AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A 1 m long rod is half dipped in a swimming pool. The sunlight is incident
at \( 45^{\circ} \) on the rod. Find the length of the shadow on the bed of swimming pool.
\( \mathbf{A} \cdot 73 \mathrm{cm} \)
B. \( 78.25 \mathrm{cm} \)
c. \( 74.17 \mathrm{cm} \)
D. \( 81.5 \mathrm{cm} \)
Subject: Maths
\( \Delta \mathrm{ABC} \sim \Delta \mathrm{LBN}, \ln \Delta \mathrm{ABC}, \mathrm{AB}=6.1 \mathrm{cm} \angle \mathrm{B} \)
\( =45^{\circ}, \mathrm{BC}=5.4 \mathrm{cm} ; \frac{A C}{L N}=\frac{4}{7} . \) Construct
\( \Delta A B C \) and \( \Delta L B N \)
Subject: Physics
Assertion
Evaporation and vapour pressure depends upon available surface area of
solvent at any temperature.
Reason
Larger is surface area of solvent for evaporation more is evaporation.
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
Assertion
An inductor coil normally produces
more current with \( D C \) source
compared to an \( A C \) source of same
value of rms voltage.
Reason
In \( D C \) source applied voltage remains
constant with time.
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
The amino acid
\( \boldsymbol{H}_{2} \boldsymbol{N} \boldsymbol{C H}(\boldsymbol{C O O H})\left(\boldsymbol{C H}_{2}\right)_{4} \boldsymbol{N} \boldsymbol{H}_{2} \) at low
\( p H \) exits as:
A \( \cdot H_{2} N C H(C O O H)\left(C H_{2}\right)_{4} N H_{2} \)
в. \( H_{3} \stackrel{+}{N} C H(C O O H)\left(C H_{2}\right)_{4} N H_{2} \)
c. \( H_{3} \stackrel{+}{N} C H(C O O H)\left(C H_{2}\right)_{4} \stackrel{+}{N} H_{3} \)
D. \( H_{2} N C H(C O O H)\left(C H_{2}\right)_{4} \stackrel{+}{N} H_{3} \)
Subject: Physics
The initial velocity of a particle is u and the acceleration is given by (kt), where k is a positive constant. The distance
traveled in time t is :
A \( . s=u t^{2}+k t^{2} \)
B. \( s=u t+\left(\frac{k t^{3}}{6}\right) \)
c. \( _{s}=u t+\left(\frac{k t^{3}}{2}\right) \)
D. \( s=\left(\frac{u t^{2}}{2}\right)+\left(\frac{k t^{3}}{6}\right) \)
Subject: Maths
\( \left.\left[\begin{array}{cc}\mathbf{2 x}+\boldsymbol{y} & \boldsymbol{y} \\ \mathbf{1 - x} & \mathbf{4 x}\end{array}\right]=\mid \begin{array}{cc}\mathbf{1} & \mathbf{- 1} \\ \mathbf{0} & \mathbf{4}\end{array}\right], \) find the
values of \( \boldsymbol{x}+\boldsymbol{y} \)
Subject: Physics
In the series \( L C R \) circuit as shown in
figure, the voltmeter and ammeter
readings are:
A. \( V=100 \) volt, \( I=2 \) amp
B. \( V=100 \) volt, \( I=5 \) amp
c. \( V=1000 \) volt, \( I=2 \) amp
D. \( V=300 \) volt, \( I=1 \) amp
Subject: Chemistry
Assertion
When \( H C l \) in a jar is poured into a jar
containing burning candle, the candle
is put out.
Reason
\( H C l \) is a fire extinguisher.
A. If both assertion and reason are CORRECT and reason is the CORRECT explanation of the assertion.
B. If both assertion and reason are CORRECT, but reason is NOT THE CORRECT explanation of the assertion.
c. If assertion is CORRECT, but reason INCORRECT
D. If assertion is INCORRECT, but reason is CORRECT
Subject: Maths
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\frac{\mathbf{3} \boldsymbol{x}+\boldsymbol{4}}{\mathbf{2} \boldsymbol{x}-\mathbf{3}}\right) \)
A \( \cdot \frac{17}{(2 x-3)^{2}} \)
B \( \cdot \frac{1}{(2 x-3)^{2}} \)
c. \( \frac{-1}{(2 x-3)^{2}} \)
D. \( \frac{-17}{(2 x-3)^{2}} \)
Subject: Maths
find the coordinate of the tip of the position vector which is equivalent to \( \overrightarrow{A B}, \) where the coordinates of \( A \) and \( B \) \( \operatorname{are}(-1,3) \) and (-2,1) respectively
\( A \cdot(+1,+2) \)
B . (+1,-2)
c. (-1,+2)
D. (-1,-2)
Subject: Maths
Evaluate:
\( \frac{5 \sin ^{2} 30^{0}+\cos ^{2} 45^{0}+4 \tan ^{2} 60^{0}}{2 \sin 30^{0} \cos 60^{0}+\tan 45^{0}}=\frac{55}{m} \)
Find \( m \)
Subject: Maths
The solution of \( x \cos ^{2} y(d x)+ \) \( \tan y(d y)=0 \) is:
\( \mathbf{A} \cdot x^{2}+\sec ^{2} y=c \)
B . \( x^{2}+c o t^{2} y=c \)
C \( \cdot x^{2}+\sin ^{2} y=c \)
D. \( x^{2}+\cos ^{2} y=c \)
Subject: Chemistry
A vessel contains 1.6 g of dioxygen at STP \( (273.15 K, 1 \text { atm pressure }) . \) The gas is now transferred to another vessel at
constant temperature, where pressure becomes half of the original pressure. The volume of the new vessel is:
A . 2.24
B. 22.4 L
c. \( 11.2 \mathrm{L} \)
D. 1.12 L
Subject: Physics
An electron enters a uniform magnetic
field with a path perpendicular to the field lines and moves in a circular path
of radius \( \boldsymbol{R} \)

A positron (same mass of an electron
but opposite charge) enters the same magnetic field in a path perpendicular to the field with four times the kinetic
energy. Compared to the electrons path, the
radius of the protons circular path is:
A. The same radius
B. Twice as large
c. \( 1 / 2 \) as large
D. 4 times larger
Subject: Physics
A mass of \( 20 \mathrm{kg} \) moving with a speed of \( 10 m / s \) collides with another stationary mass of 5 kg. As a result of the collision,
the two masses stick together. The kinetic energy of the composite mass
will be
\( \mathbf{A} \cdot 600 J \)
в. \( 1000 J \)
c. \( 800 J \)
D. \( 1200 J \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{1} \\ -\mathbf{1} & \mathbf{1}\end{array}\right] \) and \( \quad \boldsymbol{n} \boldsymbol{\epsilon} \boldsymbol{N}, \) then \( \boldsymbol{A}^{n} \) is
equal to
\( \mathbf{A} \cdot 2^{n} A \)
B \( \cdot 2^{n-1} A \)
\( c \cdot n A \)
D. None of these
Subject: Physics
A rigid body rotates about a fixed axis with variable angular velocity equal to \( (a b t) \) at \( t \) where a and \( b \) are
constants. The angle through which it rotates before it comes to rest is
A \( \cdot \frac{a^{2}}{b} \)
в. \( \frac{a^{2}}{2 b} \)
c. \( \frac{a^{2}}{4 b} \)
D. \( \frac{a^{2}}{2 b^{2}} \)
Subject: Chemistry
Find the \( \Delta H \) of the following reaction.
\( \boldsymbol{O} \boldsymbol{F}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \longrightarrow \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( 2 H F(g) . \) Average bond energies of \( O- \)
\( \boldsymbol{F}, \boldsymbol{O}-\boldsymbol{H}, \boldsymbol{O}=\boldsymbol{O} \) and \( \boldsymbol{H}-\boldsymbol{F} \) are \( \boldsymbol{4 4} \)
111,118 and 135 kcal mol \( ^{-1} \)
respectively.
A. \( \Delta H=-78 \) k cal
в. \( \Delta H=+78 \) k cal
c. \( \Delta H=-498 \) k cal
Subject: Physics
A wheel with 10 metallic spokes each
\( 0.5 m \) long is rotated with a speed of
120rev/min in a plane normal to the horizontal component of earth's
magnetic field \( \boldsymbol{H}_{\boldsymbol{E}} \) at a place.lf \( \boldsymbol{H}_{\boldsymbol{E}}= \)
\( 0.4 G \) at the place, what is the induced
emf between the axle and the rim of the
wheel? Note that \( 1 G=10^{-4} \)
Subject: Physics
A tube one metre long is filled with liquid of mass \( 1 k g \). The tube is closed at both the ends and is revolved about
one end in a horizontal plane at 2 rev / \( s \)
The force experienced by the lid at the other lid is
A \( \cdot 4 \pi^{2} N \)
B. \( 8 \pi^{2} N \)
\( \mathbf{c} \cdot 16 \pi^{2} N \)
D. \( 9.8 N \)
Subject: Physics
A nonzero external force acts on a
system of particles, The velocity and the acceleration of the centre of mass are
found to be \( v_{0} \) and \( a_{0} \) at an instant \( t . \) It
is possible that :
This question has multiple correct options
A \( \cdot v_{0}=0, a_{0}=0 \)
0
в. \( v_{0}=0, a_{0} \neq 0 \)
c. \( v_{0} \neq 0, a_{0}=0 \)
D. \( v_{0} \neq 0, a_{0} \neq 0 \)
Subject: Physics
Which of the following quantities are always zero in SHM? This question has multiple correct options
A \( \cdot \vec{F} \times \vec{a} \)
В. \( \vec{v} \times \vec{r} \)
c \( . \vec{a} \times \vec{r} \)
D. \( \vec{F} \times \vec{r} \)
Subject: Physics
A force of \( 50 k g f \) is applied to the smaller piston of a hydraulic machine. Neglecting friction, The force exerted on the large piston, if the diameters of the
piston are \( 5 c m \) and \( 25 c m \) respectively
is \( ^{\prime} X^{\prime} N . \) Find \( \frac{X}{250} \)
Subject: Maths
If two events \( A \) and \( B \) are such that
\( \boldsymbol{P}(\overline{\boldsymbol{A}})=\mathbf{0 . 3}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 5} \) and
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0 . 3}, \) then \( \boldsymbol{P}\left(\frac{\boldsymbol{B}}{\boldsymbol{A} \cup \overline{\boldsymbol{B}}}\right) \) is
equal to
A \( \cdot \frac{5}{8} \)
B. \( \frac{7}{8} \)
\( c \cdot \frac{3}{8} \)
D.
Subject: Chemistry
The correct order of dipole moments is :
A \( \cdot C H_{4}<N F_{3}<N H_{3}<H_{2} O \)
в. \( N F_{3}<C H_{4}<N H_{3}<H_{2} O \)
c. \( N H_{3}<N F_{3}<C H_{4}<H_{2} O \)
D. \( H_{2} O<N H_{3}<N F_{3}<C H_{4} \)
Subject: Maths
Two system of rectangular axes have the same origin. If a plane cuts them at
distances, \( a, b, c \) and \( a_{1}, b_{1}, c_{1} \) from the
origin, then
A \( \cdot \frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{c^{2}}=\frac{1}{a_{1}^{2}}+\frac{1}{b_{1}^{2}}+\frac{1}{c_{1}^{2}} \)
B. \( \frac{1}{a^{2}}-\frac{1}{b^{2}}+\frac{1}{c^{2}}=\frac{1}{a_{1}^{2}}-\frac{1}{b_{1}^{2}}+\frac{1}{c_{1}^{2}} \)
C \( \cdot a^{2}+b^{2}+c^{2}=a_{1}^{2}+b_{1}^{2}+c_{1}^{2} \)
D \cdot \( a^{2}-b^{2}+c^{2}=a_{1}^{2}-b_{1}^{2}+c_{1}^{2} \)
Subject: Chemistry
The variation of solubility \( (S) \) with temperature for Glauber's salt is gives
as:

Which of the following options correctly explain the above behavior?
A. Dissolution of Glauber salt is exothermic
B. Dissolution of G;auber salt is endothermic
C . At \( 32.28^{\circ} \mathrm{C} \) Glauber salt looses water of crystalization
due to which dissolution above \( 32.28^{\circ} \mathrm{C} \) becomes
exothermic and below \( 32.28^{\circ} \mathrm{C} \) it is endothermic
D. Above \( 32.28^{\circ} \mathrm{C} \) dissolution of Glauber salt is
endothermic and below \( 32.28^{\circ} \mathrm{C} \) it is exothermic
Subject: Physics
Light from a denser medium 1 passes
to a rarer medium 2. When the angle of incidence is \( \theta \) the partially reflected and
refracted rays are mutually perpendicular. The critical angle will be
A \( \cdot \sin ^{-1}(\cot \theta) \)
B. \( \sin ^{-1}(\tan \theta) \)
c. \( \sin ^{-1}(\cos \theta) \)
D. \( \sin ^{-1}(\sec \theta) \)
Subject: Maths
If \( 4 \bar{i}+7 \bar{j}+8 \bar{k}, 2 \bar{i}+3 \bar{j}+4 \bar{k} \) and \( 2 \bar{i}+ \)
\( 5 \bar{j}+7 \bar{k} \) are the position vectors of the
vertices \( A, B \) an \( C \) of triangle \( A B C, \) the position vector of the point where the bisector of \( \angle \mathrm{A} \) meets BC is?
A \( \cdot \frac{2}{3}(-6 \bar{i}-8 \bar{j}-6 \bar{k}) \)
B \( \cdot \frac{2}{3}(6 \bar{i}+8 \bar{j}+6 \bar{k}) \)
c. \( \frac{1}{3}(6 \bar{i}+13 \bar{j}+18 \bar{k}) \)
D. \( 2(\bar{i}+\bar{j}+\bar{k}) \)
Subject: Biology
Phyllotaxy is the arrangement of leaves on the stem. Identify the three types of phyllotaxy shown in the given figures, \( x \) Y and Z.
When
A. X-Alternate, Y-Opposite, Z-Whorled
B. X-opposite, Y-Whorled, Z-Alternate
c. x-whorled, Y-Alternate, Z-Opposite
D. x-opposite, Y-Alternate, Z-Whorled
Subject: Maths
The value of \( \lim _{x \rightarrow a} \frac{\sqrt{x-b}-\sqrt{a-b}}{x^{2}-a^{2}}(a> \)
\( b) \) is
A \( \cdot \frac{1}{4 a} \)
B. \( \frac{1}{a \sqrt{a-b}} \)
c. \( \frac{1}{2 a \sqrt{a-b}} \)
D. \( \frac{1}{4 a \sqrt{a-b}} \)
Subject: Maths
\( \sin ^{-1}\left(3 x-2-x^{2}\right)+\cos ^{-1}\left(x^{2}-4 x+\right. \)
3) \( =\frac{\pi}{4} \) can have a solution for \( x \epsilon \)
A . [1,2]
B \( \cdot\left(\frac{3+\sqrt{5}}{2}, 2+\sqrt{2}\right) \)
\( \left(\frac{3-\sqrt{5}}{2}, 2-\sqrt{2}\right) \)
D \( \cdot\left(2-\sqrt{2}, \frac{3-\sqrt{5}}{2}\right) \cup\left(\frac{3-\sqrt{5}}{2}, 2+\sqrt{2}\right) \cup\{2\} \)
Subject: Chemistry
\( 4 H N O_{3}+P_{4} O_{10} \longrightarrow 4 H P O_{3}+X \)
In this above reaction the product \( X \) is :
A \( . N O_{2} \)
в. \( N_{2} O_{3} \)
c. \( N_{2} O_{4} \)
D. \( N_{2} O_{5} \)
Subject: Maths
\( \operatorname{Let} g(x)=f(\log x)+f(2-\log x) \) and
\( \boldsymbol{f}^{\prime \prime}(\boldsymbol{x})<\mathbf{0} \forall \boldsymbol{x} \in(\mathbf{0}, \boldsymbol{3}) . \) Then find the
interval in which \( g(x) \) increases.
\( ^{\mathrm{A}} \cdot\left(0, \frac{1}{e}\right) \)
B. \( \left(\frac{1}{e}, e\right) \)
\( c \cdot(0, e) \)
D. None of these
Subject: Chemistry
The precipitate of
\( \boldsymbol{C a} \boldsymbol{F}_{2}\left(\boldsymbol{K}_{s p}=1.7 \times 10^{-10}\right) \) is obtained
when equal volumes of the following are \( \operatorname{mixed} \)
\( \begin{array}{lll}\text { A. } 10^{-4} M & C a^{2-}+10^{-4} M & F^{-}\end{array} \)
\( \begin{array}{lll}\text { В. } 10^{-2} M & C a^{2-}+10^{-3} M & F^{-} \\ & \end{array} \)
Subject: Physics
A condenser of capacity \( 20 \mu F \) is first charged and then discharged through a
10 \( m H \) inductance. Neglecting the
resistance of the coil, the frequency of the resulting vibrations will be
A. 356 cycle/s
B. 35.6 cycle/s
\( \mathbf{c} \cdot 356 \times 10^{3} \) cycle \( / \mathrm{s} \)
D. 3.56 cycle/s
Subject: Maths
If \( r \) be the ratio of the roots of the
equation \( a x^{2}+b x+c=0, \) then \( \frac{(r+1)^{2}}{r}= \)
A \( \cdot \frac{a^{2}}{b c} \)
в. \( \frac{b^{2}}{c a} \)
c. \( \frac{c^{2}}{a b} \)
D. None of these
Subject: Maths
The area of the triangle whose vertices
are represented by \( 0, z, z^{i \alpha}(0<\alpha<\pi) \)
equals
\( \mathbf{A} \cdot \frac{1}{2}|z|^{2} \cos \alpha \)
B . \( \frac{1}{2}|z|^{2} \sin \alpha \)
C \( \cdot \frac{1}{2}|z|^{2} \sin \alpha \cos \alpha \)
D \cdot \( \frac{1}{2}|z|^{2} \)
Subject: Maths
A flag-staff 20 metres long standing on a wall 10 metres high subtends an
angle whose tangent is 0.5 at a point on
the ground. If \( \theta \) is the angle subtended
by wall at that point then \( \tan \theta= \)
A . 1
B. \( \frac{1}{3} \)
c. \( _{1 \text { or }} \frac{1}{3} \)
D.
Subject: Chemistry
Heavy water reacts with
\( \boldsymbol{C O}_{2}, \boldsymbol{S O}_{3}, \boldsymbol{P}_{2} \boldsymbol{O}_{5} \) and \( \boldsymbol{N}_{2} \boldsymbol{O}_{5} \)
respectively, to give the compounds:
A. \( D_{2} C O_{3}, D_{2} S O_{4}, D_{3} P O_{2} \) and \( D N O_{2} \)
в. \( D_{2} C O_{3}, D_{2} S O_{4}, D_{3} P O_{4} \) and \( D N O_{2} \)
c. \( D_{2} C O_{3}, D_{2} S O_{3}, D_{3} P O_{4} \) and \( D N O_{2} \)
D. \( D_{2} C O_{3}, D_{2} S O_{4}, D_{3} P O_{4} \) and \( D N O_{3} \)
Subject: Chemistry
Out of benzene and phenol, phenol is
more easily nitrated
because
A. presene of -OH group in phenol increases the electron density at ortho and para - position
B. presene of -OH group in phenol decreases the electron density at ortho and para - position
c. nitration being electrophilic substitution requires less density at ortho and para- position
D. phenol is more reactive than benzene due to -R effect
Subject: Physics
A long solenoid has 200 turns per \( \mathrm{cm} \) and carries a current \( i . \) The magnetic
field at its centre is \( 6.28 \times \) \( 10^{-2} W b m^{-2} . \) Another solenoid has 100
turns per \( c m \) and it carries a current \( \frac{i}{3} \) The value of the magnetic field at its
centre :
A . \( 1.05 \times 10^{-4} \mathrm{Wbm}^{-2} \)
B. \( 1.05 \times 10^{-2} \mathrm{Wbm}^{-2} \)
c. \( 1.05 \times 10^{-5} \mathrm{Wbm}^{-2} \)
D. \( 1.05 \times 10^{-3} \mathrm{Wbm}^{-2} \)
Subject: Physics
Point \( ^{\prime} A^{\prime} \) moves uniformly with speed
\( v_{1}(=20 m / \text {sec}) \) so that vector \( \vec{v}_{1} \) is
continuously 'aimed' at point ' \( B^{\prime} \) which in turn moves rectilinearly and uniformly with velocity \( v_{2}(=10 m / s e c) \)
along the path \( P \rightarrow Q \) as shown in the
figure. If the time (in sec)when the
points \( A \) and \( B \) converge is \( \frac{3 k}{7} . \) Then
find the value of \( k ? \)
Subject: Chemistry
VSEPR notation of \( \boldsymbol{P C l}_{5}, \boldsymbol{H}_{2} \boldsymbol{O} \) and \( \boldsymbol{I} \boldsymbol{C l}_{\mathbf{4}}^{-} \)
are:
A \( \cdot P C l_{5}-A X_{5}, H_{2} O-A X_{2} E_{2}, I C l_{4}^{-}-A X_{4} E_{2} \)
B. \( P C l_{5}-A X_{5}, H_{2} O-A X_{2} E, I C l_{4}^{-}-A X_{4} E \)
\( \mathrm{c} \cdot P C l_{5}-A X_{5}, H_{2} O-A X_{2}, I C l_{4}^{-}-A X_{4} E \)
D. \( P C l_{5}-A X_{5}, H_{2} O-A X_{2} E_{2}, I C l_{4}^{-}-A X_{4} E \)
Subject: Physics
At constant pressure, the heat of
formation of a compound is not dependent on temperature, when:
\( \mathbf{A} \cdot \Delta C_{p}=0 \)
В. \( \Delta C_{v}=0 \)
\( \mathbf{c} \cdot \Delta C_{p}>0 \)
D. \( \Delta C_{p}<0 \)
Subject: Chemistry
If reactivity for chlorination with \( 1^{\circ} \boldsymbol{H} \)
\( 2^{\circ} H \) and \( 3^{\circ} H \) is 1: 3.8: 4.5
respectively, what is the percentage of
\( (P 2) \) formed:
(closest to the nearest integer of \( \left.\frac{(P 2)}{10}\right) \)
Subject: Physics
A particle is constrained to move on a straight line path. It returns to the starting point after 10 sec. The total
distance covered by the particle during this time is \( 30 m \). Which of the following
statements about the motion of the
particle is true?
A. Displacement of the particle is zero
B. Average speed of the particle is \( 3 m / s \)
c. Displacement of the particle is \( 30 m \)
D. both (a) and (b)
Subject: Physics
A constant force \( \boldsymbol{F}=(\hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}+\boldsymbol{4} \hat{\boldsymbol{k}}) \boldsymbol{N} \)
acts on a particle and displace it from \( (-1 m, 2 m, 1 m) \) to \( (2 m,-3 m, 1 m) \)
Then the work done by the force is:
\( \mathbf{A} \cdot 12 J \)
в. \( -10 J \)
c. \( -12 J \)
D. \( 15 J \)
Subject: Maths
If \( \int_{0}^{y} \frac{1}{\sqrt{1+9 u^{2}}} d u=u, \) then \( \frac{d^{2} y}{d u^{2}} \) is
\( \mathbf{A} \cdot \sqrt{1+9 y^{2}} \)
В. \( \frac{1}{\sqrt{1+9 y^{2}}} \)
c. \( 9 y \)
D. \( 9 y^{2} \)
Subject: Physics
Which of the following option hold true for the above heat engine?
\[
\begin{array}{ccc} 
& \begin{array}{c}
\text { Work } \\
\text { Output }
\end{array} \\
\hline \begin{array}{c}
\text { Hot } \\
\text { Reservoir }
\end{array} & \text { Q } & \begin{array}{c}
\text { Hoat } \\
\text { Engine }
\end{array} & \begin{array}{c}
\text { Q }_{\text {Reservoir }} \\
\mathbf{T}
\end{array}
\end{array}
\]
A. Positive work
B. An adiabatic process
c. An isobaric process
D. An isochoric process
E. An isothermal process
Subject: Chemistry
Amongst the following compounds (I)
\( \boldsymbol{H}_{5} \boldsymbol{P}_{3} \boldsymbol{O}_{10},(\text { II }) \boldsymbol{H}_{6} \boldsymbol{P}_{4} \boldsymbol{O}_{13},(\| \text { II }) \boldsymbol{H}_{5} \boldsymbol{P}_{5} \boldsymbol{O}_{15} \)
and \( (\mathrm{IV}) \boldsymbol{H}_{7} \boldsymbol{P}_{5} \boldsymbol{O}_{16}, \) the non-cyclic
phosphates are:
A. I and III
B. I, II and III
c. ।, ॥ and IV
D. I, II, II and IV
Subject: Maths
Point \( (\boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma}) \) lies on the plane \( \boldsymbol{x}+\boldsymbol{y}+ \)
\( z=2 . \) Let \( \vec{a}=\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k} \) and \( \hat{k} \times \)
\( (\hat{k} \times \vec{a})=0 \) then \( \gamma= \)
A .
B. 1
c. 2
D.
Subject: Physics
The linear density of rod of length \( L \) and placed along x-axis with the lighter and at origin, is given by \( \lambda=B x^{2} \) where \( B \)
is a constant. The the c-ordinates of
centre of mass are
A \( \cdot\left(\frac{3 L}{4}, 0\right) \)
B \( \cdot\left(0, \frac{3 L}{4}\right) \)
c. \( \left(\frac{4 L}{3}, 0\right) \)
D. \( \left(\frac{0,4 L}{3}\right) \)
Subject: Physics
Find out the angle \( \theta \) made by string
from vertical in equilibrium position
A \( \cdot \tan ^{-1}\left(\frac{m g}{q E}\right) \)
B. \( \sin ^{-1}\left(\frac{m g}{q E}\right) \)
c. \( \cos ^{-1}\left(\frac{m g}{q E}\right) \)
\( \tan ^{-1}\left(\frac{q E}{m g}\right) \)
Subject: Physics
An \( \alpha- \) particle of energy \( 5 \mathrm{MeV} \) is
scattered through 180 by a fixed uranium nucleus. The distance of the
closest approach is of the order of
\( \mathbf{A} \cdot \mathbf{1} \)
В. \( 10^{-10} \mathrm{cm} \)
\( \mathbf{c} \cdot 10^{-12} \mathrm{cm} \)
D. \( 10^{-15} \mathrm{cm} \)
Subject: Physics
At what angle should a body be projected with a velocity \( 24 \frac{m}{s} \) just to
pass over the obstacle \( 14 \mathrm{m} \) high of a distance of \( \left.24 m . \text { (Take } g=10 m / s^{2}\right) \)
\( \mathbf{A} \cdot \tan \theta=3.8 \)
B. \( \tan \theta=1 \)
\( \mathbf{c} \cdot \tan \theta=3.2 \)
D. \( \tan \theta=2 \)
Subject: Maths
Draw the graphs of the equations \( x= \) \( \mathbf{3}, \boldsymbol{x}=\mathbf{5} \) and \( \mathbf{2} \boldsymbol{x}+\mathbf{4} \boldsymbol{y}=\mathbf{0} . \) Also, find the
area of the quadrilateral formed by the lines and the \( x \) -axis.
Subject: Chemistry
Consider the following reaction:
\( \boldsymbol{x} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}^{-}+\boldsymbol{y} \boldsymbol{C}_{2} \boldsymbol{O}_{4}^{2-}+\boldsymbol{z} \boldsymbol{H}^{+} \rightarrow \)
\( \boldsymbol{x} \boldsymbol{M} \boldsymbol{n}^{2+}+\mathbf{2} \boldsymbol{y} \boldsymbol{C} \boldsymbol{O}_{2}+\frac{\boldsymbol{z}}{2} \boldsymbol{H}_{2} \boldsymbol{O} . \) The values
of \( x, y \) and \( z \) in the reaction are, respectively:
A .2,5 and 16
B. 5,2 and 8
c. 5,2 and 16
D. 2,5 and 8
Subject: Physics
The point at which the gravitational force acting on any mass is zero due to the Earth and the Moon system is (The mass of the Earth is approximately 81 times the mass of the Moon and the
distance between the Earth and the
Moon is \( 3,85,000 k m . \)
A. \( 36,000 \mathrm{km} \) from the Moon
B. 38,500 km from the Moon.
c. \( 34500 \mathrm{km} \) from the moon
D. 30,000 km from the Moon
Subject: Maths
ff \( f(x) \) is a function such that \( f(x y)= \) \( \boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{y}): \boldsymbol{x}, \boldsymbol{y}[\boldsymbol{R}, \text { then } \boldsymbol{f}(\mathbf{1} / \boldsymbol{e}) \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3
Subject: Physics
An iron sphere of mass \( 10 \mathrm{kg} \) is dropped from a height of \( 80 \mathrm{cm} . \) If the downward
acceleration of the sphere is \( 10 m s^{-2} \)
calculate the momentum of the sphere
when it just strikes the ground
A. \( 100 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
B. \( 40 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
c. \( 60 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
D. \( 75 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
Subject: Physics
A smooth horizontal disc rotates with a
constant angular velocity \( \omega \) about a stationary vertical axis passing through
its centre, the point \( O . A t \) a moment \( t= \)
0 a disc is set in motion from that point
with velocity \( v_{0} . \) Find the angular
momentum \( \boldsymbol{M} \)
\( (t) \) of the disc relative to the point \( O \) in the reference frame fixed
to the disc. Make sure that this angular momentum is caused by the Coriolis force.
Subject: Chemistry
The lattice energies of
\( N a C l, N a F, K C l \) and \( R b C l \) follow the
order:
A. \( K C l<R b C l<N a C l<N a F \)
в. \( N a F<N a C l<K C l<R b C l \)
c. \( R b C l<K C l<N a C l<N a F \)
D. \( N a C l<R b C l<N a F<K C l \)
Subject: Chemistry
What is the electrode potential in (in \( V \) ) of the following electrode at
\( \mathbf{2 5}^{o} \boldsymbol{C}>\boldsymbol{N} \boldsymbol{i}^{2+}(\mathbf{0 . 1} \boldsymbol{M}) \mid \boldsymbol{N} \boldsymbol{i}(\boldsymbol{s}) \)
(standard reaction potential of
\( \left.N i^{2+} / N i \text { is }-0.25 V\right) \)
A . \( -0.28 v \)
B. -0.34 V
c. \( -0.82 v \)
D. -0.22V
Subject: Maths
\( \boldsymbol{B}=\boldsymbol{A}+\boldsymbol{A}^{2}+\boldsymbol{A}^{3}+\boldsymbol{A}^{4} \)
If order of \( A \) is 3 then order of \( B \) is
\( A \cdot 3 \)
B. 6
\( c \cdot 2 \)
D. 9
Subject: Physics
Two small bodies of masses \( 10 \mathrm{kg} \) and \( 20 \mathrm{kg} \) are kept a distance \( 1.0 \mathrm{m} \) apart and released. Assuming that only mutual gravitational forces are acting, find the speeds of the particles when the separation decreases to \( 0.5 \mathrm{m} \)