AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Let \( \boldsymbol{y}=\boldsymbol{g}(\boldsymbol{x}) \) be the inverse of \( \mathbf{a} \)
bijective mapping \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \quad \boldsymbol{f}(\boldsymbol{x})= \)
\( 3 x^{3}+2 x . \) The area bounded by graph of
\( g(x), \) the axis and the ordinate at \( x=5 \)
is
A \( \cdot \frac{5}{4} \)
B. \( \frac{7}{4} \)
\( c \cdot \frac{9}{4} \)
D. \( \frac{13}{4} \)
Subject: Physics
A spherical ball of radius \( r \) and relative
density 0.5 is floating in equilibrium in water with half of its immersed in
water. The work done in pushing the ball down so that whole of it is just
immersed in water is \( 1 \rho \) is the density
of water-
A. 0.25 prg
в. \( 0.5 \rho r g \)
c. \( \frac{4}{3} \pi r^{3} \rho g \)
D. \( \frac{5}{12} \pi r^{4} \rho g \)
Subject: Physics
In the arrangement shown in the figure,
if the surface is smooth, the
acceleration of the hanging block \( \boldsymbol{m}_{2} \)
will be \( \left(m_{1} \text { is on the table }\right) \)
A \( \cdot \frac{m_{2} g}{4 m_{1}+m_{2}} \)
В. \( \frac{2 m_{2} g}{4 m_{1}+m_{2}} \)
c. \( \frac{2 m_{2} g}{m_{1}+4 m_{2}} \)
D. \( \frac{2 m_{1} g}{m_{1}+m_{2}} \)
Subject: Maths
If \( A \) and \( B \) are two events such that
\( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 4}, \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})=\mathbf{0 . 7} \) and
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0 . 2} \) then \( \boldsymbol{P}(\boldsymbol{B}) \) is equal to
A . 0.1
B. 0.3
\( c .0 .5 \)
\( D \)
Subject: Physics
A deuterium reaction that occurs in a
hypothetical experimental fusion reactor occurs in two stages
(i) two deuterium \( \left(_{1} D^{2}\right) \) nuclei fuse
together to form a tritium nucleus, with
a proton as a by-product: \( D(D, p) T \)
(ii) a tritium nucleus fuses with
another deuterium nucleus to form a
\( \left(_{2} H e^{4}\right) \) nucleus with neutron as a by-
product \( \boldsymbol{T}(\boldsymbol{D}, \boldsymbol{n})_{2} \boldsymbol{H} \boldsymbol{e}^{4} \)
Compute
(a) the energy released in
each of two the stages and the energy released in the combined reaction.
(b) the energy released per deuterium nucleus.
Given \( \left(_{1} D^{2}\right)=2.014102 \) a.m.u
\( _{1} T^{3}=3.016049 a . m . u \)
\( _{2} H e^{4}=4.002603 a . m . . \)
\( \mathbf{1} \boldsymbol{H}^{\mathbf{1}}=\mathbf{1} . \mathbf{0 0 7 8 2} \mathbf{5} \boldsymbol{a} . \boldsymbol{m} . \boldsymbol{u} \)
\( \mathbf{o} \boldsymbol{n}^{\mathbf{1}}=\mathbf{1 . 0 0 8 6 6 5 a} . \boldsymbol{m} . \boldsymbol{u} \)
Subject: Maths
If \( e_{1} \) and \( e_{2} \) are the eccentricities of \( a \)
hyperbola \( 3 x^{2}-3 y^{2}=25 \) and its
conjugate respectively, then
A \( \cdot e_{1}^{2}+e_{2}^{2}=2 \)
B . \( e_{1}^{2}+e_{2}^{2}=4 \)
\( \mathbf{c} \cdot e_{1}+e_{2}=4 \)
D. \( e_{1}+e_{2}=\sqrt{2} \)
Subject: Chemistry
Benzene carbaldehyde is reacted with concentrated \( N a O H \) solution to give the products \( A \) and \( B \). The product \( A \) can be used as food preservative and the product \( B \) is an aromatic hydroxy compound where \( O H \) group is linked to
\( s p^{3} \) hybridised carbon atom next to
benzene ring. The products \( A \) and \( B \) respectively are :
A. sodium benzoate and phenol
B. sodium benzoate and phenyl methanol
c. sodium benzoate and cresol
D. sodium benzoate and picric acid
Subject: Physics
\( N^{\prime} \) moles of a diatomic gas in a
cylinder are at a temperature \( ^{\prime} \boldsymbol{T}^{\prime} . \) Heat
is supplied to the cylinder such that the
temperature remains constant but \( n \)
moles of the diatomic gas get converted
into monatomic gas.What is the change in the total kinetic energy of the
gas?
A \( \cdot \frac{5}{2} n R T \)
B. \( \frac{1}{2} n R T \)
c. 0
D. \( \frac{3}{2} n R T \)
Subject: Maths
\( \cos ^{3} \theta+\cos ^{3}\left(120^{\circ}+\theta\right)+\cos ^{3}\left(120^{\circ}-\right. \)
\( \boldsymbol{\theta})= \)
\( A \cdot \frac{3}{4} \sin 3 \theta \)
B . \( \frac{3}{4} \cos 3 \theta \)
\( \mathrm{c} \cdot \frac{3}{4} \tan 3 \theta \)
D. \( \frac{3}{4} \cot 3 \theta \)
Subject: Physics
In an a.c. circuit, the instantaneous
e.m.f. and current are given by
\( e=100 \sin 30 t \)
\( i=20 \sin \left(30 t-\frac{\pi}{4}\right) \)
In one cycle of a.c., the average power consumed by the circuit and the wattless current are, respectively:
\( \mathbf{A} \cdot 50,10 \)
B. \( \frac{1000}{\sqrt{2}}, 10 \)
c. \( \frac{50}{\sqrt{2}}, 0 \)
D. 50,0
Subject: Physics
A train is moving at a constant speed \( \mathrm{V} \) when its driver observes another train
in front of him on the same track and
moving in the same direction with constant speed v. If the distance
between the trains is \( x, \) then what
should be the minimum retardation of
the train so as to avoid collision?
A \( \cdot \frac{(V+v)^{2}}{x} \)
B. \( \frac{(V-v)^{2}}{x} \)
C \( \frac{(V+v)^{2}}{2 x} \)
D. \( \frac{(V-v)^{2}}{2 x} \)
Subject: Chemistry
For the reaction, \( \boldsymbol{C}_{3} \boldsymbol{H}_{8}(\boldsymbol{g})+ \)
\( \mathbf{5} O_{2}(\boldsymbol{g}) \longrightarrow \mathbf{3} \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{4} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \) at
constant temperature, \( \Delta \boldsymbol{H}-\Delta \boldsymbol{E} \) is:
\( \mathbf{A} \cdot+3 R T \)
B . \( -R T \)
\( \mathbf{c} \cdot+R T \)
D. \( -3 R T \)
Subject: Physics
Which of the following relations for the displacement of a partide undergoing simple harmonic motion is not correct
dimensionally?
A \( \cdot Y=a \sin \frac{2 \pi t}{T} \)
B. \( Y=a \cos \omega t \)
c. \( Y=\frac{a}{T} \sin \left(\frac{t}{a}\right. \)
\( V=a \sqrt{2}\left(\sin \frac{2 \pi t}{T}+\cos \frac{2 \pi t}{T}\right) \)
Subject: Chemistry
Assertion
Covalent bonds are broken when sugars
are dissolved in water.
Reason
In molecules with covalent bonds,
electrons are shared by two or more
atoms
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect
Subject: Physics
If \( n_{t}, \) number of radio atoms are present
at time \( t, \) the following expression will
be a constant
A \( \cdot \frac{n_{t}}{t} \)
в. \( \ln \frac{n_{t}}{t} \)
c. \( \frac{d}{d t}\left(\ln n_{t}\right) \)
D. \( t \cdot n_{t} \)
Subject: Physics
If \( |\vec{A}+\vec{B}|=|\vec{A}|=|\vec{B}| \) the angle
between \( A \) and \( B \) will be :-
A \( \cdot 90^{\circ} \)
B . \( 120^{\circ} \)
\( c \cdot 0^{c} \)
D. \( 60^{\circ} \)
Subject: Chemistry
Which of the reagents listed below could be added to water to make \( 0.1 \mathrm{M} \)
solutions of \( C H_{3} C O O^{\ominus} \) ions?
¡. \( \boldsymbol{C H}_{3} \) COOH
¡i. \( C H_{3} C O O N a \)
A. \( C H_{3} C O O H \) because it is a strong electrolyte
B. \( C H_{3} \) COONa because it is a strong electrolyte
\( \mathrm{c} \cdot C H_{3} C O O H \) because it is a weak electrolyte
D. \( C H_{3} C O O N a \) because it is a weak electrolyte
Subject: Maths
The value of 'a' for which the function
\( f(x)=(a+2) x^{3}-3 a x^{2}+9 a x-1 \)
decreases for all real values of \( x \) is
B \( \cdot(-\infty,-3) \)
\( c \cdot(-\infty,-2) \)
D. \( (-\infty,-3] \cup[0, \infty) \)
Subject: Maths
If \( \bar{a}=a_{1} \hat{i}+a_{2} \hat{j}+a_{3} \hat{k}, \bar{b}=b_{1} \hat{i}+b_{2} \hat{j}+ \)
\( b_{3} \hat{k}, \bar{c}=c_{1} \hat{i}+c_{2} \hat{j}+c_{3} \hat{k} \) are non zero
vectors such that \( \bar{c} \) is a unit vector \( \perp \) to
both the vectors \( \bar{a} \) and \( \bar{b} \), if angle between \( \bar{a} \) and \( \bar{b} \) is \( \frac{\pi}{6} \) then \( \left|\begin{array}{lll}\boldsymbol{a}_{1} & \boldsymbol{a}_{2} & \boldsymbol{a}_{3} \\ \boldsymbol{b}_{1} & \boldsymbol{b}_{2} & \boldsymbol{b}_{3} \\ \boldsymbol{c}_{1} & \boldsymbol{c}_{2} & \boldsymbol{c}_{3}\end{array}\right|^{2} \) equals
A \( \cdot \frac{1}{4}\left(a_{1}^{2}+a_{2}^{2}+a_{3}^{2}\right)\left(b_{1}^{2}+b_{2}^{2}+b_{3}^{2}\right) \)
B \( \cdot \frac{3}{4}\left(a_{1}^{2}+a_{2}^{2}+a_{3}^{2}\right)\left(b_{1}^{2}+b_{2}^{2}+b_{3}^{2}\right)\left(c_{1}^{2}+c_{2}^{2}+c_{3}^{2}\right) \)
c. 1
D. 0
Subject: Physics
A tin nucleus has charge \( 50 e V \). If the
proton is \( 10^{-12} m \) from the nucleus.
Then, the potential at this position will
be:
A \( .7 .2 \times 10^{8} V \)
B. \( 3.6 \times 10^{4} V \)
c. \( 1.44 \times 10^{4} V \)
D. \( 7.2 \times 10^{4} V \)
Subject: Chemistry
Chloretone is:
A. \( C C l_{3} N O_{2} \)
в. \( C H_{3} C O C H_{2} C H C l_{2} \)
c. \( \left(C H_{3}\right)_{2} \) СОСНС\( l_{2} \)
D \( \cdot\left(C H_{3}\right)_{2} C(O H) C C l_{3} \)
Subject: Maths
State whether the statement is
true/false.
The lines \( 2 x+3 y=19 \) and \( 2 x+3 y+ \)
\( \mathbf{7}=\mathbf{0} \) are not equidistant from the line
\( 2 x+3 y=6 \)
A. True
B. False
Subject: Chemistry
Use the bond energies to estimate \( \Delta \boldsymbol{H} \)
for this reaction:
\[
\boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{H}_{2} \boldsymbol{O}_{2}(\boldsymbol{g})
\]
Bond
\[
H-H
\]
\( 436 k J_{m o l}-1 \)
\( \mathbf{A} \cdot-127 k J \)
B . \( -209 k J \)
c. \( -484 k J \)
D. \( -841 k J \)
Subject: Biology
Select the wrong statement.
A. Proteins are heteropolymers made of amino acids.
B. Ribozymes are nucleic acids with catalytic power.
C. Nucleic acids serve as genetic material.
D. Proteins, nucleic acids are macromolecules found in the living system.
E. Collagen is the most abundant protein in the whole of the biosphere and RuBisCo is the most abundant proteins in animal world.
Subject: Physics
Figure shows the position-time graph of
a particle of mass \( 4 k g . \) What is the \( (a) \)
force on the particle for \( t<0, t> \)
\( 4 s, 0<t<4 s \)
(b) impulse at \( t=0 \) and \( t \)
\( =4 \) s? (Consider one-dimensional
motion only).
Subject: Chemistry
\( \boldsymbol{P}_{\boldsymbol{A}}=\boldsymbol{X}_{\boldsymbol{A}} \boldsymbol{P}_{\boldsymbol{A}} \) and \( \boldsymbol{P}_{\boldsymbol{B}}=\boldsymbol{X}_{\boldsymbol{B}} \boldsymbol{P}_{\boldsymbol{B}} \)
\( \boldsymbol{P}_{\boldsymbol{T}}=\boldsymbol{X}_{\boldsymbol{A}} \boldsymbol{P}_{\boldsymbol{A}}+\boldsymbol{X}_{\boldsymbol{B}} \boldsymbol{P}_{\boldsymbol{B}_{\boldsymbol{B}}} \)
Vapour pressure of mixtures of Benzene \( \left(C_{6} H_{6}\right) \) and toluene \( \left(C_{7} H_{8}\right) \) at \( 50^{\circ} C \) are given by \( \boldsymbol{P}_{M}=\mathbf{1 7 9} \boldsymbol{X}_{\boldsymbol{B}}+\mathbf{9 2} \) where
\( X_{B} \) is mole fraction of \( C_{6} H_{6} \)
What is the vapour pressure of pure liquids?
A \( \cdot P_{B}=92 m m, P_{T}=179 m m \)
B . \( P_{B}=271 \mathrm{mm}, P_{T}=92 \mathrm{mm} \)
c. \( P_{B}=180 m m, P_{T}=91 m m \)
D. None of these
Subject: Physics
If three particles each of mass \( m \) are placed at the corners of an equilateral triangle of side \( a \), the potential energy of the system and the work done if the side of the triangle is changed from \( a \) to
\( \mathbf{2} \boldsymbol{a}, \) are
\( ^{\mathbf{A}} \cdot \frac{3 G M}{a^{2}}, \frac{3 G M}{2 a} \)
в. \( -\frac{3 G M^{2}}{a}, \frac{3 G M^{2}}{2 a} \)
c. \( -\frac{3 G M^{2}}{a^{2}}, \frac{3 G M^{2}}{4 a^{2}} \)
D. \( -\frac{3 G M^{2}}{a}, \frac{3 G M}{2 a} \)
Subject: Physics
Moment about the point \( \vec{i}+2 \vec{j}-\vec{k} \) of a force represented by \( \vec{i}+2 \vec{j}+\vec{k} \) acting through the point \( 2 i+3 j+k \) is
\( \mathbf{A} \cdot 3 \vec{i}+\vec{j}-\vec{k} \)
B. \( 3 \vec{i}-\vec{j}+\vec{k} \)
c. \( -3 \vec{i}+\vec{j}+\vec{k} \)
D. \( 3 \vec{i}+\vec{j}+\vec{k} \)
Subject: Biology
The critical checkpoints that control the
cell cycle are at the
\( \mathbf{A} \cdot G_{1} \) to \( \mathrm{S} \) stage and \( G_{2} \) to \( \mathrm{M} \) stage
B. \( \mathrm{S} \) to \( G_{2} \) stage and \( G_{2} \) to M stage
\( \mathbf{C} \cdot \mathbf{M} \) to \( G_{1} \) stage and \( G_{2} \) to \( \mathbf{M} \) stage
D. M to \( G_{1} \) stage and \( \mathrm{S} \) to \( G_{2} \) stage
Subject: Maths
\( \operatorname{Let} f(x)=\frac{\sin \{x\}}{x^{2}+a x+b} . \) If \( f\left(5^{+}\right) \& \)
\( f\left(3^{+}\right) \) exists finitely and are not zero, then the value of
\( (a+b) \) is (where \( \{\cdot\} \) represents
fractional part function).
\( A \cdot 7 \)
B . 10
c. 11
D. 20
Subject: Physics
In the diffraction pattern due to a single slit of width ' \( d \) with incident light of
wavelength ' \( \lambda^{\prime}, \) at an angle of
diffraction ' \( \boldsymbol{\theta}^{\prime} \), the condition for first
minimum is
\( \mathbf{A} \cdot \lambda \sin \theta=d \)
B. \( d \cos \theta=\lambda \)
\( \mathbf{c} \cdot d \sin \theta=\lambda \)
\( \mathbf{D} \cdot \lambda \cos \theta=d \)
Subject: Physics
1 ampere current is equivalent to
\( \mathbf{A} \cdot 6.25 \times 10^{18} \) electrons \( s^{-1} \)
B. \( 2.25 \times 10^{18} \) electrons \( s^{-1} \)
C \( .6 .25 \times 10^{14} \) electrons \( s^{-1} \)
D. \( 2.25 \times 10^{14} \) electrons \( s^{-1} \)
Subject: Chemistry
\( 17.4 \% \) (w/v) \( K_{2} S O_{4} \) solution at \( 27^{0} C \) is
isotonic with \( 5.85 \% \) (w/v) NaCl solution
at \( 27^{0} C . \) If \( \mathrm{NaCl} \) is \( 100 \% \) ionised, what is
\( \% \) ionisation of \( K_{2} S O_{4} \) in aq. solution?
Subject: Physics
The natural frequency \( \left(\omega_{0}\right) \) of
oscillations in LC Circuit is given by:
A \( \cdot \frac{1}{2 \pi} \frac{1}{\sqrt{L C}} \)
B. \( \frac{1}{\pi} \frac{1}{\sqrt{2 L C}} \)
c. \( \frac{1}{\sqrt{L C}} \)
D. \( \sqrt{L C} \)
Subject: Physics
A ball is thrown up at a speed of \( 4 \mathrm{m} / \mathrm{s} \) with constant acceleration. Find the
maximum height reached by the ball. Take \( g=10 m s^{-2} \)
A. \( 0.4 \mathrm{m} \)
B. \( 0.8 \mathrm{m} \)
c. \( 1.0 \mathrm{m} \)
D. 1.4 \( m \)
Subject: Physics
What should be the minimum force \( \boldsymbol{P} \)
to be applied to the string so that block
of mass \( m \) just begins to move up the
frictionless plane.
\( \mathbf{A} \cdot M g \tan \theta / 2 \)
в. \( M g \cot \theta / 2 \)
c. \( \frac{M g \cot \theta / 2}{1+\sin \theta} \)
D. \( M g \cos \theta / 2 \)
Subject: Physics
A copper weight and iron weight of the same mass were dropped from the same height on the ground Which of the weights had the higher temperature
after the impact ? (specific heat of \( \mathrm{Cu}= \)
\( 0.1 \mathrm{Kcal} / \mathrm{kg}^{o} \mathrm{C} \);specific heat of iron \( = \)
\( \left.0.11 \mathrm{Kcal} / \mathrm{kg}^{\circ} \mathrm{C}\right) \)
A. Iron weight
B. Copper weight
c. Both iron and copper
D. Cannot be answered
Subject: Physics
For the circuit shown in the Figure, the current through the inductor is \( 0.9 A \)
while the current through the condenser
is \( 0.4 A \)
A. current drawn from generator \( 1=1.13 \mathrm{A} \)
B. \( \omega=\frac{1}{(1.5 L C)} \)
\( \mathbf{C} \cdot I=0.5 \mathrm{A} \)
\( D \cdot I=0.6 A \)
Subject: Physics
The velocity \( v \) of a particle at time \( t \) is
given by \( v=a t+\frac{b}{t+c}, \) where \( a, b \) and \( c \)
are constants.The dimensions of
\( a, b \) and \( c \) are respectively:
\( \mathbf{A} \cdot \mathrm{LT}^{-2}, \mathrm{L} \) and \( \mathrm{T} \)
B. \( L^{2}, \) T and \( L T^{2} \)
c. \( L^{2} \), LT and \( L \)
D. L, LT and \( T^{2} \)
Subject: Physics
Two circular coils of radii \( 5 \mathrm{cm} \) and 10
cm carry currents of 2 A.The coils have 50 and 100 turns respectively and are placed in such a way that their planes as well as their centres
coincide.Magnitude of magnetic field at the common centre of coil is
This question has multiple correct options
A. \( 8 \pi \times 10^{-4} T \) if currents in the coils are in same ser
B . \( 4 \pi \times 10^{-4} T \) if currents in the coils are in opposite
sense
c. zero if currents in the coils are in opposite sense
D. \( 8 \pi \times 10^{-4} T \) if currents in the coils are in opposite
sense
Subject: Physics
Two rods having thermal conductivities in the ratio of 5: 3 and having equal length length and equal cross-section are joined by face to face. If the temperature of free end of first rod is
\( 100^{\circ} \mathrm{C} \) and temperature of free end of
second rod is \( 20^{\circ} c, \) then temperature of the junction, is-
A \( \cdot 90^{\circ} \mathrm{C} \)
B . \( 85^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot 70^{\circ} \mathrm{C} \)
D. \( 50^{\circ} \mathrm{C} \)
Subject: Maths
If the line \( x=\alpha \) divides the area of the
region \( \boldsymbol{R}= \)
\( \left\{(x, y) \in \mathbb{R}^{2}: x^{3} \leq y \leq x, 0 \leq x \leq 1\right\} \)
into two equal parts, then
A \( \cdot 0<\alpha \leq \frac{1}{2} \)
в. \( \frac{1}{2}<\alpha<1 \)
c. \( 2 \alpha^{4}-4 \alpha^{2}+1=0 \)
D. \( \alpha^{4}+4 \alpha^{2}-1=0 \)
Subject: Physics
In an experiment a sphere of aluminium
of mass \( 0.20 k g \) is heated upto \( 150^{\circ} C \)
Immediately, it is put into water of
volume \( 150 c c \) at \( 27^{\circ} C \) kept in a
calorimeter of water equivalent of
\( 0.025 k g . \) Final temperature of the
system is \( 40^{\circ} \mathrm{C} \). The specific heat of
aluminium is :
(take 4.2 Joule \( =1 \) calorie)
\( \mathbf{A} \cdot 434 J / k g-^{o} C \)
B . \( 378 J / k g-^{o} C \)
\( \mathbf{c} \cdot 476 J / k g-^{o} C \)
D . \( 315 \mathrm{J} / \mathrm{kg}-^{\circ} \mathrm{C} \)
Subject: Chemistry
Which of the follwing is the correct electronic configuration of
\( \boldsymbol{F} \boldsymbol{e}^{+3} \boldsymbol{i o n}\left(\boldsymbol{Z}_{\boldsymbol{F} e}=\boldsymbol{2} \boldsymbol{6}\right) ? \)
\( \mathbf{A} \cdot[A r] 3 d^{6} \)
B . \( [A r] 3 d^{5} \)
\( \mathbf{c} \cdot[A r] 3 d^{6} 4 s^{2} \)
D \cdot \( [A r] 3 d^{6} 4 s^{1} \)
Subject: Biology
Given figure depicts the light
harvesting complex (LHC) of
photosystem I (PSI). Select the correct identification for \( \mathbf{A}, \mathbf{B} \)
C and \( D \)
A. A-molecules; B- Antenna molecule; C- \( P_{680} ; \) D- Primary
\( e^{-} \) acceptor.
B. A-Antenna molecules; B-Core molecule; \( P_{700} ; \) D-
Primary \( e^{-} \) acceptor.
C. A-Antenna molecules; B-Core molecule; \( P_{700} ; \) D-
Plastocyanin
D. A-Core molecules; B- Reaction centre; \( P_{680} ; \) D-
Plastocyanin
Subject: Physics
single Correct Answer Type The path of a projectile is given by the
equation \( y=a x-b x^{2}, \) where \( a \) and \( b \)
are constants and \( x \) and \( y \) are
respectively horizontal and vertical distances of projectile from the point of projection. The maximum height attained by the projectile and the angle of projection are respectively:
A \( \cdot \frac{2 a^{2}}{b}, \tan ^{-1}(a) \)
B. \( \frac{b^{2}}{2 a}, \tan ^{-1}(b) \)
c. \( \frac{a^{2}}{b}, \tan ^{-1}(2 b) \)
D \( \cdot \frac{a^{2}}{4 b}, \tan ^{-1}(a) \)
Subject: Chemistry
Choose the correct statement for
chemical adsorption:

This question has multiple correct options
A. Value of adsorption enthalpy is above \( -20 k J m o l^{-1} \)
B. Van der Waals forces exist between adsorbent and
adsorbate
C. Usually monomolecular layer is formed on adsorbent
D. Multimolecular layer may be formed on adsorbent
Subject: Maths
Represent the following mixed infinite decimal periodic fractions as common fractions:
\( \left(\frac{a^{1 / 2}+2}{a+2 a^{1 / 2}+1}-\frac{a^{1 / 2}-2}{a-1}\right) \cdot \frac{a^{1 / 2}+1}{a^{1 / 2}} \)
Subject: Physics
A wheel having moment of inertia
\( 4 k g m^{2} \) about its symmetrical axis, rotates at rate of 240 rpm about it. The torque which can stop the rotation of the wheel in one minute is:
\( ^{\mathbf{A}} \cdot \frac{5 \pi}{7} N m \)
в. \( \frac{8 \pi}{15} \mathrm{Nm} \)
c. \( \frac{2 \pi}{9} N m \)
D. \( \frac{3 \pi}{7} N m \)
Subject: Physics
Jet plane is traveling west at the speed of \( 1800 \mathrm{km} / \mathrm{h} \). What is the voltage difference developed between the ends of the wing \( 25 \mathrm{m} \) long, if the earth's magnetic field at the location has a magnitude of \( 5 \times 10^{-4} \) and the dip
angle is 30
A. 0
B. 3.12 \( v \)
\( c \cdot 10.20 v \)
D. 50 v
Subject: Chemistry
Which choice below is the rate law of
the following reaction?
\( \mathbf{2} \boldsymbol{H}_{\mathbf{2}}(\boldsymbol{g})+\boldsymbol{O}_{\mathbf{2}}(\boldsymbol{g}) \rightarrow \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O}(\boldsymbol{g}) \)
A . Rate\( =k[H][O] \)
B. Rate \( =k\left[H_{2}\right]^{x}\left[O_{2}\right]^{y} \)
c. Rate\( =k\left[H_{2}\right]^{2}\left[O_{2}\right] \)
D. Rate \( =k\left[H_{2}\right]\left[O_{2}\right] \)
Subject: Physics
In a series LCR circuit connected to an
ac source of variable frequency and
voltage \( \boldsymbol{v}=\boldsymbol{v}_{m} \sin \omega \boldsymbol{t}, \) draw a plot
showing the variation of current \( (\boldsymbol{I}) \)
with angular frequency \( (\omega) \) for two
different values of resistance \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2} \)
\( \left(R_{1}>R_{2}\right) . \) Write the condition under
which the phenomenon of resonance occurs. For which value of
the resistance out of the two curves a
sharper resonance is produced? Define Q-factor of the circuit and give its
significance.
Subject: Maths
A RC circuit has an emf of \( 300 \cos (2 t) \)
volts, a resistance of 150 ohms, a
capacitance of \( \frac{1}{600} \) farad, and an initial
charge on the capacitor of 5 coulombs.
Find the charge on the capacitor at any
time \( t \)
A \( \cdot \frac{2}{5}\left(23 e^{-4 t}+\sin (2 t)+2 \cos (2 t)\right) \)
B \( \cdot \frac{1}{5}\left(23 e^{-4 t}+\sin (2 t)+2 \cos (2 t)\right) \)
c. \( \frac{3}{5}\left(23 e^{-4 t}+\sin (2 t)+2 \cos (2 t)\right) \)
D \( \cdot \frac{1}{6}\left(23 e^{-4 t}+\sin (2 t)+2 \cos (2 t)\right) \)
Subject: Physics
An \( L C R \) series circuit with \( R=100 \Omega \)
is connected to a \( 200 \mathrm{V}, 50 \mathrm{Hz} \) a.c source. When only the capacitance is removed, the current leads the voltage
by \( 60^{\circ} . \) When only the inductance is removed, the current leads the voltage
by \( 60^{\circ} . \) The current in the circuit is :
A \( .2 A \)
в. \( 1 A \)
c. \( \frac{\sqrt{3}}{2} A \)
D. \( \frac{2}{\sqrt{3}} A \)
Subject: Chemistry
Plot of \( \log \left(\frac{x}{m}\right) \) against \( \log P \) is a
straight line inclined at an angle of \( 45^{\circ} \)
When the pressure is 0.5 atm and
Freundlich parameter, \( k \) is \( 10, \) the
amount of solute adsorbed per gram of adsorbent will be:
\( [\log 5=0.6990] \)
A . \( 1 g \)
B. \( 2 g \)
\( c .3 g \)
D. \( 5 g \)
Subject: Chemistry
The legal limit for human exposure to \( C O \) in the work place is 35 ppm. Assuming that the density of air is \( 1.3 g / l, \) how many grams of \( C O \) are in \( 1.0 L \) of air at the maximum allowable
concentration?
A \( \cdot 4.55 \times 10^{-5} g \)
В . \( 3.5 \times 10^{-5} g \)
c. \( 2.69 \times 10^{-5} g \)
D. \( 7.2 \times 10^{-5} g \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{cc}\frac{x\left(3 e^{1 / x}+4\right)}{2-e^{1 / x}}, & x \neq 0 \text { then } f(x) \\ 0 & , x=0\end{array}\right. \)
A. \( f \) is not continuous
B. \( f \) is continuous but not differentiable at \( x=0 \)
C \( \cdot f^{\prime \prime}(0) \) exist
\( \mathbf{D} \cdot f^{\prime}(0+)=2 \)
Subject: Chemistry
Based upon your understanding of the basic principles of molecular orbitals it
should be possible to answer the following question.Consider the six
molecular orbitals of benzene shown.
How many of these orbitals will contain
electrons?
(I)
\( (\mathrm{II}) \)
(III)
\( (\mathrm{IV}) \)
\( (\mathrm{V}) \)
A. Only one molecular orbitals
B. Only two molecular orbitals
C. Only three molecular orbitals
D. All six molecular orbitals
Subject: Physics
A man rows upstream a distance of
\( 9 k m \) or downstream a distance of
\( 18 k m \) taking 3 hours each time. The
speed of the boat in still water is
A \( \cdot 7 \frac{1}{2} k m / h \)
В \( \cdot 6 \frac{1}{2} k m / h \)
c. \( _{5} \frac{1}{2} k m / h \)
D. \( 4 \frac{1}{2} k m / h \)
Subject: Chemistry
A chemical reaction \( 2 A \rightleftharpoons 4 B+C \) in
gas phase occurs in a closed vessel. The
concentration of \( B \) is found to be
increased by \( 5 \times 10^{-3} \) mole 1: 1 in 10
second. Calculate \( C O \) the rate of
appearance of \( B \) (ii) the rate of
disappearance of \( \boldsymbol{A} \)