AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The potential across a 25.0 microfarad capacitor is \( 5.0 V . \) What is the charge on
the capacitor?
A. 0.20 microcoulombs
B. 5.0 microcoulombs
c. 125 microcoulombs
D. 30.0 microcoulombs
E. We cannot determine the charge on the capacitorwith the given information
Subject: Maths
An artillery target may be either at point
\( I \) with probability \( \frac{8}{9} \) or at point \( I I \) with
probability \( \frac{1}{9} . \) We have 21 shells each of which can be fired at point \( I \) or \( I I \). Each
shell may hit the target independently of the other shell with probability \( \frac{1}{2} . \) How
many shells must be fired at point \( I \) to hit the target with maximum
probability?
A. \( P(A) \) is maximum where \( x=11 \).
B. \( P(A) \) is maximum where \( x=12 \)
c. \( P(A) \) is maximum where \( x=14 \)
D. \( P(A) \) is maximum where \( x=15 \)
Subject: Maths
Evaluate \( \int x e^{x} d x \)
A \( .-x e^{x}-e^{x}+c \)
B. \( -x e^{x}+e^{x}+c \)
c. \( x e^{x}+e^{x}+c \)
D. \( x e^{x}-e^{x}+c \)
Subject: Maths
If \( A \) is a square matrix of order \( m \times n \)
then \( a d j(a d j A) \) is equal to
B \( \cdot|A|^{n-1} A \)
\( \mathbf{c} \cdot|A|^{n-2} A \)
D \( \cdot|A|^{n-3} A \)
Subject: Chemistry
Assertion
The concepts of atom was firstly used by Dalton.
Reason
Atom is the smallest particle of matter
that takes part in a chemical reaction. Atom is also defined as the small-est
particle of an element that retains all
the properties of an element.
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
Find the angles of a triangle whose
sides are \( \boldsymbol{x}+\mathbf{2} \boldsymbol{y}-\mathbf{8}=\mathbf{0}, \mathbf{3} \boldsymbol{x}+\boldsymbol{y}- \)
\( \mathbf{1}=\mathbf{0} \) and \( \boldsymbol{x}-\mathbf{3} \boldsymbol{y}+\mathbf{7}=\mathbf{0} \)
Subject: Chemistry
For the reaction \( 3 A(g)+B(g) \rightleftharpoons 2 C(g) \)
at a given temperaature, \( \boldsymbol{K}_{c}=\mathbf{9 . 0} \)
What must be the volume of the flask, if
a mixture of 2.0 mol each of \( A, B \) and \( C \)
exist in equilibrium?
Subject: Physics
A right angles prism \( \left(45^{\circ}, 90^{\circ}, 45^{\circ}\right) \) of refractive index n has a plate of
refractive index \( \left(n_{1}<n\right) \) cemented to
its diagonal face. The assembly is in air.
A ray is incident on AB. Assuming \( n= \)
1.351, calculate the angle of incidence
(in degrees rounded off to nearest integer) at \( A B \) for which the refracted
ray passes through the diagonal face undeviated
Subject: Chemistry
Assertion
Hybridisation influences the bond length and bond enthalpy in organic compounds.
Reason
More the s character of hybrid orbital, shorter and stronger will be the bond
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
A length of \( 150 \mathrm{cm} \) of a potentiometer wire is required to balance the emf of a cell. When a \( 5 \Omega \) resistor is connected
across the terminals of the cell, the
length required for balance is \( 125 \mathrm{cm} \)
The internal resistance of the cell is
A . 1 ohm
B. 1.1 ohm
c. 1.2 ohm
D. 1.3 ohm
Subject: Chemistry
During the formation of \( M g C l_{2} \) by Born Haber cycle, which of the following
occurs?
A . lonisation of \( M g \) to \( M g^{+2} \)
B. Bond dissociation of \( C l_{2} \)
c. Sublimation of \( M g \)
D. Electron gained by \( C l \)
E. All of these
Subject: Maths
\( \boldsymbol{i}^{n}+\boldsymbol{i}^{\boldsymbol{n}+1}+\boldsymbol{i}^{\boldsymbol{n}+\mathbf{2}}+\boldsymbol{i}^{\boldsymbol{n}+\mathbf{3}}(\boldsymbol{n} \in \boldsymbol{N}) \) is
equal to
\( \mathbf{A} \cdot \mathbf{4} \)
B.
c.
D.
Subject: Chemistry
If the balanced reaction is as given below, find the value of \( x, y \) and \( z \)
\( \boldsymbol{T} \boldsymbol{i}_{2} \boldsymbol{O}_{3}(\boldsymbol{s})+\boldsymbol{x} \boldsymbol{N} \boldsymbol{H}_{2} \boldsymbol{O} \boldsymbol{H}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \)
\( 2 T i O H(s)+y N_{2}(g)+z H_{2} O \)
A. \( x=4, y=2, z=5 \)
в. \( x=3, y=2, z=5 \)
c. \( x=4, y=2, z=4 \)
D. None of the above
Subject: Physics
A circular loop of radius \( \boldsymbol{R} \), carrying
current \( I, \) lies in \( x \) -y plane with its
center at origin. The total magnetic flux through x-y plane is
A. directly proportional to \( I \)
B. directly proportional to \( R \)
c. inversely proportional to \( R \)
D. inversely proportional to \( I \)
E. zero
Subject: Chemistry
Assertion
In chemisorption, adsorption keeps on increasing with temperature.
Reason
Heat keeps on providing more and more
activation energy
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Chemistry
The correct order of the strength of \( \boldsymbol{H}- \) bonds is:
A. \( H . . F>H . . O>H \ldots N \)
в. \( H . . N>H . . O>H \ldots . \)
c. \( H . . O>H . . N>H \dots F \)
D. \( H . . F>H . . N>H . . . O \)
Subject: Maths
\( y+x^{2}=\frac{d y}{d x} \) has the solution
A. \( y+x^{2}+2 x+2=c . e^{x} \)
B . \( y+x+2 x^{2}+2=c . e^{x} \)
C \( \cdot y+x+x^{2}+2=c \cdot e^{2 x} \)
D . \( y^{2}+x+x^{2}+2=c . e^{2 x} \)
Subject: Maths
The least value of \( \frac{1}{2}+\frac{2}{3} \operatorname{cosec}^{2} \theta+ \)
\( \frac{3}{8} \sec ^{2} \theta \) is
A \( \cdot \frac{13}{24} \)
в. \( \frac{61}{48} \)
c. \( \frac{61}{25} \)
D. \( \frac{61}{24} \)
Subject: Chemistry
The \( E_{1} \) of \( H \) is \( 13.6 e V . \) It is exposed to electromagnetic waves of \( 1028 \dot{A} \) and gives out induced radiation. Find the
wavelengths of these induced radiation.

This question has multiple correct options
A \( \cdot \lambda_{3}=1216 \hat{A} \)
B . \( \lambda_{2}=6568 \AA \)
c. \( \lambda_{2}=1000 \dot{A} \)
D. \( \lambda_{2}=2432 \hat{h} \)
Subject: Chemistry
A high-altitude balloon is filled with 1.41
\( \times 10^{4} \mathrm{L} \) of hydrogen at a temperature of
\( 21^{\circ} \mathrm{C} \) and a pressure of 745 Torr. What is the volume of the balloon at a height of
\( 20 \mathrm{km}, \) where the temperature is \( -48^{\circ} \mathrm{C} \) and the pressure is 63.1 Torr.
A \( .1 .274 \times 10^{5} \mathrm{L} \)
В. \( 1.66 \times 10^{5} \mathrm{L} \)
c. \( 1.66 \times 10^{4} \mathrm{L} \)
D. None of these
Subject: Physics
A plane electromagnetic wave is incident on a material surface. If the
wave delivers momentum \( p \) and energy
\( \boldsymbol{E}, \) then:
A \( , p=0, E=0 \)
0
В. \( p \neq 0, E \neq 0 \)
c. \( p \neq 0, E=0 \)
D. \( p=0, E \neq 0 \)
Subject: Physics
toppr
Q Type your questic
instantaneous axis passing through the center of mass. These axes need not be
stationary. Consider, for example, a thin uniform disc welded (rigidly fixed) horizontally at its rim to a mass less stick, as shown in the figure. When the disc-stick system is rotated about the
origin on a horizontal friction less plane
with angular speed \( \omega \), the motion at any instant can be taken as a combination
of (i) a rotation of the center of mass of
the disc about the z-axis, and (ii) a
rotation of the disc through an
instantaneous vertical axis passing
through its center of mass (as is seen from the changed orientation of points
\( P \) and \( Q . \) Both these motions have the
same angular speed \( \omega \) in this case. Now consider two similar systems as
shown in the figure: Case
(a) the disc
with its face vertical and parallel to \{it
\( x-z\} \) plane; Case
(b) the disc with its
face making an angle of \( 45^{\circ} \) with \( \{\text { it } x-y\} \)
plane and its horizontal diameter parallel to x-axis. In both the cases, the
disc is welded at point \( P, \) and the
systems are rotated with constant
angular speed \( \omega \) about the z-axis.
Which of the following statements regarding the angular speed about the instantaneous axis (passing through the center of mass) is correct?
A. It is \( \sqrt{2} \omega \) for both the cases
B. It is \( \omega \) for case
(a); and \( \frac{\omega}{\sqrt{2}} \) for case (b)
\( c . \) It is \( \omega \) for case (a); and \( \sqrt{2} \omega \) for case (b)
D. It is \( \omega \) for both the ca
Subject: Chemistry
The conductivity of a saturated solution of \( B a S O_{4} \) is \( 3.06 \times 10^{-6} \) ohm \( ^{-1} c m^{-1} \)
and its molar conductance is \( 1.53 o h m^{-1} c m^{2} m o l^{-1} . \) The \( K_{s p} \) of
\( B a S O_{4} \) will be:
A \( \cdot 4 \times 10^{-12} \)
В. \( 2.5 \times 10^{-9} \)
c. \( 2.5 \times 10^{-13} \)
D. \( 4 \times 10^{-6} \)
Subject: Maths
If \( \vec{a}=2 \hat{m}+\hat{n}, \vec{b}=\hat{m}-2 \hat{n} \) and angle
between the unit vectors \( \hat{m} \) and \( \hat{n} \) is \( 60^{\circ} \)
\( a, b \) are the sides of a
parallelogram,then the lengths of the diagonals are
A \( . \sqrt{7}, \sqrt{5} \)
B. \( \sqrt{13}, \sqrt{5} \)
C \( . \sqrt{7}, \sqrt{13} \)
D. \( \sqrt{11}, \sqrt{13} \)
Subject: Maths
\( A B \) and \( C D \) are two parallel chords of a circle of radius \( 3 \mathrm{cm} . \) If \( A B=4 \mathrm{cms} \)
and \( C D=5 \mathrm{cm} . \) Then the distance
between them (in \( \mathrm{cm} \) ) is
A \( \cdot \frac{\sqrt{5}}{2}+\sqrt{11} \)
B. \( \sqrt{5}+\sqrt{11} \)
\( ^{c} \cdot \sqrt{5}+\frac{\sqrt{11}}{2} \)
D. \( \sqrt{2}+\frac{\sqrt{11}}{\sqrt{5}} \)
Subject: Chemistry
A mixture of \( N_{2} \) and \( H_{2} \) is the molar
ratio 1: 3 at 50 atm and 650 is allowed
to react till equilibrium is obtained. The
\( N H_{3} \) present at equilibrium is \( 25 \% \) by
weight, \( \boldsymbol{K}_{\boldsymbol{p}} \) for
\[
\begin{array}{r}
\boldsymbol{N}_{2}+\mathbf{3} \boldsymbol{H}_{2} \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{3} \\
\text { is } \boldsymbol{X} \times \mathbf{1 0}^{-4} \boldsymbol{a} \boldsymbol{t m}^{-2} \cdot(\mathbf{1 0 0 0} \boldsymbol{X})
\end{array}
\]
is
A \( \cdot 1434 \)
B. 35844
c. 21370
D. none of these
Subject: Chemistry
The percentage composition of \( \boldsymbol{P b} \) in
\( \left[\boldsymbol{P b}_{3}\left(\boldsymbol{P O}_{4}\right)_{3}\right] \) is: (Given molar mass of
\( \left.\left[\boldsymbol{P b}_{3}\left(\boldsymbol{P O}_{4}\right)_{3}\right]=\mathbf{8 1 1 . 0} \boldsymbol{g} \boldsymbol{m o l}\right) \)
A. 73.4
в. 76.5
c. 80.1
D. 68.54
Subject: Biology
\( \ln 4 t h, 5 t h \) and \( 6 t h \) segments of Earthworm, lying above the pharyngeal mass and connected with pharyngeal glands are found small, red coloured follicular bodies called
A. Septal glands
B. Blood glands
c. Salivary glands
D. Nephridia
E. Intestinal caecae
Subject: Physics
A plano-convex lens fits exactly into a plano-concave lens. Their plane
surfaces are parallel to each other. If the lenses are made of different material of
refractive indices \( \mu_{1} \) and \( \mu_{2} \) and \( R \) is the
radius of curvature of the curved
surface of the lenses, then focal length
of the combination is :
A \( \cdot \frac{R}{\mu_{1}-\mu_{2}} \)
В. \( \frac{2 R}{\mu_{2}-\mu_{1}} \)
c. \( \frac{R}{2\left(\mu_{1}-\mu_{2}\right)} \)
D. \( \frac{R}{2-\left(\mu_{1}+\mu_{2}\right)} \)
Subject: Chemistry
The total number of possible isomer for the complex compound:
\( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]\left[\boldsymbol{P t} \boldsymbol{C l}_{4}\right] \)
\( A \cdot 3 \)
B. 6
\( c \cdot 5 \)
\( D \)
Subject: Maths
If \( a_{r}>0 ; \forall r, n \in N \) and
\( a_{1}, a_{2}, a_{3}, \dots . a_{2 n} \) are in A.P, then \( \frac{\boldsymbol{a}_{\mathbf{1}}+\boldsymbol{a}_{\mathbf{2} n}}{\sqrt{\boldsymbol{a}_{1}}+\sqrt{\boldsymbol{a}_{2}}}+\frac{\boldsymbol{a}_{\mathbf{2}}+\boldsymbol{a}_{\mathbf{2} n-1}}{\sqrt{\boldsymbol{a}_{2}}+\sqrt{\boldsymbol{a}_{3}}}+ \)
\( \frac{\boldsymbol{a}_{\boldsymbol{3}}+\boldsymbol{a}_{\boldsymbol{2} \boldsymbol{n}-\boldsymbol{2}}}{\sqrt{\boldsymbol{a}_{\boldsymbol{3}}}+\sqrt{\boldsymbol{a}_{\boldsymbol{4}}}}+\ldots+\frac{\boldsymbol{a}_{\boldsymbol{n}}+\boldsymbol{a}_{\boldsymbol{n}+1}}{\sqrt{\boldsymbol{a}_{\boldsymbol{n}}}+\sqrt{\boldsymbol{a}_{\boldsymbol{n}+1}}}= \)
\( \mathbf{A} \cdot n-1 \)
в. \( \frac{n\left(a_{1}+a_{2 n}\right)}{\sqrt{a_{1}}+\sqrt{a_{n+1}}} \)
c. \( \frac{n-1}{\sqrt{a_{1}}+\sqrt{a_{n+1}}} \)
D. \( n+1 \)
Subject: Physics
A steel girder of length \( l \) rests freely on two supports (figure shown above). The moment of inertia of its cross-section is
equal to \( I . \) Neglecting the mass of the
girder and assuming the sagging to be slight, if the deflection \( \lambda \) due to the
force \( \boldsymbol{F} \) applied to the middle of the \( \operatorname{girderis} \lambda=\frac{1}{(40+x)} \frac{F l^{3}}{E I}, \) find the
value of \( \boldsymbol{x} \)
Subject: Maths
Lines \( m \) and \( n \) are cut by a transversal
so that \( \angle 1 \) and \( \angle 5 \) are corresponding
angles. If \( \angle \mathbf{1}=\mathbf{2 6} \boldsymbol{x}-\mathbf{7}^{o} \) and \( \angle \mathbf{5}= \)
\( 20 x+17^{\circ} . \) What value of \( x \) makes the
lines \( m \) and \( n \) parallel?
A . 5
B. 4
c. \( _{4} \frac{1}{2} \)
D. \( _{3} \frac{1}{4} \)
Subject: Physics
The energy released per fission of Uranium is \( 200 \mathrm{MeV} \). Determine the
number of fission per second required to generate 2MW power.
\( \mathbf{A} \cdot 6.25 \times 10^{16} \)
B. \( 0.25 \times 10^{16} \)
C. \( 1.25 \times 10^{16} \)
D \( .25 \times 10^{16} \)
Subject: Physics
A convex lens of focal length \( f_{1} \) and \( a \)
concave lens of focal length \( f_{2} \) are placed in contact. The focal length of the combination is
A \( \cdot\left(f_{1}+f_{2}\right) \)
B. \( \left(f_{1}-f_{2}\right) \)
c. \( \frac{f_{1} f_{2}}{f_{2}-f_{1}} \)
D. \( \frac{f_{1} f_{2}}{f_{2}+f_{1}} \)
Subject: Chemistry
At equilibrium of the reaction
\( \boldsymbol{P C l}_{5}(\boldsymbol{g}) \Leftrightarrow \boldsymbol{P C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \) the
concentrations of \( \boldsymbol{P} \boldsymbol{C l}_{5}(\boldsymbol{g}) \) and \( \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g}) \)
are 0.2 and 0.1 moles/lit.respectively \( \boldsymbol{K}_{c} \) is \( 0.05 . \) The equilibrium concentration
of \( C l_{2}\left(\text { moles.lit }^{-1}\right) \) is:
A. 0.5
B. 0.1
c. 1.5
D. 0.75
Subject: Chemistry
What is the order of mobilities of the
alkali metal ions in aqueous solution?
\( \mathbf{A} \cdot L i^{+}>N a^{+}>K^{+}>C s^{+}>R b^{+} \)
B. \( N a^{+}<L i^{+}<K^{+}<R b^{+}<C s^{+} \)
c. \( L i^{+}>K^{+}>N a^{+}>R b^{+}>C s^{+} \)
D. \( L i^{+}<N a^{+}<K^{+}<R b^{+}<C s^{+} \)
Subject: Physics
A stream of water flowing horizontally with a speed of \( 15 m s^{-1} \) gushes out of a
tube of cross-sectional area \( 10^{-2} m^{2} \)
and hits a vertical wall normally. Assuming that it does not rebound from the wall, the force exerted on the wall by the impact of water is:
A \( \cdot 1.25 \times 10^{3} N \)
В. \( 2.25 \times 10^{3} N \)
c. \( 3.25 \times 10^{3} N \)
D. \( 4.25 \times 10^{3} N \)
Subject: Physics
Two small beads having positive
charges \( 3 q \) and \( q \) are fixed at the
opposite ends of a horizontal, insulating
rod, extending from the origin to the
point \( \boldsymbol{x}=\boldsymbol{d} . \) As shown in figure, a third
small charged bead is free to slide on
the rod. At what position is the third
bead in equilibrium? Can it be in stable equilibrium?
A \( \cdot \frac{\sqrt{3} d}{(1+\sqrt{3})} \) from \( +3 q \) charge, yes
B. \( \frac{\sqrt{5} d}{(1+\sqrt{3})} \) from \( +3 q \) charge, yes
C \( \frac{\sqrt{3} d}{(1+\sqrt{2})} \) from \( +3 q \) charge, yes
D. \( \frac{\sqrt{2} d}{(1+\sqrt{3})} \) from \( +3 q \) charge, yes
Subject: Physics
An automobile moves on a road with a
speed of \( 54 k m h^{-1} . \) The radius of its
wheel is \( 0.45 m \) and the moment of
inertia of the wheel about its axis of
rotation is \( 3 \mathrm{kgm}^{2} \). If the vehicle is
brought to rest in \( 15 s \), the magnitude of average torque transmitted by its brakes to the wheels is:
A . \( 2.86 \mathrm{kg} \mathrm{m}^{2} \mathrm{s}^{-2} \)
B. \( 6.66 \mathrm{kg} \mathrm{m}^{2} \mathrm{s}^{-2} \)
c. \( 8.58 \mathrm{kg} \mathrm{m}^{2} \mathrm{s}^{-2} \)
D. \( 10.86 \mathrm{kg} \mathrm{m}^{2} \mathrm{s}^{-2} \)
Subject: Chemistry
Ethanol is heated with excess
concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) at \( 443 \mathrm{K} \)
i) Name the reaction that occurs and
explain it.
ii) Write the equation for the above reaction.
iii) What is the product formed? What happens when this gas is passed through bromine water?
iv) When ethanol vapour is passed through bromine water, why does no change occur?
Subject: Chemistry
The correct order of increasing \( s- \)
character (in percentage) in the hybrid orbitals of following molecules/ions is:
(।) \( C O_{3}^{2-} \)
\( (\|) \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\boldsymbol{4}} \)
\( (\|\|) \boldsymbol{I}_{3}^{-} \)
\( (\mid V) N C l_{3} \)
\( (\vee) B e C l_{2} \)
\( A \cdot\|<\| I<I V<I<V \)
B. \( \|<I V<\| I<V<1 \)
\( c \cdot \||<||<|<V<\mid V \)
D. \( \|<I V<\| I<1<V \)
Subject: Chemistry
Identify \( Z \) in the following sequence.
\[
\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Br} \stackrel{\mathrm{KCN}}{\longrightarrow}(\mathrm{Q}) \frac{\mathrm{dil.HCl}}{\Delta}>\widehat{\mathrm{Z}}
\]
A \( \cdot \mathrm{CH}_{3} \mathrm{COCl} \)
в. \( \mathrm{CH}_{3} \mathrm{CONH}_{2} \)
c. \( \mathrm{CH}_{3} \mathrm{COOH} \)
D. \( \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COOH} \)
Subject: Physics
Two points \( P \) and \( Q \) are maintained at
the potential of \( 10 ~ V \) and \( -4 V \)
respectively. The work done in moving
100 electrons from \( P \) to \( Q \) is:
A. \( -19 \times 10^{-7} J \)
\( J \)
В. \( 9.60 \times 10^{-17} J \)
c. \( -2.24 \times 10^{-16} J \)
D. 2.24 \( \times 10^{-16} \mathrm{J} \)
Subject: Chemistry
A sample of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) solution labelled as 28 volume has density of \( 26.5 g / L \) Mark the correct option(s)
representing concentration of same solution in other units.
This question has multiple correct options
\( \mathbf{A} \cdot M_{H_{2}} o_{2}=2.5 \)
В \( \cdot \% \frac{w}{v}=17 \)
C. Mole fraction of \( H_{2} O_{2}=0.2 \)
D \( \cdot m_{H_{A}} o_{2}=13.88 \)
Subject: Physics
Assertion
In a constant pressure process if we neglect the friction between piston then
we can definetly say that the process
has to be reversible.
Reason
Since there is always an equilibrium on
piston due to constant pressure we can say that it is reversible process.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
Figure shows two processes \( A \) and \( B \) on
a system. Let \( \Delta Q_{1} \) and \( \Delta Q_{2} \) be the heat
given to the system in processes \( A \) and
B respectively. Then
A \( \cdot \Delta Q_{1}>\Delta Q_{2} \)
B . \( \Delta Q_{1}=\Delta Q_{2} \)
c. \( \Delta Q_{2}<\Delta Q_{2} \)
\( \mathbf{D} \cdot \Delta Q_{1}<=\Delta Q_{2} \)
Subject: Chemistry
Assertion
Catalytic converters must be used in
cars.
Reason
Catalytic converter helps to reduce the
formation of acid rain.
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 \( x^{2}+y^{2}=t-\frac{1}{t} \) and \( x^{4}+y^{4}=t^{2}+ \)
\( \frac{1}{t^{2}}, \) then prove that \( \frac{d y}{d x}=\frac{1}{x^{3} y} \)
Subject: Physics
Which of the following point is not
shown by Rutherford alpha scattering experiment?
A. \( \alpha \) - particle can come within a distance of the order of \( 10^{-14} \mathrm{m} \) of the nucleus
B. The radius of the nucleus is less than \( 10^{-14} m \)
C. Sattering follows coulombs law
D. The positively charged parts of an atom move with extremely high velocities
Subject: Maths
If \( A \) is a \( 3- \) rowed square matrix and
\( |\boldsymbol{A}|=\mathbf{4} \) then \( \boldsymbol{a} \boldsymbol{d} \boldsymbol{j}(\boldsymbol{a} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A})=? \)
A \( .4 A \)
в. \( 16 A \)
\( c \cdot 64 A \)
D. None of these
Subject: Maths
Which of the following is equivalent set
(i) \( \boldsymbol{A}=\{\mathbf{2}, \mathbf{3}, \mathbf{5}, \mathbf{7}\} \)
(ii) \( B=\{a, e, i, o, u\} \)
(iii) \( \boldsymbol{C}=\{-\mathbf{1},-\mathbf{9},-\mathbf{8},-\mathbf{7}\} \)
A. (i) and (ii)
B. (i) and (iii)
c. (ii) and (iii)
D. None of these
Subject: Physics
Figure shows three circular arcs, each
of radius \( \mathrm{R} \) and total charge as
indicated. The net electric potential at
the centre of curvature is?
A \( \cdot \frac{Q}{2 \pi \varepsilon_{R}} \)
B・ \( \frac{Q}{3 \pi \varepsilon_{R}} \)
c. \( \frac{2 Q}{\pi_{c e R} R_{R}} \)
D. \( \frac{Q}{\pi \varepsilon R} \)
Subject: Physics
Unpolarized light falls on two polarizing sheets placed one on top of the other.
What must be the angle between the characteristic directions of the sheets.
If the intensity of the final transmitted
light is one-third the maximum, intensity of the first transmitted beam?
\( \mathbf{A} \cdot 75^{\circ} \)
B . \( 55^{\circ} \)
\( c \cdot 35^{\circ} \)
D. \( 15^{\circ} \)
Subject: Physics
An inductive coil has resistance of
100\Omega. When an ac signal of frequency 1000 \( H z \) is fed to the coil, the applied
voltage leads the current by \( 45^{\circ} . \) What
is the inductance of the coil?
\( \mathbf{A} \cdot 2 m H \)
в. 3.3 тН
c. \( 16 m H \)
D. \( \sqrt{5} \) m Н
Subject: Maths
Which of the following is true
This question has multiple correct options
\( \mathbf{A} \cdot(3+\sqrt{-5})(3-\sqrt{-5})=14 \)
B \( \cdot(-2+\sqrt{-3})(-3+2 \sqrt{-3})=-7 \sqrt{3} i \)
\( \mathbf{c} \cdot(2+3 i)^{2}=(-5+12 i) \)
D. \( (\sqrt{5}-7 i)^{2}=-44-14 \sqrt{5} i \)
Subject: Physics
Two planets revolves around the sun
with frequencies \( N_{1} \) and \( N_{2} \) revolutions
per year. If their average radii (orbital)
be \( R_{1} \) and \( R_{2} \) respectively, then \( R_{1} / R_{2} \)
is equal to:
A \( \cdot\left(N_{1} / N_{2}\right)^{2 / 3} \)
a
B . \( \left(N_{1} / N_{2}\right)^{3 / 2} \)
C \( \cdot\left(N_{2} / N_{1}\right)^{2 / 3} \)
D. \( \left(N_{2} / N_{1}\right)^{3 / 2} \)
Subject: Maths
The probability distribution of a
discrete random variable \( X \) is:
\[
\boldsymbol{X}=\boldsymbol{x} \quad \mathbf{1} \quad \boldsymbol{2} \quad \boldsymbol{3}
\]
\( P(X= \)
\( x) \)
\[
3 k
\]
\( 4 k \) \( k \quad 2 k \)
\[
\text { Find } P(X \leq 4)
\]
\( \mathbf{A} \cdot \frac{2}{3} \)
B. \( \frac{3}{4} \)
\( c \cdot \frac{4}{5} \)
D. \( \frac{5}{6} \)
Subject: Chemistry
For the reaction2 \( \boldsymbol{A}+\boldsymbol{B} \rightarrow \boldsymbol{A}_{2} \boldsymbol{B} \) rate \( = \)
\( \boldsymbol{k}[\boldsymbol{A}][\boldsymbol{B}]^{2} \) with \( \boldsymbol{k}=\boldsymbol{2} . \boldsymbol{0} \times \)
\( 10^{-6} m o l^{-2} L^{2} s^{-1}, \) what is the rate of the
reaction when \( [\mathrm{A}] \) is reduced to 0.060 molL'-13. the initial rate of reaction
when \( [A]=0.1 m o l L^{-1} a n d[B]= \)
\( 0.2 m o l L^{-1} i s 8 \times 10^{-9} m o l L^{-1} s^{-1} \)
Subject: Maths
In the following figure, ABCD is a parallelogram and EFCD is a rectangle. Also, \( A L \perp D C . \) Prove that
(i) \( \operatorname{ar}(\mathrm{ABCD})=\operatorname{ar}(\mathrm{EFCD}) \)
(ii) \( \operatorname{ar}(\mathrm{ABCD})=\mathrm{DC} \times \mathrm{AL} \)