AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
An \( A C \) rms voltage of \( 2 V \) having a frequency of \( 50 \mathrm{KHz} \) is applied to a
condenser of the capacity of \( 10 \mu F . \) The maximum value of the magnetic field between the plates of the condenser if
the radius of a plate is \( 10 \mathrm{cm} \) is
Subject: Physics
A steel wire of length \( 7 m \) and cross
section 1 mm\( ^{2} \) is hung from a rigid
support with a steel weight of volume 1000 \( c c \) hanging from the other end. Find the decreases in the length of wire, when steel weight is completely immersed in water
\( \left(\boldsymbol{Y}_{\text {steel}}=\mathbf{2} \times \mathbf{1 0}^{\mathbf{1 1}} \mathbf{N} / \boldsymbol{m}^{2}\right) \)
Density of water \( =\mathbf{1} \boldsymbol{g} / \boldsymbol{c} . \boldsymbol{c} \)
Subject: Maths
The domain of the function \( f(x)= \) \( \sqrt{\sec ^{-1}\left\{\frac{1-|x|}{2}\right\}} \)
A \( \cdot(-\infty,-3] \cup[3,+\infty) \)
B. \( [3,+\infty) \)
\( c . \Phi \)
D. \( R \)
Subject: Physics
A parallel plate condenser with plate separation d is charged with the help of
battery so that \( V_{0} \) energy is stored in
the system. The battery is now removed. a plate of dielectric constant k and thickness d is placed between the plates of condenser. The new energy of
the system will be :
A. \( V_{0} k^{-2} \)
B. \( k^{2} V_{0} \)
c. \( V_{0} k^{-1} \)
D. \( k V_{0} \)
Subject: Physics
Two bodies \( A \) and \( B \), moving in the same direction collide and after collision,
move with the common velocity in the direction of \( \mathbf{A} \)
A. The magnitude of force exerted by A on B is greater than the magnitude of force exerted by B on \( A \)
B. Both exertequal but opposite force on each other
c. The change in momentum of A and B are equal but opposite in direction
D. Both (B) and (C)
Subject: Chemistry
Elements after atomic number 103
have not been discovered till now. If an
element with atomic number 106 were
ever discovered which of the following electronic configuration will it possess.
\( \mathbf{A} \cdot[R n] 5 f^{14} 6 d^{4} 7 s^{1} \)
B \( \cdot[R n] 5 f^{14} 6 d^{5} 7 s^{1} \)
\( \mathbf{c} \cdot[R n] 5 f^{14} 6 d^{6} 7 s^{0} \)
D \cdot \( [R n] 5 f^{14} 6 d^{1} 7 s^{2} 7 p^{3} \)
Subject: Physics
When two tuning forks \( A \) and \( B \) are
sounded together, 4 beats per second
are heard. The frequency of the fork \( B \) is
\( 384 H z . \) When one of the prongs of the
fork \( A \) is filed and sounded with \( B \), then
beat frequency increases, then
frequency of the fork \( \boldsymbol{A} \) is
A. \( 380 H z \)
в. 388 Нг
c. 379 Н \( z \)
D. \( 389 ~ H z \)
Subject: Biology
Study the following lists:
List-I
(A) Anucleate
(1) Spirogyra gamciangium
(B) Uninucleate
(2) Rhizopus chlamydospore
(C) Multinucleate
(3) Pteris
neck canal cell
(D) Binucleate
(4) Vitis
matured sieve element
(5) Akinite of
Spirogyra
\( A \cdot A-(1 V), B-(1), C-(11), D-(1) \)
B. A-(I), B-(III), C-(II),D-(IV)
\( c \cdot A-(1 V), B-(1), C-(11), D-(11) \)
D. A-(1), B-(IV), C-(V), D-(II)
Subject: Physics
Radiations of intensity \( 0.5 \mathrm{W} / \mathrm{m} 2 \) are striking a metal plate. The pressure on the plate is
A \( \cdot 0.166 \times 10^{-8} N / m 2 \)
В. \( 0.332 \times 10-8 N / m^{2} \)
c. \( 0.111 \times 10-8 N / m^{2} \)
D. \( 0.083 \times 10-8 N / m^{2} \)
Subject: Biology
Assertion
Enzymes becomes inactive below
minimum temperature.
Reason
The inactivity of the enzyme is due to
denaturation.
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
In the formula \( X=3 Y Z^{2}, X \) and \( Z \) have
dimensions of capacitance and magnetic induction respectively. The dimensions of Y in MKSQ system are
A. -2 in mass, -2 in length, 4 in time and 5 in charge.
B. - 3 in mass, - 2 in length, 4 in time and 4 in charge.
c. -4 in mass, -5 in length, 4 in time and 4 in charge.
D. -3 in mass, -2 in length, 8 in time and 7 in charge.
Subject: Maths
The equation of an altitude of an equilateral triangle is \( \sqrt{\mathbf{3}} x+y=2 \sqrt{3} \)
and one of the vertices is \( (3, \sqrt{3}), \) then the possible number of triangles are,
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 3 \)
D. 4
Subject: Chemistry
Aryl halides are less reactive towards nucleophilic substitution reaction as
compared to alkyl halides due to:
This question has multiple correct options
A. the formation of less stable carbonium ion
B. resonance stabilisation
C . longer carbon-halogen bond
D. the inductive effect
\( \mathrm{E} \cdot s p^{2}- \) hybridised carbon attached to the halogen
Subject: Maths
An equation of the tangent to the circle \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}+\mathbf{4} \boldsymbol{x}-\mathbf{4} \boldsymbol{y}+\boldsymbol{4}=\mathbf{0} \) which
makes equal intercepts on the coordinate axes, is given by This question has multiple correct options
A \( . x+y=2 \sqrt{2} \)
В. \( x-y=2 \sqrt{2} \)
c. \( x+y+2 \sqrt{2}=0 \)
D. \( x-y+2 \sqrt{2}=0 \)
Subject: Physics
Find the ratio between the depths where the pressures are \( 3 \times 10^{5} N m^{-2} \) and
\( \mathbf{5} \times \mathbf{1 0}^{\mathbf{5}} \mathbf{N} \boldsymbol{m}^{-\mathbf{2}} \cdot\left(\boldsymbol{P}_{\boldsymbol{A}}=\mathbf{1 0}^{\mathbf{5}} \boldsymbol{N} \boldsymbol{m}^{-\mathbf{2}}\right) \)
Subject: Maths
Let ABCD be a parallelogram. Let AP, CQ be the \( \perp \) from \( A \) and \( C \) on its diagonal
BD. Which of the following is true. This question has multiple correct options
A. \( C Q=P D \)
в. \( P D=Q B \)
c \( . A P=C Q \)
D. \( A P=B Q \)
Subject: Physics
A charge of \( 1 \mu C \) is given to one plate of
a capacitors and a charge of \( 2 \mu \mathrm{C} \) is
given to the other plate of a \( 0.1 \mu \mathrm{F} \) capacitor. Find the potential difference across the two plates of the capacitor:
\( \mathbf{A} \cdot 5 V \)
в. \( 10 V \)
\( \mathrm{c} \cdot 15 \mathrm{V} \)
D. 30 \( V \)
Subject: Maths
Let \( f(x)=x^{3}-12 x \) be function
such that the equation \( |\boldsymbol{f}(|\boldsymbol{x}|)|= \) \( \boldsymbol{n}(\boldsymbol{n} \in \boldsymbol{N}) \) has exactly \( \boldsymbol{6} \) distinct real
roots then number of possible values of
\( \boldsymbol{n} \) are :
A . 15
B . 16
c. 17
D. 14
Subject: Maths
If \( a+b+2 c=0, \) then the value of \( a^{3}+ \)
\( b^{3}+8 c^{3} \) is equal to
A . \( 3 a b c \)
B. \( 4 a b c \)
\( c \cdot a b c \)
D. \( 6 a b c \)
Subject: Physics
Two identical cycle wheels (geometrically) have different number of spokes connected from center to rim.
One is having 20 spokes and the other
having only 10 (the rim and the spokes are resistanceless). One resistance of
value \( R \) is connected between center
and rim. The current in \( \boldsymbol{R} \) will be
A. double in the first wheel than in the second wheel
B. four times in the first wheel than in the second wheel
c. will be double in the second wheel than that of the first whee
D. will be equal in both these wheels
E . answer required
Subject: Physics
A body starts from rest and with a
uniform acceleration of \( 10 m s^{-2} \) for 5
seconds. During the next 10 seconds it moves with uniform velocity. The total distance travelled by the body is :-
\( \mathbf{A} \cdot 100 m \)
B. \( 125 \mathrm{m} \)
c. \( 500 m \)
D. \( 625 \mathrm{m} \)
Subject: Physics
Two blocks are resting on ground with masses \( 5 k g \) and \( 7 k g . \) A string
connected them which goes over a massless pulley A. There is no friction between pulley an d string A. force \( \boldsymbol{F}= \)
\( 124 N \) is applied on pulley A.Find
acceleration of centre of mass of the
system of two masses \( \left(\operatorname{in} m / s^{2}\right) \)
Subject: Physics
The band gaps of an insulator, conductor and semi conductor are
respectively \( \boldsymbol{E}_{\boldsymbol{g} 1}, \boldsymbol{E}_{\boldsymbol{g} \mathbf{2}} \) and \( \boldsymbol{E}_{\boldsymbol{g} \mathbf{3}} . \) The
relationship between them is given as
A \( . E_{g 1}>E_{g 2}<E_{g 3} \)
В. \( E_{g 1}>E_{g 2}>E_{g 3} \)
C \( . E_{g 1}<E_{g 2}>E_{g 3} \)
D. \( E_{g 1}<E_{g 2}<E_{g 3} \)
Subject: Physics
Fill in the blanks to complete the
following sentences:
i) A ray travelling towards the mirror is
the
ii) Angle between reflected ray and normal is the
iii) The angle between reflecting
surface and the reflected ray is the
A. i-incident ray, ii-angle of reflection, iii-glancing angle of reflection
B. i-normal ray, ii-glancing angle of reflection, liii-angle of incidence
C. i-reflected ray, ,ii glancing angle of incidence , iiiglancing angle of reflection
D. i-reflected ray, ,ii-angle of incidence, iii- angle of reflection
Subject: Chemistry
Hydrochloric acid solution \( A \) and \( B \) have a concentration of \( 0.5 N \) and \( 0.1 N \)
respectively. The volume of solutions \( \boldsymbol{A} \)
and \( B \) required to make 2 litres of
\( \mathbf{0 . 2} \mathbf{N} \mathbf{H} \mathbf{C l} \) are:
A. 0.5 Lof \( A+1.5 \) Lof \( B \)
B. 1.5 Lof \( A+0.5 \) Lof \( B \)
c. 1.0 Lof \( A+1.0 \) Lof \( B \)
D. 0.75 Lof \( A+1.25 \) Lof \( B \)
Subject: Chemistry
Assertion
Rectified spirit can be further purified by adding a dehydrating agent.
Reason
Addition of \( H_{2} S O_{4} \) to \( 96 \% \) ethyl alcohol
gives \( 100 \% \) ethyl alcohol
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
A buffer solution with \( p H=9 \) is to be
prepared by mixing \( N H_{4} C I \) and
\( N H_{4} O H . \) Calculate the number of
moles of \( N H_{4} C I \) that should be added
to one litre pf \( 1.0 M N H_{4} O H .\left[K_{b}=\right. \)
\( \left.1.8 \times 10^{-5}\right] \)
A . 3.4
B . 2.
c. 1.5
D. 1.8
Subject: Chemistry
The value of \( K_{c}=4.24 \) at \( 800 \mathrm{K} \) for the
reaction
\( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \)
Calculate equilibrium concentrations of
\( C O_{2}, H_{2}, C O \) and \( H_{2} O \) at \( 800 \mathrm{K}, \) if any
\( C O \) and \( H_{2} O \) are present initially at
concentration of \( 0.10 \mathrm{M} \) each?
Subject: Chemistry
Assertion
The bond angle of \( P B r_{3} \) is greater than
\( P H_{3} \) but the bond angle of \( N B r_{3} \) is
lesser than \( \boldsymbol{N} \boldsymbol{H}_{3} \)
Reason
Electronegativity of \( P \) -atom is less than
that of \( N \) -atom.
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: Biology
Match the entries in column I with those
in column II and choose the correct
combination from the options given.
Column I
1. Cerebrum and basal
a. Diencephalon \( \quad \) ganglia
b. Telencephalon
2. Medulla
3. Cerebellum and pons Myelencephalon
d. Metencephalon
4. Thalamus
A. \( a-4, b-3, c-1, d-2 \)
B. \( a-3, b-4, c-1, d-2 \)
c. \( a-4, b-3, c-2, d-1 \)
D. \( a-1, b-2, c-3, d-4 \)
E \( . a-4, b-1, c-2, d-3 \)
Subject: Physics
A particle is projected at an angle \( \theta \)
from ground with speed \( u\left(g=10 m / s^{2}\right) \)
then which of the following is true? This question has multiple correct options
A \( \cdot \) If \( u=10 m / s \) and \( \theta=30^{\circ}, \) then time of flight will be 1
\( \sec \)
B . If \( u=10 \sqrt{3} m / s \) and \( \theta=60^{\circ} \), then time of flight will be \( 3 \sec \)
C . If \( u=10 \sqrt{3} m / s \) and \( \theta=60^{\circ} \), then after 2 sec velocity
becomes perpendicular to initial velocity
D. If \( u=10 m / s \) and \( \theta=30^{\circ} \), then velocity never becomes
perpendicular to intial velocity during its flight
Subject: Physics
An ideal gas is enclosed in a cylinder with a movable piston on top of it. The
piston has a mass of \( 8000 g \) and an
area of \( 5.00 \mathrm{cm}^{2} \) and is free to slide up
and down, keeping the pressure of the gas constant. How much work in
Joules is done on the gas as the
temperature of 0.200 mol of the gas is
raised from \( 20.0^{\circ} \mathrm{C} \) to \( 300^{\circ} \mathrm{C} ? \)
Subject: Chemistry
Which of the following reaction(s) gives a gem-dichloride?
This question has multiple correct options
A. \( C H_{3} C H O \) and \( P C l_{5} \)
в. \( C H_{3} C O C H_{3} \) and \( P C l_{5} \)
c. \( C H_{2}=C H_{2} \) and \( C l_{2} \)
D. \( C H_{2}=C H C l \) and \( H C l \)
Subject: Chemistry
\( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{b}} \) for \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{O} \boldsymbol{H} \) at certain
temperature is 4.74 The pH of basic buffer containing equimolar
concentration of \( N H_{4} O H \) and \( N H_{C} I \)
will be:
Subject: Chemistry
For the reaction at \( 25^{\circ} C, X_{2} O_{4(l)} \longrightarrow \)
\( \mathbf{2} \boldsymbol{X} \boldsymbol{O}_{\mathbf{2}(\boldsymbol{g})} \)
\( \Delta H=2.1 k c a l \) and \( \Delta S=20 c a l \quad K^{-1} \)
The reaction would be:
A. spontaneous
B. non-spontaneous
c. at equilibrium
D. unpredictable
Subject: Physics
projected with a velocity \( v_{0} \) towards a
circular region having a uniform
magnetic field \( B \) perpendicular and
into the plane of paper from point \( \boldsymbol{P} \) as
shown in the figure. \( \boldsymbol{R} \) is the radius and
O is the center of the circular region. If
the line \( O P \) makes an angle \( \theta \) with the
direction of \( v_{0} \) then the value of \( v_{0} \) so
that particle passes through \( \boldsymbol{O} \) is
A \( \cdot \frac{q B R}{m \sin \theta} \)
B. \( \frac{q B R}{2 m \sin \theta} \)
c. \( \frac{2 q B R}{m \sin \theta} \)
D. \( \frac{3 q B R}{2 m \sin \theta} \)
Subject: Maths
If positive numbers \( x, y, z \) are in \( A . P \) then the minimum value of \( \frac{\boldsymbol{x}+\boldsymbol{y}}{\mathbf{2} \boldsymbol{y}-\boldsymbol{x}}+ \)
\( \frac{y+z}{2 y-z} \) is equal to
Subject: Physics
Two identical flutes produce fundamental notes of frequency \( 300 H z \)
at \( 27^{\circ} \mathrm{C} \). If the temperature in the air in
one of the flutes is increased to \( 31^{\circ} C \)
the number of beats heard per second will be:
A . 3
B. 2
\( c \cdot 1 \)
D.
Subject: Maths
\( \left|\begin{array}{ccc}\boldsymbol{x}^{2}+\boldsymbol{x} & \boldsymbol{3} \boldsymbol{x}-\boldsymbol{1} & -\boldsymbol{x}+\boldsymbol{3} \\ \boldsymbol{2} \boldsymbol{x}+\mathbf{1} & \boldsymbol{2}+\boldsymbol{x}^{2} & \boldsymbol{x}^{3}-\boldsymbol{3} \\ \boldsymbol{x}-\boldsymbol{3} & \boldsymbol{x}^{2}+\boldsymbol{4} & \boldsymbol{3} \boldsymbol{x}\end{array}\right|=\boldsymbol{a}_{0}+ \)
\( a_{1} x+a_{2} x^{2}+\ldots+a_{7} x^{7}, \) then the value
of \( a_{0} \) is
A . 25
B . 24
\( c \cdot 23 \)
D. None of the above
Subject: Chemistry
The solubility of \( N a C l \) in water is \( 38 g \)
in \( 100 m L \) at \( 50^{\circ} C \)
I. If \( 50 g \) of salt is added to water, a
dynamic equilibrium will be reached. II. A dissociation equilibrium will
result in \( 50 \% \) of the solute being in the aqueous state and \( 50 \% \) being in the
solid state.
A. Statement \( I \) is true, Statement \( I I \) is true
B. Statement I is true, Statement II is false
c. statement \( I \) is false, statement \( I I \) is true
D. Statement I is false, Statement II is false
Subject: Physics
Two protons are kept at a separation of
\( 40 A^{o} . F_{n} \) is the nuclear force and \( F_{e} \) is
the electrostatic force between them.
Then
A. \( F_{n} \gg F_{e} \)
в. \( F_{n}=F_{e} \)
\( \mathrm{c} \cdot F_{n} \ll F_{e} \)
D. \( F_{n} \approx F_{e} \)
Subject: Maths
The locus of the centre of the circles
which touch both the circles \( x^{2}+y^{2}= \)
\( a^{2} \) and \( x^{2}+y^{2}=4 a x \) externally has the
equation:
A \( \cdot 12(x-a)^{2}-4 y^{2}=3 a^{2} \)
B \( \cdot 9(x-a)^{2}-5 y^{2}=2 a^{2} \)
C \( \cdot 8 x^{2}-3(y-a)^{2}=9 a^{2} \)
D. None of these
Subject: Physics
un
connected in the circuit as shown in fig.
Initially capacitor A has no charge and
capacitor \( \mathrm{B} \) has \( \mathrm{CV} \) charge. Assume that
the circuit has no resistance at all. At
\( t=0, \) switch \( S \) is closed, then \( [ \) given \( \boldsymbol{L} \boldsymbol{C}=\frac{\boldsymbol{2}}{\boldsymbol{\pi}^{2} \times \mathbf{1 0}^{4}} \boldsymbol{s}^{2} \) and \( \boldsymbol{C V}=\mathbf{1 0 0 m C} \)
This question has multiple correct options
A. when current in the circuit is maximum, charge on each capacitor is same
B. when current in the circuit is maximum, charge on capacitor A is twice the charge on capacitor
C \( . q=50(1+\cos 100 \pi t) m C, \) where \( q \) is the charge on
capacitor B at time t
D. \( q=50(1-\cos 100 \pi t) m C \), where q is the charge on
capacitor B at time t
Subject: Maths
The variance of the random variable \( x \)
whose probability distribution is given by
\( \boldsymbol{X}=\boldsymbol{x}_{i}: \quad-1 \quad, \boldsymbol{0}, \quad+1 \)
\( \boldsymbol{p}\left(\boldsymbol{X}=\boldsymbol{x}_{i}\right): \mathbf{0 . 4}, \mathbf{0 . 2}, \quad \mathbf{0 . 4} \) is
A . 0.4
B. 0.6
\( c .0 .8 \)
D. 1.0
Subject: Physics
A \( 40 \mathrm{cm} \) long wire having a mass \( 3.2 \mathrm{gm} \)
and area of c.s \( 1 \mathrm{mm}^{2} \) is stretched
between the support \( 40.05 \mathrm{cm} \) apart. In its fundamental mode. It vibrate with a
frequency \( 1000 / 64 H z . \) Find the young's
modulus of the wire.
A \( \cdot 1 \times 10^{9} \mathrm{Nm}^{2} \)
B . \( 2 \times 10^{9} \mathrm{Nm}^{2} \)
c. \( 1 \times 10^{8} \mathrm{Nm}^{2} \)
D. \( 4 \times 10^{9} \mathrm{Nm}^{2} \)
Subject: Chemistry
Use the given standard enthalpies of formation to determine the heat of
reaction of the following reaction:
\[
\begin{array}{c}
2 L i O H+C O_{2}(g) \longrightarrow \\
L i_{2} C O_{3}(s)+H_{2} O(l) \\
\Delta H_{f} L i O H(s)=-487.23 k J / \text {mole} \\
\Delta H_{f} L i_{2} C O_{3}(s)=-1215.6 k J / \text {mole} \\
\Delta H_{f} H_{2} O(l)=-285.85 k J / \text {mole} \\
\Delta H_{f} C O_{2}(g)=-393.5 k J / \text {mole}
\end{array}
\]
A . \( +303 . \)
в. -133.5
c. -198.6
D. +198.6
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=(\boldsymbol{x}-\boldsymbol{p})^{2}+(\boldsymbol{x}-\boldsymbol{q})^{2}+(\boldsymbol{x}- \)
\( \boldsymbol{r})^{2} . \) Then \( \boldsymbol{f}(\boldsymbol{x}) \) has a minimum at \( \boldsymbol{x}=\boldsymbol{\lambda} \)
where \( \lambda \) is equal to
A. \( \frac{p+q+r}{3} \)
B. \( \sqrt[3]{p q r} \)
c. \( \frac{3}{\frac{1}{p}+\frac{1}{q}+\frac{1}{r}} \)
D. none of these
Subject: Physics
Assertion
A capacitor blocks direct current in the
steady state.
Reason
The capacitive reactance of the capacitor is inversely proportional to
frequency f of the source of e.m.f...
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
Assertion
A particle is projected upwards with
speed \( v \) and it goes to a height \( h . \) If we double the speed then it will move to height \( 4 h \)
Reason
In case of earth, acceleration due to gravity \( g \) varies as \( g \propto \frac{1}{r^{2}} r \geq R \)
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 reagent(s) required for the following
conversion is:
A \( \cdot\left(\text { i) } N a B H_{4} \text { (ii) Raney } N i / H_{2} \text { (iii) } H_{3} O^{+}\right. \)
B \( \cdot\left(\text { i) } B_{2} H_{6} \text { (ii) } \operatorname{SnCl}_{2} / H C l \text { (iii) } H_{3} O^{+}\right. \)
C . (i) \( \operatorname{LiAlH}_{4} \) (ii) \( H_{3} O^{+} \)
\( \mathbf{D} \cdot(\mathbf{i}) B_{2} H_{6} \)
(ii) DIBAL-H (iii) \( H_{3} O^{+} \)
Subject: Chemistry
The hydrolysis constant Kh of a salt of NaOH anda weak acid (HX) if the Ka of
the acid is \( 2 \times 10^{-6} \) is:
A \( .5 \times 10^{-8} \)
B . \( 5 \times 10^{-6} \)
c. \( 5 \times 10^{-9} \)
D. \( 5 \times 10^{-7} \)
Subject: Maths
fthe matrix \( A \) is such that \( \left[\begin{array}{ll}1 & 3 \\ 0 & 1\end{array}\right] A= \) \( \left[\begin{array}{cc}\mathbf{1} & \mathbf{1} \\ \mathbf{0} & -\mathbf{1}\end{array}\right], \) then what is equal to \( \mathbf{A} ? \)
A. \( \left[\begin{array}{cc}1 & 4 \\ 0 & -1\end{array}\right] \)
в. \( \left[\begin{array}{ll}1 & 4 \\ 0 & 1\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{cc}-1 & 4 \\ 0 & -1\end{array}\right] \)
D. \( \left[\begin{array}{cc}1 & -4 \\ 0 & -1\end{array}\right] \)
Subject: Maths
If \( \operatorname{cosec} x-c o t x=\frac{1}{3}, \) where \( x \neq 0 \)
then the value of \( \cos ^{2} x-\sin ^{2} x \) is
A \( \cdot \frac{16}{25} \)
в. \( \frac{9}{25} \)
\( c \cdot \frac{8}{25} \)
D. \( \frac{7}{25} \)
Subject: Biology
Match the following books in column \( \mathbf{A} \)
with their authors in column B.
Column A

Column B
(A) Genera Plantarum
(1) Aristotle (3 volumes)
(B) Species Plantarum
(2) Linnaeus
(C) Historia Generalis
(3) Bentham and Plantarum Hooker
(D) Scala Naturae
(4) Plato
(5) John Ray
\( A \cdot A-4, B-2, C-5, D-3 \)
B. A- 4, B- 2, C-1, D-3
c. \( A-4, B-2, C-3, D-1 \)
D. \( A-3, B-2, C-5, D-1 \)
Subject: Chemistry
Which of the following is correct for acid buffer?
\( [\text { salt }=H A, \text { acid }=A] \)
A \( \cdot p^{K a}=p^{H}-\log \frac{[H A]}{|A|} \)
B・ \( p^{H}=p^{K a}+\log \frac{[H A]}{|A|} \)
c. \( p^{K a}=p^{H}-\log \frac{[A]}{[H A]} \)
D・ \( p^{H}=p^{K a}+\log \frac{[A]}{[H A]} \)
Subject: Maths
If \( P\left(E_{k}\right) \propto k \) for \( 0 \leq k \leq n, \) the \( P(A) \)
equals
A. \( 3 n /(4 n+1) \)
B. \( (2 n+1) / 3 n \)
c. \( 1 /(n+1) \)
D. \( 1 / n^{2} \)
Subject: Chemistry
Nodal planes of \( \pi \) -bonds \( (\mathrm{s}) \) in \( \boldsymbol{C} \boldsymbol{H}_{2}= \)
\( C=C=C H_{2} \) are located in:
A. all are in molecular plane
B. perpendicular plane which contains \( C-C \sigma \) -bond
c. one in molecular plane and two in a plane perpendicular to molecular plane which contains \( C \) \( C \sigma \) -bonds
D. two in molecular plane and one in a plane perpendicular to molecular plane which bisects \( C-C \) \( \sigma \) -bonds at right angle
Subject: Physics
A current of \( 4 A \) flows through 5 turn coil
of a tangent galvanometer having a diameter of \( 30 \mathrm{cm} . \) If the horizontal
component of Earth's magnetic induction is \( 4 \times 10^{-5} T \), find the
deflection produced in the coil. \( \left[\text { Given } \mu_{0}=4 \pi \times 10^{-7} H m^{-1}\right] \)
Subject: Chemistry
Which of the following is(are) example(s) of Sandmeyer reaction? This question has multiple correct options
A \( \cdot C_{6} H_{5} N_{2}^{+} C l^{-} \rightarrow C_{6} H_{5} C l \)
в. \( C_{6} H_{5} N_{2}^{+} C l^{-} \rightarrow C_{6} H_{5} O H \)
c. \( C_{6} H_{5} N_{2}^{+} C l^{-} \rightarrow C_{6} H_{5} C N \)
D. \( C_{6} H_{5} N_{2}^{+} I^{-} \rightarrow C_{6} H_{5} I \)
Subject: Physics
A potentiometer wire has a length \( 2 \mathrm{m} \) and resistance of \( 10 \Omega \). It is connected in
series with a Resistance of \( 990 \Omega \) and a
cell of e.m.f. 2V. The potential gradient along the wire is
A. \( 0.01 \mathrm{v} / \mathrm{m} \)
B. \( 0.02 \mathrm{V} / \mathrm{m} \)
c. \( 0.03 \mathrm{V} / \mathrm{m} \)
D. \( 0.025 \mathrm{V} / \mathrm{m} \)
Subject: Maths
Solve for \( \boldsymbol{x}: \boldsymbol{3} \boldsymbol{x}=\frac{\boldsymbol{2} \mathbf{0}}{\mathbf{7}}-\boldsymbol{x} \)
A \( \cdot \frac{2}{7} \)
B.
\( c \cdot \frac{4}{7} \)
D.