AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
What should be subtracted from \( 2 a+ \)
\( 6 b-5 \) to get \( -3 a+2 b+3 ? \)
A. \( 5+4 b-8 \)
в. \( 5 a+4 b-8 \)
c. \( 5 a+4 a b-8 \)
D. \( 5 a+4 b-10 \)
Subject: Physics
If a cylinder of diameter \( 1.0 \mathrm{cm} \) at \( 30^{\circ} \mathrm{C} \)
is to be slid into a hole of diameter
\( 0.9997 \mathrm{cm} \) in a steel plate at the same temperature, the minimum required rise in the temperature of the plate is: (Coefficient of linear expansion of \( \left.\operatorname{steel}=12 \times 10^{-6} /^{\circ} C\right) \)
A \( \cdot 25^{\circ} \mathrm{C} \)
В \( \cdot 35^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 45^{\circ} \mathrm{C} \)
D. \( 55^{\circ} \mathrm{C} \)
Subject: Maths
For \( i=1,2,3,4 \) let \( T_{i} \) denote the event
that the students \( S_{i} \) and \( S_{i+1} \) do NOT sit adjacent to each other on the day of the examination. Then the probability of the
event \( \boldsymbol{T}_{\mathbf{1}} \cap \boldsymbol{T}_{\mathbf{2}} \cap \boldsymbol{T}_{\mathbf{3}} \cap \boldsymbol{T}_{\mathbf{4}} \) is?
A \( \cdot \frac{1}{15} \)
в. \( \frac{1}{10} \)
c. \( \frac{7}{60} \)
D.
Subject: Maths
Solution of differential equation
\( \sin y \cdot \frac{d y}{d x}+\frac{1}{x} \cos y=x^{4} \cos ^{2} y \) is
A \( \cdot x \) sec \( y=x^{6}+C \)
B. \( 6 x \) sec \( y=x+C \)
c. \( 6 x \) secy \( =x^{6}+C \)
D. \( 6 x \) sec \( y=6 x^{6}+C \)
Subject: Maths
The point(s) on the curve \( y^{3}+3 x^{2}= \)
\( 12 y \) where the tangent is vertical, is
\( (\operatorname{are}) \)
A \( \cdot\left(\pm \frac{4}{\sqrt{3}},-2\right) \)
B \( \cdot\left(\pm \frac{\sqrt{11}}{3}, 1\right) \)
\( \mathbf{c} \cdot(0,0) \)
D. \( \left(\pm \frac{4}{\sqrt{3}}, 2\right) \)
Subject: Chemistry
I. Oxidizing agents must include
oxygen.
II. Oxygen is a good electron acceptor.
A. Statement \( I \) is true, statement \( I I \) is true and is a correct explanation of the phenomena described in \( I \)
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 \( I I \) is false
Subject: Biology
Arrange the following in descending order of their role in soil erosion.
(i) Wind erosion
(ii) Chemical degradation
(ii) Physical degradation
(iv) Water erosion
\( \mathbf{A} \cdot \mathbf{i}, \) i, i ii, iv
B. iv, i, ii, iii
c. iv , iii, ii, i
D. iv, ii, iii, i
Subject: Physics
If the angular distance between the
stars turns out to be approximately 1100
arcseconds, or 0.30 degrees. The moon
appears to shift 0.3 degrees when we
observe it from two vantage points 2360
\( \mathrm{km} \) apart, then find the distance of the
moon from the surface of the
earth.Given angular diameter of moon
is 0.5 degrees.
A. \( 450642 \mathrm{km} \)
B. 450392 km
\( c .325684 \mathrm{km} \)
D. \( 480264 \mathrm{km} \)
Subject: Physics
If an electron in hydrogen atom jumps from an orbit of level \( n=3 \) to an orbit of
level \( n=2 \), emitted radiation has a
frequency (R=Rydberg's constant, C=velocity of light)
\( ^{A} \cdot \frac{3 R C}{27} \)
в. \( \frac{R C}{25} \)
c. \( \frac{8 R C}{9} \)
D. \( \frac{5 R C}{36} \)
Subject: Maths
Area bounded by the curve \( y^{2}(2 a- \)
\( x)=x^{3} \) and the line \( x=2 a \), is
A \( .3 \pi a^{2} \)
B. \( \frac{3 \pi a^{2}}{2} \)
c. \( \frac{3 \pi a^{2}}{4} \)
D. \( \frac{\pi a^{2}}{4} \)
Subject: Physics
A body is thrown up with velocity \( u \) to
reach a height \( h \). When the velocity is half the initial velocity, its height from the point of projection is:
A \( \cdot \frac{h}{2} \)
B. \( \frac{h}{4} \)
\( c \cdot \frac{3 h}{4} \)
\( D \)
Subject: Physics
When a star of mass \( 9 \times 10^{30} \) kg ends
as a black hole, the
Schwarzschild radius of the star is
\( \left(G=6.7 \times 10^{-11} \mathrm{Nm}^{2} \mathrm{kg}^{-2}\right) \)
A . \( 13.4 \mathrm{m} \)
B. 6.7 \( m \)
\( c \cdot 13.4 \mathrm{km} \)
D. \( 26.8 \mathrm{km} \)
Subject: Maths
n the figure \( D \) and \( E \) are the mid-
points of sides \( A B \) and \( A C \) respectively
of \( \Delta A B C . \) Find \( \angle E D B \)
A \( .110^{\circ} \)
B . \( 120^{\circ} \)
\( c \cdot 70 \)
\( D \cdot 80 \)
Subject: Physics
Position -time(x-t) grapg of a particle
moving along \( x \) -axis is as shown in the figure.The average speed of particle in
time interval \( t=0 \) to \( t=10 s \) is
\( \mathbf{A} \cdot 2 m s^{-1} \)
в. \( \frac{4}{5}^{m s^{-1}} \)
\( \mathbf{c} \cdot 1 m s^{-1} \)
D. \( \frac{5}{4} m s^{-} \)
Subject: Chemistry
Ammonium carbamate when heated to
\( 200^{0} C \) gives a mixture of \( N H_{3} \) and
\( C O_{2} \) with a vapour density of \( 13 . \) What is the degree of dissociation of
ammonium carbamate?
A \( \cdot \frac{3}{2} \)
B \( \cdot \frac{1}{2} \)
\( c \cdot 2 \)
D. 1
Subject: Chemistry
Assertion
Insulin is a globular protein.
Reason
It has two polypeptide chains with 21
and 30 amino acids joined by sulphur
bridges connecting cysteine amino acid
on the two chains.
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 plano convex lenses of focal lengths
\( f_{1} \) and \( f_{2} \) set for minimising spherical aberration are kept apart by \( 2 \mathrm{cm} \). If the equivalent focal length of combination
is \( 10 \mathrm{cm}, \) the values of \( f_{1} \) and \( f_{2} \) are :
A. \( 18 \mathrm{cm}, 16 \mathrm{cm} \)
в. \( 18 \mathrm{cm}, 20 \mathrm{cm} \)
c. \( 20 c m, 22 c m \)
D. \( 14 \mathrm{cm}, 20 \mathrm{cm} \)
Subject: Chemistry
Which one is the oxidising agent in the reaction given below? \( \mathbf{2} \boldsymbol{C r} \boldsymbol{O}_{\mathbf{4}}^{2-}+\mathbf{2} \boldsymbol{H}^{+} \rightarrow \boldsymbol{C r}_{2} \boldsymbol{O}_{\mathbf{7}}^{2-}+\boldsymbol{H}_{2} \boldsymbol{O} \)
A . \( H^{+} \)
в. \( C r_{2} O_{7}^{-2} \)
\( c \cdot C r^{2} \)
D. None
Subject: Physics
If a star converts all of its Helium into
Oxygen nucleus, find the amount of
energy released per nucleus of Oxygen. \( (H e=4.0026 a m u \)
\( \boldsymbol{O}=\mathbf{1 5 . 9 9 9 4} \boldsymbol{a m u} \)
A. \( 7.26 \mathrm{MeV} \)
B. 7 MeV
c. 10.24 MeV
D. \( 5.12 \mathrm{MeV} \)
Subject: Chemistry
1
11
\( \left\{\begin{array}{l}= \\ \frac{1}{4}\end{array}\right. \)
\( \mid \begin{array}{c}- \\ + \\ ++\end{array}+ \)
\( -\quad- \)
\( \quad+\frac{j}{+} \)
\( \left\{\begin{array}{l}-- \\ ++++++\end{array}\right. \)
Subject: Chemistry
In the leaching of \( A g_{2} S \) with \( \mathrm{NaCN} \), a
stream of air is also passed. It is
because of:
A. Reversible nature of reaction between \( A g_{2} S \) and NaCN
B. To oxide \( N a_{2} S \) formed into \( N a_{2} S_{2} O_{3} \) and sulphur
c. Both (A) and (B)
D. None of the above
Subject: Chemistry
In the Leibigs method, if \( w \) is the mass of compound taken and \( x \) is the amount
of \( C O_{2} \) formed then
\( \mathbf{A} \cdot \% C=\frac{12 \times x}{16 \times w} \)
B . \% \( C=\frac{12}{44} \times \frac{w}{x} \times 100 \)
C \( \cdot \) \% \( C=\frac{12}{44} \times \frac{x}{w} \times 100 \)
D・\% \( C=\frac{12}{44} \times \frac{x}{w} \)
Subject: Physics
In which direction from \( \beta \) Saptarish (or
Ursa Major or Great Bear) shown in the
figure, do we search for Pole star?
\( A \cdot \alpha \) to \( \beta \)
B. \( \gamma \) to \( \delta \)
\( c \cdot \beta \) to \( \alpha \)
D. \( \delta \) to \( \gamma \)
Subject: Maths
An automobile dealer provides motor
cycles and scooters in three body
patterns and 4 different colours each The number of choices open to
a customer is
\( A \cdot^{5} C_{3} \)
в. \( ^{4} C_{3} \)
c. \( 4 \times 3 \)
D. \( 4 \times 3 \times 2 \)
Subject: Physics
Q Type your question
chord is attached to the object through
this hole The object is set into motion
with initial velocity of magnitude \( v_{0} \) at
right angle to the chord and at tehsame
time the chord is pulled through the
hole at uniform speed c m/s. Initially
object is at point \( \mathbf{A}\left(0, r_{0}\right) \) and at any
time I it is at point \( P(r \cos \theta, r \sin \theta) \)
Neglect the dimension of object Choose
CORRECT options(s)
This question has multiple correct options
A \( \cdot \) tension in the chord at any time t is \( \frac{m r_{0}^{2} v_{0}^{2}}{\left(r_{0}-c t\right)^{3}} \)
B. Tension in the chord at any time t is \( \frac{2 m_{0}^{2} v_{0}^{2}}{\left(r_{0}-c t\right)^{2}} \)
Condar speed of the object at any time is \( \frac{2 r_{0} v_{0}}{\left(r_{0}-c t\right)^{2}} \)
D. Angular speed of the object at any time t is \( \frac{r_{0} v_{0}}{\left(r_{0}-c t\right)^{2}} \)
Subject: Physics
The position vector of a particle is determined by the expression \( \vec{r}= \) \( 3 t^{2} \hat{i}+4 t^{2} \hat{j}+7 \hat{k}, \) The distance
traversed in first 10 sec is
\( \mathbf{A} \cdot 500 m \)
B. \( 300 m \)
\( c \cdot 150 m \)
D. \( 100 m \)
Subject: Chemistry
A \( 100 m L, 0.1 M \) solution of ammonium acetate is diluted by
adding \( 100 m L \) of water. The pH of the
resulting solution will be \( \left(p K_{a} \) of acetic \right.
acid is nearly equal o \( \left.p K_{b} \text { of } N H_{4} O H\right) \)
A . 4.9
B. 5.0
c. 7.0
D. 10.0
Subject: Physics
If the velocity of sound in a gas is 360 \( \mathrm{m} / \mathrm{s} \) and the distance between
compression and the nearest rarefraction is \( 1 \mathrm{m} \), then the frequency of sound is
\( A \cdot 90 \mathrm{Hz} \)
в. 180 Н \( z \)
c. 360 нz
D. 720 нz
Subject: Chemistry
\( \mathbf{N} i(p y)_{4}\left(C l O_{4}\right)_{2} \) exists in a yellow
diamagnetic form containing the cation
\( \left[N i(p y)_{4}\right]^{2+} \) and \( C l O_{4}^{-} \) icons, and in a blue paramagnetic form containing
\( \operatorname{trans}\left[N i(p y)_{4}\left(C l O_{4}\right)_{2}\right] \) molecules in
which oxygen atoms form the \( \mathrm{Cl} \mathrm{O}_{4} \)
icons completed the octahedral coordination of the metal ion. The
hybridisation of nickel in the yellow \( \& \) blue complexes respectively are:
A \( \cdot s p^{3} \) and \( d^{2} s p^{3} \)
B. \( d s p^{2} \) and \( d^{2} s p^{3} \)
C \( \cdot d s p^{2} \) and \( s p^{3} d^{2} \)
D. \( s p^{3} \) and \( s p^{3} d^{2} \)
Subject: Chemistry
A gas with formula \( C_{n} H_{2 n+2} \) diffuses
through the porous plug at a rate onesixth of the rate of diffusion of hydrogen gas under similar conditions. The
formula of gas is?
A. \( C_{2} H_{6} \)
в. \( C_{10} H_{22} \)
c. \( C_{5} H_{12} \)
D. \( C_{6} H_{14} \)
Subject: Chemistry
Metal X form 2 oxide. Formula of 1 \( ^{s t} \) is
\( X O_{2} 1^{s t} \) oxide contain \( 50 \% O_{2} . \) If \( 2^{n d} \)
oxide contain \( 60 \% O_{2} \). Formula of \( 2^{n d} \)
oxide?
A. \( X_{2} O \)
в. \( X O_{3} \)
\( c \cdot X_{2} O_{3} \)
D. \( X_{3} O_{2} \)
Subject: Physics
A man travels along a straight line. He covers the first half distance with
constant velocity \( v_{1} \) and the next half
distance with constant velocity \( v_{2} . \) The average velocity of man will be :
A \( \cdot \frac{v_{1}+v_{2}}{2} \)
B. \( v=\frac{2 v_{1} v_{2}}{v_{1}+v_{2}} \)
\( \mathbf{c} \cdot\left(v_{1} v_{2}\right)^{1 / 2} \)
D \( \cdot\left(\frac{v_{2}}{v_{1}}\right)^{1 / 2} \)
Subject: Maths
If \( \boldsymbol{x}=\mathbf{1}+\mathbf{2} \boldsymbol{i} \) and \( \boldsymbol{A}=\boldsymbol{x}^{\mathbf{3}}+\mathbf{7} \boldsymbol{x}^{\mathbf{2}}-\boldsymbol{x}+ \)
\( 26, \) then one of the value of \( \sqrt{A} \) equals
A \( .4-3 i \)
B. \( 3-4 i \)
\( c .-3+4 i \)
D. \( 3+4 i \)
Subject: Physics
f \( r_{2}=3 r_{1} \) and time period of revolution
for \( B \) be \( T \) than time taken by \( A \) in
moving from position 1 to position 2 is :
\( ^{A} \cdot \frac{\sqrt{3}}{\sqrt{2}} \)
3. \( T \frac{\sqrt{3}}{2} \)
c. \( \frac{T \sqrt{2}}{3 \sqrt{3}} \)
D. \( \frac{T \sqrt{2}}{3} \)
Subject: Maths
Let \( \boldsymbol{E}, \boldsymbol{F}, \boldsymbol{G} \) be pairwise independent events with \( P(G)>0 \) and \( P(E \cap F \cap \)
\( G)=0 . \) Then \( P\left(E^{\prime} \cap F^{\prime} \mid G\right) \) equals
\( \mathbf{A} \cdot P\left(E^{\prime}\right)+P\left(F^{\prime}\right) \)
B . \( P\left(E^{\prime}\right)-P\left(F^{\prime}\right) \)
c. \( P\left(E^{\prime}\right)-P(F) \)
D. \( P(E)-P\left(F^{\prime}\right) \)
Subject: Physics
Two point charges in air at a distance
of \( 20 c m . \) from each other interact with a
certain force. At what distance from
each other should these charges be placed in oil of relative permittivity 5 to obtain the same force of interaction
A. \( 8.94 \times 10^{-2} \mathrm{m} \)
В. \( 0.894 \times 10^{-2} \mathrm{m} \)
\( c \cdot 89.4 \times 10^{-2} m \)
D. \( 8.94 \times 10^{2} m \)
Subject: Chemistry
Assertion
Two different reactions can never have
same rate of reaction.
Reason
Rate of reaction always depends only on
frequency of collision and Arrhenius
factor.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
Assertion
Derivative of \( \frac{x^{n}-a^{n}}{x-a} \) for some
constant \( n \) is
\( \frac{(n-1) x^{n}-n a x^{n-1}+a^{n}}{(x-a)^{2}} \)
Reason \( \frac{\boldsymbol{d}}{\boldsymbol{x}}\left(\frac{\boldsymbol{u}}{\boldsymbol{v}}\right)=\frac{\boldsymbol{u}^{\prime} \boldsymbol{v}-\boldsymbol{u} \boldsymbol{v}^{\prime}}{\boldsymbol{v}^{2}} \)
where \( u \) and \( v \) are two distinct
functions.
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 value of the determinant \( \Delta=\left|\begin{array}{ccc}1 ! & 2 ! & 3 ! \\ 2 ! & 3 ! & 4 ! \\ 3 ! & 4 ! & 5 !\end{array}\right| \) is
A . 2
в. 3
\( c \cdot 4 \)
D. 5
Subject: Chemistry
The standard reduction potential \( E^{\circ} \) for half reaction are:
\( Z n \rightarrow Z n^{2+}+2 e^{-} ; E^{o}=+0.76 V \)
\( \boldsymbol{F e} \rightarrow \boldsymbol{F} \boldsymbol{e}^{2+}+\boldsymbol{2} \boldsymbol{e}^{-} ; \boldsymbol{E}^{o}=+\boldsymbol{0 . 4 1} \boldsymbol{V} \)
The EMF of the cell reaction is:
\( \boldsymbol{F} \boldsymbol{e}^{2+}+\boldsymbol{Z} \boldsymbol{n} \rightarrow \boldsymbol{Z} \boldsymbol{n}^{2+}+\boldsymbol{F} \boldsymbol{e} \)
A. \( -0.35 V \)
в. \( +0.35 V \)
\( \mathrm{c} \cdot+1.17 V \)
D. -1.17V
Subject: Chemistry
Iron fillings and water are placed in a 5 litre vessel and sealed. The tank was
heated to \( 1000^{\circ} \mathrm{C} \). Upon analysis the
tank was found to contain \( 1.1 g \) of
hydrogen and \( 42.5 g \) of water vapour. If the reaction in the tank is represented by
\( 3 F e(s)+4 H_{2} O(g) \rightleftharpoons F e_{3} O_{4}(s)+ \)
\( 4 H_{2}(g) \)
the value of equilibrium constant, \( \boldsymbol{K}_{c} \) is
A . 30
B. 0.03
\( c .3 \)
D. 0.003
Subject: Maths
6 married couples are standing in a
room. If 4 people are chosen at random, then the chance that exactly one
married couple is among the 4 is?
A \( \cdot \frac{16}{33} \)
в. \( \frac{8}{33} \)
c. \( \frac{17}{33} \)
D. \( \frac{24}{33} \)
Subject: Maths
\( \mathbf{f} \mathbf{A}=\left[\begin{array}{ccc}\mathbf{0} & \mathbf{1} & \mathbf{4} \\ \mathbf{- 1} & \mathbf{0} & \mathbf{7} \\ \mathbf{- 4} & \mathbf{- 7} & \mathbf{0}\end{array}\right] \) then \( \mathbf{A}^{\mathbf{T}}= \)
\( A \)
в. - А
\( c \)
D. \( A^{2} \)
Subject: Maths
Calculate mean deviation about
median
\begin{tabular}{lllll} 
Scores & 145 & 155 & 165 & 175 \\
Frequency & 4 & 6 & 10 & 18 \\
\hline
\end{tabular}
A. 11.56
B. 6.66
c. 11.25
D. 10.56
Subject: Chemistry
When \( A g N O_{3} \) was treated with \( 5.08 g \) of a sample iron chloride, \( 11.48 g \) pf \( \mathrm{AgCL} \) was formed \( 6.51 g \) of another iron chloride gave \( 17.22 g \) of \( A g C l \) on
treatment with \( A g N O_{3} . \) Show that
these results illustrate the law of
multiplle proportions. [R.A.M. \( A g=108, F e=56 \text { and } C l=35.5] \)
Subject: Biology
Assertion
According to the Medical Termination of
Pregnancy act of \( 2017, \) pregnancy may be terminated on certain considered
grounds within the first 12 weeks of
pregnancy on the opinion of one registered medical practitioner.
Reason

The continuation of the pregnancy
would involve a risk to the life of the
pregnant woman or of grave injury of physical or mental health.
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 geo-stationary satellite is orbiting around earth at height of \( 30,000 \mathrm{km} \) in circular orbit. The radius of the earth is
taken as \( 6000 \mathrm{km} . \) The geo-stationary satellite comes back to its position
after one revolution in exactly 24 hours.
Let the acceleration due to gravity \( (g) \) \( 10 m / s^{2} \) and mass of satellite be 1000
kg; calculate the work done in 12 hours when moving under gravitational force.
A \( \left..3 .6 \pi \times 10^{14}\right\rfloor \)
В \( \cdot 2 \pi \times 7.2 \pi \times 10^{14} \)
C \( .1 .8 \pi \times 10^{14} \mathrm{J} \)
D. 0
Subject: Physics
In Fig. voltmeter is not ideal. If the
voltmeter is removed from \( \boldsymbol{R}_{1} \) and then
put across \( R_{2}, \) what will be the effect on
current I? Given \( \boldsymbol{R}_{1}>\boldsymbol{R}_{2} \)
This question has multiple correct options
A . decreases
B. remains same
\( c \). increases
D. it would have been same if voltmeters were idea
Subject: Maths
The locus of the feet of perpendiculars drawn from the point \( (a, 0) \) on tangents
to the circle \( x^{2}+y^{2}=a^{2} \) is
A \( \cdot a^{2}\left(x^{2}+y^{2}+a x\right)^{2}=a^{2}\left(y^{2}+(x+a)^{2}\right) \)
B \( \cdot a^{2}\left(x^{2}+y^{2}-a x\right)^{2}=y^{2}+(x-a)^{2} \)
C \( \cdot\left(x^{2}+y^{2}-a x\right)^{2}=a^{2}\left(y^{2}+(x-a)^{2}\right) \)
D \cdot a \( ^{2}\left[\left(x^{2}+y^{2}\right)-a^{2} x^{2}\right]=\left(y^{2}+(x-a)^{2}\right) \)
Subject: Physics
The pressure applied from all directions
on a cube is \( p . \) How much its
temperatures should be raised to maintain the original volume? The
volume elasticity of the cube is \( \beta \) and
the coefficient of volume expansion is \( \alpha \)
A \( \cdot \frac{p}{\alpha \beta} \)
B. \( \frac{p \alpha}{\beta} \)
\( c \cdot \frac{p \beta}{\alpha} \)
D. \( \frac{\alpha \beta}{p} \)
Subject: Physics
A body starts moving with a velocity \( v_{0}=10 m s^{-1} . \) It experiences a retardation equal to \( \frac{1}{5} v^{2} \). Its velocity after \( 2 s \) is given by
\( \mathbf{A} \cdot-3.33 m s^{-1} \)
B. \( +4 m s^{-1} \)
c. \( +3.33 m s^{-1} \)
D. \( +6 m s^{-1} \)
Subject: Physics
A person has a \( 18 \mathrm{cm} \) wide face and his
two eyes are separated by \( 8 \mathrm{cm} . \) Find the minimum width of a mirror required for the person to view is face laterally is
A. \( 9 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
\( c .5 \mathrm{cm} \)
D. \( 13 \mathrm{cm} \)
Subject: Chemistry
Consider a certain reaction \( \boldsymbol{A} \rightarrow \)
Products with, \( k=2.0 \times 10^{-2} s^{-1} \)
Calculate the concentration of \( \mathbf{A} \)
remaining after 100 s, if the initial
concentration of \( A \) is \( 1.0 m o l L^{-1} \)
Subject: Maths
The point of intersection of the lines \( \frac{x-5}{3}=\frac{y-7}{-1}=\frac{z+2}{1} \) and \( \frac{x+3}{-36}= \)
\( \frac{y-3}{2}=\frac{z-6}{4} \) is
A \( \cdot\left(21, \frac{5}{3}, \frac{10}{3}\right) \)
в. (2,10,4)
c. (-3,3,6)
D. (5,7,-2)
Subject: Physics
Match the following
¡.
a. Back surface of eye where image is Cornea formed
ii. Pupil
b. Coloured part of eye
iii.
c. Membrane that refracts light and Retina protects the eye
¡V. Iris
d. Transparent opening of eye.Light passes through it
\( A \cdot \) i-c ,ii-d,iii-a,iv-b
B. i-a,ii-c,iii-b,iv-d
C . i-d,ii-a,iii-b,iv-c
D. i-b,ii-c,iii-d,iv-a
Subject: Physics
Three point charges \( -q, q \) and \( Q \) are arranged as given in figure:

If \( d \) is distance from centre of \( -q \) and \( +\boldsymbol{q} \) to \( \boldsymbol{Q} \) and \( \boldsymbol{d}>>>\boldsymbol{a}, \) then the
potential energy of given system is:
\[
\mathbf{q}
\]
\( A \)
\[
\left(\frac{k q Q a}{d^{2}}\right)
\]
в.
\[
\left(\frac{+k q^{2}}{a}+\frac{k q Q a}{d^{2}}\right)
\]
c.
\[
\left(\frac{-k q^{2}}{a}+\frac{k q Q a}{2 d^{2}}\right)
\]
D.
\[
\left(\frac{-k q^{2}}{a}+\frac{k q Q a}{d^{2}}\right)
\]
Subject: Chemistry
According to Kohlrausch law, the limiting value of molar conductivity of
an electrolyte \( A_{2} B \) is:
\( \mathbf{A} \cdot \Lambda_{A}^{\infty}+\Lambda_{B}^{\infty} \)
B \( \cdot \Lambda_{A}^{\infty}-\Lambda_{B}^{\infty} \)
\( \mathbf{C} \cdot \Lambda_{A}^{\infty}+\frac{1}{2} \Lambda_{B}^{\infty} \)
\( \mathbf{D} \cdot 2 \Lambda_{A}^{\infty}+\Lambda_{B}^{\infty} \)
Subject: Maths
The solution of \( (s e c \boldsymbol{\theta}+1)=(2+ \) \( \sqrt{3}) \tan \theta(0<\theta<2 \pi) \) are
\( \mathbf{A} \cdot \pi / 6, \pi \)
в. \( \pi / 3, \pi / 4 \)
c. \( \pi / 6,2 \pi / 3 \)
D. none of these
Subject: Physics
and \( B \) inside a sphere of radius \( R . A \)
small ball slips along wire. The time
taken by the ball to slip from \( \boldsymbol{A} \) to \( \boldsymbol{B} \) will
be:
A \( \frac{2 \sqrt{g r}}{g \cos \theta} \)
\( \frac{2 \sqrt{g R \cos \theta}}{g} \)
\( \mathbf{c} \cdot 2 \sqrt{R / g} \)
D. \( \frac{g R}{\sqrt{g \cos \theta}} \)
Subject: Chemistry
Emission transitions in the Paschen
series end at orbit \( n=3 \) and start from
orbit \( n \) and can be represented as \( v= \)
\( \mathbf{3} . \mathbf{2 9} \times \mathbf{1 0}^{\mathbf{1 5}}(\mathbf{H z})\left[\mathbf{1} / \mathbf{3}^{\mathbf{2}}-\mathbf{1} / \mathbf{n}^{\mathbf{2}}\right] \)
Calculate the value of \( n \) if the transition
is observed at 1.285 nm. Find the region
of the spectrum.
Subject: Chemistry
Assertion
\( I O_{3}^{-} \) is reduced to \( I^{+} \) but intermediate
gives violet color in \( C C I_{4} \) (taken as
medium).
Reason
\( I_{2} \) is formed as the intermediate
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: Chemistry
Assertion
Red phosphorus is less reactive than
yellow phosphorus.
Reason
Red phosphorus is insoluble in \( C S_{2} \) whereas white phosphorus is soluble.
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
Assertion (A): The points on the curve
\( y=x^{3}-3 x \) at which the tangent is
parallel to \( x \) -axis are (1,-2) and (-1,2)
Reason (R): The tangent at \( \left(x_{1}, y_{1}\right) \) on the curve \( y=f(x) \) is vertical then \( \frac{d y}{d x} \)
\( \operatorname{at}\left(x_{1}, y_{1}\right) \) is not defined
A. Both A and R are true and R is the correct explanation for A
B. Both A and R are true but R is not the correct explanation for \( A \)
C. A is true but R is false
D. A is false but R is true
Subject: Physics
Calculate the ratio of the speed of sound in neon to that in water vapour at any temperature. Given that molecular
weight of neon gas \( =2.02 \times \)
\( 10^{-2} k g m o l e^{-1} \) and molecular weight of
watervapour \( =1.8 \times 10^{-2} \) kgmole \( ^{-1} \)
A .0 .944
B. 1.944
c. 2.944
D. 3.944
Subject: Maths
Evaluate the following:
i. \( \sin \left(\cot ^{-1} x\right) \)
ii. \( \sin \left(\frac{\pi}{2}-\sin ^{-1}\left(-\frac{\sqrt{3}}{2}\right)\right) \)
\( ^{\mathbf{A}} \cdot(\mathrm{i}) \frac{1}{\sqrt{x^{2}+1}},(\mathrm{ii}) \frac{1}{2} \)
B. \( \quad(i) \frac{1}{\sqrt{x^{2}-1}},\left(\text { ii) } \frac{-\sqrt{3}}{2}\right. \)
\( c \cdot(i) \frac{-1}{\sqrt{x^{2}+1}},\left(\text { ii) } \frac{1}{2}\right. \)
D. \( \left(\text { i) } \frac{-1}{\sqrt{x^{2}-1}} \text { , (ii) } \frac{+\sqrt{3}}{2}\right. \)