AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Two point charges \( +9 q \) and \( +q \) are kept \( 16 \mathrm{cm} \) apart. Where should a third charge \( Q \) be placed between them so that the system remains in equilibrium
\( ? \)
A. \( 24 \mathrm{cm} \) from \( +9 q \)
в. \( 12 \mathrm{cm} \) from \( +9 q \)
c. 24 cm from \( +q \)
D. \( 12 \mathrm{cm} \) from \( +q \)
Subject: Maths
Left \( \boldsymbol{f} \) be an odd function defined on the
set of real numbers such that for \( x \geq \)
\( \mathbf{0}, \boldsymbol{f}(\boldsymbol{x})=\mathbf{3} \sin \boldsymbol{x}+\mathbf{4} \cos \boldsymbol{x} \)
Then \( f(x) \) at \( x=-\frac{11 \pi}{6} \) is equal to
A \( \cdot-\frac{3}{2}-2 \sqrt{3} \)
B. \( \frac{3}{2}-2 \sqrt{3} \)
c. \( \frac{3}{2}+2 \sqrt{3} \)
D. \( -\frac{3}{2}+2 \sqrt{3} \)
Subject: Maths
If \( A \) and \( B \) are invertible matrices, which
one of the following statement is/are
correct
This question has multiple correct options
A \( . A d j(A)=|A| A^{-1} \)
B. \( \operatorname{det}\left(A^{-1}\right)=|\operatorname{det}(A)|^{-1} \)
c. \( (A+B)^{-1}=B^{-1}+A^{-1} \)
D. \( (A B)^{-1}=B^{-1} A^{-1} \)
Subject: Physics
A bullet moving at \( 250 \mathrm{m} / \mathrm{s} \) penetrates \( 5 \mathrm{cm} \) into a tree limb before coming to
rest. Assuming that the force exerted by the tree limb is uniform, find its magnitude. Mass of the bullet is \( 10 g \).
A . \( 625 N \)
В. \( 6250 N \)
\( c \cdot 62.50 N \)
D. \( 6.250 N \)
Subject: Maths
From a solid cylinder whose height is \( 4 \mathrm{cm} \) and radius \( 3 \mathrm{cm}, \) a conical cavity of height \( 4 \mathrm{cm} \) and base radius \( 3 \mathrm{cm} \) is
hollowed out. What is the volume of the
remaining solid?
\( \mathbf{A} \cdot 9 \pi c m^{3} \)
В. \( 15 \pi c m^{3} \)
\( \mathrm{c} \cdot 21 \pi c m^{3} \)
D. \( 24 \pi c m^{3} \)
Subject: Maths
If \( A=\left[\begin{array}{ccc}1 & 2 & 3 \\ 2 & 3 & 4 \\ 0 & 5 & 6\end{array}\right], \) then \( 2 A= \)
A. \( \left[\begin{array}{lll}2 & 4 & 6 \\ 2 & 3 & 4 \\ 0 & 5 & 6\end{array}\right] \)
в. \( \left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 6 & 8 \\ 0 & 5 & 6\end{array}\right] \)
с. \( \left[\begin{array}{lll}1 & 2 & 3 \\ 2 & 3 & 4 \\ 0 & 10 & 12\end{array}\right] \)
D. \( \left[\begin{array}{lll}2 & 4 & 6 \\ 4 & 6 & 8 \\ 0 & 10 & 12\end{array}\right] \)
Subject: Physics
A tyre pumped to a pressure 3.375 atm
at \( 27^{\circ} C \) suddenly bursts. What is the
final temperature \( (\gamma=\mathbf{1 . 5}) ? \)
A \( \cdot 27^{\circ} \mathrm{C} \)
B . \( -27^{\circ} \mathrm{C} \)
\( c \cdot 0^{\circ} C \)
D. \( -73^{\circ} \mathrm{C} \)
Subject: Physics
Assertion
A capacitor blocks the direct current in
the steady state.
Reason
The capacitive reactance of the capacitor is inversely proportional to
frequency \( f \) of the source of emf.
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
A particle starts from point \( A \) moves along a straight line path with an acceleration given by \( a=p-q x, \) where
\( p, q \) are constants and \( x \) is distance
from point \( A . \) The particle stops at point
B. The maximum velocity of the particle is
A. \( \underline{p} \) \( q \)
B. \( \frac{p}{\sqrt{q}} \)
c. \( \frac{q}{p} \)
D. \( \frac{\sqrt{q}}{p} \)
Subject: Maths
If \( \frac{3 \pi}{4}<\alpha<\pi, \) then \( \sqrt{2 \cot \alpha+\frac{1}{\sin ^{2} \alpha}} \)
is equal to
A. \( 1-\cot \alpha \)
B. \( 1+\cot \alpha \)
c. \( -1+\cot \alpha \)
D. \( -1-\cot \alpha \)
Subject: Maths
If the projection of point \( \boldsymbol{P}(\overrightarrow{\boldsymbol{p}}) \) on the
plane \( \vec{r} \cdot \vec{n}=q \) is the point \( S(\vec{s}), \) then?
A \( \cdot \vec{s}=\frac{(q-\vec{p} \cdot \vec{n}) \vec{n}}{|\vec{n}|^{2}} \)
В \( \cdot \vec{s}=\vec{p}+\frac{(\vec{p} \cdot \vec{n}-q)}{|\vec{n}|^{2}} \vec{n} \)
C・ \( _{\vec{s}}=\vec{p}-\frac{(\vec{p} \cdot \vec{n}) \vec{n}}{|\vec{n}|^{2}} \)
D \( \vec{s}=\vec{p}-\frac{(q-\vec{p} \cdot \vec{n}) \vec{n}}{|\vec{n}|^{2}} \)
Subject: Maths
The sum of the infinite series
\( 1+\frac{1+2}{2 !}+\frac{1+2+2^{2}}{3 !}+\frac{1+2+2^{2}+2^{3}}{4 !} \)
is \( e^{y}-e^{x} \) Find \( x+y^{2} \)
Subject: Physics
A force \( F=x^{2}+2 x+1 \) acts on a
particle in the x direction, where \( \boldsymbol{F} \) is in
newton and \( x \) in metre. Find the work
done by this force during a displacement from \( \boldsymbol{x}=-\mathbf{1} \boldsymbol{m} \) to \( \boldsymbol{x}= \)
\( \mathbf{2 . 0 m} \)
Subject: Maths
represents the solution set to which of
the following systems of inequalities?
A \( \cdot\left\{\begin{array}{l}y<-x+2 \\ (x-1)^{2}+(y-2)^{2}<9\end{array}\right. \)
B \cdot \( \left\{\begin{array}{l}y>-x+2 \\ (x-1)^{2}+(y-2)^{2}<9\end{array}\right. \)
c. \( \left\{\begin{array}{l}y>-x+2 \\ (x-1)^{2}+(y-2)^{2}>9\end{array}\right. \)
D \cdot \( \left\{\begin{array}{l}y<-x+2 \\ (x-1)^{2}+(y-2)^{2}>9\end{array}\right. \)
E \( \left\{\begin{array}{l}(y-2)<3 \\ (x-1)>3\end{array}\right. \)
Subject: Physics
Force \( \boldsymbol{F} \) is given in terms of time \( t \) and
distance \( \boldsymbol{x} \) by \( \boldsymbol{F}=\boldsymbol{A} \boldsymbol{\operatorname { s i n }} \boldsymbol{C t}+\boldsymbol{B} \cos \boldsymbol{D} \boldsymbol{x} \)
Then the dimensions of \( \frac{A}{B} \) and \( \frac{C}{D} \) are given by :
A \( \cdot M L T^{-2}, M^{\circ} L^{\circ} T^{-} \)
B. \( M L T^{-2}, M^{\circ} L^{-1} T^{c} \)
c. \( M^{\circ} L^{\circ} T^{\circ}, M^{\circ} L^{1} T^{-1} \)
D. \( M^{\circ} L^{1} T^{-1}, M^{\circ} L^{\circ} T^{\circ} \)
Subject: Maths
A car is parked among \( N \) cars standing
in a row, but not at either end. On his
return, the owner finds that exactly \( r \) of
the \( N \) places are still occupied. What is
the probability that both the places neighboring his car are empty?
A \( . \) Required probability \( =\frac{(N-r)(N-r-2)}{(N-1)(N-2)} \)
B. Required probability \( =\frac{(N-r)(N-r-1)}{(N-1)(N-2)} \)
c. Required probability \( =\frac{(N-r-2)(N-r-1)}{(N-1)(N-2)} \)
D. none of these
Subject: Maths
\( \int \frac{x}{\sqrt{x^{2}+2}} d x \)
\( ^{\mathbf{A}} \cdot \frac{x^{2}+2}{2}+C \)
B . \( x^{2}+2+C \)
c. \( \frac{1}{2} \sqrt{x^{2}+2}+C \)
D. \( \sqrt{x^{2}+2}+C \)
Subject: Physics
The activity of a radioactive element decreases to one-third of the origina
activity \( A_{0} \) in a period of 9 years. After \( a \) further lapse of 9years, its activity will be
\( A \cdot A_{0} \)
B. \( \frac{2}{3} A_{0} \)
c. \( \frac{A_{0}}{9} \)
D. \( \frac{A_{0}}{6} \)
Subject: Physics
A voltmeter of reading up to \( 1000 m V \) is calibrated by a potentiometer. An emf of \( 1.08 V \) is balanced across \( 5.4 m \) length
of the wire. When voltmeter reading is \( 0.9 V, \) the balancing length is \( 4.55 m \)
The error in the voltmeter reading is:
A. -0.01mV
B. 0.5 mv
c. \( 0.25 \mathrm{mv} \)
D. No error
Subject: Chemistry
For a first order reversible reaction \( A_{K_{b}}^{K_{f}} B, \) the initial concentration of \( A \)
and \( B \) are \( [A]_{0} \) and zero respectively. If
concentrations at equilibrium are \( [\boldsymbol{A}]_{e q} \)
and \( [\boldsymbol{B}]_{e q} ., \) derive an expression for the time taken by \( B \) to attain concentration
equal to \( [\boldsymbol{B}]_{e q / 2} \)
Subject: Physics
Obtain the maximum kinetic energy of
\( \boldsymbol{\beta} \) -particles, and the
radiation frequencies of \( \gamma \) decays in the
decay scheme shown
You are given that
\( \boldsymbol{m}\left(^{198} \boldsymbol{A u}\right)=\mathbf{1 9 7 . 9 6 8 2 3 3} \boldsymbol{u} \)
\( m\left(^{198} H g\right)=197.966760 u \)
Subject: Biology
Read the given statements about algae and select the correct option.
(i) Plant body is thalloid.
(ii) They are largely aquatic.
(iii) Reproduction occurs by vegetative, asexual and sexual methods.
(iv) Chlamydomonas, Volvox and Ulothrix are the multicellular algae.
A. Statements (i) and (ii) are true
B. Statements (ii) and (iii) are true
c. Statements (i), (ii) and (iii) are true
D. All statements are true
Subject: Physics
Compare how the magnitude of the electric field decreases with distance
from a uniform charged sphere and a uniform charged wire.
A. Both decrease with a one over the square of the distance relationship.
B. From the sphere, the electric field decreases with a one over the distance relationship. From the wire, the electric field decreases with a one over the distance squared relationship
c. Both decrease with a one over the distance relationship.
D. From the wire, the electric field decreases with a one over the distance relationship. From the sphere, the electric field decreases with a one over the distance squared relationship
Subject: Chemistry
The feasibility of a chemical reaction can be explained based on \( \Delta \boldsymbol{H}, \boldsymbol{\Delta} \boldsymbol{S} \)
and \( \Delta G \)
For \( 2 O_{3}(g) \rightarrow 3 O_{2}(g), \) if the reaction is
feasible, then:
This question has multiple correct options
\( \mathbf{A} \cdot \Delta S=+v e \)
в. \( \Delta G=+v e \)
c. \( \Delta H=-v e \)
\( \mathbf{D} \cdot \Delta G=-v e \)
Subject: Maths
The chance that a person with two dices, the faces of each being numbered 1 to \( 6, \) will throw aces exactly
4 times in 6 trials is
\( ^{\mathrm{A}} \cdot\left(\frac{1}{36}\right)^{4} \)
\( ^{\mathrm{B}}\left(\frac{1}{36}\right)^{4}\left(\frac{35}{36}\right)^{2} \)
\( ^{\mathbf{c}} \cdot_{4} C\left(\frac{1}{36}\right)^{4}\left(\frac{35}{36}\right)^{2} \)
\( ^{\mathrm{D}} \cdot_{4}^{6} C\left(\frac{1}{36}\right)^{2}\left(\frac{35}{36}\right)^{4} \)
Subject: Maths
\( \mathbf{f}\left|\begin{array}{lll}\boldsymbol{x}^{\boldsymbol{k}} & \boldsymbol{x}^{\boldsymbol{k}+\boldsymbol{2}} & \boldsymbol{x}^{\boldsymbol{k}+\boldsymbol{3}} \\ \boldsymbol{y}^{\boldsymbol{k}} & \boldsymbol{y}^{\boldsymbol{k}+\boldsymbol{2}} & \boldsymbol{y}^{\boldsymbol{k}+\boldsymbol{3}} \\ \boldsymbol{z}^{\boldsymbol{k}} & \boldsymbol{z}^{\boldsymbol{k}+\boldsymbol{2}} & \boldsymbol{z}^{\boldsymbol{k}+\boldsymbol{3}}\end{array}\right| \)
三室 \( (x-y)(y-z)(z-x)\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right) \)
then
A. \( k=-3 \)
B. \( k=-1 \)
\( \mathbf{c} \cdot k=1 \)
D. \( k=3 \)
Subject: Physics
A rod \( A B \) moves with a uniform velocity
\( \boldsymbol{v} \) in a uniform magnetic field as shown in figure :
\[
\begin{array}{llllll}
x & x & x & x & x & x \\
x & x & x & A & x & x \\
x & x & x & x & x & x \\
x & x & x & B x & x & x
\end{array}
\]
A. The rod becomes electrically charged
B. The end A becomes positively chargedd
C. The end B becomes positively charged
D. The rod becomes hot because of Joule heating
Subject: Physics
Assertion Even Though \( \oint_{\mathbf{c}} \overrightarrow{\mathbf{B}} \mathbf{d} \bar{l} \) is zero along a
closed Amperian loop \( \mathrm{C} \), the magnetic
field \( \overline{\mathbf{B}} \) may not be zero over \( \mathbf{C} \)
Reason \( \oint_{\mathbf{s}} \overline{\mathbf{B}} \mathrm{d} \overline{\mathbf{S}} \) is always zero for any closed
surface S.
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
Two spheres of radius \( 5 \mathrm{cm} \) and \( 10 \mathrm{cm} \) both charged to \( 120 \mu C \), are joined by a metal wire and then metal wire is
removed. What is the charge on each after removal of the wire?
\( \mathbf{A} \cdot 120 \mu C, 120 \mu C \)
в. \( 80 \mu C, 160 \mu C \)
c. \( 100 \mu C, 140 \mu C \)
D. None of these
Subject: Physics
A ball weighing 15 g is tied to a string 10 cm long. Initially the ball is held in position such that the string is
horizontal. The ball is now released. A
nail \( N \) is situated vertically below the
support at a distance \( L \)

The minimum value of \( L \) such that the
string will be wound round the nail is
\( A \cdot 2 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
\( \mathbf{c} .6 \mathrm{cm} \)
\( \mathbf{D} \cdot 8 \mathrm{cm} \)
Subject: Physics
Two balls are dropped from height \( h_{1} \)
and \( h_{2} \) respectively. What is the ratio of
their velocities on reaching the ground is?
A. \( \sqrt{\frac{h_{2}}{h_{1}}} \)
B. \( \sqrt{\frac{h_{1}}{h_{2}}} \)
\( c \cdot \frac{h_{2}}{h_{1}} \)
D. \( \frac{h_{1}}{h_{2}} \)
Subject: Maths
Construct a \( 2 \times 2 \) matrix \( A=\left[a_{i j}\right] \)
whose element \( \boldsymbol{a}_{\boldsymbol{i} j} \) is \( \boldsymbol{a}_{\boldsymbol{i} j}=\frac{|\mathbf{2} \boldsymbol{i}-\boldsymbol{3} \boldsymbol{j}|}{\boldsymbol{2}} \)
Subject: Physics
A jet of water with area of cross-section
\( 3 c m^{2} \) strikes a wall at an angle \( \boldsymbol{\theta}=\mathbf{6 0}^{\circ} \)
to the normal and be rebounds
elastically from the wall with the same speed. If the speed of water in the jet is \( 12 \mathrm{m} / \mathrm{s}, \) then the force acting on the wall
is
A . \( 4.31 N \)
В. \( 4.32 \times 10^{-2} N \)
c. \( 4.32 \times 10^{-3} N \)
D. 43.2N
Subject: Physics
A man slides down a snow covered hill
along a curved path and falls \( 20 m \) below his initial position. The velocity in \( \boldsymbol{m} / \boldsymbol{s e c}, \) with which he finally strikes the ground is \( ?\left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s e c}^{2}\right) \)
A . 20
в. 400
\( c \cdot 200 \)
D. 40
Subject: Physics
A nucleus of sodium- \( 21, \frac{21}{11} N a, \) decays to form a new nucleus containing 10 protons and 11 neutrons.

Which leptons are emitted from the
sodium-21 nucleus during the decay?
A. A positron and an antineutrino
B. A positron and a neutrino
c. An electron and an antineutrino
D. An electron and a neutrino
Subject: Physics
The eye can be regarded as a single refracting surface. The radius of this surface is equal to that of cornea (7.8 \( \mathrm{mm} \) ). This surface separates two media of refractive indices 1 and 1.34 . Calculate
the distance from the refracting surface
at which a parallel beam of light will
come to focus.
A . \( 2 \mathrm{cm} \)
B. \( 1 \mathrm{cm} \)
c. \( 3.1 \mathrm{cm} \)
D. 4.0 \( \mathrm{cm} \)
Subject: Physics
The resistance in the two arms of the
meter bridge are \( 5 \Omega \) and \( R \Omega \)
respectively. When the resistance R
is shunted with an equal resistance, the
new balance point is at \( 1.6 l_{1} . \) The
resistance 'R' is
A . \( 10 \Omega \)
В. \( 15 \Omega \)
\( c .20 \Omega \)
D. \( 25 \Omega \)
Subject: Physics
(a) A student suffering from myopia is not able to see distinctly the objects
placed beyond \( 5 m . \) List two possible
reasons due to which this defect of
vision may have arisen. With the help of ray diagrams, explain
(i) why the student is unable to see distinctly the objects placed beyond \( 5 m \) from his eyes.
(ii) the type of the corrective lens used
to restore proper vision and how this defect is corrected by the use of this lens.
(b) If, in this case, the numerical value of the focal length of the corrective lens is \( 5 m \), find the power of the lens as per the new Cartesian sign convention.
Subject: Maths
A bag contains a certain number of
balls, some of which are white;a ball is drawn and replaced, another is then drawn and replaced' and so on. If p be the chance of white balls that is most
likely to have been drawn in n trials. For
\( p=\frac{1}{2} \) and \( n=12, \) the number of white
balls required to be drawn is \( k \). Find the
value of \( k \)
Subject: Physics
toppr
Q Type your question
does this affect the size and intensity of
the central diffraction band?
(b) In what way is diffraction from each
slit related to the interference pattern in a double-slit experiment?
(c) When a tiny circular obstacle is placed in the path of light from a distant source, a bright spot is seen at the centre of the shadow of the obstacle.
Explain why?
(d) Two students are separated by a \( 7 \mathrm{m} \) partition wall in a room \( 10 \mathrm{m} \) high. If both light and sound waves can bend
around obstacles, how is it that the
students are unable to see each other
even though they can converse easily.
(e) Ray optics is based on the assumption that light travels in a straight line. Diffraction effects (observed when light propagates through small apertures/slits or around small obstacles) disprove this assumption. Yet the ray optics assumption is so commonly used in understanding location and several other properties of images in optical instruments. What is the justification?
Subject: Chemistry
What will be the value of \( \Delta G^{o}, \) if the
equilibrium constant of the reaction is 10 at \( 27^{0} C ? \)
A. \( -50.44 \mathrm{kJ} \mathrm{mol}^{-1} \)
B. - 5.744 k \( J \) mol \( ^{-1} \)
c. \( -25.44 \mathrm{kJ} \mathrm{mol}^{-1} \)
D. \( -10 ~ k J \) mol\( ^{-1} \)
Subject: Physics
The intensity at the maximum in a
Young's double slit experiment is \( \boldsymbol{I}_{0} \)
Distance between two slits is \( \boldsymbol{d}=\mathbf{5} \boldsymbol{\lambda} \)
where \( \lambda \) is the wavelength of light used
in the experiment. What will be the intensity in front of one of the slits on
the screen placed at a distance \( D= \)
\( 10 d ? \)
\( \mathbf{A} \cdot I_{0} \)
в. \( \frac{I_{0}}{4} \)
c. \( \frac{3}{4} I_{0} \)
D. \( \frac{I_{0}}{2} \)
Subject: Physics
The time period of a particle executing
\( \boldsymbol{S H} \boldsymbol{M} \) is \( \boldsymbol{8} \boldsymbol{s} . \) At \( \boldsymbol{t}=\boldsymbol{0} \) it is at the mean
position. The ratio of distance covered
by the particle in \( 1^{s t} \) second to the \( 2^{n d} \) second is
A \( \cdot\left(\frac{1}{\sqrt{2}-1}\right) \)
B. \( \sqrt{2} \)
c. \( (\sqrt{2}+1) \)
D. \( \frac{1}{\sqrt{2}} \)
Subject: Chemistry
In corrosion of iron,
A. electrons flow from anode to cathode through the metal, while ions flow through the water droplets
B. an electrochemical (galvanic) cell is formed in which \( F e \) acts as anode and \( O_{2} \) is reduced at cathode
C \( . \) dissolved \( O_{2} \) oxidizes \( F e^{2+} \) to \( F e^{3+} \) before it is
deposited as rust \( \left(F e_{2} O_{3} \cdot x H_{2} O\right) \)
D. All of the above takes place
Subject: Physics
A car (open at the top) of mass \( 9.75 \mathrm{kg} \) is coasting along a level track at 1.36 \( \mathrm{m} / \mathrm{s}, \) when it begins to rain hard. The raindrops fall vertically with respect to the ground. When it has collected 0.5 kg of rain, the speed of the car is
A. \( 0.68 \mathrm{m} / \mathrm{s} \)
B. 1.29 \( \mathrm{m} / \mathrm{s} \)
c. \( 2.48 \mathrm{m} / \mathrm{s} \)
D. \( 9.8 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
When gas (A) is passed through dry
KOH at low temperature, a deep red coloured compound (B) and a gas (C) are obtained. The gas \( A, \) on reaction with but-2-ene, followed by treatment
with \( Z n / H_{2} O \) yields acetaldehyde. \( (A) \)
(B) and
(C) are identified as \( \boldsymbol{O}_{\boldsymbol{x}}, \boldsymbol{K} \boldsymbol{O}_{\boldsymbol{y}} \)
and \( O_{z} . \) What is \( x+y+z ? \)
Subject: Chemistry
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C l} \stackrel{\text {alc.KOH}}{\longrightarrow} \)
\( \frac{B r_{2} / C C l_{4}}{Z n / a l c o h o l i c} C \)
\( C \) is:
A. acetylene
B. ethylene
c. ethane
D. methane
Subject: Chemistry
In which of the following molecule, the number of possible \( \angle X A X \) angles is maximum in the anionic part of their
solid state? \( [\boldsymbol{A}: \text { Central atom, } \boldsymbol{X} \)
surrounding atom]
A. \( P B r_{5} \)
в. \( N_{2} O_{5} \)
c. \( P C l_{5} \)
D. \( C l_{2} O_{6} \)
Subject: Physics
Assertion
Mean free path of a gas molecules varies inversely as density of the gas
Reason
Mean free path varies inversely as
pressure of the gas
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 and Reason is correct
Subject: Biology
Match the names of the parts listed
with the names of the organs.
\begin{tabular}{lll|l} 
List I (Parts) & \multicolumn{3}{c} { List II } \\
& (Organs) & \\
A & Bicuspid valve & p & Brain \\
B & Nephron & q & Liver \\
C & Alveoli & r & Heart \\
D & Cerebrum & s & Kidney \\
& t & Lungs
\end{tabular}
\( \mathbf{A} \)
\( A-r, B-t, C-s, D-R \)
B. \( A-r, B-s, C-t, D-B \)
\( c \cdot A-s, B-q, C-p, D-t \)
D. A-s, B-r, C- p, D-
Subject: Chemistry
Which of the following is true?
This question has multiple correct options
A. A configuration with the maximum spin multiplicity has the minimum energy and thus is most stable
B. The energy of 3d orbital may be grater than or lesser than, equal to that 4 s orbital depending upon the atomic number of the atom
C. All p orbital have the same type of angular dependence irrespective of the value of principal quantum number
\( n \)
D. In a given electrical field, \( \beta \) -particles are deflected more than \( \alpha \) -particles in spite of \( \alpha \) -particles having larger charge
Subject: Physics
In vacuum, to travel distance \( d \), light
takes time \( t \) and in medium to travel \( 5 d \)
it takes time \( T \). The critical angle of the
medium is :
A \( \cdot \sin ^{-1}\left(\frac{5 T}{t}\right) \)
в. \( \sin ^{-1}\left(\frac{5 t}{3 T}\right) \)
\( ^{\mathbf{c}} \cdot \sin ^{-1}\left(\frac{5 t}{T}\right) \)
D. \( \sin ^{-1}\left(\frac{3 t}{5 T}\right) \)
Subject: Physics
The area of the parallelogram whose adjacent sides are \( \overline{\boldsymbol{P}}=\mathbf{3} \overline{\boldsymbol{i}}+\mathbf{4} \overline{\boldsymbol{j}}, \overline{\boldsymbol{Q}}= \)
\( -5 \bar{i}+7 \bar{j} \) is (in sq. units)
A . 20.
B. 82
\( c \cdot 4 \)
D. 46
Subject: Physics
Positive charge q is given to each plate of a parallel plate air capacitor having area of each plate \( A \) and separation between them, d. Then find Energy stored between the plates:
\( ^{A} \cdot \frac{1}{2} \cdot \frac{q^{2}}{C} \)
в. \( \frac{1}{3} \frac{q^{2}}{c} \)
c. \( \frac{1}{2} \cdot \frac{q}{C} \)
D. \( \frac{1}{2} \cdot \frac{q^{3}}{C} \)
E \( \cdot \frac{1}{2} \cdot \frac{q^{4}}{C} \)
Subject: Maths
If \( \frac{\cos (\theta-\alpha)}{\sin (\theta+\alpha)}=\frac{m+1}{m-1}, \) then \( m \) is equal
to
A \( \cdot \tan \left(\frac{\pi}{4}-\theta\right) \tan \left(\frac{\pi}{4}-\alpha\right) \)
B. \( \tan \left(\frac{\pi}{4}-\theta\right) \tan \left(\frac{\pi}{4}+\alpha\right) \)
c. \( \tan \left(\frac{\pi}{4}+\theta\right) \tan \left(\frac{\pi}{4}+\alpha\right) \)
D. \( \tan \left(\frac{\pi}{4}+\theta\right) \tan \left(\frac{\pi}{4}-\alpha\right) \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})=\left[\mathbf{9}^{x}-\mathbf{3}^{x}+\mathbf{1}\right], \boldsymbol{x} \in(-\infty, \mathbf{1}) \)
then number of integers in the range of
\( f(x) \) is (where [.] denotes greatest integer function)
Subject: Maths
The value of \( \left|\begin{array}{cc}\boldsymbol{x} & \boldsymbol{x}-\mathbf{1} \\ \boldsymbol{x}+\mathbf{1} & \boldsymbol{x}\end{array}\right| \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( x \)
\( \mathbf{c} \cdot x^{2} \)
D.
Subject: Chemistry
Equal masses of \( H_{2^{\prime}} O_{2} \) and methane
have been take in a contaier of volume
at temperature \( 27^{\circ} \mathrm{C} \) in identical
conditions. the ratio of the volume of
\( \operatorname{gases} H_{2}: O_{2}: \) methane would be:
A. 8: 16: 1
B . 16: 8: 1
c. 16: 1: 2
D. 8: 1: 2
Subject: Maths
If in the expansion of \( \left(\frac{1}{x}+x \tan x\right)^{5}, \) the ratio of \( 4^{t h} \) term to the \( 2^{n d} \) term is \( \frac{2}{27} \pi^{4} \) then the value of \( x \) can be
A \( \cdot \frac{-\pi}{6} \)
в. \( \frac{-\pi}{3} \)
c.
D. \( \frac{\pi}{12} \)
Subject: Maths
\( \lim _{x \rightarrow 0} \frac{e^{x^{2}}-\cos x}{x^{2}} \) is equal to
A \( \cdot \frac{3}{2} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{2}{3} \)
D. none of these