AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The distance between an object and the screen is \( 100 \mathrm{cm} . \) A lens produces an image on the screen when the lens is
placed at either of the positions \( 40 \mathrm{cm} \) apart. The power of the lens is nearly
A. 3diopter
B. 5 diopter
c. 2 diopter
D. 9 diopter
Subject: Physics
Assertion
A sphere is performing pure rolling on a rough horizontal surface with constant angular velocity,frictional force acting
on the sphere is zero
Reason
Velocity of conduct point is zero.
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
Three distinct numbers, \( x, y, z \) form a geometric progression in that order,
and the numbers \( \boldsymbol{x}+\boldsymbol{y}, \boldsymbol{y}+\boldsymbol{z}, \boldsymbol{z}+\boldsymbol{x} \)
form an arithmetic progression in that
order. Find the common ratio of the
geometric progression.
Subject: Maths
Size of the agriculture holding in a survey of 200 families is given in the following table:
\( \begin{array}{lll}\text { Size of } & \text { o- } & \text { 5- } \\ \text { Agriculture } & \text { 5 } & \text { 10 }\end{array} \)
10
15 २०
Number of
family \( \quad 10 \)
15 \( \quad \) 30 \( \quad 80 \)
Complete median and mode size of the
holdings.
Subject: Physics
Temperature coefficient of resistance of
platinum is \( 4 \times 10^{-3} / K \) at \( 20^{\circ} C \)
Temperature at which increase in resistance of platinum is \( 10 \% \) is value
at \( 20^{\circ} C \) is
A \( \cdot 25^{\circ} \mathrm{C} \)
B . \( 70^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 45^{\circ} C \)
D. \( 100^{\circ} \mathrm{C} \)
Subject: Maths
Consider three matrices \( A= \) \( \left[\begin{array}{ll}\mathbf{2} & \mathbf{1} \\ \mathbf{4} & \mathbf{1}\end{array}\right] \quad \boldsymbol{B}=\left[\begin{array}{ll}\mathbf{3} & \mathbf{4} \\ \mathbf{2} & \mathbf{3}\end{array}\right] \quad \) and \( \quad \boldsymbol{C}= \)
\( \left[\begin{array}{cc}\mathbf{3} & -\mathbf{4} \\ -\mathbf{2} & \mathbf{3}\end{array}\right] \)
The value of the sum \( t r(A)+ \) \( \operatorname{tr}\left(\frac{A B C}{2}\right)+\operatorname{tr}\left(\frac{A(B C)^{2}}{4}\right)+ \)
\( \operatorname{tr}\left(\frac{\boldsymbol{A}(\boldsymbol{B C})^{3}}{\boldsymbol{8}}\right)+\ldots \ldots \ldots .+\infty \) is
\( (\operatorname{tr}(A) \text { denotes trace of a matrix } A) \)
A . 6
B. 9
c. 12
D. none of these
Subject: Chemistry
Larger number of oxidation states are
exhibited by the actinides than those by lanthanoids, the main reason
being
A. more energy difference between 5 f and 6d than between 4 f and 5 d orbital
B. more reactive nature of the actinoids than the lanthanoids
c. \( 4 f \) orbitals more diffused than the 5 orbital
D. lesser energy difference between 5 fand 6 than between \( 4 \mathrm{f} \) and \( 5 \mathrm{d} \) orbital
Subject: Maths
Obtain the differential equation of the
family of circles \( x^{2}+y^{2}+2 g x+ \)
\( 2 f y+c=0 ; \) where \( g, f \) and \( c \) are
arbitrary constants.
\( ^{A} \cdot\left[1+\left(y^{\prime}\right)^{2}\right] y^{\prime \prime}-3 y^{\prime}\left(y^{\prime \prime}\right)^{2}=0 \)
\( ^{\mathrm{B}}\left[1+\left(y^{\prime \prime}\right)^{3}\right] y-2 y^{\prime}\left(y^{\prime \prime}\right)^{2}=0 \)
\( ^{\mathbf{C}}\left[1+\left(y^{\prime \prime}\right)^{2}\right] y^{\prime \prime}-3 y^{\prime}\left(y^{\prime \prime}\right)^{2}=0 \)
D. None of these
Subject: Physics
The displacement of a particle executing SHM at any instant \( t \) is \( x= \) \( 0.01 \sin 100(t+0.05) \) then its time
period will be
A . \( 0.06 \mathrm{s} \)
B. 0.2
c. \( 0.1 \mathrm{s} \)
D. 0.02
Subject: Biology
Assertion
Some cells enter \( G_{0} \) phase leading to
inactivation of cell cycle.
Reason
\( G_{0} \) phase occurs due to non-availability
of mitogen and energy rich compounds.
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
\( A, B \) and \( C \) are three mutually
exclusive and exhaustive events such
that \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{2} \boldsymbol{P}(\boldsymbol{B})=\mathbf{3} \boldsymbol{P}(\boldsymbol{C}) \)
What is \( \boldsymbol{P}(\boldsymbol{B}) \) ?
A \( .6 / 11 \)
B. \( 6 / 22 \)
c. \( 1 / 6 \)
D. \( 1 / 4 \)
Subject: Chemistry
Given that the equilibrium constant for
the reaction, \( 2 S O_{2(g)}+O_{2(g)} \rightleftharpoons \)
\( 2 S O_{3(g)} \) has a value of 278 at a particular temperature. What is the value of the equilibrium constant for the following reaction at the same temperature?
\( \boldsymbol{S} \boldsymbol{O}_{\boldsymbol{3}(\boldsymbol{g})} \rightleftharpoons \quad \boldsymbol{2} \boldsymbol{S} \boldsymbol{O}_{2(\boldsymbol{g})}+\boldsymbol{1} / \boldsymbol{2} \boldsymbol{O}_{2(\boldsymbol{g})} \)
A \( .3 .6 \times 10^{-3} \)
в. \( 6.0 \times 10^{-2} \)
c. \( 1.3 \times 10^{-5} \)
D. \( 2.2 \times 10^{-4} \)
Subject: Maths
Between 1 and \( 31, m \) arithmetic means
are inserted, so that the ratio of the \( 7^{t h} \)
and \( (m-1)^{t h} \) mean is \( 5: 9 . \) Then the
value of \( m \) is
A . 12
B. 13
c. 14
D. 15
Subject: Physics
The melting point of mercury is:
A \( .38 .8^{\circ} \mathrm{C} \)
B . \( -38.8^{\circ} \mathrm{C} \)
c. \( 4250^{\circ} \mathrm{C} \)
D. \( 452^{\circ} \mathrm{C} \)
Subject: Chemistry
The molar conductivities of \( K C l, N a C l \)
and \( K N O_{3} \) are 152,128 and
\( 111 S c m^{2} m o l^{-1} \) respectively. What is
the molar conductivity of \( N a N O_{3} ? \)
\( \mathbf{A} \cdot 101 S \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
B. \( 87 S \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
c. \( -101 S \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
D. \( -391 S \mathrm{cm}^{2} \mathrm{mol}^{-} \)
Subject: Chemistry
The dissociation constant of uric acid is
\( \boldsymbol{K}_{\boldsymbol{a}}=\mathbf{4 . 0} \times \mathbf{1 0}^{-\mathbf{6}} \boldsymbol{M} . \) The \( \boldsymbol{p} \boldsymbol{H} \) of a
sample is \( 6.0 . \) What is the ratio of urate
ion to uric acid in the urine??
Subject: Maths
One of the diagonals of a rhombus is equal to a side of the rhombus. The
angles of the rhombus are
\( \mathbf{A} \cdot 60^{\circ} a n d 80^{\circ} \)
B \( \cdot 60^{\circ} \) and \( 120^{\circ} \)
c. \( 120^{\circ} \) and \( 240^{\circ} \)
D. \( 100^{\circ} \) and \( 120^{\circ} \)
Subject: Physics
A wire of \( 1 \mathrm{m} \) long has an area of cross section of \( 2 \times 10^{-3} \mathrm{cm}^{2} \) and has a
resistance of 10 ohm. The resistivity of
the material of the wire is:
A \( \cdot 2 \times 10^{-6} \Omega c m \)
В. \( 2 \times 10^{-4} \Omega c m \)
c. \( 2 \times 10^{-2} \Omega c m \)
D. \( 2 \times 10^{-8} \Omega c m \)
Subject: Maths
Per day expenses of 25 families of the frequency distribution of a Dhani of a village is given as follows.
Per day 25
\( \begin{array}{lll}\text { 35- } & \text { 45- } & \text { 55 }\end{array} \) expense \( \quad 35 \quad 45 \quad 55 \quad 65 \)
(In Rs.)
Number
of
families
Find the mean expense of families by Direct Method.
Subject: Physics
A bullet of mass \( 20 g \) has an initia
speed of \( 1 m s^{-1} \),just before it starts penetrating a mud wall of thickness \( 20 c m . \) if the wall offers a mean
resistance of \( 2.5 \times 10^{-2} N, \) the speed of
the bullet after emerging from the other
side of the wall is close to :
A \( \cdot 0.4 m s^{-1} \)
В. \( 0.1 m s^{-1} \)
\( \mathbf{c} \cdot 0.3 m s^{-1} \)
D. \( 0.7 m s^{-1} \)
Subject: Chemistry
What is the molecular formula of
Oleum?
A. \( H_{2} S O_{3} \)
в. \( H_{2} S O_{5} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{7} \)
D. \( H_{2} S_{2} O_{8} \)
Subject: Chemistry
Equivalent weight of \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) in each of
the reaction will be respectively:
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}+\boldsymbol{O} \boldsymbol{H}^{-} \rightarrow \boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}^{-}+\boldsymbol{H}_{2} \boldsymbol{O} \)
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}+\boldsymbol{2} \boldsymbol{O} \boldsymbol{H}^{-} \rightarrow \boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{4}^{2-}+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O} \)
\( \boldsymbol{H}_{3} \boldsymbol{P O}_{4}+\boldsymbol{3} \boldsymbol{O} \boldsymbol{H}^{-} \rightarrow \boldsymbol{P} \boldsymbol{O}_{4}^{3-}+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O} \)
A . 98,49,32.67
B. 49, 98, 32.67
c. 98,32.67,49
D. 32.67, 49, 98
Subject: Physics
A solid sphere is rolling purely on a rough horizontal surface with speed of center \( u=12 \mathrm{m} / \mathrm{s} \). It collides
inelastically with a smooth vertical wall at a certain moment, with the coefficient of restitution being \( \frac{1}{2} . \) How long (in sec) after the collision, does the sphere begin pure rolling? [coefficient of friction between the sphere and the ground is \( \frac{\mathbf{3}}{\mathbf{3 5}} \)
Subject: Biology
Select the correct option:
Identify \( A, B, C, D \) and \( E \) in the given flow
chart showing Z-scheme of light
reaction
\( \mathbf{A} \cdot A-P_{700} ; \mathrm{B}-H^{+} \) acceptor; \( \mathrm{C}-e^{-} \) acceptor; \( \mathrm{D}-P_{680} ; \mathrm{E} \)
\( N A D P^{+} \)
B. A-Photo -system I ; B- \( e^{-} \) acceptor; C- \( e^{-} \) transport
system; D-Photo system II; E- NADPH
C. A-Photo-system II; B- \( H^{+} \) acceptor; \( \mathrm{C}-e^{-} \) acceptor; \( \mathrm{D} \) -
\( P_{700} ; \) E- NADPH.
D. A-Photo-system II; B- \( e^{-} \) acceptor; \( C-e^{-} \) transport
system; D- photo-system I; E- NADPH.
Subject: Chemistry
Write structural formulae of the organic
compounds \( ^{\prime} \boldsymbol{A}^{\prime},^{\prime} \boldsymbol{B}^{\prime},^{\prime} \boldsymbol{C}^{\prime} \) and \( ^{\prime} \boldsymbol{D}^{\prime} \) in the
following sequence of reaction. \( \boldsymbol{A}^{\prime}+\boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{M} \boldsymbol{g} \boldsymbol{B} \boldsymbol{r} \stackrel{\boldsymbol{H}_{2} \boldsymbol{O}}{\longrightarrow} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}(\boldsymbol{O H}) \boldsymbol{C H}_{3} \frac{c o n c . \boldsymbol{H}_{2} \boldsymbol{S O}_{4}}{\boldsymbol{1}} \)
\( ^{\prime} \boldsymbol{B}^{\prime} \stackrel{\boldsymbol{B} \boldsymbol{r}_{2}}{\longrightarrow}^{\prime} \boldsymbol{C}^{\prime} \stackrel{\text {alc.} \boldsymbol{K O H}}{\longrightarrow} \boldsymbol{D}^{\prime} \)
Subject: Physics
A gas is compressed isothermally to half its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then.
A. compressing the gas isothermally will require more work to be done
B. compressing the gas through adiabatic process will require more work to be done
c. compressing the gas isothermally or adiabatically will require the same amount of work
D. which of the case(whether compression through isothermal or through adiabatic process) requires more work will depend upon the atomicity of the gas
Subject: Maths
If the one of the roots of the equation is zero find 'a'
\( \boldsymbol{x}^{2}-2 \boldsymbol{a} \boldsymbol{x}+\boldsymbol{a}^{2}+\boldsymbol{a}-\boldsymbol{2}=\mathbf{0} \)
Selective the positive answer.
Subject: Chemistry
Select the correct statements:
This question has multiple correct options
A. The +1 oxidation state compared to the +3 oxidation state gets gradually more stabilized as we move from top to bottom in III group.
B. TI (III) being unstable, acts as a good oxidizing agent to get reduced to TI (II).
\( \mathrm{C} \cdot \operatorname{Sn} \mathrm{Cl}_{2} \) is good oxidizing agent.
D. All are incorrect.
Subject: Maths
\( \int \frac{1}{(2 x+1) \sqrt{x^{2}-x-2}} d x= \)
A. \( -\frac{1}{\sqrt{5}} \sin ^{-1} \frac{7+4 x}{3(2 x+1)}+c \)
B. \( -\frac{1}{\sqrt{5}} \cos \frac{7+4 x}{3(2 x+1)}+c \)
c. \( -\frac{1}{\sqrt{5}} \sinh ^{-1} \frac{7+4 x}{3(2 x+1)}+c \)
D. \( -\frac{1}{\sqrt{5}} \cosh ^{-1} \frac{7+4 x}{3(2 x+1)}+c \)
Subject: Physics
A skylab of mass \( \mathrm{m} \) kg is first launched from the surface of the earth in a
circular orbit of radius \( 2 \mathrm{R} \) (from the
centre of the earth) and then it is
shifted from this circular orbit to
another circular orbit of radius 3 R. The
minimum energy required to place the
lab in the first orbit and to shift the lab
from first orbit to the second orbit are.
\( \mathbf{A} \cdot \frac{3}{4} m g R, \frac{m g R}{6} \)
В. \( \frac{3}{4} m g R, \frac{m g R}{12} \)
c. \( \mathrm{mgR}, \mathrm{mgR} \)
\( \mathbf{D} \cdot 2 m g R, \) mgR
Subject: Physics
A solenoid of length \( 1.5 m \) and \( 4 c m \) in
diameter possesses 10 turns per metre. A current of \( 5 A \) is flowing
through it. The magnetic induction at a point inside the solenoid along the axis
is \( _{-}------\left(\mu_{0}=4 \pi \times\right. \)
\( \mathbf{1 0}^{-\mathbf{7}} \boldsymbol{W b} / \mathbf{A . m} \)
A \( \cdot \pi \times 10^{-5} T \)
В. \( 2 \pi \times 10^{-5} T \)
c. \( 3 \pi \times 10^{-5} T \)
D . \( 4 \pi \times 10^{-5} T \)
Subject: Physics
The work done to split a liquid drop of radius R into N identical drops is (take
\( \sigma \) as the surface tension of the liquid):
A \( \cdot 4 \pi R^{2}\left(N^{1 / 3}-1\right) \sigma \)
B . \( 4 \pi R^{2} N \sigma \)
C \( \cdot 4 \pi R^{2}\left(N^{1 / 2}-1\right) \)
D. None of these
Subject: Maths
Find the next term of the sequence:
\( \frac{1}{2}, \frac{1}{6}, \frac{1}{18}, \frac{1}{54}, \dots \)
A \( \cdot \frac{1}{168} \)
в. \( \frac{1}{164} \)
c. \( \frac{1}{162} \)
D. \( \frac{1}{17} \)
Subject: Physics
Three rings each of mass \( m \) kg and
radius \( a \) are arranged as shown in the
figure. The moment of inertia of the arrangement about \( x-x^{\prime} \) axis will be
A \( \cdot \frac{3}{2} m a^{2} \)
B.
\( c \)
D. \( \frac{2}{5} m a^{2} \)
Subject: Maths
Area bounded by curve \( y=x^{2} \) and \( y= \)
\( 2-x^{2} \) is \( ? \)
A \( \cdot \frac{8}{3} \) sq units
B. \( \frac{3}{8} \) sq units
c. \( \frac{3}{2} \) sq units
D. None of these
Subject: Physics
Find out elongation in a rod Given :
\( Y=2 \times 1011 \mathrm{N} / \mathrm{m} 2, \mathrm{p}=104 \mathrm{kg} / \mathrm{m} 3 \mathrm{Y}=2 \times 1011 \mathrm{N} / \mathrm{m} \)
\( 2, p=104 \mathrm{kg} / \mathrm{m} 3 \)
\( A .9 m n \)
в. \( 10 m m \)
\( c .18 m m \)
D. \( 3 m m \)
Subject: Chemistry
Assertion
The angular momentum of an electron in an atom is quantized.
Reason
In an atom only those orbits are permitted in which angular momentum of the electron is integral multiple of \( \frac{h}{2 \pi} \) where \( h \) is a plank's constant.
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 hollow cylinder with a very thin wall and a block are placed at rest at the top
of a plane with inclination \( \boldsymbol{\theta}=\mathbf{4 5}^{\circ} \)
above the horizontal. The cylinder rolls down the plane without slipping and the block slides down the plane; it is found
that both objects reach the bottom of the plane simultaneously. If the coefficient of kinetic friction between
the block and the plane is \( \mu, \) the value of
\( 18 \mu \) is
Subject: Chemistry
Assertion
Alcohols are dehydrated to hydrocarbons in the presence of acidic
zeolites.
Reason
Zeolites are microporous catalysts.
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: Chemistry
Peroxodisulphate salts (e.g., \( N a_{2} S_{2} O_{8} \) ) are
strong oxidizing agents used as bleaching agents for fats, oils, etc. Given :
\( O_{2}(g)+4 H^{\oplus}(a q)+4 e^{-} \rightarrow 2 H_{2} O(l) \)
\( E^{\ominus}=1.23 V \)
\( S_{2} O_{8}^{2-}(a q)+2 e^{-} \rightarrow S O_{4}^{2-}(a q) \)
\( E^{\ominus}=2.01 V \)
Which of the following statements is (are) correct?
This question has multiple correct options
A. Oxygen gas can oxidize sulphate ion to per-oxo disulphate ion \( \left(S_{2} O_{8}^{2-}\right) \) in acidic solution
в. \( O_{2}(g) \) is reduced to water
c. water is oxidized to \( O_{2} \)
D. \( S_{2} O_{8}^{2-} \) ions are reduced to \( S O_{4}^{2-} \) ions
Subject: Physics
A body loses half of its velocity on penetrating \( 6 \mathrm{cm} \) in a wooden block.
How much will it penetrate more before coming to rest?
A. \( 1 ~ c m \)
B. 2 cm
\( \mathrm{c} .3 \mathrm{cm} \)
D. \( 4 \mathrm{cm} \)
Subject: Maths
\( \int \frac{d x}{\sin ^{2} x \cos ^{2} x} \) equals
A \( \cdot \tan x-\cot x+C \)
B. \( \tan x+\cot x+c \)
\( c \cdot \tan x \cot x+c \)
D. \( \tan x-\cot 2 x+c \)
Subject: Chemistry
The oxyacids of phosphorous which show powerful reducing properties but no oxidizing
properties are :
A. \( H_{3} P O_{2}, H_{3} P O_{3} \)
в. \( H_{3} P O_{2}, H_{3} P O_{4} \)
\( \mathrm{c} \cdot H_{3} P O_{3}, H_{3} P O_{4} \)
D. \( H P O_{3}, H_{3} P O_{3} \)
Subject: Physics
An AC circuit containing \( 80 m H \)
inductor and a \( 60 \mu F \) capacitor is in series with \( 15 \Omega \) resistance. They are
connected to \( 230 V, 50 H z \) AC supply
What is the total average power absorbed by the circuit?
A . zero
B. 5 watt
c. 40 watt
D. 10 watt
Subject: Chemistry
Statement \( I- \) Zinc and berylium have
electron affinities which are
significantly different from each other.
Statement \( I I- \) Electron affinity is a
measure of the energy used to add an
electron to an atom.
A. Statement \( I \) is true, Statement \( I I \) is true
B. Statement I is true, Statement II is false
c. statement \( I \) is false, statement \( I I \) is true
D. Statement I is false, Statement \( I I \) is false
E. Statement I is true, Statement \( I I \) is true and is a correct explanation of the phenomena described in 1
Subject: Physics
A thermometer has wrong calibration. It
reads the melting point of ice as \( -10^{\circ} \)
If it reads \( 60^{\circ} \) in place of \( 50^{\circ} \mathrm{C}, \) what is the temperature of the boiling point of water on this scale.
\( \mathbf{A} \cdot 130^{\circ} \)
B. 90
\( c \cdot 110^{\circ} \)
D. 120
Subject: Maths
If \( \vec{x} \) and \( \vec{y} \) be unit vectors and \( |\vec{z}|=\frac{2}{\sqrt{7}} \)
such that \( \vec{z}+\vec{z} \times \vec{x}=\vec{y}, \) then the angle
\( \theta \) between \( \vec{x} \) and \( \vec{z} \) can be
\( A \cdot 30^{\circ} \)
B. \( 60^{\circ} \)
\( c .90^{\circ} \)
D. None of these
Subject: Chemistry
During the discharge of a lead storage battery, the density of sulphuric acid
fell from 1.294 to \( 1.139 g m L^{-1} . H_{2} S O_{4} \) of
density \( 1.294 g m L^{-1} \) is \( 39 \% \) and that of
density \( 1.139 g m L^{-1} \) is \( 20 \% \)
by weight.The battery holds 3.5 L of acid and the volume practically remains constant during discharge. The number of ampere hours for which the battery must have been used are..

The discharging and charging reactions
are:
\( \boldsymbol{P b}+\boldsymbol{S O}_{4}^{2-} \rightarrow \boldsymbol{P b S O}_{4}+\boldsymbol{2} \boldsymbol{e}^{-} \)
(charging) \( \boldsymbol{P b O}_{2}+\mathbf{4 H}^{+}+\boldsymbol{S O}_{4}^{2-}+\boldsymbol{2 e}^{-} \rightarrow \)
\( P b S O_{4}+2 H_{2} O \) (discharging)
Subject: Maths
The contrapositive of \( \boldsymbol{p} \rightarrow(\sim \boldsymbol{q} \rightarrow \sim \boldsymbol{r}) \)
is equivalent to
\( \mathbf{A} \cdot(\sim q \wedge r) \rightarrow \sim p \)
В \( \cdot(q \wedge \sim r) \rightarrow \sim p \)
c. \( p \rightarrow(\sim r \vee q) \)
D. \( p \wedge(q \vee r) \)
Subject: Physics
(a) Show, giving via suitable diagram, how unpolarized light can be polarised by reflection.
(b) Two polaroids \( P_{1} \) and \( P_{2} \) are placed with their pass axes perpendicular to
each other. Unpolarised light of
intensity \( I_{0} \) is incident on \( P_{1} . \) A third
Polaroid \( P_{3} \) is kept in between \( P_{1} \) and \( P_{2} \)
such that its pass axis makes an angle
of \( 60^{\circ} \) with that of \( P_{1} \). Determine the
intensity of light transmitted through
\( P_{1}, P_{2} \) and \( P_{3} \)
Subject: Physics
A satellite of mass \( \mathrm{m} \) is orbiting the earth in a circular orbit of radius r. It
starts losing energy due to small air
resistance at the rate of \( C J s^{-1} \). The
time taken for the satellite to reach the earth is: \( \frac{G M m}{x C}\left[\frac{1}{R}-\frac{1}{r}\right] . \) Find the value of \( \boldsymbol{x} \)
Subject: Physics
The horizontal component \( N_{x} \) and
vertical component \( N_{y} \) of the reaction
at end \( P \) are given by:
A \( \cdot \mathrm{N}_{\mathrm{x}}=1300 \mathrm{N}, \mathrm{N}_{\mathrm{y}}=960 \mathrm{N} \)
B. \( \mathrm{N}_{\mathrm{x}}=960 \mathrm{N}, \mathrm{N}_{y}=140 \mathrm{N} \)
C. \( \mathrm{N}_{\mathrm{x}}=960 \mathrm{N}, \mathrm{N}_{\mathrm{y}}=960 \mathrm{N} \)
D. \( \mathrm{N}_{\mathrm{x}}=1300 \mathrm{N}, \mathrm{N}_{\mathrm{y}}=1300 \mathrm{N} \)
Subject: Chemistry
The work function of a metal is 4 eV. If
light of frequency \( 2.3 \times 10^{15} \mathrm{Hz} \) is
incident on metal surface, then:
A. no photoelectron will be ejected
B. 2 photoelectron of zero kinetic energy are ejected
C. 1 photoelectron of zero kinetic energy is ejected it
D. 1 photoelectron is ejected, which required the stopping potential of 5.52 volt
Subject: Physics
The mass of the electron is given \( 9.1 \times \) \( 10^{-31} k g . \) Find the order of magnitude of
the number of electrons of \( 1 k g \)
\( \mathbf{A} \cdot 10^{31} \)
B. \( 10^{-30} \)
\( c \cdot 10^{3} \)
D. \( 10^{-31} \)
Subject: Physics
According to Bohr's model of hydrogen atom, relation between principal quantum number n and radius of stable orbit is
\( \mathbf{A} \cdot r \propto \frac{1}{n} \)
B . \( r \propto n \)
\( c \cdot r \propto \frac{1}{n^{2}} \)
D \( \cdot r \propto n^{2} \)
Subject: Maths
If \( \vec{x} \& \vec{y} \) are two non collinear vectors
and \( a, b, c \) represent the sides of a
\( \Delta A B C \) satisfying \( (a-b) \vec{x}+ \)
\( (b-c) \vec{y}+(c-a)(\vec{x} \times \vec{y})=0 \) then
\( \Delta A B C \) is
A. an acute angle triangle
B. an obtuse angle triangle
c. a right angle triangle
D. a scalene triangle
Subject: Maths
The differential equation of all circles passing through the origin and having their centres on the \( x \) -axis is
A \( \cdot y^{2}=x^{2}+2 x y \frac{d y}{d x} \)
B. \( y^{2}=x^{2}-2 x y \frac{d y}{d x} \)
c. \( x^{2}=y^{2}+x y \frac{d y}{d x} \)
D. \( x^{2}=y^{2}+3 x y \frac{d y}{d x} \)
Subject: Maths
The area bounded by the curves \( y= \)
\( \log _{e} x \) and \( y=\left(\log _{e} x\right)^{2} \) is
\( \mathbf{A} \cdot 3-e \)
B . \( e-3 \)
C \( \cdot \frac{1}{2}(3-e) \)
D. \( \frac{1}{2}(e-3) \)
Subject: Physics
Two light waves are represented by \( \boldsymbol{y}_{1}=\mathbf{3} \sin \omega t \) and \( \boldsymbol{y}_{2}=\mathbf{4} \sin \left(\boldsymbol{\omega} \boldsymbol{t}+\frac{\boldsymbol{\pi}}{\mathbf{3}}\right) \)
The resultant amplitude due to interference will be
A \( \cdot \sqrt{21} \)
B. \( \sqrt{26} \)
c. \( \sqrt{37} \)
D. \( \sqrt{41} \)
Subject: Physics
A body of mass ' \( m \) ' is raised to a height
\( 10 R^{\prime} \) from the surface of the Earth,
where ' \( R^{\prime} \) is the radius of the Earth. The
increase in potential energy is \( G= \) universal constant of gravitation,
\( M= \) mass of earth and \( g= \) acceleration due to gravity)
\( ^{A} \cdot \frac{G M m}{11 R} \)
в. \( \frac{G M m}{10 R} \)
c. \( \frac{m g R}{11 G} \)
D. \( \frac{10 G M m}{11 R} \)
Subject: Physics
A weightless rod is acted on by upward parallel forces of \( 2 N \) and \( 4 N \) ends \( A \)
and \( B \) respectively.; The total length of
the rod \( A B=3 m . \) To keep the rod in
equilibrium a force of \( 6 N \) should act in
the following manner.
A. Downwards at any point between \( A \) and \( B \).
B. Downwards at mid point of \( A B \).
c. Downwards at a point \( C \) such that \( A C=1 m \).
D. Downwards at a point \( D \) such that \( B D=1 m \).