AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
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Q туре your question
reactions that are physically separated. So that the electrons must travel
through a wire from the reducing agent to the oxidizing agent.

The reducing agent loses electrons and is oxidized in a reaction that takes
place at an electrode is called the anode. The oxidizing agent gains electrons and is reduced in a reaction
that takes at an electrode is called the
cathode.

To maintain a net zero charge in each compartment, there is a limited flow of ions through a salt bridge. For example, in a car battery the reducing agent is oxidized by the following reaction, which involves a lead
\( (P b) \) anode and sulfuric acid \( \left(H_{2} S O_{4}\right) \)
Lead sulfate \( \left(P b S O_{4}\right), \) protons \( (H) \)
and electrons \( \left(e^{-}\right) \) are produced
At the cathode, the below reaction
occurs :
\( \boldsymbol{P b O}_{2}+\boldsymbol{H}_{2} \boldsymbol{S O}_{4}+\mathbf{2 H}^{+}+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \)
PbSO \( _{-} 4+2 H_{-} 20 \$ \$ \)
At the anode, the below reaction occurs
\( \boldsymbol{P b}+\boldsymbol{H}_{2} \boldsymbol{S O}_{4} \rightarrow \boldsymbol{P b S O}_{4}+\boldsymbol{2} \boldsymbol{H}^{+}+\boldsymbol{2} \boldsymbol{e}^{-} \)
Electrons are produced by a chemical reaction that takes place at the:
A. anode
B. cathode
c. lead oxide electrode
D. oxidizer
E. salt bridge,
Subject: Physics
A gas has an average speed of \( 10 \mathrm{m} / \mathrm{s} \)
and a collision frequency of \( 10 s^{-1} . \) What
is its mean free path?
A. \( 1 m \)
в. \( 2 m \)
c. \( 3 m^{\text {- }} \)
D. \( 4 m \)
Subject: Physics
A dielectric of thickness \( 5 \mathrm{cm} \) and a
dielectric constant 10 is introduced
between the plates of a parallel plate capacitor having plate area 500 sq. \( \mathrm{cm} \) and separation between the plates \( 10 \mathrm{cm} \)
The capacitance of the capacitor with the dielectric slab is \( \varepsilon_{0}=8.8 \times 10^{-12} C^{2} / N- \)
\( m^{2} \)
A \( .4 .4 p F \)
B. \( 6.2 p F \)
c. \( 8 p F \)
D. \( 10 p F \)
Subject: Chemistry
During the charging of lead accumulator battery voltage varies from:
\( \mathbf{A} \cdot 2 \cdot 15 \vee \) to \( 1.88 \mathrm{v} \)
в. 1.88 V to 2.0 v
c. \( 1.88 \vee \) to 2.15 v
D. does not change
Subject: Physics
A charged particle of unit mass and
unit charge moves with velocity \( \vec{v}= \) \( (8 \hat{i}+6 \hat{j}) m s^{-1} \) in a magnetic field of \( \vec{B}=2 \hat{k} T . \) Choose the correct
alternative(s).
This question has multiple correct options
A \( \cdot \) the path of the particle may be \( x^{2}+y^{2}-4 x-21=0 \)
B. the path of the particle may be \( x^{2}+y^{2}=25 \)
c. the path of the particle may be \( y^{2}+z^{2}=25 \)
D. the time period of the particle will be 3.14 s
Subject: Physics
A steel wire \( 1.5 m \) long and of radius
1 \( m m \) is attached with a load \( 3 k g \) at one
end the other end of the wire is fixed it
is whirled in a vertical circle with a
frequency \( 2 H z . \) Find the elongation of
the wire when the weight is at the
lowest position:
\( \left(Y=2 \times 10^{11} N / m^{2} \text { and } g=10 m / s^{2}\right) \)
A \( .1 .77 \times 10^{-3} m \)
В. \( 7.17 \times 10^{-3} m \)
c. \( 3.17 \times 10^{-7} m \)
D . \( 1.37 \times 10^{-7} m \)
Subject: Chemistry
Among the following options, which molecule contains both ionic and
covalent bonds?
A. \( C_{6} H_{14} \)
в. \( M g C l_{2} \)
\( \mathrm{c} \cdot\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4} \)
D. \( H_{2} O \)
E \( \cdot C_{2} H_{4} \)
Subject: Maths
vertices of an ellipse are (0,±10) and its eccentricity \( e=4 / 5 \) then its
equation is
A \( \cdot 90 x^{2}-40 y^{2}=3600 \)
B . \( 80 x^{2}+50 y^{2}=4000 \)
c. \( 36 x^{2}+100 y^{2}=3600 \)
D. \( 100 x^{2}+36 y^{2}=3600 \)
Subject: Physics
Proton, denteron and alpha particles of the same kinetic energy and moving in circular trajectories in a constant magnetic field. The radii of proton, denteron and alpha particles are
respectively \( r_{p}, r_{d} \) and \( r_{\alpha} . \) Which one of the following relations is correct?
A \( \cdot r_{\alpha}=r_{p}=r_{d} \)
B . \( r_{\alpha}=r_{p}<r_{d} \)
c. \( r_{\alpha}>r_{d}>r_{p} \)
D \( \cdot r_{\alpha}=r_{d}>r_{p} \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{1} \\ \mathbf{1} & \mathbf{1}\end{array}\right], \) then \( \boldsymbol{A}^{100} \) is equal to
\( \mathbf{A} \cdot 2^{100} A \)
в. \( 2^{99} \) А
\( c \cdot 100 A \)
D . \( 299 A \)
Subject: Physics
Length of a wire at room temperature is \( 4.55 m, \) when the temperature increase
upto \( 100^{\circ} \mathrm{C} \) then its length becomes
4.57 \( m \). The coefficient of linear
expansion \( (\alpha) \) of the given wire is
A. \( 5.021 \times 10^{-5} K^{-1} \)
B. \( 6.021 \times 10^{-5} K^{-1} \)
c. \( 7.021 \times 10^{-5} K^{-1} \)
D. \( 8.021 \times 10^{-5} K^{-1} \)
Subject: Physics
Assertion
The relative velocity between the bodies
is equal to the sum of the velocities of
two bodies.
Reason
When body moves in opposite directions, the magnitude of the
relative velocity is equal to sum of magnitudes of individual velocities.
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect
Subject: Physics
Three forces \( \vec{P}, \vec{Q} \) and \( \vec{R} \) acting along \( I A \)
IB and IC, where I is the incentre of a
\( \Delta \mathrm{ABC}, \) are in equilibrium. Then \( \overrightarrow{\mathbf{P}}: \overrightarrow{\mathbf{Q}}: \)
\( \overrightarrow{\mathbf{R}} \) is:
\( ^{A} \cdot \cos \frac{A}{2}: \cos \frac{B}{2}: \cos \frac{C}{2} \)
B \( \cdot \sin \frac{\mathrm{A}}{2}: \sin \frac{\mathrm{B}}{2}: \sin \frac{\mathrm{C}}{2} \)
c. \( \sec \frac{\mathrm{A}}{2}: \sec \frac{\mathrm{B}}{2}: \sec \frac{\mathrm{C}}{2} \)
D \( \operatorname{cosec} \frac{\mathrm{A}}{2}: \operatorname{cosec} \frac{\mathrm{B}}{2}: \operatorname{cosec} \frac{\mathrm{C}}{2} \)
Subject: Physics
Assertion
The atomic mass of potassium is 39
Reason
An atom of potassium is 39 times heavier than \( \frac{1}{12} \) th of the mass of carbon
\( \operatorname{atom}\left(\boldsymbol{C}^{12}\right) \)
Read the above assertion and reason
and choose the correct option regarding
¡t.
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
The displacement of a charge \( Q \) in the
electric field \( \boldsymbol{E}=\boldsymbol{e}_{1} \boldsymbol{l}+\boldsymbol{e}_{2} \boldsymbol{j}+\boldsymbol{e}_{3} \boldsymbol{k} \) is
\( \boldsymbol{r}=\boldsymbol{a} \boldsymbol{i}+\boldsymbol{b} \boldsymbol{j} . \) The work done is
A \( Q\left(a e_{1}+b e_{2}\right) \)
() \( a\left(a_{1}+b_{2}\right)+b_{2}+b_{2} \)
в. \( Q \overline{a e_{1}^{2}+b e_{2}^{2}} \)
c. \( Q\left(e_{1}+e_{2}\right) \overline{a^{2}+b^{2}} \)
D. \( Q \overline{e_{1}^{2}+e_{1}^{2}} a+b \)
Subject: Maths
A line through \( \boldsymbol{A}(-\mathbf{5},-\mathbf{4}) \) meets the
line \( \boldsymbol{x}+\mathbf{3} \boldsymbol{y}+\mathbf{2}=\mathbf{0}, \mathbf{2} \boldsymbol{x}+\boldsymbol{y}+\mathbf{4}=\mathbf{0} \)
and \( x-y-5=0 \) at the point \( B, C \) and
\( D \) respectively. If \( \left(\frac{15}{A B}\right)^{2}+ \) \( \left(\frac{10}{A C}\right)^{2}=\left(\frac{6}{A D}\right)^{2} . \) Find the equation
of the line.
Subject: Chemistry
The compound shown above exibits cis-
trans isomerism. Identify the correct statement(s).
This question has multiple correct options
A. \( C \) is isomer has neither plane of symmetry and nor centre of symmetry
B. \( C \) is isomer has planar symmetry and is optically inactive
C. Trans isomer has centre of symmetry and is optically inactive
D. Trans isomer has no plane of symmetry and is optically inactive
Subject: Biology
Which is correctly matched?
1. Arsenic poisoning- Black foot disease
2. Secondary Effluent treatment-
Biological process
3. Pyrolysis- Solid soil waste disposal
4. Tubifex- Water pollution indicator
5. Biomagnification - Degradable pollutants
A .1,2,3,5
в. 1,3,4,5
c. 2,3,4,5
D. 1,2,3,4
E .1,2,4,5
Subject: Physics
Two half life radioactive substance is
20 minutes. The approximate time
interval \( \left(t_{2}-t_{1}\right) \) between the time \( t_{2} \)
when \( \frac{2}{3} \) of it has decayed and time \( t_{1} \) and \( \frac{1}{3} \) of it had decayed is:
A . 14 min
B. 20 min
\( c .28 \) min
D. 7 min
Subject: Maths
In the figure \( \angle A=\angle C E D, C D= \)
\( \mathbf{8} \boldsymbol{c m}, \boldsymbol{C} \boldsymbol{E}=\mathbf{1 0} \boldsymbol{c m}, \boldsymbol{B} \boldsymbol{E}= \)
\( 2 c m, A B=9 c m, A D= \)
\( b \) and \( D E=a \). The value of \( a+b \) is
A. \( 13 \mathrm{cm} \)
В. \( 15 \mathrm{cm} \)
\( c \cdot 12 \mathrm{cm} \)
D. \( 9 \mathrm{cm} \)
Subject: Maths
If the function \( f(x)=\frac{a x+b}{(x-1)(x-4)} \)
has a local maxima at \( (2,-1), \) then
A. \( b=1, a=0 \)
В. \( a=1, b=0 \)
c. \( b=-1, a=0 \)
D. \( a=-1, b=0 \)
Subject: Maths
The domain of the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \log _{3+x}\left(x^{2}-1\right) \) is
A \( \cdot(-3,-1) \cup(1, \infty) \)
B . [-3,-1)\( \cup[1, \infty) \)
c. (-3,-2)\( \cup(-2,-1) \cup(1, \infty) \)
D \( \cdot[-3,-2) \cup(-2,-1) \cup[1, \infty) \)
Subject: Chemistry
Number of paramagnetic molecules
from the following are:
\( \boldsymbol{C N}^{-}, \boldsymbol{N O}, \boldsymbol{O}_{2}^{2-}, \boldsymbol{O}_{2}, \boldsymbol{N} \boldsymbol{O}_{2}, \boldsymbol{O}_{2}^{-}, \boldsymbol{B}_{2}, \boldsymbol{C}_{2}, \boldsymbol{l} \)
Subject: Physics
If the angle of incidence is i and that of refraction is \( r \). Then the speed of light in the medium to which the light is
reflected from air is?
A \( \cdot v=C \frac{\sin i}{\cos r} \)
B. \( v=C \frac{\cos r}{\cos i} \)
c. \( v=C \frac{\sin r}{\sin i} \)
D. \( v=C \frac{\sin i}{\sin r} \)
Subject: Chemistry
Extraction of aluminium from oxide
\( \left(A l_{2} O_{3}\right) \) is best done by:
A . Electrolytic reduction of \( A l_{2} O_{3} \)
B. Reduction of \( A l_{2} O_{3} \) with carbon
c. Reduction of \( A l_{2} O_{3} \) with sodium
D. Reduction of \( A l_{2} O_{3} \) with \( c 0 \)
Subject: Chemistry
For the gaseous reaction \( N_{2} O_{4} \Leftrightarrow 2 N O_{2} \)
\( \mathbf{A} \cdot \Delta H>\Delta E \)
B. \( \Delta H<\Delta E \)
c. \( \Delta H=\Delta E \)
D. \( \Delta H \geq \Delta E \)
Subject: Maths
The angle between the lines \( y-x+ \)
\( \mathbf{5}=\mathbf{0} \) and \( \sqrt{\mathbf{3}} x-\boldsymbol{y}+\mathbf{7}=\mathbf{0} \) is/are:
A \( \cdot 15^{\circ} \)
В. \( 60^{\circ} \)
\( \mathbf{c} \cdot 165^{\circ} \)
D. \( 75^{\circ} \)
Subject: Chemistry
Assertion
The voltage of mercury cell remains
constant for its life time.
Reason
Overall cell reaction does not involve
any ion.
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: Maths
The range of values of \( a \) such that the
angle \( \theta \) between the pair of tangents drawn from \( (a, 0) \) to the circle \( x^{2}+ \) \( y^{2}=1 \) satisfies \( \frac{\pi}{2}<\theta<\pi \), is
A \( .(1,2) \)
B. \( (1, \sqrt{2}) \)
c. \( (-\sqrt{2},-1) \)
(年) \( (-\sqrt{2},-1) \)
D. \( (-\sqrt{2},-1) \cup(1, \sqrt{2}) \)
Subject: Physics
A photon of energy 10.2 eV corresponds
to light of wavelength \( \lambda_{0} . \) Due to an electron transition from \( x=2 \) to \( x=1 \) in a
hydrogen atom, light of wavelength A is emitted. If we take into account the
recoil of the atom when the photon is
emitted, then :
\( A \cdot \lambda<\lambda_{0} \)
B. \( \lambda>\lambda_{0} \)
c. \( \lambda=\lambda_{0} \)
D. None of these
Subject: Maths
The sides of a triangle \( A B C \) are
positive integers. The smallest side has
length \( l . \) What of the following
statements is true?
A. The area of ABC is always a rational number
B. The area of ABC is always an irrational number
c. The perimeter of ABC is an even integer.
D. The information provided is not sufficient to conclude any of the statements A, B or C above
Subject: Chemistry
A current of \( 10.0 \mathrm{A} \) flows for \( 2.00 \mathrm{hrs} \) through an electrolytic cell containing a molten salt of metal \( X . \) This results in
the decomposition of 0.250 mol of metal \( X \) at the cathode. The oxidation state of \( X \) in the molten salt is: \( (F= \)
\( 96500 C) \)
\( A \cdot+1 \)
\( B \cdot+2 \)
\( c \cdot+3 \)
\( D \cdot+4 \)
Subject: Physics
A stream line body with relative density
\( d_{1} \) falls into air from a height \( h_{1} \) on the
surface of a liquid of relative density \( \boldsymbol{d}_{2} \)
where \( d_{2} \) is greater than \( d_{1} \). The time of immersion of the body into the liquid will be
\( A \)
\[
\sqrt{\left(\frac{2 h_{1}}{g}\right)} \times \frac{d_{1}}{d_{2}-d_{1}}
\]
в.
\[
\sqrt{\left(\frac{2 h_{1}}{g}\right)}
\]
\( c \)
\[
\sqrt{\left(\frac{2 h_{1}}{g}\right)} \times \frac{d_{1}}{d_{2}}
\]
D.
\[
\sqrt{\left(\frac{2 h_{1}}{g}\right)} \times \frac{d_{2}}{d_{1}}
\]
Subject: Physics
The potentiometer wire AB is made of
two equal parts \( A N \) and \( N B \) of cross
sectional radius \( 2 r \) and \( r \)
respectively.The material of both parts is same. A cell is connected between \( \mathbf{A} \)
and B. The potential gradient in the part
AN is \( 1 V / m . \) Potential difference
between two points \( C \) and \( D \) (shown in figure) separated by \( 20 \mathrm{cm} \) is found to
be \( 0.5 V . \) The separation between \( C \) and \( \mathrm{N} \) is \( \frac{t}{3} \mathrm{cm} . \) Then \( t \) is
Subject: Physics
A compound microscope has an objective lens of \( 1.0 \mathrm{cm} \) focal length and
an eye-piece of \( 2.5 \mathrm{cm} \) of focal length.
When the object is placed at \( 1.1 \mathrm{cm} \) from the objective, the final image is at the least distance of direct vision. Thus,
the magnification produced is
A . 10
B. 11
\( c .100 \)
D. 110
Subject: Physics
Assertion (A): The displacement time graph for a particle in SHM begins from mean position. Reason
(R): The displacement of a particle in SHM is given by \( y=A \sin \omega t \)
A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true and R is not the correct explanation of
C. A is true and R is false
D. A is false and R is true
Subject: Chemistry
The ions responsible for the bleaching action of bleaching powder and the ions responsible for loss of bleaching action of bleaching powder due to the storage for long time respectively are:
A \( \cdot C l^{-}, O C l \)
в. \( O C l^{-}, C l \)
c. \( O C l^{-}, C l O_{3} \)
D. \( C l^{-}, C l O^{-} \)
Subject: Physics
For Bohr's model of the hydrogen atom,
the energy of the electron in its ground state is found to be \( -13.6 e V \). (i) Draw
an energy level diagram for the hydrogen atom and mark the values of energy (in eV) at \( n=2 \) to \( n=\infty \) to.
Obtain the maximum energy of a
photon emitted by the hydrogen atom in \( \mathrm{eV} \)
Subject: Chemistry
A magnetic moment of 1.73 BM will be
shown by which one among the following compounds?
A \( \cdot\left[C u\left(N H_{3}\right)_{4}\right]^{2} \)
B \( \cdot\left[N i(C N)_{4}\right]^{2-} \)
c. \( T i C l_{4} \)
D. \( \left[C o C l_{6}\right]^{4} \)
Subject: Physics
A billiard ball, initially at rest, is given a
sharp impulse by cue. The cue is held
horizontally at a distance \( h \) above the
central line as shown in the figure. The
ball leaves the cue with a speed \( \boldsymbol{v}_{\mathbf{0}} . \) It
rolls and slides while moving forward
and eventually acquires a final speed
\( (9 / 7) v_{0} . \) If \( R \) is the radius of the ball,
then \( h \) is
\( A \cdot \frac{2 R}{5} \)
B. \( \frac{3 R}{5} \)
c. \( \frac{4 R}{5} \)
D. \( \frac{R}{5} \)
Subject: Physics
A plane electromagnetic wave of frequency 50 MHz travels in free space along the x-direction. At a particular point in space and time, \( \vec{E}=6.3 \hat{j} \vee m^{-1} \) At this point \( \vec{B} \) is equal to
A. \( 8.33 \times 10^{-8} \hat{k} T \)
B . \( 18.9 \times 10^{-8} \hat{k} T \)
c. \( 4.1 \times 10^{-8} \hat{k} T \)
D. \( 2.1 \times 10^{-8} \hat{k} T \)
Subject: Physics
A point object is placed on the axis of a
thin convex lens of focal length \( 0.05 m \)
at a distance of \( 0.2 m \) from the lens and
its image is formed on the axis. If the object is now made to oscillate along the axis with a small amplitude of \( \boldsymbol{A} \) \( \mathrm{cm}, \) then what is the amplitude of oscillation of the image? [you may assume \( \frac{1}{1+x} \approx 1-x, \) where \( x<<1 \)
A \( \cdot \frac{4 A}{9} \times 10^{-2} m \)
в. \( \frac{5 A}{9} \times 10^{-2} m \)
c. \( \frac{A}{3} \times 10^{-2} m \)
D. \( \frac{A}{9} \times 10^{-2} m \)
Subject: Physics
The de Broglie wavelength associated with an electron of energy 500 ev is given by (take \( \boldsymbol{h}=\mathbf{6 . 6 3} \times \mathbf{1 0}^{-\mathbf{3 4} \mathbf{J}} \boldsymbol{s}, \boldsymbol{m}=\mathbf{9 . 1 1} \times \)
\( \left.10^{-31} k g\right) \)
A \( \cdot 0.28 A^{0} \)
B . 1.410 \( A^{\circ} \)
\( c \cdot 0.66 A^{0} \)
D. 0.55 \( A^{\circ} \)
Subject: Chemistry
\( \boldsymbol{C H}_{3} \boldsymbol{C H O}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{C}(\boldsymbol{C O O R})_{2} \frac{(i) \boldsymbol{P i p}}{(i i) \boldsymbol{H}_{3} O \oplus, \boldsymbol{\Delta}} \boldsymbol{A} \)
If \( \mathbf{A} \) is \( \boldsymbol{C} \boldsymbol{H}_{\boldsymbol{p}}-\boldsymbol{C} \boldsymbol{H}=\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{O}_{\boldsymbol{q}} \boldsymbol{H} \)
Then find the value of \( \boldsymbol{p}+\boldsymbol{q} \)
Subject: Maths
Bag \( A \) contains 2 white and 3 red balls
and bag \( B \) contains 4 white and 5 red
balls. One ball is drawn at random from
one of the bag is found to be red. Find the probability that it was drawn from
bag \( \boldsymbol{B} \)
\( A \cdot \frac{3}{8} \)
в. \( \frac{25}{52} \)
\( c \cdot \frac{1}{8} \)
D. \( \frac{3}{14} \)
Subject: Physics
Q Type your question
performing SHM with an amplitude of
1 \( m \). When the cannon reaches \( x= \)
\( \frac{\sqrt{3}}{2} m \) from the equilibrium
moving along +x direction, a bullet of \( \frac{1}{2} k g \) is suddenly fired from it with \( a \)
velocity of \( 20 m / s \) relative to the ground. What will be the new amplitude of the
cannon?
\( ^{A} \cdot \frac{\sqrt{3}}{2} \)
B. \( \frac{\sqrt{5}}{2} \)
c. \( \frac{\sqrt{7}}{2} \)
D. \( \frac{\sqrt{11}}{2} \)
Subject: Physics
A wire has resistance of 3.1 at \( 30 C \) and
resistance 4.5 at \( 100^{\circ} C . \) The
temperature coefficient of resistance of the wire is
B. \( 0.0024^{\circ} \mathrm{C}^{-1} \)
c. \( 0.0032^{\circ} \mathrm{C}^{-1} \)
D. \( 0.0064^{\circ} \mathrm{C}^{-1} \)
Subject: Physics
write a general expression for the wave
function
\( y=(15 \mathrm{cm}) \sin \left[\left(16 \pi s^{-1}\right) t-\left(\frac{\pi \mathrm{rad}}{20 \mathrm{cm}}\right) x+\frac{\pi}{2}\right] \)
\( y=(30 \mathrm{cm}) \sin \left[\left(16 \pi s^{-1}\right) t-\left(\frac{\pi r a d}{20 \mathrm{cm}}\right) x+\frac{\pi}{2}\right] \)
\( y=(15 \mathrm{cm}) \sin \left[\left(8 \pi s^{-1}\right) t-\left(\frac{\pi \mathrm{rad}}{20 \mathrm{cm}}\right) x+\frac{\pi}{2}\right] \)
\( y=(15 \mathrm{cm}) \sin \left[\left(16 \pi s^{-1}\right) t-\left(\frac{\pi r a d}{10 \mathrm{cm}}\right) x+\frac{\pi}{2}\right] \)
Subject: Physics
A closed surface S is constructed
around a conducting wire connected to
a battery and switch (Fig) As the switch
is closed, the free electrons in the wire
start moving along the wire. In any time
interval, the number of electrons
entering the closed surface \( S \) is equal to
the number of electrons leaving it. After
closing the switch, the flux of the
electric field through the closed surface
will :
This question has multiple correct options
A. increase
B. decrease
C. remain unchanged
D. be zero
Subject: Physics
For the transition from \( \boldsymbol{n}=\mathbf{2} \rightarrow \boldsymbol{n}=\mathbf{1} \)
which of the following will produce shortest wavelength?
A. H atom
B. D atom
\( \mathbf{c} \cdot H e^{+} i o n \)
D. \( L i^{2+} \) ion
Subject: Chemistry
Based on the compounds of group 15 elements, the correct statement(s)
is/are:
This question has multiple correct options
\( \mathbf{A} \cdot B i_{2} O_{5} \) is more basic than \( N_{2} O_{5} \)
B. \( N F_{3} \) is more covalent than \( B i F_{3} \)
\( \mathrm{C} \cdot P H_{3} \) boils at lower temperature than \( N H_{3} \)
D. The \( N-N \) single bond is stronger than the \( P-P \)
single bond.
Subject: Chemistry
Which of the following behaviour is true for an ideal binary solution?
A. Plot of \( P_{\text {total}} \) versus \( y_{B} \) (mole fraction of B in vapour phase) is linear
B. Plot of \( P_{\text {total}} \) versus \( y_{A} \) is linear
c. plot of \( \frac{1}{P_{\text {total }}} \) versus \( y_{A} \) (or \( y_{B} \) ) is non-linear
D. plot of \( \frac{1}{P_{\text {total }}} \) versus \( y_{A} \) (or \( y_{B} \) ) is linear
Subject: Maths
Express the matrix \( \left[\begin{array}{ccc}\mathbf{3} & -\mathbf{2} & \mathbf{- 4} \\ \mathbf{3} & -\mathbf{2} & -\mathbf{5} \\ -\mathbf{1} & \mathbf{1} & \mathbf{2}\end{array}\right] \) as
the sum of a symmetric and skew-
symmetric matrix
Subject: Maths
In the following, figure, seg DE II side BC
n \( \triangle A B C . \) If \( 3 A(\triangle A D E)= \)
\( A(D E C B), \) then find the ratio \( B C \)
\( D E ? \)
\( A \cdot 1: 2 \)
в. 16:
\( c \cdot 1: 16 \)
D.
Subject: Physics
A juggler tosses a ball up in the air with speed \( u \). At the instant it reaches its
maximum height \( \boldsymbol{H}, \) he tosses up a second ball with the same initial speed. The two balls will collide at a height.
A \( \cdot \frac{H}{4} \)
в. \( \frac{H}{2} \)
c. \( \frac{3 H}{4} \)
D. \( \sqrt{\frac{3}{4}} H \)
Subject: Maths
If \( \int \frac{\boldsymbol{d x}}{\left(\boldsymbol{x}^{2}+\mathbf{1}\right)\left(\boldsymbol{x}^{2}+\mathbf{4}\right)}= \)
\( \boldsymbol{A} \tan ^{-1}+\boldsymbol{B} \tan ^{-1}\left(\frac{\boldsymbol{x}}{2}\right)+\boldsymbol{C}, \operatorname{then} \boldsymbol{B}= \)
A . \( 1 / 6 \)
B. \( -1 / 6 \)
\( c \cdot 6 \)
D.
Subject: Chemistry
Which of the following carboxylic acids undergoes decarboxylation easily?
A. \( C_{6} H_{5} \) СОСН\( _{2} \) СООН
в. \( C_{6} H_{5} \) СОСООН
c. \( C_{6} H_{5} C H-\underset{O H}{_{O H}} \) С ООН
D. \( C_{6} H_{5} \) СНСООН
\( N H_{2} \)
Subject: Chemistry
The lattice energy of \( N a C l \) is \( 788 \mathrm{kJ} \)
mol \( ^{-1} \). This means that 788 kJ of
energy is required:
A. to separate one mole of solid \( N a C l \) into one mole of \( N a_{(g)} \) and one mole of \( C l_{(g)} \) to infinite distance
B. to separate one mole of solid \( N a C l \) into one mole of \( N a_{(g)}^{+} \) and one mole of \( C l^{-}(g) \) to infinite distance
c. to convert one mole of solid \( N a C l \) into one mole of gaseous \( N a C l \)
D. to convert one mole of gaseous \( N a C l \) into one mole of solid \( N a C l \)
Subject: Chemistry
An electrochemical cell is constructed
with an open swtich as shown below:
When the switch is closed, mass of tin-
electrode increases. If \( \boldsymbol{E}^{\circ}\left(\boldsymbol{S} \boldsymbol{n}^{2+} / \boldsymbol{S} \boldsymbol{n}\right)= \)
\( -0.14 V \) and for \( E^{\circ}\left(X^{n+} / X\right)= \)
\( -0.78 V \) and initial emf of the cell is
\( 0.65 \mathrm{V}, \) determine \( n \)
\( A \cdot 3 \)
в.
\( c .5 \)
\( D \)
Subject: Maths
Prove that \( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}-\mathbf{1}|+|\boldsymbol{x}-\mathbf{1}|+ \)
\( |x-3| \) is continuous on \( R \) but not
differentiable at \( x=1,2 \) and 3 only.
Subject: Chemistry
Balance the following redox reactions in acidic medium :
\[
Z n+N O_{3}^{-} \longrightarrow Z n^{2+}+N_{2}
\]
A \( \cdot 5 Z n+2 N O_{3}^{-}+12 H^{+} \rightarrow 5 Z n^{2+}+N_{2}+3 H_{2} O \)
B . \( 5 Z n+2 N O_{3}^{-}+12 H^{+} \rightarrow 5 Z n^{2+}+N_{2}+6 H_{2} O \)
\( \mathrm{c} \cdot 5 Z n+2 N O_{3}^{-}+6 H^{+} \rightarrow 3 Z n^{2+}+N_{2}+6 H_{2} O \)
D. None of these