AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Which of the following statements are
correct?
This question has multiple correct options
A. A reaction in which different stereisomers produce different products or act at different rates is called stereospecific reaction
B. A reaction in which a given substrate produces diastereoisomeric products in different amounts and where one diastereomer predominates very much over the other is called stereoselective reaction
C. If the replacement of one group at an a chiral centre by a new substituent generates a chiral centre, the original molecule is said to be enantiopic
D. The E and Z system of naming geometrical isomers is based on the CIP sequence rule
Subject: Physics
The angular velocity \( (\omega \) of a particle is
related to the linear velocity \( v \) of the particle moving in a circular motion or radius R using the formula
\( \mathbf{A} \cdot v=R \omega \)
B. \( v=2 R \omega \)
c. \( v=R \omega^{2} \)
D. \( v=R \sqrt{(} \omega) \)
Subject: Maths
Let \( A=Q \times Q \) and let \( ^{\star} \) be a binary
operation on \( A \) defined by \( (a, b) * \)
\( (c, d)=(a c, b+a d) \) for \( (a, b),(c, d) \in \)
A. Determine, whether \( ^{*} \) is
commutative and associative. Then
with respect to \( ^{*} \) on \( A \).Find the identity
element of \( \boldsymbol{A} \)
Subject: Biology
The relative contribution of various
green house gases to global warming is given in the following diagram:
Identify the green house gases.
A \( \cdot A=C O_{2} ; B=C H_{4} ; C=N_{2} O ; D=C F C s \)
B. \( A=C O_{2} ; B=C F C s ; C=C H_{4} ; D=N_{2} O \)
C. \( A=C F C s ; B=C O_{2} ; C=C H_{4} ; D=N_{2} O \)
D. \( A=C F C s ; B=C H_{4} ; C=C O_{2} ; D=N_{2} O \)
Subject: Chemistry
Acetic acid is titrated with \( N a O H \)
solution. Which of the following statement is correct for this titration?
A. Conductane increases upto equivalence point, then it it decreases
B. Conductance decreases upto equivalence point, then it increases
c. First conductance increases slowly upto equivalence point and then increases rapidly
D. First conductance increases slowly upto equivalence point and then drops rapidly
Subject: Chemistry
The two aqueous solutions; \( \boldsymbol{A}\left(\boldsymbol{A} \boldsymbol{g} \boldsymbol{N} \boldsymbol{O}_{3}\right) \)
and \( \boldsymbol{B}(\boldsymbol{L} \boldsymbol{i} \boldsymbol{C l}) \) were electrolysed using
Pt electrodes. The pH of the resulting solutions will :
A. increase in A and decrease in B
B. decrease in both
c. increase in both
D. decrease in A and increase in B
Subject: Chemistry
The standard heat of combustion of
graphite carbon is \( -393.5 \mathrm{KJ} \mathrm{mol}^{-1} \). The
standard enthalpy
of \( \mathrm{CO}_{2} \) is
A \( \cdot+393.5 \) KJ \( \mathrm{mol}^{-1} \)
B . - -393. 5 KJ mol-1
C . +196.75 КJ \( \mathrm{mol}^{-1} \)
D . -196.75 KJ mol-
Subject: Chemistry
When in excess, a very dilute aqueous
solution of \( K I \) is added to a very dilute
aqueous solution of silver nitrate, the colloidal particles of silver iodide, associated with the Helmholtz double
layer, are
A \( . A g I: A g^{+}: N O_{3}^{-} \)
B. \( A g I: K^{+}: N O_{3}^{-} \)
c. \( A g I: N O_{3}^{-}: A g^{+} \)
D. \( A g I: I^{-}: K^{+} \)
Subject: Biology
Statement 1: The stem tubers are the
swollen ends of specialized underground stem branches, which help in vegetative propagation of the plant. Statement 2: Solanum tuberosum is an
example of a stem tuber which stores inulin as the main reserve food
material.
A. Both statement 1 and 2 are correct
B. Statement 1 is correct but statement 2 is incorrect
c. statement 1 is incorrect but statement 2 is correct
D. Both statement 1 and 2 are incorrect
Subject: Physics
A bomber plane moves horizontally with a speed of \( 600 \mathrm{m} / \mathrm{s} \) and a bomb released from it, strikes the ground in 10 \( s \). The angle with horizontal at which it strikes the ground will be
\( A \cdot \tan ^{-1}(1 / 2) \)
B \cdot \( \tan ^{-1}(1 / 6) \)
C \( \cdot \tan ^{-1}(4 / 5) \)
\( \mathbf{D} \cdot \tan ^{-1}(3 / 4) \)
Subject: Maths
Let \( f \) and \( g \) be two functions defined on
an interval I such that \( f(x) \geq 0 \) and
\( g(x) \leq 0 \) for all \( x \epsilon I \) and \( f \) is strictly decreasing on \( I \) while \( g \) is strictly
increasing on \( I \) then

This question has multiple correct options
A. The product function \( f g \) is strictly increasing on \( I \)
B. The product function \( f g \) is strictly decreasing on \( I \)
c. \( \operatorname{Fog}(x) \) is monotonically increasing on \( I \)
D. \( \operatorname{Fog}(x) \) is monotonically decreasing on \( I \)
Subject: Maths
Construct \( \triangle M N O \) such that \( N O= \)
\( \mathbf{6 . 2} \mathrm{cm}, \angle \boldsymbol{N}=\mathbf{5 0}^{\circ} \) and \( \boldsymbol{M} \boldsymbol{O}-\boldsymbol{M} \boldsymbol{N}= \)
\( 2.4 \mathrm{cm} \)
Subject: Maths
Find a particular solution of the differential equation \( \frac{d y}{d x}+y \cot x= \) \( 4 x \operatorname{cosec} x(x \neq 0), \) given that \( y=0 \)
when \( \boldsymbol{x}=\frac{\boldsymbol{\pi}}{\boldsymbol{2}} \)
Subject: Chemistry
Assertion
Chemical messengers are chemicals that enable communication of a
message between two neurons or
between neurons and muscles.
Reason

Chemicals enter the cell through receptor.
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 standard reduction potentials of \( C u^{2+} \mid C u \) and \( C u^{2+} \mid C u^{\oplus} \) are 0.337 V
and \( 0.153 \mathrm{V} \), respectively. The standard electrode potential of \( C u \oplus \mid C u \) half cell
is:
A . \( 0.184 \mathrm{v} \)
в. 0.827
c. \( 0.521 \mathrm{v} \)
D. 0.490
Subject: Chemistry
The chemicals and the reaction
conditions required for the preparation
of ethanol are:
\( \mathbf{A} \cdot C_{2} H_{5} I, N a O H(a q) \)
B \( \cdot C H_{3} C l, N a, H_{2} O \)
c. \( K O O C-C H=C H-C O O K \), electrolysis
D. \( C H_{3} C O_{2} N a, N a O H, C a O, \Delta \)
Subject: Chemistry
The density of nucleus is of the order of:
A \( \cdot 10^{5} k g m^{-3} \)
В. \( 10^{16} \) kgm \( ^{-3} \)
\( \mathbf{c} \cdot 10^{17} k g m^{-3} \)
D. \( 10^{25} \mathrm{kgm}^{-3} \)
Subject: Maths
Two different families \( A \) and \( B \) are
blessed with equal number of children.
There are 3 tickets to be distributed
amongst the children of these families so that no child gets more than one
ticket. If the probability that all the tickets go to the children of the family \( B \) is \( \frac{1}{12}, \) then the number of children in
each family is?
A .4
B. 6
\( c .3 \)
\( D \)
Subject: Maths
In the group \( G=\{1,5,7,11\} \) under \( \otimes_{12} \)
the value of \( 7 \otimes_{12} 11^{-1} \) is equal to
\( \left(\otimes_{12}: \text { under multiplication modulo } 12\right) \)
A . 5
B. 7
c. 11
D.
Subject: Physics
A constant torque of \( 1000 N \) m turns a wheel of moment of inertia \( 200 k g m^{2} \) about an axis through its centre. The wheel is at rest initially. Its angular velocity after \( 3 s \) is :
A \( \cdot 15 \) rads\( ^{-1} \)
B. 0.6 rads\( ^{-1} \)
c. 6000 rads\( ^{-1} \)
D. 5 rads\( ^{-1} \)
Subject: Chemistry
Select the correct statements:
This question has multiple correct options
A. The value of \( Q_{c} \) for a given reaction is constant.
B. A change in the physical state of a gaseous product shows a change in the value of equilibrium constant of that reaction.
C the value of ratio \( \frac{Q_{c}}{K_{c}} \) can be used to predict the direction in which a system will proceed spontaneously towards equilibrium.
D. The rate constants for forward and backward reaction
for a reversible reaction always increases with temperature but their ratio \( \left(i . e ., \frac{K_{f}}{K_{b}}\right) \) may increase or decrease with temperature.
Subject: Physics
The electrical potential on the surface of a
sphere of radius \( ^{\prime} r^{\prime} \) due to a charge \( 3 \times \)
\( 10^{-6} \) is \( 500 V \). The intensity of electric field
on the surface of the sphere is \( \left[\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} N m^{2} C^{-2}\right]\left(i n N C^{-1}\right) \)
A \( .250 / 27 \)
B. \( 27 / 250 \)
\( c .250 \)
D. 27
Subject: Maths
Find the value of \( x \) which satisfy equation \( : \sin ^{-1} x+\sin ^{-1} 2 x=\frac{\pi}{3} \)
A \( \cdot x=\frac{1}{2} \sqrt{\frac{3}{7}} \)
B・ \( x=\frac{1}{3} \sqrt{\frac{4}{7}} \)
c. \( x=\frac{1}{3} \sqrt{\frac{3}{7}} \)
D. \( x=\frac{1}{2} \sqrt{\frac{4}{7}} \)
Subject: Physics
From the position time graph for two particles and B is shown below. Graph and particles A making angles \( 60^{\circ} \) and
\( 30^{\circ} \) with the time axis. The ratio of
velocities \( \boldsymbol{v}_{A}: \boldsymbol{v}_{B} \) is
\( A \cdot 1: 1 \)
в. 4: 1
c. \( \sqrt{2}: 1 \)
D. 1: 3
Subject: Maths
Considre the sequence \( \left(a_{n}\right) n \geq 0 \) given
by the following relation: \( a_{0}=4, a_{1}= \)
\( 22, \) and for all \( n \geq 2, a_{n}=6 a_{n-1}- \)
\( a_{n-2} . \) Prove that there exist sequences
of positive integers \( \left(x_{n}\right) n \geq \)
\( \mathbf{0},\left(\boldsymbol{y}_{n}\right) \boldsymbol{n} \geq \mathbf{0} \) such that \( \boldsymbol{a}_{\boldsymbol{n}}=\frac{\boldsymbol{y}_{\boldsymbol{n}}^{\boldsymbol{2}}+\boldsymbol{7}}{\boldsymbol{x}_{\boldsymbol{n}}-\boldsymbol{y}_{\boldsymbol{n}}} \)
for all \( n \geq 0 \)
Subject: Chemistry
Among the metal carbonyls
\( \left[\boldsymbol{M} \boldsymbol{n}(\boldsymbol{C O})_{\boldsymbol{6}}\right]^{+},\left[\boldsymbol{T} \boldsymbol{i}(\boldsymbol{C} \boldsymbol{O})_{\boldsymbol{6}}\right],\left[\boldsymbol{C r}(\boldsymbol{C O})_{\boldsymbol{6}}\right] \)
and \( \left[V(C O)_{6}\right]^{-} \) the \( C-O \) bond order
would be lowest in :
\( \mathbf{A} \cdot\left[M n(C O)_{6}\right]^{+} \)
в. \( \left[T i(C O)_{6}\right]^{2} \)
\( \mathbf{c} \cdot\left[C r(C O)_{6}\right] \)
D. \( \left[V(C O)_{6}\right]^{-} \)
Subject: Physics
The distance between two point sources
of light is \( 24 \mathrm{cm} \) and a converging lens is kept in between two sources. The object distances of two sources from a converging lens of focal length of \( 9 \mathrm{cm} \) so that the image distances of two
sources are equal
\( A \cdot 12 \mathrm{cm} \)
B. \( 24 \mathrm{cm} \) or \( 18 \mathrm{cm} \)
\( c .18 \mathrm{cm} \) or \( 6 \mathrm{cm} \)
D. \( 24 \mathrm{cm} \)
Subject: Physics
Two point charges exert force of \( \boldsymbol{F} \) Newton when separated by a distance of \( 10 \mathrm{cm} \) in air. The distance for which the
force between them will be same if the
medium them has \( \varepsilon_{r}=4, \) is:-
\( A \cdot 10 \mathrm{cm} \)
B. 20 cm
\( c \cdot 5 \mathrm{cm} \)
D. 2.5 cm
Subject: Chemistry
\( 28 g \) of \( N_{2} \) and \( 6 g \) of \( H_{2} \) were kept at
\( 400^{\circ} \mathrm{C} \) in 1 litre vessel, the equilibrium
mixture contained \( 27.54 g \) of \( N H_{3} . \) The
appropriate value of \( \boldsymbol{K}_{c} \) for the above reaction can be (in mole\( ^{-2} \) litre\( ^{2} \) )
\( \mathbf{A} \cdot 75 \)
B. 50
c. 25
D. 100
Subject: Physics
A cannon ball of mass \( 500 g \) is fired
with a speed of \( 15 m s^{-1} \). Find its
momentum.
A . \( 7500 k g \) m \( s^{-1} \)
B. \( 3750 k g \) m \( s^{-1} \)
c. \( 7.5 k g m s^{-1} \)
D. 3.75kg m s \( ^{-1} \)
Subject: Physics
The work function of cesium metal is
2eV. It means that
A. The energy necessary to emit electrons from metal surface is \( 2 \mathrm{eV} \)
B. The energy of electrons emitted from metallic surface is \( 2 e v \)
C. The value of photoelectric current is \( 2 \mathrm{eV} \)
D. The value of threshold frequency is \( 2 e v \)
Subject: Physics
A simple harmonic motion is represented by \( \boldsymbol{x}(\boldsymbol{t})=\sin ^{2} \boldsymbol{\omega} \boldsymbol{t}- \)
\( 2 \cos ^{2} \omega t . \) The angular frequency of
oscillation is given by?
\( A \cdot \omega \)
B. 2
c. \( 4 \omega \)
D. \( \frac{\omega}{2} \)
E.
Subject: Maths
Range of \( \boldsymbol{f}(\boldsymbol{x})=\sin ^{-1} \boldsymbol{x}+\tan ^{-1} \boldsymbol{x}+ \)
\( \cos ^{-1} x \) is
\( \mathbf{A} \cdot[0, \pi] \)
В. \( \left[\frac{\pi}{4}, \frac{3 \pi}{4}\right] \)
с. \( [-\pi, 2 \pi] \)
D. None of these
Subject: Chemistry
How much \( N H_{3} \) should be added to
a \( 0.004 \mathrm{M} A g^{+} \) solution to prevent
the precipitation of AgCl when \( C l^{-} \) ion
reaches \( 0.001 ? K_{s p} A g C l=1.8 \times \)
\( \mathbf{1 0}^{-\mathbf{1 0}}, \boldsymbol{K}_{\boldsymbol{d}} \boldsymbol{A} \boldsymbol{g}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}^{+}=\mathbf{6} \times \mathbf{1 0}^{-\boldsymbol{8}} \)
A. 0.0011 molar
B. 0.36 molar
c. 0.0036 molar
D. 1.6 molar
Subject: Physics
The circuit below shows a 6.0 V battery
In a circuit with three resistors, labeled
1,2 and \( 3 . \) If each resistor has a
resistance of 6.0 ohms, what is the rate
at which energy is used by resistor \( 2 ? \)
\( A \cdot 10 W \)
B. 36.0 W
c. \( 6.0 \mathrm{w} \)
D. \( 24.0 \mathrm{W} \)
E. \( 18.0 \mathrm{w} \)
Subject: Physics
Assertion
In both radio activity and photoelectric effect electrons may be ejected.
Reason
In photoelectric effect and radio activity emission occurs only of unstable elements.
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
You invested Rs. 1500 and received Rs.
\( \mathbf{5 0 0 0} \) after three years. What had been
the interest rate?
A. \( 111.11 \% \)
B . \( 222.22 \% \)
c. \( 333.33 \% \)
D. \( 77.77 \% \)
Subject: Chemistry
The time in which activity of an element reduces to \( 90 \% \) of its original value is:
The half-life period of element is \( 1.4 \times \)
\( 10^{10} \) years.
A \( \cdot 2.128 \times 10^{9} \) years
B . \( 1.578 \times 10^{7} \) years
c. \( 6.954 \times 10^{7} \) years
D. none of these
Subject: Physics
If \( v_{e} \) is escape velocity and \( v_{o} \) is orbital
velocity of a satellite for orbit close to the earth's surface, then these are
related by :
A \( \cdot v_{o}=v_{e} \)
B. \( v_{e}=\sqrt{2 v_{o}} \)
c. \( v_{e}=\sqrt{2} v_{o} \)
D. \( v_{o}=\sqrt{2} v_{e} \)
Subject: Physics
A conducting disc of radius \( r \) spins about its axis with an angular velocity
\( \omega . \) There is a uniform magnetic field of
magnetude B perpendicular to the plane of the disc. \( C \) is the centre of the
ring. This question has multiple correct options
A. No emf is induced in the disc.
B. The potential difference between C and the rim is \( \frac{1}{3} B r^{2} \omega \)
c. \( c \) is at a higher potential than the rim
D. Current flows between c and the rim
Subject: Physics
A diatomic molecule has moment of
inertia \( I . \) By Bohrs quantization
condition its rotational energy in the \( n^{t h} \) level \( (n=0 \) is not allowed) is
A \( \cdot \frac{1}{n^{2}}\left(\frac{\mathrm{h}^{2}}{8 \pi^{2} \mathrm{I}}\right) \)
B. \( \frac{1}{\mathrm{n}}\left(\frac{\mathrm{h}^{2}}{8 \pi^{2} \mathrm{I}}\right) \)
\( ^{c} \cdot\left(\frac{h^{2}}{8 \pi^{2} I}\right) \)
D. \( _{\mathrm{n}^{2}}\left(\frac{\mathrm{h}^{2}}{8 \pi^{2} \mathrm{I}}\right) \)
Subject: Maths
\( \int_{-1 / \sqrt{3}}^{1 / \sqrt{3}} \frac{x^{4}}{1-x^{4}} \cos ^{-1} \frac{2 x}{1+x^{2}} d x= \)
\( \frac{\pi}{2}\left[\frac{1}{2} \log (2+\sqrt{3})+\frac{\pi}{6}-\frac{2}{\sqrt{3}}\right] \)
\( \frac{\pi}{2}\left[\frac{1}{2} \log (2+\sqrt{3})+\frac{\pi}{4}-\frac{2}{\sqrt{2}}\right] \)
D. \( \frac{\pi}{2}\left[\frac{1}{2} \log (2-\sqrt{3})-\frac{\pi}{6}+\frac{2}{\sqrt{3}}\right] \)
\( \frac{\pi}{2}\left[\frac{1}{3} \log (3+\sqrt{3})+\frac{\pi}{5}-\frac{1}{\sqrt{3}}\right] \)
Subject: Biology
gm molar solution is :
A. \( 1 \mathrm{gm} \) mole of solute dissolved in \( 1000 \mathrm{ml} \) of solvent.
B. \( 1 \mathrm{gm} \) mole of solute dissolved in \( 1000 \mathrm{ml} \) of solution.
C. \( 1 \mathrm{gm} \) of solute dissolved in \( 1000 \mathrm{ml} \) of solvent
D. \( 1 \mathrm{gm} \) of solute dissolved in \( 1000 \mathrm{ml} \) of solution.
Subject: Physics
A ball is dropped from the top of a building. The ball takes 0.2 s to fall past the \( 3 \mathrm{m} \) length of a window some
distance from the top of the
building. Speed of the ball as it crosses the top edge of the window is \( (g= \)
\( \left.10 m s^{-2}\right) \)
A. \( 3.5 \mathrm{m} / \mathrm{s} \)
B. \( 8.5 \mathrm{m} / \mathrm{s} \)
\( c \cdot 5 m / s \)
D. \( 14 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
When solid \( K C l \) is added to a saturated
solution of \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C} \boldsymbol{I} \) in \( \boldsymbol{H}_{2} \boldsymbol{O} \)
A. Nothing happens
B. Solubility of \( A g C l \) decreases
c. Solubility of \( A g C l \) increases
D. Solubility product of \( A g C l \) increases
Subject: Physics
A bulb is connected to an ideal battery
of emf \( 10 \mathrm{V} \) so that the resulting current is \( 10 \mathrm{mA} \). When the bulb is connected to
\( 220 \mathrm{V} \) mains (ideal), the current is 50
mA. choose the correct alternative
A. the resistance of the bulb is 1 k ohm and in the second case, it is \( 4.4 \mathrm{k} \) ohm
B. it is not possible since ohm's law is not followed
c. the increase in resistance is due to heating of the filament of the bulb when it is connected to \( 220 \mathrm{v} \) main
D. none of these
Subject: Maths
If one of the roots of \( a x^{2}+b x+c=0 \) is
\( \mathbf{7}+\sqrt{\mathbf{2}} \) then find the other root
A. \( -7+\sqrt{2} \)
B. \( 7-\sqrt{2} \)
c. \( -7-\sqrt{2} \)
D. Cannot be determined
Subject: Physics
In the nuclear fusion reaction, \( _{1}^{2} \mathbf{H}+_{1}^{3} \) \( \mathbf{H} \rightarrow_{2}^{4} H e+n \) given that the repulsive potential energy between the two nuclei is \( 7.7 \times 10^{-14} J, \) the temperature at
which the gases must be heated to initiate the reaction is nearly [Boltzmann's constant \( \mathbf{k}=\mathbf{1 . 3 8} \times \)
\( \left.\mathbf{1 0}^{-\mathbf{2 3} \mathbf{J}} / \mathbf{K}\right] \)
\( \mathbf{A} \cdot 10^{7} K \)
В. \( 10^{5} K \)
\( \mathbf{c} \cdot 10^{3} K \)
\( \mathbf{D} \cdot 10^{9} K \)
Subject: Chemistry
Electrolyte \( \quad \wedge^{\infty}\left(S c m^{2} m o l^{-1}\right) \)
\( K C l \quad 149.9 \)
\( K N O_{3} \)
145.0
\( H C l \quad 426.2 \)
\( N a O A c \quad 91.0 \)
\( N a C l \quad 126.5 \)
Calculate \( \Lambda^{\infty}_{H O A c} \) using appropriate
molar conductances of the electrolytes
listed above at infinite dilution with \( H_{2} O \)
at \( 25^{\circ} \mathrm{C} ? \)
A. 217. 5 \( \operatorname{Scm}^{2} \) mol \( ^{-1} \)
В. 390.7 \( S c m^{2} \) mol \( ^{-1} \)
c. \( 552.7 \mathrm{Scm}^{2} \mathrm{mol}^{-1} \)
D. 517.2 \( S c m^{2} m o l^{-1} \)
Subject: Chemistry
What is the total translational and
rotational energy of 1 mole of oxygen at
\( 300 K: \)
\( \left[\boldsymbol{R}=\mathbf{8 . 3 1 4} \boldsymbol{J} \boldsymbol{m o l}^{1} \boldsymbol{K}^{1}\right] \)
A. \( 6235.5 J \)
B. 623.25 \( J \)
c. \( 62.325 J \)
D. 6.2325 \( J \)
Subject: Physics
A particle is projected with an angle of
projection \( \theta \) to the horizontal line
passing through the points \( (P, Q) \) and
\( Q, P) \) referred to horizontal and vertical
axes (can be treated as x-axis and y-
axis respectively).

The angle of projection can be given by
\( ^{\mathbf{A}} \cdot \tan ^{-1}\left[\frac{P^{2}+P Q+Q^{2}}{P Q}\right] \)
B. \( \tan ^{-1}\left[\frac{P^{2}+Q^{2}-P Q}{P Q}\right] \)
\( ^{\mathbf{c}} \tan ^{-1}\left[\frac{P^{2}+Q^{2}}{2 P Q}\right] \)
D. \( \tan ^{-1}\left[\frac{P^{2}+Q^{2}+P Q}{2 P Q}\right] \)
Subject: Chemistry
In hypothetical reaction, \( \boldsymbol{A}_{2}+\boldsymbol{B}_{2} \longrightarrow \)
\( 2 A B, \) follows the mechanism as given
below:
\( A_{2} \rightleftharpoons A+A \quad \) (fast reaction)
\( A+B_{2} \longrightarrow A B+B \quad \) (slow reaction)
\( A+B \longrightarrow A B \quad \) (fast reaction)
Give the rate law and order of reaction.
Subject: Physics
The velocity of electromagnetic waves
in a dielectric medium \( \left(\varepsilon_{r}=2\right) \) is:
A \( \cdot 3 \times 10^{8} \) meter/second
B . \( 1.5 \times 10^{8} \) meter/second
C. \( 6 \times 10^{8} \) meter/second
D. \( 7.5 \times 10^{7} \) meter/second
Subject: Physics
Four wires made of same materials are
stretched by the same load. Their dimensions are given below. The one which elongates more is?
A. Wire of length \( 1 \mathrm{m} \) and diameter \( 1 \mathrm{mm} \)
B. Length 2m, diameter 2 mm
c. Length 3m, diameter 3 mm
D. Length 0.5m, diameter 0.5mm
Subject: Chemistry
The distillation of phenol with zinc dust gives:
\( \mathbf{A} \cdot C_{6} H_{6} \)
в. \( C_{6} H_{5}-C_{6} H_{5} \)
c. \( C_{6} H_{1} \)
D. \( C_{6} H_{5}-O-C_{6} H_{5} \)
Subject: Physics
Mercury orbits the sun in about one-
fifth of the earth year. If \( 1 A U \) is defined
as the distance from the earth to the
sum, what is the approximate distance between mercury and the sun?
A \( \cdot 1 / 25^{1 / 3} A U \)
B . \( 1 / 9^{1 / 3} A U \)
\( \mathbf{c} \cdot 1 / 5^{1 / 3} A U \)
D. \( 1 / 3^{1 / 3} \) AU
Subject: Chemistry
g mixture of glucose and urea present in \( 250 \mathrm{mL} \) aqueous solution shows the
osmotic pressure of 0.74 atm at \( 27^{\circ} C \)
Assuming solution to be diluted, which
are correct?
1. Percentage of urea in the mixture is
17.6
2. Relative lowering of the vapour
pressure of this solution is \( 5.41 \times 10^{-4} \)
3. The solution will boil at \( 100.015^{\circ} C \), if
\( K_{b} \) of water is \( 0.5 \mathrm{K} \) molality \( ^{-1} \)
4. If glucose is replaced by the same amount of sucrose, the solution will
show higher osmotic pressure at \( 27^{\circ} C \)
5. If glucose is replaced by the same amount of \( N a C l \), the solution will show
lower osmotic pressure at \( 27^{\circ} \mathrm{C} \)
A. 1,2,3
в. 1,2,3,5
c. 2,4,5
D. 1,4,5
Subject: Physics
A car acquires a velocity of \( 72 \mathrm{kmh}^{-1} \) in 10 s starting from rest. Calculate the
acceleration.
A. \( 7.2 m s^{-2} \)
B. \( 20 m s^{-2} \)
c. \( 200 m s^{-2} \)
D. \( 2 m s^{-2} \)
Subject: Maths
A circus artist is climbing a \( 20 m \) long
rope, which is tightly stretched and tied from the top of a vertical pole of the
ground. Find the height of the pole if the angle made by the rope with the ground
level is \( 30^{\circ} \)
A . \( 12 \mathrm{m} \)
B. 10
\( c \cdot 8 m \)
\( D \cdot 6 m \)
Subject: Chemistry
\( \boldsymbol{C C l}_{4} \rightleftharpoons \boldsymbol{C}+\mathbf{2 C l}_{2} \)
The equilibrium constant \( p K \) for the given reaction at \( 700^{0} C \) is 0.76 atm.
The initial pressure of carbon tetrachloride that will produce a total equilibrium pressure of 1.20 atm at
\( \mathbf{7} \mathbf{0 0}^{\mathbf{o}} \mathbf{C} \) is:
A. 0.22 atm
B. 0.44 atm
c. 0.84 atm
D. 0.11 atm
Subject: Physics
The magnifying power of a telescope is
9. When it is adjusted for parallel rays, the distance between the objective and the eye piece is found to be 20 cm. The
focal length of lenses are
\( \begin{array}{lll}\text { A. } 18 & \text { cm, } 2 & \text { cm }\end{array} \)
\( \begin{array}{lll}\text { В. } 11 & c m, 9 & c m\end{array} \)
\( \begin{array}{lll}\text { c. } 10 & c m, 10 & c m\end{array} \)
D. \( 15 \quad \) cm \( , 5 \) cm
Subject: Biology
Identify the correct sequence of
taxonomic hierarchical arrangement in
ascending order.
A. Spermatophyta, Sapindales, Dicotyledons, Anacardiaceae, Mangifera
B. Mangifera, Dicotyledons, Anacardiaceae, Spermatophyta, Sapindales
C. Mangifera, Anacardiaceae, Sapindales, Dicotyledons, Spermatophyta
D. Dicotyledons, Anacardiaceae, Sapindales, Spermatophyta, Mangifera
Subject: Maths
Find the slope and \( y \) -intercept of the
line \( 2 x+5 y=1 \)
A \( \cdot \) slope \( =-\frac{2}{5}, y \) -intercept \( =\frac{1}{5} \)
B. slope \( =-\frac{1}{5}, y \) -intercept \( =\frac{1}{5} \)
c. slope \( =-\frac{2}{3}, y \) -intercept \( =\frac{1}{5} \)
D. slope \( =-\frac{2}{5}, y \) -intercept \( =\frac{2}{5} \)