AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
In the circuit above, \( \boldsymbol{R}_{1}=\mathbf{2} \boldsymbol{R}_{3} \) and
\( R_{3}=2 R_{2} . \) If the source voltage is \( V_{1} \)
find the power dissipated in \( \boldsymbol{R}_{\mathbf{1}} \)
\( \mathbf{A} \cdot \frac{\left(V_{1}\right)^{2}}{7 R_{2}} \)
B. \( \frac{\left(V_{1}\right)^{2}}{14 R_{2}} \)
c. \( \frac{\left(3 V_{1}\right)^{2}}{7 R_{2}} \)
D. \( \frac{\left(V_{1}\right)^{2}}{49 R_{2}} \)
E \( \cdot \frac{\left(3 V_{1}\right)^{2}}{49 R_{2}} \)
Subject: Maths
One root of the equation \( \cos x-x+ \)
\( \frac{1}{2}=0 \) lies in the interval:
A \( \cdot\left(0, \frac{\pi}{2}\right) \)
B \( \cdot\left(-\frac{\pi}{2}, 0\right) \)
c. \( \left(\frac{\pi}{2}, \pi\right) \)
D. \( \left(\pi, \frac{3 \pi}{2}\right) \)
Subject: Chemistry
The number of metals from the
following:
\( \boldsymbol{A} \boldsymbol{s}, \boldsymbol{F} \boldsymbol{e}, \boldsymbol{X} \boldsymbol{e}, \boldsymbol{L} \boldsymbol{i}, \boldsymbol{B}, \boldsymbol{C l}, \boldsymbol{B} \boldsymbol{a}, \boldsymbol{P}, \boldsymbol{I}, \boldsymbol{S} \boldsymbol{i} \)
Subject: Biology
Identify following \( A, B \& C \) structures in
given diagram:-
A. \( A \) - Right lobe, \( B \) - Left lobe \( C \) - Diaphragm
B. A - Left lobe, B - Right lobe C - Diaphragm
C. A - Diaphragm, B - Left lobe C - Right lobe
D. A - Diaphragm, B - Right lobe C - Left lobe
Subject: Chemistry
Which of the following relation is
correct?
\( \mathbf{A} \cdot I^{s t} \) IE of \( C>I^{s t} \) IE of \( B \)
B \( \cdot I^{s t} \) IE of \( C<I^{s t} \) IE of \( B \)
C \( \cdot I I^{n d} \) IE of \( C>I I^{n d} \) IE of \( B \)
D. Both (B) and (C)
Subject: Physics
Which of the following statements is
correct?
A. Diffraction is because of interference of light from same sources whereas interference is due to light form two isolated sources.
B. Diffraction is due to interaction of light from same wave fronts whereas interference is due to interaction
of two waves derived from the same source.
C. Diffraction is due to interference of waves derived from the same source whereas interference is bending of light from the same source
D. Diffraction is due to reflected waves whereas interference is due to transmitted waves from a
source.
Subject: Physics
Arrange the following steps in the conversion of hydel energy to electricity
in a proper sequence.
(a) Released water is made to fall on the
blades of the turbines.
(b) Water in the dam is released
(c) Water is collected in the dam.
(d) Potential energy is converted to kinetic energy.
(e) The armature of the electric
generator rotates to produce electricity.
A. b c de a
B. a d b ce
\( c \cdot e c d b a \)
D. \( c b d \) a e
Subject: Chemistry
Classify the following equilibrium
reactions into homogeneous and
heterogeneous
\( \mathbf{A} \cdot 2 N O_{2}(g) \rightleftharpoons 2 N_{2}(g)+O_{2}(g) \)
B \( .2 N H_{3}(g) \rightleftharpoons N_{2}(g)+3 H_{2}(g) \)
\( \mathbf{c} \cdot 2 C u\left(N O_{3}\right)(s) \rightleftharpoons 2 C u O(s)+4 N O_{2}(g) \)
D \( \cdot P C I_{5}(g) \rightleftharpoons P C I_{3}(g)+C I_{2}(g) \)
Subject: Chemistry
At \( 25 C \) molar conductance of 0.1 molar
aqueous solution of ammonium hydroxide is 9.54 ohm \( ^{1} c m^{2} \) mol \( ^{1} \) and at
infinite dilution its molar conductance
is 238 ohm \( ^{1} \mathrm{cm}^{2} \) mol \( ^{1} \). The degree of
ionisation of ammonium hydroxide at the same concentration and
temperature is:
A. \( 2.080 \% \)
B. 20.800 \%
c. 4.008 \%
D. \( 40.800 \% \)
Subject: Physics
Four capacitor are connected, as shown
Calculate the equivalent capacitance between the points \( \boldsymbol{P} \) and \( \boldsymbol{Q} \)
\begin{tabular}{c|cc|c|c}
\hline \( \mathbf{P} \) & & & & \\
\hline & & & & \\
\( 2 \mu \mathbf{F} \) & \( 3 \mu \mathbf{F} \) & \( \mathbf{5} \mu \mathbf{F} \) & \( \mathbf{1 0 \mu F} \) & \\
\hline
\end{tabular}
Subject: Chemistry
Coal is a fossil fuel and it cannot be
prepared in a laboratory or industry because the formation of coal.
(A) is a very slow process.
(B) needs very low pressure and low
temperature
(C) needs very high pressure and high temperature
(D) causes air pollution Select the correct alternatives.
A. A and B
B. B and
\( c \cdot c \) and \( A \)
D. D and A
Subject: Physics
Assertion
When charges are shared between any
two bodies no charge is really lost some
loss of energy does occurs.
Reason
Some energy disappears in the form of heat, sparking etc.
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
The vapour pressure of pure benzene at
a certain temperature is 0.850 bar. \( A \) non-volatile, non-electrolyte solid weighing \( 0.5 g \) is added to \( 39.0 g \) of benzene (molar mass \( 78 g / \)mol ). The vapour pressure of the solution then is
\( \mathbf{0 . 8 4 5} \) bar. What is the molecular mass
of the solid substance?
\( \mathbf{A} .58 \)
в. 180
\( c .170 \)
D. 145
Subject: Physics
The potential energy (in Sl units) of a particle of mass \( 2 k g \) in a conservative
field is \( U=6 x-8 y . \) If the initial velocity of the particle is \( \vec{u}=-1.5 \hat{i}+ \) \( 2 \hat{j} \) then the total distance travelled by
the particle in first two seconds is:
A. \( 10 \mathrm{m} \)
B. 12m
\( c .15 \mathrm{m} \)
D. 18m
Subject: Physics
An equilateral prism deviates a ray
through \( 45^{\circ} \) for the two angles of
incidence differing by \( 20^{\circ} . \) The angle of incidence is
A . \( 62.5^{\circ} \)
в. \( 42.5^{\circ} \)
c. Both are correct
D. Both are wrong
Subject: Chemistry
Read below given tabular form and
answer the questions.
\begin{tabular}{llll} 
Element & Electronic configuration & Element & Elec conf \\
\( \mathrm{He} \) & \( 1 s^{2} \) & \( \mathrm{Kr} \) & \( 4 s^{2} 4 \) \\
\( \mathrm{Ne} \) & \( 2 s^{2} 2 p^{6} \) & \( \mathrm{xe} \) & \( 5 s^{2} 5 \) \\
\( \mathrm{Ar} \) & \( 3 s^{2} 3 p^{6} \) & \( \mathrm{Rn} \) & \( 6 s^{2} 6 \) \\
\hline
\end{tabular}
Write the names of 'noble gas' elements
Subject: Physics
Assertion
Magnetic field interacts with a moving charge and not with a stationary charge.
Reason

A moving charge produces a magnetic field.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Maths
If \( \vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=4 \hat{i}+3 \hat{j}+4 \hat{k} \) and
\( \vec{c}=\hat{i}+\alpha \hat{j}+\beta \hat{k} \) are linearly dependent
vectors and \( |\vec{c}|=\sqrt{3} \) then
A. \( \alpha=1, \beta=-1 \)
В. \( \alpha=1, \beta=\pm 1 \)
c. \( \alpha=-1, \beta=\pm 1 \)
D. \( \alpha=\pm 1, \beta=1 \)
Subject: Physics
The formula relating youngs modulus
(Y), rigidity modulus (n) and Poisson's ratio \( (\sigma) \) is
\( \mathbf{A} \cdot Y=2 n(1-\sigma) \)
В . \( Y=2 n(1+\sigma) \)
c. \( Y=n(1-2 \sigma) \)
D. \( Y=n(1+2 \sigma) \)
Subject: Chemistry
Which of the following is true for the reaction?
\( \boldsymbol{H}_{2} \boldsymbol{O}(l) \rightleftharpoons \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \) at \( \mathbf{1 0 0}^{\circ} \mathbf{C} \) and \( \mathbf{1} \) atm
pressure.
A \( . \Delta S=0 \)
в. \( \Delta H=T \Delta S \)
c. \( \Delta H=\Delta U \)
D. \( \Delta H=0 \)
Subject: Maths
The distance from the origin to the centroid of the tetrahedron formed by
the points \( (0,0,0),(a, 0,0),(0, b, 0),(0,0, c) \) is:
A \( \cdot \frac{\sqrt{a+b+c}}{4} \)
B. \( \frac{\sqrt{a+b+c}}{3} \)
c. \( \frac{\sqrt{a^{2}+b^{2}+c^{2}}}{16} \)
D. \( \frac{\sqrt{a^{2}+b^{2}+c^{2}}}{4} \)
Subject: Physics
A solid cylinder is rolling down on an inclined plane without slipping. The length of the plane is \( 30 m \) and its angle
of inclination is \( 30^{\circ} . \) If the cylinder starts from rest then its velocity at the bottom of the inclined plane is:
A \( \cdot 14 m s^{-1} \)
B. \( 28 m s^{-1} \)
\( \mathbf{c} \cdot 7 m s^{-1} \)
D. \( 35 m s^{-1} \)
Subject: Physics
Assertion (A): Stress is restoring force per unit area.

Reason (R) : Interatomic forces in solids
are responsible for the property of
elasticity
A. Both Assertion and Reason are true and the reason is correct explanation of the assertion
B. Both Assertion and Reason are true, but reason is not correct explanation of the assertion
c. Assertion is true, but the Reason is false
D. Assertion is false, but the reason is true
Subject: Physics
A wheel with 10 metallic spokes each \( 0.5 \mathrm{m} \) long is rotated with a speed of 120 rev/min in a plane normal to the earth's magnetic field at the place.lf the magnetic of the field is \( 0.4 \mathrm{G} \), what is the induced emf between the axle and the
rim of the wheel?
Subject: Physics
Two person each of mass \( m \$ \) are
standing at the two extremes of a
railroad car of mass left \( M \) resting on a
smooth track. The person on the left
jumps to with a velocity \( u \). Find the velocity of the train when both the person have jumped off.
A \( \cdot \frac{m^{2} u}{m(m+M)} \) towards left
B. \( \frac{m^{2} u}{M(m+M)} \) towards left
c. \( \frac{m^{2} u}{M(m+M)} \) towards right
D. \( \frac{m^{2} u}{m(m+M)} \) towards right
Subject: Chemistry
At \( 10^{0} C, \) the osmotic pressure of urea solution is \( 500 \mathrm{mm} \). The solution is
diluted and the temperature is raised to
\( 25^{0} C, \) so that the osmotic pressure became \( 105.3 \mathrm{mm} . \) The number of times,
the solution diluted is:
A . 6
B. 5
\( c \cdot 4 \)
D. 3
Subject: Physics
A battery of e.m.f. \( 15 \mathrm{V} \) and internal resistance \( 2 \Omega \) is connected to two
resistors of resistance 4 ohm and 6 ohm
joined in series. What is the electrical energy spent per minute in 6 ohm
resistor?
A . 562.5
B. 180 J
c. 456.5 J
D. 360 J
Subject: Maths
Find the middle terms of the equation of
\( \left(x^{4}-\frac{1}{x^{3}}\right)^{11} \)
\( \mathbf{A} \cdot-462 x^{9}, 462 x^{2} \)
B . \( -462 x^{8}, 462 x^{4} \)
c. \( 462 x^{7},-462 x^{3} \)
D. None of these
Subject: Physics
A thin equiconvex lens of refractive index \( 3 / 2 \) is placed on a horizontal plane mirror as shown in figure. The
space between the lens and the mirror
is filled with a liquid of refractive index 4/3. It is found what when a point object is placed \( 15 \mathrm{cm} \) above the lens on its
principal axis, the object coincides with its own image.
If another liquid is filled instead of
water, the object and the image coincide at a distance \( 25 \mathrm{cm} \) from the
lens. Calculate the refractive index of
the liquid.
\( \mathbf{A} \cdot 1.6 \)
в. 2.6
\( c .2 .8 \)
D. 3.2
Subject: Physics
\( \boldsymbol{\alpha}, \boldsymbol{\beta} \) and \( \gamma \) -rays emitted from a radioactive source are passed through
a \( 0.5 c m \) thick aluminium sheet. The out
going radiations will consist of
A. \( \alpha, \beta \) and \( \gamma \) -rays
B. \( \gamma \) and \( \beta \) -rays only
c. \( \gamma \) rays only
D. \( \alpha \) rays only
Subject: Maths
If \( a=2 \overline{3}+2 \overline{3}, \) then
A. \( a^{3}-6 a-6=0 \)
В . \( a^{3}-6 a+6=0 \)
c. \( a^{3}+6 a-6=0 \)
D. \( a^{3}+6 a+6=0 \)
Subject: Chemistry
We define p value of a term (say \( x \) ) as
\( \boldsymbol{p}_{\boldsymbol{x}}=-\log \boldsymbol{x} \)
Calculate the value of \( 1000 p \) for \( N O_{3} \) in a solution that is \( 4.78 \times 10^{-2} \mathrm{M} \) in
\( \boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2} \) and \( \boldsymbol{0 . 1 0 4} \boldsymbol{M} \) in \( \boldsymbol{Z} \boldsymbol{n}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2} \)
Subject: Physics
What is the order of magnitude of the distance of a quasar from us if light takes 2.9 billion years to reach us?
A \( \cdot 2.7 \times 10^{25} \mathrm{m} \)
В. \( 10^{25} \mathrm{m} \)
\( \mathbf{c} \cdot 10^{2} 4 m \)
D. \( 3 \times 10^{25} m \)
Subject: Chemistry
Name in IUPAC System:
(a) \( \boldsymbol{K}_{2}\left[\boldsymbol{P t C l}_{6}\right] \)
(b) \( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right] \boldsymbol{C l}_{3} \)
Subject: Maths
Evaluate \( \int \frac{\boldsymbol{x}+\mathbf{9}}{(\boldsymbol{x}+\mathbf{1 0})^{2}} \boldsymbol{e}^{x} \boldsymbol{d} \boldsymbol{x}= \)
A \( \cdot \quad e^{x} \frac{1}{x+9}+c \)
B \( \cdot e^{x} \frac{1}{x+10}+c \)
c. \( \quad e^{x} \frac{1}{(x+9)^{2}}+c \)
D. \( e^{x}+c \frac{1}{(x+10)^{2}} \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}\frac{20^{x}+3^{x}-6^{x}-10^{x}}{1-\cos 8 x} ; \text { for } x \neq 0 \\ \left(\frac{k}{16}\right) \log \left(\frac{10}{3}\right) \cdot \log 2 ; \text { for } x=0\end{array}\right. \)
continous at \( x=0, \) then the value of \( k \)
is
\( A \cdot \sin ^{2} 30^{\circ} \)
B. \( \log _{3}\left(\frac{1}{2}\right) \)
\[
3
\]
\( c \cdot \sqrt[3]{1} \)
D. \( \frac{\log 2^{2}}{3} \)
Subject: Maths
Evaluate :
\( \int \frac{1}{\sin ^{2} x \cos ^{2} x} d x \)
A . \( -\tan 2 x+C \)
B. \( -2 \cot 2 x+C \)
\( c \cdot \tan x+\cot 2 x+C \)
D. None of these
Subject: Chemistry
mole of a substance (X) was treated
with an excess of water. 2 moles of
readily combustible gas were produced along with solution which when reacted
with \( C O_{2} \) gas produced a white turbidity. The substance (X) could be:
A. \( C a \)
в. \( C a H_{2} \)
\( \mathbf{c} \cdot \operatorname{Ca}(O H)_{2} \)
\( \mathrm{D} \cdot \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2} \)
Subject: Chemistry
The reaction of \( P_{4} \) with \( X \) leads
selectively to \( \boldsymbol{P}_{4} \boldsymbol{O}_{6} . \) The \( \boldsymbol{X} \) is:
\( A \cdot \operatorname{dry} O_{2} \)
B. a mixture of \( O_{2} \) and \( N_{2} \)
\( \mathrm{c} \cdot \) moist \( O_{2} \)
D. \( O_{2} \) in presence of aq. \( N a O H \)
Subject: Maths
The value of \( \cos ^{-1}\left(\cos \left(\frac{4 \pi}{3}\right)\right) \) is
A \( \cdot 2 \pi / 3 \)
в. \( -2 \pi / 3 \)
c. \( 4 \pi / 3 \)
D. \( -4 \pi / 3 \)
Subject: Maths
A conic \( C \) passing through \( P(1,2) \) is
such that the slope of its tangent at any point on the conic is inversely proportional to the ordinate of that point and conic \( C \) passes through origin. If a circle touches the conic \( C \) at the
point \( \boldsymbol{P}(1,2) \) and passes through the focus of the conic then its radius is-
A.
B. \( \sqrt{2} \)
\( c \cdot 2 \)
D. \( \sqrt{3} \)
E. \( \sqrt{5} \)
Subject: Chemistry
Assertion
An element (X) with an atomic number
of 16 has 14 electrons in \( X^{2-} \)
Reason
Two protons bind the two outermost electrons
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
Select the correct statements for
Ellingharn diagram:
This question has multiple correct options
A. The slope of the curves of the formation of metal oxide is +ve because \( \Delta \hat{G} \) becomes less negative or increases with the rise in temperature
B. Each curve is a straight line except when some change takes place in phase \( (s \rightarrow \operatorname{lor} l \rightarrow g) \)
C. Each curve is not a straight line except when some change takes place in phase \( (s \rightarrow \operatorname{lor} l \rightarrow g) \)
D. The slope of the curves of the formation of metal oxide is -ve because \( \Delta G \) becomes less negative or increases with the rise in temperature
Subject: Chemistry
For the following half cell reactions, \( \boldsymbol{E}^{\boldsymbol{o}} \) values are also given:
\( M n^{2+}+2 H_{2} O \rightarrow M n O_{2}+4 H^{+}+ \)
\( \mathbf{2} e^{-} ; \quad \boldsymbol{E}^{o}=-\mathbf{1 . 2 3} \mathbf{V} \)
\( M n O_{4}^{-}+4 H^{+}+3 e^{-} \rightarrow M n O_{2}+ \)
\( 2 H_{2} O ; \quad E^{o}=+1.70 V \)
Select the correct statements.
A. \( M n^{2+} \) reacts with \( M n O_{4}^{-} \) in acid solution to form \( M n O_{2} \)
в. \( M n\left(M n O_{4}\right)_{2} \) is stable in acid solution
c. \( M n O_{2} \) disproportionates to \( M n^{2+} \) and \( M n O_{4}^{-} \) in acid solution
D. None of the above
Subject: Chemistry
Find the number of delta bonding molecular orbital from the following set if \( z \) is the inter-nuclear axis :
\( \boldsymbol{d}_{\boldsymbol{x}^{2}-\boldsymbol{y}^{2}} \) and \( \boldsymbol{d}_{\boldsymbol{x} z}, \boldsymbol{d}_{\boldsymbol{x}^{2}-\boldsymbol{y}^{2}} \) or \( \boldsymbol{d}_{\boldsymbol{x} \boldsymbol{z}} \)
Subject: Physics
A uniform rope of mass \( 0.1 \mathrm{kg} \) and length 2.5 m. hangs from ceiling. The speed of transverse wave in the rope at upper end and at a point \( 0.5 \mathrm{m} \) distance from lower end will be:
\( A \cdot 5 \mathrm{m} / \mathrm{s}, 2.24 \mathrm{m} / \mathrm{s} \)
B. \( 10 \mathrm{m} / \mathrm{s}, 3.23 \mathrm{m} / \mathrm{s} \)
c. \( 1.5 \mathrm{m} / \mathrm{s}, 1.2 \mathrm{m} / \mathrm{s} \)
D. none of these
Subject: Chemistry
Which of the following primary and
secondary valencies are not correctly
marked against the compound?
\( \mathbf{A} \cdot\left[C r\left(N H_{3}\right)_{6}\right] C l_{3}, p=3, s=6 \)
В \( \cdot K_{2}\left[P t C l_{4}\right], p=2, s=4 \)
\( \mathbf{C} \cdot\left[P t\left(N H_{3}\right)_{2} C l_{2}\right], p=0, s=4 \)
\( \mathbf{D} \cdot\left[C u\left(N H_{3}\right)_{4}\right] S O_{4}, p=4, s=4 \)
Subject: Maths
\( \int \frac{3.2^{x}-2.3^{x}}{2^{x}} d x= \)
A \( \cdot 3 x+\frac{2(1.5)^{x}}{\log (1.5)}+c \)
B. \( 3 x-\frac{2(1.5)^{x}}{\log (1.5)}+c \)
\( \mathbf{c} \cdot 3 x-2(1.5)^{x} \log 1.5+c \)
D. \( 3 x+2 \log 1.5(1.5)^{x}+c \)
Subject: Maths
Let \( \boldsymbol{S}=\{1,2,3, \ldots, 100\} . \) The number
of non-empty subsets \( \boldsymbol{A} \) of \( \boldsymbol{S} \) such
that the product of elements in \( \boldsymbol{A} \) is even is :-
A \( \cdot 2^{50}\left(2^{50}-1\right) \)
B . \( 2^{100}-1 \)
c. \( 2^{50}-1 \)
D. \( 2^{50}+1 \)
Subject: Chemistry
Which of the following is/are ionization?
This question has multiple correct options
A \( \cdot N a \rightarrow N a^{+}+e^{-} \)
B. \( C l+e^{-} \rightarrow C l^{-} \)
c. \( N a C l \rightarrow N a^{+}+C l^{-} \)
D. \( M g B r_{2} \rightarrow M g^{2+}+2 B r \)
Subject: Biology
Assertion
When people have muscle cramps
during exercise, they are asked to use the hot bag to relieve the muscle cramp.
Reason
Anaerobic respiration happens in muscle cells during intense workout.
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
From which height a block of ice must be dropped in order that it melts completely. Assume that all the energy
is retained by the ice. \( \left(g=10 m s^{-2}, L=80 J g m^{-1} a n d J=4.2\right. \)
\( \mathrm{J} / \mathrm{cal} \)
A. \( 1000 \mathrm{Km} \)
B. 100Km
c. 33.6кm
D. \( 1 \mathrm{Km} \)
Subject: Maths
fin a \( \triangle D E F, G H \| E F \) and \( D G \)
\( \boldsymbol{E G}=\boldsymbol{2}: \boldsymbol{3} \) then the value of
\( \frac{\operatorname{ar}(\triangle D G H)}{\operatorname{ar}(\triangle D E F)} \)
A \( \cdot \frac{2}{15} \)
B. \( \frac{4}{15} \)
c. \( \frac{4}{25} \)
D. \( \frac{2}{25} \)
Subject: Physics
The electric field at point Pjust outside the outer surface of a hollow spherical conductor of inner radius \( 10 \mathrm{cm} \) and
outer radius \( 20 \mathrm{cm} \) has magnitude 450 \( \mathrm{N} / \mathrm{C} \) and is directed outward. When an
unknown point charge \( Q \) is placed at the center of the sphere, the electric field at point \( P \) is still pointing outward but is now \( 180 \mathrm{N} / \mathrm{C} \). What is the value of
charge Q?
A . 4.5 nc
в. 1.5 nc
\( c .-1.5 \mathrm{nc} \)
D. -1.2 nc
Subject: Physics
Figure shows three vectors \( \vec{a}, \vec{b} \) and \( \vec{c} \) where \( R \) is the midpoint of \( P Q \). Then
which of the following relations is
correct?
A. \( \vec{a}+\vec{b}=2 \vec{c} \)
в. \( \vec{a}+\vec{b}=\vec{c} \)
c. \( \vec{a}-\vec{b}=2 \vec{c} \)
D. \( \vec{a}-\vec{b}=\vec{c} \)
Subject: Physics
The temperature of the centre of the Earth is about
A \( \cdot 4000^{\circ} \mathrm{C} \)
в. \( 6000^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 10^{4^{\circ}} C \)
D. \( 10^{6^{\circ}} \mathrm{C} \)
Subject: Chemistry
In a three litre vessel, 2 moles of \( N_{2} \) and
3 moles of length \( \boldsymbol{H}_{2} \) are taken. If at
equilibrium \( x \) moles of \( N_{2} \) were obtained then the concentration of
\( N H_{3} \) at equilibrium will be:
\( \mathbf{A} \cdot 2-x \)
B. \( 4-2 x \)
c. \( \frac{2 x}{3} \)
D. \( \frac{4-2 x}{3} \)
Subject: Physics
A stress \( 10^{7} \) Pa produces a strain of \( 4 x \)
\( 10^{-3} . \) The energy stored per unit volume
of the body \( \left(\operatorname{in} \mathrm{J} . \mathrm{m}^{-3}\right) \) is
\( A \cdot 2 \times 10^{3} \)
B. \( 2 \times 10^{4} \)
c. \( 2.5 \times 10^{10} \)
D. \( 0.8 \times 10^{4} \)
Subject: Maths
If \( \sin (\alpha+\beta)=1 \) and \( \sin (\alpha-\beta)=1 / 2 \)
where \( \boldsymbol{\alpha}, \boldsymbol{\beta} \boldsymbol{\epsilon}[\mathbf{0}, \boldsymbol{\pi} / 2] \) then
This question has multiple correct options
A \( \cdot \tan (\alpha+2 \beta)=-\sqrt{3} \)
B. \( \tan (2 \alpha+\beta)=-1 / \sqrt{3} \)
\( \mathbf{c} \cdot \tan (\alpha+2 \beta)=\sqrt{3} \)
D. \( \tan (\alpha+2 \beta)=1 / \sqrt{3} \)
Subject: Maths
Construct a quadrilateral \( \boldsymbol{A B C D} \), with \( \boldsymbol{B C}=\mathbf{5} \mathrm{cm}, \boldsymbol{C D}=\mathbf{9} \mathrm{cm}, \boldsymbol{D} \boldsymbol{A}=\mathbf{6} \mathrm{cm} \)
\( \angle C=60^{\circ}, \angle D=75^{\circ} \)
Subject: Physics
Which of the following is a proper
sequence?
A. Elastic region, Yielding, Fracture stress, Strain hardening, Necking
B. Elastic region, Yielding, Strain hardening, Necking Fracture stress
C. Elastic region, Strain hardening, Yielding, Necking , Fracture stress
D. Elastic region, Strain hardening, Necking, Yielding, Fracture stress
Subject: Chemistry
If the standard electrode potential
constant for a cell is \( 2 V \) at \( 300 K \) the
equilibrium constant (K) for the
reaction
\( Z n(s)+C u^{2+}(a q) \rightleftharpoons Z n^{2+}(a q)+ \)
\( C u(s) \) at \( 300 K \) is approximately.
\( \left(\boldsymbol{R}=\mathbf{8} \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1}, \boldsymbol{F}=\right. \)
\( 96000 C m o l^{-1} \)
A \( \cdot e^{16} \)
B. \( e^{32} \)
\( c \cdot e^{-160} \)
D. \( e^{-8} \)
Subject: Maths
The value of \( \cos \left[\frac{1}{2} \cos ^{-1} \cos \left(-\frac{14 \pi}{5}\right)\right] \)
is
This question has multiple correct options
\( ^{A} \cdot \cos \left(-\frac{7 \pi}{5}\right) \)
B \cdot \( \sin \left(\frac{\pi}{10}\right) \)
c. \( \cos \left(\frac{2 \pi}{5}\right) \)
D. \( -\cos \left(\frac{3 \pi}{5}\right) \)
Subject: Chemistry
Magnetic moment \( \sqrt{35} \) is true for which
of the following pair:
A. \( C o^{+2}, F e^{+2} \)
B . \( F e^{+3}, M n^{+2} \)
c. \( C o^{+3}, C r^{+2} \)
D. \( F e^{+2}, M n^{+2} \)
Subject: Chemistry
A balanced reaction between \( F e \) and \( O_{2} \)
to give magnetic oxide is :
A \( \cdot 2 F e+O_{2} \rightarrow 2 F e O \)
B. \( 2 F e+2 O_{2} \rightarrow F e_{2} O_{3} \)
\( \mathrm{c} \cdot 3 \mathrm{Fe}+2 \mathrm{O}_{2} \rightarrow \mathrm{Fe}_{3} \mathrm{O}_{4} \)
D. \( F e+2 O_{2} \rightarrow F e_{3} O_{4} \)
Subject: Physics
Consider a magnet surround by a wire with a on/of switch \( \mathrm{S} \) (figure) if the
switch is thrown from the off position (open circuit) to the on position (closed circuit.)
A. The current will flow in clock wise direction as seen from left side
B. The current will flow in anti clock wise direction as seen from left hand side
c. The current will not flow
\( D \)
be decided
Subject: Maths
Goods were bought for \( R s .600 \) and sold
the same for \( R s .688 .50 \) at a credit of 9
months and thus gaining \( 2 \% \). The rate of interest per annum is:
A \( \cdot 16 \frac{2}{3} \% \)
в. \( 14 \frac{1}{2} \% \)
c. \( _{13} \frac{1}{3} \% \)
D. 15\%