AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A uniform cylinder of radius \( r \) and
length L and mass \( m \) is lying on the ground with the curved surface touching the ground. If it is to be oriented on the ground with the flat circular end in contact with the ground the work to be done is:
\( ^{\mathbf{A}} \cdot_{m g}\left[\left(\frac{L}{2}\right)-r\right] \)
\( ^{\mathrm{B}}_{m g}\left[\left(\frac{g}{2}\right)-r\right] \)
c. \( m(g L-1) \)
D. \( M g L r \)
Subject: Physics
In the series LCR circuit, the voltmeter
and ammeter readings are respectively.
\( \mathbf{A} \cdot V=250 V, I=4 A \)
B. \( V=150 V, I=2 A \)
C . \( V=1000 V, I=5 A \)
D. \( V=100 V, I=2 A \)
Subject: Chemistry
The standard enthalpy of formation of ammonia gas is
Given \( : N_{2} H_{4}(g) \rightarrow 2 N H_{3}(g) \)
\( \Delta H_{r}^{\circ}=-40 k J / m o l \) and
\( \Delta \boldsymbol{H}_{f}^{\circ}\left[\boldsymbol{N}_{2} \boldsymbol{H}_{4}(\boldsymbol{g})\right]=-120 k \boldsymbol{J} / \boldsymbol{m o l} \)
A . - 60
B . -180
\( c \cdot 40 \)
D. - 80
Subject: Chemistry
Equilibrium constant, \( \boldsymbol{K}_{c} \) for the
reaction
\( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \) at \( 500 K \)
is 0.061
At a particular time, the analysis shows that composition of the reaction
mixture is 3.0 mol \( L^{-1} N_{2}, 2.0 \) mol \( L^{-1} \)
\( \boldsymbol{H}_{2} \) and \( \mathbf{0 . 5 m o l} \boldsymbol{L}^{-1} \boldsymbol{N} \boldsymbol{H}_{3} . \) Is the
reaction at equilirbium? IF not in which direction does the reaction tend to
proceed to reach equilibrium?
Subject: Physics
In the following circuit, the battery \( \boldsymbol{E}_{\mathbf{1}} \)
has an emf of \( 12 V \) and zero internal
resistance while the battery \( E \) has emf
of 2 volt. If the galvanometer \( G \) reads
zero, then the value of the resistance \( \boldsymbol{X} \)
in ohm is
A . 10
в. 100
c. 500
D. 200
Subject: Chemistry
Write chemical equation to represent the most probable outcome in the following reaction and choose the
correct option.
\[
\boldsymbol{C d C O}_{3} \stackrel{\boldsymbol{\Delta}}{\rightarrow}
\]
A \( \cdot \mathrm{CdCO}_{3} \stackrel{\Delta}{\longrightarrow} \mathrm{Cd} \mathrm{O}+\mathrm{CO}_{2} \)
в. \( 2 \mathrm{CdCO}_{3} \) 오 \( 2 \mathrm{CdO}+2 \mathrm{CO}+\mathrm{O}_{2} \)
c. No reaction
D. None of these
Subject: Physics
Assertion
Spring balances show incorrect
readings after using for a long time.
Reason
On using for a long time, springs in the
balances lose their elastic strength
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 order of size is:
A. \( S^{2-}>C l^{-}>O^{2-}>F^{-} \)
B. \( C l^{-}>S^{2-}>O^{2-}>F^{-} \)
c. \( S^{2-}>O^{2-}>C l^{-}>F^{-} \)
D. \( S^{2-}>O^{2-}>F^{-}>C l^{-} \)
Subject: Physics
A radioactive sample has initial
concentration \( N_{0} \) of nuclei. Then
This question has multiple correct options
A. the number of undecayed nuclei present in the sample decays exponentially with time
B. the activity
(R) of the sample at any instant is directly proportional to the number of undecayed nuclei present in the sample at that time
c. the number of decayed nuclei growth exponentially with time
D. the number of decayed nuclei grows linearly with time
Subject: Maths
Find the ratio of the volume of sphere \( \boldsymbol{A} \)
to sphere \( B \), if the ratio of the surface
area of sphere \( A \) to the surface area of
sphere \( \boldsymbol{B} \) is \( \mathbf{7 2 9}: \mathbf{1} \)
A .27: 1
в. 81: 1
C. 19,683: 1
D. 26,224: 1
E . 531,441: 1
Subject: Physics
The magnetic force between the infinite
wire and the square loop is
A \( \frac{\mu_{0} i^{2}}{4 \pi}, \) repulsiv
B. \( \frac{\mu_{0} i^{2}}{2 \pi}, \) repulsive
C \( \frac{\mu_{0} i^{2}}{4 \pi}, \) attractive
D. \( \frac{\mu_{0} i^{2}}{2 \pi}, \) attractive
Subject: Physics
object and screen are fixed \( 90 \mathrm{cm} \) apart. The lens is displaced. two sharp images
are obtained when lens is at \( L_{1} \) and \( L_{2} \)
respectively such that \( I_{1}=4 I_{2} \). Find
the focal length of the lens?
\( \mathbf{A} \cdot 18 \mathrm{cm} \)
B. \( 15 \mathrm{cm} \)
c. \( 16 \mathrm{cm} \)
D. 20 cm
Subject: Chemistry
Match the polymers given in column
with the monomers in column II and
mark the appropriate choice.
\( \mathbf{A} \)
\( (A) \rightarrow(i i),(B) \rightarrow(i),(C) \rightarrow(i i i),(D) \rightarrow(i v) \)
B. \( (A) \rightarrow(\text { iii) },(B) \rightarrow(i v),(C) \rightarrow(i),(D) \rightarrow( \text { ii) } \)
, (C) \( \rightarrow \) (ii), (D) \( \rightarrow \) (iv)
\( c \)
\( (A) \rightarrow(i),(B) \rightarrow(i i i) \)
\( (A) \rightarrow(i v) \)
\( D \)
\( (\mathrm{B}) \rightarrow(\mathrm{ii}) \)
\( (C) \)
\( \rightarrow \) (iii) (D) \( \rightarrow \) (i)
Subject: Maths
Show that the equations to the straight
lines passing through the point (3,-2) and inclined at \( 60^{\circ} \) to the line \( \sqrt{3} x+ \) \( \boldsymbol{y}=1 \) are \( \boldsymbol{y}+\boldsymbol{2}=\boldsymbol{0} \) and \( \boldsymbol{y}-\sqrt{\mathbf{3}} \boldsymbol{x}+ \)
\( \mathbf{2}+\mathbf{3} \sqrt{\mathbf{3}}=\mathbf{0} \)
Subject: Chemistry
What is the main product obtained by the cross-aldol condensation of benzene
carbaldehyde and 1-Phenyl-Ethane-1
one?
\( A \)
\[
\sqrt{\square}>\mathrm{cH}_{2}-\mathrm{cH}=\mathrm{cH}-\mathrm{co} \sqrt{\bigcirc}
\]
B.
\( \langle\square\rangle-\mathrm{cH}_{2}-\mathrm{cH}=\mathrm{cH} \sqrt{\Delta} \)
\( D \)
Subject: Physics
The work function of a certain metal is
4.2 eV. Which among the wavelengths \( 390 \mathrm{nm}, 440 \mathrm{nm}, 550 \mathrm{nm} \) and \( 70 \mathrm{nm} \) will
this metal give photoelectric emission?
A. 390 nm only
B. 390 nm, 440 nm only
\( \mathrm{c} .390 \mathrm{nm}, 440 \mathrm{nm} \) and \( 550 \mathrm{nm} \)
D. None of them
Subject: Chemistry
Very strong acids, such as \( H N O_{3} \) and
\( H C l, \) appear to be equally strong in
water. This "leveling effect" of water is because
A \( \cdot O H^{-} \) is a stronger base than the conjugate bases of
\( H N O_{3} \) and \( H C l \)
B. \( H_{3} O^{+} \) is a stronger acid than \( H N O_{3} \) and \( H C l \)
c. \( H_{2} O \) is a stronger base than the conjugate bases of \( H N O_{3} \) and \( H C l \)
D. \( H_{2} O \) is a weaker base than the conjugate bases of \( H N O_{3} \) and \( H C l \)
Subject: Maths
The differential coefficient of \( \boldsymbol{f}\left(\log _{e} \boldsymbol{x}\right) \)
with respect to \( x, \) where \( f(x)=\log _{e} x \)
is
A \( \cdot \frac{x}{\log _{e} x} \)
в. \( \frac{1}{x} \log _{e} x \)
c. \( \frac{1}{x \log _{e} x} \)
D. none of these
Subject: Chemistry
The average atomic mass of a mixture containing 79 mole percent of \( ^{24} \mathrm{Mg} \) and
remaining 21 mole percent of \( ^{25} \mathrm{Mg} \) and \( ^{26} \mathrm{Mg}, \) is \( 24.31 . \) Mole percent of \( ^{26} \mathrm{Mg} \) is :
A. 5
B. 20
\( c \cdot 10 \)
D. 15
Subject: Chemistry
All the oxygen in a 0.5434 sample of a pure oxide of iron is removed by
reduction in a stream of \( \boldsymbol{H}_{2} . \) The loss in
weight is 0.1210 g. Hence, formula of the iron oxide is \( (\boldsymbol{F e}=\mathbf{5 6}) \)
A. \( F e O \)
в. \( F e_{2} O_{3} \)
\( \mathrm{c} \cdot \mathrm{Fe}_{3} \mathrm{O}_{4} \)
D. \( \mathrm{FeO}_{2} \)
Subject: Chemistry
Nickel forms a compound with carbon
monoxide, \( N i_{x}(C O)_{y} . \) To determine its formula, you carefully heat a \( 0.0973 \mathrm{g} \) sample in air to convert the nickel to \( 0.0426 \mathrm{g} \) of \( N i O \) and the \( C O \) to
\( 0.100 g C O_{2} \). If the empirical formula is
of the form \( N i_{x}(C O)_{y}[N i=58.7], \) then
\( x+y \) is :
Subject: Chemistry
Consider the following molecules
\( \boldsymbol{I}: \boldsymbol{O}_{2} \)
\( \boldsymbol{I} \boldsymbol{I}: \boldsymbol{O}_{2}\left(\boldsymbol{A} \boldsymbol{s} \boldsymbol{F}_{6}\right) \)
\( \boldsymbol{I} \boldsymbol{I} \boldsymbol{I}: \boldsymbol{K} \boldsymbol{O}_{2} \)
Choose the correct answer.
A. The correct decreasing bond order is \( I>I I I>I I \)
B. The correct decreasing order of bond length is \( I I I> \) \( I>I I \)
C. The bond strength of I is less than that of \( I I I \)
D. Bond dissociation energy is highest in case of \( I I I \)
Subject: Maths
The equation \( \frac{x^{2}}{10-\lambda}+\frac{y^{2}}{6-\lambda}=1 \)
represents This question has multiple correct options
A. a hyperbola if \( \lambda<6 \)
B. an ellipse if \( \lambda>6 \)
c. a hyperbola if \( 6<\lambda<10 \)
D. an ellipse if \( 0<\lambda<6 \)
Subject: Maths
The total number of local maxima and
local minima of the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( \left\{\begin{array}{cc}(2+x)^{3}, & -3<x \leq-1 \\ x^{2 / 3}, & -1<x<2\end{array}\right. \)
\( A \cdot O \)
B.
\( c \cdot 2 \)
\( D \)
Subject: Physics
An oil drop falls through air with a terminal velocity of \( 5 \times 10^{-4} m / s . \) The
terminal velocity of a drop with half of the initial radius will be ? Neglect density of air as compared to that of oil.
(Viscosity of air \( =\frac{18 \times 10^{-5}}{5} N-s / m^{2} \)
\( g=10 m / s^{2}, \) density of oil \( =900 \mathrm{kg} / \mathrm{m}^{3} \) )
A \( \cdot 3.25 \times 10^{-4} m / s \)
в. \( 2.10 \times 10^{-4} \mathrm{m} / \mathrm{s} \)
c. \( 1.5 \times 10^{-4} m / s \)
D. \( 1.25 \times 10^{-4} \mathrm{m} / \mathrm{s} \)
Subject: Maths
ff \( \mathbf{5} \boldsymbol{A}=\left(\begin{array}{cc}\mathbf{3} & \mathbf{- 4} \\ \mathbf{4} & \boldsymbol{x}\end{array}\right) \) and \( \boldsymbol{A} \boldsymbol{A}^{\boldsymbol{T}}= \)
\( A^{T} A=I, \) then the value of \( x, \) is
\( A \cdot 3 \)
B. -3
\( c \cdot 2 \)
D. - 2
Subject: Physics
With the help of a neat labelled diagram, describe the Geiger- Marsden experiment. What is mass defect? The photoelectric work function for a metal surface is \( 2.3 \mathrm{eV} \). If the light of wavelength \( 6800 A^{\circ} \) is incident on the
surface of metal find threshold
frequency and incident frequency. Will there be an emission of photoelectrons or not?
[Velocity of light \( c=3 \times 10^{8} m / s \)
Planck's constant, \( \boldsymbol{h}=\mathbf{6} \cdot \mathbf{6 3} \times \mathbf{1 0}^{-\mathbf{3 4}} \mathbf{J s} \)
Subject: Maths
A survey was conducted in a small industrial plant having 50 workers to find the number of \( k m \) each person
commuted to work and the details are
given below. Represent it by a histogram and frequency polygon.
commuted Distance
\[
\begin{array}{lll}
50- & 40- & 30- \\
59 & 49 & 39
\end{array}
\]
\( (k m) \)
No. of workers
Subject: Chemistry
Among the following, which is the strongest acid?
A. \( C H F_{2}-C H_{2}-C H_{2}-C O O H \)
в. \( C H_{3}-C H_{2}-C F_{2}- \) СООН
c. \( C H_{2} F-C H F-C H_{2}-C O O H \)
D. \( C H_{3}-C F_{2}-C H_{2}-C O O H \)
Subject: Maths
Find the quadratic equation in \( x, \) whose
solutions are 3 and 2
A \( \cdot x^{3}-5 x+6=0 \)
B. \( x^{2}-5 x+6=0 \)
c. \( x^{2}-3 x+6=0 \)
D. \( x^{2}-5 x+7=0 \)
Subject: Maths
The moon's distance from the earth is
\( 360000 \mathrm{km} \) and its diameter subtends
an angle of \( 42^{\prime} \) at the eye of the observer. The diameter of the moon is?
A. \( 4400 \mathrm{km} \)
B . \( 1000 \mathrm{km} \)
\( \mathbf{c} .3600 \mathrm{km} \)
D. \( 8800 \mathrm{km} \)
Subject: Physics
A cube of sponge rubber with edge length \( 5 \mathrm{cm} \) has a force of \( 2 \mathrm{N} \) applied horizontally to the top face (parallel to an edge) while the bottom face is held fixed. If the top face is displaced horizontally through a distance of \( 1 \mathrm{mm} \) find the shear modulus for the sponge rubber.
A. \( S=7 \times 10^{4} N m^{-2} \)
B. \( S=6 \times 10^{4} N m^{-2} \)
c. \( S=4 \times 10^{4} N m^{-2} \)
D. \( S=5 \times 10^{4} N m^{-2} \)
Subject: Physics
The quantity \( \boldsymbol{X}=\frac{\boldsymbol{\epsilon}_{0} \boldsymbol{L} \boldsymbol{V}}{\boldsymbol{t}}: \boldsymbol{\epsilon}_{0} \) is the
permittivity of free space, \( \boldsymbol{L} \) is length, \( \boldsymbol{V} \)
is potential difference and \( t \) is time. The
dimensions of \( X \) are same as that of
A . Resistance
B. Charge
c. voltage
D. current
Subject: Maths
\( \frac{x^{4}}{(x-a)(x-b)(x-c)}=p(x)+ \)
\( \frac{\boldsymbol{A}}{\boldsymbol{x}-\boldsymbol{a}}+\frac{\boldsymbol{B}}{\boldsymbol{x}-\boldsymbol{b}}+\frac{\boldsymbol{C}}{\boldsymbol{x}-\boldsymbol{c}} \Rightarrow \boldsymbol{p}(\boldsymbol{x})= \)
\( A \)
B. x+a
c. \( x+a+b \)
D. \( x+a+b+c \)
Subject: Chemistry
For the equilibrium of the reaction:
\( N H_{4} C l(s) \rightleftharpoons N H_{3}(g)+ \)
\( \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g}) ; \boldsymbol{K}_{\boldsymbol{p}}=\boldsymbol{8} 1 \boldsymbol{a} \boldsymbol{t} \boldsymbol{m}^{2} \)
Total pressure at equilibrium will be \( x \)
times the pressure of \( \boldsymbol{N} \boldsymbol{H}_{3} \)
The value of \( x \) will be:
Subject: Physics
Two balls of the same size but of
different materials, rubber and iron are
kept on the smooth floor of a moving train. The brakes are applied suddenly to stop the train. Will the balls start
rolling? If so, in which direction? Will they move with the same speed?
A. Iron ball is faster than rubber ball
B. Rubber ball is faster than iron bal
c. Both move at the same speed
D. None of them move
Subject: Maths
ff \( y=\tan ^{-1} \frac{1}{x^{2}+x+1}+ \)
\( \tan ^{-1} \frac{1}{x^{2}+3 x+3}+ \)
\( \tan ^{-1} \frac{1}{x^{2}+5 x+7}+\ldots . \) to \( n \) terms
then
A \( \cdot \frac{d y}{d x}=\frac{1}{1+(x+n)^{2}}-\frac{1}{1+x^{2}} \)
B. \( \frac{d y}{d x}=\frac{1}{(x+n)^{2}}-\frac{1}{1+x^{2}} \)
c. \( \frac{d y}{d x}=\frac{1}{1+(x+n)^{2}}+\frac{1}{1+x^{2}} \)
D. None of these
Subject: Chemistry
All of the following processes involve a separation of either a mixture into its components or a compound into elements. For each, decide whether the physical process or chemical reaction is required.
a. Sodium metal is obtained from the
substance Sodium chloride.
b. Iron filings are separated from the sand by using a magnet,
c. Sugar crystals are separated from sugar syrup by evaporation of water.
d. Fine crystals of Silver chloride are separated from a suspension of the crystals in water.
e. Copper is produced when Zinc metal is placed in a solution of Copper (II) sulphate, a compound.
A. a, b, c, d, e-physical
B. a, d, b, c, e - chemical
c. b, c, d- physical ; a, e- chemical
D. e a, b - physical ; c, d- chemical
Subject: Chemistry
Which of the following xenon compound has the same number of lone pairs on
central atom as in \( \boldsymbol{I}_{\mathbf{3}}^{-} \) ?
\( \mathbf{A} \cdot X e O_{4} \)
в. \( X e F_{4} \)
c. \( X e F_{2} \)
D. \( X e O_{3} \)
Subject: Physics
A cyclotron is operated at an oscillator frequency of \( \frac{80}{\pi} M H z \) and has a Dee of radius \( R=60 \mathrm{cm} . \) The magnitude of
magnetic field \( B \) (in Tesla) to accelerate deuteron is \( \frac{x}{10} \) Tesla. Find \( x ? \)
(charge on deuteron \( e=1.6 \times 10^{-19} \)
mass of deuteron \( =\mathbf{3 . 2 4} \times \mathbf{1 0}^{-\mathbf{2 7}} \mathbf{K} \boldsymbol{g} \)
A . 32.4
в. 16.2
\( c \cdot 64 \)
D.
Subject: Maths
\( \operatorname{Given} \vec{P}=2 \hat{i}-3 \hat{j}+4 \widehat{k} \) and \( Q=\hat{j}- \)
2 \( \widehat{k} \). The magnitude of their resultant is:
A. \( \sqrt{3} \)
B. \( 2 \sqrt{3} \)
c. \( 3 \sqrt{3} \)
D. \( 4 \sqrt{3} \)
Subject: Maths
Evaluate:
\( \left(\begin{array}{c}1+\cos \frac{\pi}{6}-i \sin \frac{\pi}{6} \\ 1+\cos \frac{\pi}{6}+i \sin \frac{\pi}{6}\end{array}\right) \)
\( A \)
B. -1
\( c \cdot 2 \)
\( D \cdot \underline{1} \)
Subject: Biology
Identify the triplet codons which code for amino acids serine and proline.
(a) UCC
(d) \( \mathrm{AAG} \)
(b) \( \mathrm{CCA}(\mathrm{c}) \mathrm{GGG} \)
The correct answer is
A. a and c
B. b and d
\( c \cdot c \) and \( d \)
D. a and
Subject: Biology
Name the germ layers from which the following tissues or organs are produced.
I. Kidneys
II. Internal ear
III. Trachea
A. I- Endoderm; II- Ectoderm; III- Mesoderm
B. I- Endoderm; II- Mesoderm; III-Ectoderm
c. I- Ectoderm; II- Endoderm; III- Mesoderm
D. I- Mesoderm; II-Endoderm; III-Ectoderm
E. I- Mesoderm; II- Ectoderm; II- Endoderm
Subject: Physics
A body starts from rest and travels a
distance \( x \) with uniform acceleration,
then it travels a distance \( 2 x \) with
uniform speed, finally it travels a distance \( 3 x \) with uniform retardation
and comes to rest. If the complete motion of the particle is along a straight line, then the ratio of its average velocity to maximum velocity is
A \( \cdot 2 / 5 \)
B. \( 3 / 5 \)
\( c \cdot 4 / 5 \)
D. 6/7
Subject: Physics
An electric dipole with dipole moment \( \overrightarrow{\boldsymbol{p}}=(3 i+4 j) \times 10^{-30} C-m \) is placed
in an electric field \( \overrightarrow{\boldsymbol{E}}=\mathbf{4 0 0 0 \hat { \boldsymbol { i } }}(\boldsymbol{N} / \boldsymbol{C}) \)
An external agent turns the dipole and its dipole moment becomes \( (-4 \hat{\mathbf{i}}+ \)
\( \mathbf{3} \hat{\boldsymbol{j}}) \times \mathbf{1 0}^{-\mathbf{3 0}} \boldsymbol{C}-\boldsymbol{m} . \) The work done by
the external agent is equal to:
A \( \cdot 4 \times 10^{-27} J \)
в. \( -4 \times 10^{-27} \mathrm{J} \)
c. \( 2.8 \times 10^{-26} J \)
D. \( -2.8 \times 10^{-26} J \)
Subject: Maths
If the mean of \( x \) and \( 1 / x \) is \( M \) then the
mean of \( x^{2} \) and \( 1 / x^{2} \) is
A \( \cdot M^{2} \)
B . \( M^{2} / 4 \)
c. \( 2 M^{2}-1 \)
D. \( 2 M^{2}+1 \)
Subject: Physics
A uniform disc of mass \( m \) and radius \( R \)
is rotating with angular velocity \( \omega \) on a smooth horizontal surface. Another
identical disc is moving translationally
with velocity \( v \) as shown. When they
touch each other, they stick together.
The angular velocity of centre of mass of
the system after contact will be
A. Zero
B.
c. \( \frac{v}{R} \)
D. \( \frac{\omega}{2^{2}} \)
Subject: Physics
toppr
Q туре your question
perpendicular to the plane of the
triangle. The base of the triangle AB has
a resistance \( 1 \Omega \) while the other two
sides have resistance \( 2 \Omega \) each. The
magnitude of potential difference between the points \( A \) and \( B \) will be
\( 4 \cdot 0.4 \)
\( (\mathrm{A}) \)
8. 0.6 v
\( (\mathrm{B}) \)
c. \( 1.2 v \)
\( (C) \)
D. Non
\( (\mathrm{D}) \)
Subject: Physics
In deriving a formula for the combined
resistance of three different resistors in
series, Kirchhoffs laws are used.
Which physics principle is involved in this derivation?
A. The conservation of charge
B. The direction of the flow of charge is from negative to positive
c. The potential difference across each resistor is the \( \operatorname{same} \)
D. The current varies in each resistor, in proportion to the resistor value
Subject: Maths
\( A \) took 15 seconds to cross a
rectangular field diagonally walking at the rate of \( 52 \mathrm{m} / \mathrm{min} \) and \( \mathrm{B} \) took the
same time to cross the same field along
its sides, walking at the rate of 68 \( \mathrm{m} / \mathrm{min.} \) The area of the field is:
A \( \cdot 30 m^{2} \)
в. \( 40 \mathrm{m}^{2} \)
\( \mathbf{c} \cdot 50 m^{2} \)
D. \( 60 m^{2} \)
Subject: Maths
\( S_{r} \) denotes the sum of the first \( r \) terms
of an AP. Then \( S_{3 n}:\left(S_{2 n}-S_{n}\right) \) is
This question has multiple correct options
A . \( n \)
B. \( 3 n \)
\( c .3 \)
D. independent of \( n \)
Subject: Maths
The value of \( \frac{1}{1 \cdot 2 \cdot 3}+\frac{1}{2 \cdot 3 \cdot 4}+ \)
\( \frac{1}{3 \cdot 4 \cdot 5}+\frac{1}{4 \cdot 5 \cdot 6} \) is equal to
\( A \cdot \frac{7}{30} \)
в. \( \frac{11}{30} \)
c. \( \frac{13}{30} \)
D. \( \frac{17}{30} \)
Subject: Chemistry
Identify the reaction taking place at
cathode in fuel cell.
A. \( O_{2}+2 H_{2} O+4 e^{-} \rightarrow 4 O H^{-} \)
B \( \cdot 2 H_{2}+4 O H^{-} \rightarrow 4 H_{2} O+4 e^{-} \)
c. \( O_{2}+2 H_{2} O+4 e^{-} \rightarrow 4 O H^{-}+H^{+} \)
D. \( 4 H_{2} O+4 e^{-} \rightarrow 2 H^{2}+4 O H^{-} \)
Subject: Physics
Water waves coming into shore arrive
every 4 seconds. The waves at \( 2.0 m / s \)
How long are the waves?
A . \( 4.0 \mathrm{m} \)
в. \( 8.0 m \)
\( c .2 .0 m \)
D. \( 0.50 m \)
E . \( 16.0 m \)
Subject: Chemistry
\( \mathbf{A} \)
1.00 molal aqueous solution of trichloroacetic acid \( \left(C C l_{3} C O O H\right) \) is heated to its boiling point. The solution
has the boiling point of \( 100.18^{\circ} \mathrm{C} \) Determine the van't Hoff factor for
trichloroacetic acid. \( \left(K_{b} \text { for water }=\right. \)
\( 0.512 \mathrm{K} \mathrm{kg} \mathrm{mol}^{-1} \) )
Subject: Physics
The charges of \( 2 \mu c, 4 \mu c \) and \( 6 \mu c \) are
placed at the corner \( A, B \quad \) and
respectively of a square \( A B C D \) of side
\( 0.2 m \) calculate the work done to
transfer a charge of \( 2 \mu c \) from \( D \) to the
center of the square.
Subject: Maths
The D.E whose solution is \( y=A \sin 2 x+B \) \( \cos 2 x \) given as:
A \( \cdot y_{2}=4 y \)
B . \( y_{2}+3 y=0 \)
\( \mathbf{c} \cdot y_{2}+y=0 \)
D . \( y_{2}+4 y=0 \)
Subject: Physics
A particle having initial velocity \( u \) moves with a constant acceleration \( a \)
for a time \( t . \) Find the displacement of the particle in the last one second.
A \( \cdot u+\frac{a}{2}(t-1) \)
в. \( u+\frac{a}{2}(2 t-1) \)
c. \( u+\frac{a}{2}(4 t-1) \)
D. \( u t+\frac{1}{2} a t^{2} \)
Subject: Chemistry
\( \ln \) a reaction \( \boldsymbol{A} \longrightarrow \boldsymbol{B}+\boldsymbol{C}, \) The
following data were obtained:
t in seconds
\( \begin{array}{lll}0 & 900 & 1800\end{array} \)
conc. of \( \mathbf{A} \)
\[
\begin{array}{lll}
50.8 & 19.7 & 7.62
\end{array}
\]
Prove that it is a first order reaction.
Subject: Physics
Assertion
In an irreversible process, finite
changes are made; therefore the system is not at equilibrium throughout the
process.
Reason
An ideal constant pressure process that has no internal entropy generation and no friction in its system can be considered as ideal reversible process.
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
Which one of the following occurs by an
addition elimination mechanism?
A. Toluene, \( \mathrm{Br}_{2}, \mathrm{FeBr}_{3} \rightarrow \rho \) -bromotoluene
B. Benzene, HNO \( _{3}, \mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow \) nitrobenzene
C. Benzene, \( \mathrm{CO}, \mathrm{HCl} \), AlCl \( _{3} \), \( \mathrm{CuCl} \rightarrow \) benzaldehyde
D. 2, 4-dinitrochlorobenzene, NaOH, heat, then H \( ^{+} \rightarrow 2,4- \) dinitrophenol
Subject: Chemistry
Which of the following order is true regarding the acidic nature of phenol?
A. Phenol> 0 -cresol > O-nitrophenol
B. Phenol> 0 -nitrophenol > 0-cresol
c. o-cresol < phenol < 0- nitrophenol
D. Phenol < O-cresol < O-nitrophenol
Subject: Maths
Choose the correct answers from the
alternatives given.

Directions for question 71 to 73: Study the following bar chart and answer the questions based on it. The histogram below shows the marks of 50 students in an examination.
Examine the diagram and answer the
questions.

How many students obtained less than
40 marks?
\( A \)
\( B .2 \)
\( c \)
\( D \)
Subject: Chemistry
Hydrolysis of sucrose with dilute aqueous sulphuric acid yields:
\( \mathbf{A} \cdot 1: 1 \) of \( D-(+)- \) glucose \( ; D-(-)- \) fructose
B. 1: 2 of \( D-(+)- \) glucose; \( D-(-)- \) fructose
\( \mathbf{c} \cdot 1: 1 \) of \( D-(-)- \) glucose \( ; L-(+)- \) fructose
D. 1: 2 of \( D-(-)- \) glucose; \( D-(+)- \) fructose
Subject: Maths
\( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{a} & \boldsymbol{a}^{2}-\boldsymbol{b} \boldsymbol{c} \\ \mathbf{1} & \boldsymbol{b} & \boldsymbol{b}^{2}-\boldsymbol{c} \boldsymbol{a} \\ \mathbf{1} & \boldsymbol{c} & \boldsymbol{c}^{2}-\boldsymbol{a} \boldsymbol{b}\end{array}\right|=? \)
\( \mathbf{A} \cdot \mathbf{5} \)
B. abc
\( c \cdot 1 \)
\( D \)