AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
The area bounded by \( \frac{|\boldsymbol{x}|}{\boldsymbol{a}}+\frac{|\boldsymbol{y}|}{\boldsymbol{b}}=\mathbf{1} \)
where \( a>0 \) and \( b>0 \) is
A \( \cdot \frac{1}{2} a b \)
в. \( a b \)
c. \( 2 a b \)
D. \( 4 a b \)
Subject: Chemistry
Which of the following reduction
processes are correct? This question has multiple correct options
A \( \cdot F e_{2} O_{3}+C^{\text {Reduction}} F e \)
B . \( Z n O+C \stackrel{\text {Reduction}}{\longrightarrow} \) Zn
\( \mathrm{c} \cdot \operatorname{Sn} \mathrm{O}_{2}+C^{\text {Redution}} S n \)
D \( \cdot P b O+C \stackrel{\text {Reduction}}{\rightarrow} P b \)
Subject: Maths
For what value of " \( c^{\prime \prime} \) will the equations
\( 3 x-4 y=7 \) and \( x+c y=13 \) have no
solution?
A \( \cdot \frac{3}{4} \)
B. \( \frac{4}{3} \)
\( c .-4 \)
D. \( \frac{-4}{3} \)
Subject: Chemistry
In Freundlich isotherm, \( \frac{x}{m} \propto P^{a} \). Find the value of \( a \) from the following graph.
\( A \cdot \frac{2}{3} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{3}{2} \)
\( D \)
Subject: Physics
A fixed mass of a gas is first heated isobarically to double the volume and then cooled isochorically to decrease the temperature back to the initial
value. By what factor would the work done by the gas decrease, had the process been isothermal?
\( A \cdot 2 \)
B. 1/2
\( c \cdot \ln 2 \)
D. \( \ln 3 \)
Subject: Maths
The solution of the differential equation \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\tan \left(\frac{\boldsymbol{y}}{\boldsymbol{x}}\right)+\frac{\boldsymbol{y}}{\boldsymbol{x}} \) is:
A \( \cdot \cos \left(\frac{y}{x}\right)=c x \)
B. \( \sin \left(\frac{y}{x}\right)=c x \)
\( \mathbf{c} \cdot \cos \left(\frac{y}{x}\right)=c y \)
D \( \cdot \sin \left(\frac{y}{x}\right)=c y \)
Subject: Physics
A black body at \( 200 \mathrm{K} \) is bound to exit maximum energy at a wavelength \( 14 \mu \)
m. When its temperature is raised to \( 1000 \mathrm{K}, \) then wavelength at which maximum energy emitted is:
\( A \cdot 14 \mathrm{mm} \)
в. \( 7 \mu m \)
c. \( 2.8 \mu m \)
D. 28 mm
Subject: Maths
For each operation \( * \) defined below, determine whether \( * \) is binary, commutative or associative.
(i) On \( Z, \) define \( a * b=a-b \)
(ii) On \( Q, \) defined \( a * b=a b+1 \)
(iii) On \( Q, \) defined \( a * b=\frac{a b}{2} \)
(iv) \( \operatorname{On} Z^{+}, \) defined \( a * b=2^{a b} \)
(v) \( \operatorname{On} Z^{+}, \) defined \( a * b=a^{b} \)
\( (v i) \) on \( R-\{-1\}, \) defined \( a * b=\frac{a}{b+1} \)
Subject: Maths
Find the distance of a perpendicular
from the centre of a circle to the chord if
the diameter of the circle is \( 30 \mathrm{cm} \) and
its chord is \( 24 \mathrm{cm} \)
A \( .6 \mathrm{cm} \)
B. \( 7 \mathrm{cm} \)
\( c .9 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)
Subject: Maths
The diameter of the circle is \( 2 \mathrm{cm} \). What
is the circumference?
\( \mathbf{A} \cdot 12.28 \mathrm{cm} \)
B. \( 6.2 \mathrm{cm} \)
c. \( 18.28 \mathrm{cm} \)
D. \( 10.28 \mathrm{cm} \)
Subject: Physics
In a transverse wave the distance
between a crest and neighbouring trough at the same instant is \( 4.0 \mathrm{cm} \) and the distance between a crest and
trough at the same place is \( 1.0 \mathrm{cm} . \) The next crest appears at the same place after a time interval of 0.4 s. The
maximum speed of the vibrating
particles in the medium is:
A \( \cdot \frac{5 \pi}{2} \mathrm{cm} / \mathrm{s} \)
B. \( 2 \pi c m / s \)
c. \( \frac{\pi}{2} \mathrm{cm} / \mathrm{s} \)
D. \( \frac{3 \pi}{2} \mathrm{cm} / \mathrm{s} \)
Subject: Maths
The temperature at 12 noon was \( 10^{\circ} \mathrm{C} \)
above zero. If it decreases at the rate of
\( 2^{o} C \) per hour until midnight, at what
time would the temperature be \( 8^{\circ} C \)
below zero? What would be the
temperature at midnight?
A \( \cdot 14^{\circ} \mathrm{C} \)
B. \( -14^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 16^{\circ} C \)
D. \( -16^{\circ} \mathrm{C} \)
Subject: Physics
A circular platform is mounted on a
frictionless vertical axle. Its radius \( \mathrm{R}=2 \mathrm{m} \)
and its moment of inertia about the axle
is \( 200 k g m^{2} \). It is initially at rest. A \( 50 \mathrm{kg} \)
man stands on the edge of the platform and begins to walk along the edge at the speed of \( 1 \mathrm{ms}^{-1} \) relative to the ground.
Time taken by the man to compete one
revolution with respect to disc is:
\( \mathbf{A} \cdot \pi s \)
B . \( \frac{3 \pi}{2} s \)
\( \mathbf{c} \cdot 2 \pi s \)
D. \( \frac{\pi}{2} s \)
Subject: Maths
If \( \boldsymbol{\alpha}=\mathbf{3}, \boldsymbol{\beta}=\mathbf{5} \) and \( \gamma=\mathbf{8}, \) then the
value of \( \boldsymbol{\alpha}^{3}+\boldsymbol{\beta}^{3}+\boldsymbol{\gamma}^{3} \) is
A. -240
в. 240
c. -360
D.
Subject: Physics
resting on a smooth horizontal ground
attached to one end of a spring of force
constant \( k \) in natural length. If another
block of same mass and moving with a
velocity u toward right is placed on the
block which stick to it due to friction.
The time it will take to reach its
extreme position. Also find the
amplitude of oscillations of the combined mass \( 2 \mathrm{m} \)
\( ^{\mathbf{A}} \cdot A=\sqrt{\frac{m}{2 k}}, t=\sqrt{\frac{k}{2 m}} \)
В. \( A=u \sqrt{\frac{m}{2 k}}, t=\frac{\pi}{2} \sqrt{\frac{2 m}{k}} \)
c. \( A=\sqrt{\frac{u m}{2 k}}, t=\pi \sqrt{\frac{2 m}{k}} \)
D. none of these
Subject: Maths
Find the values of \( x \) and \( y, \) if \( \left[\begin{array}{cc}\boldsymbol{x}+\mathbf{1 0} & \boldsymbol{y}^{2}+\mathbf{2} \boldsymbol{y} \\ \mathbf{0} & -\mathbf{4} \\ \mathbf{3} \boldsymbol{x}+\mathbf{4} & \mathbf{3} \\ \mathbf{0} & \boldsymbol{y}^{\mathbf{2}}-\mathbf{5} \boldsymbol{y}\end{array}\right]= \)
Subject: Maths
\( \operatorname{Let} \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{\boldsymbol{x}(\mathbf{1}+\boldsymbol{a} \cos \boldsymbol{x})-\boldsymbol{b} \sin \boldsymbol{x}}{\boldsymbol{x}^{3}}, \boldsymbol{x} \neq \mathbf{0} \) and
\( f(0)=1 . \) The value of \( a \) and \( b \) so that \( f \)
is a continuous function are-
A \( \cdot \frac{5}{2}, \frac{3}{2} \)
В. \( \frac{5}{2},-\frac{3}{2} \)
c. \( -\frac{5}{2},-\frac{3}{2} \)
D. None of these
Subject: Maths
Assertion(A): The difference of the focal
distances of any point on the hyperbola \( \frac{\boldsymbol{x}^{2}}{\mathbf{3 6}}-\frac{\boldsymbol{y}^{2}}{\mathbf{9}}=\mathbf{1} \) is 12
Reason(R): The difference of the focal
distances of any point on the hyperbola is equal to the length of it transverse axis
A. Both A and R are true and R is the correct
explanation of \( A \)
B. Both A and R are 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: Physics
A sphere of mass \( \mathrm{M} \) and radius \( \mathrm{R} \) is falling in a viscous fluid. The terminal velocity attained by the falling object will be proportional to:
A \( \cdot R^{2} \)
B.
c. \( \frac{1}{R} \)
D. \( \frac{1}{R^{2}} \)
Subject: Chemistry
At \( 100^{\circ} \mathrm{C} \), value of \( \boldsymbol{K}_{\boldsymbol{w}} \) is
\( \begin{array}{ll}\text { A. } 1.0 \times 10^{-14} & m^{2}\end{array} \)
B. less than 1.0 \( \times 10^{-14} \mathrm{m}^{2} \)
C. greater than \( 1.0 \times 10^{-14} \mathrm{m}^{2} \)
D. zero
Subject: Physics
The angle between two vectors given by \( (6 \hat{i}+6 \hat{j}+3 \hat{k}) \) and \( (7 \hat{i}+4 \hat{j}+4 \hat{k}) \) is
A \( \cdot \cos ^{-1}\left(\frac{26}{27}\right) \)
B. \( \cos ^{-1}\left(\frac{5}{3 \sqrt{3}}\right) \)
c. \( \sin ^{-1}\left(\frac{2}{3 \sqrt{3}}\right) \)
D. \( \sin ^{-1}\left(\frac{-2}{27}\right) \)
Subject: Chemistry
In bimolecular reaction, the steric
factor \( P \) was experimentally
determined to be \( 4.5 . \) The correct
option(s) among the following is (are):
This question has multiple correct options
A. the activation energy of the reaction is unaffected by the value of the steric factor
B. experimentally determined value of frequency factor is higher than that predicted by Arrheneius equation
C . since \( P=4.5 \), the reaction will not proceed unless an
effective catalyst is used
D. tThe value of frequency factor predicted by Arrhenius equation is higher than that determined experimentally
Subject: Physics
The magnetic field is varying as \( \boldsymbol{B}(\boldsymbol{t})= \)
\( B_{o} t \) in the circuit as shown in the figure
Then the emf induced in the circuit will
be
\( \mathbf{A} \cdot 2 \pi a^{2} B_{0} \)
В . \( \pi a^{2} B_{0} \)
c. \( \frac{a^{2} B_{0}}{2} \)
D. \( \frac{\pi a^{2} B_{0}}{2} \)
Subject: Chemistry
Major product of following reaction:
\( \boldsymbol{C H}_{3} \)
\( \boldsymbol{C H}_{3} \dot{\boldsymbol{C}}-\boldsymbol{C H}-\boldsymbol{C H}_{3} \frac{\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O}^{-}}{\mid} \)
\( \boldsymbol{C H}_{3} \quad \boldsymbol{C l} \)
\( ^{\text {A. }} C H_{3}-\stackrel{C H_{3}}{C}-C_{\mid}^{\perp}-C_{3}-C H_{3} \)
B. \( \quad C H_{3}-\stackrel{C H_{3}}{_{I}}-C H=C H_{2} \)
C.
\[
C H_{3}-C=C_{1}^{H_{3}}
\]
\( _{C H_{3}}-C H_{3} \)
Subject: Physics
Two identical containers each of volume \( V \)
0 are joined by a small pipe. The containers contain identical gases at
temperature \( T_{0} \) and pressure \( P_{0} . \) One
container is heated to temperature \( 2 \mathrm{T}_{0} \)
while maintaining the other at the
same temperature. The common pressure of the gas is \( \mathrm{P} \) and \( \mathrm{n} \) is the number of moles of gas in container at
temperature \( 2 T_{0} \)
\( \mathbf{A} \cdot P=2 P_{0} \)
в. \( \quad P=\frac{4}{3} P_{0} \)
c. \( _{n}=\frac{2 P_{0} V_{0}}{3 R T_{0}} \)
D. \( n=\frac{3 P_{0} V_{0}}{2 R T_{0}} \)
Subject: Physics
Can a traingle have
A \( \cdot 55^{\circ}, 55^{\circ} \) and \( 80^{\circ} \)
B . \( 33^{\circ}, 74^{\circ} \) and \( 73^{\circ} \)
c. \( 85^{\circ}, 95^{\circ} \) and \( 22^{\circ} \)
D. \( 25^{\circ}, 95^{\circ} \) and \( 32^{\circ} \)
Subject: Maths
In the figure if \( D E \| B C \) and \( A D= \)
\( \mathbf{3} \boldsymbol{x}-\mathbf{2}, \boldsymbol{A} \boldsymbol{E}=\mathbf{5} \boldsymbol{x}-\mathbf{4}, \boldsymbol{B} \boldsymbol{D}=\mathbf{7} \boldsymbol{X}-\mathbf{4} \)
\( B D-7 x-5 \) AND \( C E=5 x-3 . \) Find
\( \mathbf{x} \)
Subject: Maths
Inverse of the matrix \( \left[\begin{array}{cc}\cos 2 \theta & -\sin 2 \theta \\ \sin 2 \theta & \cos 2 \theta\end{array}\right] \)
is.
\( \mathbf{A} \cdot\left[\begin{array}{cc}\cos 2 \theta & -\sin 2 \theta \\ \sin 2 \theta & \cos 2 \theta\end{array}\right] \)
B. \( \left[\begin{array}{cc}\cos 2 \theta & \sin 2 \theta \\ \sin 2 \theta & -\cos 2 \theta\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{cc}\cos 2 \theta & \sin 2 \theta \\ \sin 2 \theta & \cos 2 \theta\end{array}\right] \)
D. \( \left[\begin{array}{cc}\cos 2 \theta & \sin 2 \theta \\ -\sin 2 \theta & \cos 2 \theta\end{array}\right] \)
Subject: Physics
A thin conducting ring is ruptured when it is given a charge q. Consider another thin conducting ring, radius of which is n times and tensile strength is k times of the former ring. How much maximum charge can this second ring be given
without rupturing?
\( \mathbf{A} .<q n k \)
B. \( <q n \sqrt{k} \)
\( \mathbf{c} \cdot<q n^{2} \sqrt{k} \)
D. Insufficient information
Subject: Chemistry
Which of the following pair of monomers are used in preparation of PHBV ?
A. \( \beta \) - hydroxy valeric acid, amino caproic acid
B. \( \beta \) - hydroxy butyric acid, \( \beta \) - hydroxy valeric acid
c. \( \beta \) - hydroxy butyric acid, adipic acid
D. Lactic acid, adipic acid
Subject: Physics
The graph below represents the velocity of some subatomic particle in an
electric field. The graph represents the
particle' s velocity at its moves in a
straight line in positive and negative
directions.
During which of the labeled time intervals is the particles slowing down
during the entire interval?
A . 1 only
B. 4 only
c. 6 only
D. 1 and 4 only
E. 1 and 6 only
Subject: Physics
A planet has mass and radius both half
of earth. Acceleration due to gravity \( (g) \)
at its surface should be
A \( \cdot 29.4 m / s^{2} \)
в. \( 19.6 m / s^{2} \)
C. \( 9.8 m / s^{2} \)
D. \( 4.9 \mathrm{m} / \mathrm{s}^{2} \)
Subject: Maths
f the matrix \( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{6} & \boldsymbol{x} & \mathbf{2} \\ \mathbf{2} & \mathbf{- 1} & \mathbf{2} \\ \mathbf{- 1 0} & \mathbf{5} & \mathbf{2}\end{array}\right] \) is
singular matrix. Find the value of \( x \)
Subject: Physics
of intensity \( I \) is incidents on a glass plate as shown, in the figure. Another identical glass plate is kept close to the
first-one and parallel to it. Each glass plate reflects \( 25 \% \) of the light incident on it and transmits the remaining. Then
the ratio of the maximum and
minimum intensities in the
interference pattern formed by the two
beams obtained after one reflection at
each plate is
A . 7: 1
B. 49: 1
c. 4: 1
D. 16: 9
Subject: Maths
If \( \boldsymbol{p} \rightarrow(\sim \boldsymbol{p} \vee \boldsymbol{q}) \) is false then the truth
value of \( p \) and \( q \) are respectively
A \( . T, T \)
в. \( T, F \)
c. \( F, T \)
D. \( F, F \)
Subject: Physics
The same mass of copper is drawn into two wires \( A \) and \( B \) or radii \( r \) and \( 3 r \)
respectively. They are connected in series, and electric current is passed. The ratio of the heat produced in \( A \) and \( \mathrm{Bis} \)
A .1: 9
в. 1: 81
\( c .81: \)
D. 9:
Subject: Chemistry
The pH of a solution containing
\( N H_{4} O H \) and \( N H_{4}^{+} \) is \( 9 . \) If \( \left[N H_{4}^{+}\right]=0 . \)
\( \mathrm{M} \) and \( \mathrm{Ka} \) of \( N H_{4}^{+} \) is \( 5 \times 10^{-10} \) then
what is \( \left[\boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{O} \boldsymbol{H}\right] ? \)
Subject: Chemistry
In the pinwheel galaxy, atomic number of all elements are the same as that on
earth and paulis principle is obeyed
However the shell closest to the nucleus
is saturated with electrons before the
next shell starts to fill and the process
continues this way, also each orbital can accommodate only one electron having \( +\frac{1}{2} \) spin. If noble gases are defined as the elements with
completely filled outermost shell, which elements would be the nobel gas in
their periodic table?
A \( . A r \)
в. \( S i \)
\( c . F \)
D. Ne
Subject: Maths
The value of
\( \sec \left[\sin ^{-1}\left(\sin \frac{50 \pi}{9}\right)+\cos ^{-1} \cos \left(\frac{31 \tau}{9}\right.\right. \)
is equal to
A \( \cdot \sec \frac{10 \pi}{9} \)
в. \( \sec 9 \pi \)
c. -1
D.
Subject: Chemistry
For a homogeneous gaseous reaction, \( \boldsymbol{A} \longrightarrow \boldsymbol{B}+\boldsymbol{C}+\boldsymbol{D}, \) the initial pressure
was \( P_{0} \) while pressure at time \( t \) was \( P \) Derive an expression for rate constant
\( K \) in terms of \( P_{0}, P \) and \( t \) [Assume first-order reaction]
Subject: Chemistry
Butane can be converted into 2
methyl propane, if heated with:
A. \( A l_{2} C l_{6} \)
в. \( C r_{2} O_{3} \)
\( \mathrm{c} \cdot \mathrm{Cr} \mathrm{O}_{2} \mathrm{Cl}_{2} \)
D. \( N i \)
Subject: Maths
\( \left|\begin{array}{lll}\mathbf{1} & \boldsymbol{\omega} & \boldsymbol{\omega}^{2} \\ \boldsymbol{\omega} & \boldsymbol{\omega}^{2} & \mathbf{1} \\ \boldsymbol{\omega}^{2} & \mathbf{1} & \boldsymbol{\omega}\end{array}\right|=\ldots \)
\( A \)
B.
\( c \cdot 2 \)
D. -1
Subject: Chemistry
The boiling point \( T_{b}^{*} \) of a solvent becomes \( T_{b} \) on addition of \( X_{1} \) mole
fraction of solute. Heat of vaporisation
of solvent is \( \Delta \boldsymbol{H}_{\boldsymbol{v} \boldsymbol{a} \boldsymbol{p}} . \) The relation
between elevation in b.pt. \( \Delta T_{b}\left(=T_{b}-\right. \)
\( \left.T_{B}^{*}\right) \) can be given by:
\( \frac{\Delta T_{b}}{T_{b} \times T_{b}^{*}}=-\frac{R I n X_{1}}{\Delta H_{v a p}} \)
A graph plotted between \( \log _{10} X_{1} \) vs. \( \frac{1}{T_{b}} \) gives:
A.
\[
\text { straight line with slope } \frac{R}{\Delta H_{v a p}} \text { and intercept } T_{b}^{*}
\]
B. a straight line with slope \( \frac{2.303 R}{\Delta H_{v a p}} \) and intercept \( \frac{1}{T_{b}} \)
c. a straight line with slope \( \frac{\Delta H_{v a p}}{2.303 R} \) and intercept \( \frac{1}{T_{b}^{*} \times 2.303} \)
D. a straight line with slope \( \frac{\Delta H_{v a p}}{2.303 R} \) and intercept \( -\frac{\Delta H_{v a p}}{2.303 R T_{b}^{*}} \)
Subject: Chemistry
The \( A s F_{5} \) molecule is trigonal bipyramidal.The atomic orbitals used
by the \( A s \) atoms for bonding are:
A \( \cdot d_{x^{2}-y^{2}}, d_{z}^{2}, s, p_{x}, p_{y} \)
В. \( s, p_{x}, p_{y}, p_{z} \)
c. \( s, p_{x}, p_{y}, p_{z}, d_{z^{2}} \)
D \( \cdot d_{x^{2}-y^{2}}, s, p_{x}, p_{y} \)
Subject: Physics
A \( 20 \mathrm{kg} \) metal block is place on a horizontal surface. The block just begins to slide when horizontal force of \( 100 \mathrm{N} \) is applied to it. Calculate the coefficient of static friction.
A . 78.4
B. 100 N
\( c \cdot 84 \mathrm{N} \)
D. 9.5 N
Subject: Chemistry
Which of the given statements is incorrect for the complex
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]^{3+} ? \)
A. It is a low spin complex
B . It is \( d^{2} s p^{3} \) hybridised
c. It is paramagnetic
D. None of these
Subject: Physics
A converging lens of focal length \( 15 \mathrm{cm} \) and a converging mirror of focal length
\( 20 c m \) are placed with their principal
axis coinciding. A point source \( S \) is
placed on the principal axis at a
distance of \( 12 \mathrm{cm} \) from the lens as
shown in the figure. It is found that the final beam comes out parallel to the principal axis. Find the separation between the mirror and the lens.
Subject: Physics
In YDSE The intensity of central bright fringe is \( 8 m W / m^{2} . \) What will be the intensity at \( \lambda / 6 \) path difference?
\( \mathbf{A} \cdot 8 m W / m^{2} \)
в. \( 6 m W / m^{2} \)
\( \mathbf{c} \cdot 4 m W / m^{2} \)
\( \mathbf{D} \cdot 2 m W / m^{2} \)
Subject: Physics
In one model of the electron, the electron
of mass \( m_{e} \) is thought to be a uniformly
charged shell of radius \( R \) and total charge \( e, \) whose electrostatic energy \( E \)
is equivalent to its mass \( m_{e} \) via
Einstein's mass energy relation \( \boldsymbol{E}= \) \( \boldsymbol{m}_{e} \boldsymbol{c}^{2} . \) In this model, \( \boldsymbol{R} \) is approximately
\( \left(\boldsymbol{m}_{e}=\mathbf{9 . 1} \times \mathbf{1 0}^{-\mathbf{3 1}} \mathbf{k g}, \boldsymbol{c}=\mathbf{3} \times \mathbf{1 0}^{\mathbf{8}} \mathbf{m s}^{-\mathbf{1}}\right. \)
\( \mathbf{1} / \mathbf{4} \boldsymbol{\pi} \varepsilon_{\mathbf{0}}=\mathbf{9} \times \mathbf{1 0}^{\mathbf{9}} \boldsymbol{F} \boldsymbol{a} \boldsymbol{r} \boldsymbol{a} \boldsymbol{d} \boldsymbol{s} \boldsymbol{n}^{-1} \)
magnitude of the electron charge \( = \) \( \left.\mathbf{1} . \mathbf{6} \times \mathbf{1 0}^{-\mathbf{1 9}} \mathbf{C}\right) \)
A. \( 1.4 \times 10^{-15} \mathrm{m} \)
B . \( 2 \times 10^{-13} m \)
c. \( 5.3 \times 10^{-11} m \)
D. 2.8 \( \times 10^{-35} \mathrm{m} \)
Subject: Maths
Solve graphically, the following pairs of equations:
\( 3 x+7 y=27 \)
\( 3-y=\frac{5}{2} x \)
A . \( x=2, y=3 \)
в. \( x=7, y=2 \)
c. \( x=4, y=1 \)
D. \( x=4, y=6 \)
Subject: Maths
The magnitude of resultant of three vectors of magnitude 1,2 and 3 whose direction are those of the sides of an
equilateral triangle taken in order is:
\( A \cdot 0 \)
B. \( 2 \sqrt{2} \) units
c. \( 4 \sqrt{3} \) units
D. \( \sqrt{3} \) units
Subject: Physics
\( \ln \) an oscillating \( \boldsymbol{L}-\boldsymbol{C} \) circuit, the
maximum charge on the capacitor is \( Q \) The charge on the capacitor, when the energy is stored equally between the electric and magnetic field is:
A \( \cdot \frac{Q}{2} \)
B. \( \frac{Q}{\sqrt{2}} \)
c. \( \frac{Q}{\sqrt{3}} \)
D. \( \frac{Q}{3} \)
Subject: Chemistry
The \( \mathrm{E}^{o} \) for reduction of \( \mathrm{HNO}_{2} \) to \( \mathrm{NO} \) is
\( 0.99 \mathrm{V} \) and \( \mathrm{E}^{\circ} \) for reduction of \( \mathrm{NO}_{3}^{-} \) to
\( \mathrm{HNO}_{2} \) is \( 0.94 \mathrm{V} . \) The equilibrium
constant at \( 25^{\circ} \mathrm{C} \) for the
disproportionation of 3 mole of aqueous
\( \mathrm{HNO}_{2} \) to yield \( \mathrm{NO} \) and \( \mathrm{N} \mathrm{O}_{3}^{-} \) ions is:
A. \( K_{c}=344.64 \)
В. \( K_{c}=336.97 \)
c. \( K_{c}=639.73 \)
D. None of these
Subject: Physics
A wire of length \( L \) and cross sectional
area \( A \) is made of a material of Young's
modulus \( Y \). If the wire is stretched by
an amount \( x, \) the work done is
A \( \cdot \frac{Y A x^{2}}{3 L} \)
в. \( \frac{Y A x^{2}}{4 L} \)
c. \( \frac{Y A x^{2}}{L} \)
D. \( \frac{Y A x^{2}}{2 L} \)
Subject: Maths
Natesh borrowed some money at rate \( 6 \% \) p.a.for the first 3 years, \( 9 \% \) p.a.for the next five years and 13 p.a. beyond 8 years. The above are all simple interest
rates. If Natesh pays a total of Rs. 8160
as an interest after 11 years, how much money did he borrow?
A . Rs. 8000
B. Rs. 10000
c. Rs. 12000
D. Rs. 14000
Subject: Physics
A fusion reaction consists of combining
four protons into an \( \alpha \) - particle. The
mass of \( \boldsymbol{\alpha} \) - particle is 4.002603 amu
and that of proton is 1.007825 amu
This question has multiple correct options
\( \mathbf{A} \cdot \) the equation \( 4 p_{1}^{1} \rightarrow H e_{2}^{4} \) does not satisfy
conservation of charge
B. the correct reaction equation may be \( 4 p_{1}^{1} \rightarrow H e_{2}^{4}+ \)
\( 2 \beta^{+}+2 v \) where \( \beta^{+} \) is positron and \( v \) is the neutrino
(zero rest mass and uncharged)
c. loss of mass in the reaction is \( 0.028697 a m u \)
D. the energy equivalent of the mass defect is \( 26.7 \mathrm{MeV} \)
Subject: Biology
Assertion
Amoebiasis is caused by Amoeba
Reason
The protist feeds on red blood
corpuscles
A. If both the assertion and the reason are true and the
reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the
reason is not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false
Subject: Maths
The differential equation of the family of parabolas with vertex at (0,-1) and having axis along the \( y \) -axis is:
A \( \cdot y y^{\prime}+2 x y+1=0 \)
В . \( x y^{\prime}+y+1=0 \)
c. \( x y^{\prime}+2 y+2=0 \)
D. \( x y^{\prime}-y-1=0 \)
Subject: Maths
If the \( m^{t h} \) term of an \( A . P . \) is \( \frac{1}{n} \) and \( n^{t h} \) term is \( \frac{1}{m}, \) then the sum of first \( m n \)
terms is
A \( . m n+1 \)
в. \( \frac{m n+1}{2} \)
c. \( \frac{m n-1}{2} \)
D. \( \frac{m n-1}{3} \)
Subject: Physics
A rod is made of uniform material and
has non-uniform cross-section. It is
fixed at both ends as shown and heated
at the mid-section. Which of the
following statements are not correct?
his question has multiple correct options
A. Force of compression in the rod will be maximum at mid-section
B. Compressive stress in the rod will be maximum at left end
c. since the rod is fixed at both the ends, its length will remain unchanged. Hence, no strain will be induced in it.
D. None of above
Subject: Chemistry
Four ten litre flasks are separately filled
with the gases hydrogen, helium, oxygen and ozone at the same
temperature and pressure. The ratio of
the total number of atoms of these
gases present in different flasks would
be?
A .1: 2: 3: 2
B. 2: 1: 2: 3
\( \mathbf{c} \cdot 1: 3: 2: 2 \)
Subject: Physics
The top of the atmosphere is about
\( 400 k V \) with respect to the surface of earth, corresponding to an electric field that decreases with altitude. Near the
surface of earth the field is about
\( 100 V m^{-1}, \) but still don't get an electric
shock, as we set out of our houses in to open because (assume the house is
free from electric field)
A. our body is a perfect insulator
B. our body and ground form an equipotential surface
c. the original euipotential surfaces of open air remain same
D. none of these
Subject: Physics
In YDSE, find the missing wavelength in front of one of the slits.
\( ^{A} \cdot \frac{d^{2}}{2 D} \)
B. \( \frac{2 d^{2}}{D} \)
c. \( \frac{d^{2}}{3 D} \)
D. \( \frac{d^{2}}{4 D} \)
Subject: Maths
A point \( P \) lies on a line whose ends are \( A(1,2,3) \) and \( B(2,10,1) . \) If \( z \)
component of \( \boldsymbol{P} \) is \( \boldsymbol{7}, \) then the
coordinates of \( \boldsymbol{P} \) are
A \( \cdot(-1,-14,7) \)
B. (1,-14,7)
c. (-1,14,7)
D. (1,14,7)