AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A thin semicircular conducting ring of
radius \( \mathrm{R} \) is falling with its plane vertical
in a horizontal magnetic field B. At the
position MNQ, the speed of the ring is \( \mathbf{v} \) and the potential difference across the
ring is
A. zero
B \( \cdot \frac{1}{2} B v \pi R^{2} \) and \( \mathrm{M} \) is at higher potential
\( \mathrm{c} . \pi R B v \) and \( \mathrm{Q} \) is at higher potential
D. \( 2 R B v \) and \( Q \) is at higher potential
Subject: Chemistry
If 0.765 gm of an acid gives 0.535 gm of \( C O_{2} \) and \( 0.138 \mathrm{gm} \) of \( H_{2} O . \) Then, the ratio of the percentage of carbon and hydrogen is :
\( \mathbf{A} \cdot 19: 2 \)
B. 18: 12
c. 20: 17
D. 1: 7
Subject: Maths
Using properties of determinant, prove
the following:
\[
\mid \begin{array}{ccc}
1+a^{2}-b^{2} & 2 a b & -2 b \\
2 a b & 1-a^{2}+b^{2} & 2 a \\
2 b & -2 a & 1-a^{2}-b^{2}
\end{array}
\]
\( \left(1+a^{2}+b^{2}\right)^{3} \)
Subject: Maths
Two similar boxes \( B_{i}(i=1,2) \) contains \( (i+1) \) red and \( (5-i-1) \) black balls.
One box is chosen at random and two
balls are drawn randomly. What is the probability that both the balls are of
different colours?
A \( \cdot \frac{1}{2} \)
B. \( \frac{3}{10} \)
\( c \cdot \frac{2}{5} \)
D.
Subject: Physics
A demagnetize a small ferromagnet, a current of \( 2 A \) is required to be passed
in a solenoid of length \( 20 \mathrm{cm} \) and
number of turns 100. The coercivity of
the magnet is:
B. \( 1000 A m^{-1} \)
c. \( 1250 A m^{-1} \)
D. \( 3750 A m^{-1} \)
Subject: Maths
Consider the following data gathered from a survey of a colony:

Cricket \( \begin{array}{ll}\text { Favourate } & \text { cricket } \quad \text { Basket } \\ \text { port: }\end{array} \) sport:
1240 470 watching
Participating 620 320
Draw a double bar graph choosing an appropriate scale. What do you infer from the bar graph? Which sport is most popular?
Subject: Physics
Why is AMBULANCE written laterally
inverted on an Ambulance van?
A. It gathers more attention since it is laterally inverted.
B. Vehicle in front sees a laterally inverted image and perceives it correctly, hence giving side to the ambulance van.
C. Vehicle in front sees a virtually erect image and perceives it correctly, hence giving side to the ambulance van.
D. None of the above.
Subject: Physics
An excerpt from a book by Einstein and Infeld gives the following remarks concerning wave phenomena:
"A bit of gossip starting in Washington reaches New York [by word of mouth] very quickly, even though not a single individual who takes part in spreading it travels between these two cities.
There are two quite different motions involved, that of the rumor, Washington
to New York, and that of the persons who
spread the rumor."
Identify a correct inference from the above text.
A. The particles of the medium perform motion from one place to another
B. The particles of the medium perform random motion to constitute wave motion
c. The particles constituting the medium perform only small vibrations, but the whole motion is that of a progressive wave.
D. None of these
Subject: Physics
Needles \( N_{1}, N_{2}, N_{3} \) are made of a
ferromagnetic, a paramagnetic and a diamagnetic substance respectively. A
magnet when brought close to them will:
A. attract \( N_{1} \) and \( N_{2} \) strongly but repel \( N_{3} \)
B. attract \( N_{1} \) strongly, \( N_{2} \) weakly and repel \( N_{3} \) weakly
C. attract \( N_{1} \) strongly, but repel \( N_{2} \) and \( N_{3} \) weakly
D. attract all three of them
Subject: Physics
A solenoid has a core of a material with
relative permeability \( 400 . \) The windings of the solenoid are insulated from the
core and carry a current of \( 2 A \).f the
number of turns is 1000 per meter, calculate (a) \( \boldsymbol{H} \)
(b) \( B \) and
\( (c) \) the
magnetising current \( \boldsymbol{I}_{m} \)
Subject: Physics
Figure shows the trajectory of a projections fired at an angle \( \theta \) with the horizontal. The elevation angle of the
highest point as seen from the point of
launching is \( \varphi . \) The relation between \( \varphi \)
\( \operatorname{ans} \theta \) is
A \( \cdot \tan \phi=\frac{1}{2} \tan \theta \)
B. \( \tan ^{2} \phi=\frac{1}{2} \tan ^{2} \)
\( \mathbf{c} \cdot \sin \phi=\frac{1}{2} \sin \theta \)
D. \( \cos ^{2} \phi=\frac{1}{2} \cos ^{2} \theta \)
Subject: Physics
A copper solid cube of \( 60 \mathrm{mm} \) side is
subjected to a compressible pressure of \( 2.5 \times 10^{7} \) Pa. If the bulk modulus of
copper is \( 1.25 \times 10^{11} \) pascals, the change in the volume of cube is
A. \( -43.2 m m^{3} \)
В. \( -43.2 m^{3} \)
c. \( -43.2 \mathrm{cm}^{3} \)
D. \( -432 m m^{3} \)
Subject: Chemistry
Fill in the blanks with the correct choice.
The undesired impurities present in the
the volatile impurities from the ore, the
(ii) process is carried out. Flux combines with non-fusible impurities to form
(iii) \( C a O \) acts as a
(iv) flux.
A. (i) - gangue,
(iii) - slag, (iv) -acidic
(ii) -roasting,
(ii) - calcination, (iii) - slag, (iv) - basic
B. (i) - gangue,
c. (i) - anode mud,
(ii) - - leaching,
(iii) - matrix, (iv) -acidic
D. (i) - gangue,
(ii) -roasting, (iii) - solution, (iv) -acidic
Subject: Physics
Two long parallel wires carrying currents \( 2.5 \mathrm{A} \) and I A in the same
direction (directed Into the plane of the paper) are held \( \mathrm{M} \mathrm{P} \) and \( \mathrm{Q} \) respectively such that they are perpendicular to the
plane of the paper. The points \( P \) and \( Q \) are located at a distance of \( 5 \mathrm{m} \) and 2
\( \mathrm{m}, \) respectively, from a collinear point \( \mathrm{R} \) as shown in figure. An electron moving with a velocity of \( 4 \times 10^{5} m s^{-1} \) along
the positive \( X \) -direction experiences a
force of magnitude \( 3.2 \times 10^{-20} \mathrm{N} \) at the
point \( R \) The current lin wire Q is
\( A \cdot 1 A \)
B. 2 A
\( c \cdot 3 A \)
\( D \cdot 4 A \)
Subject: Chemistry
\( 1.5 \mathrm{g} \) of a hydrocarbon on combustion gave \( 4.4 g \) of \( C O_{2} \) and \( 2.7 g \) of \( H_{2} O . \) The vapour density of the compound is 15 Calculate the molecular formula.
A \( \cdot C_{2} H_{6} \)
в. \( C H_{4} \)
\( c \cdot O_{2} \)
D. \( N_{2} \)
Subject: Maths
In \( \triangle A B C, \) if \( a, b, c \) are in \( A . P . \) then \( \cot \frac{\boldsymbol{A}}{2} \cot \frac{\boldsymbol{C}}{2}= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D.
Subject: Physics
A mass 'm' is fixed at \( x=a \) on a
parabolic wire with its axis vertical and
vertex at the origin as shown in the
figure. The equation of parabola is \( x^{2}= \)
4ay. The wire frame is rotating with
constant angular velocity \( \omega \) about \( Y \)
axis. The acceleration of the bead is
\( A \cdot \frac{a}{4} \omega^{2} \)
B. \( a \omega^{2} \)
c. zero
\( D \)
Subject: Physics
The inductor in a \( L-C \) oscillation has
a maximum potential difference of \( 16 V \) across the inductor of \( 3 m H \) and
maximum energy of \( 160 \mu J . \) The value
of capacitor in \( L-C \) circuit is :
\( \mathbf{A} \cdot 0.8 \mu F \)
B. \( 0.625 \mu F \)
c. \( 1.6 \mu F \)
D. \( 1.25 \mu F \)
Subject: Maths
\( f(x)=\frac{3 x^{2}+a x+a+1}{x^{2}+x-2}, \) then which
of the following can be correct? This question has multiple correct options
A \( \cdot \lim _{x \rightarrow 1} f(x) \) exists \( \Rightarrow a=-2 \)
B. \( \lim _{x \rightarrow-2} f(x) \) exists \( \Rightarrow a=13 \)
C if the limit exists, lim \( f(x)=\frac{4}{3} \)
D. If the limit exists, \( \lim _{x \rightarrow-2} f(x)=-\frac{1}{3} \)
Subject: Maths
Calculate the mean deviation from the
median of the following data.
\[
\begin{array}{llll}
\begin{array}{l}
\text { Wages } \\
\text { per } \\
\text { week }
\end{array} & \begin{array}{l}
\mathbf{1 0}- \\
\mathbf{2 0}
\end{array} & \begin{array}{l}
\mathbf{2 0}- \\
\mathbf{3 0}
\end{array} & \begin{array}{l}
\mathbf{3 0}- \\
\mathbf{4 0}
\end{array} \\
\begin{array}{l}
\text { No. of } \\
\text { workers }
\end{array} & 4 & 6 & 10
\end{array}
\]
Subject: Chemistry
Density of equilibrium mixture of \( N_{2} O \)
and \( N O_{2} \) at 1 atm and 384 Kis
\( 1.84 g / d m^{3} . \) Equilibrium constant of the following reaction is:
\( N_{2} O_{4} \rightleftharpoons 2 N O_{2} \)
A. 1.98 atm
B. 2.09 atm
c. 2.36 atm
D. 1.48 atm
Subject: Physics
Use Gauss's law to show that due to a
uniformly charged spherical shell of radius \( \mathrm{R} \), the electric field at any point
situated outside the shell at a distance
r from its centre is equal to the electric field at the same point, when the entire charge on the shell were concentrated
at its centre. Also plot the graph showing the variation of electric field
with \( r, \) for \( r \leq R \) and \( r \geq R \)
Subject: Physics
A neutral conducting spherical shell is kept near a charge \( q \) as shown. The
potential at point \( P \) due to the induced
charges is :
\( A \cdot \frac{k q}{r} \)
в. \( \frac{k q}{r^{\prime} q} \)
с. \( \frac{k q}{r}-\frac{k q}{r^{\prime}} \)
D. \( \frac{k q}{C P} \)
Subject: Physics
The magnetic induction due to circular current-carrying conductor of radius \( a \)
at its centre is \( B_{c} \). The magnetic
induction on its axis at a distance \( a \)
from its centre is \( B_{a} . \) The value of \( B_{c}: \)
\( \boldsymbol{B}_{\boldsymbol{a}} \) will be :
A \( \cdot \sqrt{2}: 2 \)
B. \( 1: 2 \sqrt{2} \)
c. \( 2 \sqrt{2}: 1 \)
D. \( 2: \sqrt{2} \)
Subject: Physics
t is desired to orbit an erect image of an object, using concave mirror of a
focal length of \( 12 \mathrm{cm} \)
1. What should be the range of distance
\( p \) an object placed in front of the mirror?
2. Will the image be smaller or large then the object? Draw the ray diagram to show the formation of an image in this case?
3. Will the image be smaller or large then the object? Draw the ray diagram to show the formation of the image in this case?
4. Where will the image of the object be, fit is placed \( 24 c m \) in front of the
mirror?
Draw ray diagram for this situation also justify your answer
Subject: Maths
If \( \tan \theta \cdot \tan \phi=\sqrt{\frac{(a-b)}{(a+b)}}, \) then
\( (a-b \cos 2 \theta)(a-b \cos 2 \phi)= \)
A \( \cdot a^{2} \)
в. \( b^{2} \)
\( \mathbf{c} \cdot a^{2}+b^{2} \)
D. \( a^{2}-b^{2} \)
Subject: Physics
\( 1300 J \) of heat energy is supplied to
raise the temperature of \( 0.5 k g \) of lead
from \( 20^{\circ} \mathrm{C} \) to \( 40^{\circ} \mathrm{C} \). Calculate the
specific heat capacity of lead
A \( \cdot 130 J k g^{-1} K^{-1} \)
B . \( 260 J k g^{-1} K^{-1} \)
c. \( 650 J k g^{-1} K^{-1} \)
D. None of the above
Subject: Physics
Two sound waves, each of amplitude \( \boldsymbol{A} \)
and frequency \( \omega, \) superpose at a point with a phase difference of \( \frac{\pi}{2} \) The amplitude and the frequency of the
resultant wave are, respectively
A \( \cdot A^{2}, \omega \)
B. \( 2 A, \omega \)
c. \( A, \omega \)
D. \( \sqrt{2} A, \omega \)
Subject: Physics
A prism is made of glass of unknown refractive index. A parallel beam of light is incident on a face of the prism. The angle of minimum deviation is
measured to be \( 40^{\circ} . \) What is the
refractive index of the material of the
prism? The refracting angle of the prism
is \( 60^{\circ} . \) If the prism is placed in water (refractive index 1.33 ), predict the new angle of minimum deviation of a parallel beam of light.
Subject: Physics
The simple harmonic motion of a particle is given by \( \boldsymbol{x}=\boldsymbol{a} \sin 2 \boldsymbol{\pi} \boldsymbol{t} . \) Then
the location of the particle from its
mean position at a time \( 1 / 8 \) th of a second is:
\( \mathbf{A} \cdot \boldsymbol{a} \)
B. \( \frac{a}{2} \)
c. \( \frac{a}{\sqrt{2}} \)
D. \( \frac{a}{4} \)
E \( \cdot \frac{a}{8} \)
Subject: Physics
A transmitter transmits at a wave
length of 300 meters. A capacitor of a
capacitance \( 9.6 \mu \mathrm{F} \) is being used. The value of the inductance for the resonant
circuit is approximately
A . 2.5 \( \mathrm{mH} \)
в. 2.5 \( \mu \) Н
c. 2.5 n
D. 2.5 ph
Subject: Maths
Sequences and Their limits. An
infinitely Decreasing Geometric Progression. limits of Functions. The sum of the terms of an infinitely decreasing geometric progression is equal to the greatest value of the function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+\boldsymbol{3} \boldsymbol{x}-\boldsymbol{9} \) on the
interval [-2,3]\( ; \) the difference between the first and the second terms of the
progression is \( \boldsymbol{f}^{\prime}(\mathbf{0}) . \) Find the common
ratio of the progression.
Subject: Physics
A ball of mass 'm' moving horizontally
which velocity 'u' hits a wedge of mass
\( M^{\prime} . \) The wedge is situated on a smooth
horizontal source. If after striking with wedge the ball starts moving in vertica
direction and the wedge starts moving
in horizontal plane. Calculated
a) The velocity of wedge \( V \)
b) The velocity (v) at which the ball
moves in vertical direction.
c) The impulse imparted by the ball on
the wedge.
d) The coefficient of restitution \( e=? \)
Subject: Chemistry
A gas absorbs a photon of \( 355 n m \) and
emits two wavelengths. If one of the emission is at \( 680 n m \), the other is at:
\( \mathbf{A} .518 n m \)
в. \( 1035 n m \)
c. \( 325 n m \)
D. \( 743 n m \)
Subject: Physics
The angle of incidence at which
reflected light is totally polarized for
reflection from air to glass (refractive
index \( n \) ), is:
\( A \cdot \sin ^{-1} \)
B. \( \sin ^{-1}(1 / \mathrm{n}) \)
\( c \cdot \tan ^{-1}(1 / \mathrm{n}) \)
D. \( \tan ^{-1}(n) \)
Subject: Maths
Class
\( 0- \)
\( \begin{array}{llll}0- & 20- & 40- & 60 \\ 20 & 40 & 60 & 80\end{array} \)
Frequency
\( f_{1} \)
32
\( f_{2} \)
Mean of the above frequency table is
given as \( 50 . \) Find \( f_{1} \) and \( f_{2} \)
A. 28 and 22
B. 25 and 25
c. 24 and 26
D. 20 and 30
Subject: Chemistry
The methods for extracting metals from
their ores are:
1. roasting a metal sulphide
2. chemical reduction of a metal oxide
3. electrolysis,
The preferred method depends on \( \boldsymbol{E}^{\circ} \)
value for the reducing half-reaction:
\( M^{n+}(a q)+n e^{-} \rightarrow M(s) \)
Which method is preferred for the
metals with the most positive \( \boldsymbol{E}^{\circ} \)
values?
Subject: Maths
A man earns \( x \% \) on the first Rs. 2,000
and \( y \% \) on the rest of his income. If he
earns Rs.700 from Rs. 4,000 and Rs. 900
from Rs. 5,000 of income, find \( x \% \)
A . 20 \%
B . 15 \%
c. 25 \%
D. None of these
Subject: Maths
Solve the differential equation \( \left(1-x^{2}\right) \frac{d y}{d x}+x y=a \)
A \( .-y=-a x+c \sqrt{\left(1-x^{2}\right)} \)
В . \( y=-a x+c \sqrt{\left(1-x^{2}\right)} \)
C. \( -y=a x+c \sqrt{\left(1-x^{2}\right)} \)
D. None of these
Subject: Chemistry
Select the correct I.U.P.A.C. name for
\( \left[\left(\mathrm{NH}_{3}\right)_{4} \mathrm{CoNH}_{2} \mathrm{NO}_{2} \mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\right]\left(\mathrm{NO}_{3}\right)_{4} \)
This question has multiple correct options
A. Tetraamminecobalt (III)- \( \mu \) -amido- \( \mu \) -nitrito-n
tetraamminecoball (III) nitrate
B. \( \mu \) -Amido- \( \mu \) -nitrito- N-octaamminedicobalt (III)
nitrate
C \( . \mu \) - Amido- \( \mu \) -nitrito - N-bis(tetraammine)dicobalt
(III) nitrate
D. \( \mu \) -Amido- \( \mu \) -nitrito-O-octaamminedicobaltate (III)
nitrate
Subject: Physics
Statement 1: In simple harmonic motion, the motion is to and fro and
periodic.

Statement 2: Velocity of the particle
\( (v)=\omega \sqrt{k^{2}-x^{2}} \) (where \( x \) is the
displacement).
A. Statement 1 is false, Statement 2 is true
B. Statement 1 is true, Statement 2 is true; Statement 2 is the correct explanation for Statement 1
c. statement 1 is true, Statement 2 is true; Statement 2 is not the correct explanation for Statement
D. Statement 1 is true, Statement 2 is false
Subject: Chemistry
If the density of a certain gas at \( 30^{\circ} \mathrm{C} \)
and 768 torr is \( 1.35 k g / m^{3}, \) the density at STP would be:
A. \( 1.48 \mathrm{kg} / \mathrm{m}^{3} \)
в. 1.58 kg \( / m^{3} \)
c. \( 1.25 \mathrm{kg} / \mathrm{m}^{3} \)
D. \( 1.4 \mathrm{kg} / \mathrm{m}^{3} \)
Subject: Physics
A parallel-plate air capacitor of
capacitance \( C_{0} \) is connected to a cell of emf \( V \) and then disconnected from it. \( A \)
dielectric constant \( K, \) which canjust fill the air gap of capacitor, is now inserted in it. Which of the following is incorrect?
A. The potential difference between the plates decreases \( K \) times
B. The energy stored in the capacitor decreases \( K \) times.
C ' the change in energy is \( \frac{1}{2} C_{0} \varepsilon^{2}(K-1) \)
D. The change in energy is \( \frac{1}{2} C_{0} \varepsilon^{2}\left(1-\frac{1}{k}\right) \)
Subject: Chemistry
An aqueous solution contains 0.53 g of
anhydrous \( N a_{2} C O_{3}(\text { Mol. wt. } 106) \) dissolved in \( 100 \mathrm{ml} \) of solution. The
molarity of the solution is:
\( \mathbf{A} \cdot 0.1 M \)
в. \( 0.05 M \)
\( \mathbf{c} \cdot 0.2 M \)
D. \( 0.4 M \)
Subject: Maths
\( \boldsymbol{A}(\mathbf{1}, \mathbf{2}, \mathbf{5}), \boldsymbol{B}(\mathbf{5}, \mathbf{7}, \mathbf{9}) \) and \( \boldsymbol{C}(\mathbf{3}, \mathbf{2},-\mathbf{1}) \) are
given three points \( A \) unit Vector normal
to the plane of the triangle \( A B C \)
A \( \cdot \frac{15 \bar{i}+16 \bar{j}-5 \bar{k}}{\sqrt{506}} \)
B. \( \frac{-15 \bar{i}+16 \bar{j}-5 \bar{k}}{\sqrt{506}} \)
c. \( \frac{-15 \bar{i}+16 \bar{j}+5 \bar{k}}{\sqrt{506}} \)
D. \( \frac{\bar{i}+\bar{j}+\bar{k}}{\sqrt{506}} \)
Subject: Chemistry
Assertion
For drying \( \boldsymbol{H}_{2} \mathrm{H} 2, \) Conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
H2SO4 cannot be used.
Reason
Conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) H2 on
absorbing H20H20 form moist \( \boldsymbol{H}_{2} \) H2 along with large amount of heat
which burn \( \boldsymbol{H}_{2} \) H2
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
Using properties of determinants, prove
\[
\operatorname{that}\left[\begin{array}{ccc}
\boldsymbol{b}+\boldsymbol{c} & \boldsymbol{q}+\boldsymbol{r} & \boldsymbol{y}+\boldsymbol{z} \\
\boldsymbol{c}+\boldsymbol{a} & \boldsymbol{r}+\boldsymbol{p} & \boldsymbol{z}+\boldsymbol{x} \\
\boldsymbol{a}+\boldsymbol{b} & \boldsymbol{p}+\boldsymbol{q} & \boldsymbol{x}+\boldsymbol{y}
\end{array}\right]=
\]
\( \mathbf{2}\left[\begin{array}{lll}\boldsymbol{a} & \boldsymbol{p} & \boldsymbol{x} \\ \boldsymbol{b} & \boldsymbol{q} & \boldsymbol{y} \\ \boldsymbol{c} & \boldsymbol{r} & \boldsymbol{z}\end{array}\right] \)
Subject: Maths
\( \mathbf{f}\left[\begin{array}{cc}\boldsymbol{x}+\mathbf{3} & \mathbf{4} \\ \boldsymbol{y}-\mathbf{4} & \boldsymbol{x}+\boldsymbol{y}\end{array}\right]=\left[\begin{array}{ll}\mathbf{5} & \mathbf{4} \\ \mathbf{3} & \mathbf{9}\end{array}\right], \) find \( \boldsymbol{x} \) and
\( \boldsymbol{y} \)
Subject: Physics
Two objects \( A \) and \( B \) are moving towards
each other with velocities \( 10 \mathrm{m} / \mathrm{s} \) and
12 \( \mathrm{m} / \mathrm{s} \) respectively as shown. Find the velocity of A with respect to B.
\( \mathbf{A} \)
A. \( 22 \mathrm{m} / \mathrm{s} \)
в. \( -22 \mathrm{m} / \mathrm{s} \)
c. \( 12 m / s \)
D. \( 40 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
For the following reaction
\( \left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{3} \boldsymbol{C C l}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \)
\( \left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{3} \boldsymbol{C O H}+\boldsymbol{H} \boldsymbol{C l}\left(\frac{d \boldsymbol{x}}{d t}\right)= \)
\( \boldsymbol{k}\left[\left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{3} \boldsymbol{C C l}\right] \)
the rate determining step is:
A \( \cdot\left(C H_{3}\right)_{3} C C l \rightarrow\left(C H_{3}\right)_{3} C \oplus+C l \)
B . \( \left(C H_{3}\right)_{3} C C l+H_{2} O \rightarrow\left(C H_{3}\right)_{3} C O H+H C l \)
C. \( \left(C H_{3}\right)_{3} C \oplus+H_{2} O \rightarrow\left(C H_{3}\right)_{3} C O H+H^{+} \)
D. \( H^{+}+C l^{-} \rightarrow H C l \)
Subject: Chemistry
For a first order reaction rate constant
is \( 1 \times 10^{-5} \sec ^{-1} \) having \( E_{a}= \)
\( 1800 k J / \) mol. Then the value of \( \ell n A \) at
\( \boldsymbol{T}=\mathbf{6 0 0} \boldsymbol{K} \) is:
A . 151.7
в. 349.3
c. 24.7
D. 11.34
Subject: Chemistry
In a reaction carried out at \( 400 \mathrm{K} \)
\( 0.0001 \% \) of the total number of
collisions are effective. The energy of
activation of the reaction is:
A . zero
B. 7.37 k cal/mol
c. \( 9.212 \mathrm{k} \) cal/mol
D. 11.05 k cal/mol
Subject: Chemistry
In which one of the following equilibria,
\( \boldsymbol{K}_{\boldsymbol{p}} \neq \boldsymbol{K}_{c} ? \)
A \( \cdot N O_{2}(g)+S O_{2}(g) \rightleftharpoons N O(g)+S O_{3}(g) \)
B . \( 2 H I(g) \rightleftharpoons H_{2}(g)+I_{2}(g) \)
c. \( 2 N O(g) \rightleftharpoons N_{2}(g)+O_{2}(g) \)
D \( \cdot 2 C(s)+O_{2}(g) \rightleftharpoons 2 C O(g) \)
Subject: Chemistry
Which among the following is not a disproportionation reaction i?
A \( \cdot 3 H_{3} P O_{3} \rightarrow 2 H_{3} P O_{2}+P H_{3} \)
c. \( 4 P+3 N a O H+3 H_{2} O \rightarrow P H_{3}+3 N a H_{2} P O_{2} \)
D. \( N H_{4} N O_{3} \rightarrow N_{2} O+2 H_{2} O \)
Subject: Physics
Assertion
There is no dispersion of light refracted through a rectangular glass slab.
Reason
Dispersion of light is the phenomenon of splitting of a beam of white light into
its constituent colours.
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: Maths
If \( 0.4 \hat{i}+0.7 \widehat{j}+c \hat{k} \) is a unit vector, then
the value of \( c \) is:
A \( \cdot \sqrt{0.67} \)
the 0.66
B. \( \sqrt{0.12} \)
c. \( \sqrt{1.44} \)
D. \( \sqrt{0.35} \)
Subject: Maths
If \( \boldsymbol{A}=\left\{\boldsymbol{x} \in \boldsymbol{R}: \boldsymbol{x}^{2}+\boldsymbol{6} \boldsymbol{x}-\boldsymbol{7}<\mathbf{0}\right\} \) and
\( \boldsymbol{B}=\left\{\boldsymbol{x} \in \boldsymbol{R}: \boldsymbol{x}^{2}+\boldsymbol{9} \boldsymbol{x}+\mathbf{1 4}<\mathbf{0}\right\}, \) then
which of the following is/are correct?
1. \( (\boldsymbol{A} \cap \boldsymbol{B})=(-\mathbf{2}, \mathbf{1}) \)
2. \( (\boldsymbol{A} \backslash \boldsymbol{B})=(-\mathbf{7},-\mathbf{2}) \)
Select the correct answer using the code given below:
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2
Subject: Chemistry
Which of the following arrangments does not represent the correct order of
the property stated against it?
(1) \( V^{2+}<C r^{2+}<M n^{2}<F e^{2+} \)
paramagnetic behaviour
(2) \( N i^{2+}<C o^{2+}<F e^{2+}<M n^{2+} \)
ionic size
(3) \( C o^{3+}<F e^{3+}<C r^{3+}<S c^{3+} \)
stability in aqueous solution
(4) \( S c<T i<C r<M n: \) number of
oxidation states
Subject: Physics
The length of potentiometer wire is \( 10 \mathrm{m} \) and is connected in series with an
accumulator. The e.m.f. of a cell balances against \( 250 \mathrm{cm} \) length of wire. If the length of potentiometer wire is increased by \( 1 \mathrm{m} \), calculate the new balancing length of wire.
Subject: Maths
\( \boldsymbol{P}(\boldsymbol{A})=\mathbf{3} / \mathbf{8} ; \boldsymbol{P}(\boldsymbol{B})=\mathbf{1} / \mathbf{2} ; \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})= \)
\( \mathbf{5} / \mathbf{8}, \) which of the following do/does hold
good? This question has multiple correct options
A \( \cdot P\left(A^{C} / B\right)=2 P\left(A / B^{C}\right) \)
B . \( P(B)=P\left(A^{C} / B\right) \)
C \( \cdot 15 P\left(A^{C} / B^{C}\right)=8 P\left(B / A^{C}\right) \)
D \( \cdot P\left(A / B^{C}\right)=(A \cap B) \)
Subject: Chemistry
The temperature at which the \( \boldsymbol{R} \boldsymbol{M} \boldsymbol{S} \)
velocity of \( C O_{2} \) is equal to the RMS
velocity of \( N_{2} O \) at \( 27^{\circ} C \) is:
\( \mathbf{A} \cdot 0^{\circ} C \)
В. \( 27^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot 273^{\circ} \mathrm{C} \)
D. \( -273^{\circ} \mathrm{C} \)