AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Pure water, cooled to \( -15^{\circ} \mathrm{C} \), is kept in an
insulated flask. Some ice is dropped
into the flask. The fraction of water
frozen into ice is (specific heat of ice =
\( 0.5 \mathrm{cal} / \mathrm{g}^{-0} \mathrm{C}, \) specific heat of water \( =1 \)
\( \left.\operatorname{cal} / g^{-o} C\right) \)
A \( .6 / 29 \)
B. 3/35
\( c \cdot 6 / 35 \)
D. 2/35
Subject: Chemistry
For the half reaction
\( \boldsymbol{B}(\boldsymbol{s}) \rightarrow \boldsymbol{B}^{2+}+\boldsymbol{2} \boldsymbol{e}^{-} \quad \boldsymbol{E}_{1}^{\circ}=-\mathbf{0 . 4 4} \boldsymbol{V} \)
and \( B_{2}+\rightarrow B^{3+}+e^{-} \quad E_{2}^{\circ}=1.3 V \)
What is \( E^{\circ} \) for the reaction,
\( \boldsymbol{3} \boldsymbol{e}^{-}+\boldsymbol{B}^{+\boldsymbol{3}} \rightarrow \boldsymbol{B}(\boldsymbol{s}) \)
A . \( 0.86 \mathrm{v} \)
B. \( 0.14 \mathrm{v} \)
c. -0.14 v
D. - 0.28 v
Subject: Maths
If \( A \) is a \( 3 * 3 \) singular matrix then
\( \boldsymbol{A}(\boldsymbol{A} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A})= \)
\( A \cdot \) Det \( A \)
B.
\( c \cdot c \)
D. ±1
Subject: Maths
If \( \boldsymbol{X}=\left\{\mathbf{8}^{n}-\mathbf{7} \boldsymbol{n}-\mathbf{1}, \boldsymbol{n} \in \boldsymbol{N}\right\} \) and \( \boldsymbol{Y}= \)
\( \mathbf{4} 9(n-1), n \in N, \) then \( (\operatorname{given} n>1) \)
A. \( X \subset Y \)
в. \( Y \subset X \)
c. \( X=Y \)
D. \( X \nsubseteq Y \)
Subject: Maths
\( \boldsymbol{L}_{1}: \frac{\boldsymbol{x}-\mathbf{1}}{\mathbf{2}}=\frac{\boldsymbol{y}-\mathbf{2}}{\mathbf{3}}=\frac{\boldsymbol{z}-\mathbf{3}}{\mathbf{4}} \)
\( L_{2}: \frac{x-2}{3}=\frac{y-4}{2}=\frac{z-5}{5} \) be two
given lines, point P lies on \( L_{1} \) and Q lies
on \( L_{2} \) then distance between \( P \) and \( Q \)
can be
This question has multiple correct options
A \( \cdot \frac{1}{3} \)
B.
c. 15
D. 30
Subject: Physics
In the adjoining figure, the position time graph of a particle of mass \( 0.1 \mathrm{kg} \) is shown. The impulse at \( t=2 s \) is :
A . \( 0.02 \mathrm{kgm} / \mathrm{s} \)
B. \( 0.1 \mathrm{kgm} / \mathrm{s} \)
c. \( 0.2 k g m / s \)
D. \( 0.4 k g m / s \)
Subject: Physics
If there is only one type of charge in the
universe, then what is the flux to the
entire universe.
\( (\vec{E} \rightarrow \text { Electric field, } \overrightarrow{d s} \rightarrow \) Area vector)
\( \mathbf{A} \cdot \oint \vec{E} \cdot \overrightarrow{d s} \neq 0 \) on any surface
B. \( \oint \vec{E} \cdot \overrightarrow{d s} \) could not be defined
\( \mathbf{c} \cdot \oint \vec{E} \cdot \overrightarrow{d s}=\infty \) if charge is inside
D \( \cdot \oint \vec{E} \cdot \overrightarrow{d s}=0 \) if charge is outside, \( =\frac{q}{\epsilon_{0}} \) if charge is
inside
Subject: Chemistry
The cell in which the following reaction
occurs:
\( 2 F e_{(a q)}^{3+}+2 I_{(a q)}^{-} \rightarrow 2 F e_{(a q)}^{2+}+I_{2(s)} \) has
\( E_{c e l l}^{o}=0.236 V \) at \( 298 K \)
The equilibrium constant of the cell reaction is:
A. \( 6.69 \times 10^{-7} \)
B . \( 7.69 \times 10^{-7} \)
c. \( 9.69 \times 10^{7} \)
D. \( 6.69 \times 10^{7} \)
Subject: Physics
A long straight wire carrying current \( I \) is bent at its mid-point to form an angle
of \( 45^{\circ} . \) The field at point \( P \) as shown in
the figure is
A \( \cdot \frac{\mu_{0} I}{4 \pi R}(\sqrt{2}-1) \)
в. \( \frac{\mu_{0} I}{4 \pi R}(\sqrt{2}+1) \)
с. \( \frac{\mu_{0} I}{4 \sqrt{2} \pi R}(\sqrt{2}+1) \)
D. \( \frac{\mu_{0} I}{4 \sqrt{2} \pi R}(\sqrt{2}-1) \)
Subject: Chemistry
The following acids have been arranged in order of decreasing acid strength. Identify the correct order. \( \boldsymbol{C l O H}(\boldsymbol{I}), \boldsymbol{B r O H}(\boldsymbol{I I}), \boldsymbol{I O H}(\boldsymbol{I I I}) \)
A \( . I>I I>I I I \)
\( I \)
В. \( I I>I>I I I \)
c. \( I I I>I I>I \)
I II \( I>I I I>I I \)
\( I \)
Subject: Physics
Angle of minimum deviation for a prism of refractive index 1.5 is equal to the angle of prism of given prism. Then, the
angle of prism is \( \left(\sin 48^{\circ} 36^{\prime}=\right. \)
0.75)
A . \( 80^{\circ} \)
B . \( 41^{\circ} 24^{\prime} \)
\( c \cdot 60 \)
D . \( 82^{\circ} 48^{\prime} \)
Subject: Maths
The average length of time required to complete a jury questionnaire is 40 minutes, with a standard deviation of 5 minutes. What is the probability that it will take a prospective juror between 35 and 45 minutes to complete the questionnaire?
A. About \( 68 \% \)
B. About \( 72 \% \)
c. About \( 76 \% \)
D. About \( 84 \% \)
Subject: Physics
\( A \) and \( B \) are two points on the axis and the perpendicular bisector respectively of an electric dipole. \( A \) and \( B \) are far away from the dipole and at equal distance from it. The field at \( A \) and \( B \)
\( \operatorname{are} \overrightarrow{\boldsymbol{E}}_{\boldsymbol{A}} \) and \( \overrightarrow{\boldsymbol{E}}_{\boldsymbol{B}} \)
\( \mathbf{A} \cdot \vec{E}_{A}=\vec{E}_{B} \)
B . \( \vec{E}_{A}=2 \vec{E}_{B} \)
c. \( \vec{E}_{A}=-2 \vec{E}_{B} \)
D・ \( \left|E_{B}\right|=\frac{1}{2}\left|E_{A}\right|, \vec{E}_{B} \) is perpendicular to \( \vec{E}_{A} \)
Subject: Chemistry
The oxidation state of sulphur in the
anions \( S_{2} O_{4}^{2-}, S_{2} O_{4}^{2-} \) and \( S_{2} O_{6}^{2-} \)
follows the order:
\( \mathbf{A} \cdot S_{2} O_{6}^{2-}-<S_{2} O_{4}^{2-}<S O_{3}^{2} \)
B . \( S_{2} O_{4}^{2-}<S O_{3}^{2-}<S_{2} O_{6}^{2} \)
\( \mathrm{c} \cdot S O_{3}^{2-}<S_{2} O_{4}^{2-}<S_{2} O_{6}^{2} \)
D. \( S_{2} O_{4}^{2-}<S_{2} O_{6}^{2-}-<S O_{3}^{2} \)
Subject: Chemistry
Which of the following compounds
would exhibit co-ordination isomerism?
\( \mathbf{A} \cdot\left[C r\left(H_{2} O\right)_{5}\right] C l_{2} \)
B . \( \left[C r\left(N H_{3}\right)_{5}\right]\left[C o(C N)_{5}\right] \)
\( \mathrm{c} \cdot\left[\mathrm{Cr}(\mathrm{en})_{2}\right] \mathrm{NO}_{2} \)
D. \( \left[N i\left(N H_{3}\right)_{5}\right]\left[B F_{4}\right]_{3} \)
Subject: Maths
The eccentricity of the conic \( x^{2}+ \)
\( 2 y^{2}-2 x+3 y+2=0 \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{1}{\sqrt{2}} \)
\( c \cdot \frac{1}{2} \)
D. \( \sqrt{2} \)
\( E \)
Subject: Physics
A body is released at a distance far away from the surface of the earth.
Calculate its speed when it is near the
surface of earth. Given \( \boldsymbol{g}=\mathbf{9 . 8 m s}^{-2} \)
radius of earth \( \boldsymbol{R}=\mathbf{6 . 3 7} \times \mathbf{1 0}^{\mathbf{6}} \mathbf{m} \)
A \( \cdot 22 \times 10^{3} m s^{-1} \)
В. \( 11.2 \times 10^{3} m s^{-1} \)
\( \mathbf{c} \cdot 23 \times 10^{3} m s^{-1} \)
D. \( 10 \times 10^{3} \mathrm{ms}^{-1} \)
Subject: Physics
Which of the following processes requires the most energy input? Given below is the properties of the
water
Value Property
Specific Heat
Latent Heat of Fusion \( 80 \mathrm{cal} / \mathrm{g} \)
Latent Heat of Vaporization 540 cal/g 1
A. Melting \( 100 \mathrm{g} \) of ice at \( 0^{\circ} \mathrm{C} \)
B. Freezing 100 g of water at \( 0^{\circ} \mathrm{C} \)
c. Boiling \( 100 \mathrm{g} \) of water at \( 100^{\circ} \mathrm{C} \)
D. condensing 100 g of steam at 100 \( ^{\circ} \mathrm{C} \)
E. Heating \( 100 \mathrm{g} \) of water from \( 0 \mathrm{c} \) to \( 100^{\circ} \mathrm{C} \)
Subject: Physics
The recoil speed of a hydrogen atom after it emits a photon in going from \( \boldsymbol{n}=\mathbf{5} \) state to \( \boldsymbol{n}=\mathbf{1} \) state is
\( \mathbf{A} \cdot 4.718 \mathrm{m} \mathrm{s}^{-1} \)
B. \( 7.418 \mathrm{m} \mathrm{s}^{-1} \)
c. \( 4.178 \mathrm{m} \mathrm{s}^{-1} \)
D. \( 7.148 \mathrm{m} \mathrm{s}^{-1} \)
Subject: Physics
Assertion
It is hotter over the top of a fire than at
the same distance on the sides.
Reason
Air surrounding the fire conducts more heat upwards.
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
The axes being inclined at an angle of
\( 60^{\circ}, \) the inclination of the straight line
\( \boldsymbol{y}=2 \boldsymbol{x}+\mathbf{5} \) with \( \mathbf{x} \) -axis is
\( A \cdot 30 \)
B . \( \tan ^{-1}(\sqrt{3} / 2) \)
\( c \cdot \tan ^{-1} 2 \)
D. \( 60^{\circ} \)
Subject: Physics
The electric potential \( V \) at any point \( P(x, y, z) \) in space is given by \( V= \)
\( 4 x^{2} V . \) The electric field at the point
\( (1 m, 2 m) \) is:
A . \( -8 i \)
B. \( 8 \hat{i} \)
\( \mathrm{c} \cdot-16 \hat{i} \)
D. \( 16 \hat{i} \)
Subject: Maths
The value of \( \int_{-\pi}^{\pi} \frac{\cos ^{2} x}{1+a^{x}} d x, a>0 \) is
\( \mathbf{A} \cdot \pi / 2 \)
в. \( a \pi \)
c. \( \pi \)
D. \( 2 \pi \)
Subject: Physics
A paricle executes SHM with time period of 4 s. find the minimum time interval in which the velocity of the particle changes by an amount equal to its maximum velocity:
A \( \cdot \frac{1}{2} s \)
B. \( \frac{2}{3} \) s
c. \( \frac{9}{3} \) s
D. \( \frac{5}{3} \) s
Subject: Physics
A body of volume \( V \) and density \( \rho \) is initially submerged in a liquid of density \( \rho^{\prime} . \) If it lifted through a height \( h \) in the liquid, its potential energy will:
A . increase by \( h V\left(\rho-\rho^{\prime}\right) g \)
B. decrease by \( h V\left(\rho-\rho^{\prime}\right) g \)
C . increase by \( h V_{\rho g / \rho} \)
D. decrease by \( h V_{\rho g / \rho} \)
Subject: Physics
Two rods of the same length and
diameter having thermal
conductivities \( \boldsymbol{K}_{\mathbf{1}} \boldsymbol{K}_{\mathbf{2}} \) are joined in
parallel. The equivalent thermal conductivity of the combination is:
A. \( \frac{K_{1} K_{2}}{K_{1}+K_{2}} \)
в. \( K_{1}+K_{2} \)
c. \( \frac{K_{1}+K_{2}}{2} \)
D. \( \sqrt{K_{1} K_{2}} \)
Subject: Physics
Two particles projected from the same point with same speed \( u \) at angles of
projection \( \alpha \) and \( \beta \) strike the horizontal
ground at the same point. If \( \boldsymbol{h}_{1} \) and \( \boldsymbol{h}_{\mathbf{2}} \) are the maximum heights attained by
the projectile, \( \boldsymbol{R} \) is the range for both \( \boldsymbol{t}_{1} \)
and \( t_{2} \) are their times of flights,
respectively, then This question has multiple correct options
\( \mathbf{A} \cdot \alpha+\beta=\frac{\pi}{2} \)
B . \( R=4 \sqrt{h_{1} h_{2}} \)
c. \( \frac{t_{1}}{t_{2}}=\tan \alpha \)
D \( \cdot \tan \alpha=\sqrt{\frac{h_{1}}{h_{2}}} \)
Subject: Physics
Assertion
Optical fibres make use of total internal reflection
Reason
Light undergoes successive total internal reflections as it moves through
an optical fibre.
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
When two bodies move uniformly towards each other,the distance
between them diminishes by \( 16 m \) every
10s.If bodies move with velocities of the
same magnitude and in the same direction as before the distance
between then will decease \( 3 m \) every \( 5 s \)
The velocity of each body is
\( \mathbf{A} \cdot 1.5 m / s, 0.8 m / s \)
B. \( 1.1 \mathrm{m} / \mathrm{s}, 0.5 \mathrm{m} / \mathrm{s} \)
c. \( 2.4 m / s, 1.5 m / s \)
D. \( 3.0 m / s, 1.5 m / s \)
Subject: Maths
Assertion \( (A): f(x)=\sin (\pi[x]) \) is
differentiable every where [] is greatest
integer function
Reason \( (\mathrm{R}): \) If \( \mathbf{x}=\mathbf{n} \boldsymbol{\pi} \Rightarrow \sin \boldsymbol{x}=\mathbf{0} \forall \mathbf{n} \in \)
\( \mathbf{Z} \) then
A. Both (A) and (R) are true and R is correct explanation for A
B. Both (A) and (R) are true and R is not correct explanation for
c. (A) is true (R) is false
D. (A) is false (R) is true
Subject: Maths
If the lines \( \boldsymbol{p}_{1} \boldsymbol{x}+\boldsymbol{q}_{1} \boldsymbol{y}=\mathbf{1}, \boldsymbol{p}_{2} \boldsymbol{x}+\boldsymbol{q}_{2} \boldsymbol{y}= \)
1 and \( p_{3} x+q_{3} y=1 \) be concurrent
show that the points \( \left(p_{1}, q_{1}\right),\left(p_{2}, q_{2}\right) \)
and \( \left(p_{3}, q_{3}\right) \) are collinear
A. vertices of right angle triangle
B. vertices of an equilateral triangle
c. vertices of an isosceles triangle
D. Collinear
Subject: Physics
The resultant of \( \vec{A} \) and \( \vec{B} \) makes an angle \( \alpha \) with \( \vec{A} \) and an angle \( \beta \) with \( \vec{B} \)
then :-
\( \mathbf{A} \cdot \alpha<\beta \)
B. \( \alpha<\beta \) if \( A<B \)
c. \( \alpha<\beta \) if \( A>B \)
D. \( \alpha<\beta \) if \( A=B \)
Subject: Chemistry
For the equilibrium, \( M g C O_{3}(s) \Leftrightarrow \)
\( M g O(s)+C O_{2}(g), \) which of
the following expression is correct?
\( ^{\mathrm{A}} \cdot_{K_{p}}=\frac{P_{M g} o+P_{C O_{2}}}{P_{M g C O_{3}}} \)
в. \( _{K_{p}}=\frac{[M g O]+\left[C O_{2}\right]}{\left[M g C O_{3}\right]} \)
\( ^{\mathrm{c}} \cdot_{K_{p}}=\frac{P_{M g} o \cdot P_{C O_{2}}}{P_{M g C O_{3}}} \)
D. \( K_{p}=P_{C O_{2}} \)
Subject: Physics
Four curves \( A, B, C \) and \( D \) are drawn in
figure for a given amount of gas. The curves which represent adiabatic and
isothermal changes are.
A. \( C \) and \( D \), respectively
B. \( D \) and \( C \), respectively
c. \( A \) and \( B \), respectively
D. \( B \) and \( A \), respectively
Subject: Chemistry
Which of the following quantum numbers are correct for the outermost
electron of sodium atom?
A. \( n=4, l=0, m=0, s=\pm 1 / 2 \)
В. \( n=3, l=0, m=0, s=-1 / 2 \)
c. \( n=3, l=1, m=\pm 1, s=+1 / 2 \)
Subject: Chemistry
If \( z \) is internuclear axis, then which type of overlapping is/are not possible? This question has multiple correct options
A \( . \) sand \( p_{x} \)
B. \( s \) and \( p_{y} \)
\( \mathbf{c} \cdot p_{x}+p_{z} \)
D. \( p_{y}+p_{z} \)
Subject: Physics
In the arrangement shown, the solid cylinder of mass \( \mathrm{m} \) is slightly rolled to the left and released. It starts
oscillating on the horizontal surface without slipping. Then time period of oscillation is
\( ^{\mathrm{A}} \cdot \pi \sqrt{\frac{3 K}{m}} \)
в. \( 2 \pi \sqrt{\frac{3 M}{2 K}} \)
c. \( _{2 \pi} \sqrt{\frac{2 K}{3 M}} \)
D. \( 2 \pi \sqrt{\frac{3 K}{2 m}} \)
Subject: Physics
Ram moves in east direction at a speed
of \( 6 m / s \) and Shyam moves \( 30^{\circ} \) east of
north at a speed of \( 6 m / s \). The magnitude of their relative velocity is
A. \( 3 m / s \)
в. \( 6 m / s \)
c. \( 6 \sqrt{3} \mathrm{m} / \mathrm{s} \)
D. \( 6 \sqrt{2} \mathrm{m} / \mathrm{s} \)
Subject: Maths
Factorize \( 16 x^{6}-8 x^{3} y^{3}+y^{6} ? \)
A \( \cdot\left(4 x^{3}-y^{3}\right)^{2} \)
B. \( \left(4 x^{3}+y^{3}\right)^{2} \)
\( \mathbf{c} \cdot(4 x+y)^{6} \)
D. \( \left(16 x^{2}+y\right)^{2} \)
Subject: Chemistry
Which of the following reactions is used
to make a fuel cell?
\( \mathbf{A} \cdot 2 H_{2}(g)+O_{2}(g) \rightarrow 2 H_{2} O(l) \)
B. \( 2 F e(s)+O_{2}(g)+4 H^{+}(a q) \rightarrow 2 F e^{2+}(a q)+2 H_{2} O(l) \)
\( \mathbf{c} \cdot P b(s)+P b O_{2}(s)+2 H_{2} S O_{4}(a q) \rightarrow 2 P b S O_{4}(s)+ \)
\( H_{2} O(l) \)
D. \( C d(s)+2 N i(O H)_{3}(s) \rightarrow C d O(s)+2 N i(O H)_{2}+ \)
\( 2 H_{2} O(l) \)
Subject: Maths
If \( \boldsymbol{m}=\mathbf{2}(\mathbf{1 5}-\mathbf{4} \boldsymbol{x}), \boldsymbol{n}=\frac{\mathbf{5} \boldsymbol{x}+\mathbf{3}}{\mathbf{2}} \) and
\( \boldsymbol{m}: \boldsymbol{n}=\boldsymbol{2}: \boldsymbol{3} ; \) find \( \boldsymbol{n} \)
\( \mathbf{A} \cdot n=2 \)
В . \( n=7 \)
c. \( n=9 \)
D. \( n=12 \)
Subject: Physics
Assertion
The radio and TV signals from
broadcasting stations carry energy.
Reason
Electromagnetic waves are capable to
carry energy from one place to another.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
If \( \overrightarrow{\boldsymbol{A}}=\boldsymbol{i}-\boldsymbol{j}, \overrightarrow{\boldsymbol{B}}=\boldsymbol{i}+\boldsymbol{j}+\boldsymbol{k} \) are two
vectors and \( \vec{C} \) is another vector such that \( \vec{A} \times \vec{C}+\vec{B}=\overrightarrow{0} \) and \( \vec{A} \cdot \vec{C}=0, \) then
\( |\vec{C}|^{2}= \)
A \( \cdot \frac{3}{2} \)
в. 8
c. \( \frac{19}{2} \)
D. \( \frac{17}{2} \)
Subject: Physics
Two identical blocks \( A \) and \( B \), each of
mass 'm' resting on a smooth horizontal surface, are inter connected by spring of stiffness 'K'. If the block B is acted on by
a horizontal force ' \( \mathrm{F}^{\prime} \) and the elongation
of the spring is 'e', the relative acceleration between the
blocks is equal to
A \( \cdot \frac{F}{2 m} \)
B. \( \frac{F-K e}{m} \)
\( \mathbf{c} \cdot \frac{F-2 K e}{m} \)
D. \( \frac{K e}{m} \)
Subject: Chemistry
Which of the following pairs give \( C l_{2} \) at
room temperature?
A. \( \operatorname{conc.HCl}+ \) KMnO\( _{4} \)
в. \( N a C l+ \) conc. \( H_{2} S O_{4} \)
c. \( N a C l+M n O_{2} \)
D. \( N a C l+ \) conc. \( H N O_{3} \)
Subject: Biology
Identify the correct and incorrect statements.
A. The four nucleotide bases are not
necessarily present in DNA in exact equal proportions.
B. The total amount of purines are equal to the total amount of pyrimidines.
C. DNA ligase enzyme act to hydrolyse or breakdown a polynucleotide chain into its component nucleotides.
D. Nuclease enzymes are capable of restoring an intact DNA duplex.
A. B is correct but A, C and D are wrong
B. A and B are wrong but C and D are correct
c. \( A, B \) and \( C \) are correct but D is wrong
D. A and B are correct but C and D are wrong
E. B, C and D are correct but A is wrong
Subject: Chemistry
A molecular compound is composed of \( 60.4 \% \mathrm{Xe}, 21.1 \% \mathrm{O} \) and \( 17.5 \% \mathrm{F}, \) by mass. If
the molecular weight is \( 217.3 \mathrm{u} \), what is the molecular formula?
\( \mathbf{A} \cdot X e O_{3} F_{2} \)
в. \( X e O_{3} F \)
c. \( X e O_{2} F_{3} \)
D. None of these
Subject: Physics
represents the position-time graph for a
spring-mass system oscillating with simple harmonic motion. The colored, dashed graphs represent shapes of possible velocity time graphs
for the same motion.

The vertical axis stands for position or
velocity, but the scaling does not matter. The time axis is the same for all
graphs.
Which colored graph best represents
the possible velocity for the mass in
this spring-mass system?
A. Red
B. Blue
c. Green
D. The velocity graph is the same as the position graph
E. All three colored graphs are equally possible
Subject: Maths
Compute the missing frequencies \( \boldsymbol{f}_{1} \) and \( f_{2} \) in the following data if the mean
is \( 166 \frac{9}{26} \) and the sum of the frequencies is 52
c.ı \( \begin{array}{lll}140- & 150- & 160- \\ 150 & 160 & 170\end{array} \) 170180
Freq. 5
\( f_{1} \)
20
Subject: Physics
reported by two students \( X \) and \( Y \) for
an experiment on the study of
temperature-time graph. The experiment is likely to have been
performed correctly by
\begin{tabular}{lll} 
Time (in min) & Student \( \boldsymbol{X} \) & Student \( \boldsymbol{Y} \) \\
0 & \( 61^{\circ} \mathrm{C} \) & \( 61^{\circ} \mathrm{C} \) \\
2 & \( 60.5^{\circ} \mathrm{C} \) & \( 59.0^{\circ} \mathrm{C} \) \\
4 & \( 60.0^{\circ} \mathrm{C} \) & \( 58.0^{\circ} \mathrm{C} \) \\
\hline 6 & \( 59.0^{\circ} \mathrm{C} \) & \( 57.5^{\circ} \mathrm{C} \) \\
\hline 10 & \( 58.0^{\circ} \mathrm{C} \) & \( 57.0^{\circ} \mathrm{C} \) \\
\hline 12 & \( 56.5^{\circ} \mathrm{C} \) & \( 56.5^{\circ} \mathrm{C} \) \\
\hline
\end{tabular}
\( A \cdot X \)
B. \( Y \)
c. both \( X \) and \( Y \)
D. neithe
Subject: Physics
A steady current I flows along an infinitely long hollow cylindrical
conductor of radius R. This cylinder is placed coaxially inside an infinite
solenoid of radius \( 2 R \). The solenoid has
n turns per unit length and carries a
steady current I. Consider a point \( P \) at a distance r from the common axis. The
correct statement(s) is(are)?
A. In the region \( 0<r<R \), the magnetic field is non-zero
B. In the region \( R<r<2 R \), the magnetic field is along
the common axis
C. In the region \( R<r<2 R \), the magnetic field is tangential to the circle of radius \( r, \) centered on the axis
D. In the region \( r>2 R \), the magnetic field is non-zero
Subject: Maths
\( \lim _{x \rightarrow \infty} \frac{2 \sqrt{x}+3 \sqrt[3]{x}+4 \sqrt[4]{x}}{\sqrt{(2 x-3)}+\sqrt[3]{(2 x-3)}+\sqrt[4]{(2}} \)
is equal to
A . 1
B. \( \alpha \)
c. \( \sqrt{2} \)
D. None of these
Subject: Physics
Two billiard balls \( A \) and \( B \), each of mass
\( 50 \mathrm{g} \) and moving in opposite directions
with speed of \( 5 m s^{-1} \) each, collide and
rebound with the same speed. The
impulse imparted to each ball is:
A. \( 0.25 \mathrm{Kgms}^{-1} \)
B. \( 0.5 \mathrm{Kgms}^{-1} \)
c. \( 0.1 \mathrm{Kgms}^{-1} \)
D. \( 0.125 \mathrm{Kgms}^{-1} \)
Subject: Maths
Prove that
\( \mathbf{2 5}_{\mathbf{4}}^{C}+\sum_{r=\mathbf{0}}^{4}(\mathbf{2 9}-\boldsymbol{r})_{\mathbf{3}}^{\boldsymbol{C}}=\mathbf{3 0}_{\mathbf{4}}^{\boldsymbol{C}} \)
Subject: Biology
Many persons like to use asthma as an excuse for not being able to do well in sports. Try telling them about Down Fraser, who was the first women to
break 60 sec in 100 m freestyle swimming. The first women to win four
Olympic gold medals and the first swimmer to win the same event in three
consecutive Olympics was asthmatic. On the basis of the above passage, answer the following question.
i) What do you mean by asthma?
Subject: Maths
\( \int \frac{1+2 x^{2}}{x^{2}\left(1+x^{2}\right)} d x= \)
A. \( \quad \tan ^{-1} x+\frac{1}{x}+c \)
B. \( \tan ^{-1} x-\frac{1}{x}+c \)
c. \( \frac{\tan ^{-1} x}{x}+c \)
D. \( \frac{\tan ^{-1} x}{x^{2}}+c \)
Subject: Physics
Two wires carrying equal current \( I \) are a
distance \( a \) apart.
If the current through wire one is doubled while the current through the wire two is tripled, what is the ratio of the force that wire two exerts on wire 1
\( F_{1} \) ) to the force that wire one exerts on
wire \( 2\left(F_{2}\right) ? \)
A . 4: 09
B. 2:03
\( c \cdot 1: 0 \)
D. 3:02
E. 9: 04
Subject: Physics
As a builder lifts a \( 3.0 \mathrm{kg} \) brick at a steady speed from the ground to a platform 2.0 meters high. How much work is done on the brick by the builder and by the earth while it is being lifted, and what is the net work done on the
brick by all forces while it is being lifted?
A. \( 60 \mathrm{N},-60 \mathrm{N}, \mathrm{O} \)
в. - -60 N, 60 N, 0
c. \( 60 \mathrm{N}, 60 \mathrm{N}, 0 \)
D. - -60 N,-60 N, 0
E. 60 N, 60 N, -60 N
Subject: Chemistry
Calculate the heat of combustion (in KJ)
of
methane from the following data
i) \( \mathrm{C}(\text { graphite })+2 \mathrm{H}_{2}(\mathrm{g}) \rightarrow \mathrm{CH}_{4}(\mathrm{g}), \Delta \mathrm{H}= \)
\( -74.8 k J \)
ii) \( C(\text { graphite })+O_{2}(g) \rightarrow C O_{2}(g), \Delta H= \)
\( -393.5 \mathrm{kJ} \)
iii) \( \mathrm{H}_{2}(\mathrm{g})+1 / 2 \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{H}_{2} \mathrm{O}(l), \Delta \mathrm{H}=-286.2 \)
KJ.
A. - 891.1
B . -816.3
c. -965.9
D. -1040.7
Subject: Maths
If \( y=\ln (\operatorname{cosec} x-\cot x) \) then \( \frac{d y}{d x} \)
equals to
A. \( \operatorname{cosec} x+\cot x \)
B. \( \cot x \)
\( \mathbf{c} \cdot \sec x+\tan x \)
D. \( \operatorname{cosec} x \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{\epsilon}[\mathbf{1}, \mathbf{2}] \) when \( \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{R} \) and for a fixed
positive real number \( \boldsymbol{p} \) \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{p})=1+\sqrt{2 \boldsymbol{f}(\boldsymbol{x})-|\boldsymbol{f}(\boldsymbol{x})|^{2}} \) for al
\( x \epsilon R \) then prove that \( f(x) \) is a periodic function.
Subject: Chemistry
Assertion: Rusting of Fe is quicker in saline water than in ordinary water.
Reason: Presence of \( N a^{+} \) and \( C l^{-} \) ions
increase the conductance of the saline
water
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false