AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Masses of two isobars \( _{29}^{64} \mathrm{Cu} \) and \( _{30}^{64} \mathrm{Zn} \) are \( 63.9298 a m u \) and \( 63.9292 a m u \)
respectively. It can be concluded from these data that
A. Both the isobars are stable
B. \( 64 Z n \) is radioactive, decaying to \( ^{64} C u \) through \( \beta- \) decay
c. \( ^{64} C u \) is radioactive, decaying to \( ^{64} Z n \) through \( \lambda \) \( \operatorname{decay} \)
D. \( ^{64} C u \) is radioactive, decaying to \( ^{64} Z n \) through \( \beta- \) decay
Subject: Maths
Form two digit numbers using the digit
0,1,2,3,4,5 without repeating the digits.
\( P \) is the event that the number so
formed is even
\( Q \) is the event that the number so
formed is divisible by 3
\( R \) is the event that the number so
formed is greater than 50 . \( S \) is the sample space.
Which of the following options is
correct?
A \( . n(S)=25, n(P)=13, n(Q)=9, n(R)=5 \)
в. \( n(S)=25, n(P)=13, n(Q)=9, n(R)=2 \)
C. \( n(S)=25, n(P)=13, n(Q)=9, n(R)=4 \)
D. \( n(S)=25, n(P)=13, n(Q)=9, n(R)=8 \)
Subject: Physics
Q Type your question
\( +\sigma \) and \( -\sigma \) respectively are separated by a small distance. The medium
between the plates is vacuum. If \( \varepsilon_{0} \) is
the dielectric permittivity of vacuum then the electric field in the region
between the plates is :
A \( \cdot 0 \mathrm{Vm}^{-1} \)
В \( \cdot \frac{\sigma}{2 \varepsilon_{0}} V m^{-1} \)
c. \( \frac{\sigma}{\varepsilon_{0}} V m^{-1} \)
D. \( \frac{2 \sigma}{\varepsilon_{0}} V m^{-1} \)
Subject: Maths
Observations of a data are
\( \mathbf{1 6}, \mathbf{7 2}, \mathbf{0}, \mathbf{5 5}, \mathbf{6 5}, \mathbf{5 5}, \mathbf{1 0}, \) and \( \mathbf{4 1} \)
Chaitanya calculated the mode and median without taking the zero into consideration. Did Chaitanya do the right thing?
Subject: Chemistry
Equal weights of mercury and \( l_{2} \) are allowed to react completely to form a mixture of mercurous and mercuric
iodide leaving none of the reactants. Calculate the ratio of the weights of
\( H g_{2} l_{2} \) and \( H g l_{2} \) formed
A . 1: 0653
B . 0.732: 1
c. 1: 0.523
D. 0.532: 1
Subject: Physics
Find the speed of two objects if, when they move uniformly towards each other they get 4 m closer in every sec and when they move uniformly in the same direction with their original speeds,
they get \( 4 \mathrm{m} \) closer every \( 10 \mathrm{s} \)
A. \( 1.8 \mathrm{m} / \mathrm{s}, 1.6 \mathrm{m} / \mathrm{s} \)
B. 2 \( \mathrm{m} / \mathrm{s}, 1.8 \mathrm{m} / \mathrm{s} \)
c. \( 2.2 \mathrm{m} / \mathrm{s}, 1.8 \mathrm{m} / \mathrm{s} \)
D. \( 1.6 \mathrm{m} / \mathrm{s}, 1.4 \mathrm{m} / \mathrm{s} \)
Subject: Physics
Which of the following functions represent a simple harmonic motion?
\( \mathbf{A} \cdot \sin \omega t-\cos \omega t \)
B. \( \sin ^{2} \omega t \)
\( \mathbf{c} \cdot \sin \omega t+\sin ^{2} \omega t \)
D. \( \sin \omega t-\sin ^{2} \omega t \)
Subject: Chemistry
How many kilograms of wet NaOH containing \( 10 \% \) water are required to prepare 60 litre of a \( 0.5 \mathrm{M} \) solution?
A . \( 1.23 \mathrm{kg} \)
B. \( 1.13 \mathrm{kg} \)
c. \( 1.33 \mathrm{kg} \)
D. \( 1.24 \mathrm{kg} \)
Subject: Maths
Find the range and coefficient of range of the following data.
\( \mathbf{5 9}, \mathbf{4 6}, \mathbf{3 0}, \mathbf{2 3}, \mathbf{2 7}, \mathbf{4 0}, \mathbf{5 2}, \mathbf{3 5}, \mathbf{2 9} \)
A . 36,0.44
в. 32,0.44
c. 36,0.84
D. None of these
Subject: Physics
Two waves are represented by \( x_{1}= \) \( A \sin \left(\omega t+\frac{\pi}{6}\right) \) and \( x_{2}=A \cos \omega t \) then
the phase difference between them is :
A \( \cdot \frac{\pi}{6} \)
в. \( \frac{\pi}{2} \)
\( c \cdot \frac{\pi}{3} \)
D. \( \pi \)
Subject: Chemistry
On long standing, bleaching powder undergoes auto-oxidation into:
A \( \cdot C a\left(C l O_{3}\right)_{2}, C a C l_{2} \)
в. \( C a O, C a C l_{2} \)
c. \( c a C l O, C a C l O_{3} \)
D. \( C a C l O_{2}, C a C l_{2} \)
Subject: Physics
The resultant of two resistances
connected in parallel is 2 oh \( m \) and when
connected in series, the resultant
becomes 9 oh \( m \). The values of the
resistance are:
A. 7 ohm, 2 ohm
B. 11ohm, 7ohm
c. 4.5 and 8 ohm
D. 3ohm, 6ohm
Subject: Physics
An impulse is supplied to a moving
object with the force at an angle of \( 120^{\circ} \) with the velocity vector. The angle
between the impulse vector and the change in momentum vector is
A \( \cdot 120^{\circ} \)
в. \( 0^{\circ} \)
\( c \cdot 60^{0} \)
D. \( 240^{\circ} \)
Subject: Physics
A balloonist is ascending at a velocity of
\( 12 m s^{-1} . A \) packet is dropped from it
when it is at height of \( 65 m \) from the ground, it drops a packet. Time taken by the packet to reach the ground is
\( \mathbf{A} \cdot 5 s \)
B. \( -5 s \)
c. \( 7 s \)
D. \( \frac{13}{5} s \)
Subject: Maths
\( \lim _{x \rightarrow-1} \frac{\sqrt{\pi}-\sqrt{\cos ^{-1} x}}{\sqrt{x+1}} \) is equal to
\( \mathbf{A} \cdot \frac{1}{\sqrt{2 \pi}} \)
B. \( \frac{1}{\sqrt{\pi} \pi} \)
\( c \cdot \frac{1}{\sqrt{2}} \)
D. none of these
Subject: Physics
Which of the following is true regarding dimagnetic substances (symbols have their usual meaning)?
\( \mathbf{A} \cdot \mu_{r}>1, \chi_{m}>1 \)
B \( \cdot \mu_{r}>1, \chi_{m}<1 \)
\( \mathbf{c} \cdot \mu_{r}<1, \chi_{m}<0 \)
D. \( \mu_{r}<1, \chi_{m}>0 \)
Subject: Physics
The convex surface of a thin concavo-
convex lens of glass of refractive index
1.5 has a radius of curvature \( 20 \mathrm{cm} . \) The
concave surface has a radius of
curvature \( 60 \mathrm{cm} . \) The convex side is
silvered and placed on a horizontal
surface.
(i) Where should a pin be placed on the optical axis such that its image is
formed at the same place?
(ii) If the concave part is filled with
water of refractive index \( 4 / 3, \) find the distance through which the pin should
be moved so that the image of the pin again coincidence with the pin.
Subject: Physics
A body of mass 5 kg moving with a speed of \( 3 m s^{-1} \) collides head on with a
body of mass \( 3 \mathrm{kg} \) moving in the
opposite direction at a speed of \( 2 m s^{-1} \) The first body stops after the collision. Find the final velocity of the second
body.
\( \mathbf{A} \cdot 3 m s^{-1} \)
B . \( 5 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot-9 \mathrm{ms}^{-1} \)
D. \( 30 m s^{-1} \)
Subject: Physics
A source emits electromagnetic waves of wavelength \( 3 m . \) One beam reaches
the observer directly and other after reflection from a water surface, travelling 1.5 m extra distance and with intensity reduced to \( \frac{1}{4} \) as compared to
intensity due to the direct beam alone.
The resultant intensity will be.
A \( \cdot\left(\frac{1}{4}\right) \) fold
B \( \cdot\left(\frac{3}{4}\right) \) fold
c. \( \left(\frac{5}{4}\right) \) fold
D. \( \left(\frac{9}{4}\right) \) fold
Subject: Maths
In \( \Delta A B C, \angle B=30^{\circ}, \angle C=80^{\circ} \) and
\( \angle A=70^{\circ} \) then
A \( . A B>B C<A C \)
В. \( A B<B C>A C \)
c. \( A B>B C>A C \)
D. \( A B<B C<A C \)
Subject: Physics
A monkey of mass \( 40 \mathrm{kg} \) climbs on a massless rope of breaking strength 600
N. The rope will break if the monkey
\( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{\mathbf{2}}\right) \)
A. climbs up with a uniform speed of \( 5 \mathrm{m} / \mathrm{s} \)
B. climbs up with an acceleration of \( 6 m / s^{2} \)
C . climbs down with an acceleration of \( 4 \mathrm{m} / \mathrm{s}^{2} \)
D. Moves down with a uniform speed of \( 5 \mathrm{m} / \mathrm{s} \)
Subject: Physics
When a rubber-band is stretched by a
distance \( x, \) it exerts a restoring force of
magnitude \( F=a x+b x^{2} \) where \( a \) and \( b \)
are constants. The work done in stretching the unstretched rubber band
by \( \boldsymbol{L} \) is
\( ^{\mathbf{A}} \cdot \frac{a L^{2}}{2}+\frac{b L^{3}}{3} \)
B \( \cdot \frac{1}{2}\left(\frac{a L^{2}}{2}+\frac{b L^{3}}{3}\right) \)
\( \mathbf{c} \cdot a L^{2}+b L^{3} \)
D \( \cdot \frac{1}{2}\left(a L^{2}+b L^{3}\right) \)
Subject: Maths
There is \( 30 \% \) chance that it rains on any particular day. Given that there is at least one rainy day in a week, what is the probability that there are at least two rainy days in the week?
A \( \frac{1-4(0.7)^{7}}{1-(0.7)^{7}} \)
В. \( \frac{4(0.7)^{7}}{1-(0.7)^{7}} \)
c. \( \frac{1-(0.7)^{7}}{1-4 .(0.7)^{7}} \)
D. \( \frac{(0.7)^{7}}{1-4 .(0.7)^{7}} \)
Subject: Chemistry
For a reaction \( \frac{\boldsymbol{d} \boldsymbol{X}}{\boldsymbol{d} \boldsymbol{t}}=\boldsymbol{K}\left[\boldsymbol{H}^{+}\right]^{n} . \) If \( \boldsymbol{p} \boldsymbol{H} \) of
reaction medium changes from two to one, the rate becomes 100 times of the
value at \( p H=2 . \) The order of reaction
is:
\( A \)
B. 2
\( c \cdot 0 \)
D. 3
Subject: Chemistry
Assertion
Silver bromide is used in photography.
Reason

Silver bromide is used in photography
because silver bromide is
photosensitive. It decomposes and is converted into metallic silver grains
when light is incident on it.
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 10 pF parallel plate capacitor is charged with a \( 4.0 \mathrm{V} \) battery. While the capacitor is still connected to the battery, a dielectric slab ( \( k=5.0 \) ) is inserted between the plates to
completely fill the gap. How much electric potential energy is stored in the capacitor after inserting the dielectric?
\begin{tabular}{l} 
A \( .5 .3 \times 10^{-10} J \) \\
\hline
\end{tabular}
В . \( 4.0 \times 10^{-10} \mathrm{J} \)
c. \( 4.6 \times 10^{-10} J \)
D. \( 5.6 \times 10^{-10} \mathrm{J} \)
Subject: Chemistry
The relationship between the values of osmotic pressure of \( 0.1 \mathrm{M} \) solutions of \( \boldsymbol{K} \boldsymbol{N} \boldsymbol{O}_{3}\left(\boldsymbol{P}_{1}\right) \) and \( \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C O O H}\left(\boldsymbol{P}_{2}\right) \) is:
A \( \cdot P_{1}>P_{2} \)
в. \( P_{2}>P_{1} \)
\( \mathrm{c} \cdot P_{1}=P_{2} \)
D. \( \frac{P_{1}}{P_{1}+P_{2}}=\frac{P_{2}}{P_{1}+2 P_{2}} \)
Subject: Physics
A solid cylinder of mass ' \( m \) ' is kept in
balance position on a fixed incline of
angle \( \alpha=37^{\circ} \) with the help of a thread
fastened to its jacket. The cylinder does not slip. What force \( \boldsymbol{F} \) is required to
keep the cylinder in balance when the
thread is held vertically?
\( \mathbf{A} \cdot m g / 2 \)
в. \( 3 m g / 4 \)
\( \mathrm{c} .3 \mathrm{mg} / 8 \)
D. \( 5 m g / 8 \)
Subject: Physics
If a body of mass \( 5 g \) initially at rest is acted upon by a force of 50 dynes for \( 3 s \)
Then the impulse will be
A \( \cdot 0.98 \times 10^{-3} N s \)
В. \( 1.5 \times 10^{-3} N s \)
c. \( 2.0 \times 10^{-3} N s \)
D. 2.5 \( \times 10^{-3} \mathrm{Ns} \)
Subject: Chemistry
The experimental value of dis found to
be smaller than the estimate obtained
using Graham's law. This is due to:
A. larger mean free path for \( x \) as compared to that of \( Y \)
B. larger mean free path for Y as compared to that of \( x \)
C. increased collision frequency of Y with the inert gas as compared to that \( X \) with the inert gas
D. increased collision frequency of \( X \) with the inert gas as compared to that of Y with inert gas
Subject: Physics
A boy blowing a whistle, is running away from a wall towards an observer with a
speed of 1 ms \( ^{-1} \). The frequency of
whistle is \( 680 \mathrm{Hz} \). The number of beats
heard per second by the observer will be
\( \left(\operatorname{given} v=340 m s^{-1}\right) \)
A. zero
B. 2
\( c \cdot 4 \)
D. 8
Subject: Maths
n fig, \( A B C D \) is a parallelogram and
\( B C \) is produced to a point \( Q \) such that
\( \boldsymbol{A D}=\boldsymbol{C Q} . \) If \( \boldsymbol{A Q} \) intersect \( \boldsymbol{D} \boldsymbol{C} \) at \( \boldsymbol{P} \)
show that \( a r(B P C)=a r(D P Q) \)
Subject: Maths
In the sequence
\( \mathbf{1}, \mathbf{2}, \mathbf{2}, \mathbf{3}, \mathbf{3}, \mathbf{3}, \mathbf{4}, \mathbf{4}, \mathbf{4}, \mathbf{4}, \dots, \) where \( \boldsymbol{n} \)
consecutive terms have the value \( n \), the
\( 150^{t h} \) term is
A . 17
B . 16
c. 18
D. none of these
Subject: Chemistry
When 100 g of ethylene polymerizes to polyethylene according to the above given equation. The weight of polyethylene produced will be :
\[
\left.n\left(\mathrm{CH}_{2}=\mathrm{CH}_{2}\right) \rightarrow+\mathrm{CH}_{2}-\mathrm{CH}_{2}-\right)_{\pi}
\]
\( A \)
\[
\frac{n}{2} g
\]
в. \( 100 \mathrm{g} \)
\( c \)
\[
\frac{100}{n} \mathrm{g}
\]
D. \( 100 \mathrm{mg} \)
Subject: Maths
The distance between the straight lines \( \mathbf{7} \boldsymbol{x}+\mathbf{2 4} \boldsymbol{y}-\mathbf{1 3}=\mathbf{0}, \mathbf{7} \boldsymbol{x}+\mathbf{2 4} \boldsymbol{y}+\mathbf{1 2}=\mathbf{0} \)
is
\( A \cdot 1 \)
B . 2
\( c \cdot 25 \)
D. 50
Subject: Maths
Let \( f \) and \( g \) be continuous function on
\( a \leq x \leq b \) and \( \operatorname{set} p(x)=\max \)
\( \{f(x), g(x)\} \) and \( q(x)=\min \)
\( \{f(x), g(x)\}, \) the area bounded by the
curves \( \boldsymbol{y}=\boldsymbol{p}(\boldsymbol{x}), \boldsymbol{y}=\boldsymbol{q}(\boldsymbol{x}) \) and the
ordinates \( \boldsymbol{x}=\boldsymbol{a} \) and \( \boldsymbol{x}=\boldsymbol{b} \) is given by
This question has multiple correct options
A \( \cdot \int_{a}^{b}(f(x)-g(x)) d x \)
B \( \cdot \int_{a}^{b}(p(x)-q(x)) d x \)
c \( \cdot \int_{a}^{b}|p(x)-q(x)| d x \)
D \( \cdot \int_{a}^{b}|f(x)-g(x)| d x \)
Subject: Physics
A star is receding away from earth with
a velocity of \( 10^{5} m / s . \) If the wavelength of its spectral line is \( 5700 A \), then Doppler shift will be
\( A \cdot 200 \stackrel{\circ}{A} \)
B \( \cdot 1.9 A \)
c. \( 20 \stackrel{\circ}{A} \)
D. \( 0.2 \stackrel{\circ}{A} \)
Subject: Maths
Let the co - ordinates of the point where the line joining the points
(2,-3,1),(3,-4,-5) cuts the plane
\( \mathbf{2} \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\mathbf{7} \) be \( (\boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z}) . \) Find \( \boldsymbol{x}+ \)
\( \boldsymbol{y}+\boldsymbol{z} ? \)
Subject: Physics
An insulated charged conducting sphere of radius \( 5 \mathrm{cm} \) has a potential of \( 10 \mathrm{V} \) at
the surface. What is the potential at
centre?
A . \( 10 V \)
в. zero
c. same as that at \( 5 \mathrm{cm} \) from the surface
D. same as that at \( 25 \mathrm{cm} \) from the surface
Subject: Maths
If the height of a triangle is decreased by \( 40 \% \) and its base is increased by \( 40 \% \). What will be the effect on its area?
A. Decreased by \( 16 \% \)
B. Increased by \( 16 \% \)
c. Decreased by \( 20 \% \)
D. Increased by \( 20 \% \)
Subject: Chemistry
Which of the following represents the oxide of cerium?
This question has multiple correct options
A. \( C e_{3} O_{4} \)
в. \( C e O_{4} \)
\( \mathrm{c} \cdot \mathrm{Ce}_{2} \mathrm{O}_{3} \)
D. \( \operatorname{Ce} \mathrm{e}_{2} \)
Subject: Chemistry
The number of oxygen atoms in 20 gm of sulphur tri-oxide \( S O_{3} \) is the same as
these present in \( x \) gms of Ozone. The atomic mass of sulphur and oxygen are \( 32 \mu \) and \( 16 \mu \) respectively. Find the value of \( \mu .(12 \mathrm{gm}) \)
Subject: Biology
Given are some organisms.
(I) Fowl
(II) Humans (III) Grasshopper Following alphabets related to the given
animals.
Male homogametic - \( A \) Female heterogametic - \( \mathrm{B} \) Male heterogametic - \( C \) Female homogametic - D Which of the following options correctly describes the given animals in terms of sex determination?
\( A \cdot(\text { () } A, B \text { (II) } C, D \text { (III) } C, D \)
B. (I) C, D (II) A, B (III) C, D
C . (I) A, D (II) C, D (III) A, D
D. (I) B, C (II) C, D (III) A, B
Subject: Maths
Suppose \( f \) is differentiable at \( x=1 \) and \( \lim _{h \rightarrow 0} \frac{1}{h} f(1+h)=5, \) then
\( \mathbf{A} \cdot f^{\prime}(1)=4 \)
B \( \cdot f^{\prime}(1)=3 \)
\( \mathbf{c} \cdot f^{\prime}(1)=6 \)
D. None of these
Subject: Chemistry
Which of the following reactions is not used for the preparation of a colloidal solution?
A \( \cdot 2 A u C l_{3}+3 S n C l_{2} \rightarrow 3 S n C l_{4}+2 A u \)
B . \( F e C l_{3}+3 H_{2} O \longrightarrow F e(O H)_{3}+3 H C l \)
\( \mathbf{c} \cdot 2 M g+C O_{2} \rightarrow 2 M g O+C \)
D. \( 2 H_{2} S+2 S O_{2} \rightarrow 2 H_{2} O+3 S \)
Subject: Physics
A solenoid of 500 turns, diameter \( 20 c m \)
and resistance \( 2 \Omega \) is rotated about its
vertical diameter through \( \pi \) radian in
\( 1 / 4 \) s, when a horizontal field of \( 3 x \)
\( 10^{-5} T \) acts normal to its plane. Find the
emf induced and current thereof
Subject: Physics
The mirror formula is given by \( \frac{1}{v}+\frac{1}{u}=\frac{1}{f} \) where the symbols have
their usual meanings. Then the lens formula is given by
A \( \cdot \frac{1}{v}+\frac{1}{u}=\frac{1}{f} \)
в. \( \frac{1}{v}-\frac{1}{u}=\frac{1}{f} \)
c. \( \frac{1}{v}+\frac{1}{u}=-\frac{1}{f} \)
D. \( \frac{1}{u}-\frac{1}{v}=\frac{1}{f} \)
Subject: Chemistry
Assertion
The handle and bristles of a tooth brush
should be made of different material
Reason

The handle of a toothbrush should be
hard and strong while the bristles
should be soft and flexible.
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
At \( 25^{\circ} C, \) the equivalent conductance at
infinite dilution of \( H C l, C H_{3} C O O N a \)
and \( N a C l \) are 426.1,91.0 and
\( 126.45 c m^{2} \Omega^{-1} e q^{-1} \) respectively, the
\( \wedge_{\infty} \) for \( \boldsymbol{C H}_{3} \boldsymbol{C O O H}\left(\boldsymbol{i n} \boldsymbol{c m}^{-1} \boldsymbol{\Omega}^{-1} \boldsymbol{e q}^{-1}\right) \)
is:
\( \mathbf{A} \cdot 391.6 \)
B. 390.6
\( c .389 .6 \)
D. 388.6
Subject: Maths
Find the mean deviation about mean
and median for the following data.
\begin{tabular}{lllll}
\multirow{2}{*} {\( \boldsymbol{C I} \)} & \( \boldsymbol{5}- \) & \( \mathbf{1 0}- \) & \( \mathbf{1 5}- \) & \( \mathbf{2 0}- \) \\
& \( \mathbf{1 0} \) & \( \mathbf{1 5} \) & \( \mathbf{2 0} \) & \( \mathbf{2 5} \)
\end{tabular}
12
Subject: Maths
The differential equation of all
parabola's with axis parallel to axis of \( y \)
-axis is:
A \( \cdot y_{2}=2 y_{1}+x \)
B \( \cdot y_{3}=2 y_{1} \)
c. \( y_{2}^{3}=y_{1} \)
D . \( y_{3}=0 \)
Subject: Chemistry
For \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \) and \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) the correct
choice is :
A \( \cdot H_{3} P O_{3} \) is dibasic and reducing agent
B. \( H_{3} P O_{3} \) is diabasic and non-reducing agent
c. \( H_{3} P O_{4} \) is tribasic and reducing agent.
D. \( H_{3} P O_{3} \) is tribasic and non-reducing agent
Subject: Physics
A cylinder is sandwiched between two
planks. Two constant horizontal forces
\( F \) and \( 2 F \) are applied on the planks as
shown. If there is no slipping at the top
and bottom of cylinder, then
This question has multiple correct options
A . acceleration of the centre of mass of cylinder is \( \frac{21 F}{26 M} \)
B. acceleration of the centre of mass of cylinder is \( \frac{13 F}{26 M} \)
C. acceleration of the top plank is \( \frac{F}{2 G M} \)
D. acceleration of the top plank is \( \frac{F}{13 M} \)
Subject: Chemistry
Which of the following is the parent element of the element \( \frac{102}{20} \Omega \) if it is
formed as a result of \( 3 \alpha \) and \( 2 \beta^{-} \)
decays?
A \( \cdot \frac{90}{16} \Gamma \)
B . \( \frac{114}{24} \Phi \)
\( \mathrm{c} \cdot_{28}^{114} \mathrm{\Theta} \)
D. \( _{8}^{12} \Delta+_{12}^{90} \Xi \)
Subject: Chemistry
Which of the following statements is
not correct?
\( \mathbf{A} \cdot L a(O H)_{3} \) is less basic than \( L u(O H)_{3} \)
B. In lanthanide series, radii of elements decreases with an increase in atomic number
C . \( L a \) is actually an element of transition series rather than lanthanides
D. Atomic radii of \( Z r \) and \( H f \) are same because of lanthanide contraction
Subject: Maths
State whether the following statement is true or false.
If \( Z_{r}=\cos \frac{\pi}{3^{r}}+i \sin \frac{\pi}{3^{r}}, r= \)
\( \mathbf{1}, \mathbf{2}, \mathbf{3}, \dots \dots \operatorname{then} z_{1} z_{2} z_{3} \dots \dots \dots=i \)
A. True
B. False
Subject: Chemistry
Which of the following reactions is not
correct?
\( \mathbf{A} \cdot M n O_{4}^{-}+8 H^{+}+5 F e^{2+} \rightarrow 5 F e^{3+}+M n^{2+}+4 H_{2} O \)
B \( \cdot 2 M n O_{2}+4 K O H+O_{2} \rightarrow 4 K M n O_{4}+2 H_{2} O \)
\( \mathbf{c} \cdot 2 N a_{2} C r O_{4}+2 H^{+} \rightarrow N a_{2} C r_{2} O_{7}+2 N a^{+}+H_{2} O \)
D. \( K_{2} C r_{2} O_{7}+7 H_{2} S O_{4}+6 K I \rightarrow 4 K_{2} S O_{4}+ \)
\( C r_{2}\left(S O_{4}\right)_{3}+3 I_{2}+7 H_{2} O \)
Subject: Physics
The current that passes through 20 ohm resistance when it is connected in
parallel with a 30 ohm resistance and this set is connected to a battery of \( 2 \mathrm{V} \)
is
A . \( 0.2 A \)
B. \( 0.3 \mathrm{A} \)
c. \( 0.1 \mathrm{A} \)
D. 0.016A
Subject: Maths
If \( \vec{A}=2 \hat{i}+7 \hat{j}+3 \hat{k} \) and \( \vec{B}=3 \hat{i}+2 \hat{j}+ \)
\( \mathbf{5} \hat{k}, \) then find the projection of \( \overrightarrow{\boldsymbol{a}} \) on \( \overrightarrow{\boldsymbol{b}} \)
Subject: Chemistry
For the reaction \( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \rightleftharpoons \)
\( 2 H I(g) \) The equilibrium constant \( K_{p} \)
changes with:
A. Total pressure
B. Catalyst
C. The amounts of \( H_{2} \) and \( I_{2} \) present
D. Temperature
Subject: Physics
Two concentric circular coil of radius
\( 20 c m \) and \( 30 c m \) carries current \( 2 A \) and
\( 3 A \) respectively in opposite direction
then magnetic field at centre will be :-
A. \( 4 \pi \times 10^{-7} \)
В. \( 2 \pi \times 10^{-7} \)
c. \( 2 \times 10^{-7} \)
D. 0
Subject: Physics
Find the cost of operating an electric toaster for \( 2 h r s, \) if it draws a current of
\( 8 A \) on a \( 110 V \) circuit. The cost of
electric energy is \( \boldsymbol{R} \boldsymbol{s} \boldsymbol{2} . \boldsymbol{5} / \boldsymbol{k} \boldsymbol{W} \boldsymbol{h} \)
A. Rs 4.40
в. Rs 6
c. \( R s 8.20 \)
D. Rs 2.20
Subject: Maths
The vector equation of the plane passes through the points \( A \& B \) with position vector \( 2 \hat{i}+\hat{j}-\hat{k} \&-\hat{i}+3 \hat{j}+4 \hat{k} \)
respectively \( \& \) Ler to the plane \( \bar{r} \cdot(\hat{i}-2 \hat{j}+4 \hat{k})=10 \) is
A \( \cdot \bar{r} \cdot(18 \hat{i}+17 \hat{j}-3 \hat{k})=49 \)
B . \( \bar{r} .(18 \hat{i}-17 \hat{j}-3 \hat{k})+22=0 \)
c. \( \bar{r} .(18 \hat{i}+17 \hat{j}+4 \hat{k})=25 \)
D・ \( \bar{r} .(18 \hat{i}+17 \hat{j}+4 \hat{k})=24 \)
Subject: Maths
ff \( y=\tan ^{-1}\left[\frac{\sqrt{1+x^{2}}-\sqrt{1-x^{2}}}{\sqrt{1+x^{2}}+\sqrt{1-x^{2}}}\right] \)
what would be \( \frac{d y}{d x} \)
A \( \cdot \frac{-x}{\sqrt{1-x^{4}}} \)
в. \( \frac{1}{\sqrt{1-x^{4}}} \)
c. \( \frac{x}{\sqrt{1-x^{4}}} \)
D. none of thes
Subject: Physics
The children are at opposite ends of metal rod. One strikes the end of the rod
with big pebble. Find the ratio of time
taken by the sound waves in air and in the metal to reach it second child. (Speed in rod \( =6420 \mathrm{m} / \mathrm{s} \) ).
A . 221.3
B. 18.55
c. 22.13
D. 185.5
Subject: Maths
\( A B C \) is a triangle right angled at \( C . A \) line through the mid-point \( M \) of
hypotenuse \( A B \) and parallel to \( B C \)
intersects \( A C \) and \( D . \) Show that
(i) \( D \) is the mid-point of \( A C \)
(ii) \( M B \perp A C \)
(iii) \( \boldsymbol{C M}=\boldsymbol{M} \boldsymbol{A}=\frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{A} \boldsymbol{B} \)
Subject: Chemistry
Which of the following orbit is impossible for an electron according to Bohr's theory?
A \( \cdot m v r=\frac{n h}{2 \pi} \)
в. \( _{m v r}=\frac{h}{\pi} \)
c. \( _{m v r}=\frac{2 h}{\pi} \)
D. \( m v r=\frac{4 h}{2 \pi} \)
Subject: Chemistry
Which of the following solution cannot act as a buffer?
A. \( N a H_{2} P O_{4}+H_{3} P O_{4} \)
в. \( C H_{3} \) СООН \( +C H_{3} \) СОО Na
c. \( H C l+N H_{4} C l \)
D. \( H_{3} P O_{4}+N a_{2} H P O_{4} \)