AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Ten charges having charge \( \mathbf{1} \mu C, 8 \mu C, 27 \mu C, \dots \dots 1000 \mu C \) are
placed on the \( x \) -axis with co-ordinates \( \boldsymbol{x}=\mathbf{1} \boldsymbol{m}, \mathbf{2} \boldsymbol{m}, \mathbf{3} \boldsymbol{m}, \mathbf{4} \boldsymbol{m}, \dots . . \mathbf{1 0} \boldsymbol{m} . \) The
net electric field intensity at the origin is:
A \( \cdot 9 \times 10^{5} N / C \)
в. \( 9 \times 10^{4} N / C \)
C \( .4 .95 \times 10^{-5} \mathrm{N} / \mathrm{C} \)
D. \( 4.95 \times 10^{5} N / C \)
Subject: Chemistry
\( H_{2} S \) is bubbled into a \( 0.2 \mathrm{M} \) NaCN solution which is, \( 0.02 \mathrm{M} \) each in
\( A g(C N)_{2}^{\ominus} \) and \( \left(C d(C N)_{4}\right)^{2-} . \) If \( K_{s p} \) of
\( A g_{2} S \) and \( C d S \) are \( 10^{-50} \) and \( 7.1 \times \)
\( 10^{-28} \) and \( K \) instability for \( \left[A g(C N)_{2}^{\ominus}\right] \)
and \( \left[\boldsymbol{C d}(\boldsymbol{C N})_{4}^{2-}\right] \) are \( 1.0 \times 10^{-20} \) and
\( \mathbf{7} .8 \times 10^{-18}, \) which sulphide will
precipitate first?
A. \( C d S \)
в. \( A g_{2} S \)
c. \( N a_{2} S \)
D. Either \( A g_{2} S \) or \( N a_{2} S \) depending on acidity of solution
Subject: Physics
A capacitor connected to a \( 10 V \) battery
collects a charge \( 40 \mu C \) with air as dielectric and \( 100 \mu \mathrm{C} \) with oil as
dielectric. The dielectric constant of oil
is
\( A \cdot 2 \)
в. 2.5
\( c \cdot 4 \)
D. 10
Subject: Physics
Electric field at point (30,30,0) due to a
point charge of \( 8 \times 10^{-3} \mu C \) placed at
origin will be (coordinates are in \( \mathrm{cm} \) )
A. \( 8000 N / C \)
в. \( 4000(\hat{i}+\hat{j}) N / C \)
c. \( 200 \sqrt{2}(\hat{i}+\hat{j}) N / C \)
D. \( 400 \sqrt{2}(\hat{i}+\hat{j}) N / C \)
Subject: Physics
A ball is thrown vertically upwards. It
has a speed of \( 10 \mathrm{m} s^{-1} \) when it has
reached one half of its maximum
height. How high does the ball rise?
(Take \( \left.g=10 \mathrm{m} s^{-2}\right) \)
A. \( 10 \mathrm{m} \)
B. \( 5 \mathrm{m} \)
\( c \cdot 15 m \)
D. 20 \( m \)
Subject: Chemistry
A sample of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) (density
\( 1.787 g c m^{-3} \) ) labelled as \( 86 \% \) by weight. What is the normality of acid?
A . 20
B. 13.6
c. 36.36
D. 15.68
Subject: Chemistry
During complete combustion of one
mole of butane, \( 2658 k J \) of heat is
released. The thermochemical reaction
for above change is:
\( \mathbf{A} \cdot 2 C_{4} H_{10}(g)+13 O_{2}(g) \rightarrow 8 C O_{2}(g)+10 H_{2} O(l) \Delta_{c} H= \)
\( -2658.0 k J \mathrm{mol}^{-1} \)
B.
\[
C_{4} H_{10}(g)+\frac{13}{2} O_{2}(g) \rightarrow 4 C O_{2}(g)+5 H_{2} O(g) \Delta_{c} H=
\]
\( -1329.0 k J \mathrm{mol}^{-1} \)
\( c \)
\[
C_{4} H_{10}(g)+\frac{13}{2} O_{2}(g) \rightarrow 4 C O_{2}(g)+5 H_{2} O(l) \Delta_{c} H=
\]
\( -2658.0 k J m o l^{-1} \)
D.
\[
C_{4} H_{10}(g)+\frac{13}{2} O_{2}(g) \rightarrow 4 C O_{2}(g)+5 H_{2} O(l) \Delta_{c} H=
\]
\( +2658.0 k J \mathrm{mol}^{-1} \)
Subject: Chemistry
The arrangement of following
compounds:
i. Bromomethane
ii. Bromoform
iii. Chloromethane
iv. Dibromomethane
In the increasing order of their boiling point is :
A . \( i i i<i<i v<i i \)
в. \( i v<i i i<i<i i \)
c. \( i i<i i i<i<i v \)
D. \( i<i i<i i i<i v \)
Subject: Maths
If \( \boldsymbol{I}=\int_{\boldsymbol{\pi} / \mathbf{6}}^{\boldsymbol{\pi} / \mathbf{3}} \frac{\boldsymbol{d} \boldsymbol{x}}{\mathbf{1}+\sqrt{\tan \boldsymbol{x}}} \) then \( \boldsymbol{I} \) equals
A \( \cdot \frac{\pi}{12} \)
в. \( \frac{\pi}{6} \)
\( c \cdot \frac{\pi}{4} \)
D. \( \frac{\pi}{3} \)
Subject: Physics
A charge \( q \) is located at the centre of a cube. The electric flux through any face is :
A \( \cdot \frac{\pi q}{6\left(4 \pi \varepsilon_{0}\right)} \)
в. \( \frac{q}{6\left(4 \pi \varepsilon_{0}\right)} \)
c. \( \frac{4 \pi q}{6\left(4 \pi \varepsilon_{0}\right)} \)
D. \( \frac{4 \pi q}{\frac{1}{6}\left(4 \pi \varepsilon_{0}\right)} \)
Subject: Physics
The figure shows the position -time \( \left(x^{-}\right. \)
t) graph of one-dimensional motion of a
body of mass 0.4 kg. The magnitude of
each impulse is :
\( \mathbf{t}(\mathrm{s}) \)
A . \( 0.4 \mathrm{Ns} \)
B. 0.8 Ns
c. 1.6 Ns
D. 0.2 Ns
Subject: Physics
Consider the following statements A and B given below and identify the
correct answer:
A) If \( \vec{A} \) is a vector, then the magnitude of the vector is given by \( \sqrt{\overrightarrow{\boldsymbol{A}} \times \overrightarrow{\boldsymbol{A}}} \)
B) If \( \vec{a}=m \vec{b} \) where 'm' is a scalar, the
value of 'm' is equal to \( \frac{\vec{a} \cdot \vec{b}}{b^{2}} \)
A. both \( A \& B \) are correct
B. A is correct but B is wrong
c. A is wrong but B is correct
D. both A and B are wrong
Subject: Physics
Determine the relationship between the
torque \( N \) and the torsion angle \( \varphi \) for the solid rod of circular cross-section. Their
length \( l, \) radius \( r, \) and shear modulus \( G \)
are supposed to be known.
\( ^{\mathbf{A}} \cdot_{N}=5 \frac{\pi r^{4} G \varphi}{3 l} \)
B. \( N=\frac{\pi r^{4} G \varphi}{2 l} \)
c. \( _{N}=3 \frac{\pi r^{4} G \varphi}{2 l} \)
D. None of these
Subject: Physics
A block of mass \( 1 \mathrm{kg} \) slides down a curved track which forms one quadrant of a circle of radius \( 1 \mathrm{m} \) as shown in
figure. The speed of the block at the
bottom of the track is \( v=2 m s^{-1} \). The
work done by the force of friction
is (Take \( \left.g=10 m s^{-2}\right) \)
\( A \cdot+4 J \)
B. - -4
\( c \cdot-8 \)
D. +83
Subject: Maths
Triangle \( A \) has a base of \( x \) and a height of \( 2 x . \) Triangle \( B \) is similar to triangle \( A \) and has a base of \( 2 x \). What is the ratio
of the area of triangle \( A \) to triangle \( B ? \)
A . 1: 2
B. 2:
\( c \cdot 2: 3 \)
D. 1: 4
Subject: Physics
8
cylinder to be negligible, find the time dependence of the kinetic energy of the
whole system.
\( ^{\mathbf{A}} \cdot_{T}=\frac{m g^{2} t^{2}}{2\left(1+\frac{2 M}{m}\right)} \)
\( ^{\mathbf{B}} \cdot_{T}=\frac{m g^{2} t^{2}}{2\left(1+\frac{M}{2 m}\right)} \)
\( ^{\mathbf{C}} T=\frac{m g^{2} t^{2}}{2\left(1+\frac{M}{m}\right)} \)
\( ^{\mathrm{D}} T=\frac{2 m g^{2} t^{2}}{2\left(1+\frac{M}{2 m}\right)} \)
Subject: Physics
Two open pipes of length \( 20 \mathrm{cm} \) and \( 20 . \) \( \mathrm{cm} \) produces 10 beats/s. The velocity of sound in the gas is
A. \( 804 \mathrm{m} / \mathrm{s} \)
B. 402 m/s
c. \( 420 \mathrm{m} / \mathrm{s} \)
D. 330 \( \mathrm{m} / \mathrm{s} \)
Subject: Maths
\( A B C \) is a triangle whose altitudes \( B E \)
and \( C F \) to sides \( A C \) and \( A B \)
respectively, are equal. Which of these conditions is not required to prove \( \triangle A B E \cong \triangle A C F ? \)
A \( . \angle B=\angle C \)
B. \( \angle B A E=\angle F A C \)
c. \( \angle A F C=\angle A E B \)
D. \( B E=C F \)
Subject: Maths
General value of \( \theta \) satisfying equation
\( \tan ^{2} \theta+\sec 2 \theta=1 \) is
A \( . n \pi \)
B . \( n \pi+\frac{\pi}{3} \)
\( \mathbf{c} \cdot n \pi-\frac{\pi}{3} \)
D. All of these
Subject: Physics
In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are \( 70 m s^{-1} \) and \( 63 m s^{-1} \)
respectively. What is the lift on the wing
if its area is \( 2.5 \mathrm{m}^{2} \) ? Take the density of
air to be \( 1.3 \mathrm{kgm}^{-3} \)
Subject: Physics
(a) Draw the circuit diagram for
studying the characteristics of a
transistor in common emitter
configuration. Explain briefly and show how input and output characteristics are drawn.
(b) The figure shows input waveform \( A \)
and \( \mathrm{B} \) to a logic. Draw the output
waveform for an OR gate. Write the truth
table for this logic gate and draw its logic symbol.
Subject: Physics
For a cell terminal potential difference is \( 2.2 \mathrm{V} \) when circuit is open and
reduces to \( 1.8 \mathrm{V} \) when cell is
connected to a resistance of \( \boldsymbol{R}=\mathbf{5} \Omega \)
then determine internal resistance of
cell is :-
A \( \cdot \frac{10}{9} \Omega \)
в. \( \frac{9}{10} \Omega \)
c. \( \frac{11}{9} \Omega \)
D. \( \frac{5}{9} \Omega \)
Subject: Physics
A famous relation in physics relates
'moving mass' \( \mathrm{m} \) to the 'rest mass' \( \boldsymbol{m}_{\mathbf{0}} \) of a particle in terms of its speed v and the speed of light, c. (This relation first arose asa consequence of special relativity due to Albert Einstein). A boy recalls the relation almost correctly but forgets where to put the constant c. He
writes:
\( \boldsymbol{m}=\frac{\boldsymbol{m}_{o}}{\left(\mathbf{1}-\boldsymbol{v}^{2}\right)^{1 / 2}} \)
Guess where to put the missing c.
Subject: Physics
\( F_{p p}, F_{n n} \) and \( F_{n p} \) are the nuclear forces
between proton-proton, neutron-neutron and neutron-proton respectively. Then relation between them is
\( \mathbf{A} \cdot F_{p p}=F_{n n} \neq F_{n p} \)
B . \( F_{p p} \neq F_{n n}=F_{n p} \)
\( \mathbf{c} \cdot F_{p p}=F_{n n}=F_{n p} \)
D \( \cdot F_{p p} \neq F_{n n} \neq F_{n p} \)
Subject: Physics
A particle executing SHM of amplitude \( 4 c m \) and \( T=4 s . \) The time taken by it to
move from positive extreme position to half the amplitude is
A . \( 1 s \)
B. \( \frac{1}{3} s \)
c. \( \frac{2}{3} \)
D. \( \sqrt{\frac{3}{2}} s \)
Subject: Maths
Form the differential equation of all family of lines \( \boldsymbol{y}=\boldsymbol{m} \boldsymbol{x}+\frac{\boldsymbol{4}}{\boldsymbol{m}} \) by
eliminating the arbitrary constant ' \( m^{\prime} \)
is
A \( \cdot \frac{d^{2} y}{d x^{2}}=0 \)
в. \( \quad x\left(\frac{d y}{d x}\right)^{2}-y \frac{d y}{d x}+4=0 \)
\( ^{\mathrm{c}} x\left(\frac{d y}{d x}\right)^{2}+y \frac{d y}{d x}+4=0 \)
D. \( \frac{d y}{d x}=0 \)
Subject: Physics
A given length of wire can be bent to form a circle or a square of single turn and a current may be established in it. The ratio of magnetic field at the centre of circle to that at the centre of square is :
A \( \cdot \frac{\pi^{2}}{8 \sqrt{2}} \)
B. \( \frac{4 \sqrt{2}}{\pi^{2}} \)
c. \( \frac{\pi}{2 \sqrt{2}} \)
D.
Subject: Physics
\( A B \) and \( C D \) are smooth, parallel, horizontal rails on which a conductor \( T \)
can slide. A cell, E, drives current
through the rails and \( T \)

This question has multiple correct options
A. The current in the rails will set up a magnetic field ove
B. T will experience a force to the right
C. \( T \) will experience a force to the left
D. Twill not experience any force
Subject: Maths
If the equations \( (\boldsymbol{b}+\boldsymbol{c}) \boldsymbol{x}+(\boldsymbol{c}+\boldsymbol{a}) \boldsymbol{y}+(\boldsymbol{a}+\boldsymbol{b})= \)
\( \mathbf{0}, \boldsymbol{c} \boldsymbol{x}+\boldsymbol{a} \boldsymbol{y}+\boldsymbol{b}=\mathbf{0} \) and \( \boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{y}+\boldsymbol{c}=\mathbf{0} \)
are consistent, then show that either
\( \boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c}=\boldsymbol{0} \) or \( \boldsymbol{a}=\boldsymbol{b}=\boldsymbol{c} \)
Subject: Physics
How does the electric field(E) between
the plates of a charged cylindrical capacitor vary with the distance r from the axis of the cylinder?
A \( \cdot E \propto \frac{1}{r^{2}} \)
в. \( \quad E \propto \frac{1}{r} \)
c. \( E \propto r^{2} \)
D. \( E \propto r \)
Subject: Chemistry
Carbon and \( C O \) gas are used to reduce
which of the following pairs of metal oxides for extraction of metals?
A. \( F e O, S n O \)
в. \( \operatorname{Sn} O, Z n O \)
с. Ва а,\( _{N a_{2}} \)О\( _{2} \)
D. \( F e O, Z n O \)
Subject: Maths
Two vertices of a rectangle are on the
positive \( \mathbf{x} \) -axis. The other two vertices lie on the lines \( y=4 x \) and \( y=-5 x+6 \)
Then the maximum area of the
rectangle is?
\( A \cdot \frac{2}{3} \)
B. \( \frac{2}{4} \)
\( c \cdot \frac{1}{3} \)
D. \( \frac{4}{3} \)
Subject: Maths
\( \int_{-\pi / 2}^{\pi / 2} \cos t \cdot \sin \left(2 t-\frac{\pi}{4}\right) d t= \)
A \( \frac{\sqrt{2}}{3} \)
B. \( -\frac{\sqrt{2}}{3} \)
\( c \cdot \frac{\sqrt{3}}{1} \)
D. \( \frac{1}{\sqrt{3}} \)
Subject: Chemistry
Heavy water \( \left(D_{2} O\right) \) freezes at:
\( \mathbf{A} \cdot 0^{\circ} C \)
в. \( -3.8^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 0.8^{\circ} \mathrm{C} \)
D. \( 3.82^{\circ} \mathrm{C} \)
Subject: Physics
How will the reading in the ammeter \( \mathbf{A} \)
of figure be affected if another identical
bulb \( Q \) is connected in parallel to \( P \) as
shown. The voltage in the mains is
maintained at a constant value
A. the reading will be reduced to one-half.
B. the reading will not be affected.
C. the reading will be double of the previous one
D. the reading will be increased fourfold.
Subject: Physics
The refractive index of the core of an
optical fibre is \( \mu_{2} \) and that of the
cladding is \( \mu_{1} . \) The angle of incidence on the face of the core so that the light ray just under goes total internal reflection at the cladding is:
A \( \cdot \sin ^{-1}\left(\frac{\mu_{1}}{\mu_{2}}\right) \)
B. \( \sin ^{-1} \sqrt{\mu_{2}^{2}-\mu_{1}^{2}} \)
c. \( \sin ^{-1} \sqrt{\mu_{2}-\mu_{1}} \)
D. \( \sin ^{-1} \sqrt{\mu_{1}^{2}+\mu_{2}^{2}} \)
Subject: Maths
Complex number \( z \) satisfy the equation
\( |z-(4 / z)|=2 . \) Locus of \( z \) if \( \left|z-z_{1}\right|= \)
\( \left|z-z_{2}\right|, \) where \( z_{1} \) and \( z_{2} \) are complex
numbers with the greatest and the least moduli, is
A. line parallel to the real axis
B. line parallel to the imaginary axis
c. line having a positive slope
D. line having a negative slope
Subject: Maths
The number of solutions of the equation \( 2 \sin ^{-1}(\sqrt{x^{2}-x+1})+ \)
\( \cos ^{-1}(\sqrt{x^{2}-x})=\frac{3 \pi}{2} \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. Infinite
\( c \cdot 2 \)
D.
Subject: Maths
Construct a frequency distribution
table for the data on weights \( (\text { in } k g \) ) of
20 students of a class using intervals \( 30-35,35-40 \) and so on
\( \mathbf{3 9}, \mathbf{3 8}, \mathbf{4 7}, \mathbf{4 4}, \mathbf{4 2}, \mathbf{6 5}, \mathbf{4 9}, \mathbf{5 5}, \mathbf{4 9}, \mathbf{3 6}, \mathbf{3 4}, \mathbf{4} \)
Also, draw histrogram for the above data
Subject: Maths
The equation of parabola whose latus rectum is 2 units, axis is \( x+y-2=0 \)
and tangent at the vertex is \( x-y+ \)
\( 4=0 \) is given by
A \( \cdot(x+y-2)^{2}=4 \sqrt{2}(x-y+4)^{2} \)
B . \( (x-y-4)^{2}=4 \sqrt{2}(x+y-2) \)
C. \( (x+y-2)^{2}=2 \sqrt{2}(x-y+4) \)
D. \( (x-y-4)^{2}=2 \sqrt{2}(x-y+2)^{2} \)
Subject: Physics
A circular loop of radius \( 3 \mathrm{cm} \) is having a current of 12.5 A. The magnitude of magnetic field at a distance of \( 4 \mathrm{cm} \) on its axis is
В \( \cdot 5.27 \times 10^{-5} T \)
\( \mathrm{c} \cdot 6.54 \times 10^{-5} T \)
D. \( 9.20 \times 10^{-5} T \)
Subject: Physics
A string of length 0.4 m and mass \( 10^{-2} k g \) is tightly clamped at its ends.
The tension in the string is \( 1.6 N \) Identical wave pulses are produced at one end at equal intervals of time \( \Delta t \)
The value of \( \Delta t \) which allows
constructive interference between
successive pulses is
A . \( 0.05 s \)
B. \( 0.10 s \)
c. \( 0.20 s \)
D. \( 0.40 s \)
Subject: Chemistry
Write IUPAC name of the following coordinate compounds:
(i) \( \boldsymbol{K}\left[\boldsymbol{A} \boldsymbol{g}(\boldsymbol{C} \boldsymbol{N})_{2}\right] \)
(ii) \( \boldsymbol{K}_{\mathbf{4}}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right] \)
(iii) \( \left[\boldsymbol{A} \boldsymbol{g}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}\right] \boldsymbol{C l} \)
\( (\text { iv })\left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right] \boldsymbol{C l}_{3} \)
Subject: Maths
Order and degree of \( \left(1+y_{1}^{2}\right) y_{3}= \)
\( \mathbf{3} \boldsymbol{y}_{2} \boldsymbol{y}_{1}^{2} \) are:
A . 2,3
B. 2,
\( c \cdot 3, \)
D. 3,2
Subject: Maths
In a town of 10000 families, it was found
that \( 40 \% \) families buy a newspaper \( A \) \( 20 \% \) families buy newspaper \( B \) and \( 10 \% \) families buy newspaper C. 5\% families buy both \( A \) and \( B, 3 \% \) buy \( B \) and \( C \) and 4\% buy A and C. If 2\% families buy all the three newspapers, then the number of families which buy A only.
A . 3300
в. 3500
\( c .3600 \)
D. 3700
Subject: Physics
Highlousuelto thaligic ul olut \( u \) lias
charges \( \boldsymbol{q},+2 \boldsymbol{q} \) and \( -\boldsymbol{q} \) arranged on its
vertices, as shown.What does the sign
of \( U \) signify?
A. The negative sign means that work was done on the agent who assembled these charges in moving them in from infinity.
B. The positive sign means that work was done on the agent who assembled these charges in moving them in from infinity
C. The negative sign means that work was done by the agent who assembled these charges in moving them in from infinity
D. The positive sign means that work was done by the agent who assembled these charges in moving them in from infinity
Subject: Physics
Two concentric shells carry charges \( q \)
and Q. Their radius are r and R. The potential difference between the two is :
A \( \cdot \frac{q}{4 \pi \varepsilon_{0} R^{2}}-\frac{Q}{4 \pi \varepsilon_{0} R} \)
в. \( \frac{Q-q}{4 \pi \varepsilon_{\Omega} R} \)
\( ^{\mathrm{c}} \cdot \frac{q}{4 \pi \varepsilon_{0}}\left[\frac{1}{r}-\frac{1}{R}\right] \)
D. \( \frac{(Q-q)}{4 \pi \varepsilon_{0}}\left[\frac{1}{r}-\frac{1}{R}\right] \)
Subject: Physics
An alpha particle of \( 5 \mathrm{MeV} \) at a large
distance proceeds towards a gold nucleus \( (Z=79) \) to make a head on
collision. The closest distance of
approach from the centre of gold nucleus
is:
A. \( 20 f m \)
B. 15 fm
c. \( 10 f m \)
D. 45 fm
Subject: Chemistry
Citric acid \( \left(\boldsymbol{H}_{3} \boldsymbol{A}\right) \) is a polyprotic acid
with \( K_{1}, K_{2}, \) and \( K_{3} \) equals to \( 7.4 \times \)
\( 10^{-4}, 1.7 \times 10^{-5}, \) and \( 4.0 \times 10^{-7} \)
respectively. Calculate the
\( \left[\boldsymbol{H}^{\oplus}\right],\left[\boldsymbol{H}_{2} \boldsymbol{A}^{\ominus}\right],\left[\boldsymbol{H} \boldsymbol{A}^{2-}\right], \) and \( \left[\boldsymbol{A}^{3-}\right] \) in
\( 0.01 M \) citric acid.
\( \mathbf{A} \cdot\left[H^{\oplus}\right]=\left[H_{2} A^{\ominus}\right]=2.4 \times 10^{-3} M,\left[H A^{2-}\right]=1.7 \times \)
\[
10^{-5},\left[A^{3-}\right]=2.8 \times 10^{-9}
\]
B . \( \left[H^{\oplus}\right]=\left[H_{2} A^{\ominus}\right]=2.4 \times 10^{-6} M,\left[H A^{2-}\right]=1.75 \times \)
\[
10^{-5},\left[A^{3-}\right]=2.8 \times 10^{-6}
\]
C \( \cdot\left[H^{\oplus}\right]=\left[H_{2} A^{\ominus}\right]=2.4 \times 10^{-5} M,\left[H A^{2-}\right]=1.75 \times \)
\[
10^{-5},\left[A^{3-}\right]=2.8 \times 10^{-8}
\]
D. \( \left[H^{\oplus}\right]=\left[H_{2} A^{\ominus}\right]=2.4 \times 10^{-7} M,\left[H A^{2-}\right]=1.75 \times \)
\[
10^{-5},\left[A^{3-}\right]=2.8 \times 10^{-6}
\]
Subject: Physics
A point moves along \( x \) axis. Its position
at time \( t \) is given by \( x^{2}=t^{2}+1 . \) Its
acceleration at time \( t \) is:
A \( \cdot 1 / x^{3} \)
B . \( 1 / x^{4} \)
c. \( -1 / x^{3} \)
D. \( 1 / x \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}, \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{2} \boldsymbol{x}^{2}+\mathbf{1} \) and \( \boldsymbol{h}(\boldsymbol{x})= \)
\( x+1 \) then \( (\text {hogof})(x) \) is equal to
A \( \cdot x^{2}+2 \)
B. \( 2 x^{2}+1 \)
c. \( x^{2}+1 \)
D. \( 2\left(x^{2}+1\right) \)
Subject: Physics
Transverse waves on a string have wave
speed \( 8.00 \mathrm{m} / \mathrm{s}, \) amplitude \( 0.0700 m \)
and wavelength 0.32 m. The waves
travel in the negative \( x \) -direction and
\( t=0 \) the \( x=0 \) end of the string has its
maximum upward displacement. Write a wave function describing the wave.
A \( \cdot y(x, t)=(0.07 m) \sin 2 \pi\left(\frac{x}{0.32 m}+\frac{t}{0.04 s}\right) \)
B. \( y(x, t)=(77 m) \cos 2 \pi\left(\frac{x}{0.32 m}+\frac{t}{0.04 s}\right) \)
c. \( y(x, t)=(0.7 m) \sin 4 \pi\left(\frac{x}{0.32 m}+\frac{t}{0.04 s}\right) \)
D \( y(x, t)=(0.97 m) \sin 2 \pi\left(\frac{x}{0.32 m}+\frac{t}{0.04 s}\right) \)
Subject: Physics
Assertion
Smaller the orbit of the planet around
the sun, shorter is the time it takes to
complete one revolution.
Reason
According to Kepler's third law of
planetary motion, square of the time period is proportional to the cube of the mean distance from the sun.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Physics
Two light waves are represented by
\( \boldsymbol{y}_{1}=\mathbf{4} \sin \omega \boldsymbol{t} \) and \( \boldsymbol{y}_{2}=\boldsymbol{3} \sin \left(\boldsymbol{\omega} \boldsymbol{t}+\frac{\pi}{2}\right) \)
The resultant amplitude due to interference will be
A \( .5 \mathrm{cm} \)
B. \( 7 \mathrm{cm} \)
c. \( 1 \mathrm{cm} \)
D.
Subject: Chemistry
A quantity of 15.8 g of \( K M n O_{4} \) can be decolourized in acidic medium by \( (\mathrm{K}= \)
\( 39, M n=55, F e=56 \)
This question has multiple correct options
A . \( 18.25 \mathrm{g} \) HCll
B . \( 22.5 g H_{2} C_{2} O_{4} \)
c. \( 32 g S O_{4} \)
\( \mathrm{D} \cdot 38 \mathrm{g} \mathrm{FeSO}_{4} \)
Subject: Maths
If \( \boldsymbol{y}=\boldsymbol{a} e^{4 x}+\boldsymbol{b} e^{5 x}, \) then prove \( \boldsymbol{y}_{2}- \)
\( \mathbf{9} \boldsymbol{y}_{1}+\mathbf{2 0} \boldsymbol{y}=\mathbf{0} \)
Subject: Physics
The focal length of the objective and eye lenses of a microscope are \( 1.6 \mathrm{cm} \) and \( 2.5 \mathrm{cm} \) respectively. The distance between the two lenses is \( 21.7 \mathrm{cm} \). If the
final image is formed at infinity, what is the linear magnification?
A . 11
B. 110
\( c \cdot 1 \)
D. 44
Subject: Maths
Triangles \( A B C \) and DEF are similar. If their areas are \( 64 \mathrm{cm}^{2} \) and \( 49 \mathrm{cm}^{2} \) and
if \( A B \) is \( 7 \mathrm{cm}, \) then find the value of DE.
\( A \cdot 8 \mathrm{cm} \)
в. \( \frac{49}{8} \mathrm{cm} \)
c. \( \frac{8}{49} \mathrm{cm} \)
D. \( \frac{64}{7} \mathrm{cm} \)
Subject: Physics
Calculate the capacitance (in farads) of
a charged, parallel-plate capacitor. Given the potential difference between
the plates is equal to \( X \) volts and the
amount of charge on the POSITIVE plate
is equal to \( Y \) coulombs.
A \( \cdot \frac{X}{2 Y} \)
в. \( \frac{Y}{2 X} \)
\( c \cdot \frac{Y}{X} \)
D. \( \frac{2 Y}{X} \)
E \( \cdot \frac{2 X}{Y} \)
Subject: Maths
The sum of the co-efficients of all odd
degree terms in the expansion of \( (x+\sqrt{x^{3}-1})^{5}+(x+\sqrt{x^{3}-1})^{5} \)
\( (x>1) \) is:
A . 2
B. -
\( c \cdot 0 \)
\( D \)
Subject: Physics
Assertion: When two coils are wound on
each other, the mutual induction
between the coils is maximum.
Reason: Mutual induction does not
depend on the orientation of the coils.
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
Subject: Maths
Find the values of \( x, \) if
(i) \( \left|\begin{array}{ll}2 & 4 \\ 5 & 1\end{array}\right|=\left|\begin{array}{ll}2 x & 4 \\ 6 & x\end{array}\right| \)
(ii) \( \left|\begin{array}{ll}2 & 3 \\ 4 & 5\end{array}\right|= \)
\( \left|\begin{array}{ll}\boldsymbol{x} & \boldsymbol{3} \\ \boldsymbol{2} \boldsymbol{x} & \boldsymbol{5}\end{array}\right| \)
Subject: Chemistry
Same quantity of electricity being used to liberate iodine (at anode) and a metal (at
cathode). The mass of metal liberated at
cathode is 0.617 g and the liberated iodine completely reduced by \( 46.3 \mathrm{ml} \) of \( 0.124 \mathrm{M} \) sodium thiosulphate solution. What is
equivalent weight of metal?
A . 23 \( g \)
в. \( 127 \mathrm{g} \)
c. \( 108 \mathrm{g} \)
D. 46