2}+C \)
B. \( \sin \frac{x}{2}-\cos \frac{x}{2}+\frac{\pi}{2}+C \)
c. \( 2 \sin x-2 \cos x+2 \)
D. None of these
Subject: Physics
In the Bohr's model of hydrogen atom, the electron moves around the nucleus
in a circular orbit of-radius \( 5 \times 10^{-11} \)
meters. If its time period is \( 1.5 \times 10^{-16} \)
sec, then current associated with the
electron motion is
A. zero
B. \( 1.6 \times 10^{-19} A \)
c. 0.17 А
D. \( 1.07 \times 10^{-3} A \)
Subject: Physics
Two stationary particles of masses \( \mathbf{M}_{1} \)
and \( \mathrm{M}_{2} \) are at distance d apart. A third
particle, lying on the line joining the particles, experiences no resultant gravitational force. The distance of this particle from \( \mathbf{M}_{\mathbf{1}} \) is
\( ^{\mathrm{A}} \cdot \mathrm{d}\left(\frac{\sqrt{\mathrm{M}_{2}}}{\sqrt{\mathrm{M}_{1}}-\sqrt{\mathrm{M}_{2}}}\right) \)
В. \( \mathrm{d}\left(\frac{\sqrt{\mathrm{M}_{1}}}{\sqrt{\mathrm{M}_{1}}+\sqrt{\mathrm{M}_{2}}}\right) \)
\( ^{\mathrm{c}} \cdot \mathrm{d}\left(\frac{\sqrt{\mathrm{M}_{1}}}{\sqrt{\mathrm{M}_{1}}-\sqrt{\mathrm{M}_{2}}}\right) \)
D. \( \mathrm{d}\left(\frac{\mathrm{M}_{1}}{\mathrm{M}_{1}+\mathrm{M}_{2}}\right) \)
Subject: Maths
The radius of a circle with centre 0 is 13
\( \mathrm{cm} . \) The distance of a chord from the
centre is \( 5 \mathrm{cm} . \) Find the length of the chord.
\( \mathbf{A} \cdot 24 \mathrm{cm} \)
B. \( 12 \mathrm{cm} \)
\( \mathrm{c} \cdot 13 \mathrm{cm} \)
D. \( 26 \mathrm{cm} \)
Subject: Physics
A parallel plate capacitor has a
capacity \( 80 \times 10^{-6} F \) when air is
present between the plates. The volume between the plates is then completely
filled with a dielectric slab of dielectric
constant \( 20 . \) The capacitor is now connected to a battery of \( 30 \mathrm{V} \) by wires. The dielectric slab is then removed.
Then, the charge that passes now through the wire is :
A \( \cdot 45.6 \times 10^{-3} C \)
B . \( 25.3 \times 10^{-3} C \)
C. \( 120 \times 10^{-3} C \)
D. \( 12 \times 10^{-3} C \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{p}|\sin \boldsymbol{x}|+\boldsymbol{q} e^{|\boldsymbol{x}|}+\boldsymbol{r}|\boldsymbol{x}|^{3} \) and if
\( f(x) \) is differentiable at \( x=0, \) then
A \( \cdot p=q=r=0 \)
B. \( p+q=0 ; r \) is any real number
c. \( q+r=0 ; p \) is any real number
D. \( r=0 ; p=0, q \) is any real number
Subject: Maths
If \( \vec{n} \) is a unit vector in the direction of
the vector \( \vec{A}, \) then:
\( \mathbf{A} \cdot \vec{n}=|\vec{A}| / \vec{A} \)
В . \( \vec{n}=\vec{n} \times \vec{n} \)
C \( \cdot \vec{n}=\vec{A} /|\vec{A}| \)
D . \( \vec{n}=\vec{A}|\vec{A}| \)
Subject: Physics
An equilateral triangle frame PQR of
mass \( \mathrm{M} \) and side a is kept under the
influence of magnetic force due to inward perpendicular magnetic field B and gravitational field as shown in the
figure.The magnitude and direction of current in the frame so that the frame
remains at rest is
\( A \)
\[
I=\frac{2 M g}{a B} ; \text { anticlockwise }
\]
в.
\[
I=\frac{2 M g}{a B} ; \text { clockwise }
\]
\( c \)
\[
I=\frac{M g}{a B} ; \text {anticlockwise}
\]
\( D \)
\[
I=\frac{M g}{a B} ; \text { clockwise }
\]
Subject: Maths
If the vertices of a \( \Delta A B C \) are \( A= \)
\( (1,-1,-3), B=(2,1,-2) \) and \( C= \)
(-5,2,-6) then the length of the
internal bisector of angle \( \boldsymbol{A} \) is
A \( \cdot \frac{3 \sqrt{10}}{2} \)
в. \( \frac{3 \sqrt{10}}{5} \)
c. \( \frac{3 \sqrt{10}}{7} \)
D. \( \frac{3 \sqrt{10}}{4} \)
Subject: Chemistry
The hardness of water caused by 0.25
moles of \( M g C l_{2} \) is equal to :
1) the hardness of water caused by 25
grams of \( \boldsymbol{C a} \boldsymbol{C O}_{3} \)
II) the hardness of water caused by 0.25
moles of \( \boldsymbol{C a C O}_{3} \)
III) the hardness of water caused by 1
moles of \( \boldsymbol{C a} \boldsymbol{C O}_{3} \)
A. only II is correct.
B. I and II are correct.
c. I and III are correct.
D. only I is correct.
Subject: Maths
ff \( (x)=3 e^{x^{2}}, \) then \( f^{\prime}(x)-2 x f(x)+ \)
\( \frac{1}{3} f(0)-f^{\prime}(0) \) is equal to
A.
B.
\( \mathrm{c} \cdot \frac{7}{3} \mathrm{e}^{x} \)
D. ex \( ^{x^{2}} \)
Subject: Physics
Two point charges, each of charge \( q, \) are
placed at a separation of \( 2 a \). The
electric potential at their midpoint will
be :
A. zero
в. \( \frac{q}{2 \pi \varepsilon_{0} a} \)
c. \( \frac{q}{8 \pi \varepsilon_{0} a} \)
D. \( \frac{q}{2 \pi \varepsilon_{0} a^{2}} \)
Subject: Physics
Three voltmeters, all having different resistances, are joined as shown.When some potential difference is applied \( \operatorname{across} A \) and \( B, \) their readings are
\( \boldsymbol{V}_{1}, \boldsymbol{V}_{2}, \boldsymbol{V}_{3} \)
A \( \cdot V_{1}=V_{2} \)
B. \( V_{1} \neq V_{2} \)
c. \( V_{1}+V_{2}=V_{3} \)
D. \( V_{1}+V_{2}>V_{3} \)
Subject: Chemistry
A gaseous carbon compound is soluble in dilute HCI. The solution on treating
with \( N a N O_{2} \) gives off nitrogen leaving
behind a solution which smells of wood
spirit. The carbon compound is :
A. \( H C H O \)
в. \( C O \)
c. \( C_{2} H_{5} N H_{2} \)
D. \( C H_{3} N H_{2} \)
Subject: Physics
A straight road has two sections \( A B \) (highly rough) and \( B C( \) slightly rough),a body of mass m rolling without friction in \( A B \) at \( t=0 . \) After some time it enters
the section \( B C \) then in this section,
A . friction start acting
B. pure rolling in BC
C. forward slipping takes place
D. none of the above
Subject: Maths
If \( \tan \alpha=\frac{m}{m+1} \) and \( \tan \beta=\frac{1}{2 m+1} \)
find the possible values of \( (\boldsymbol{\alpha}+\boldsymbol{\beta}) \)
\( A \cdot 30 \)
B. 90
\( c \cdot 60 \)
D. \( 45^{\circ} \)
Subject: Chemistry
\( C a C_{2} \stackrel{H_{2} O}{N H_{4} C l} \frac{C u_{2} C l_{2}}{(2) M g / \text { ether }} B \frac{(1) 1 \text { eqv. } H C l}{(3) C O_{2} / H_{2} O / H^{+}} C \)
In above reaction product \( (C) \) is?
\( \mathbf{A} \cdot C H_{2}=C H-C O O H \)
\( \mathbf{B} \cdot H C \equiv C-C O O H \)
c. \( H O O C-C \equiv C-C O O H \)
\( \mathbf{D} \cdot C H_{2}=C H-\underset{\cot }{C}=C H_{2} \)
Subject: Maths
Let \( S(\alpha)=\left\{(x, y): y^{2} \leq x, 0 \leq x \leq \alpha\right\} \)
and \( A(\alpha) \) is area of the region \( S(\alpha) . \) If
for a \( \lambda, 0<\lambda<4, A(\lambda): A(4)=2: 5 \)
then \( \lambda \) equals
\( ^{\mathrm{A}} \cdot\left(\frac{4}{25}\right)^{\frac{1}{3}} \)
\( ^{\mathrm{B}} 4\left(\frac{4}{25}\right)^{\frac{1}{3}} \)
\( ^{c} \cdot\left(\frac{2}{5}\right)^{\frac{1}{3}} \)
\( ^{\mathrm{D}} 4\left(\frac{2}{5}\right)^{\frac{1}{3}} \)
Subject: Physics
An electron moving in a circular orbit of radius r makes n rotations per second. The magnetic field produced at the centre has magnitude
\( ^{\mathrm{A}} \cdot \frac{\mu_{o} n^{2} e}{r} \)
в. \( \frac{\mu_{o} n e}{2 r} \)
c. \( \frac{\mu_{o} n e}{2 \pi r} \)
D. zero
Subject: Chemistry
Arrange the following species in the correct order of their stability.
\( \boldsymbol{C}_{2}, \boldsymbol{L} \boldsymbol{i}_{2}, \boldsymbol{O}_{2}^{+}, \boldsymbol{H} \boldsymbol{e}_{2}^{+} \)
A \( \cdot L i_{2}<H e_{2}^{+}<O_{2}^{+}<C_{2} \)
B. \( C_{2}<O_{2}^{+}<L i_{2}<H e_{2}^{+} \)
\( \mathbf{c} \cdot H e_{2}^{+}<L i_{2}<C_{2}<O_{2}^{+} \)
D. \( O_{2}^{+}<C_{2}<L i_{2}<H e_{2}^{+} \)
E \( \cdot C_{2}<L i_{2}<H e_{2}^{+}<O_{2}^{+} \)
Subject: Maths
If \( 2 a+3 b+6 c=0, \) then at least one
root of the equation \( \boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{c}=\mathbf{0} \)
lies in the interval
\( \mathbf{A} \cdot(0,1) \)
B \( \cdot(1,2) \)
\( \mathbf{c} \cdot(2,3) \)
D \( \cdot(-1,0) \)
Subject: Chemistry
Washing soda \( \left(N a_{2} C O_{3} .10 H_{2} O\right) \) is widely used in softening of hard water. If 1 L of hard water requires 0.0286 g of
washing soda, the hardness of \( C a C O_{3} \) in ppm is :
A . 10
B. 5
c. 8
D. 6
Subject: Physics
A body of mass \( \mathrm{M} \) is kept on a rough horizontal surface (friction coefficient =
\( \mu \) ). A person is trying to pull the body by applying a horizontal force but the body is not moving. The force by the surface on A is F where
A. \( F=M g \)
в. \( F=\mu M g \)
c. \( M g \leq F \leq M g \sqrt{1+\mu^{2}} \)
D. \( M g \geq F \geq M g \sqrt{1-\mu^{2}} \)
Subject: Physics
Two plane mirrors are parallel to each other and spaced \( 20 \mathrm{cm} \) apart. \( \mathrm{A} \) luminous point is placed between them at a distance \( 5 \mathrm{cm} \) from one mirror
Determine the distances of the first
nearest images from each other.
A . 10
B. 70
\( c .35 \)
D. 40
Subject: Physics
A car is travelling on a straight road. The maximum velocity the car can
attains is \( 24 m s^{-1} . \) The maximum
acceleration and deceleration it can
attain are \( 1 m s^{-2} \) and \( 4 m s^{-2} \)
respectively. The shortest time the car
takes from rest to rest in a distance of
\( 500 \mathrm{m} \) is
A . 22.4
B. 30 s
c. \( 11.2 \mathrm{s} \)
D. 35.8 s
Subject: Physics
Assertion
The terms action and reaction in the
third law of motion stand for
simultaneous mutual forces between a
pair of bodies.
Reason
In this contex action always precede or
cause reaction.
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
An organic compound of mass 0.39
gave \( 50 \mathrm{ml} \) nitrogen at \( 27^{0} \mathrm{C} \) and \( 715 \mathrm{mm} \)
pressure. The \( \% \) of nitrogen in the compound is:
A. 17.83
B. 50
\( c \cdot 25 \)
D. 20
Subject: Maths
Let \( \alpha \) and \( \beta \) be the roots of the equation \( x^{2}-\left(1-2 a^{2}\right) x+\left(1-2 a^{2}\right)=0 . \) Under
what condition does the given equation have real roots.
A \( \cdot a^{2}<\frac{1}{2} \)
B. \( a^{2}>\frac{1}{2} \)
\( c \cdot a^{2} \leq \frac{1}{2} \)
D. \( a^{2} \geq \frac{1}{2} \)
Subject: Maths
The asymptotes of a hyperbola \( 4 x^{2}- \)
\( 9 y^{2}=36 \) are
A. \( 2 x \pm 3 y=1 \)
в. \( 2 x \pm 3 y=0 \)
c. \( 3 x \pm 2 y=1 \)
D. None
Subject: Maths
If \( y=\sqrt{x+\sqrt{x+\sqrt{x}}}+\ldots . \infty, \) then
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=? \)
A. \( \frac{1}{y^{2}-1} \)
в. \( \frac{1}{2 y+1} \)
c. \( \frac{2 y}{y^{2}-1} \)
D. \( \frac{1}{2 y-1} \)
Subject: Physics
A particle is projected from ground with some initial velocity making an angle
\( 45^{\circ} \) with the horizontal. It reaches at
height of \( 7.5 \mathrm{m} \) above the ground while it travels a horizontal distance of \( 10 \mathrm{cm} \) from the point of projection. The initia speed of the projection is
\( A \cdot 5 m / s \)
B. \( 10 \mathrm{m} / \mathrm{s} \)
\( c \cdot 20 m / s \)
D. \( 40 \mathrm{m} / \mathrm{s} \)
Subject: Maths
Find the value of \( x, y \) and \( z \) in the
adjoining figure.
\( \mathbf{A} \cdot x=160, y=60, z=80 \)
B . \( x=60, y=80, z=40 \)
C \( . x=80, y=60, z=140 \)
D. \( x=140, y=80, z=60 \)
Subject: Maths
The area of the parallelogram ABCD is
\( 90 c m^{2}(\text { see Fig.9.13 ) EC }=F D . \) Find
\( \boldsymbol{A}(\boldsymbol{A} \boldsymbol{B} \boldsymbol{E} \boldsymbol{F}) \)
\( \mathbf{A} \cdot 45 c m^{2} \)
B. \( 60 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 90 \mathrm{cm}^{2} \)
D. \( 180 \mathrm{cm}^{2} \)
Subject: Maths
Solve the following quadratic equation by factorization, the roots are \( \boldsymbol{x}^{2}-(\sqrt{\mathbf{3}}+\mathbf{1}) \boldsymbol{x}+\sqrt{\mathbf{3}}=\mathbf{0} \)
A . 3,1
в. \( \sqrt{2}, \)
c. \( \sqrt{3}, 1 \)
D. \( \sqrt{5}, \)
Subject: Maths
If \( \boldsymbol{x}=\log _{5} \boldsymbol{3}+\log _{7} \mathbf{5}+\log _{9} \boldsymbol{7} \) then
A \( \cdot x \geq \frac{3}{2} \)
в. \( x \geq \frac{1}{\sqrt[3]{2}} \)
c. \( x \geq \frac{3}{\sqrt[3]{2}} \)
D. none of these
Subject: Physics
The coercivity of a small magnet where the ferromagnet gets demagnetised is
\( 3 \times 10^{3} A m^{-1} . \) The current required to
be passed in a solenoid of length \( 10 \mathrm{cm} \)
and number of turns \( 100, \) so that the magnet gets demagnetised when inside the solenoid, is:
A . \( 6 A \)
в. 30 тА
\( c .60 m A \)
D. \( 3 A \)
Subject: Physics
The resistance across \( \mathrm{M} \) and \( \mathrm{N} \) in the
given figure where each resistor shown
if of \( r \Omega \) is:
\( A \cdot \frac{r}{2} \)
B. \( \frac{r}{3} \)
\( c \cdot 6 r \)
D. 2r
Subject: Physics
Identify the mirrors
a)
\( \mathbf{b}) \)
A. \( a= \) Convex mirror \( b= \) Concave mirror
B. \( a= \) Concave mirror \( b= \) Convex mirror
C \( . a= \) Concave mirror \( b= \) Concave mirror
D. \( a= \) Convex mirror \( b= \) Convex mirror
Subject: Physics
Two closed vessels of the equal volume
contain air at \( 105 \mathrm{kPa} \) at \( 300 \mathrm{K} \) and are
connected through a narrow tube. If one
of the vessels is now maintained at \( 300 \mathrm{K} \)
and the other at \( 400 \mathrm{K} \) then the pressure
becomes.
A . 120kPa
B. 105kPa
c. \( 150 k P a \)
D. 300kPa
Subject: Chemistry
For the reaction, \( A \rightarrow B \), the rate law is,
rate \( =\boldsymbol{k}[\boldsymbol{A}] . \) Which of the following
statements is incorrect?
A. The reaction follows first order kinetics
B. The \( t_{1 / 2} \) of the reaction depends on initial concentration
c. \( k \) is constant for the reaction at a constant temperature.
D. The rate law provides a simple way of predicting the
of the reaction
Subject: Physics
A particle \( P \) is sliding down a frictionless hemispherical bowl. It
passes the point \( A \) at \( t=0 . \) At this
instant of time, the horizontal
component of its velocity is \( v . A \) bead \( Q \) of the same mass as \( P \) is ejected from
\( A \) at \( t=0 \) along the horizontal string
\( A B, \) with the speed \( v . \) Friction between
the bead and the string may be
neglected. Let \( t_{p} \) and \( t_{q} \) be the respective times taken by \( P \) and \( Q \) to reach the
point \( \boldsymbol{B} \). Then
\( \mathbf{A} \cdot t_{p}<t_{q} \)
B . \( t_{p}=t_{q} \)
\( c \cdot t_{p}>t_{q} \)
D. \( _{t_{p} / t_{q}}=\frac{\text {length of are } A C D}{\text {length of cord } A B} \)
Subject: Chemistry
Using the standard half-cell potential listed, calculate the equilibrium constant for the reaction:
\( \boldsymbol{C o}(s)+\mathbf{2} \boldsymbol{H}^{+}(\boldsymbol{a q}) \longrightarrow \boldsymbol{C o}^{2+}(\boldsymbol{a q})+ \)
\( \boldsymbol{H}_{2}(\boldsymbol{g}) \quad \boldsymbol{a t} \quad \boldsymbol{2} \boldsymbol{9} \boldsymbol{8} \boldsymbol{K} \)
\( \boldsymbol{C o}^{2+}(\boldsymbol{a q})+\boldsymbol{2 e}-\longrightarrow \boldsymbol{C o}(\boldsymbol{s}) \boldsymbol{E}^{0}= \)
\( -0.277 V \)
A \( \cdot 2.3 \times 10^{9} \)
B . \( 4.8 \times 10^{4} \)
C \( .4 .8 \times 10^{7} \)
D. \( 4.8 \times 10^{11} \)
Subject: Physics
The temperature of an isolated black
body falls from \( T_{1} \) to \( T_{2} \) in time \( t, \) then \( t \)
is (Let \( c \) be a constant)
A \( \cdot t=c\left(\frac{1}{T_{2}}-\frac{1}{T_{2}}\right) \)
B \( t=c\left(\frac{1}{T_{2}^{2}}-\frac{1}{T_{1}^{2}}\right) \)
\( ^{\mathrm{c}} \cdot_{t=c}\left(\frac{1}{T_{2}^{3}}-\frac{1}{T_{1}^{3}}\right) \)
D \( t=c\left(\frac{1}{T_{2}^{4}}-\frac{1}{T_{1}^{4}}\right) \)
Subject: Maths
\( \mathbf{f}_{\mathbf{0}}=\left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{x} & \boldsymbol{y} & \boldsymbol{z} \\ \boldsymbol{p} & \boldsymbol{q} & \boldsymbol{r}\end{array}\right| \) and \( \boldsymbol{\Delta}_{2}=\left|\begin{array}{lll}\boldsymbol{y} & \boldsymbol{b} & \boldsymbol{q} \\ \boldsymbol{x} & \boldsymbol{a} & \boldsymbol{p} \\ \boldsymbol{z} & \boldsymbol{c} & \boldsymbol{r}\end{array}\right| \)
then \( \Delta_{1} \) is equal to
\( A \cdot 2 \Delta_{2} \)
в. \( \Delta_{2} \)
\( c \cdot-\Delta_{2} \)
D. none of these
Subject: Chemistry
Which is correct statement about \( \sigma- \)
and \( \pi- \) molecular orbitals? Statements
are
(i) \( \pi- \) bonding orbitals are ungerade
(ii) \( \pi- \) antibonding orbitals are
ungerade
(iii) \( \sigma- \) antibonding orbitals are gerade
\( A \cdot( \) i) only
B. (ii) and (iii) only
c. (iii) only
D. (ii) only
Subject: Maths
The differential equation of a body projected from the earth is given by \( \frac{d v}{d t}=-g-k v . \) The distance travelled by the body at any time \( t \) is given by \( x= \) \( \left(\frac{\boldsymbol{g}}{\boldsymbol{k}^{2}}+\frac{\boldsymbol{u}}{\boldsymbol{k}}\right)\left(\mathbf{1}+\boldsymbol{e}^{-\boldsymbol{k} \boldsymbol{t}}\right)-\frac{\boldsymbol{g}}{\boldsymbol{k}} \boldsymbol{t} \)
A. True
B. False
Subject: Physics
A student performs an experiment for determination of \( \boldsymbol{g}=\left[\frac{\mathbf{4} \boldsymbol{\pi}^{2} \boldsymbol{L}}{\boldsymbol{T}^{2}}\right], \boldsymbol{L}=\mathbf{1} \boldsymbol{m} \)
and he commits an error of \( \triangle L \). For The
takes the time of n oscillations with the
stopwatch of least count \( \triangle T . \) For which
of the following data, the measurement of \( g \) will be most accurate?
A. \( \triangle L=0.5, \Delta T=0.1, n=20 \)
B. \( \triangle L=0.5, \Delta T=0.1, n=50 \)
c. \( \triangle L=0.5, \Delta T=0.01, n=30 \)
D. \( \triangle L=0.5, \Delta T=0.05, n=50 \)
Subject: Biology
Select the correct statement regarding the specific disorder of muscular or
skeletal system.
A. Myastenia gravis - Auto immune disorder, which inhibits sliding of myosin filments
B. Osteoporosis - Decrease in bone mass and higher chances of fractures with advancing age
c. Gout- Inflammation of joints due to extra deposition of calcium
D. Muscular dystrophy - Age related shortening of muscles
Subject: Maths
The point of intersection of the line
joining the points (-3,4,-8) and (5,-6,4) with the \( X Y \) -plane is
\( \mathbf{A} \cdot\left(\frac{7}{3},-\frac{8}{3}, 0\right) \)
в. \( \left(-\frac{7}{3},-\frac{8}{3}, 0\right) \)
\( ^{\mathbf{c}} \cdot\left(-\frac{7}{3}, \frac{8}{3}, 0\right) \)
D. \( \left(\frac{7}{3}, \frac{8}{3}, 0\right) \)
Subject: Chemistry
Identify disproportionation reaction.
\( \mathbf{A} \cdot C H_{4}+2 O_{2} \rightarrow C O_{2}+2 H_{2} O \)
\( \mathbf{B} \cdot C H_{4}+4 C l_{2} \rightarrow C C l_{4}+4 H C l \)
\( \mathbf{c} \cdot 2 F_{2}+2 O H^{-} \rightarrow 2 F^{-}+O F_{2}+H_{2} O \)
D. \( 2 N O_{2}+2 O H^{-} \rightarrow N O_{2}^{-}+N O_{3}^{-}+H_{2} O \)
Subject: Maths
A bag contains 4 white, 5 red and 6 black balls. Three are drawn at random.
Find the probability that (i) no ball drawn is black, (ii) exactly 2 are black
(iii) all are of the same colour.
A \( \cdot \frac{12}{65}, \frac{27}{91}, \frac{6}{91} \)
В. \( \frac{12}{65}, \frac{27}{91}, \frac{24}{455} \)
c. \( \frac{12}{65}, \frac{27}{91}, \frac{14}{455} \)
D. \( \frac{12}{65}, \frac{27}{91}, \frac{34}{455} \)
Subject: Maths
Find the value of \( x \) and \( y \)
A \( \cdot 60^{\circ}, 45^{\circ} \)
B \( .45^{\circ}, 60^{\circ} \)
\( \mathbf{c} \cdot 45^{\circ}, 45 \)
D. \( 60^{\circ}, 60^{\circ} \)
Subject: Physics
A soap bubble of radius \( R \) with wall
thickness \( t \) is charged to a potential \( V_{0} \)
The bubble bursts and becomesa
spherical drop of soap solution of
radius \( r . \) Now, it has potential, \( V \)
Assume, the soap solution to be a
conductor.

Then the charge carried by the soap
bubble is :

Spherical drop
A \( \cdot 4 \pi \varepsilon_{0} R V_{0} \)
В \( \cdot 2 \pi \varepsilon_{0} R V_{0} \)
\( \mathbf{c} \cdot 4 \pi \varepsilon_{0} r V \)
D. Both (A) and (C)
Subject: Physics
A body starts from rest with uniform acceleration. If its velocity after \( \boldsymbol{n} \) seconds is \( \boldsymbol{v} \) then assuming straight line motion, its displacement in last two seconds is
A \( \cdot \frac{v(n-1)}{n} \)
B. \( \frac{2 v(n-1)}{n} \)
c. \( \frac{2 v(n+1)}{n} \)
D. \( \frac{v(n+1)}{n} \)
Subject: Physics
A block of mass m rests on a rough inclined plane. The coefficient of friction between the surface and the block if \( \mu \)
At what angle of inclination \( \theta \) of the plane to the horizontal will the block just start to slide down the plane?
A \( \cdot \theta=\tan ^{-1} \mu \)
в. \( \theta=\cos ^{-1} \mu \)
c. \( \theta=\sin ^{-1} \mu \)
D. \( \theta=s e c^{-1} \mu \)
Subject: Maths
\( f \frac{a_{0}}{n+1}+\frac{a_{1}}{n}+\frac{a_{2}}{n-1}+\dots+\frac{a_{n-1}}{2}+ \)
\( a_{n}=0, \) then the equation \( a_{0} x^{n}+ \)
\( a_{1} x^{n-1}+\cdots+a_{n-1} x+a_{n}=0 \) has, in
the interval \( (\mathbf{0}, \mathbf{1}) \)
A. Exactly one root
B. Atleast one root
c. Atmost one root
D. No root
Subject: Maths
Which of the following statement is
true?
A \( \cdot \frac{3}{-8}>\frac{-12}{32} \)
B. \( \frac{3}{-8}=\frac{-12}{32} \)
c. \( \frac{3}{-8}<\frac{-12}{32} \)
D. \( \frac{3}{5}>\frac{4}{3} \)