AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If paintbrushes cost \( \$ 1.50 \) each and canvases cost 6 times that much, which of the following represents the cost, in dollars, of p paintbrushes and c
canvases?
A. 7.5pc
B. 10.5pc
c. \( 9 c+1.5 p \)
D. \( 10.5(p+c) \)
Subject: Physics
Two particles \( A \) and \( B \) move on a circle. Initially particles \( A \) and \( B \) are diagonally opposite to each other.
Particle \( A \) moves with angular velocity
\( \pi \) rad \( s^{-1} \) and angular acceleration
\( \pi / 2 r a d s^{-2} \) and particle \( B \) move with
constant angular velocity \( 2 \pi \) rad \( s^{-2} \)
Find the time after which both the
particles \( A \) and \( B \) will collide.
Subject: Maths
If the mean deviation of the numbers 1
\( \mathbf{1}+\mathbf{d}, \mathbf{1}+\mathbf{2} \mathbf{d}, \ldots, \mathbf{1}+\mathbf{1 0 0} \mathbf{d} \) from their
mean is \( 255, \) then the dis equal to
A . 10.0
в. 20.0
c. \( 10 . \)
D. 20.2
Subject: Maths
The number of solutions of the equation
\( \tan ^{-1}(x-1)+\tan ^{-1}(x)+\tan ^{-1}(x+ \)
1) \( =\tan ^{-1}(3 x) \) is :
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 4
Subject: Maths
Find the value of a given \( \mathbf{3}+\frac{\mathbf{1}}{\mathbf{4}}(\mathbf{3}+\boldsymbol{p})+\frac{\mathbf{1}}{\mathbf{4}^{2}}(\mathbf{3}+\mathbf{2} \boldsymbol{p})+\frac{\mathbf{1}}{\mathbf{4}^{3}}(\mathbf{3}+ \)
\( \mathbf{3} \boldsymbol{p})+\ldots=? \)
Subject: Chemistry
For the reaction \( : \boldsymbol{P C l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g})+ \)
\( \boldsymbol{C l}_{2}(\boldsymbol{g}) \)
The forward reaction at constant
temperature is favoured by:
This question has multiple correct options
A. introducing chlorine gas at constant volume
B. introducing an inert gas at constant pressure
c. increasing the volume of the container
D. introducing \( P C l_{5} \) at constant volume
Subject: Maths
Evaluate: \( 96 a b c(3 a-12)(5 b-30) \div \)
\( \mathbf{1 4 4}(\boldsymbol{a}-\mathbf{4})(\boldsymbol{b}-\mathbf{6}) \)
\( \mathbf{A} \cdot 10 a b c \)
B. 2abc
\( c \cdot 2 a b \)
D. \( 2 b c \)
Subject: Physics
Assertion
(A): When a solid Copper sphere and solid Wooden sphere, both having the same mass, are pinning about their own axis with same
angular velocity, then the wooden sphere has greater angular momentum.
Reason (R): Wood is less denser than
Copper. So radius of Wooden sphere is
more than that of Copper and so greater
moment of inertia.
A. Both A and R are true and R is correct explanation of A
B. Both A and R are true and R is not correct explanation of A
c. \( A \) is true and \( R \) is false
D. A is false and R is true
Subject: Maths
A curve \( C \) has the property that if the tangent drawn at any point 'P' on C meets the coordinate axes at \( A \) and \( B \)
and \( P \) is midpoint of \( A B . \) If the curve passes through the point (1,1) then the equation of the curve is?
A \( . x y=2 \)
в. \( x y=3 \)
c. \( x y=1 \)
D. \( x y=4 \)
Subject: Maths
A and B are mutually exclusive events,
then
\( \mathbf{A} \cdot P(A) \leq P(\bar{B}) \)
B \( . P(\mathrm{A})>P(\bar{B}) \)
\( \mathbf{c} \cdot \mathrm{P}(\mathrm{A})<\mathrm{P}(\mathrm{B}) \)
D. \( P(A)=P(B) \)
Subject: Physics
A body dropped from a height \( h \) with an
initial speed zero reaches the ground with a velocity of \( 3 k m / h \). Another body of the same mass was dropped from the same height \( h \) with an initial speed \( 4 k m / h \) will reach the ground with a
velocity of
\( \mathbf{A} \cdot 3 k m / h \)
в. \( 4 k m / h \)
c. \( 5 k m / h \)
D. \( 12 k m / h \)
Subject: Maths
If \( f^{n}(x) \) be continuous at \( x=0, f(0) \neq \)
\( \mathbf{0}, \boldsymbol{f}^{\prime}(\mathbf{0}) \neq \mathbf{0} \) and
\( \lim _{x \rightarrow 0} \frac{2 f(x)-3 a f(2 x)+b f(8 x)}{\sin ^{2} x} \) exists
Then the values of \( a \) and \( b \) are
A \( \cdot b=\frac{1}{3}, a=\frac{7}{9} \)
В. \( a=1, b=1 \)
c. \( a=b=-1 \)
D. \( a=-1, b=1 \)
Subject: Chemistry
\( \left[N i(C O)_{4}\right]>\left[C o(C O)_{4}\right]^{-}>\left[F e(C O)_{4}\right]^{2-} \)
is the correct order with respect to M-C \( \pi \)
bond. Where \( \mathrm{M}=\mathrm{Ni}, \mathrm{Fe} \), and \( \mathrm{Co} \)
A . True
B. False
Subject: Maths
If \( \boldsymbol{\alpha}+\boldsymbol{i} \boldsymbol{\beta}=\tan ^{-1} \boldsymbol{z}, \boldsymbol{z}=\boldsymbol{x}+\boldsymbol{i} \boldsymbol{y} \) and \( \boldsymbol{\alpha} \) is
constant then the locus of \( z \) is
A \( \cdot x^{2}+y^{2}+2 x \cot 2 \alpha=1 \)
B \cdot \( \cot 2 \alpha\left(x^{2}+y^{2}\right)=1+x \)
c. \( x^{2}+y^{2}+2 y \tan 2 \alpha=1 \)
D. \( x^{2}+y^{2}+2 x=1 \)
Subject: Maths
The outer length, breadth and height of
a wooden box open at the top are \( 10 \mathrm{cm} \) \( 8 \mathrm{cm} \) and \( 5 \mathrm{cm} \) respectively. If the thickness of the wood is \( 1 \mathrm{cm} \), the total surface area of the box is
A \( \cdot 420 \mathrm{cm}^{2} \)
В. \( 452 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 451 \mathrm{cm}^{2} \)
D. \( 483 \mathrm{cm}^{2} \)
Subject: Chemistry
Which of the following has the highest molar conductivity?
\( \mathbf{A} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{6}\right] C l_{3} \)
B . \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}\right] \mathrm{Cl}_{2} \)
c. \( \left[C o\left(N H_{3}\right)_{4} C l_{2}\right] C l \)
D. \( \left[C o\left(N H_{3}\right)_{3} C l_{3}\right] \)
Subject: Chemistry
Write condition under which a
bimolecular reaction is kinetically first order. Given an example of such a reaction.
(Given: \( \log 2=0.3010, \log 3= \)
\( \mathbf{0 . 4 7 7 1}, \log \mathbf{5}=\mathbf{0 . 6 9 9 0}) \)
Subject: Physics
A particle \( (\boldsymbol{m}=\mathbf{1} \boldsymbol{k} \boldsymbol{g}) \) slides down a
frictionless rack (AOC) starting from
rest at a point \( A \) (height \( 2 m \) ). After
reaching \( C, \) the particle continuous to
move freely in air as a projectile. When
it reaching its highest point \( \boldsymbol{P} \) (height
1 \( m \) ), the kinetic energy of the particle
(in J) is : (Figure drawn is schematic and not to scale; take \( g=10 m s^{-2} \)
Subject: Chemistry
Sulphuric acid is produced by lead chamber process with following exothermic reaction
\[
2 S O_{2}+O_{2} \stackrel{N O}{\rightleftharpoons} 2 S O_{3} \stackrel{H_{2} O}{\longrightarrow} H_{2} S O_{4}
\]
What is the role of NO in the given
exothermic reaction?
A. Oxidizing agent
B. Reducing agent
c. catalyst
D. None of these
Subject: Biology
Which of the following combination of characters is true for slime moulds?
A. Parasitic, plasmodium with true walls, spores dispersed by air currents.
B. Saprophytic, plasmodium without walls, spores dispersed by water.
c. Parasitic, plasmodium without walls, spores dispersed by water.
D. Saprophytic, plasmodium without walls, spores dispersed by air currents.
Subject: Chemistry
In the reaction \( \boldsymbol{P b O}+\boldsymbol{C} \rightarrow \boldsymbol{P b}+\boldsymbol{C O} \)
A. \( P b O \) is oxidised
B. c acts as oxidising agentt
\( c \cdot c \) acts as a reducing agent
D. This reaction does not represent a redox reaction
Subject: Chemistry
In Carius method for the quantitative
estimation of phosphorous, by using magnesia mixture, phosphorous is
estimated by
A. \( M g N H_{4} \cdot P O_{4} \)
В. \( M g_{2} P_{2} O_{7} \)
c. \( \left(N H_{4}\right)_{3} P O_{4} \cdot 12 M o O_{3} \)
D. All
Subject: Physics
The Young's modulus of steel is twice that of brass. Two wires of sample
length and of same area of cross section, one of steel and another of
brass are suspended from the same
roof. If we want the lower ends of the
wires to be at the same level, then the
weights added to the steel and brass wires must be in the ratio of:
A. 1: 1
B. 1: 3
c. 2: 1
D. 4: 1
Subject: Chemistry
Which of the following graph shows the best relationship of the number of
grams of a solid that are soluble in 100
\( \operatorname{grams} \) of \( H_{2} O \) at varying temperature if
the solubility begins at a small quality and increases at a slow, steady pace as the temperature is increased?
\( A \cdot A \)
B. B
\( c \cdot c \)
D.
E.
Subject: Chemistry
The following two redox reactions are
given:
¡) \( M n O_{4}^{-}+8 H^{+}+5 e^{-} \rightarrow M n^{2+}+ \)
\( \mathbf{4} \boldsymbol{H}_{2} \boldsymbol{O} ; \boldsymbol{E}^{\boldsymbol{o}}=\boldsymbol{X}_{\mathbf{1}} \boldsymbol{V} \)
ii) \( \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{2}+\boldsymbol{4} \boldsymbol{H}^{+}+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{M} \boldsymbol{n}^{2+}+ \)
\( \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O} ; \boldsymbol{E}^{o}=\boldsymbol{X}_{2} \boldsymbol{V} \)
Find \( E^{o} \) for the following reaction.
\( M n O_{4}^{-}+4 H^{+}+3 e^{-} \rightarrow M n O_{2}+ \)
\( 2 H_{2} O \)
A. \( X_{2}-X_{1} \)
В. \( X_{1}-X_{2} \)
c. \( \frac{5 X_{1}-2 X_{2}}{3} \)
D. \( \frac{2 X_{1}-5 X_{2}}{3} \)
Subject: Chemistry
Amount of \( C u \) deposited from
\( \boldsymbol{C u} \boldsymbol{S O}_{4}(\boldsymbol{a q}) \) when 5 amp current is
passed for 965 seconds through it, is \( \boldsymbol{C u}=\mathbf{6 3 . 5 g m o l}^{-1} \mathbf{)} \)
A . \( 1.6 g \)
B. \( 3.2 g \)
c. \( 1.45 g \)
D. \( 2.9 g \)
Subject: Chemistry
The electronic configuration of
gadolinium is:
\( \mathbf{A} \cdot[X e] 4 f^{3} 5 d^{5} 6 s^{2} \)
\( \mathbf{B} \cdot[X e] 4 f^{6} 5 d^{2} 6 s^{2} \)
\( \mathbf{c} \cdot[X e] 4 f^{8} 5 d^{9} 6 s^{2} \)
\( \mathbf{D} \cdot[X e] 4 f^{7} 5 d^{1} 6 s^{2} \)
Subject: Physics
The energy stored per unit volume in copper wire, which produces longitudinal strain of \( 0.1 \% \) is:
\( \left(\boldsymbol{Y}=\mathbf{1 . 1} \times \mathbf{1 0}^{\mathbf{1 1}} \boldsymbol{N} / \boldsymbol{m}^{2}\right) \)
A \( \cdot 11 \times 10^{3} \mathrm{J} / \mathrm{m}^{3} \)
В . \( 5.5 \times 10^{3} J / m^{3} \)
\( \mathbf{c} \cdot 5.5 \times 10^{4} J / m^{3} \)
D. \( 11 \times 10^{4} J / m^{3} \)
Subject: Physics
Assertion
If the distance traveled by body is directly proportional to the square of
time taken, then its speed is increasing
with time.
Reason
The speed is equal to the time rate of change of distance.
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 \( \boldsymbol{y}=\cot ^{-1}\left(\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right) \)
then \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}} \) is equal to
A .
B. 1/2
c. \( \frac{1}{1+\sin x} \)
D. \( \frac{1}{\sqrt{1+\sin x}}+\frac{1}{\sqrt{1-\sin x}} \)
Subject: Physics
The value of wavelength of radiation emitted due to transition of electrons
from \( n=4 \) to \( n=2 \) state in hydrogen atom
will be
A \( \cdot \frac{5 R}{36} \)
в. \( \frac{16}{3 R} \)
c. \( \frac{36}{5 R} \)
D. \( \frac{3 R}{16} \)
Subject: Physics
Arrange the process of image formation in proper order
a. Brain processes the signal so that we see the objects as they are.
b. Light sensitive cells activate upon illumination and generate electric signals.
c. Optical nerves carry the signals to the brain.
d. Light falls on the retina.
A \( \cdot \) c, \( d, b, a \)
в. b, d, c.
\( c \cdot d, c, b, a \)
D. \( d, b, c, a \)
Subject: Physics
A force of \( 100 N \) acting on a body for 5
second gives it a velocity of \( 20 m s^{-1} \) Calculate the mass of the body.
A. \( 50 \mathrm{kg} \)
B. 25 kg
c. \( 75 \mathrm{kg} \)
D. \( 100 \mathrm{kg} \)
Subject: Chemistry
Which of the following statement(s)
is/are correct?
This question has multiple correct options
A. Anti conformation of \( N H_{2}-C H_{2}-C H_{2}-N H_{2} \) is
always more stable than its Gauche conformation.
B. Gauche conformation of \( O H-C H_{2}-C H_{2}-F \) is
more stable than anti-conformation at room
temperature
C. On increasing temperature dipole moment of pure \( C I-C H_{2}-C H_{2}-C I \) increases
D. In case of 1,4 -dihydroxycyclohexane twist boat conformer is most stable.
Subject: Maths
If \( A, B \) be two events such that \( P(A \cup \)
\( B)=\frac{5}{6}, P(A \cap B)=\frac{1}{3} \) and \( P\left(B^{\prime}\right)=\frac{1}{2} \)
then events \( A, B \) are
A. dependent
B. independent
c. mutually exclusive
D. none of these
Subject: Physics
A parallel beam of natural light is
incident at an angle of \( 58^{\circ} \) on a plane glass surface. The reflected beam is
completely linearly polarized(tan \( 58^{\circ}= \)
1.6). The angle of refraction of the transmitted beam and the refractive
index of the glass are :
A \( \cdot 32^{\circ}, 1.6 \)
B. 3.2^,1.6
c. \( 32^{\circ}, 1.3 \)
D. 3.2?, 1.3
Subject: Maths
Calculalte R,when \( \boldsymbol{R}= \) \( \sqrt{A^{2}+B^{2}+2 A B \cos \theta} \) given that, \( A=6 \)
\( \mathrm{m}, \mathrm{B}=8 \mathrm{m} \) and angle is \( 60^{0} \)
Subject: Chemistry
Which of the following statements is
not correct?
This question has multiple correct options
\( \mathbf{A} \cdot L u(O H)_{3} \) is less basic than \( L a(O H)_{3} \)
B. In lanthanide series, ionic radius of \( L a^{3+}-L n^{3+} \) ion
increases
C. La is actually an element of transition series rather lanthanide
D. Atomic radius of Zr and Hf are same because of lanthanide contraction
Subject: Maths
A sphere is melted and half of the
molten liquid is used to form 11 identical cubes, whereas the remaining
half is used to form 7 identical smaller
spheres. The ratio of the side of the cube to the radius of the new small sphere is
\( A \)
\[
\left(\frac{4}{3}\right)^{\frac{1}{3}}
\]
в.
\[
\left(\frac{8}{3}\right)^{\frac{1}{3}}
\]
c. \( (3)^{\frac{1}{5}} \)
D.
Subject: Physics
An ideal solenoid of cross-sectional
\( \operatorname{area} 10^{-4} m^{2} \) has 500 turns per metre.
At the centre of this solenoid, another
coil of 100 turns is wrapped closely around it, if the current in the coil
charges from 0 to \( 2 A \) in 3.14 ms, the
emf developed in the second coil is:
\( \mathbf{A} \cdot 1 m V \)
B. \( 2 m V \)
\( \mathbf{c} .3 m V \)
D. \( 4 \mathrm{mV} \)
Subject: Chemistry
The correct thermodynamic conditions
for the spontaneous reaction at all
temperatures is:
\( \mathbf{A} \cdot \triangle H<0 \) and \( \Delta S=0 \)
B. \( \triangle H=0 \) and \( \triangle S<0 \)
c. \( \triangle H<0 \) and \( \Delta S>0 \)
D. \( \triangle H<0 \) and \( \triangle S<0 \)
Subject: Maths
\( \operatorname{Let}\left(1+x^{2}\right)^{2}(1+x)^{n}=A_{0}+A_{1} x+ \)
\( A_{2} x^{2}+\ldots . \) If \( A_{0}, A_{1}, A_{2} \) are in A.P, then
the value of \( n \)
\( A \cdot 2 \)
B. 3
\( c \cdot 5 \)
D. 7
Subject: Maths
\( \operatorname{Let} D_{1}=\left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{a}+\boldsymbol{b} \\ \boldsymbol{c} & \boldsymbol{d} & \boldsymbol{c}+\boldsymbol{d} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{a}-\boldsymbol{b}\end{array}\right| \) and \( D_{2}= \)
\( \left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{c} & \boldsymbol{a}+\boldsymbol{c} \\ \boldsymbol{b} & \boldsymbol{d} & \boldsymbol{b}+\boldsymbol{d} \\ \boldsymbol{a} & \boldsymbol{c} & \boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c}\end{array}\right| \) then the value of \( \frac{D_{1}}{D_{2}} \)
where \( b \neq 0 \) and \( a d \neq b c, \) is
A . -2
B. 0
\( c \cdot-2 b \)
D. \( 2 b \)
Subject: Physics
Unpolarised light of intensity I passes through an ideal polarizer A. Another identical polarizer B is placed behind A. The intensity of light beyond B is found to be \( \frac{1}{2} . \) Now another identical polarizer \( \mathrm{C} \) is placed between \( \mathrm{A} \) and \( \mathrm{B} \). The intensity beyond B is now found to be \( \frac{1}{8} \) The angle between polarizer A and C is?
A \( \cdot 45^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 0^{\circ} \)
D. \( 30^{\circ} \)
Subject: Chemistry
IUPAC name of the compound
\( \left(\boldsymbol{C}_{2} \boldsymbol{H}_{5}\right)_{2} \boldsymbol{N} \boldsymbol{C} \boldsymbol{H}_{3} \) is:
A. 2, 2-diethylmethanamine
B. \( N, N \) - diethylmethanamine
c. \( N \) -ethyl- \( N \) -methylethanamine
D. \( N \) -methylbutanamine
Subject: Physics
For the circuit shown, with \( \boldsymbol{R}_{1}= \)
\( \mathbf{1 . 0 \Omega}, \boldsymbol{R}_{\mathbf{2}}=\mathbf{2 . 0 \Omega}, \boldsymbol{E}_{\mathbf{1}}=\mathbf{2} \boldsymbol{V} \) and \( \boldsymbol{E}_{\mathbf{2}}= \)
\( E_{3}=4 V, \) the potential difference
between the points \( ^{\prime} a^{\prime} \) and \( ^{\prime} b^{\prime} \) is
approximately (in \( V \) )
\( A \cdot 2.7 \)
в. 3.3
\( c .2 . \)
3.3 .3
Subject: Physics
An electron makes a transition from
\( \boldsymbol{n}=\mathbf{2} \) to \( \boldsymbol{n}=\mathbf{1} \) state in a hydrogen like
atom
This question has multiple correct options
A. magnetic field at the site of nucleus is decreased by 16 times
B. magnetic field at the site of nucleus is increased by 32 times
c. angular momentum of electron is changed
D. none of these
Subject: Maths
f \( A=\{a, b\}, B=\{x, y\} \) and \( C= \)
\( \{a, c, y\}, \) then verify that \( A \times \)
\( (\boldsymbol{B} \cap \boldsymbol{C})=(\boldsymbol{A} \times \boldsymbol{B}) \cap(\boldsymbol{A} \times \boldsymbol{C}) \)
Subject: Physics
An engine draws water from a depth of \( 10 m \) with constant speed \( 2 m / s \) at the rate of \( 10 \mathrm{Kg} \) per 10 second The power
of the engine is (in \( w a t t): \) (Take: \( g= \) \( 9.8 m / s^{2} \)
A. 102
B. 98
\( c .100 \)
D. 200
Subject: Physics
A circular disc of radius \( 10 \mathrm{cm} \) is free to
rotate about an axis passing through its centre without friction and its moment of inertia is \( \frac{1}{2} \pi k g m^{2} . A \) tangential force of \( 20 N \) is acting on the
disc along its rim. Starting from rest, the number of rotations made by the disc in \( 10 s \) is:
A . 50
в. 100
\( c .150 \)
D. 200
Subject: Physics
A uniform rod is suspended horizontally from its mid-point. A piece of metal whose weight is \( \boldsymbol{w} \) is suspended at a
distance \( l \) from the mid-point. Another
weight \( W_{1} \) is suspended on the other
side at a distance \( l_{1} \) from the mid-point to bring the rod to a horizontal position. When \( \boldsymbol{w} \) is completely immersed in
water, \( \boldsymbol{w}_{1} \) needs to be kept at a distance
\( l_{2} \) from the mid-point to get the rod
back into horizontal position. The specific gravity of the metal piece is
A \( \cdot \frac{w}{w_{1}} \)
в. \( \frac{w l_{1}}{w l-w_{1} l_{2}} \)
c. \( \frac{l_{1}}{l_{1}-l_{2}} \)
D. \( \frac{l_{1}}{l_{2}} \)
Subject: Maths
\( \cos x+\cos y=\frac{4}{5}, \cos x-\cos y=\frac{2}{7} \)
The value of \( 14 \tan \left(\frac{x-y}{2}\right)+ \)
\( \mathbf{5} \cot \left(\frac{\boldsymbol{x}+\boldsymbol{y}}{\mathbf{2}}\right) \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot \frac{5}{4} \)
D.
Subject: Physics
A conducting straight wire \( P Q \) of length
is fixed along a diameter of a nonconducting ring as shown in the figure. The ring is given a pure rolling motion
on a horizontal surface such that its
centre of mass has a veleocity \( v \). There
exists a uniform horizontal magnetic field \( B \) in horizontal direction
perpendicular to the plane of ring. The magnitude of induced emf in the wire
\( P Q \) at the position shown in the figure
will be :
A. \( B v \)
в. 2 Ву
c. \( 3 B v l / 2 \)
D. zer
Subject: Physics
The two plate \( X \) and \( Y \) of a parallel-
plates capacitor of capacitance \( \mathbf{C} \) are
given a charge of amount Q each. \( X \) is
now joined to the positive terminal and
y to the negative terminal of a cell of
emf \( \varepsilon=Q / C \)
This question has multiple correct options
A. Charge of amount Q will flow from the positive terminal to the negative terminal of the cell through the capacitor.
B. The total charge on the plate \( X \) will be \( 2 Q \)
C. The total charge on the plate Y will be zero.
D. The cell will supply \( C \varepsilon^{2} \) amount of energy.
Subject: Physics
In the given circuit, initially \( \boldsymbol{K}_{\mathbf{1}} \) is
closed and \( K_{2} \) is open. Then \( K_{1} \) is
opened and \( K_{2} \) is closed. If \( q_{1}^{\prime} \) and \( q_{2}^{\prime} \) are
charges on \( C_{1} \) and \( C_{2} \) and \( V_{1} \) and \( V_{1} \)
are the voltage respectively, then
A. charge on \( C_{1} \) gets redistributed such that \( V_{1}=V_{2} \)
B. charge on \( C_{1} \) gets redistributed such that \( q_{1}^{\prime}=q_{2}^{\prime} \)
C. charge on \( C_{1} \) gets redistributed such that \( C_{1} V_{1}= \) \( C_{2} V_{2}=C_{1} V \)
D. charge on \( C_{1} \) gets redistributed such that \( q_{1}^{\prime}+q_{2}^{\prime}=2 q \)
Subject: Physics
There is a small block in the centre \( C \) of
solid glass sphere of refractive index \( \mu \) When seen from outside the block will
appear to be located:
A. Away from C for all values of \( \mu \)
B. at C for all values of \( \mu \)
c. at \( \mathrm{C} \) for \( \mu=1.5 \) but away from c for \( \mu \neq 1.5 \)
D. at c only for \( \sqrt{2} \leq \mu \leq 1.5 \)
Subject: Maths
If \( \hat{\boldsymbol{i}}-\boldsymbol{3} \hat{\boldsymbol{j}}+\boldsymbol{5} \hat{\boldsymbol{k}} \) bisects the angle between
\( \hat{a} \) and \( -\hat{i}+2 \hat{j}+2 \hat{k}, \) where \( \hat{a} \) is a unit
vector, then
A \( \cdot \hat{a}=\frac{1}{105}(41 \hat{i}+88 \hat{j}-40 \hat{k}) \)
B・ \( \hat{a}=\frac{1}{105}(41 \hat{i}+88 \hat{j}+40 \hat{k}) \)
C \( \quad \hat{a}=\frac{1}{105}(-41 \hat{i}+88 \hat{j}-40 \hat{k}) \)
D・ \( \hat{a}=\frac{1}{105}(41 \hat{i}-88 \hat{j}-40 \hat{k}) \)
Subject: Physics
In a given reaction \( z^{\boldsymbol{A}^{A}} \longrightarrow z_{+1} \boldsymbol{Y}^{\boldsymbol{A}} \longrightarrow z_{-1} \)
\( \boldsymbol{K}^{\boldsymbol{A}-\boldsymbol{4}} \longrightarrow \boldsymbol{z}-\mathbf{1} \boldsymbol{K}^{\boldsymbol{A}-\boldsymbol{4}} \)
Radioactive radiations are emitted in
the sequence of
\( \mathbf{A} \cdot \alpha, \beta, \gamma \)
в. \( \gamma, \alpha, \beta \)
\( \mathbf{c} \cdot \beta, \alpha, \gamma \)
D. \( \gamma, \beta, \alpha \),
Subject: Chemistry
What are the products of the above
reaction?
\( \mathbf{A} \cdot\left(C H_{3}\right)_{2} C H-N H\left(C H_{3}\right) \) and \( C O \)
B. \( \left(C H_{3}\right)_{2} C H-N\left(C H_{3}\right)_{2} \) and \( C O \)
\( \mathbf{c} \cdot\left(C H_{3}\right)_{2} C H-N H\left(C H_{3}\right) \) and \( C O_{2} \)
\( \mathrm{D} \cdot\left(C H_{3}\right)_{2} C H-N\left(C H_{3}\right)_{2} \) and \( C O_{2} \)
Subject: Maths
\( \int \frac{d x}{x\left(x^{7}+1\right)} \)
is equal to:
\( ^{\mathbf{A}} \cdot \log \left(\frac{x^{7}}{x^{7}+1}\right) \)
в. \( \frac{1}{7} \log \left(\frac{x^{7}}{x^{7}+1}\right)+c \)
\( ^{\mathbf{c}} \cdot \log \left(\frac{x^{7}+1}{x^{7}}\right)+c \)
D \( \cdot \frac{1}{7} \log \left(\frac{x^{7}+1}{x^{7}}\right)+c \)
Subject: Chemistry
What is the amount of work done when
0.5 mole of methane, \( C H_{4(g)}, \) is subjected to combustion at \( 300 \mathrm{K} ? \)
\( \left(\operatorname{given}, R=8.314 J K^{-1} \mathrm{mol}^{-1}\right) \)
в. -4988.5
\( \mathrm{c} \ldots+4988 \mathrm{J} \)
D. +2494.5
Subject: Physics
An excited \( H e^{+} \) ion emits two photons in succession, with wavelengths
\( 108.5 n m \) and \( 30.4 n m, \) in making a
transition to ground state. The quantum number \( n, \) corresponding to its initial excited state is (for photon of wavelength \( \lambda \), energy \( E=\frac{1240 e V}{\lambda(\operatorname{in} n m)} \) )
\( \mathbf{A} \cdot n=5 \)
B . \( n=4 \)
\( \mathbf{c} \cdot n=6 \)
D. \( n=7 \)
Subject: Chemistry
Select the incorrect statement about
Nylon - \( 2- \) nylon - 6
A. It is a copolymer
B. It is biodegradable.
C . It is an alternating polyamide.
D. It is made up of \( C H_{3}-C_{N H_{2}} H-C O O H \) and \( H_{2} N\left(C H_{2}\right)_{5} C O O H \)
Subject: Chemistry
Ammonium hydrogen sulphide dissociates according to the equations:
\( N H_{4} H S(s) \rightleftharpoons N H_{3}(g)+H_{2} S(g) \)
If the observed pressure at equilibrium is \( 1.12 a t m \) at \( 380 K, \) what is the
equilibrium constant \( \boldsymbol{K}_{\boldsymbol{p}} \) of the
reaction?
Subject: Maths
The function \( \boldsymbol{f}(\boldsymbol{x})=\log _{e}\left[\boldsymbol{x}^{3}+\sqrt{\boldsymbol{x}^{6}+\mathbf{1}}\right] \)
is an
This question has multiple correct options
A. even function
B. odd function
c. increasing function
D. decreasing function