AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
There are three different Urns, Urn-I,
Urn-II and Urn-III containing 1 Blue, 2
Green, 2 Blue, 1 Green, 3 Blue, 3 Green
balls respectively. If two Urns are
randomly selected and a ball is drawn
from each Urn and if the drawn balls are
of different colours then the probability
that chosen Urn was Urn-I and Urn-II is
A \( \cdot \frac{1}{7} \)
B. \( \frac{5}{13} \)
c. \( \frac{5}{14} \)
D. \( \frac{5}{7} \)
Subject: Physics
A block of mass \( m k g \) is sliding from
rest on an inclined rough surface of
inclination \( \theta \) as shown in the figure
under the action of three forces, weight normal and frictional force only. The
magnitude of force are \( 20 N, 40 N \) and
\( \mathbf{5 0} N \) not necessarily in the same order The value of \( g \) is \( 10 m / s^{2} . \) Now match
the physical quantity in \( L i s t-I \) with
their magnitude in \( L i s t-I I \) in \( S I \) unit
and select the correct answer using the
codes given below the lists: (assume
that the coefficient of kinetic friction is
less than 1 ).
Subject: Physics
Two free charges \( +q \) and \( +4 q \) are
placed at a distance \( ^{\prime} r^{\prime} \) between them.
A third charge is placed in between them and find the third charge when the system is in equilibrium.
A \( \cdot \frac{4 q}{3} \)
в. \( \frac{4 q}{9} \)
c. \( \frac{2 q}{9} \)
D. \( \frac{q}{9} \)
Subject: Physics
A long straight wire of radius R carries current \( i . \) The magnetic field inside the wire at distance \( r \) from its centre is
expresses as:
\( \mathbf{A} \cdot\left(\frac{\mu_{0} i}{\pi R^{2}}\right) \cdot r \)
в. \( \left(\frac{2 \mu_{0} i}{\pi R^{2}}\right) \cdot \pi \)
\( ^{\text {c. }}\left(\frac{\mu_{0} i}{2 \pi R^{2}}\right) \cdot r \)
D. \( \left(\frac{\mu_{0} i}{2 \pi R}\right) \cdot \)
Subject: Physics
In an orbit of radius \( 0.4 A^{0} \) an electron
revolves with a frequency of \( 6.25 \times 10^{15} \)
Hz. The magnetic induction field at its
centre is (in Tesla):
A . \( 4 \pi \)
в. \( 2 \pi \)
\( c \cdot 4 \)
\( D \cdot 2 \)
Subject: Physics
Let the \( x \) -z plane be the boundary between two transparent media. Medium 1 in \( z \geq 0 \) has a refractive index of \( \sqrt{2} \) and medium 2 with \( z<0 \) has refractive index of \( \sqrt{3} . \) A ray of light in medium 1 given by the vector \( \vec{A}= \) \( 6 \sqrt{3} \hat{i}+8 \sqrt{3} \hat{j}-10 \hat{k} \) is incident on the
plane of separation. The angle of refraction in medium 2 is:
A \( \cdot 45^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 75^{\circ} \)
D. \( 30^{\circ} \)
Subject: Chemistry
Aqueous solution of \( \mathrm{PBr}_{3} \) conducts
electricity due to the presence of:
\( A . \) HOBr
в. НВг
c. \( \mathrm{H}_{3} \mathrm{PO}_{4} \)
D. \( \mathrm{H}_{2} \mathrm{O} \)
Subject: Physics
The strength of gravity on Mars is only \( 40 \% \) of that on earth. If a child has a
mass of \( 60 \mathrm{kg} \) on earth, what would the
child's weight be on Mars?
A . 24
в. 60 N
c. \( 240 N \)
D. \( 600 N \)
E. None of the above is correct within \( 10 \% \)
Subject: Physics
Which of the following statements is
not true about Gauss's law?
A. Gauss's law is true for any closed surface
B. The term \( q \) on the right side of Gauss's law includes the sum of all charges enclosed by the surface
C. Gauss's law is not much useful in calculating electrostatic field when the system has some symmetry
D. Guss's law is based on the inverse square dependence on distance contained in the coulomb's law
Subject: Physics
An open U-tube contains mercury. When \( 13.6 \mathrm{cm} \) of water is pourd into one of the
\( \operatorname{arms} \) of the tube then the mercury rise
in the other arm from its initial level is:
A . \( 1 c m \)
B. \( 0.5 \mathrm{cm} \)
\( \mathbf{c} \cdot 10 \mathrm{cm} \)
D. \( 5 \mathrm{cm} \)
Subject: Physics
A circuit consists of a resistor,an
inductor and a capacitor connected in series. If the resistance of a resistor is
\( 25 \Omega \) and the value of inductive
reactance is equal to capacitive
reactance, then the net impedance of the circuit will be :
A . \( 5 \Omega \)
B. 25\Omega
c. \( 125 \Omega \)
D. \( 625 \Omega \)
Subject: Chemistry
¡) \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}+(\boldsymbol{o}) \)
ii) \( \boldsymbol{H}_{2} \boldsymbol{O}_{2}+\boldsymbol{2} \boldsymbol{I}^{-} \rightarrow \boldsymbol{I}_{2}+\boldsymbol{2} \boldsymbol{O} \boldsymbol{H}^{-}, \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
acts as:
A. oxidising agent in both (i) and (ii)
B. reducing agent in both (i) and (ii)
c. oxidising agent in (i) and reducing agent in (ii)
D. reducing agent in (i) and oxidising agent in (ii)
Subject: Chemistry
Some hydrogen-like atom in ground state absorb \( n \) photons having the same energy and on de-excitation, it
emits exactly \( n \) photons. Then the energy of absorbed photon may be:
This question has multiple correct options
A. \( 91.8 e V \)
B. \( 40.8 e V \)
c. \( 48.4 e V \)
D. \( 54.4 e V \)
Subject: Chemistry
Ethylene on combustion gives carbon dioxide and water. Its heat of
combustion is \( 1410.0 \mathrm{kJ} \). \( \mathrm{mol}^{-1} \). If the
heat of formation of \( C O_{2} \) and \( H_{2} O \) are
\( 393.3 k J \) and \( 286.2 k J, \) respectively
Calculate the heat of formation of
ethylene.
\( \mathbf{A} \cdot \Delta_{f} H=51.0 k J m o l^{-1} \)
B . \( \Delta_{f} H=102.0 k J m o l^{-1} \)
C \( . \Delta_{f} H=25.0 k J m o l^{-1} \)
D. None of these
Subject: Physics
A child is sitting on a swing. Its minimum and maximum heights from
the ground are \( 0.75 m \) and \( 2 m \) respectively, its maximum speed will be:
A. \( 5 m / s \)
в. \( 8 m / s \)
c. \( 10 m / s \)
D. \( 15 \mathrm{m} / \mathrm{s} \)
Subject: Physics
A man wearing a wingsuit glides through the air with a constant velocity
of \( 47 ~ m s^{-1} \) at an angle of \( 24^{\circ} \) to the horizontal. The path of the man is shown
in Fig.
The total mass of the man and the
wingsuit is 85 kg. The man takes a time
of 2.8 minutes to glide from point \( A \) to
point \( \boldsymbol{B} \)

For the movement of the man from \( A \) to
\( B, \) determine:
the magnitude of the force on the man
due to air resistance.
Subject: Physics
In the situation of resonance, frequency
of L-C circuit is:
\( ^{\mathrm{A}} \cdot \frac{1}{2 \pi} \sqrt{\frac{1}{L C}} \)
в. \( 2 \pi \sqrt{\frac{1}{L C}} \)
c. \( 2 \pi \sqrt{L C} \)
D. \( \frac{1}{2 \pi} \sqrt{L C} \)
Subject: Physics
A solid conducting sphere having charge \( 4 \mu C \) is placed on nonconducting stand. A point charge \( 2 \mu C \)
is placed at a distance from the centre
of the sphere, at a double distance of radius of the sphere as shown in the
figure. If conducting sphere is earthed
then charge flow into the ground is :
\( A \cdot 5 \mu C \)
B. \( 2 \mu C \)
\( c \cdot 10 \mu C \)
D. \( 1 \mu C \)
Subject: Chemistry
Give the chemical formula of calcium
sulphate hemihydrate.
A \( \cdot \operatorname{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \)
в. \( \operatorname{caSO}_{4}: \frac{1}{2} H_{2} \mathrm{O} \)
c. \( \operatorname{cas} O_{4} \cdot 10 H_{2} O \)
D. \( \operatorname{CaSO}_{4} . \mathrm{H}_{2} \mathrm{O} \)
Subject: Maths
If \( \int \frac{\operatorname{cosec}^{2} x-2010}{\cos ^{2010 x}} d x= \)
\( -\frac{\boldsymbol{f}(\boldsymbol{x})}{(\boldsymbol{g}(\boldsymbol{x}))^{2010}}+C ; \) then the number of
solutions where equation \( \frac{f(x)}{g(x)}=\{x\} \)
in \( [\mathbf{0}, \mathbf{2} \boldsymbol{\pi}] \) is / are:
\( A \cdot 0 \)
B. 1
c. 2
D. 3
Subject: Chemistry
\( \mathbf{3} C_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{H}+\boldsymbol{P} \boldsymbol{C l}_{3} \rightarrow \mathbf{3} \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{C l}+\boldsymbol{X} \)
Where \( X \) is an oxyacid of phosphorus.
\( \boldsymbol{X} \) is:
A \( . H_{3} P O_{4} \)
в. \( H_{3} P O_{3} \)
c. \( H_{3} P O_{2} \)
D. \( H P O \)
Subject: Physics
In a hydroelectric power station water is allowed to fall at the rate of 2000 kg per
second on a turbine kept \( 100 \mathrm{m} \) below the water level. Calculate the potential energy of water falling every one second at the highest point.
A \( .2 \times 10^{6} J^{2} \)
В. \( 2 \times 10^{8} J \)
c. \( 2 \times 10^{7} J \)
D. \( 2 \times 10^{6} J \)
Subject: Chemistry
The reaction \( \boldsymbol{C} \boldsymbol{H}_{2}=\boldsymbol{C} \boldsymbol{H}_{2}+ \)
\( \boldsymbol{H}_{2} \underbrace{\frac{N i}{250-300^{\circ}}} \boldsymbol{C} \boldsymbol{H}_{3}-\boldsymbol{C H}_{3} \) is called
A. Wurtz reaction
B. Kolbe's reaction
c. Sabatier - Sendern's reaction
D. Cabylamine reaction
Subject: Maths
Find the value of a for which the
function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{a} \boldsymbol{x}^{3}-\boldsymbol{3}(\boldsymbol{a}+\boldsymbol{2}) \boldsymbol{x}^{2}+ \)
\( 9(a+2) x-1 \) is decreasing for all \( x \in \)
\( \boldsymbol{R} \)
Subject: Physics
After the capacitor gets fully charged,
\( \mathbf{S}_{1} \) is opened and \( \mathbf{S}_{2} \) is closed so that the
inductor is connected in series with the
capacitor. Then,
A \( . \) at \( t=0, \) energy stored in the circuit is purely in the form of magnetic energy
B. at any time \( t>0 \), current in the circuit is in the same
c. at \( t>0, \) there is no exchange of energy between the inductor and capacitor
D. at any time \( t>0 \), instantaneous current in the circuitt \( \operatorname{may} \mathrm{v} \sqrt{\frac{\mathrm{c}}{\mathrm{L}}} \)
Subject: Physics
Two waves represented by \( y_{1}= \)
\( 10 \sin (2000 \pi t) \) and \( y_{2}= \)
\( 10 \sin (2000 \pi t+\pi / 2) \) are
superimposed at any point at a particular instant. The resultant amplitude is?
A. 10 units
B. 20 units
c. 14.1 units
D. zero
Subject: Physics
The ratio (R) of output resistance \( r_{0} \)
and and the input resistance \( r_{i} \) in
measurements of input and output
characteristics of a transistor is
typically in the range:
A . \( R \sim 10^{2}-10^{3} \)
В. \( R \sim 1-10 \)
c. \( R \sim 0.1-1.0 \)
D. \( R \sim 0.1-0.01 \)
Subject: Maths
In the adjoining figure \( \boldsymbol{A B}= \)
\( 12 c m, C D=8 c m, B D=20 \mathrm{cm} \)
\( \angle A B D=\angle A E C=\angle E D C=90^{\circ} . \) If
\( B E=x, \) then
A. \( x \) has two possible values whose difference is 4
B. \( x \) has two possible values whose sum is 28
c. \( x \) has only one value and \( x \geq 12 \)
D. \( x \) cannot be determined with the given information
Subject: Physics
A man standing unsymmetrically between two parallel cliffs, claps his hand and starts hearing a series of echoes at intervals of 1 s. If the speed of
sound in air is \( 340 \mathrm{ms}^{-1} \), then the distance between the two prallel cliffs,
is
A . \( 170 \mathrm{m} \)
B. 340 \( \mathrm{m} \)
\( c .510 \mathrm{m} \)
D. \( 680 \mathrm{m} \)
Subject: Physics
Suppose that the acceleration of a free fall at the surface of a distant planet
was found to be equal to that at the surface of the earth. If the diameter of
the planet were twice the diameter of
the earth, then the ratio of mean density
of the planet to that of the earth would be:
A . 4: 1
B . 2: 1
c. 1: 1
D. 1: 2
Subject: Chemistry
Which of the following statement is
correct?
\( \mathbf{A} \cdot p K_{w}=14 \) at all temperature
B \( \cdot p K_{w}=0 \) at \( 0^{0} C \)
C \( \cdot p K_{w} \) decreases with increase temperature
D. \( p K_{w} \) increases with increase in temperature
Subject: Chemistry
Which of the following statements
is/are correct?
This question has multiple correct options
A. Liebig's method is used for the quantitative estimation of both \( C \) and \( H \)
B. Dumas method is used for the quantitative estimation of \( \mathrm{N} \) in all nitrogen-containing organic compounds.
C. In Liebig's combustion method, dry CuO is used.
D. Silver salt method is a chemical method for the determination of equivalent mass of organic acids.
Subject: Maths
\( A \) and \( B \) are two sets such that \( n(A \cup \)
\( B)=25, n\left(A^{\prime} \cap B\right)=8 \) and \( n(A \cap \)
\( \left.\boldsymbol{B}^{\prime}\right)=\mathbf{9} \)
Use venn -diagram to find \( n(B-A) \)
Subject: Chemistry
Heat of combustion \( \Delta H^{o} \) for
\( \boldsymbol{C}(\boldsymbol{s}), \boldsymbol{H}_{2}(\boldsymbol{g}) \) and \( \boldsymbol{C H}_{4}(\boldsymbol{g}) \) are \( -\mathbf{9 4},-\mathbf{6 8} \)
and \( -213 k c a l / \) mol respectively. Then
\( \Delta H^{o} \) for \( C(s)+2 H_{2}(g) \rightarrow C H_{4} \) is:
A \( .-17 k c a l / m o l \)
B. -111 kcal / mol
c. \( -170 \mathrm{kcal} / \mathrm{mol} \)
D. \( -85 k c a l / m o l \)
Subject: Physics
A particle is moving in a circle of radius \( R \) in such a way that at any instant the normal and tangential components of its acceleration are
equal. If its speed at \( t=0 \) is \( v_{o} \) the time
taken to complete the first revolution is
A \( \cdot R / v_{o} \)
в. \( v_{o} / R \)
C \( \cdot\left(R / v_{o}\right) \times\left(1-e^{-2 \pi}\right) \)
D. \( \left(R / v_{o}\right) \times\left(e^{-2 \pi}\right) \)
Subject: Chemistry
\( \boldsymbol{A}_{\text {organic }} \)Compound\( +\boldsymbol{O}_{2} \rightarrow \boldsymbol{X}+\boldsymbol{Y}+\boldsymbol{Z} \)
Compound \( (A) \) in pure form does not
give ppt. with \( A g N O_{3} \) solution. mixture containing \( 70 \% \) of \( (A) \) and \( 30 \% \) of ether is used as an anaesthetic.
Compound \( (X) \) and \( (Y) \) are oxides while \( (\mathrm{Z}) \) is a pungent smelling gas. \( (\mathrm{X} \) is a neutral oxide which turns cobalt
chloride paper pink. Compound (Y) turns lime water milky and produces an acidic solution with water. Compounds
\( (A),(X),(Y) \) and \( (Z) \) respectively will be :
A \( \cdot C H_{4}, H_{2} O, C O_{2}, C l \)
в. \( C H C l_{3}, H_{2} O, C O_{2}, C l_{2} \)
c. \( C H_{3} \) ОН \( , H_{2} \) О \( , \mathrm{CO}_{2}, \mathrm{N}_{2} \)
D. \( N H_{2} C O N H_{2}, H_{2} O, N_{2} O, C O_{2} \)
Subject: Maths
The value of \( \int_{-\pi / 2}^{\pi / 2} \log \left(\frac{2-\sin \theta}{2+\sin \theta}\right) d \theta \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. None of these
Subject: Chemistry
In a reaction, \( \Delta H \) and \( \Delta S \) both are
more than zero. In which of the following cases, the reaction would not be
spontaneous? This question has multiple correct options
\( \mathbf{A} \cdot \Delta H>T \Delta S \)
в. \( T \Delta S>\Delta H \)
c. \( \Delta H=T \Delta S \)
D. \( \Delta G<0 \)
Subject: Physics
After absorbing a slowly moving
neutron of Mass \( m_{N} \) (momentum \( \approx 0 \) )
a nucleus of mass M breaks into two
nuclei of masses \( \boldsymbol{m}_{1} \) and \( \mathbf{5 m}_{\mathbf{1}}\left(\boldsymbol{6} \boldsymbol{m}_{\mathbf{1}}=\right. \)
\( \left.M+\boldsymbol{m}_{N}\right) \) respectively. If the de Broglie
wavelength of he nucleus with mass \( m_{1} \)
is \( \lambda, \) the de Broglie wavelength of the
nucleus will be.
A \( .5 \lambda \)
B. \( \lambda / 5 \)
\( c \cdot \lambda \)
D. \( 25 \lambda \)
Subject: Physics
The electric field between the plates of
two oppositely charged plane sheets of
charge density' \( \sigma^{\prime} \) is :
A \( \cdot+\frac{\sigma}{2 \epsilon_{0}} \)
в. \( -\frac{\sigma}{2 \epsilon_{0}} \)
c. \( \frac{\sigma}{\epsilon_{0}} \)
D. zero
Subject: Physics
The critical angle of a medium B with
respect another medium A is \( 45^{\circ} \) and
the critical angle of a medium C with
respect the medium B is \( 30^{\circ} . \) The
critical angle of medium \( C \) with respect
to A is :
A. Less than 30
B. Greater than \( 30^{\circ} \)
\( c \cdot 30 \)
D. Cannot be determined
Subject: Chemistry
Which of the following is an example of
exothermic reaction?
\( \mathbf{A} \cdot H_{2}(g)+C l_{2}(g) \rightarrow 2 H C l(g) ; \Delta H=-184.6 k J \)
B. \( N_{2}(g)+O_{2}(g) \rightarrow 2 N O(g) ; \Delta H=+180.8 k J \)
\( \mathbf{c} \cdot C(\text {graphite})+H_{2} O(g) \rightarrow C O(g)+H_{2}(g) ; \Delta H= \)
\( +1314 k J \)
D. \( C(\text { graphite })+2 S(s) \rightarrow C S_{2}(l) ; \Delta H=+91.9 k J \)
Subject: Physics
If \( 0.1 J \) of energy is stored for the flow of current of \( 0.2 A \) in an inductor, then its
inductance value is:
A \( .5 H \)
в. \( 0.5 H \)
\( \mathrm{c} \cdot 5 m H \)
D. \( 50 H \)
E . \( 50 \mathrm{mH} \)
Subject: Chemistry
The frequency of radiation emitted when the electron falls from \( n=4 \) to
\( \boldsymbol{n}=\mathbf{1} \) in a hydrogen atom will be :
\( \left(\text { Given, } \boldsymbol{h}=\mathbf{6 . 6 2 5} \times \mathbf{1 0}^{-\mathbf{3 4}} \mathbf{J s}\right): \)
A \( \cdot 3.08 \times 10^{15} s^{-1} \)
В. \( 2.00 \times 10^{16} s^{-1} \)
c. \( 1.54 \times 10^{17} s^{-1} \)
D. \( 1.03 \times 10^{14} s^{-1} \)
Subject: Physics
A small coil is introduced between the
poles of an electromagnet so that its axis coincides with the magnetic field
direction. The cross-sectional area of
the coil is equal to \( S=3.0 m m^{2}, \) the
number of turns is \( N=60 . \) When the
coil turns through \( 180^{\circ} \) about its diameter, a galvanometer connected to the coil indicates a charge \( \boldsymbol{q}=\mathbf{4 . 5} \boldsymbol{\mu} \boldsymbol{C} \)
flowing through it. Find the magnetic induction magnitude between the poles, provided the total resistance of the electric circuit equals \( R=40 \Omega \)
Subject: Physics
The velocity of progressive wave which produces the stationary wave, \( y=2 \)
\( \sin \left(\frac{\pi x}{100}\right) \cos (\pi t) \mathrm{m}: \)
A. \( 100 m / s \)
в. \( 1 \mathrm{m} / \mathrm{s} \)
c. \( 50 m / s \)
D. \( 1000 \mathrm{m} / \mathrm{s} \)
Subject: Physics
In a physical balance working on the principle of moments, when \( 5 \mathrm{mg} \) weight is placed on the left plan, the beam becomes horizontal. Both the
empty pans of the balance are of equal mass. Which of the following statements is correct?
A. Both the arms are of same length.
B. Every object that is weighed using this balance appears lighter than its actual weight
c. Left arm is longer than the right arm.
D. Left arm is shorter than the right arm.
Subject: Chemistry
Find the total number of cations for
which I.P of cation is lower than
corresponding atom: \( \boldsymbol{K}^{+}, \boldsymbol{O}^{+}, \boldsymbol{N} \boldsymbol{e}^{+}, \boldsymbol{P}^{+} \)
\( \boldsymbol{B} \boldsymbol{e}^{+}, \boldsymbol{N} \boldsymbol{a}^{2+} \)
Subject: Maths
Let \( \boldsymbol{f}: \boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z} \rightarrow(\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}) \) be a one-one
function. It is known that only one of the following statements is true:
(i) \( \boldsymbol{f}(\boldsymbol{x}) \neq \boldsymbol{b} \)
(ii) \( f(y)=b \)
(iii) \( f(z) \neq a \)
A \( . f=\{(x, a),(y, b),(z, c)\} \)
B. \( f=\{(x, b),(y, a),(z, c)\} \)
c. \( f=\{(x, b),(y, c),(z, c)\} \)
D. \( f=\{(x, b),(y, c),(z, a)\} \)
Subject: Maths
Consider the following statements:
1. The general solution of \( \frac{d y}{d x}=f(x)+ \) \( x \) is of the form \( y=g(x)+c, \) where \( c \) is
an arbitrary constant.
2. The degree of \( \left(\frac{d y}{d x}\right)^{2}=f(x) \) is 2 Which of the above statements is/are
correct?
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2
Subject: Chemistry
For the reaction, \( 2 N_{2} O_{5}(g) \longrightarrow \)
\( 4 N O_{2}(g)+O_{2}(g), \) if the concentration
of \( N O_{2} \) increases by \( 5.2 \times 10^{-3} M \) in
100 sec, then the rate of reaction is:
A \( \cdot 1.3 \times 10^{-5} M s^{-1} \)
В \( \cdot 5 \times 10^{-4} \mathrm{M} s^{-1} \)
c. \( 7.6 \times 10^{-4} M s^{-1} \)
D. \( 2 \times 10^{-3} M s^{-1} \)
E \( .2 .5 \times 10^{-5} M s^{-1} \)
Subject: Physics
A parallel plate capacitor with circular
plates and a capacitance \( C \) has the
radius of each plate doubled and the
distance between the plates doubled.
What is the new capacitance?
\( ^{A} \cdot \frac{C}{2} \)
в. \( C \)
\( c \cdot 2 C \)
D. \( 4 C \)
Subject: Physics
A particle executing SHM has a
maximum speed of \( 0.5 m s^{-1} \) and
maximum acceleration of \( 1 m s^{-2} \)
The angular frequency of oscillation is:
A \( \cdot 2 r a d s^{-1} \)
B . 0.5 rads\( ^{-1} \)
C \( .2 \pi r a d s^{-1} \)
D. \( 0.5 \pi r a d s^{-1} \)
Subject: Maths
Which one of the following statements
are correct?
\( \mathbf{A} \cdot \) If \( g(x)(\neq 0) \) and \( f(x) \) are two polynomials \( \in F(x) \), then there exists unique polynomials \( q(x) \) and \( r(x) \in F(x) \) such that \( f(x)=g(x) q(x)+r(x) \) where \( \operatorname{deg} . r(x)< \)
\( \operatorname{deg} . g(x) \)
B. If \( g(x)(\neq 0) \) and \( f(x) \) are two polynomials \( \in F(x) \), then there exists unique polynomials \( q(x) \) and \( r(x) \in F(x) \) such that \( f(x)=g(x) q(x)+r(x) \) where \( \operatorname{deg} . r(x) \leq \)
\( \operatorname{deg} . g(x) \)
C \( \cdot \) If \( g(x)(\neq 0) \) and \( f(x) \) are two polynomials \( \in F(x) \), then there exists unique polynomials \( q(x) \) and \( r(x) \in F(x) \)
such that \( f(x)=g(x) q(x)+r(x) \) where either \( r(x)=0 \) or \( \operatorname{deg} . r(x)<\operatorname{deg} . g(x) \)
D. If \( g(x)(\neq 0) \) and \( f(x) \) are two polynomials \( \in F(x) \), then there exists unique polynomials \( q(x) \) and \( r(x) \in F(x) \) such that \( f(x)=g(x) q(x)+r(x) \) where \( f(x)=0 \) or \( \operatorname{deg} . r(x)=\operatorname{deg} . g(x) \)
Subject: Chemistry
Which of the following is an energy consuming process?
A \( \cdot O(g)+e^{-} \rightarrow O^{-}(g) \)
B . \( N a^{+}(g)+e^{-} \rightarrow N a(g) \)
\( \mathrm{c} \cdot O^{-}+e^{-} \rightarrow O^{2-}(g) \)
D. \( O^{2-}(g) \rightarrow O^{-}(g)+e^{-} \)
Subject: Physics
For a particle moving along \( x \) -axis,
acceleration is given as \( a=v \). Find the
position as a function of time? Given that \( \operatorname{at} t=0, x=0, v=1 \)
A \( \cdot e-1 \)
B \( \cdot e^{2}-1 \)
c. \( \frac{e}{2} \)
D. \( e+1 \)
Subject: Maths
Let \( a=2 i+j-2 k \) and \( b=i+j . \) If \( c \) is
a vector such that \( \quad \boldsymbol{a} . \boldsymbol{c}=|\boldsymbol{c}| \cdot|\boldsymbol{c}-\boldsymbol{a}|= \)
\( 2 \sqrt{2} \) and the angle between \( (a \times b) \) and
\( c \) is \( 30^{\circ}, \) then \( |(a \times b) \times c| \) is equal to
A \( \cdot \frac{2}{3} \)
B. \( \frac{3}{2} \)
c. 2
D. 3
Subject: Chemistry
Assertion
A tube light emits white light.
Reason
Emission of light in a tube takes place
at a very high temperature.
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
ff \( D=\left|\begin{array}{ccc}a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3}\end{array}\right| \) and \( D_{0}= \)
\( \left|\begin{array}{ccc}\boldsymbol{k} \boldsymbol{a}_{1} & \boldsymbol{k} \boldsymbol{b}_{1} & \boldsymbol{k} \boldsymbol{c}_{1} \\ \boldsymbol{k} \boldsymbol{a}_{2} & \boldsymbol{k} \boldsymbol{b}_{2} & \boldsymbol{k} \boldsymbol{c}_{2} \\ \boldsymbol{k} \boldsymbol{a}_{3} & \boldsymbol{k} \boldsymbol{b}_{3} & \boldsymbol{k} \boldsymbol{c}_{3}\end{array}\right| \) then show that
\( \boldsymbol{D}_{0}=\boldsymbol{k}^{3} \boldsymbol{D} \)
Subject: Physics
Assertion (A): Ductile metals are used
to prepare thin wires. Reason (R) : In the stress-strain curve
of ductile metals, the length between the points representing elastic limit and breaking point is very small.
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 correct explanation of (A)
c. (A) is true but (R) is false.
D. (A) is false but (R ) is true
Subject: Chemistry
Which of the following solution in water will have the lowest vapour pressure?
A. \( 0.1 M, \) NaCI
B. \( 0.1 M, \) Sucrose
с. \( 0.1 M, \)ВаС\( I_{2} \)
D. \( 0.1 M N a_{3} P O_{4} \)