AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
If the unit of velocity is equal to the velocity of light and the unit of
acceleration is \( 10 m s^{-2}, \) then the unit
of time is
\( \mathbf{A} \cdot 3 \times 10^{7} s \)
В. \( 3 \times 10^{-7} s \)
c. \( 3 \times 10^{-5} s \)
D. \( 3 \times 10^{-4} s \)
Subject: Physics
Metal nails weighing \( 100 g \) are heated
to \( 100^{\circ} C \) and dropped into a copper calorimeter of mass \( 100 g \) containing \( 40 g \) of water at \( 1^{\circ} C . \) If the resulting
temperature is \( 10^{\circ} \mathrm{C} \), the specific heat of metal is (Sp. heat of copper is
\( 0.1 \mathrm{calg}^{-1 o} C^{-1} \) ):
A . 0.01 calg \( ^{-1} \) o \( C^{-1} \)
B. 0.05 calg\( ^{-1} \) o \( C^{-1} \)
c. 0.03 calg \( ^{-1} \) o \( C^{-1} \)
D. 0.5 calg\( ^{-1} \) o \( C^{-1} \)
Subject: Chemistry
On passing \( 1.5 F \) charge, the number of moles of aluminum deposited at the
cathode is:
[Molar mass of \( \boldsymbol{A l}=\mathbf{2 7} \) gram mol \( ^{-1} \) ]
A . 1.0
в. 13.5
c. 0.50
D. 0.75
Subject: Physics
For a given distance from a current
element, the magnetic induction is
maximum at an angle measured with
respect to axis of the current. The angle
is :
A \( \cdot \frac{3 \pi}{4} \)
B. \( \frac{\pi}{4} \)
c. \( \frac{\pi}{2} \)
D. \( 2 \pi \)
Subject: Maths
The angle between the lines whose direction cosines are \( \left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2}\right) \)
and \( \left(\frac{\sqrt{3}}{4}, \frac{1}{4},-\frac{\sqrt{3}}{2}\right) \) is :
\( A \)
в. \( \frac{\pi}{2} \)
c. \( \frac{\pi}{3} \)
D.
Subject: Physics
At what height \( ^{\prime} h^{\prime} \) from the earth
surface, acceleration due to gravity
becomes half as that of acceleration
due to gravity on the surface of earth. \( [R=\text { Radius of earth }] \)
\( \mathbf{A} \cdot h=R \)
в. \( h=\frac{R}{2} \)
c. \( h=\frac{R}{3} \)
D. \( h=\frac{R}{4} \)
Subject: Maths
For positive integers \( n_{1}, n_{2} \) the value of
the expression \( (1+i)^{n_{1}}+\left(1+i^{3}\right)^{n_{1}}+ \)
\( \left(1+i^{5}\right)^{n_{2}}+\left(1+i^{7}\right)^{n_{2}}, \) where \( i=\sqrt{-1} \)
is a real number if
A \( \cdot n_{1}=n_{2}+1 \)
В . \( n_{1}=n_{2}-1 \)
c. \( n_{1}=n_{2} \)
D \( . n_{1}>0, n_{2}>0 \)
Subject: Maths
If \( \mathbf{0} \leq \boldsymbol{x} \leq \mathbf{3} \boldsymbol{\pi}, \mathbf{0} \leq \boldsymbol{y} \leq \)
\( 3 \pi \) and \( \cos x . \sin y=1 \) then the
possible number of values of the
ordered pair \( (x, y) \) is
\( A \cdot 6 \)
B. 12
c. 8
D. 15
Subject: Chemistry
The treatment of a compound \( X \) with
\( H I O_{4} \) produces \( C H_{3} C H O \) and
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H O} \). The compound \( \mathbf{X} \) is :
A. \( C H_{3} C H=C H C H_{2} C H_{3} \)
в. \( C H_{3} C H(O H) C H(O H) C H_{2} C H_{3} \)
c. \( C H_{3} C H=C H C H=C H_{2} \)
D. \( C H_{3} C H(O H) C H_{2} C H O \)
Subject: Maths
If (5,12) and (24,7) are the foci of an
ellipse passing through the origin, then the eccentricity of the conic is
A \( \cdot \frac{\sqrt{386}}{12} \)
B. \( \frac{\sqrt{386}}{13} \)
c. \( \frac{\sqrt{386}}{25} \)
D. \( \frac{\sqrt{386}}{38} \)
Subject: Chemistry
The unit of equilibrium constant for the following reaction is:
\( \mathbf{2} N \boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{N}_{2} \boldsymbol{O}_{4}(\boldsymbol{g}) \)
A \( . \) mol \( L^{-1} \)
B. \( L \) mol \( ^{-1} \)
c. \( m o l^{-1} L^{-1} \)
D. Equilibrium constant is unitless
Subject: Physics
A beam of cross section area \( A \) is made
of a material of Young modulus Y. The beam is bent into the arc of a circle of
radius R. The bending moment is proportional to
A \( \cdot \frac{Y}{R} \)
в. \( \frac{Y}{R A} \)
c. \( \frac{R}{Y} \)
D. \( Y R \)
Subject: Chemistry
In which cases are the law of
conservation of mass followed?
This question has multiple correct options
\( \mathbf{A} \cdot 10 \mathrm{g} \mathrm{CaCO}_{3} \) on heating gives \( 0.1 \mathrm{mole} \mathrm{CaO} \) and \( 2.24 \mathrm{L} \)
\( C O_{2} \) at \( \mathrm{NTP} \)
B. 1 mole \( N_{2} \) and 1 mole \( H_{2} \) combine to form 2 moles of
\( N H_{3} \)
C. 0.2 mole \( S O_{2} \) combines with 3.2 g \( O_{2} \) to form 0.2
moles \( S O_{3} \)
D. 1 g \( H_{2} \) combines with 0.5 g \( O_{2} \) to form 1.5 g \( H_{2} O \)
Subject: Maths
Let \( \boldsymbol{S}=\{1,2,3, \ldots . ., 9\} . \) For \( \boldsymbol{k}= \)
\( \mathbf{1}, \mathbf{2}, \dots . ., \mathbf{5}, \) let \( N_{k} \) be the number of
subsets of \( S \), each containing five
elements out of which exactly \( k \) are odd
Then \( \boldsymbol{N}_{\mathbf{1}}+\boldsymbol{N}_{\mathbf{2}}+\boldsymbol{N}_{\mathbf{3}}+\boldsymbol{N}_{\mathbf{4}}+\boldsymbol{N}_{\mathbf{5}}= \)
A . 210
в. 252
c. 125
D. 126
Subject: Physics
Q Type your question
connected to a resistance \( R \) and two
ideal inductors \( L_{1} \) and \( L_{2} \) through a
switch \( S \) as shown. There is no mutual
inductance between the two inductors.
The switch \( S \) is initially open. At \( t=0 \)
the switch is closed and current begins
to flow. Which of the following options is/are correct?
This question has multiple correct options
A \( \cdot \) At \( t=0, \) the current through the resistance \( R \) is \( \frac{V}{R} \)
B. After a long time, the current through \( L_{2} \) will be \( \frac{V}{R} \frac{L_{1}}{L_{1}+L_{2}} \)
C. After a long time, the current through \( L_{1} \) will be \( \frac{V}{R} \frac{L_{2}}{L_{1}+L_{2}} \)
D. The ratio of the currents through \( L_{1} \) and \( L_{2} \) is fixed at all times \( (t>0) \)
Subject: Physics
An \( \alpha- \) particle passes through a
potential difference of \( 2 \times 10^{6} V \) and
then it becomes incident on a silver foil.
The charge number of silver is 47. The
distance of closest approach of the particle to the nucleus will be:
A. \( 6.4 \times 10^{-13} \mathrm{m} \)
B. \( 4.3 \times 10^{-13} \mathrm{m} \)
c. \( 2.1 \times 10^{-13} m \)
D. \( 3.76 \times 10^{-15} \mathrm{m} \)
Subject: Physics
A man can see distinctly from a distance of \( 0.5 m . \) If he wants to read a
book placed at a distance of \( 25 \mathrm{cm} \), then
what kind of lens should he use??
A. Convex lens with focal length of \( -50 \mathrm{cm} \)
B. Concave lens with focal length of \( -50 c m \)
c. convex lens with focal length of \( 50 \mathrm{cm} \)
D. Concave lens with focal length of \( 50 \mathrm{cm} \)
Subject: Physics
A parallel beam of monochromatic light is incident normally on a narrow slit. A diffraction pattern is formed on a screen placed perpendicular to the direction of the incident beam. At
the first minimum of the diffraction
pattern, the phase difference between the rays coming from the two edges of the slit is :
A. zero
в. \( \frac{\pi}{2} \)
\( c \)
D. \( 2 \pi \)
Subject: Maths
\( \int\left(e^{\sin ^{-1} x}+\frac{1}{\sqrt{1-x^{2}}}\right) d x \)
\( ^{\mathbf{A}} \cdot e^{\sin ^{-1} x}\left(\frac{\sqrt{1-x^{2}}+x}{2}\right)+\sin ^{-1} x+c \)
B . \( e^{x}\left(1+\tan ^{2} x\right)+c \)
\( \mathbf{c} \cdot e^{x} \tan 2 x+c \)
D. \( e^{x}(1+\tan x)+c \)
Subject: Physics
A planet is revolving in an elliptical orbit around the sun. Its closest
distance from the sun is \( r \) and the
farthest distance is \( R \). If the velocity of
the planet nearest to the sun be \( v \) and
that farthest away from the sun be \( \boldsymbol{V} \)
then \( \boldsymbol{v} / \boldsymbol{V} \) is :
A \( \cdot \frac{R^{2}}{r^{2}} \)
B. \( \frac{r^{2}}{R^{2}} \)
\( \mathbf{c} \cdot \frac{R}{r} \)
D. \( \frac{r}{R} \)
Subject: Maths
(i) If area \( (\triangle A B C)=16 \mathrm{cm}^{2}, \) area \( (\triangle \)
\( \mathrm{DEF}=25 \mathrm{cm}^{2} \) and \( \mathrm{BC}=2.3 \mathrm{cm}, \) find EF.
(ii) If area \( (\triangle A B C)=9 c m^{2}, \operatorname{area}(\triangle D E F) \)
\( =64 \mathrm{cm}^{2} \) and \( \mathrm{DE}=5.1 \mathrm{cm}, \) find \( \mathrm{AB} \)
(iii) If \( A C=19 \mathrm{cm} \) and \( \mathrm{DF}=8 \mathrm{cm}, \) ratio of
the area of two triangles.
(iv) If area \( (\triangle A B C)=36 \mathrm{cm}^{2}, \) area \( (\triangle \)
DEF) \( =64 \mathrm{cm}^{2} \) and \( \mathrm{DE}=6.2 \mathrm{cm}, \) find \( \mathrm{AB} \)
(v) If \( A B=1.2 \mathrm{cm} \) and \( \mathrm{DE}=1.4 \) find the ratio
of the areas of triangle \( A B C \) and DEF.
Subject: Physics
\( \ln \) an \( A C \) circuit voltage \( V=V_{0} \sin w t \)
and inductor L is connected across the
circuit. Then the instentaneous power
will be
A \( \cdot \frac{V_{0}^{2}}{2 w l} \sin w t \)
B. \( \frac{-V_{0}^{2}}{2 w l} \sin w t \)
c. \( \frac{V_{0}^{2}}{2 w l} \sin 2 w t \)
D. \( \frac{V_{0}^{2}}{w l} \sin w t \)
Subject: Maths
For the equation \( \boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{c}=\boldsymbol{0}, \boldsymbol{a}, \boldsymbol{b} \)
and \( c \) are real
Statement 1: If the equation \( a x^{2}+b x+ \)
\( c=0,0<a<b<c, \) has non-real
complex roots \( z_{1} \) and \( z_{2}, \) then \( \left|z_{1}\right|> \)
\( \mathbf{1},\left|\boldsymbol{z}_{2}\right|>\mathbf{1} \)
Statement 2: Complex roots always
occur in conjugate pairs.
A. Both the statements are true, and Statement 2 is the correct explanation for Statement 1
B. Both the statements are true, but Statement 2 is not the correct explanation for Statement 1
c. Statement 1 is true and Statement 2 is false.
D. Statement 1 is false and Statement 2 is true
Subject: Physics
A transverse wave of frequency \( 100 \mathrm{Hz} \) passes through water. The refractive index of water is \( 1.33, \) what will be the
frequency of the wave in water
A . 133 Н \( z \)
в. 100 Н \( z \)
\( c \cdot 75 \mathrm{Hz} \)
D. 165 нz
Subject: Physics
What is the electric potential at a
distance \( ^{\prime} x^{\prime} \) from the centre, inside a
conducting sphere having a charge \( Q \)
and radius \( R ? \)
A. \( \frac{1}{4 \pi \epsilon_{0}} \frac{Q}{R} \)
в. \( \frac{1}{4 \pi \epsilon_{6}} \frac{Q}{x} \)
c. \( \frac{1}{4 \pi \epsilon_{0}} \frac{Q X}{R^{2}} \)
D. zero
Subject: Physics
A uniform cube of mass \( m \) and side \( a \) is
resting in equilibrium on a rough \( 45^{\circ} \)
inclined surface. The distance of the
point of application of normal reaction measured from the lower edge of the
cube is:
A . zero
B. \( \frac{a}{2} \)
c. \( \frac{a}{\sqrt{2}} \)
D. \( \frac{a}{4} \)
Subject: Physics
A long cylindrical pipe of radius \( 20 \mathrm{cm} \) is closed at its upper end and has an airtight piston of negligible mass as
shown. When a \( 50 \mathrm{Kg} \) mass is attached
to the other end of piston, it moves down
by a distance \( \Delta l \) before coming to
equilibrium. Assuming air to be an ideal gas, \( \Delta l / L( \) see figure ) is close to \( \left(g=10 m / s^{2}, \) atmospheric pressure is \right.
\( 10^{5} \) Pascal
A .0 .01
в. 0.02
\( c .0 .04 \)
D. 0.0
Subject: Physics
In the Millikan's oil drop experiment the oil drop is subjected to a horizontal electric field of \( 4 \mathrm{N} / \mathrm{C} \) and the drop moves with a constant velocity
making an angle \( 45^{0} \) to the horizontal. If
the weight of the drop is W. The charge on the drop is (neglect buoyancy)
A. w
B. W/4
c. w/2
D. 3W/4
Subject: Chemistry
The electron configuration
\( 1 s^{2} 2 s^{2} p^{6} 3 s^{2} p^{6} 4 s^{2} 3 d^{7} \) represents an
atom of the element
A. \( B r \)
в. \( C o \)
c. \( C d \)
D. \( G a \)
E . \( M g \)
Subject: Chemistry
Which of the following have state of hybridization of the central atom not same as in the others?
\( A \cdot B \) in \( B F_{3} \)
B. \( \operatorname{oin} H_{3} O^{+} \)
c. \( \mathrm{N} \) in \( N H_{3} \)
D. \( \operatorname{Pin} P C l_{3} \)
Subject: Physics
Q Type your question
experimentally verified by Davisson and Germer by diffraction experiment. Wave character of matter
has significance only for microscopic particles. de Broglie wavelength or wavelength of matter wave can be calculated using
the following relation:
\( \lambda=\frac{h}{m v} \)
where, ' \( m \) ' and ' \( v \) ' are the mass and
velocity of the particle. de Broglie hypothesis suggested that
electron waves were being
diffracted by the target, much as \( X \)
rays are diffracted by planes of atoms in the crystals.

The wavelength of matter waves
associated with a body of mass \( 1000 g \)
moving with a velocity of \( 100 m / \)sec is:
A \( \cdot 6.62 \times 10^{-39} \mathrm{cm} \)
B . \( 6.62 \times 10^{-36} \mathrm{cm} \)
C \( .6 .626 \times 10^{-36} m \)
D. \( 3.31 \times 10^{-32} m \)
Subject: Physics
Calculate the amount of heat required
to convert 100 g of ice at \( 0^{\circ} \mathrm{C} \) into the
water at \( 0^{\circ} \mathrm{C}: \) Given:Specific latent heat of fusion of ice \( =336 J / g \)
A. 33600
B. 3360 J
c. 67200
D. 6720 J
Subject: Chemistry
Write a balanced equation for each of the following observations:
\( H N O_{3} \) turns brown when exposed to
air.
A \( \cdot 2 H N O_{3} \longrightarrow H_{2} O+2 N O+3(O), 2 N O+O_{2} \rightarrow \)
\( 2 N O_{2} \)
в. \( 2 H N O_{3} \rightarrow H_{2} O+2 N O+2(O), 2 N O+O_{2} \rightarrow \)
\( 2 N O_{2} \)
c. \( 2 H N O_{3} \longrightarrow H_{2} O+N O+3(O), N O+O_{2} \longrightarrow 2 N O_{2} \)
D. \( 2 H N O_{3} \rightarrow H O+2 N O_{2}+3(O), 2 N O_{2}+O_{2} \longrightarrow \)
\( 2 N O_{2} \)
Subject: Physics
The relation between \( u, v \) and \( f \) for a
mirror is given by
A \( \cdot f=\frac{u \times v}{u-v} \)
в. \( f=\frac{2 u \times v}{u+v} \)
c. \( _{f}=\frac{u \times v}{u+v} \)
D. \( f=\frac{u-v}{u+v} \)
Subject: Chemistry
The equilibrium constant for the
isomerisation of butane at \( 25^{\circ} C \) is
\( \boldsymbol{K}_{c}=\mathbf{8} \)
Butane \( \rightarrow \) Isobutane
If \( 5.8 \mathrm{g} \) butane is introduced into a \( 12.5 \mathrm{L} \) vessel at \( 25^{\circ} C . \) What mass of isobutane
will be present at equilibrium?
A. \( 5.15 \mathrm{g} \)
B. 2.56
c. 7.49 g
D. 5.80 g
Subject: Chemistry
toppr
Q Type your question
whicn grapn correctly represents \( \boldsymbol{E}_{\text {cell}} \) \( (Y-a x i s) \) as a function of \( \log \frac{\left[Z n^{2+}\right]}{\left[C u^{2+}\right]} \)
axis)?
\( A \)
B.
\( c \)
\( D \)
Subject: Chemistry
Which of the following is a \( 1^{\circ} \) amine?
A \( \cdot\left(C H_{3}\right)_{3} C N H_{2} \)
в. \( C_{6} H_{5} N H C H_{3} \)
\( \mathbf{c} \cdot_{C H_{3} N H C H}\left(C H_{3}\right)_{2} \)
D. \( \left(C H_{3} C H_{2}\right)_{2} N C H_{3} \)
Subject: Maths
If \( A=\{a, b, c\}, B=\{1,2\}, \) then find
\( \boldsymbol{A} \times \boldsymbol{B}, \boldsymbol{B} \times \boldsymbol{A} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{A} \times \boldsymbol{A} \)
Subject: Physics
Two coils, \( A \) and \( B \), are lined such that
emf \( \epsilon \) is induced in \( B \) when the current
in \( A \) is changing at the rate \( I \). If \( i \) current
is now made to flow in \( \mathrm{B} \), the flux linked
with \( A \) will be :
A. \( (\epsilon / I) i \)
i
B. \( \epsilon i I \)
c. \( (\epsilon I) \)
D. \( i I / \epsilon \)
Subject: Physics
The acceleration due to gravity on the planet \( A \) is 9 times the acceleration due to gravity on the planet B. A manjumps to a height of \( 2 \mathrm{m} \) on the surface \( \mathrm{A} \). What is the height of jump by the same person on the plane B?
\( A \cdot 6 m \)
B. 2/9 m
\( c \cdot 2 / 3 m \)
D. 18 m
Subject: Physics
A wave travels on a light string. The equation of the wave is \( \boldsymbol{Y}= \)
\( \boldsymbol{A} \sin \left(\boldsymbol{k} \boldsymbol{x}-\boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{3} \boldsymbol{0}^{\circ}\right) . \) It is reflected
from a heavy string tied to an end of the
light string at \( x=0 . \) If \( 64 \% \) of the
incident energy is reflected the equation of the reflected wave is
A. \( Y=0.8 A \sin \left(k x-\omega t+30^{\circ}+180^{\circ}\right) \)
B. \( Y=0.8 A \sin \left(k x+\omega t+30^{\circ}+180^{\circ}\right) \)
C. \( Y=0.8 A \sin \left(k x+\omega t-30^{\circ}\right) \)
D. \( Y=0.8 A \sin \left(k x+\omega t+30^{\circ}\right) \)
Subject: Chemistry
In the figure, \( A \) and \( B \) are two adiabatic
curves for two different gases. Then \( \mathbf{A} \)
and B correspond to:
A. Ar and He respectively
B. He and \( H_{2} \) respectively
\( \mathrm{c} \cdot \mathrm{O}_{2} \) and \( \mathrm{H}_{2} \) respectively
D. \( H_{2} \) and He respectively
Subject: Physics
Assertion
A ball of mass \( m \) is released from the
top of a smooth inclined plane. At the
same time another ball of same mass
allowed to fall freely from same height. When both balls reaches the bottom of
the plane, momentum will not be equal.
Reason

Momentum depends on the direction of
velocity as well as its magnitude.
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
Read the following statements carefully
1. Photochemical smog always contains
ozone
2. The toxic effect of carbon monoxide is
due to its greater affinity for haemoglobin as compared to oxygen.
3. Lead is the most hazardous metal
pollutant of automobile exhaust. Which of the above statements is not
true?
A.
B. 2
\( c .3 \)
D. None of these
Subject: Physics
If \( \Delta Q \) and \( \Delta W \) represents the heat
supplied to the system and the work done on the system respectively, then the first law of thermodynamics can be written as
A. \( \Delta Q=\Delta U+\Delta W \)
в. \( \Delta Q=\Delta U-\Delta W \)
c. \( \Delta Q=\Delta W-\Delta U \)
D. \( \Delta Q=-\Delta W-\Delta U \)
Subject: Maths
The value of \( \tan ^{-1}\left(\frac{1}{2} \tan 2 A\right)+ \)
\( \tan ^{-1}(\cot A)+\tan ^{-1}\left(\cot ^{3} A\right) \) for \( 0< \)
\( \boldsymbol{A}<\frac{\boldsymbol{\pi}}{\boldsymbol{4}} \) is?
\( \mathbf{A} \cdot 4 \tan ^{-1} 1 \)
B. \( 2 \tan ^{-1} 2 \)
\( c \cdot 0 \)
D. None
Subject: Chemistry
Choose the correct reagent required to
carry out the transformation:
\( \mathbf{A} \cdot Z n+ \) conc. \( H C l \)
B. conc. \( H_{2} S O_{4} \)
\( \mathbf{c} \cdot L i, \) then \( H_{2} O \)
\( \mathbf{D} \cdot H_{2} / P t \)
Subject: Physics
In a surface tension experiment with a
capillary tube water rises up to 0.1 m. If the same experiment is repeated on an artificial satellite which is revolving around the earth. The rise of water in a
capillary tube will be
A. \( 0.1 m \)
в. \( 9.8 m \)
\( \mathrm{c} \cdot 0.98 \mathrm{m} \)
D. Full length of capillary tube
Subject: Maths
\( \operatorname{Let} f(x)=\frac{\sin 4 \pi[x]}{1+[x]^{2}}, \) where \( [x] \) is the
greatest integer less than or equal to \( x \)
then
A. \( f(x) \) is not differentiable at some points
B. \( f(x) \) exists but is different from zero
c. \( L H D(a t x=0)=0 . R H D(a t x=1)=0 \)
D. \( f(x)=0 \) but \( f \) is not a constant function
Subject: Physics
The velocity \( v \) of waves produced in
water depends on their wavelength \( \lambda \)
the density of water \( \rho, \) and acceleration
due gravity \( g \). The square of velocity is
proportional to:
\( \mathbf{A} \cdot K \sqrt{(g \lambda)} \)
B . \( \lambda^{-1} g^{-1} \rho^{-1} \)
c. \( \lambda \rho g \)
D. \( \lambda^{2} g^{-2} \rho^{-1} \)
Subject: Physics
Consider elastic collision of a particle of mass \( m \) moving with a velocity \( u \) with
another particle of the same mass at rest. After the collision the projectile and the stuck particle move in
directions making angles \( \theta_{1} \) and \( \theta_{2} \)
respectively with the initial direction
of motion. The sum of the angles \( \boldsymbol{\theta}_{1}+\boldsymbol{\theta}_{2} \)
is
Subject: Maths
If \( f(x)=\frac{x^{2}-b x+25}{x^{2}-7 x+10} \) for \( x \neq 5 \) is
continuous at \( x=5, \) then the value of
\( \boldsymbol{f}(\mathbf{5}) \) is
A . 0
B.
\( c \cdot 2 \)
D. 3
Subject: Physics
Calculate the energy emitted by the sun
in one second. Also estimate the mass
of the sun that is converted to energy in one second.
(Take solar constant as \( 1.4 \times \)
\( 10^{3} W m^{-2}, \) distance between the earth
and the sun as \( 1.5 \times 10^{11} m \) and the
velocity of light as \( 3 \times 10^{8} m S^{-1} \) ).
Subject: Maths
\( \lim _{x \rightarrow 1} \frac{(\log (1+x)-\log 2)\left(3.4^{x-1}-3 x\right)}{1} \)
\( \left.\left.\left\{(7+x)_{3}^{1}\right)-(1+3 x)^{\frac{1}{2}}\right)\right\} \sin \pi x \)
Subject: Chemistry
A solution containing 500 g of a protein per liter is isotonic with a solution
containing 3.42 g of sucrose per liter. The molecular mass of protein is:
\( A \cdot 58 \)
B. \( 146 \mathrm{g} \)
c. \( 34200 \mathrm{g} \)
D. 50000 \( g \)
Subject: Chemistry
Assertion \( (\mathrm{A}): N O_{2} \) is paramagnetic
molecule, whereas \( N_{2} O_{4} \) is
diamagnetic Reason (R): Molecules with unpaired electrons are Diamagnetic.
A. Both (A) and (R) are true and (R) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not the correct explanation of (A)
\( c \cdot(A) \) is true and
(R) is false
D. (A) is false but (R) is true
Subject: Chemistry
At \( p H=3 \) and rest all reductant and oxidant in change (I) being in standard
state, \( M n O_{4}^{-} \) can oxidise:
A \( \cdot I^{-} \) and \( B r^{-} \) both
B. \( I^{-} \) and \( C l^{-} \) both
c. \( I^{-}, B r^{-} \) and \( C l^{-} \) all
D. \( B r^{-} \) and \( C l^{-} \) both
Subject: Physics
A gas in a cylinder held at a constant pressure of \( 1.7 \times 10^{5} P a \) and is cooled
and compressed from \( 1.20 m^{3} \) to \( 0.8 m^{3} \) The internal energy of the gas decreses by \( 1.1 \times 10^{5} J . \) The magnitude of the
heat flow into or out of the gas is given
as \( x \times 10^{4} \) J. Find \( x \) ( \( x \) is a two digit
integer)
Subject: Physics
\( Q \) тур
When the fan runs at full speed, its speed becomes constant. This is because the torque due to magnetic field inside the fan is balanced by the torque due to air resistance on the
blades of the fan and the torque due to friction between the fixed part and the shaft of the fan. The electric power going into the fan is spent (i) in the internal resistance as heat, call it \( P_{1}, \) (ii) in doing work against internal friction and air resistance producing heat, sound,
etc., call it \( P_{2} \). When the coil of fan
rotates, an emf is also induced in the coil. This opposes the external emf is also induced in the coil. This opposes
the external emf applied to send the current to the fan. This emf is called
back emf, call it \( e . \) Answer the following questions when the fan is running at full speed.The current flowing into the
fan and the value of back emf \( e \) is
A. \( 200 A, 5 V \)
B . \( 5 A, 200 V \)
c. \( 5 A, 195 V \)
D. \( 1 A, 0 V \)
Subject: Chemistry
The velocity of sound in a gas is
\( 30 m s^{-1} \) at \( 27^{\circ} C . \) What is the velocity of
the sound in the same gas at \( 127^{\circ} \mathrm{C} \) ?
A \( \cdot 20 m s^{-1} \)
B. \( 30 m s^{-1} \)
D. \( 60 m s^{-1} \)
Subject: Physics
A man produce sound with trumpet. A wave has a wavelength of \( 8.75 \mathrm{mm} \) and frequency of \( 40 \mathrm{kHz} \). If the man receives an echo after reflecting from the wall 0.4 s later. Calculate the distance between
man and the wall.
\( A \cdot 35 \mathrm{m} \)
B. 70
c. \( 105 \mathrm{m} \)
D. \( 140 \mathrm{m} \)
E. \( 175 \mathrm{m} \)
Subject: Physics
A body of mass \( 2 \mathrm{kg} \) makes an elastic collision with another body at rest and continues to move in the original direction at a speed equal to \( 1 / 3 \) of its original speed. The mass of the second body is
A. \( 2 k g \)
в. \( 3 k g \)
c. \( 1 k g \)
D. \( 4 k g \)
Subject: Maths
\( \int \frac{1-\cos x}{\cos x(1+\cos x)} d x \)
A. \( \log (\sec x-\tan x)-2 \tan \frac{x}{2} \)
B. \( \log (\sec x+\tan x)-\tan \frac{x}{2} \)
C \( \cdot \log (\sec x+\tan x)+2 \tan \frac{x}{2} \)
D \( \cdot \log (\sec x+\tan x)-2 \tan \frac{x}{2} \)
Subject: Maths
If \( \vec{a}+\vec{b}+\vec{c}=0, \) then the angle \( \theta \) between \( \vec{b} \) and \( \vec{c} \) is given by
\( ^{\mathrm{A}} \cdot \cos \theta=\frac{a^{2}-b^{2}-c^{2}}{2 b c} \)
B. \( \cos \theta=\frac{b^{2}+c^{2}-a^{2}}{2 b c} \)
c. \( \cos \theta=\frac{a^{2}+b^{2}-c^{2}}{2 b c} \)
D. none of these
Subject: Chemistry
The correct order of ionization energies
of \( \boldsymbol{F}^{-}, \boldsymbol{C l}^{-} \boldsymbol{F} \) and \( \boldsymbol{C l} \) is:
A \( \cdot C l<F<C l^{-}<F^{-} \)
B . \( C l^{-}<F^{-}<C l<F \)
c. \( F^{-}<C l^{-}<C l<F \)
D. \( C l^{-}<C l<F^{-}<F \)