AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Find the area of a regular polygon of 7 sides whose each side measures \( 4 \mathrm{cm} \)
and the circumradius is \( 3 \mathrm{cm}(\sqrt{5}= \) \( \mathbf{2 . 2 3 6}) \)
A \( \cdot 31.304 \mathrm{cm}^{2} \)
B. \( 31.804 \mathrm{cm}^{2} \)
c. \( 31.304 m^{2} \)
D. None of these
Subject: Physics
Assertion
Perspiration fro human body helps in
cooling the body.
Reason
A thin layer of water on the skin
enhances its emissivity.
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
Compare boiling point of isomeric alkyl amines.
A \( \cdot 1^{\circ}>2^{\circ}>3^{\circ} \)
B . \( 1^{\circ}>2^{\circ}<3^{\circ} \)
c. \( 1^{\circ}<2^{\circ}<3^{\circ} \)
D. \( 1^{\circ}<2^{\circ}>3^{\circ} \)
Subject: Physics
The diagram shows two circular loops a wire(A and B) centred on and
perpendicular to the \( x \) -axis, and
oriented with their planes parallel to
each other. The y-axis passes vertically through loop A(dashed line). There is a
current \( I_{B} \) in loop \( \mathrm{B} \) as shown. Possible
actions which we might perform on loop
\( \mathbf{A} \) are
A. Move A to the right along x axis closer to B
B. Move A to the left along x axis away from B
C. As viewed from above, rotate A clockwise about y-axis
D. As viewed from above, rotate A anticlockwise about y axis
Subject: Maths
If \( A \) is a matrix of order \( 3 \times 4 \), then both
\( A B^{T} \) and \( B^{T} A \) are defined if order of \( B \)
is
\( A \cdot 3 \times 3 \)
B. \( 4 \times 4 \)
c. \( 4 \times 3 \)
D. \( 3 \times 4 \)
Subject: Physics
toppr
Q Type your question
volume. I ne cyıınaer nas a cnarge per
unit length of \( \lambda \)

A Gaussian surface is imagined that is
also shown in the diagram. This
Gaussian surface is also a cylinder
having the same axis as the charged
cylinder. The Gaussian cylinder's radius
is \( a, \) where \( a<R, \) and its length is \( L \)
What is the charge enclosed in the
Gaussian cylinder?
\( ^{\mathbf{A}} \cdot Q_{e n c}=\lambda \frac{a}{R} \)
\( ^{\mathrm{B}} \cdot_{e n c}=\lambda L \frac{a}{R} \)
\( \mathrm{C}_{e n c}=\lambda L \frac{a^{3}}{R^{3}} \)
\( \mathrm{D} \cdot \mathrm{Q}_{e n c}=\lambda \frac{a^{3}}{R^{3}} \)
\( \mathrm{E} \cdot Q_{e n c}=\lambda L \frac{a^{2}}{R^{2}} \)
Subject: Physics
Linear velocity of the \( C M \) of rod is
\( \mathbf{A} \cdot \frac{<F>(\Delta t)}{2 m}(\sqrt{3 \hat{i}}+\hat{j}) \)
B. \( \frac{<F>(\Delta t)}{2 m}(\sqrt{5 \hat{i}}+2 \hat{j}) \)
\( \mathbf{c} \cdot \underline{\leq F>(\Delta t)}(\sqrt{3 \hat{i}}+\hat{j}) \)
\( \mathbf{D} \cdot \frac{<F>(\Delta t)}{2 m}(\sqrt{5 \hat{i}}+\hat{j}) \)
Subject: Chemistry
The minimum angular momentum that can be possessed by an electron in a hydrogen atom is:
A \( \cdot 2 \times 10^{-34} \operatorname{kg} m^{2} s^{-1} \)
B. \( 1 \times 10^{-34} \mathrm{gm}^{2} \mathrm{s}^{-1} \)
C . \( 1 \times 10^{-34} \mathrm{kgm}^{2} \mathrm{s}^{-1} \)
D. none of these
Subject: Maths
\( \frac{\sin (n+1) A+2 \sin n A+\sin (n-1) A}{\cos (n-1) A-\cos (n+1) A} \)
is equal to
A \( \cdot \tan \frac{A}{2} \)
B. \( \cot \frac{A}{2} \)
\( c \cdot \tan A \)
D. \( \cot A \)
Subject: Chemistry
Arrange these haloalkanes in correct
order of density:
A \( \cdot C H_{3} I<C_{2} H_{5} I<C_{3} H_{7} \)
в. \( C H_{3} I>C_{2} H_{5} I>C_{3} H_{7} I \)
c. \( C H_{3} I<C_{2} H_{5} I>C_{3} H_{7} \)
D. \( C H_{3} I>C_{2} H_{5} I<C_{3} H_{7} I \)
Subject: Physics
A neutron of energy 1 Me \( V \) and mass
\( 1.6 \times 10^{-27} \) kg passes a proton at such
a distance that the angular momentum of the neutron relative to the proton approximately equals \( 10^{-33} \mathrm{J} \) s. The distance of closest approach neglecting the interaction between particles is
A. \( 0.44 n m \)
B. \( 0.44 m m \)
c. \( 0.44^{\circ} \)
D. \( 0.44 f m \)
Subject: Chemistry
Following chemical reaction involves a
heterogeneous catalyst \( \mathbf{2} \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \stackrel{N O(\boldsymbol{g})}{\longrightarrow} \boldsymbol{2} \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) \)
If true enter 1 , else enter 0 .
\( A \)
Subject: Physics
While connecting 6 cells in a battery in series, in a tape recorder, by mistake one cell is connected with reverse
polarity. If the effective resistance of load is 24 ohm and internal resistance
of each cell is one ohm and emf \( 1.5 V \)
the current delivered by the battery is
\( \mathbf{A} \cdot 0.1 A \)
B. \( 0.2 A \)
\( \mathbf{c} \cdot 0.3 A \)
D. \( 0.4 A \)
Subject: Physics
A Sound wave with an amplitude of \( 3 \mathrm{cm} \)
starts towards right from origin and
gets reflected at a rigid wall after a
second. If the velocity of the wave is
\( 340 m s^{-1} \) and it has a wavelength of \( 2 m \)
the equations of incident and reflected
waves respectively could be
\( \mathbf{A} . \quad y=3 \times 10^{-2} \sin \pi(340 t-x) \)
\[
y=-3 \times 10^{-2} \sin \pi(340 t+x) \text { towards left }
\]
B. \( \quad y=3 \times 10^{-2} \sin \pi(340 t+x) \)
\[
y=-3 \times 10^{-2} \sin \pi(340 t+x) \text { towards left }
\]
c. \( y=3 \times 10^{-2} \sin \pi(340 t-x) \)
\[
y=-3 \times 10^{-2} \sin \pi(340 t-x) \text { towards left }
\]
D. \( y=3 \times 10^{2} \sin \pi(340 t-x) \)
\[
I=3 \times 10^{-2} \sin \pi(340 t+x) \text { towards left }
\]
Subject: Chemistry
For the process
\( \boldsymbol{A}\left(\boldsymbol{l}, \mathbf{0 . 0 5} \boldsymbol{a t m}, \boldsymbol{3} \boldsymbol{2}^{\circ} \boldsymbol{C}\right) \rightarrow \)
\( \boldsymbol{A}\left(\boldsymbol{g}, \boldsymbol{0 . 0 5} \boldsymbol{a t m}, \boldsymbol{3} \boldsymbol{2}^{\circ} \boldsymbol{C}\right) \)
The correct set of thermodynamic
parameters is :
A \( . \Delta G=0 \) and \( \Delta S=-v e \)
B. \( \Delta G=0 \) and \( \Delta S=+v e \)
c. \( \Delta G=+v e \) and \( \Delta S=0 \)
D. \( \Delta G=-v e \) and \( \Delta S=0 \)
E . \( \Delta G=0 \) and \( \Delta S=0 \)
Subject: Biology
The difference(s) between mRNA and
tRNA is/are that:
(i) mRNA has more elaborate 3
dimensional structure due to extensive
base - pairing
(ii) tRNA has more elaborate \( 3- \)
dimensional structure due to extensive
pairing
(iii) tRNA is usually smaller than mRNA
(iv) mRNA bears anticodon but tRNA
has codons
A. (i) and (iii)
B. All of these
c. (ii) and (iii)
D. (i), (ii) and (iii)
Subject: Biology
Assertion : "The Biological Species" concept helps us to ask how species are formed.
Reason : The concept of biological species focuses our attention on the
question of how reproductive isolation
comes about.
A. If both the assertion and the reason are true and the reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
c. If the assertion is true but the reason is false
D. If both the assertion and reason are false
E. If the assertion is false but reason is true
Subject: Maths
Value of \( \tan 15^{\circ} \) is
This question has multiple correct options
A \( \cdot \frac{\sqrt{3}-1}{\sqrt{3}+1} \)
B. \( 2-\sqrt{3} \)
\( c \cdot 2+\sqrt{3} \)
D. \( \sqrt{3}-1 \)
Subject: Chemistry
1 mole of \( H N O_{3} \) absorbs 4 moles of
electrons in a redox reaction. The
reduced product of this reaction is :
A. 1 mole \( N_{2} \)
B. 1 mole \( N_{2} \) O
c. 1 mole \( N O_{2} \)
D. 1 mole \( N H_{3} \)
Subject: Physics
If \( W_{1} \) work is done against gravitational
attraction to carry \( 10 \mathrm{kg} \) mass from earth's surface to infinity, then the magnitude of work done by the gravitational attraction in bringing 20 kg mass from infinity to the centre of earth is
\( \mathbf{A} \cdot 2 W_{1} \)
в. \( 3 W_{1} \)
\( c \cdot \frac{w_{1}}{2} \)
D. \( 4 W_{1} \)
Subject: Maths
Find the length of altitude through \( A \) of
the triangle \( A B C, \) where \( A \equiv \)
\( (-\mathbf{3}, \mathbf{0}), \boldsymbol{B} \equiv(\mathbf{4},-\mathbf{1}), \boldsymbol{C} \equiv(\mathbf{5}, \mathbf{2}) \)
Subject: Physics
A block of mass \( \mathrm{m} \) is placed on a rough horizontal surface. The coefficient of
friction between them is \( \mu . \) An external
horizontal force is applied to the block
and its magnitude is gradually increased. The force exerted by the block on the surface is \( \mathrm{R} \) then :
This question has multiple correct options
A. the magnitude of R will gradually increase
B . \( R \leq m g \sqrt{\mu^{2}+1} \)
c. the angle made by R with the vertical will gradually increase.
D. the angle made by R with the vertical \( \leq \tan ^{-1} \mu \)
Subject: Maths
The incorrect statement is
\( \mathbf{A} \cdot \sin \theta=-\frac{1}{5} \)
\( \mathbf{B} \cdot \cos \theta=1 \)
\( \mathbf{c} \cdot \sec \theta=\frac{1}{2} \)
\( \mathbf{D} \cdot \tan \theta=20 \)
Subject: Physics
A straight wire of mass \( 200 g \) and length
\( 1.5 m \) carries a current of \( 2 A . \) It is
suspended in mid air by a uniform
horizontal magnetic field \( B \). The
magnitude of \( B \) (in tesla) is :
A . 0.65
в. 0.55
c. 0.75
D. 0.45
Subject: Maths
Let 'f' be a function defined from
\( \boldsymbol{R}^{+} \longrightarrow \boldsymbol{R}^{+} \cdot \boldsymbol{I} \boldsymbol{f}(\boldsymbol{f}(\boldsymbol{x} \boldsymbol{y}))=\boldsymbol{x}(\boldsymbol{f}(\boldsymbol{y}))^{2} \) for
all positive numbers \( x \) and \( y . I f f(2)= \) \( \operatorname{find} f(50)= \)
A . 20
B. 30
\( c .3 \)
D. 40
Subject: Maths
Match the following.
Order of rotational
symmetry
\( (P) \)
(i) 5
\( (\mathrm{Q}) \)
(ii) 2
\( (\mathbf{R}) \)
(iii) 3
\( (\mathbf{S}) \)
(iv) 4
\( \mathbf{A} \cdot(\mathrm{P}) \rightarrow(\mathrm{iv}),(\mathrm{Q}) \rightarrow(\mathrm{i}),(\mathrm{R}) \rightarrow(\mathrm{i}),(\mathrm{S}) \rightarrow(\mathrm{iii}) \)
B. \( (P) \rightarrow(\text { iv) },(Q) \rightarrow(\text { iii) },(R) \rightarrow(\text { ii) },(S) \rightarrow\text { (i) } \)
C. \( (P) \rightarrow(\text { ii) },(Q) \rightarrow(\text { iv }),(R) \rightarrow(\text { iii) },(S) \rightarrow(i) \)
\( \mathbf{D} \cdot(\mathbf{P}) \rightarrow(\mathbf{i} \mathbf{i}),(Q) \rightarrow(\mathbf{i}),(R) \rightarrow(i \mathbf{v}),(S) \rightarrow(\text { iii }) \)
Subject: Maths
If \( \boldsymbol{I}=\int_{2}^{3} \frac{2 \boldsymbol{x}^{5}+\boldsymbol{x}^{4}-\boldsymbol{2} \boldsymbol{x}^{3}+\boldsymbol{2} \boldsymbol{x}^{2}+\mathbf{1}}{\left(\boldsymbol{x}^{2}+\mathbf{1}\right)\left(\boldsymbol{x}^{4}-\mathbf{1}\right)} \boldsymbol{d} \boldsymbol{x} \)
then Iequals
A \( \cdot \frac{1}{2} \log 6+\frac{1}{10} \)
B \( \cdot \frac{1}{2} \log 6-\frac{1}{10} \)
c. \( \frac{1}{2} \log 3-\frac{1}{10} \)
D. \( \frac{1}{2} \log 2+\frac{1}{10} \)
Subject: Maths
If \( f(x)=x^{2 / 3}, x \geq 0 . \) Then,the area of
the region enclosed by the curve \( y= \) \( f(x) \) and the three lines \( y=x, x=1 \)
and \( x=8 \) is
\( ^{\mathrm{A}} \cdot \frac{63}{2} \)
в. \( \frac{93}{5} \)
\( ^{c} \cdot \frac{105}{7} \)
D. \( \frac{129}{10} \)
Subject: Physics
Height of the image of an principal axis produced by a convex lens is double the object height. If the focal length of the
lens is \( 20 \mathrm{cm} \), then the image distance from lens is :
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
B. \( 30 \mathrm{cm} \)
\( \mathbf{c} \cdot 40 \mathrm{cm} \)
D. Both (1)\( \&(2) \)
Subject: Chemistry
In which of the following pairs, both members liberate methane gas on reaction with water?
A. \( M g_{2} C_{3} \) and \( C a C_{2} \)
B. \( M g_{2} C_{3} \) and \( A l_{4} C_{3} \)
c. \( B e_{2} C \) and \( C a C_{2} \)
D. \( B e_{2} C \) and \( A l_{4} C_{3} \)
Subject: Maths
The area of the figure bounded by the \( \operatorname{lines} x=0, x=\frac{\pi}{2}, f(x)=\sin x \) and
\( g(x)=\cos x \) is
A \( \cdot 2(\sqrt{2}-1) \)
B. \( \sqrt{3}-1 \)
c. \( 2(\sqrt{3}-1) \)
D \( \cdot 2(\sqrt{2}+1) \)
Subject: Physics
A radioactive substance \( X \) decays into
another radioactive substance \( Y \)

Initially only \( X \) was present, \( \lambda x \) and \( \lambda y \)
are the disintegration constants of \( \boldsymbol{X} \)
and \( Y . N_{x} \) and \( N_{y} \) are the number of
nuclei of \( X \) and \( Y \) at any time \( t \)

Number of nuclei \( N_{y} \) will be maximum
when
A \( \cdot \frac{N_{y}}{N_{x}-N_{y}}=\frac{\lambda_{y}}{\lambda_{x}-\lambda_{y}} \)
В. \( \frac{N_{x}}{N_{x}-N_{y}}=\frac{\lambda_{x}}{\lambda_{x}-\lambda_{y}} \)
\( c \cdot \frac{\lambda_{y}}{N_{y}}=\frac{\lambda_{x}}{N_{x}} \)
\( \mathbf{D} \cdot \lambda_{y} N_{y}=\lambda_{x} N_{x} \)
Subject: Maths
The angry Arjun carried some arrows for fighting with Bheeshm. With half the arrows, he cut down the arrows thrown
by Bheeshm on him and with six other
arrows he killed the rath driver of
Bheeshm. With one arrow each, he
knocked down respectively the rath, flag and the bow of Bheeshm. Finally, with one more than four times the square
root of arrows he laid Bheeshm
unconscious on an arrow bed. Find the
total number of arrows Arjun had.
Subject: Maths
Three wires of length \( l_{1}, l_{2}, l_{3} \) form a
triangle surmounted by another
circular wire, If \( l_{3} \) is the diameter and
\( l_{3}=2 l_{1}, \) then the angle between \( l_{1} \) and
\( l_{3} \) will be
A \( .30^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 90^{\circ} \)
Subject: Physics
Three masses are placed on the x-axis:
\( 300 \mathrm{g} \) at origin, \( 500 \mathrm{g} \) at \( \mathrm{x}=40 \mathrm{cm} \) and \( 400 \mathrm{g} \) at \( x=70 \mathrm{cm} . \) The distance of the center of mass from the origin is:
A. \( 45 \mathrm{cm} \)
B. 50cm
c. зост
D. \( 40 \mathrm{cm} \)
Subject: Chemistry
Predict whether the following equation
will take place or not. \( \boldsymbol{C u}_{(s)}+\mathbf{2 H}_{(a q)}^{+} \rightarrow \boldsymbol{C u}_{a q}^{2+}+\boldsymbol{H}_{2(g)} \)
Given that \( \boldsymbol{E}_{\boldsymbol{C u}^{2+} \mid \boldsymbol{C u}}^{0}=\boldsymbol{0 . 4 4} \boldsymbol{V} ; \boldsymbol{E}_{\boldsymbol{H}^{+} \mid \boldsymbol{H}_{2}}^{0}= \)
0
Subject: Maths
If \( A \) and \( B \) are non-empty sets such that
\( A \supset B, \) then
\( \mathbf{A} \cdot B^{\prime}-A^{\prime}=A-B \)
B \( \cdot B^{\prime}-A^{\prime}=B-A \)
\( \mathbf{C} \cdot A^{\prime}-B^{\prime}=A-B \)
D \( \cdot A^{\prime} \cap B^{\prime}=B-A \)
E \( \cdot A^{\prime} \cup B^{\prime}=A^{\prime}-B^{\prime} \)
Subject: Physics
A system consisting of two masses connected by a mass less rod lie along the \( x- \) axis. \( A 0.4 k g \) mass is at a
distance \( x=2 m \) while a 0.6 kg mass is
at a distance \( \boldsymbol{x}=\mathbf{7} \) m. The \( \boldsymbol{x} \)
coordinate of the centre of mass is
\( \mathbf{A} \cdot 5 m \)
B. \( 3.5 m \)
c. \( 4.5 \mathrm{m} \)
D. \( 4 m \)
Subject: Maths
Let \( f(x)=x^{2}-3 x+2 \) then area
bounded by the curve \( f(|x|) \) (in square
units) and \( x \) -axis is
A \( \cdot \frac{1}{3} \)
в. \( \frac{5}{6} \)
c. \( \frac{5}{3} \)
D. None of thes
Subject: Biology
Pick up the correct statements:
(a) Mitosis occurs in somatic cells and
meiosis in germ cells.
(b) DNA replicates once in mitosis and twice in meiosis.
(c) Mitosis and meiosis occur both in
sexually and asexually reproducing organisms.
A. a only
B. b only
c. c only
D. a and b only
E. b and conly
Subject: Chemistry
The potential energies of first, second
and third Bohr's orbits of \( H e^{+} \) cation
are \( E_{1}, E_{2} \) and \( E_{3} . \) The correct sequence
of these energies is:
A \( . E_{1}>E_{2}>E_{3} \)
B . \( E_{1}=E_{2}>E_{3} \)
c. \( E_{1}=E_{2}=E_{3} \)
D. \( E_{3}>E_{2}>E_{1} \)
Subject: Maths
By the principle of Mathematical induction, prove that, for \( n \geq 1 \)
\[
\mathbf{1}^{2}+\mathbf{2}^{2}+\mathbf{3}^{2}+\cdots+\boldsymbol{n}^{2}>\frac{\boldsymbol{n}^{\mathbf{3}}}{\mathbf{3}}
\]
Subject: Maths
\( \operatorname{Given}(\boldsymbol{a}-\mathbf{2}, \boldsymbol{b}+\mathbf{3})=(\mathbf{6}, \mathbf{8}), \) are equal
ordered pair. Find the value of \( a \) and \( b \)
A \( . a=8 \) and \( b=5 \)
B. \( a=8 \) and \( b=3 \)
c. \( a=5 \) and \( b=5 \)
Subject: Maths
A computer solved several problems in succession. The time it took the
computer to solve each successive
problem was the same number of times smaller than the time it took it to solve
the preceding problem. How many problems were suggested to the
computer if it spent \( 63.5 \mathrm{mm} \) to solve al the problems except for the first, 127 \( \mathrm{mm} \) to solve all the problems except for the last one, and \( 31.5 \mathrm{mm} \) to solve all the
problems except for the first two?
Subject: Physics
In the figure \( m_{1} \) and \( m_{2}\left(m_{1}<m_{2}\right) \) are
joined together by a pulley. When the mass \( m_{1} \) is released from the height \( h \)
above the floor, it strikes the floor with
speed (Given: Acceleration due to gravity \( =g \) )
A \( \cdot \sqrt{2 g h\left(\frac{m_{1}-m_{2}}{m_{1}+m_{2}}\right)} \)
в. \( \sqrt{2 g h} \)
c. \( \sqrt{\frac{2 m_{2} g h}{m_{1}+m_{2}}} \)
D. \( \sqrt{\frac{2 m_{1} g h}{m_{1}+m_{2}}} \)
Subject: Chemistry
Zinc granules are added in excess to \( \mathbf{5 0 0} \boldsymbol{m L} \) of \( \mathbf{1 . 0} \boldsymbol{M} \) nickel nitrate solution
at \( 25^{\circ} C \) until the equilibrium is reached. If the standard reduction
potentials of \( Z n^{2+} / Z n \) and \( N i^{2+} / N i \)
are -0.75 and -0.24 volt respectively
find out the concentration of \( N i^{2+} \) ions
in solution at equilibrium.
Subject: Maths
Area common to the curves \( y^{2}=a x \) and
\( x^{2}+y^{2}=4 a x \) is equal to
A \( \cdot(9 \sqrt{3}+4 \pi) \frac{a^{2}}{3} \)
B . \( (9 \sqrt{3}+4 \pi) a^{2} \)
c. \( (9 \sqrt{3}-4 \pi) \frac{a^{2}}{3} \)
D. none of the above
Subject: Maths
Given, \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{2} \boldsymbol{x}^{2}+\boldsymbol{a} \)
If \( a \) is a constant and \( f(2)+f(3)= \)
\( f(5), \) calculate the value of \( a \)
\( A \cdot 6 \)
B. 12
\( c \cdot 24 \)
D. 48
Subject: Maths
\( \operatorname{Let} \boldsymbol{y}=\sqrt{\frac{(\boldsymbol{x}+\mathbf{1})(\boldsymbol{x}-\mathbf{3})}{\boldsymbol{x}-\mathbf{2}}} \)
Find all the real values of \( x \) for which \( y \)
takes real values.
Subject: Physics
The muzzle velocity of a certain rifle is
\( 330 m s^{-1} . \) At the end of one second, a
bullet fired straight up into the air will travel a distance of
A \( \cdot(330-4.9) m \)
B. \( 330 m \)
c. \( (330+4.9) m \)
D. \( (330-9.8) m \)
Subject: Chemistry
Match the List-II ans List-II and List III:
\( \begin{array}{lll}\text { List-I } & \text { List-II } & \text { List-III } \\ \text { A. } \Delta G>0 & \begin{array}{l}\text { X. } \Delta S> \\ 0\end{array} & \begin{array}{l}\text { 1. Non- } \\ \text { spontaneous }\end{array} \\ \begin{array}{l}\text { B. } \Delta G< \\ 0\end{array} & \text { Y. } \Delta S<0 & \text { 2. Spontaneous } \\ \begin{array}{l}\text { C. } \Delta G= \\ 0\end{array} & \text { Z. } \Delta S=0 & \text { 3. Equilibrium }\end{array} \) select the correct answering from the
following codes:
\( A \cdot A-(Y, 1) B-(X, Y) C-(Z, 3) \)
B. \( A-(X, 2) B-(Y, 3) C-(Z, 1) \)
C. \( A-(X, 3) B-(Y, 1) C-(Z, 2) \)
D. \( A-(Y, 1) B-(X, 3) C-(Z, 2) \)
Subject: Chemistry
A solution containing 8 g of a substances in 100 g of diethyl ether
boils at \( 36.86^{\circ} \mathrm{C} \). Where as pure ether
boils at \( 35.60^{\circ} \mathrm{C} \). Determine the
molecular mass of the solute. (For ether,
\( \boldsymbol{K}_{\boldsymbol{b}}=\mathbf{2 . 0 2 \mathrm { k }} \mathrm{kh} \boldsymbol{m o l}^{-1} \mathbf{)} \)
Subject: Chemistry
0.1M of \( \boldsymbol{H} \boldsymbol{A} \) is titrated with \( \mathbf{0 . 1} \boldsymbol{M} \)
\( N a O H, \) calculate \( p H \) at end point \( \operatorname{Given} K(H A)=5 \times 10^{-6} \) and \( \alpha \ll 1 \)
Subject: Physics
Assertion
When a rod is pulled by a force acting on one end (longitudinally) then there will be no longitudinal stress in the rod. (Assume surface is friction-less)
Reason
Longitudinal stress is internal normal
force per unit area.
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
Two tall buildings are \( 80 m \) apart. The velocity with which a ball should be thrown horizontally from a window \( 95 m \) above the ground in one building so that it will enter a window 15 m above the
ground in the second building is : \( (g= \)
\( \left.10 m / s^{2}\right) \)
A. \( 15 \mathrm{m} / \mathrm{s} \)
B. \( 5 m / s \)
c. \( 10 \mathrm{m} / \mathrm{s} \)
D. 20 \( m / s \)
Subject: Maths
A certain characteristic in a large population has a distribution that is
symmetric about the mean \( m \). If 68 percent of the distribution lies within
one standard deviation \( d \) of the mean,
what percent of the distribution is less
\( \operatorname{than} \boldsymbol{m}+\boldsymbol{d} ? \)
A . \( 16 \% \)
B. \( 32 \% \)
c. \( 48 \% \)
D. \( 84 \% \)
E \( .92 \% \)
Subject: Maths
Let \( X \) denote the number of time tail
appear in \( n \) tosses of a fair coin. If
\( \boldsymbol{P}(\boldsymbol{X}=\mathbf{1}), \boldsymbol{P}(\boldsymbol{X}=\mathbf{2}) \) and
\( \boldsymbol{P}(\boldsymbol{X}=\mathbf{3}) \) are in A.P., then value of \( \boldsymbol{n} \) is
\( \mathbf{A} \cdot \mathbf{9} \)
B . 2
\( c \cdot 7 \)
D. None of these
Subject: Physics
An inductance coil of \( 1 H \) and \( a \)
condenser of capacity \( 1 p F \) produce
resonance. The resonant frequency will be
\( ^{\text {A }} \cdot \frac{10^{6}}{\pi} H z \)
в. \( 27 \pi \times 10^{6} \mathrm{Hz} \)
c. \( \frac{2 \pi}{10^{6}} H z \)
D. \( \frac{10^{6}}{2 \pi} H z \)
Subject: Physics
Assertion
the power in an ac circuit is minimum
if the circuit has only a resistor
Reason
Power of a circuit is independent of the
phase angle
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Chemistry
At \( 298 \mathrm{K} \) the entropy of rhombic sulphur \( 32.04 \mathrm{J} / \mathrm{mol} \mathrm{K} \) and that of monoclinic
sulphur is \( 32.68 \mathrm{J} / \mathrm{mol} \) K. The heat of
their combustion are respectively
-298246 and \( -297948 J m o l^{-1} . \Delta G \)
for the reaction; \( S_{r h o r m b i c} \rightarrow S_{m o n o c l i n i c} \)
will be :
A . 107.28
B. 10.728 J
c. 107.28 k
D. 10728 J
Subject: Maths
If the matrices has 13 elements , then
the possible dimension (order) it can have are
A . \( 1 \times 13 \) or \( 13 \times 1 \)
B. \( 1 \times 26 \) or \( 26 \times 1 \)
c. \( 2 \times 13 \) or \( 13 \times 2 \)
D. None of these
Subject: Maths
Which of the following points are collinear?
A . (2a,0), (3a,0), (a, 2a)
в. \( (3 a, 0),(0,3 b),(a, 2 b) \)
c. \( (3 a, b),(a, 2 b),(-a, b) \)
D. (a,-6),(-a,3b),(-2a,-2b)
Subject: Maths
The domain of the function \( \boldsymbol{f}= \)
\( \left((x, y): x, y \in R, 3^{x}+3^{y}=3\right) \) is
\( A \cdot(0,1] \)
B. [0, 1]
\( c \cdot(-\infty, 0] \)
\( D \cdot(-\infty, 1) \)
Subject: Physics
List I contains either an action or an
observation. Match each of these,
respectively to the correct effect, or a reason from list II.
List 1 List II
\( a \)
. Two rotating discs
e. Generated force of in contact- friction is equal to are brought in contact-
coaxially
b. A contact force
exists between exists between
a rough surface and
body placed on it y placed on it d a partially into heat
Attributed to g. resultant of "
" I reaction and c. For a body on a rough
surface, maintaining
motion is easier
as compared to
initiating it normal coefficient of
friction between t the surfaces

Is \( \quad \) h. As kinetic friction \( \begin{array}{l}\text { d. Static friction is } \\ \begin{array}{l}\text { less than limiting } \\ \text { friction }\end{array} & \begin{array}{l}\text { h. AS } \\ \text { is less than static } \\ \text { friction }\end{array}\end{array} \)
\( A \cdot a-f, b-g, c-h, d-e \)
B. a-g, b-f, c-e, d-h
c. a-h, b-e, c-f, d-g
D. a-e