AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
An object launched straight up into the air is said to have parabolic motion (because it goes up, reaches a maximum height, and then comes back down). The height (h) of a projectile at time \( t \) is given by the equation \( h= \) \( \frac{1}{2} g t^{2}+u t+h_{0}, \) where \( g \) is the
acceleration due to gravity and \( u \) and \( h_{0} \) are the object's initial velocity and initial height, respectively. Which of the following equations correctly represents the object's acceleration due to gravity in terms of the other variables?
A \( \cdot g=\frac{h-u t-h_{0}}{t} \)
B. \( g=\frac{h-u t-h_{0}}{2 t^{2}} \)
c. \( g=\frac{2\left(h-u t-h_{0}\right)}{t^{2}} \)
D. \( g=t \sqrt{2\left(h-u t-h_{0}\right)} \)
Subject: Physics
An electromagnetic wave radiates outwards from a dipole antenna, with
\( E_{0} \) as the amplitude of its electric field
vector. The electric field \( B_{0} \) which
transports significant energy from the source falls off as
A \( \cdot \frac{1}{r^{3}} \)
B. \( \frac{1}{r^{2}} \)
\( c \cdot \frac{1}{r} \)
D. remains constant
Subject: Chemistry
In the extraction of \( \mathrm{Cu} \), the reaction
takes place in bessemer converter is:
This question has multiple correct options
A \( \cdot 2 C u_{2} O+C u_{2} S \rightarrow 6 C u+S O_{2} \)
в. \( 2 C u F e S_{2}+O_{2} \rightarrow C u_{2} S+F e S+S O_{2} \)
c. \( 2 C u_{2} S+3 O_{2} \rightarrow 2 C u_{2} O+2 S O_{2} \)
D. 2 FeS\( +30_{2} \rightarrow 2 \)Fe\( O+2 \)SO\( _{2} \)
Subject: Physics
Two objects \( A \) and \( B \) when placed in front of a concave mirror of focal length
\( 7.5 \mathrm{cm}, \) give images of equal size. If \( \mathrm{A} \) is three times the size of \( B \) and is placed \( 30 \mathrm{cm} \) from the mirror, what is the distance of B from the mirror?
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
в. \( 12.5 \mathrm{cm} \)
\( \mathbf{c} \cdot 15 c m \)
D. \( 17.5 \mathrm{cm} \)
Subject: Maths
Harish borrowed a certain sum of
money from Girish at \( 6 \frac{2}{3} \% \) simple
interest. If he paid an interest of \( \boldsymbol{R} \boldsymbol{s} . \boldsymbol{7} \boldsymbol{0} \boldsymbol{0} \)
for 100 days, how much money did Hari borrow from Girish?
Subject: Chemistry
Calculate the volume of gas liberated at the anode at STP during the electrolysis
of a \( C u S O_{4} \) solution by a current of \( 1 A \)
passed for 16 minutes and 5 seconds.
A . \( 224 \mathrm{mL} \)
в. \( 56 \mathrm{mL} \)
\( c \cdot 112 m L \)
D. \( 448 \mathrm{mL} \)
Subject: Chemistry
Temperature at which the equilibrium
water vapour pressure is 1.00 bar.
\( \mathbf{A} \cdot 107^{0} \mathrm{C} \)
B \( .380^{0} \mathrm{C} \)
\( \mathbf{C} \cdot 215^{0} \mathrm{C} \)
D. \( 240^{\circ} \mathrm{C} \)
Subject: Physics
High quality camera lenses are often coated to prevent reflection. A lens has
an optical index of refraction of 1.72 and a coating with an optical index of refraction of \( 1.31 . \) For near normal
incidence the minimum thickness of
the coating to prevent reflection
for wavelength of \( 5.3 \times 10^{-7} m \) is :
A. \( 0.75 \mu m \)
в. \( 0.2 \mu m \)
c. \( 0.1 \mu m \)
D. \( 1.75 \mu m \)
Subject: Chemistry
The number of optically active products
obtained from the complete ozonolysis
of the given compound are:
\[
\begin{array}{cc}
\mathrm{CH}_{3} & \mathbf{H} \\
\mathbf{I} & \mathbf{I} \\
\mathbf{G H}_{3}-\mathbf{C H}=\mathbf{C H}-\mathbf{C}-\mathbf{C H}= & \mathbf{C H}-\mathbf{C}-\mathbf{C H}=\mathbf{C H}-\mathbf{C H}_{3} \\
& \mathbf{E}
\end{array}
\]
A.
B.
\( c \cdot 2 \)
\( D \)
Subject: Physics
On conducting U tube can slide inside
the other as shown in figure 25.28
maintaining electrical contacts
between the tubes. The magnetic field
\( B \) is perpendicular to the plane of the
figure. If each tube moves towards the
other at a constant speed \( v \) then the
induced emf in terms of \( B, l \) and \( v \)
where \( l \) is the width of each tube, will be
\( \mathbf{A} \cdot B l v \)
B. \( -B l v \)
\( c .2 B l v \)
D. zero
Subject: Chemistry
The strongest - \( \mathrm{CO} \) bond is present in:
A \( \cdot\left[C r(C O)_{6}\right]^{+} \)
в \( \cdot\left[F e(C O)_{5}\right] \)
\( \mathbf{c} \cdot\left[V(C O)_{6}\right]^{-} \)
D. all have equal strength
Subject: Physics
Match the Column I with Column II.
Column Column A nn II \( \mathrm{O} \mathrm{h}_{\mathrm{m}} \)
\( \mathrm{i}_{\mathrm{S}} \)
\( \mathrm{applin}_{\mathrm{d}} \) Whe the the
(A)
\( (p) \)
metals applicable
to The
(B) Ohm's law
is not
applicable
to
\( (q) \)
grr
reer greater
resistivity
(C) alloys have \( \quad \) (r) \( \quad \) diodes,
electrolytes,
semiconductors
\( A \cdot A-r, B-q, C-p \)
B. \( A-p, B-r, C-q \)
C. \( A-r, B-p, C-q \)
D. A-q, B-r, C-p
Subject: Chemistry
16g of sulphur completely reacts with
38 g of \( F_{2} \) to form \( S F_{x} . \) The value of \( x \) is:
(Atomic mass of \( \boldsymbol{F}=\mathbf{1 9} \) )
A .
B. 2
\( c \cdot 4 \)
D. 6
Subject: Physics
A particle started moving from \( \boldsymbol{P} \)
towards \( S \) with uniform acceleration
along a straight line. The average velocity of the particle from \( P \) to
intermediate point \( Q \) is \( 8 m / s \) and that
\( Q \) to \( S \) is \( 12 m / s . \) If \( Q S=P Q, \) then the
average velocity from \( \boldsymbol{P} \) to \( \boldsymbol{S} \) is:
A. \( 9.6 \mathrm{m} / \mathrm{s} \)
B. \( 12.87 \mathrm{m} / \mathrm{s} \)
\( c .64 m / s \)
D. \( 327 \mathrm{m} / \mathrm{s} \)
Subject: Physics
The coefficient of mutual induction
between two coils is \( 4 \mathrm{H} \). If the current in
the primary reduces from 5 A to zero in \( 10^{-3} \) second then the induced emf in the
secondary coil will be
A \( \cdot 10^{4} v \)
B . \( 25 \times 10^{3} \mathrm{V} \)
C \( \cdot 2 \times 10^{4} \mathrm{V} \)
\( \mathbf{D} \cdot 15 \times 10^{3} \mathbf{v} \)
Subject: Maths
If \( m \) parallel lines in a plane are
intersected by a family of \( n \) parallel lines, the number of parallelograms than can be formed is
A \( \cdot \frac{1}{4} m n(m-1)(n-1) \)
в. \( \frac{1}{2} m n(m-1)(n-1) \)
c. \( \frac{1}{4} m^{2} n^{2} \)
D. None of these
Subject: Chemistry
The relationship between rate constant and half-life for first order reaction is:
A \( \cdot t_{1 / 2}=\frac{0.693}{k} \)
B. \( _{k=\frac{-t_{1 / 2}}{0.693}} \)
c. \( t_{1 / 2}=0.693 k \)
D \( t_{1 / 2}=\frac{k}{0.693} \)
Subject: Physics
A car is moving at a speed of 72 Km/hour. The diameter of its wheels is
\( 50 \mathrm{cm} . \) If its wheels come to rest after
20 rotations as a result of the
application of brakes, then the angular retardation produced in the car will be
A . -25.5 radians / \( s^{2} \)
B. 0.25 radians / \( s^{2} \)
C. 2.55 radians / \( s^{2} \)
D.
Subject: Chemistry
Which of the following are incorrectly
matched?
\begin{tabular}{|c|l|c|c|}
\hline & \multicolumn{1}{|c|} { Material } & Natural Source & \multirow{2}{*} { Artificial Source } \\
\cline { 3 - 5 } & & & \\
\hline (i) & Themoplastic & \( \sqrt{ } \) & \( \times \) \\
(ii) & Jute & \( \curlyvee \) & \( \times \) \\
(iii) & Cellulose & \( \times \) & \( \vee \) \\
(iv) & Polythene & \( \sqrt{ } \) & \( \times \) \\
\hline
\end{tabular}
A . (i) and (ii)
B. (i), (ii) and (iii)
\( \mathbf{C} \cdot(\mathbf{i}),(\text { iii }) \) and (iv)
D. All of these
Subject: Biology
Which of these ions are involved in
muscle contraction?
A. \( C a^{2+} \) and \( M g^{2+} \)
B. \( C a^{2+} \) and \( N a^{+} \)
c. \( N a^{+} \) and \( K^{+} \)
D. \( M g^{2+} \) and \( K^{+} \)
Subject: Physics
Two isolated point poles of strength \( 30 A m \) and \( 60 A m \) are placed at a
distance of \( 0.3 m . \) The force of repulsion
is:
A \( \cdot 2 \times 10^{-3} N \)
B . \( 2 \times 10^{-4} N \)
c. \( 2 \times 10^{5} N \)
D. \( 2 \times 10^{-5} N \)
Subject: Physics
A body of mass 100 g is moving with a velocity of \( 15 \mathrm{m} / \mathrm{s} \). The momentum associated with the ball will be:
A. \( 0.5 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
B. \( 1.5 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
c. \( 2.5 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
D. 3.2 Ns
Subject: Physics
A man can see objects clearly up to \( 3 m \) What type of lens he should use in order
to see clearly up to \( 12 m ? \)
A. Convex lens, \( f=4 m \)
B. Concave lens, \( f=4 m \)
c. convex lens, \( f=-4 m \)
D. Concave lens, \( f=-4 m \)
Subject: Physics
A wire of length \( L \) has a linear mass
density \( \mu \) and area of cross-section \( \boldsymbol{A} \)
and Young's modulus \( Y \) is suspended vertically from a rigid support. If the
mass \( M \) is hung at the free end of the
wire, then the extension produced in the
wire is:
\( ^{\mathbf{A}} \cdot \frac{\mu g L^{2}+M g L}{2 Y A} \)
\( ^{\mathbf{B}} \cdot \frac{2 \mu g L^{2}+M g L}{2 Y A} \)
c. \( \frac{\mu g L^{2}+2 M g L}{2 Y A} \)
\( \frac{\mu g L^{2}+M g L}{Y A} \)
Subject: Maths
Assertion
The circle of smallest radius passing through two given points \( A \& B \) must be of radius \( \frac{1}{2} A B \)
Reason
A straight line is a shortest distance between two points.
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
If the differential equation of a body falling from rest under gravity is given by \( v \frac{d v}{d x}+\frac{n^{2}}{g} v^{2}=g, \) then the velocity of
the body is given by \( v^{2}=\frac{g^{2}}{n^{2}}(1- \)
\( \left.e^{-2 n^{2} x / g}\right) \)
A. True
B. False
Subject: Maths
A random variable \( X \) has the following
probability distribution:
\( \boldsymbol{X} \quad \mathbf{0} \quad \mathbf{1} \quad \mathbf{2} \)
\[
P(X) \quad 0 \quad k \quad 2 k
\]
Determine
(i) \( k \)
(ii) \( \boldsymbol{P}(\boldsymbol{X}<\mathbf{3}) \)
(iii) \( \boldsymbol{P}(\boldsymbol{X}>\boldsymbol{6}) \)
(iv) \( \boldsymbol{P}(\mathbf{0}<\boldsymbol{X}<\mathbf{3}) \)
Subject: Maths
\( \int \frac{\boldsymbol{x}}{\boldsymbol{x}^{4}+\boldsymbol{x}^{2}+1} \boldsymbol{d} \boldsymbol{x} \)
( \( ^{\mathbf{B}} \cdot=\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x^{2}+1}{\sqrt{3}}\right)+C \)
\( =\frac{1}{\sqrt{3}} \sin ^{-1}\left(\frac{2 x^{2}+1}{\sqrt{3}}\right)+C \)
C \( =\frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{x^{2}+1}{\sqrt{2}}\right)+C \)
\( =\frac{1}{\sqrt{2}} \sin ^{-1}\left(\frac{x^{2}+1}{\sqrt{2}}\right)+C \)
Subject: Physics
When a proton is released vest in a room. it starts with an initial
acceleration \( a_{0} \) towards west. When it
is projected towards north with a speed
\( v_{0} \) it moves with an initial acceleration
\( 3 a_{0} \) toward west. The electric and
magnetic fields in the room are
\( \mathbf{A} \cdot \frac{m a_{0}}{e} \) east \( , \frac{3 m a_{0}}{e v_{0}} u p \)
B. \( \frac{m a_{0}}{e} \) east, \( \frac{3 m a_{0}}{e_{e 0}} \) down
\( \mathbf{C} \cdot \frac{m a_{0}}{e} \) west \( , \frac{2 m a_{0}}{e v_{0}} u p \)
D. \( \frac{m a_{0}}{e} \) west \( , \frac{2 m a_{0}}{e_{e v}} d o w n \)
Subject: Maths
The D.E whose solution is \( x y=a x^{2}+\frac{b}{x} \)
is
A \( \cdot x^{2} y_{2}+2 x y_{1}=2 y \)
в. \( x^{2} y_{2}-x y_{1}+2 y=0 \)
c. \( x^{2} y_{2}+x y_{1}+y=0 \)
D . \( x^{2} y_{2}+x y_{1}+2 y=0 \)
Subject: Maths
What are the DR's of vector parallel to
(2,-1,1) and (3,4,-1)\( ? \)
A \( \cdot(1,5,-2) \)
B \( \cdot(-2,-5,2) \)
\( \mathbf{c} \cdot(-1,5,2) \)
D \( \cdot(-1,-5,-2) \)
Subject: Physics
The magnetic moment of an electron
with orbital angular momentum \( \boldsymbol{J} \) will
be:
\( ^{\mathbf{A}} \cdot \frac{e \vec{J}}{m} \)
B. \( \frac{e \vec{J}}{2 m} \)
c. \( \frac{2 m}{e \bar{J}} \)
D. zero
Subject: Maths
\( f\left(\frac{2}{3} 1 \frac{5}{3}\right) \quad\left[\frac{2}{3} \frac{2}{3} \frac{4}{3}\right] \) and \( B=\left[\frac{2}{5} \frac{3}{5} \frac{4}{5} \frac{4}{5}\right], \) then
compute \( 3 A-5 B \)
Subject: Maths
Find the principal and general solutions of the following equation:
\( \sec x=2 \)
A ' principal solution \( =\frac{\pi}{6}, \frac{5 \pi}{6} \) and General solution \( = \)
\( n \pi \pm \frac{\pi}{6}, n \in Z \)
B. Principal solution \( =\frac{\pi}{3}, \frac{5 \pi}{3} \) and General solution \( = \)
\( n \pi \pm \frac{\pi}{3}, n \in Z \)
C ' principal solution \( =\frac{\pi}{6}, \frac{5 \pi}{6} \) and General solution \( = \)
\( 2 n \pi \pm \frac{\pi}{6}, n \in Z \)
D. principal solution \( =\frac{\pi}{3}, \frac{5 \pi}{3} \) and General solution \( = \)
\( 2 n \pi \pm \frac{\pi}{3}, n \in Z \)
Subject: Chemistry
Choose the redox reaction from the
following.
\( \mathbf{A} \cdot C u+2 H_{2} S O_{4} \rightarrow C u S O_{4}+S O_{2}+2 H_{2} O \)
B \( \cdot B a C l_{2}+H_{2} S O_{4} \rightarrow B a S O_{4}+2 H C l \)
\( \mathbf{c} \cdot 2 N a O H+H_{2} S O_{4} \rightarrow N a_{2} S O_{4}+2 H_{2} O \)
\( \mathbf{D} \cdot K N O_{2}+H_{2} S O_{4} \rightarrow 2 H N O_{2}+K_{2} S O_{4} \)
Subject: Physics
A ship is travelling due east according to
mariner's compass. If the declination at
that place is \( 20^{\circ} \) east, the actual direction
of its motion is
A \( \cdot 40^{\circ} \) south of east
B. \( 20^{\circ} \) south of east
C \( \cdot 5^{\circ} \) south of east
D. \( 20^{\circ} \) north of east
Subject: Physics
The average energy in one time period in simple harmonic motion is
A \( \cdot \frac{1}{2} m \omega^{2} a^{2} \)
B . \( m \omega^{2} a^{2} \)
\( \mathbf{c} \cdot 1.5 m \omega^{2} a^{2} \)
D. None of these
Subject: Chemistry
\( C H_{3} \)
\( C H_{3}-C_{I}^{\prime}-C H_{2}-C H_{3} \)
The correct IUPAC name of the above
compound is:
A. tert-amyl alcohol
B. 2-methylbutan-2-ol
c. 2-methylpentan-2-ol
D. 1,1 dimethyl propan-1-o
Subject: Maths
If \( \frac{(x+1)^{2}}{x\left(x^{2}+1\right)}=\frac{A}{x}+\frac{B x+C}{x^{2}+1}, \) then
\( \cos ^{-1}\left(\frac{A}{C}\right)= \)
A. \( \frac{\pi}{6} \)
в.
c.
D.
Subject: Physics
Assertion (A) : A large soap bubble expands while a small bubble shrinks, when they are connected to each other by a capillary tube. Reason (R): The excess pressure (due to surface tension) inside a spherical bubble is more due to its small volume.
A. Both Assertion
(A) and Reason
(R) are true and the Reason (R) is correct explanation of the Assertion(A)
B. Both Assertion
(A) and Reason (R) are true, but Reason
(R) is not correct explanation of the Assertion(A)
c. Assertion (A) is true, but the Reason
(R) is false
D. Assertrion
(A) is false, but the Reason (R) is true
Subject: Maths
\( \operatorname{lines} \frac{x-1}{2}=\frac{y-1}{2}=\frac{z-2}{3} \) and
\( \frac{x-1}{2}=\frac{y-2}{2}=\frac{z-3}{-2} \)
Check whether the lines are parallel, mutually perpendicular or intersecting in acute angle)
Subject: Physics
The drift current in a p-njunction is
A. from the n-side to the p-side
B. from the p-side to the n-side
C. from the n-side to the p-side if the junction is forwardbiased and in the opposite direction if it is reverse biased
D. from the p-side to the n-side if the junction is forwardbiased and in the opposite direction if it is reversebiased
Subject: Maths
A small village, having a population of \( 5000, \) requires 75 litres of water per head per day. The village has got an
overhead tank of measurement \( 40 \mathrm{m} \)
\( \times 25 \mathrm{m} \times 15 \mathrm{m} . \) For how many days will the water of this tank last?
Subject: Physics
(a)Draw a schematic sketch of a
cyclotron. Explain clearly the role of crossed electric and magnetic field in accelerating the charge. Hence derive the expression for the kinetic energy
acquired by the particles.
(b) An \( \alpha \) - particle and a photon are released from the centre of the cyclotron
and made to accelerate:
(i) Can both be accelerated at the same
cyclotron frequency? Give reason to justify your answer
(ii) When they are accelerated in turn,
which of the two will have higher velocity at the exit slit.
Subject: Chemistry
Assertion
A larger dry cell has higher emf.
Reason
The emf of a dry cell is proportional to
its size.
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
\( \int_{0}^{\pi / 4} \log (1+\tan x) d x \) is equal to
A \( \cdot \frac{\pi}{8} \log _{e} 2 \)
в. \( \frac{\pi}{4} \log _{e} e \)
c. \( \frac{\pi}{4} \log _{e} 2 \)
D \( \cdot \frac{\pi}{8} \log _{e}\left(\frac{1}{2}\right) \)
Subject: Physics
A block of mass \( 300 k g \) is set into
motion on a frictionless horizontal
surface with the help of frictionless pulley and a rope system as shown in
the figure. What horizontal force \( \boldsymbol{F} \)
should be applied to produce in the block an acceleration of \( 1 \mathrm{m} / \mathrm{s}^{2} \) ?
A. \( 150 N \)
в. \( 100 N \)
\( c .300 N \)
D. \( 50 N \)
Subject: Chemistry
\( 252 \mathrm{gm} \) of oxalic acid with molecular
formula \( C_{2} H_{2} O_{4} \cdot 2 H_{2} O \) dissolve in
water to form \( 250 \mathrm{ml} \). of the solution. Its
molarity will be:
A . 16 м
B. 8 M
c. 32 м
D. 24 M
Subject: Physics
A light ray Incidents normally on the
face of \( A B \) of a right angled prism \( A B C \). Prism is made of a material having
refractive index of \( \mu=1.5 \) as shown in
the figure. What is the largest angle \( \theta \)
for which light is totally reflected at the
surface AC?
A \( \cdot \sin ^{-1}\left(\frac{2}{3}\right) \)
B. \( \cos ^{-1}\left(\frac{2}{3}\right) \)
c. \( \sin ^{-1}\left(\frac{3}{4}\right) \)
D \( \cos ^{-1}\left(\frac{3}{4}\right) \)
Subject: Chemistry
Conductivity of \( C a C l_{2} \) solution is:
A \( \cdot 4.87 \times 10^{-4} \mathrm{Scm}^{1} \)
B. \( 7.84 \times 10^{-4} \mathrm{Scm}^{1} \)
c. \( 8.47 \times 10^{-4} \mathrm{Scm}^{1} \)
D. None of these
Subject: Physics
A particle of mass \( m \) is moving with
constant velocity \( v \) parallel to the \( x- \)
axis as shown in the figure. Its angular
momentum about origin \( O \) is
A . \( m v b \)
B. mva
c. \( m v \sqrt{a^{2}+b^{2}} \)
D. \( m v(a+b) \)
Subject: Maths
The area (in sq. units) of the region \( A=\left\{(x, y): x^{2} \leq y \leq x+2\right\} \) is?
A \( \cdot \frac{10}{3} \)
B. \( \frac{9}{2} \)
c. \( \frac{31}{6} \)
D. \( \frac{13}{6} \)
Subject: Chemistry
A monomeric complex of cobalt gave the following results on analysis :
\( C o^{3+}=21.24 \%, N H_{3}=24.77 \%, C l^{-}= \)
\( 12.81 \% \) and \( S O_{4}^{2-}=34.65 \% \)
The compound is diamagnetic and contains no other groups or elements, except water which might be present. What is probable formula of the
compound \( ?\left(M_{C o}=\mathbf{5 9}\right) \)
\( \mathbf{A} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{4} C l S O_{4}\right] \cdot H_{2} O \)
в. \( \left[\operatorname{Co}\left(N H_{3}\right)_{4} C l S O_{4}\right] .2 H_{2} O \)
c. \( \left[\operatorname{Co}\left(N H_{3}\right)_{4} C l H_{2} O\right] S O_{4} \)
D. \( \left[C o\left(N H_{3}\right)_{4} S O_{4}\right] C l .2 H_{2} O \)
Subject: Chemistry
Which of the following molecules
exhibit resonance?
I. \( \boldsymbol{A} \boldsymbol{s} \boldsymbol{F}_{\mathbf{5}} \)
।. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{\mathbf{3}} \)
III. \( \boldsymbol{S O}_{2} \)
A. I only
B. II only
c. II and III
D. III and IV
E . ।, II, and III
Subject: Chemistry
Assuming that petrol is octane \( \left(C_{8} H_{18}\right) \)
and has a density of \( 0.8 g m L^{-1}, 1.425 \)
litre of petrol on combustion will
consume:
A. 100 mole of oxygen
B. 125 mole of oxygen
c. 150 mole of oxygen
D. 175 mole of oxygen
Subject: Maths
If \( f(x+1)=3 x-9, \) then what will be
the value of \( f\left(x^{2}-1\right) ? \)
A \( \cdot 3 x^{2}-9 \)
B. \( 3 x^{2}-15 \)
c. \( x^{2}-10 \)
D. \( 3 x^{2}-10 \)
Subject: Maths
If \( \boldsymbol{f}: \boldsymbol{Z} \rightarrow \boldsymbol{Z} \) is such that \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{6} \boldsymbol{x}- \)
11 then \( f \) is
A. injective but not surjective
B. surjective but not injective
c. bijective
D. neither injective nor surjective
Subject: Chemistry
Select the correct statement(s).
This question has multiple correct options
\( \mathbf{A} \cdot \) When \( T \longrightarrow \infty \) or \( E_{a} \longrightarrow 0, \) then \( k=A \)
B. A positive catalyst can change \( \Delta H \) of the reaction.
C. A mixture of reactants may be thermodynamically unstable but kinetically stable
D. A negative catalyst increases the activation energy of the reaction.
Subject: Chemistry
Given that:
\( \boldsymbol{A}(s) \longrightarrow \boldsymbol{A}(l) ; \boldsymbol{\Delta} \boldsymbol{H}=\boldsymbol{x} \)
\( \boldsymbol{A}(l) \longrightarrow \boldsymbol{A}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}=\boldsymbol{y} \)
The heat of sublimation of A will be:
A. \( x-y \)
в. \( x+y \)
\( \begin{array}{llll}\mathbf{c} \cdot x & \text { or } & y\end{array} \)
D. \( -(x+y) \)
Subject: Physics
Suppose \( n \) conducting plates are
placed face to face, and the distance
between two successive plates is \( d \)
Each plate is half of the area of the
previous one. If area of first plate is \( A \). If
the area of the first plate is \( A \), the
equivalent capacitance of the system is \( \operatorname{given} \operatorname{as} \frac{\varepsilon_{0} A}{d\left(x^{n}-2\right)} . \) Find \( x \)
Subject: Physics
A plane sound wave traveling with velocity 'v' in a medium A reaches a point on the interface of medium \( A \) and
medium B. If velocity of sound in
medium B is \( 2 v \), the angle of incidence
for total internal reflection of the wave
will be greater than \( \left(\sin 30^{\circ}=0.5 \) and \right.
\( \left.\sin 90^{\circ}=1\right) \)
A \( \cdot 15^{\circ} \)
B . 30
\( c \cdot 45^{\circ} \)
D. \( 90^{\circ} \)
Subject: Physics
A car travelling at \( 60 k m / h \) overtakes another car travelling at \( 42 k m / h \) Assuming each car to be \( 5.0 m \) long, the time taken for the over taking is
\( \mathbf{A} \cdot 6 s \)
B . \( 4 s \)
c. \( 3 s \)
D. \( 2 s \)
Subject: Maths
The set of natural numbers is divided
into arrays of rows and columns in the
form of matrices as \( \boldsymbol{A}_{1}=(1), \boldsymbol{A}_{2}=\left(\begin{array}{ll}2 & 3 \\ 4 & 5\end{array}\right), \boldsymbol{A}_{3}= \)
\( \left(\begin{array}{ccc}\mathbf{6} & \mathbf{7} & \mathbf{8} \\ \mathbf{9} & \mathbf{1 0} & \mathbf{1 1} \\ \mathbf{1 2} & \mathbf{1 3} & \mathbf{1 4}\end{array}\right) \ldots \mathbf{s o} \) on
Find the value of \( \boldsymbol{T}_{\boldsymbol{r}}\left(\boldsymbol{A}_{\mathbf{1 0}}\right) \)
\( \left[\mathrm{Note}: T_{r}(A) \) denotes sum of diagonal \right.
elements of \( \boldsymbol{A} . \)
A . 3355
в. 3434
\( c .5533 \)
D. None of these
Subject: Physics
The correct Biot-Savart law in vector
form is?
\( ^{\mathbf{A}} \cdot d \vec{B}=\frac{\mu_{0}}{4 \pi} \frac{I(d \vec{l} \times \vec{r})}{r^{2}} \)
в. \( d \vec{B}=\frac{\mu_{0}}{4 \pi} \frac{I(d \vec{l} \times \vec{r})}{r^{3}} \)
\( ^{\mathrm{c}} \cdot d \vec{B}=\frac{\mu_{0}}{4 \pi} \frac{I d \bar{l}}{r^{2}} \)
D \( \cdot d \vec{B}=\frac{\mu_{0}}{4 \pi} \cdot \frac{I d \vec{l}}{r^{3}} \)
Subject: Physics
The reflected ray from a plane mirror is incident on another plane mirror which is placed perpendicular to the first. If the angle of incidence on the first mirror
is \( 30^{0}, \) determine the glancing angle of
reflection on the second mirror
A . \( 15^{\circ} \)
B . \( 120^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 30^{\circ} \)
Subject: Chemistry
The energy of an electron in the first Bohr orbit of H atom is -13.6 eV. The
possible energy value of the excited state for the electron in Bohr orbits of
hydrogen is:
A. -3.4 eV
B. 4.2 eV
\( \mathbf{c} .-6.8 \mathrm{eV} \)
D. \( +6.8 \mathrm{eV} \)
Subject: Physics
In the circuit shown in figure, El and E2
are two ideal sources of unknown emfs.
Some currents are shown. Potential
difference appearing across \( 6 \Omega \)
resistance is \( \boldsymbol{V}_{\boldsymbol{A}}-\boldsymbol{V}_{\boldsymbol{B}}=\mathbf{1 0} \boldsymbol{V} \)
This question has multiple correct options
A. The current in the 4.00 resistance between \( c \& B \) is \( 5 A \)
B. The unknown emf \( E_{1} \) is 36 V.
C. The unknown emf \( E_{2} \) is 54 V.
D. The resistance R is equal to \( 9 \Omega \)