AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
When \( K M n O_{4} \) act as an oxidising agent and ultimately form \( M n O_{4}^{2-}, M n O_{2}, M n_{2} O_{3} \) and \( M n^{2+} \)
then the numbers of electrons
transferred in each case, respectively,
are :
A .4,3,1,5
B. 1, 5, 3, 7
\( c \cdot 1,3,4,5 \)
D. 3, 5, 7,
Subject: Maths
If \( a, b, c \) are in G.P., then
A \( \cdot a^{2}, b^{2}, c^{2} \) are in G.P.
B . \( a^{2}(b+c), c^{2}(a+b), b^{2}(a+c) \) are in G.P.
c. \( \frac{a}{b+c}, \frac{b}{c+a}, \frac{c}{a+b} \) are in G.P
D. None of the above.
Subject: Maths
If the volume of a cube is \( 3 \sqrt{3} a^{3} \) then
total surface area of the cube is
A \( \cdot 6 a^{2} \)
B . \( \sqrt{3} a^{2} \)
\( c \cdot 18 a^{2} \)
D. \( 6 \sqrt{3} a^{2} \)
Subject: Physics
Half life of a radio active element is 5
min 10 sec. Time taken for \( 90 \% \) of it to
disintegrate is nearly This question has multiple correct options
A. 100 min
B. 1000 sec
\( \mathrm{c} \cdot 10^{4} \mathrm{sec} \)
D. \( 10^{4} \) min
Subject: Maths
f \( y=m x \) be the equation of a chord of
a circle whose radius is \( a \), the origin of
coordinates being one extremity of the
chord and the axis of \( x \) being a diameter of the circle, prove that the equations of a circle of which this chord is the diameter is \( \left(1+m^{2}\right)\left(x^{2}+y^{2}\right)- \)
\( \mathbf{2} \boldsymbol{a}(\boldsymbol{x}+\boldsymbol{m} \boldsymbol{y})=\mathbf{0} \)
Subject: Maths
What is the volume in cubic cm of a
pyramid whose area of the base is
25 sq cm height \( 9 c m ? \)
A \( \cdot 75 \mathrm{cm}^{3} \)
B. \( 70 \mathrm{cm}^{3} \)
\( \mathrm{c} \cdot 100 \mathrm{cm}^{3} \)
D. None of these
Subject: Chemistry
In three test tubes \( A, B \) and \( C, \) three
different liquids namely, distilled water, underground water and distilled water in which a pinch of calcium sulphate is dissolved, respectively are taken. An equal amount of soap solution is added
to each test tube and the contents are
shaken. In which test tube will the
ength of the foam (lather) be longest?
Justify your answer.
Subject: Chemistry
A hydrogen electrode placed in a buffer
solution of \( \mathrm{CH}_{3} \mathrm{COONa} \) and acetic acid
in the ratio's \( x: y \) and \( y: x \) has reduction electrode potential values \( \mathrm{E}_{1} \) volt and \( \mathrm{E}_{2} \)
volt respectively at \( 25^{\circ} \mathrm{C} \). The \( \mathrm{pK}_{a} \) values
of acetic acid is \( \left(\mathrm{E}_{1} \text { and } \mathrm{E}_{2} \) are oxidation \right.
potential):
A. \( \frac{E_{1}+E_{2}}{0.118} \)
в. \( \frac{E_{2}-E_{1}}{0.118} \)
c. \( -\frac{E_{1}+E_{2}}{0.118} \)
D. \( -\frac{E_{2}-E_{1}}{0.118} \)
Subject: Physics
Given that \( P \) is a point on a wheel rolling on a horizontal ground. The radius of the wheel is \( R \). Initially if the point \( P \) is
in contact with the ground, the wheel rolls through half revolution. What is the displacement of point \( P ? \)
B. \( R \sqrt{\pi^{2}+4} \)
\( c . \pi R \)
D. \( 2 \pi R \)
Subject: Physics
A proton (mass \( 1.67 \times 10^{-27} \mathrm{kg} \) ) on striking a neutron (mass nearly equal to the proton ) forms a deutron. What would be the velocity of the deutron if it is formed by a proton moving left with a velocity of \( 7.0 \times 10^{6} \mathrm{m} / \mathrm{s} \) and a neutron
moving right with a velocity of \( 4.0 \times 10^{6} \) \( \mathrm{m} / \mathrm{s} \)
Subject: Physics
A car is moving on a circular track of radius \( R \). The road is banked at \( \theta . \mu \) is the coefficient of friction. Find the
maximum speed the car can have.
\( \mathbf{A} \cdot\left[\frac{R g(\sin \theta+\mu \cos \theta)}{\cos \theta+\mu \sin \theta}\right]^{1 / 2} \)
B. \( \left[\frac{R g(\cos \theta+\mu \sin \theta)}{\cos \theta-\mu \sin \theta}\right]^{1 / 2} \)
\( ^{\mathbf{C}} \cdot\left[\frac{R g(\sin \theta+\mu \cos \theta)}{\cos \theta-\mu \sin \theta}\right]^{1 / 2} \)
D. None
Subject: Physics
The error in the measurement of length
of a simple pendulum is \( 0.1 \% \) and error in the time period is \( 2 \% \). The possible maximum error in the quantity having dimensional formula \( L T^{-2} \) is
A . \( 1.1 \% \)
в. \( 2.2 \% \)
c. \( 4.1 \% \)
D. 6.1\%
Subject: Maths
Solve the following differential
equations:
\( \boldsymbol{x} \boldsymbol{d} \boldsymbol{x}+\boldsymbol{y} \boldsymbol{d} \boldsymbol{y}=\boldsymbol{x} \boldsymbol{d} \boldsymbol{y}-\boldsymbol{y} \boldsymbol{d} \boldsymbol{x} \)
A \( \cdot \ln \left(x^{2}+y^{2}\right)=2 \tan ^{-1}\left(\frac{y}{x}\right)+c \)
B \cdot \( \ln (x+y)^{2}=2 \tan ^{-1}\left(\frac{y}{x}\right)+c \)
c. \( \ln \left(x^{2}+y^{2}\right)=2 \tan ^{-1}\left(\frac{x}{y}\right)+c \)
D \( \cdot \ln (x+y)^{2}=2 \tan ^{-1}\left(\frac{x}{y}\right)+c \)
Subject: Physics
A capacitor acquires a potential
difference of \( 200 \mathrm{V} \) when \( 10^{12} \) electrons
are taken from one plate and placed
on the other plate. Its capacitance is:
A \( \cdot 2 \times 10^{-10} F \)
В. \( 4 \times 10^{-10} F \)
c. \( 8 \times 10^{-10} F \)
D. \( 12 \times 10^{-10} F \)
Subject: Physics
\( x \)
a small block is projected along it's
length with velocity \( v \) towards front.
Coefficient of restitution for each
collision is \( e . \) The cart rests on a smooth
ground and can move freely. The time
taken by block to come to rest w.r.t. cart
is :
A \( \cdot \frac{e d}{(1-e) v} \)
B. \( \frac{e d}{(1+e) v} \)
\( c \cdot d \)
\( \bar{e} \)
D. infinite
Subject: Chemistry
A compound having the empirical
formula \( C_{3} H_{4} O, \) has a molecular
weight of \( 170 \pm 5 . \) The molecular
formula of the compound is:
A. \( C_{3} H_{4} O \)
в. \( C_{6} H_{8} O_{2} \)
\( \mathbf{c} \cdot C_{6} H_{12} O_{3} \)
D. \( C_{9} H_{12} O_{3} \)
Subject: Physics
In going from one city to another, a car travels \( 75 k m \) north, \( 60 k m \) north-west and \( 20 k m \) east. The magnitude of
displacement between the two cities is (take \( \sqrt{\mathbf{2}}=\mathbf{0 . 7}) \)
A. \( 170 k m \)
в. \( 137 k m \)
c. \( 119 k m \)
D. \( 140 k m \)
Subject: Chemistry
Which of the following order regarding acidity of the following compounds is correct?
A. \( R O H>H C \equiv C H>N H_{3} \)
B. \( R O H<H C \equiv C H<N H_{3} \)
c. \( R O H>H C \equiv C H<N H_{3} \)
D. \( R O H<H C \equiv C H>N H_{3} \)
Subject: Chemistry
At \( 25^{\circ} \mathrm{C} \) molar conductance of 0.1 molar
aqueous solution of an ammonium
hydroxide is 9.54 oh \( m^{-1} c m^{2} \) mol \( ^{-1} \) and
at infinite dilution its molar
conductance is 238 oh \( m^{-1} c m^{2} m o l^{-1} \)
The degree of ionization of ammonium hydroxide at the same concentration
and temperature is?
Subject: Physics
Three uniform spheres, each having mass \( \mathrm{m} \) and radius \( \mathrm{r}, \) are kept in such a way that each touches the other two.
The magnitude of the gravitational
force on any sphere due to the other two is?
A \( \cdot \frac{G m^{2}}{r^{2}} \)
в. \( \frac{G m^{2}}{4 r^{2}} \)
c. \( \sqrt{2} \frac{G m^{2}}{4 r^{2}} \)
D. \( \sqrt{3} \frac{G m^{2}}{4 r^{2}} \)
Subject: Physics
A linear object of size \( 1.5 \mathrm{cm} \) placed at \( 10 \mathrm{cm} \) from a lens of focal length \( 20 \mathrm{cm} \)
The optic centre of lens and the object
are displaced a distance \( \Delta=0.5 \mathrm{cm} \) as
shown in the figure. The magnification
of the image formed is \( \mathrm{m} \) (Take optic centre as origin). The coordinates of
image of \( A \) and \( B \) are \( \left(x_{1}, y_{1}\right) \) and
\( \left(x_{2}, y_{2}\right) \) respectively. Then

This question has multiple correct options
A \( \cdot\left(x_{1}, y_{1}\right)=(-20 c m,-1 c m) \)
в. \( \left(x_{2}, y_{2}\right)=(-20 c m, 2 c m) \)
\( \mathrm{c} \cdot m=3 \)
D. \( m=2 \)
Subject: Chemistry
Which has maximum number of H-
atoms per gram of the substance?
A \( \cdot C H_{4} \)
в. \( C u S O_{4}: 5 H_{2} O \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O}_{2} \)
D. \( H_{2} O \)
Subject: Maths
Let \( \boldsymbol{R}=\{(\boldsymbol{a}, \boldsymbol{a}),(\boldsymbol{b}, \boldsymbol{c}),(\boldsymbol{a}, \boldsymbol{b})\} \) be a
relation on a set \( A=\{a, b, c\} . \) Then the
minimum number of ordered pairs
which when added to R make it an
equivalence relation are
Subject: Maths
Vectors \( \vec{a}=\hat{i}+2 \hat{j}+3 \hat{k}, \vec{b}=2 \hat{i}-\hat{j}+\hat{k} \)
and \( \vec{c}=3 \hat{i}+\hat{j}+4 \hat{k} \) are so placed that
the end point of one vector is the starting point of the next vector, then
the vectors are
A. Not coplanar
B. Coplanar but cannot form a triangle
c. coplanar and form a triangle
D. coplanar and can form a right-angled triangle
Subject: Physics
In the fusion reaction \( _{1}^{2} \boldsymbol{H} \boldsymbol{e}+_{1}^{2} \boldsymbol{H} \rightarrow_{2}^{3} \)
\( H e+_{0}^{1} n, \) the masses of deuteron, helium, and neutron expressed in amu
are 2.015,3.017 and \( 1.009, \) respectively.
If \( 1 k g \) of deuterium undergoes complete fusion, find the amount of total energy
released. \( \left(1 a m u=931.5 m e V / c^{2}\right) \)
\( \mathbf{A} \cdot \approx 6.02 \times 10^{13} J \)
в. \( \approx 5.6 \times 10^{13} \mathrm{J} \)
Subject: Physics
A capacitor and resistor are connected with an \( A C \) source as shown in figure.
Reactance of capacitor is \( X_{C}=3 \Omega \) and
resistance of resistor is \( 4 \Omega \). Phase
difference between current \( I \) and \( I_{1} \) is \( \left[\tan ^{-1}\left(\frac{3}{4}\right)=37^{\circ}\right] \)
A \( .90^{\circ} \)
B. zero
\( c \cdot 53^{\circ} \)
D. 37
Subject: Chemistry
When \( H I \) is added in excess to
the unsymmetrical ether, it yields:
\( \mathbf{A} \cdot P h C H_{2} O H \)
в. \( P h I \)
c. \( H O C H_{2} C H_{2} P h-N O_{2} \)
D. \( I C H_{2} C H_{2} P h N O_{2} \)
Subject: Maths
In a trapezium. ABCD, \( \angle A D C=110^{\circ} \)
Find \( \angle \boldsymbol{A} \)
A \( .50^{\circ} \)
B. \( 60^{\circ} \)
\( c .70^{\circ} \)
D. \( 80^{\circ} \)
Subject: Chemistry
Which has the largest \( \boldsymbol{O}-\boldsymbol{N}-\boldsymbol{O} \) bond
angle?
A \( \cdot N O_{2} \)
в. \( N O_{2}^{+} \)
\( \mathrm{c} \cdot \mathrm{N} \mathrm{O}_{2}^{-} \)
D. \( N O_{3}^{-} \)
Subject: Chemistry
Ferric sulphate is represented by which formula?
A. \( F e S O_{4} \)
в. \( F e S O_{3} \)
\( \mathrm{c} \cdot \mathrm{Fe}\left(\mathrm{SO}_{4}\right)_{2} \)
D. \( F e_{2}\left(S O_{4}\right)_{3} \)
Subject: Physics
A wheel as the angular acceleration of
\( 3.0 \mathrm{rad} / \mathrm{sec}^{2} \) and initial angular speed of
2.00 rad/sec. In a time of 2 sec, it has
rotated through an angle (in radians) of
\( A \cdot 4 \)
B. 6
c. 10
D. 12
Subject: Maths
The centre of the circle \( (x-a)(x- \)
\( \boldsymbol{b})+(\boldsymbol{y}-\boldsymbol{c})(\boldsymbol{y}-\boldsymbol{c})=\mathbf{0} \) is
\( \mathbf{A} \cdot(a+b, c+d) \)
В. \( 9-a-b,-c-d) \)
\( ^{\mathbf{c}} \cdot\left(\frac{a+b}{2}, \frac{c+d}{2}\right) \)
D. none of these
Subject: Physics
Three stars \( A, B, C \) have surface
temperature \( T_{A}, T_{B} \) and \( T_{C} . \) A appears
bluish, B appears reddish and C
appears yellowish. We can conclude
that
A \( \cdot T_{A}>T_{c}>T_{B} \)
В \( \cdot T_{A}>T_{B}>T_{C} \)
c. \( T_{B}>T_{c}>T_{A} \)
D. \( T_{C}>T_{B}>T_{A} \)
Subject: Physics
An aeroplane is flying vertically upwards with a uniform speed of
\( 500 m / s \) When it is at a height of 1000 \( m \) above the ground a shot is fired at it with the speed of \( 700 m / s \) from a point directly below it.The minimum uniform acceleration of the aeroplane now so that it may escape from being hit? \( \left[\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right] \)
A \( \cdot 10 m / s^{2} \)
в. \( 8 m / s^{2} \)
\( \mathbf{c} \cdot 12 m / s^{2} \)
D. None of these
Subject: Chemistry
What is compound \( z: \)
\[
\begin{array}{l}
\boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{B} \boldsymbol{r} \stackrel{\boldsymbol{N a C} \boldsymbol{N}}{\longrightarrow} \boldsymbol{X} \stackrel{\boldsymbol{H}_{3} \boldsymbol{O}^{+}}{\rightarrow} \\
\boldsymbol{Y} \stackrel{\boldsymbol{C H}_{3} C \boldsymbol{H}_{2}}{\longrightarrow} \boldsymbol{O} \boldsymbol{H}_{\boldsymbol{H}^{+}}
\end{array}
\]
\( \mathbf{A} \)
\[
\begin{array}{c}
\mathbb{N} \\
\| \\
\mathrm{CH}_{3} \mathrm{CH}=\mathrm{CH} \mathrm{COH}
\end{array}
\]
B. \( C H_{3} C H_{2} C H_{2} C H=N O C H_{2} C H_{3} \)
\( \mathbf{c} \cdot C H_{3} C H_{2} C H_{2} C H\left(O C H_{2} C H_{3}\right)_{2} \)
D.
\[
\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{COCH}_{2} \mathrm{CH}_{3}
\]
Subject: Chemistry
The Henry's law constant for the
solubility of \( \mathrm{N}_{2} \) gas in water at \( 298 \mathrm{K} \) is
\( 1.0 \times 10^{5} \) atm. The mole fraction of \( \mathrm{N}_{2} \)
in air is \( 0.8 . \) The number of moles of \( \mathrm{N}_{2} \)
from air dissolved in 10 moles of water
at \( 298 \mathrm{K} \) and 5 atm pressure is?
A \( \cdot 4.0 \times 10^{-4} \)
B . \( 4.0 \times 10^{-5} \)
c. \( 5.0 \times 10^{-4} \)
D. \( 4.0 \times 10^{-6} \)
Subject: Maths
If \( |\boldsymbol{x}|<1, \) then \( \lim _{n \rightarrow \infty}\{(1+x)(1+ \)
\( \left.\left.\boldsymbol{x}^{2}\right)\left(1+\boldsymbol{x}^{4}\right) \ldots . .\left(1+\boldsymbol{x}^{2 n}\right)\right\} \) is equal to
A \( \cdot \frac{1}{x-1} \)
в. \( \frac{1}{1-x} \)
c. \( 1-x \)
D. \( x-1 \)
Subject: Physics
A person weighs 60 kg. The area under the foot of the person is \( 180 \mathrm{cm}^{2} \). Find
the pressure exerted on the ground by
the person. (Take \( \boldsymbol{g}=\mathbf{9 . 8 m s}^{-\mathbf{2}} \) ).
A . \( 32.6 \times 10^{2} P a \)
в. \( 32.6 \times 10^{3} P a \)
c. \( 32.6 \times 10^{4} P a \)
D. \( 32.6 \times 10^{5} P a \)
Subject: Chemistry
The vapour pressure of liquid methano
at \( 50^{0} C \) is \( 55.5 k P a . \) Which one is
correct for equilibrium reaction
attained in a vessel of 5 litres at \( 50^{0} C \)
for
\[
\boldsymbol{C H}_{3} \boldsymbol{O H}(\boldsymbol{l}) \rightleftharpoons \boldsymbol{C H}_{3} \boldsymbol{O H}(\boldsymbol{g}) ?
\]
This question has multiple correct options
\( \mathbf{A} \cdot K_{p}=55.5 k P a \)
B. \( K_{c}=2.067 \) mollitre \( ^{-1} \)
c. \( K^{0}=0.555 \)
D. \( K^{0}=0.555 k P a \)
Subject: Maths
The following data gives the information on the life - time (in hours) of 75
electrical instruments.
\( \begin{array}{ll}\text { Lifetime } & \text { o- } \\ \text { (in } & \text { 20 } \\ \text { hours) }\end{array} \)
46
\( 20- \)
40 60
Frequency 10
15
find the mean lifetime of the
instruments.
Subject: Chemistry
Determine the number of moles of \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{I} \)
which may be dissolved in 1 litre of \( 1 M \)
of \( C N^{-} \) solution \( K_{s p} \) for \( A g I \) and \( K_{c} \) for
\( A g(C N)_{2}^{-} 1.2 \times 10^{-17} M^{2} \) and \( 7.1 \times \)
\( 10^{-19} M^{-2} \) respectively.
Subject: Chemistry
When molten \( A l C l_{3} \) is electrolysed with
a current of 0.5 ampere to produce 27 g
\( \mathbf{A I} \)
litres of \( \mathrm{Cl}_{2} \) at \( \mathrm{STP} \) are formed
A . 22.4
B. 33.6
c. 24.47
D. 36.7
Subject: Maths
If a unit vector is represented by \( \mathbf{0 . 5} \overline{\mathbf{i}}+\mathbf{0 . 8} \overline{\mathbf{j}}+\mathbf{c \overline { k }} \)
then the value of 'c' is
\( A \)
B. \( \sqrt{0.8} \)
c. \( \sqrt{0.11} \)
D. \( \sqrt{0.01} \)
Subject: Physics
In \( n-p-n \) transistor circuit, the collector current is \( 5 \mathrm{mA} \). If \( 98 \% \) of electrons
emitted reach the collector then the
emitter current will be
A . \( 5.1 \mathrm{mA} \)
B. 8.1 mA
\( c \cdot 6.5 \mathrm{mA} \)
D. \( 10 \mathrm{mA} \)
Subject: Maths
\( f(x)= \)
\[
\begin{array}{ccc}
\cos ^{x} & \cos x \sin x & -\sin x \\
\cos x \sin x & \sin ^{x} & \cos x \\
\sin x & -\cos x & 0
\end{array}
\]
Prove that \( f(x)=1 \) is an identity
Subject: Physics
A plane travelling at \( 300 m / s \) banks its wings to enter into a horizontal circular
turn. The circular path has a radius of \( 2.7 k m \)
Which of these values best represents the angle of the wings relative to the horizontal if the plane experiences no change in its altitude during the turn?
A \( \cdot 8^{\circ} \)
B. 16
\( c \cdot 20^{\circ} \)
D. \( 25^{\circ} \)
E \( .32^{\circ} \)
Subject: Biology
Assertion
Hemichordata are connecting link between Chordata and non-Chordata.
Reason In vertebrates the origin of coelom is schizocoelic formed by splitting of mesoderm, whereas all invertebrates except echinoderms are enterocoelic.
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
in the given diagram, with what force must be man pull the rope the hold the
plank in position? Weight of the man is
60 kg. Neglect the weights of plank, rope
and pulley:
A. \( 15 k g f \)
в. \( 20 k g f \)
c. \( 25 k g f \)
D. \( 30 k g f \)
Subject: Maths
Factorise: \( 36 x^{2}+24 x+4 \)
A. \( 4(3 x-1)(3 x+1) \)
B. \( (3 x-1)(3 x+1) \)
c. \( (3 x+1)(3 x+1) \)
D. \( 4(3 x+1)(3 x+1) \)
Subject: Physics
A stationary source emits sound of
frequency \( f_{0}=492 H z . \) The sound is
reflected by a large car approaching the
source with a speed of \( 2 m s^{-1} \). The
reflected signal is received by the source and superposed with the original. What will be the beat frequency of the resulting signal in \( H z ? \) (Given that the speed of sound in air is \( 330 m s^{-1} \) and the car reflects the sound
at the frequency it has received)
Subject: Physics
A cotton reel of mass \( m \) and moment of
inertia \( I \) is kept at rest on a smooth horizontal surface. The reel has inner
and outer radius \( r \) and \( R \) respectively.
horizontal force \( \boldsymbol{F} \) starts acting as
shown in figure. Find the
(a) acceleration of the centre of mass of
reel
(b) angular acceleration of the reel
(c) net acceleration of point of contact
Subject: Chemistry
Write the IUPAC name of the following compound:
\( \boldsymbol{C H}_{2}=\boldsymbol{C}\left(\boldsymbol{C H}_{3}\right)-\boldsymbol{C}(\boldsymbol{H})\left(\boldsymbol{C H}_{3}\right)(\boldsymbol{B r}) \)
A. 3-Bromo-2-methylbut-1-ene
B. 2-Bromo-2-methylbut-1-ene
c. 1 -Bromo-2-methylbut-1-ene
D. none of these
Subject: Chemistry
For the chemical reaction \( N_{2}(g)+ \)
\( \mathbf{3} \boldsymbol{H}_{\mathbf{2}}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{\mathbf{3}}(\boldsymbol{g}) \) the correct option
is:
A \( \cdot-\frac{1}{3} \frac{d\left[H_{2}\right]}{d t}=-\frac{1}{2} \frac{\left[N H_{3}\right.}{d t} \)
B. \( -\frac{d\left[N_{2}\right]}{d t}=2 \frac{d\left[N H_{3}\right]}{d t} \)
c. \( -\frac{d\left[N_{2}\right]}{d t}=\frac{1}{2} \frac{d\left[N H_{3}\right]}{d t} \)
D. \( 3 \frac{d\left[H_{2}\right]}{d t}=2 \frac{d\left[N H_{3}\right]}{d t} \)
Subject: Chemistry
Which of these can absorb visible light
\( ? \)
A \( \cdot\left[\operatorname{Sc}\left(H_{2} O\right)_{6}\right] C l_{3} \)
В \( \cdot\left[T i(e n)_{3}\right]\left(S o_{4}\right)_{2} \)
\( \mathbf{c} \cdot\left[Z n\left(N H_{3}\right)_{6}\right] S O_{4} \)
D \( \cdot\left[\operatorname{Cr}\left(N H_{3}\right)_{6}\right] C l_{3} \)
Subject: Physics
Ring of radius \( R \) rotating about axis of ring such that angular velocity is given as omega \( =5 t . \) Find acceleration of a
point \( \boldsymbol{P} \) on rim after \( \mathbf{5} \) sec?
\( \mathbf{A} \cdot 5 R \)
в. 25 В
c. \( \sqrt{650} R \)
D. None of these
Subject: Maths
If \( \mathrm{M} \) and \( \mathrm{N} \) are any two events, the
probability that atleast one of them
occurs is
A \( \cdot P(M)+P(N)-2 P(M \cap N) \)
B . \( P(M)+P(N)-P(M \cap N) \)
c. \( P\left(M^{c}\right)+P\left(N^{c}\right)-2 P\left(M^{c} \cap N^{c}\right) \)
D - \( P\left(M \cap N^{c}\right)-P\left(M^{c} \cap N\right) \)
Subject: Physics
In hydrogen atom electron of charge \( -e \) and mass m revolves round the nucleus
in a circular orbit of radius r. The
electrostatic potential energy of the electron is \( \frac{1}{4 \pi \varepsilon_{0}} \) times
A \( \cdot \frac{-e}{r} \)
B. \( \frac{-e^{2}}{r} \)
c. \( \frac{e^{2}}{r} \)
D. \( \frac{-m e^{2}}{r} \)
Subject: Chemistry
Which of the following will give maximum number of isomers?
A. \( \left[\operatorname{Co}\left(N H_{3}\right)_{4} C l_{2}\right] \)
в. \( \left[N i(e n)\left(N H_{3}\right)_{4}\right]^{2+} \)
\( \mathbf{c} \cdot_{\left[N i\left(C_{2} O_{4}\right)(e n)_{2}\right]} \)
D. \( \left[C r(S C N)_{2}\left(N H_{3}\right)_{4}\right]^{2+} \)
Subject: Maths
If \( A \) is in the 3 rd quadrant and \( B \) is in the
fourth quadrant and \( \cos A= \) \( -\frac{15}{17}, \cos B=\frac{4}{5} \) find the value of
\( \cos (\boldsymbol{A}+\boldsymbol{B}) \)
A \( \cdot-\frac{84}{85} \)
в. \( \frac{84}{85} \)
\( c \cdot-\frac{34}{85} \)
D. None of these
Subject: Physics
An unknown resistance \( \boldsymbol{R}_{1} \) is connected
in series with a resistance of \( 10 \Omega \). This
combination is connected to one gap of
a metre bridge while a resistance \( \boldsymbol{R}_{2} \) is
connected in the other gap. The balance point is at \( 50 \mathrm{cm} . \) Now, when the \( 10 \Omega \)
resistance is removed the balance point
shifts to \( 40 \mathrm{cm} . \) The value of \( R_{1} \) is (in
ohms) :
A . 20
B. 10
c. 60
D. 40
Subject: Physics
Two cars 1 and 2 move with velocities \( v_{1} \)
and \( v_{2} \) respectively, on a straight road in same direction. When the cars are
separated by a distance d, the driver of car 1 applies brakes and the car moves
with uniform retardation \( a_{1} \)
Simultaneously, car 2 starts
accelerating with \( a_{2} \). If \( v_{1}>v_{2} \). Find the minimum initial separation between the cars to avoid collision between
them.
Subject: Physics
A cannon, shell is fired to hit a target at
a horizontal distance \( \boldsymbol{R} \). However, it
breaks into two equal parts at its highest point. One part (A) returns to the cannon. The other part:
This question has multiple correct options
A. will fall at a distance of \( R \) beyond the target
B. will fall at a distance of \( 3 R \) beyond the target
c. will hit the target
D. have nine times the kinetic energy of \( A \)
Subject: Chemistry
Assertion
n a reaction
\( Z n(s)+C u S O_{4}(a q) \rightarrow Z n S O_{4}(a q)+ \)
\( \boldsymbol{C u}(\boldsymbol{s}) \)
Zn is a reductant but itself get oxidized.
Reason

In a redox reaction, oxidant is reduced
by accepting electrons and reductant is oxidized by losing electrons.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Chemistry
The combustion of methane is written
as
\( \boldsymbol{C H}_{4}(\boldsymbol{g})+\mathbf{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( 2 H_{2} O(l) \)
The difference between enthalpy change and energy change is equal to:
\( \mathbf{A} \cdot-2 R T \)
B.
c. \( R T \)
D. \( \frac{R T}{2} \)
Subject: Chemistry
Assertion: In the compound \( C H_{3} C I I_{2} C I=N, \) the most
electroegative carbon is II. Reason: Carbon atom II has more s-
character.
A. Assertion is True, Reason is True and Reason is the correct explanation for Assertion
B. Assertion is True, Reason is True and Reason is NOT a correct explanation for Assertion
c. Assertion is True, Reason is False
D. Assertion is False, Reason is True
Subject: Physics
How is nuclear power derived?
A. It is derived from energy i.e. released when relatively large atoms of uranium, thorium are split by shooting neutrons on them.
B. It is derived from energy i.e. released when relatively small atoms of uranium, thorium are split by shooting neutrons on them.
C. It is derived from energy i.e. released when relatively large atoms of uranium, thorium are split by shooting electrons on them.
D. None
Subject: Maths
If \( \vec{A} \times \vec{B}=\overrightarrow{0} \) and \( \vec{B} \times \vec{C}=\overrightarrow{0}, \) then the
angle between \( \vec{A} \) and \( \vec{C} \) may be :
A . 0
в.
\( c \cdot \frac{\pi}{2} \)
D. none of these