AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A particle of mass \( m \) is at rest in a train
moving with constant velocity with
respect to ground. Now the particle is
accelerated by a constant force \( \boldsymbol{F}_{\mathbf{0}} \) acting along the direction of motion of
train for time \( t_{0} . \) A girl in the train and a boy on the ground measure the work done by this force. Which of the
following are INCORRECT?

This question has multiple correct options
A. Both will measure the same work
B. Boy will measure higher value than the girl
C. Girl will measure higher value than the boy
D. Data is insufficient for the measurement of work done by the force \( F_{0} \)
Subject: Physics
At some planet, \( g=1.96 m s^{-2} . \) If it is
safe to jump from a height of \( 2 m \) on earth, then the corresponding safe height on that planet is
\( \mathbf{A} \cdot 2 m \)
B. \( 5 m \)
c. \( 10 m \)
D. \( 20 m \)
Subject: Maths
Assertion \( (A) \). The direction ratios of the line joining origin and point \( (x, y, z) \) must be \( x, y, z \)

Reason (R): If \( P(x, y, z) \) is a point in space and \( |O P|=r, \) then the direction cosines of \( O P \) are \( \frac{x}{r}, \frac{y}{r}, \frac{z}{r} \)
A. Both A and R are individually true and R is the correct explanation of
B. Both A and R individually true but R is not the correct explanation of A
c. A is true but R is false
D. A is false but R is true
Subject: Maths
Let \( \boldsymbol{f}:(-\mathbf{1}, \mathbf{1}) \rightarrow \boldsymbol{R} \) be a differentiable
function satisfying
\[
\begin{array}{c}
\left(f^{\prime}(x)\right)^{4}=16(f(x))^{2} \text { for all } x \in \\
(-1,1) \\
f(0)=0
\end{array}
\]
The number of such functions is
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. more than 4
Subject: Chemistry
In which of the following compounds, nitrogen cannotbe tested by Lassaigne's test?
A. \( C H_{3} C O N H_{2} \)
B. \( N H_{2} . N H_{2} . H_{2} O \)
c. \( C_{6} H_{5} N H_{2} \)
D. \( C_{6} H_{5} N O_{2} \)
Subject: Physics
Assertion
A particle has constant acceleration is
x-y plane. But neither of its acceleration
components \( \left(a_{x} \text { and } a_{y}\right) \) is zero. Under
this condition particle can not have
parabolic path.
Reason
In projectile motion, horizontal component of acceleration is zero.
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
A horizontal beam of vertically polarized light of intensity \( 43 \mathrm{w} / \mathrm{m}^{2} \) is sent
through two polarizing sheets. The
polarizing direction of the first is \( 60^{0} \) to the vertical, and that of the second is
horizontal. The intensity of the light transmitted by the pair of sheets is (nearly)
A. \( 8.1 \mathrm{W} / \mathrm{m}^{2} \)
B. 7.3 \( \mathrm{W} / \mathrm{m}^{2} \)
c. \( 6.4 \mathrm{w} / \mathrm{m}^{2} \)
D. 3.8 \( \mathrm{W} / \mathrm{m}^{2} \)
Subject: Physics
A point object \( \boldsymbol{O} \) is placed in front of a
concave mirror of focal length \( 10 \mathrm{cm} . \) A glass slab of refractive index \( \mu=3 / 2 \)
and thickness \( 6 \mathrm{cm} \) is inserted between
the object and mirror. Find the position and nature of the final
image when the distance \( x \) shown in
figure, is 20 cm.
A. \( 17 c m, \) virtual
B. \( 17 \mathrm{cm} \), real
c. \( 12 c m, \) virtual
D. \( 15 \mathrm{cm} \), virtual
Subject: Chemistry
0.6 mole of \( N H_{3} \) in a reaction vessel of
\( 2 d m^{3} \) capacity was brought to
equilibrium. The vessel was then found
to contain 0.15 mole of \( H_{2} \) formed by
the reaction
\( \mathbf{2} N \boldsymbol{H}_{3}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{N}_{2}(\boldsymbol{g})+\mathbf{3} \boldsymbol{H}_{2}(\boldsymbol{g}) \)
Which of the following statements is
true?
A. 0.15 mole of the original \( N H_{3} \) had dissociated at equilibrium
B. 0.55 mole of ammonia is left in the vessel
C . At equilibrium the vessel contained 0.45 mole of \( N_{2} \)
D. The concentration of \( N H_{3} \) at equilibrium is 0.25 mole per \( d m^{3} \)
Subject: Maths
The mean of five numbers is 0 and their
variance is \( 2 . \) If three of those numbers
\( \operatorname{are}-1,1 \) and \( 2, \) then the other two numbers are :
\( \mathbf{A} \cdot-5 \) and 3
B. - 4 and 2
c. -3 and 1
D. -2 and 0
E . -1 and -1
Subject: Biology
A male rabbit of genotype AABBDDEE is crossed with a female rabbit of
genotype aabbddee to produce \( \boldsymbol{F}_{1} \) hybrid offspring. How many genetically different gametes can be produced by
this \( F_{1} \) hybrid
\( A \cdot 4 \)
B. 8
\( c \cdot 16 \)
D. 32
Subject: Chemistry
If the bond dissociation energies of
\( X Y, X_{2} \) and \( Y_{2} \) (all diatomic
molecules) are in the ratio of 1: 1: 0.5
and \( \Delta H_{f} \) for the formation of \( X Y \) is
\( -200 k J m o l^{-1}, \) the bond dissociation
energy of \( \boldsymbol{X}_{2} \) will be:
A . \( 100 k J m o l^{-1} \)
в. \( 300 k J m o l^{-1} \)
c. \( 200 k J m o l^{-1} \)
D. \( 800 k J m o l^{-1} \)
Subject: Maths
The letters of the work "Questions" are arranged in a row at random.The probability that there are exactly two letters between \( Q \) and \( S \) is.
A \( \cdot \frac{1}{14} \)
B. \( \frac{5}{7} \)
\( c \cdot \frac{1}{7} \)
D. \( \frac{5}{28} \)
Subject: Maths
Water is running into an underground right circular conical reservoir, which is 10 \( m \) deep and radius of its base is 5 m.
If the rate of change in the volume of water in the reservoir is \( \frac{3}{2} \pi m^{3} / m i n \quad, \) then the rate \( ( \) in \( \mathrm{m} / \mathrm{min} \) ) at which water rises in it, when
the water level is \( 4 \boldsymbol{m}, \) is:
\( A \cdot \frac{3}{8} \)
в. \( \frac{1}{8} \)
c. \( \frac{1}{4} \)
D. \( \frac{3}{2} \)
Subject: Chemistry
Assertion
The fraction of molecules having speed
in the range \( u \) and \( (u+d u) \) of a gas of
molar mass \( M \) at temperature \( T \) is the
same as that of gas of molar mass of
\( 2 M \) and temperature \( 2 T \)
Reason
The fraction of molecules having their speed within the range \( u \) to \( (u+d u) \propto \)
\( \frac{M}{T} \)
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
A body of mass \( m \) slides down an
incline and reaches the bottom with a
velocity \( V \). If the same mass were in the form of a ring which rolls down the same incline, the velocity of its centre of
mass at bottom of the plane is:
A. \( V \)
B. \( \sqrt{2} V \)
c. \( \frac{V}{\sqrt{2}} \)
D. \( \frac{V}{2} \)
Subject: Chemistry
In the co-ordination compound \( \boldsymbol{N} \boldsymbol{a}_{4} \)
\( \left.[\boldsymbol{F e}) \boldsymbol{C N})_{5} \boldsymbol{N O S}\right] \) oxidation state of \( \boldsymbol{F e} \)
is:
\( A \cdot+1 \)
\( B \cdot+2 \)
\( c \cdot+3 \)
\( D \cdot+4 \)
Subject: Biology
Given below are the figures of blood
vessels. Identify them and select the
correct option.
A. A - Capillary
B - Vein
\( \mathrm{C}- \) Artery
B. A - Artery
B - Capillary
C - Vein
C. A - Vein
B - Capillary
C - Artery
D. A - Vein
\( \mathrm{B}- \) Artery
C - Capillary
Subject: Physics
\( 10 c m \) and \( 100 c m \) are placed on a
horizontal plane as shown in the Figure.
Outer loop is connected to a source of
unknown emf through a key K. If a
current of \( 2 A \) flows in the inner loop as
shown aside, when the key k is closed at
time \( t=0 s, \) then the emf of the source
sending a current \( I \), should be
[Take resistance of both wire per length
\( \left.\operatorname{as} 10^{-4} \Omega m^{-1}\right) \)
of unknow
\( \mathbf{A} \cdot 4 V \)
B. \( 4 t V \)
\( \mathbf{c} \cdot 04 \mathrm{t}^{2} \mathbf{V} \)
D. \( \left(0.4 t^{2}+4 t+4\right) V \)
Subject: Physics
An electron microscope is operated at
\( 40 K v . \) The ratio of resolving power of this microscope and another one which uses yellow light of wavelength \( 6 \times 10^{7} \)
is :
\( \mathbf{A} \cdot 7 \times 10^{-25} \)
B . \( 9.78 \times 10^{4} \)
c. \( 9.78 \times 10^{-4} \)
D. \( 9.78 \times 10^{-6} \)
Subject: Chemistry
\( 200 \mathrm{ml} \) of \( 1 \mathrm{M} \) HCl is mixed with \( 400 \mathrm{m} \)
of \( 0.5 \mathrm{M} \) NaOH. The temperature rise in
the calorimeter was found to
be \( 4.00 \mathrm{C} \). Water equivalent of calorimeter is \( 25 g \) and the specific heat of the solution is 1 cal/mL/degree. If the
theoritical heat of neutralization of a
strong acid and strong base is -13.5 kcal, then the percentage error in this experiment while calculating the heat of neutralization is
A. 7.4
B. 3
\( c \cdot 5.6 \)
D. 4.5
Subject: Maths
Determine whether the product of the matrices is defined in each case. If \( s 0 \)
state the order of the product. MN,
where \( \boldsymbol{M}=\left[\boldsymbol{m}_{i j}\right]_{3 \times 1}, \boldsymbol{N}=\left[\boldsymbol{n}_{i j}\right]_{1 \times 5} \)
Subject: Physics
Q Type your question
velocity \( v \) out of a region of uniform
magnetic field whose magnitude is \( \boldsymbol{B} \)
The plane of loop and the velocity are both perpendicular to \( \vec{B} \). Then the electrical power in the circular loop at the instant when the arc (of circular
loop) outside the region of magnetic field subtends an angle \( \frac{\pi}{3} \) at centre of
the loop is
\( ^{\mathrm{A}} \cdot \frac{B^{2} a^{2} v^{2}}{R} \)
B. \( \frac{2 B^{2} a^{2} v^{2}}{R} \)
c. \( \frac{B^{2} a^{2} v^{2}}{2 R} \)
D. None of thes
Subject: Physics
A circular coil of 16 turns and radius 10
\( \mathrm{cm} \) carrying a current of \( 0.75 \mathrm{A} \) rests
with its plane normal to an external
field of magnitude \( 5.0 \times 10^{-2} \) T. The coil
is free to turn about an axis in its plane perpendicular to the filed direction. When the coil is turned slightly and released, it oscillates about its stable
equilibrium with a frequency of \( 2.0 / s \) What is the moment of inertia of the
coil about its axis of rotation?
A \( .1 .2 \times 10^{4} g-c m^{2} \)
B. \( 3 \times 10^{4} k g-m^{2} \)
c. \( 0.3 \times 10^{4} k g-m^{2} \)
D. \( 1.2 \times 10^{4} k g-m^{2} \)
Subject: Physics
A current of \( 1 /(4 \pi) \) ampere is flowing in
a long straight conductor. The line integral of magnetic induction around a closed path enclosing the current carrying conductor is
\( \mathbf{A} \cdot 10^{-7} W b m^{-1} \)
В . \( 4 \pi \times 10^{-7} \mathrm{Wb} \mathrm{m}^{-1} \)
c. \( 16 \pi^{2} 10^{-7} W b m^{-1} \)
D. zero
Subject: Maths
Let \( a, b \) be non-zero real numbers. The
equation
\( \left(a x^{2}+b y^{2}+c\right)\left(x^{2}-5 x y+6 y^{2}\right) \)
represents
A. four straight lines, when \( c=0 \) and \( a, b \) are of the same \( \operatorname{sign} \)
B. two straight lines and a circle, when \( a=b \) and \( c \) is of sign opposite to that of \( a \)
C. two straight lines and a hyperbola, when \( a \) and \( b \) are of the same sign and \( c \) is of sign opposite to that of \( a \)
D. a circle and an ellipse, when \( a \) and \( b \) are of the same
\( \operatorname{sign} \)
Subject: Chemistry
\( \boldsymbol{o}-\boldsymbol{B r}-\boldsymbol{C}_{6} \boldsymbol{H}_{4}-\boldsymbol{N} \boldsymbol{H}_{2} \) is :
A . aliphatic \( 1^{0} \) - amine
B. aromatic \( 1^{0} \) - amine
c. aliphatic \( 2^{0} \) - amine
D. aromatic \( 2^{0} \) - amine
Subject: Chemistry
If the equilibrium constant for the
reaction \( 2 A B \leftrightharpoons A_{2}+B_{2} \) is \( 36, \) then
what is the equilibrium constant for \( A B \leftrightharpoons \frac{1}{2} A_{2}+\frac{1}{2} B_{2} ? \)
\( A \cdot 2 \)
B. 6
\( c . \) 36
D. 72
Subject: Physics
A ball is thrown upward and reaches a height of 64 feet, its initial velocity
should be \( (\boldsymbol{g})=\mathbf{3} 2 \boldsymbol{f} \boldsymbol{t} / \boldsymbol{s e c}^{2} \)
A. \( (1) 64 f t / \) sec
в. \( (2) 72 f t / \) sec
c. \( (2) 32 f t / \) sec
D. \( (4) 4096 f t / \) sec
Subject: Maths
What is the average of the first 300 terms of the given sequence?
\( \mathbf{1},-\mathbf{2}, \mathbf{3},-\mathbf{4}, \mathbf{5},-\mathbf{6}, \dots, \dots, \mathbf{n} .(-\mathbf{1})^{n+1} \)
A . -1
в. 0.5
\( c \cdot 0 \)
D. - 0.5
Subject: Physics
At \( 0^{\circ} \) and 760 mm Hg pressure, a gas
occupies a volume of \( 100 \mathrm{cm}^{3} \). Kelvin
temperature of the gas is increased by one-fifth and the pressure is increased one and a half times. Calculate the final
volume of the gas
\( A \cdot 80 \)
B. 90
\( c \cdot 100 \)
D. 129
Subject: Maths
Find the volume of a hemisphere of
radius \( 6.3 \mathrm{cm}(\pi=22 / 7) \)
A \( .523 .9 \mathrm{cm}^{3} \)
B . \( 520.91 \mathrm{cm}^{3} \)
D. \( 510.91 \mathrm{cm}^{3} \)
Subject: Physics
toppr
Q Type your question
of densities \( \sigma_{1} \) and \( \sigma_{2} \) and viscosities
\( \eta_{1} \) and \( \eta_{2}, \) respectively. They float in
equilibrium with the sphere \( P \) in \( L_{1} \) and
sphere \( Q \) in \( L_{2} \) and the string being taut
f sphere \( P \) along in \( L_{2} \) has terminal
velocity \( \vec{V}_{P} \) and \( Q \) along in \( L_{1} \) has
terminal velocity \( \vec{V}_{Q}, \) then

This question has multiple correct options
\( ^{\mathbf{A} \cdot} \frac{\left|\vec{V}_{P}\right|}{\left|\vec{V}_{Q}\right|}=\frac{\eta_{1}}{\eta_{2}} \)
\( ^{\mathbf{B}} \cdot \frac{\left|\vec{V}_{P}\right|}{\left|\vec{V}_{Q}\right|}=\frac{\eta_{2}}{\eta_{1}} \)
\( \mathbf{c} \cdot \vec{V}_{P} \cdot \vec{V}_{Q}>0 \)
D. \( \vec{V}_{P} \cdot \vec{V}_{Q}<0 \)
Subject: Physics
A homogeneous block of mass \( m \), width
\( b \) and height \( h \) is resting on a rough
horizontal surface. A horizontal force \( \boldsymbol{F} \)
is applied to it, which makes it to move
with a constant velocity. The coefficient
of friction between block and surface is
\( \mu . \) Find the greatest height at which
force \( \boldsymbol{F} \) may be applied to slide the
block without tipping over.
\( ^{A} \cdot \frac{b}{2 \mu} \)
B. \( \frac{2 b}{\mu} \)
\( c \cdot b \)
\( \bar{\mu} \)
\( \frac{2 \sqrt{2} b}{\mu} \)
Subject: Chemistry
In the free radical chlorination, the two factors which determine the product
ratio of various monochlorination
products are the type of H being substituted and the number of a
specific type of H being substituted. If activation energy for H-abstraction by
chlorine radical is considered to be zero,
what would be the percentage of 1 chlorobutane amongthe monochlorobutanes obtained on free
radical chlorination of butane?
A . 6\%
B. 10\%
c. \( 40 \% \)
D. 60\%
Subject: Maths
The equation of the circle passing through the point (-1,2) and having two diameters along the pair of lines \( x^{2}-y^{2}-4 x+2 y+3=0 \) is
A \( \cdot x^{2}+y^{2}-4 x-2 y+5=0 \)
B \( \cdot x^{2}+y^{2}+4 x+2 y-5=0 \)
c. \( x^{2}+y^{2}-4 x-2 y-5=0 \)
D. \( x^{2}+y^{2}+4 x+2 y+5=0 \)
Subject: Maths
The angles in a right angled isosceles
triangle are:
A \( \cdot 60^{\circ}, 60^{\circ}, 60^{\circ} \)
B . \( 90^{\circ}, 60^{\circ}, 30^{\circ} \)
c. \( 90^{\circ}, 45^{\circ}, 45^{\circ} \)
D . \( 70^{\circ}, 50^{\circ}, 60^{\circ} \)
Subject: Chemistry
White phosphorus on reaction with concentrated \( N a O H \) solution in an
inert atmosphere of \( C O_{2} \) gives phosphine and compound \( (X) .(X) \) on acidification with \( H C l \) gives compound
\( (Y) . \) The basicity of compound \( (Y) \) is :
A .4
B. 3
c. 1
D.
Subject: Chemistry
Arrange following oxides in increasing
acidic nature.
\( \boldsymbol{L} \boldsymbol{i}_{2} \boldsymbol{O}, \boldsymbol{B} \boldsymbol{e} \boldsymbol{O}, \boldsymbol{B}_{2} \boldsymbol{O}_{3} \)
A. \( L i_{2} O<B e O<B_{2} O_{3} \)
в. \( B e O<L i_{2} O<B_{2} O_{3} \)
c. \( L i_{2} O<B_{2} O_{3}<B e O \)
D. None of these
Subject: Physics
A stationary object at \( 4^{\circ} \mathrm{C} \) weighing 3.5 kg falls from a height \( 2000 \mathrm{m} \) on a snow
mountain at \( 0^{\circ} \mathrm{C} \). If the temperature of the object before comes to rest
immediately \( \left(g=10 m / s^{2}\right) \) and latent
heat of ice \( =3.5 \times 10^{6} J / s \) ), then the
object :
A. 2 gm of ice
B. 200 gm of ice
c. 20 gm of ice
D. 2 kg of ice
Subject: Maths
\( \int \cos (\log x) d x=\ldots \ldots \ldots \ldots \quad+\quad c \)
A. \( \frac{x}{2}[\cos (\log x)+\sin (\log x)] \)
B \( \cdot \frac{x}{4}[\cos (\log x)+\sin (\log x)] \)
c. \( \frac{x}{2}[\cos (\log x)-\sin (\log x)] \)
D. \( \frac{x}{2}[\sin (\log x)+\cos (\log x)] \)
Subject: Maths
Consider the functions defined
implicitly by the equation \( y^{3}-3 y+ \)
\( x=0 \) on various intervals in the real
line. If \( \boldsymbol{x} \epsilon(-\infty,-2) \cup(2, \infty), \) the
equation implicitly defines a unique real valued differentiable function \( y= \)
\( f(x) . \) If \( x \epsilon(-2,-2) \) the equation
implicitly defines a unique real valued
differentiable function \( \boldsymbol{y}=\boldsymbol{g}(\boldsymbol{x}) \)
satisfying \( \boldsymbol{g}=\boldsymbol{g}(\mathbf{0})=\mathbf{0} \)
If \( f(-10 \sqrt{2})=2 \sqrt{2} \) then
\( f^{\prime \prime}(-10 \sqrt{2})= \)
A \( \cdot \frac{4 \sqrt{2}}{7^{3} \cdot 3^{2}} \)
B. \( -\frac{4 \sqrt{2}}{7^{3} \cdot 3^{2}} \)
c. \( \frac{4 \sqrt{2}}{7^{3} \cdot 3^{3}} \)
D. \( \frac{4 \sqrt{2}}{7 \cdot 3} \)
Subject: Maths
The line joining two points \( A(2,0) \) and
\( B(3,1) \) ir rotated about \( A \) about in the anticlock wise direction through an
angle of \( 15^{\circ} . \) The equation of the line in the new position is:
A \( . x-\sqrt{3} y-2=0 \)
В. \( x-2 y-2=0 \)
c. \( \sqrt{3} x-y-2 \sqrt{3}=0 \)
D. \( \sqrt{2} x-y-2 \sqrt{2}=0 \)
Subject: Maths
A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is \( 30 \mathrm{cm} \) long, \( 25 \mathrm{cm} \) wide and
\( 25 \mathrm{cm} \) high.
(i) What is the area of the glass?
(ii) How much of tape is needed for all the 12 edges?
Subject: Physics
The energy levels of the hydrogen spectrum is shown in figure. There are some transitions \( A, B, C, D \) and \( E \)
Transition \( A, B \) and \( C \) respectively represent
A. first member of Lyman series, third spectral line of Balmer series and the second spectral line of Paschen series
B. ionization potential of hydrogen, second spectral line of Balmer series, third spectral line of Paschen series
c. series limit of Lyman series, third spectral line of Balmer series and second spectral line of Paschen series
D. series limit of Lyman series, second spectral line of Balmer series and third spectral line of Paschen series
Subject: Chemistry
Match the list - I (enzymes) with List - II (metals) and select the correct answer
using the codes given below the lists:
List List - II
A. Nitrogenase
1. \( c \)
B. Cytochrome oxidase 2. Mo
c. cytochrome- \( c \)
3. zn
D. carboxypeptidase 4. Fe
A. A-1 B-2 C-4 D-3
B. A-2 B-1 C-3 D-4
c. \( A-2 B-1 C-4 D-3 \)
D. A-1 B-2 C-3 D-4
Subject: Maths
Find the area of a square whose
perimeter is \( 160 \mathrm{m} . \) A floor \( 3.0 \mathrm{m} \) long and \( 2.0 \mathrm{m} \) wide is to be covered with
square shaped tiles of length \( 10 \mathrm{cm} . \) Find
the cost of flooring it, if the cost of tiles
is Rs.150 per 100 tiles.
Subject: Maths
Evaluate: \( \left(7 a^{2}-5 a\right) \div 5 a \)
A \( .7 a-1 \)
B. \( 7 a-5 \)
c. \( \frac{1}{5}(7 a-5) \)
D. \( \frac{1}{5}(7 a-1) \)
Subject: Chemistry
Assertion: For every chemical reaction
at equilibrium, the standard Gibbs energy of reaction is zero.
Reason: At constant temperature and pressure, chemical reactions are
spontaneous in the direction of decreasing Gibbs energy.
A. The Assertion is True, Reason is True; Reason is the correct explanation for Assertion
B. The Assertion is True, Reason is True; Reason is NOT a correct explanation for Assertion
c. The Assertion is True, Reason is False
D. The Assertion is False, Reason is True
Subject: Physics
Akhtar, Kiran and Rahul were riding in a motorcar that was moving with a high velocity on an expressway when an insect hit the windshield and got stuck on the windscreen. Akhtar and Kiran
started pondering over the situation. Kiran suggested that the insect
suffered a greater change in momentum as compared to the change in momentum of the motorcar(because
the change in the velocity of the insect was much more than that of the
motorcar). Akhtar said that since the
motorcar was moving with a larger
velocity, it exerted a larger force on the insect. And as a result the insect died.
Rahul while putting an entirely new explanation said that both the motorcar and the insect experienced the same force and a change in their momentum. Comment on these suggestions.
Subject: Physics
A parallel beam of monochromatic unpolarised light is incident on a transparent dielectric plate of refractive index \( \frac{1}{\sqrt{3}} . \) The reflected beam is completely polarised. Then the angle of incidence is
\( A \cdot 30^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 75^{\circ} \)
Subject: Physics
A cell can be balanced against \( 110 \mathrm{cm} \)
and \( 100 \mathrm{cm} \) of potentiometer wire respectively, with and without being short-circuited through a resistance of
10\Omega. Its internal resistance is :
A . \( 1.0 \Omega \)
B. \( 0.5 \Omega \)
c. \( 2.0 \Omega \)
D. zero
Subject: Maths
A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is :
A \( \cdot \frac{10}{3^{5}} \)
в. \( \frac{17}{3^{5}} \)
c. \( \frac{13}{3^{5}} \)
D. \( \frac{11}{3^{5}} \)
Subject: Chemistry
The decomposition of \( \boldsymbol{K} \boldsymbol{C l} \boldsymbol{O}_{3} \) to \( \boldsymbol{K} \boldsymbol{C l} \)
and \( O_{2} \) on heating is an example of :
A. intermolecular redox change
B. intramolecular redox change
c. disproportionation or auto redox change
D. None of the above
Subject: Maths
Given that the events \( A \) and \( B \) are such
\( \operatorname{that} \boldsymbol{P}(\boldsymbol{A})=\frac{1}{2}, \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})=\frac{\boldsymbol{3}}{\mathbf{5}} \) and
\( \boldsymbol{P}(\boldsymbol{B})=\boldsymbol{p} . \) Find \( \boldsymbol{p} \) if they are (i)
mutually exclusive (ii) independent.
A . 0.5,0.6
в. 0.1,0.2
c. 0,2,0.4
D. 0.1,0.6
Subject: Physics
In an electromagnetic wave, the electric magnetising fields are \( 100 V / m \) and
0.265 A. The maximum energy flow is?
\( \mathbf{A} \cdot 26.5 W / m^{2} \)
B. \( 36.5 W / m^{2} \)
\( \mathbf{c} \cdot 46.7 W / m^{2} \)
\( \mathbf{D} \cdot 765 W / m^{2} \)
Subject: Maths
In the figure, if \( \boldsymbol{O A}=\mathbf{1 7 c m}, \boldsymbol{A B}= \)
\( 30 \mathrm{cm} \) and \( 0 \mathrm{D} \) is perpendicular to \( \mathrm{AB} \)
then \( \mathrm{CD} \) is equal to:
\( A \cdot 8 c m \)
в. \( 9 \mathrm{cm} \)
\( c \cdot 10 c m \)
D. \( 11 \mathrm{cm} \)
Subject: Physics
Four light waves are represented by
(i) \( y=a_{1} \sin \omega t \)
(ii) \( y=a_{2} \sin (\omega t+\varepsilon) \)
(iii) \( y=a_{1} \sin 2 \omega t(\text { iv }) y=a_{2} \sin 2(\omega t+ \)
\( \varepsilon \)
We obtain sustained interference due to
super-position of This question has multiple correct options
\( A \cdot \) (i) and (ii)
B. (i) and (iii)
c. (ii) and (iv)
D. (iii) and (iv)
Subject: Chemistry
mol of \( N a C l O_{4} \) is to be produced from
the electrolysisi of \( N a C l O_{3} \).FInd the
volume of \( H_{2} \) evolved at STP in the time
during which 12.25 g of \( N a C l_{4} \) are produced.
\( \mathbf{A} \cdot 1 \cdot 12 L \)
B. \( 5.2 L \)
c. \( 2.24 L \)
D. none
Subject: Maths
Solve the differential equation:
\( \sqrt{1+x^{2}} d x+\sqrt{1+y^{2}} d y=0 \)
A \( . x \sqrt{1+x^{2}}+y \sqrt{1+y^{2}}+ \)
\( \log [(x+\sqrt{1+x^{2}})(y+\sqrt{1+y^{2}})]=c \)
B . \( \sqrt{1+x^{2}}+\sqrt{1+y^{2}}=c \)
c. \( \frac{1}{\sqrt{1+x^{2}}}+\frac{1}{\sqrt{1+y^{2}}}=c \)
D \( \cdot \log \{(\sqrt{1+x^{2}})+(\sqrt{1+y^{2}})\}=x+c \)
Subject: Maths
\( A B \) and \( C D \) are two parallel chords of a circle such that \( A B=10 \mathrm{cm} \) and
\( C D=24 \mathrm{cm} . \) If the chords are on the
opposite sides of the centre and the distance between them is \( 17 \mathrm{cm} \), the radius of the circle is
A . \( 14 \mathrm{cm} \)
B. \( 10 \mathrm{cm} \)
c. \( 13 \mathrm{cm} \)
D. \( 15 \mathrm{cm} \)