AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The figure shows an assembly
consisting of a number of pendulums of
varying lengths. The driver pendulum is pulled aside and released so that it
oscillates in a plane perpendicular to
that of the diagram.
It will be observed that :
A. all pendulums oscillate with the frequency of the driver pendulum and have the same amplitude.
B. pendulums oscillate with different frequencies but equal amplitude, the shortest pendulum oscillating with the highest frequency,
c. all pendulums oscillate with the frequency of the driver pendulum; the pendulum with length equal to that of the driver has the greatest amplitude
D. pendulums oscillate with different frequencies and rent amplitudes
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x} \sqrt{\mathbf{4} \boldsymbol{a} \boldsymbol{x}-\boldsymbol{x}^{2}},(\boldsymbol{a}>\mathbf{0}) . \) Then
\( f(x) \) has range in
A. \( (0,3 a) \)
В. \( (a, 4 a) \)
c. \( (0,4 a) \)
D. None of the above
Subject: Physics
An electron beam is moving between two parallel plates having electric field
\( 1.125 \times 10^{-6} N / m . \) A magnetic field
\( 3 \times 10^{-10} T \) is also applied, so that
beam of electrons do not deflect. The
velocity of the electron is
\( A \cdot 4225 \mathrm{m} / \mathrm{s} \)
B. 3750 m/s
c. \( 2750 \mathrm{m} / \mathrm{s} \)
D. 3200 \( \mathrm{m} / \mathrm{s} \)
Subject: Physics
\( A \) and \( B \) are isotopes. \( B \) and \( C \) are isobars. All three are radioactive.
A. \( A, B \) and \( C \) must belong to the same element
B. \( A, B \) and \( C \) may belong to the same element
c. It is possible that \( A \) will change to \( B \) through a radioactive-decay process
D. It is possible that \( B \) will change to \( C \) through a radio active -decay process
Subject: Chemistry
Hybridization state of beryllium atom in
\( B e C l_{2} \) molecule is \( x . \) The type of
hybridization changes to \( y \) when \( B e C l_{2} \) transforms to the solid state. Then \( \boldsymbol{x}, \boldsymbol{y} \)
are respectively:
A \( . s p, s p^{2} \)
B . \( s p, s p^{3} \)
c. \( s p^{2}, s p^{3} \)
D. \( s p, s p \)
Subject: Chemistry
From the following data at constant volume for combustion of benzene,
calculate the heat of this reaction at
constant pressure condition.
\( \boldsymbol{C}_{6} \boldsymbol{H}_{6}(\boldsymbol{l})+\mathbf{1 5} / \mathbf{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{6} \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( \mathbf{3} \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O}(\boldsymbol{l}) \)
\( \Delta U \) at \( 25^{\circ} C=-3268.12 k J \)
Subject: Chemistry
The correct order of bond angles in
\( \boldsymbol{H}_{2} \boldsymbol{S}, \boldsymbol{N} \boldsymbol{H}_{3}, \boldsymbol{B} \boldsymbol{F}_{3} \) and \( \boldsymbol{S} \boldsymbol{i} \boldsymbol{H}_{4} \) is:
A. \( H_{2} S<S i H_{4}<N H_{3}<B F_{3} \)
B. \( N H_{3}<H_{2} S<S i H_{4}<B F_{3} \)
c. \( H_{2} S<N H_{3}<S i H_{4}<B F_{3} \)
D. \( H_{2} S<N H_{3}<B F_{3}<S i H_{4} \)
Subject: Chemistry
\( \boldsymbol{H} \boldsymbol{C} \boldsymbol{H} \boldsymbol{O} \stackrel{\text {Reduction}}{\longrightarrow} \boldsymbol{A} \stackrel{\boldsymbol{P}}{\longrightarrow} \)and\( \quad \boldsymbol{I}_{2} \)
\( \boldsymbol{B} \stackrel{\boldsymbol{K C N}}{\longrightarrow} \boldsymbol{C} \stackrel{\boldsymbol{H y d r o l y s i s}}{\boldsymbol{D}} \)
What is \( D ? \)
A . Acetic acid
B. Ethylamine
c. Acetamide
D. None of these
Subject: Physics
The relation between \( B_{v}, B_{h} \) and B is
\( \mathbf{A} \cdot B=\sqrt{B_{h}^{2}+B_{v}^{2}} \)
B . \( B=B_{h} \cdot B_{v} \)
c. \( _{B}=\frac{B_{v}}{B_{h}} \)
D. \( B=\frac{B_{h}}{B_{v}} \)
Subject: Chemistry
A Student planned an experiment that
would use \( 0.10 M \) propionic acid,
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C O O H} . \) Calculate the value
of \( \left[\boldsymbol{H}^{+}\right] \) and the \( \boldsymbol{p} \boldsymbol{H} \) for this solution. For
propionic acid, \( \boldsymbol{K}_{\boldsymbol{a}}=\mathbf{1 . 3 4} \times \mathbf{1 0}^{-\mathbf{5}} \)
Subject: Chemistry
What are the suitable reagent for
following conversion
\( \mathbf{A} \cdot B r_{2} / F e B r_{3}, K M n O_{4}, H N O_{3} / H_{2} S O_{4} \)
B. \( K M n O_{4}, B r_{2} / F e B r_{3}, H N O_{3} \)
\( \mathbf{c} \cdot H N O_{3}, B r_{2} / F e B r_{3}, K M n O_{4} \)
D. \( H N O_{3}, K M n O_{4}, B r_{2} / F e B r_{3} \)
Subject: Physics
A beam of length \( l \) lies on the \( +x \) axis
with its left end on the origin. A cable pulls the beam in negative y-direction with a force \( \boldsymbol{F}=\boldsymbol{F}_{0}\left(1-\frac{\boldsymbol{x}}{\boldsymbol{l}}\right) . \) If the axis
is fixed at \( x=0 \) then find the torque.
\( \mathbf{A} \cdot-F_{0} l \)
B. \( \frac{F_{0} l}{2} \)
\( c \cdot-\frac{F_{0} l}{2} \)
D. none of these
Subject: Physics
Assertion
The flow of heat energy from one body to the other depends upon the amount of heat energy in them
Reason
Heat flows from lower temperature of the body to higher temperature of the body
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 particle of mass \( m \) and positive
charge \( \boldsymbol{q}, \) moving with a uniform
velocity \( v, \) enters a magnetic field \( B \) as
shown in figure.
(a) Find the radius of the circular arc it
describes in the magnetic field
(b) Find the angle subtended by the arc
at the centre
(c) How long does the particles stay inside the magnetic field?
(d) Solve the three parts of the above
problems if the charge \( q \) on the particle is negative then.
Subject: Maths
ABCD is a parallelogram and \( A C, B D \) are its diagonals Express \( \overrightarrow{A B} \) and \( \overrightarrow{A D} \) in terms of \( \overrightarrow{\boldsymbol{A C}} \) and \( \overrightarrow{\boldsymbol{B D}} \)
A \( \cdot \overrightarrow{A B}=\frac{1}{2} \overrightarrow{A C}-\frac{1}{2} \overrightarrow{B D} \quad ; \overrightarrow{A D}=\frac{1}{2} \overrightarrow{A C}+\frac{1}{2} \overrightarrow{B D} \)
B \( \cdot \overrightarrow{A B}=\frac{1}{2} \overrightarrow{A C}+\frac{1}{2} \overrightarrow{B D} \quad ; \overrightarrow{A D}=\frac{1}{2} \overrightarrow{A C}+\frac{1}{2} \overrightarrow{B D} \)
c \( \cdot \overrightarrow{A B}=\frac{1}{2} \overrightarrow{A C}-\frac{1}{2} \overrightarrow{B D} \quad ; \overrightarrow{A D}=\frac{1}{2} \overrightarrow{A C}-\frac{1}{2} \overrightarrow{B D} \)
D・ \( \overrightarrow{A B}=\frac{1}{2} \overrightarrow{A C}+\frac{1}{2} \overrightarrow{B D} \quad ; \overrightarrow{A D}=\frac{1}{2} \overrightarrow{A C}-\frac{1}{2} \overrightarrow{B D} \)
Subject: Physics
In figure, an air lens of radius of curvature of each surface equal to
10cm is cut into a cylinder of glass of
refractive index \( 1.5 . \) The focal length
and the nature of lens are
A. \( 15 \mathrm{cm} \) diverging
B. \( 15 \mathrm{cm} \) converging
c. \( 10 \mathrm{cm} \) diverging
D. \( 10 \mathrm{cm} \) converging
Subject: Chemistry
The equilibrium constants \( \boldsymbol{K}_{\boldsymbol{p}_{1}} \) and \( \boldsymbol{K}_{\boldsymbol{p}_{2}} \)
for the reactions, \( \boldsymbol{X} \rightleftharpoons 2 \boldsymbol{Y} \) and \( \boldsymbol{Z} \rightleftharpoons \)
\( P+Q, \) respectively are in the ratio of
1 : 9. If the degree of dissociation of \( \boldsymbol{X} \)
and \( Z \) be equal then the ratio of total
pressures at the equilibrium is:
A . 1: 9
B. 1: 36
c. 1: 1
D. 1: 3
Subject: Physics
Two uniform solid spheres of equal radii
\( R, \) but mass \( M \) and \( 4 M \) have a centre
to centre separation \( 6 R \), as shown in Figure. The two spheres are held fixed. A projectile of mass \( m \) is projected from
the surface of the sphere of mass \( M \)
directly towards the centre of the second sphere. Obtain an expression for the minimum speed \( v \) of the projectile
so that it reaches the surface of the
second sphere.
Subject: Maths
\( \lim _{n \rightarrow \infty} \frac{\sqrt{x^{2}+1}-\sqrt[3]{x^{3}+1}}{\sqrt[4]{x^{4}+1}-\sqrt[5]{x^{4}+1}} \) equals
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c .-1 \)
D. none of these
Subject: Chemistry
If for the equilibrium:
\( N H_{2} C O O N H_{4}(s) \rightleftharpoons N_{2}(g)+ \)
\( \mathbf{3} \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{C} \boldsymbol{O}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \)
the value of \( \mathrm{Kp} \) at \( 800 \mathrm{K} \) is \( 27 \times 2^{\lambda / 2} \) and
the equilibrium pressure is 22 atm. Value of \( \lambda \) is :
A . 12
в. 2
c. 10
D. 1
\( E \)
Subject: Maths
ff \( x_{1}, y_{1} \) are the roots of \( x^{2}+8 x-20= \)
0 and \( x_{2}, y_{2} \) are the roots of \( 4 x^{2}+ \)
\( 32 x-57=0 \) and \( x_{3}, y_{3} \) are the roots of
\( 9 x^{2}+72 x-112=0 \) such that \( y_{i}<0 \)
then the points \( \left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right) \) and
\( \left(x_{3}, y_{3}\right) \)
A. are collinear
B. form an equilateral triangle
c. form a right angled isosceles triangle
D. are concyclic
Subject: Maths
Find the equation to the ellipse, whose focus is the point \( (-1,1), \) whose directrix is the straight line \( \boldsymbol{x}-\boldsymbol{y}+ \) \( \mathbf{3}=\mathbf{0}, \) and whose eccentricity is \( \frac{\mathbf{1}}{\mathbf{2}} \)
Subject: Maths
Construct an equilateral triangle. \( \Delta A B C . \) Construct an angle bisector of
\( \angle A \)
Let it meet side \( B C \) at \( D \). Find measures
of \( A B, A C, B D, D C \)
Find the relation between \( \frac{A B}{A C} \) and \( \frac{B D}{D C} \)
\( \mathbf{A} \cdot \frac{A B}{A C}<\frac{B D}{D C} \)
В. \( \frac{A B}{A C}>\frac{B D}{D C} \)
C \( \cdot \frac{A B}{A C}=\frac{B D}{D C} \)
D. None
Subject: Maths
The number of triplets \( (x, y, z) \) satisfies
the equation \( \boldsymbol{f}(\boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z})=\sin ^{-1} \boldsymbol{x}+ \)
\( \sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2} \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
c. 0
D. Infinite
Subject: Physics
Two identical discs of mass M and
radius \( R \) are connected by a light rod The assembly rests at a corner, the
vertical wall is smooth and there is
sufficient friction on the floor to ensure
pure rolling of disc B. The system starts
from position \( \boldsymbol{\theta}=\mathbf{0} . \) Find the velocity of
the midpoint of the rod when \( \boldsymbol{\theta}=\mathbf{6 0}^{\circ} \)
Subject: Maths
Given that \( \cos 50^{\circ} 20^{\prime}=0.6388 \) and
\( \cos 50^{\circ} 42^{\prime}=0.6334, \) then the possible
value of \( \cos 50^{\circ} 20^{\prime} \) is
A .0 .6293
B. 0.6307
c. 0.6361
D. 0.6414
Subject: Physics
A sphere of mass \( m \) and radius \( r \) is
placed on a rough plank of mass \( M . \) The
system is placed on a smooth
horizontal surface. A constant force \( \boldsymbol{F} \) is
applied on the plank such that the
sphere rolls purely on the plank. If the
acceleration of the sphere is \( \frac{2 F}{x M+2 m} \) find the value of \( x \)
Subject: Physics
Two rings of radius \( R \) and \( n R \) made up of same material have the ratio of
moment of inertia about an axis
passing through centre \( 1: 8 . \) The value
of \( n \) is
A .2
B. \( 2 \sqrt{2} \)
\( c \cdot 4 \)
D. \( \frac{1}{2} \)
Subject: Physics
Water is filled upto height H units in a tank placed on the ground and whose side walls are vertical. A hole is made in
one of the vertical wall such that the emerging stream of water strikes the
ground at the maximum range. If the level in the tank is changing at the rate of R units per second, at that instant the
rate at which range will be changing will be:
A. R/2 units per second
B. R units per second
c. 2R units per second
D. zero
Subject: Chemistry
In the Merck's process, the reagents involved for the preparation of hydrogen peroxide are:
A. \( B a O_{2}, H C l \)
в. \( N a_{2} O_{2}, H_{2} S O_{4} \)
\( \mathbf{c} \cdot B a_{2} O_{2}, H_{2} C O_{3} \)
\( \mathrm{D} \cdot P b O_{2}, H_{2} O \)
Subject: Physics
How much work would be required to move a proton from the negative to the positive plate?
A. \( -3.6 \times 10^{-18} J \)
в. \( 3.6 \times 10^{-19} \mathrm{J} \)
c. \( 3.6 \times 10^{-18} \mathrm{J} \)
D. \( -3.6 \times 10^{-19} \mathrm{J} \)
Subject: Physics
Two resistors are connected a) in series
b) in parallel. The equivalent resistance in two cases are 9 ohm and 2 ohm respectively. Then the resistance of the component
resistors are.
A. 2 ohm and 7 ohm
B. 3 ohm and 6 ohm
c. 3 ohm and 9 ohm
D. 5 ohm and 4 ohm
Subject: Chemistry
Select the correct options.
This question has multiple correct options
A. Isoelectric point is the \( \mathrm{pH} \) at which an amino acid exists primarily in its neutral from
B. Isoelectric point is the average of \( p K_{a} \) value of \( \alpha \) \( C O O H \) amino \( \alpha-N H_{3}^{+} \) groups[valid only for neutral amino acid]
C . Glycine is characterised by two \( p K_{a} \) values
D. For neutral amino acid, the concentration of zwitter ion is maximum at its isoelectric point
Subject: Chemistry
A mixture of \( S O_{3}, S O_{2} \) and \( O_{2} \) gases is
maintained in a \( 10 L \) flask at a
temperature at which the equilibrium constant for the reaction is 100 and the
reaction is, \( 2 S O_{2}(g)+O_{2}(g) \rightleftharpoons \)
\( 2 S O_{3}(g) \)
(i) If the number of moles of \( S O_{2} \) and
\( S O_{3} \) in the flask are equal, how many
moles of \( \boldsymbol{O}_{2} \) are present?
(ii) If the number of moles of \( S O_{3} \) in the
flask is twice the number of moles of
\( S O_{2}, \) how many moles of oxygen are
present?
Subject: Maths
If \( f(x) \) is continuous such that
\( |\boldsymbol{f}(\boldsymbol{x})| \leq \mathbf{1}, \forall \boldsymbol{x} \in \boldsymbol{R} \) and \( \boldsymbol{g}(\boldsymbol{x})= \)
\( \frac{e^{f(x)}-e^{|f(x)|}}{e^{f(x)}+e^{|f(x)|}} \) then range of \( g(x) \) is
A \( \cdot[0,1] \)
B. \( \left[0, \frac{e^{2}+1}{e^{2}-1}\right] \)
\( ^{\mathbf{C}} \cdot\left[0, \frac{e^{2}-1}{e^{2}+1}\right] \)
D. \( \left[\frac{1-e^{2}}{1+e^{2}}, 0\right] \)
Subject: Physics
Assertion
Smaller drops of liquid resist deforming forces better than the larger drops.
Reason

Excess pressure inside a drop is directly proportional to its surface area.
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: Physics
Assertion
The electric potential due to an electric dipole at a point on the perpendicular bisector of the dipole axis is 0 .
Reason
Any point on the perpendicular bisector of the dipole axis is equidistant from the the two equal and opposite charges.
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
A reaction is catalysed by \( \boldsymbol{H}^{+} \) ion; in presence of \( \boldsymbol{H} \boldsymbol{A} \) rate constant is \( \boldsymbol{2} \times \)
\( 10^{-3} \) min \( ^{-1} \) and in presence of \( H B \) rate
constant is \( 1 \times 10^{-3} \) min \( ^{-1} \)
\( \boldsymbol{H} \boldsymbol{A} \) and \( \boldsymbol{H} \boldsymbol{B} \) (both strong acids) have
relative strength as:
A . 0.5
B. 0.002
c. 0.001
D. 2
Subject: Maths
\( \boldsymbol{x}= \)
\( \operatorname{cosec}\left(\tan ^{-1}\left(\cos \left(\cot ^{-1}\left(\sec \left(\sin ^{-1} a\right)\right)\right)\right.\right. \)
\( \sec \left(\cot ^{-1}\left(\sin \left(\tan ^{-1}\left(\operatorname{cosec}\left(\cos ^{-1} a\right)\right)\right)\right.\right. \)
where \( a \in[0,1] . \) Then which of the
following options is correct?
A \( \cdot x^{2}+a^{2}=3 \)
В. \( x=y \)
c. \( y^{2}+a^{2}=3 \)
D. All of these
Subject: Physics
A convex lens forms a e real image three times larger than the object on a screen Object and screen are moved until the image becomes twice the size of the object. If the shift of the object is \( 6 \mathrm{cm} \) The shift of screen is
A . 36 \( \mathrm{cm} \)
B. 72 cm
c. \( 18 \mathrm{cm} \)
D. \( 9 \mathrm{cm} \)
Subject: Physics
State whether true or false:
Mean free path order for some gases at
\( 273 \mathrm{K} \) and 1 atm \( \mathrm{P} \) is
\( \boldsymbol{H} \boldsymbol{e}>\boldsymbol{H}_{2}>\boldsymbol{O}_{2}>\boldsymbol{N}_{2}>\boldsymbol{C} \boldsymbol{O}_{2} \)
A. True
B. False
Subject: Biology
Which of the following factors were responsible for the period of stagnant
growth of India's population from 1901
\( 1921 ? \)
Poor health and medical services.
2. Illiteracy of people at large.
2. Inefficient distribution system of food and other basic necessities.
A. Only 1 and 2
B. Only 1 and 3
c. only 2 and 3
D. 1,2 and 3
Subject: Chemistry
There are many gas molecules \( N H_{3} \)
\( C O, C H_{4} \) and \( S O_{2} \) in a group once. They were discussing about who would be the better absorbed on charcoal. So they
decided to have the race among themselves to prove it as to who would be absorbed more in the same time.
Who do you think won?
A. \( C O \)
в. \( N H_{3} \)
\( \mathrm{c} \cdot C H_{4} \)
\( D \cdot S O_{2} \)
Subject: Chemistry
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}(\boldsymbol{C l})-\boldsymbol{C}_{2} \boldsymbol{H}_{5} \frac{\text {Alc.}}{\boldsymbol{K O H}} \)
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C H}_{3} \)
The above reaction proceeds via \( E_{1} c b \) mechanism?
A. It is second order and bumolecular
B. It is first order and unimolecular
c. It is first order an bimolecular
D. It is second order and unimolecular
Subject: Physics
A particle of mass \( m \) is moving a
uniform velocity \( v_{1} . \) It is given an impulse such that its velocity becomes
\( \boldsymbol{v}_{2} . \) The impulse is equal to
A \( \cdot m\left[\left|v_{2}\right|-\left|v_{1}\right|\right] \)
B . \( 1 / 2 m\left[v_{1}^{2}-v_{1}^{2}\right] \)
\( \mathbf{c} \cdot m\left[v_{1}+v_{2}\right] \)
D. \( m\left[v_{2}-v_{1}\right] \)
Subject: Physics
A rectangular coil of 200 turns and area
\( 100 \mathrm{cm}^{2} \) is kept perpendicular to a
uniform magnetic field of induction
\( 0.25 T . \) If the field is reversed
in direction in 0.01 second, the average induced emf in the coil is :
A \( \cdot 10^{6} V \)
B . \( 10^{4} V \)
\( \mathbf{c} \cdot 10^{2} V \)
D. zero
Subject: Maths
The points \( \boldsymbol{O}, \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C} \) are the vertices of
a pyramid and \( P, Q, R, S \) are the mid-
points of \( \boldsymbol{O} \boldsymbol{A}, \boldsymbol{O} \boldsymbol{B}, \boldsymbol{B} \boldsymbol{C}, \boldsymbol{A} \boldsymbol{C} \)
respectively. If \( \overrightarrow{\boldsymbol{O A}}=\boldsymbol{a}, \overrightarrow{\boldsymbol{O B}}=\boldsymbol{b}, \overrightarrow{\boldsymbol{O C}}= \)
\( c, \) express in terms of \( a, b, c \) the vectors \( \boldsymbol{O P}, \overrightarrow{\boldsymbol{O Q}}, \overrightarrow{\boldsymbol{O R}} \) and \( \overrightarrow{\boldsymbol{O S}} \)
A \( \cdot \overrightarrow{O P}=\frac{1}{2} a, \overrightarrow{O Q}=\frac{1}{2} b, \overrightarrow{O R}=\frac{1}{2}(b+c), \overrightarrow{O S}=\frac{1}{2}(a+c) \)
B \( \cdot \overrightarrow{O P}=\frac{1}{2} c, \overrightarrow{O Q}=b, \overrightarrow{O R}=\frac{1}{2}(b+c), \overrightarrow{O S}=\frac{1}{2}(a+c) \)
c・ \( \overrightarrow{O P}=\frac{1}{2} c, \overrightarrow{O Q}=b, \overrightarrow{O R}=\frac{1}{2}(a+c), \overrightarrow{O S}=\frac{1}{2}(b+c) \)
D・ \( \overrightarrow{O P}=\frac{1}{2} a, \overrightarrow{O Q}=b, \overrightarrow{O R}=\frac{1}{2}(a+c), \overrightarrow{O S}=\frac{1}{2}(b+c) \)
Subject: Maths
In the figure given below \( \square P Q R S \) is a
trapezium. seg \( \boldsymbol{P Q}\|\operatorname{seg} \boldsymbol{M} \boldsymbol{N}\| \operatorname{seg} \boldsymbol{S} \boldsymbol{R} \)
If \( \boldsymbol{P} \boldsymbol{M}=\mathbf{8}, \boldsymbol{M} \boldsymbol{S}=\mathbf{1 0} \) and \( \boldsymbol{N} \boldsymbol{R}=\mathbf{5} \)
then find \( Q N \)
Subject: Chemistry
For the reaction, \( \boldsymbol{N} \boldsymbol{H}_{3}+\boldsymbol{O C l}^{-} \rightarrow \)
\( N_{2} H_{4}+C l^{-} \) occurring in basic
medium, the coefficient of \( N_{2} H_{4} \) in the
balanced equation will be :
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. 4
Subject: Physics
When a rubber-bank is stretched by a distance \( x, \) it exerts a restoring force of magnitude \( F=a x+b x^{2} \) where \( a \) and \( b \)
are constants. The work done in
stretching the unstretched rubber band
by \( \boldsymbol{L} \) is:
\( ^{\mathrm{A}} \cdot \frac{a L^{2}}{2}+\frac{b L^{3}}{3} \)
\( ^{\mathrm{B}} \cdot \frac{1}{2}\left(\frac{a L^{2}}{2}+\frac{b L^{3}}{3}\right) \)
\( \mathbf{c} \cdot a L^{2}+b L^{3} \)
D. \( \frac{1}{2}\left(a L^{2}+b L^{3}\right) \)
Subject: Physics
What is the resistance of the portion of
a circuit between \( A \) and \( B \) in the figure
given below. Points ' \( \boldsymbol{A} \) ' and ' \( \boldsymbol{a} \) ' are
connected by a copper wire of negligible resistance. Similarly, points ' \( B \) ' and ' b'
are also connected by a copper wire of negligible resistance.
\( A .3 R \)
в. \( \frac{R}{3} \)
c. \( \frac{3 R}{2} \)
D. \( \frac{2 R}{3} \)
Subject: Chemistry
Which of the following is not true about
structure of diamond and graphite?
A. In diamond, each carbon is \( s p^{3} \) hybridised while in
graphite each carbon is \( s p^{2} \) hybridised
B. In diamond, carbon atoms are closely packed in crystal lattice while graphite has layer structure.
C. Diamond is a hard substance while graphite is a soft substance.
D. Graphite is thermodynamically very less stable as compared to diamond and is amorphous form of carbon.
Subject: Physics
The amplitude and frequency of a wave represented by the equation :
\( \boldsymbol{Y}=\mathbf{2} \boldsymbol{A} \cos ^{2}(\boldsymbol{k} \boldsymbol{\gamma}-\boldsymbol{\omega} \boldsymbol{t}) \) are :
A \( \cdot 2 A, \frac{\omega}{2 \pi} \)
в. \( A, \frac{\omega}{\pi} \)
\( c \cdot \sqrt{A}, \frac{\omega}{\pi} \)
D. \( \sqrt{A}, \frac{\omega}{2 \pi} \)
Subject: Chemistry
Assertion
Nitrogenous matter produces ammonia.
Reason
Mammals excrete urea and
birds,reptiles produce uric acid which is a metabolite of amino acids
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 we wrote \( n^{3} \) as the sum of
consecutive odd numbers then what
will be the first term.
\( \mathbf{A} \cdot 2 n+1 \)
B. \( (2 n+1)(2 n-1) \)
c. \( 2 n-1 \)
D. \( n(n-1)+1 \)
Subject: Physics
A magnet is taken towards a conducting ring in such a way that a constant current of \( 10 m A \) is induced in
it. The total resistance of the ring is
\( 0.5 \Omega . \ln 5 s, \) the magnetic flux through
the ring changes by
\( \mathbf{A} \cdot 0.25 m W b \)
B. \( 25 m \) Wb
\( \mathbf{c} .50 m W b \)
D. \( 15 \mathrm{m} \mathrm{Wb} \)
Subject: Physics
A wire suspended vertically from one of its ends stretched by attaching a
weight of \( 200 N \) to the lower end. The
weight stretches the wire by 1 mm. Then the elastic energy stored in the wire is:
A. 0.25
J \( J \)
в. \( 10 J \)
\( c .20 J \)
D. \( 0.1 J \)
Subject: Maths
If an error of \( 1^{\circ} \) is made in measuring
the angle of a sector of radius \( 30 \mathrm{cm} \) then the approximate error in its area is
A \( \cdot 450 \mathrm{cm}^{2} \)
В \( \cdot 25 \pi c m^{2} \)
\( \mathbf{c} \cdot 2.5 \pi c m^{2} \)
D. none of these
Subject: Chemistry
The magnetic moment is associated with its spin angular momentum and
orbital angular momentum. Spin only
magnetic moment value of \( \boldsymbol{C r}^{3+} \) ion is :
\( \mathbf{A} \cdot 2.87 \mathrm{B} . \mathrm{M} \)
B. 3.87 В.М.
c. 3.47 В.M.
D. 3.57 В.М.