AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
An electric kettle has two coils when
one of these is switched on the water in
the kettle boils in 6 min. When the
other coil is switched on, the water boils
in 3 min. If the two coils are connected
in series, the time taken to boil the
water in the kettle is
\( \mathbf{A} \cdot 3 \min \)
B. 6 min
c. 2 min
D. 9 min
Subject: Physics
Assertion
In the falling object example, if you include the effect of air resistance
during the fall and see the situation after the object hits the ground and stays there, the total mechanical energy
is not conserved.
Reason
The general law of energy conservation, however, is still applicable but the total mechanical energy is not conserved
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 \( 0 \leq x \leq \pi \) and \( 81^{\sin ^{2} x}+81^{\cos ^{2} x}=30 \)
then \( x \) is equal to:
A \( \cdot \frac{\pi}{6} \)
в. \( \frac{\pi}{2} \)
c.
D. \( \frac{3 \pi}{4} \)
Subject: Chemistry
In the equation, \( 4 M+8 C N^{-}+ \)
\( \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{O}_{2} \rightarrow \boldsymbol{4}\left[\boldsymbol{M}(\boldsymbol{C} \boldsymbol{N})_{2}\right]^{-}+\mathbf{4} \boldsymbol{O} \boldsymbol{H}^{-} \)
Identify the metal \( \mathrm{M} \)
A. copper
B. Iron
c. Gold
D. zinc
Subject: Physics
A cell of e.m.f. \( \mathrm{E} \) and internal resistance
is connected in series with an external
resistance nr then the ratio of the
terminal potential difference to E.M.F. is
A \( \cdot 1 / n \)
B. \( 1 / n+1 \)
\( c \cdot n / n+1 \)
D. \( n+1 / n \)
Subject: Physics
Two gases A\&B having same pressure \( P \)
volume \( V \) and absolute temperature T are
mixed. If the mixture has volume and
temperature as \( \vee \& \) T respectively then
the pressure of mixture is
\( A \cdot 2 P \)
B.
\( c \cdot P / 2 \)
D. \( 4 P \)
Subject: Physics
We want a mirror that will make an
object look larger. What combination of image and object distances (from the
mirror) will accomplish this?
A. Image Distance \( 3.0 \mathrm{cm} \), Object Distance \( 3.0 \mathrm{cm} \)
B. Image Distance \( 2.0 \mathrm{cm} \), Object Distance \( 3.0 \mathrm{cm} \)
C. Image Distance \( 3.0 \mathrm{cm} \), Object Distance \( 5.0 \mathrm{cm} \)
D. Image Distance \( 3.0 \mathrm{cm} \), Object Distance \( 2.0 \mathrm{cm} \)
E. Image Distance \( 3.0 \mathrm{cm}, \) Object Distance \( 10.0 \mathrm{cm} \)
Subject: Maths
The differential equation of all nonhorizontal lines in a plane is
A \( \cdot \frac{d^{2} y}{d x^{2}}=0 \)
B. \( \frac{d^{2} x}{d y^{2}}=0 \)
c. \( \frac{d y}{d x}=0 \)
D. \( \frac{d x}{d y}=0 \)
Subject: Physics
Assertion
In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.
Reason
In an elastic collision, the linear momentum of the system is conserved.
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
\( A \) is a set containing \( n \) elements. Two subsets \( P \) and \( Q \) of \( A \) are chosen at
random. (P and Q may have elements in
common). The probability that \( \boldsymbol{P} \cup \boldsymbol{Q} \neq \)
\( A \) is
A \( \cdot(3 / 4)^{n} \)
B. 1/4n
c. \( ^{n} C_{2} / 2^{n} \)
D. \( 1-(3 / 4)^{n} \)
Subject: Physics
A solid sphere of mass \( m \) and radius \( R \) is placed on a plank of equal mass,
which lies on a smooth horizontal
surface. The sphere is given a sharp impulse in the horizontal direction so
that it starts sliding with a speed of \( v_{0} \)
Find the time taken by the sphere to
start pure rolling on the plank. The coefficient of friction between plank
and sphere is \( \mu \)
Subject: Maths
Differential equation having
\( \mathbf{y}=\left(\sin ^{-1} \mathbf{x}\right)^{2}+\mathbf{A}\left(\cos ^{-1} \mathbf{x}\right)+\mathbf{B} \) where
A, B are arbitrary constants as general solution is
A \( \cdot\left(1-x^{2}\right) y_{2}-x y_{1}=2 \)
B \( \cdot\left(1-x^{2}\right) y_{2}-x y_{1}=1 \)
c. \( (1-x) y_{2}-x y_{1}=2 \)
D. \( \left(1-\mathrm{x}^{2}\right) \mathrm{y}_{2}-\mathrm{xy}_{1}=4 \)
Subject: Physics
A charge \( +q \) is fixed to each of three
corners of a square. On the empty corner a charge \( Q \) is placed such that there is no
net electrostatic force acting on the
diagonally opposite charge. Then:
A. \( Q=-2 q \)
в. \( Q=-2 \sqrt{2} q \)
c. \( Q=-\sqrt{2} q \)
D. \( Q=-4 q \)
Subject: Maths
Let \( [x] \) be the greatest integar function. Then the equation \( \sin x=[1+\sin x]+[1- \)
\( \cos x] \) has
A . one solution in \( \left[\frac{-\pi}{2}, \frac{\pi}{2}\right] \)
B. one solution in \( \left[\frac{\pi}{2}, \pi\right] \)
c. one solution in R
D. no solution in R
Subject: Physics
Assertion
Diffraction takes place for all types of
waves mechanical or non-mechanical,
transverse or longitudinal.
Reason
Diffraction's effect are perceptible only if wavelength of wave is comparable to dimensions of diffracting device.
A. Both Assertion are not correct and Reason is the correct
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect;Reason is not correct explanation for Assertion
D. Both Assertion is correct and Reason are incorrect
Subject: Physics
An electric dipole of length \( 20 \mathrm{cm} \) having \( \pm 3 \times 10^{-3} C \) charge placed at \( 60^{\circ} \) with
respect to a uniform electric field
experiences a torque of magnitude \( 6 N m . \) The potential energy of the dipole
is
A. \( -2 \sqrt{3} J \)
\( J \)
B. \( 5 \sqrt{3} J \)
c. \( -2 \sqrt{2} J \)
D. \( 3 \sqrt{5} \)
Subject: Chemistry
Match the chemicals in column I with
their uses on column II:
Column I
(A) Sodium perborate
(I) Disinfectant
(B) Chlorine
(II) Antiseptic
(C) Bithional
(III) Milk bleaching agent
(D) Potassium sterate
(IV) Soap
B. A=II, B=|II, C=IV, D=1
C \( . A=\| I, B=I, C=11, D=I V \)
D. A=IV, B=I, C=II, D=III
Subject: Maths
If three events \( A, B, C \) are mutually
exclusive, then which one of the
following is correct?
A \( \cdot P(A \cup B \cup C)=0 \)
B . \( P(A \cup B \cup C)=1 \)
c. \( P(A \cap B \cap C)=0 \)
D \cdot \( P(A \cap B \cap C)=1 \)
Subject: Chemistry
Considering only lattice enthalpy, arrange them in the increasing order of their stability:
Na \( C l, M g C l_{2}, M g O \)
A. \( N a C l, M g O, M g C l_{2} \)
в. маСl, М \( g \) Са\( _{2}, \) М \( g \) О
c. \( M g C l, M g O, M g C l_{2} \)
D. none of these
Subject: Chemistry
Zinc reacts with dil. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) to give \( \boldsymbol{H}_{2} \)
It also reacts with conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) to give
\( \boldsymbol{S} \boldsymbol{O}_{2} \)
If true enter 1 , else enter 0
Subject: Physics
Anushka noted down the following observations in her practical book.
i. Weight of the metal block in air \( =260 \)
\( \boldsymbol{g}-\boldsymbol{w} \boldsymbol{t} \)
i \( i . \) Weight of the metal block in water \( = \) \( 220 g-w t \)
iii. Weight of the metal block in salt
water \( =180 g-w t \)
Find the relative density of the salty
water
Subject: Physics
If a long straight wire carries a current
of \( 40 \mathrm{A} \), then the magnitude of the field B at a point \( 15 \mathrm{cm} \) away from the wire is:
A \( \cdot 5.34 \times 10^{5} \mathrm{T} \)
B. \( 8.34 \times 10^{5} \mathrm{T} \)
c. \( 9.6 \times 10^{5} \mathrm{T} \)
D . 10.2 \( \times 10^{5} \) न
Subject: Maths
The area of the triangle whose vertices \( \operatorname{are} A(1,2,3), B(2,-1,1) \) and
\( \boldsymbol{C}(\mathbf{1}, \mathbf{2},-\mathbf{4}) \) is
A . \( 7 \sqrt{10} \) sq units
B. \( \frac{1}{2} \sqrt{10} \) sq units
c. \( \frac{7}{2} \sqrt{10} \) sq units
D. None of these
Subject: Maths
\( \mathbf{f} \boldsymbol{p}(\boldsymbol{x})=\boldsymbol{a} \boldsymbol{x}^{3}+\boldsymbol{3} \boldsymbol{x}-\mathbf{1} \boldsymbol{3} \) and \( \boldsymbol{q}(\boldsymbol{x})= \)
\( 2 x^{3}-5 x+1 \) are divided by \( x+2 \)
remainder is same in each case. find
the value of \( a \)
Subject: Biology
Assertion
Nitrogen-fixing enzyme in legume root nodules function at low oxygen
concentration.
Reason
Low oxygen concentration is provided by leghaemoglobin.
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 point starts from rest and moves
along a circular path of radius \( 20 \mathrm{cm} \) with a constant tangential acceleration
of \( 5 \mathrm{cm} / \mathrm{s}^{2} . \) The time needed for the
centripal acceleration of the point to be equal to its tangential acceleration is:
A . \( 0.2 s \)
в. \( 0.5 s \)
\( c \cdot 1 s \)
D. 2 s
Subject: Biology
Experiments were carried out to
investigate the effect of different \( \boldsymbol{p} \boldsymbol{H} \)
values on enzyme activities. (Time and temperature was kept constant)
(a) What interpretation can you draw from the graph?
(b) What happens to the pepsin reaction between \( p H 4 \) and \( 5 ? \) Why?
Observe the given graph and answer:
Subject: Maths
Given two mutually exclusive events \( \boldsymbol{A} \) and \( B \) such that \( P(A)=\frac{1}{2} \) and \( P(B)=\frac{1}{3}, \) find \( P(A \text { or } B) \)
A \( \cdot \frac{3}{5} \)
в. \( \frac{5}{6} \)
\( c \cdot \frac{4}{5} \)
D. None of these
Subject: Maths
Evaluate: \( \int \frac{x^{4}+1}{1+x^{6}} d x \)
A \( \cdot \tan ^{-1}(x)-\tan ^{-1}\left(x^{3}\right)+c \)
B \cdot \( \tan ^{-1}(x)-\frac{1}{3} \tan ^{-1}\left(x^{3}\right)+c \)
c. \( \tan ^{-1}(x)+\tan ^{-1}\left(x^{3}\right)+c \)
D. \( \tan ^{-1}(x)+\frac{1}{3} \tan ^{-1}\left(x^{3}\right)+c \)
Subject: Chemistry
\( 5 g \) of zinc is treated separately with an excess of
(a) dilute hydrochloric acid and
(b) aqueous sodium hydroxide.
The ratio of the volumes of \( \boldsymbol{H}_{2} \) evolved
in these two reactions is :
A . 1: 1
B . 2: 1
\( c \cdot 1: 4 \)
D. 1: 2
Subject: Maths
Let \( f(x)=x \) and \( g(x)=|x| \) for all \( x \in R \)
The function \( \phi(x) \) given that \( \phi(x) \geq 0 \)
satisfying \( (\phi(x) f(x))^{2}+ \)
\( (\phi(x) g(x))^{2}=x^{4} \) is.
This question has multiple correct options
A \( . \phi(x)=x, x \in[0, \infty) \)
B. \( \phi(x)=x, x \in R \)
c. \( \phi(x)=-x, x \in(-\infty, 0] \)
D. \( \phi(x)=x+|x|, x \in R \)
Subject: Physics
All resistance are connected in the
series. The current is flowing through
circuit is \( 2 A \) and battery is of 20 Volts. What is the power dissipated through one of the \( 4 \Omega \) :
\( A \cdot 4 w \)
B. 8 w
\( c \cdot 16 w \)
D. 32 \( w \)
E. 36
Subject: Chemistry
\( N H_{4} C I(s) \) is heated in a test tube,
vapours are brought in contact with red litmus paper, which changes to blue
and then to red. it is because of :
A . formation of \( N H_{4} O H \) and \( H C I \)
B. formation of \( N H_{3} \) and \( H C I \)
c. greater diffusion of \( N H_{3} \) than \( H C I \)
D. grater diffusion of \( H C I \) than \( N H_{3} \)
Subject: Physics
Three resistors \( (2,5 \text { and } 7 \text { ohm }) \) are
wires as shown in the diagram
below. The equivalent resistance of this
combination (in ohm) is:
A \( \cdot \frac{59}{70} \)
B. \( \frac{70}{59} \)
\( c \cdot \frac{1}{14} \)
D. 14
E. Cannot be determined without additional information
Subject: Physics
Choose the INCORRECT options:-
This question has multiple correct options
A. If relative velocity of one object with respect to other is towards the line joining them, then they must collide.
B. If relative velocity of one object with respect to other is towards the line joining them, then they may collide.
C . A particle staring from rest under the action of constant acceleration must follow a straight line trajectory
D. Motion under constant magnitude acceleration can never result in a closed path trajectory with some area enclosed.
Subject: Chemistry
The correct statement about the
following disaccharide is:
\( (\mathbf{i}) \)
il
A. ring (i) is pyranose with \( \alpha- \) glycosidic link
B. ring (i) is furanose with \( \alpha- \) glycosidic link
C . ring
(ii) is furanose with \( \alpha- \) glycosidic link
D. ring
(ii) is pyranose with \( \beta- \) glycosidic link
Subject: Maths
PQRS is a parallelogram whose diagonals intersect at \( \mathrm{M} \)
If \( \angle P M S=54^{\circ}, \angle Q S R=25^{\circ} \) and
\( \angle \boldsymbol{S} \boldsymbol{Q} \boldsymbol{R}=\boldsymbol{3} \boldsymbol{0}^{\circ}: \) find \( \angle \boldsymbol{R} \boldsymbol{P} \boldsymbol{S} \)
A \( .86^{\circ} \)
B. \( 96^{\circ} \)
\( c \cdot 92^{\circ} \)
D. \( 100^{\circ} \)
Subject: Physics
Write a wave function describing the
wave
A. \( y=0.075 \cos (1.05 x-4 \pi t) \)
\( t \)
B. \( y=0.075 \cos (1.05 x-2 t) \)
c. \( y=0.075 \sin (1.05 x-4 \pi t) \)
D. None
Subject: Physics
Driver of a train travelling at \( 115 k m / h \) sees on a same track, \( 100 m \) infront of him, a slow train travelling in the same direction at \( 25 k m / h \). The least
retardation that must be appiled to faster train to avoid a collision is
A. \( 3.125 \mathrm{m} / \mathrm{s}^{2} \)
в. \( 3.5 m / s^{2} \)
\( \mathbf{c} \cdot 2.75 m / s^{2} \)
D. \( 3.0 m / s^{2} \)
Subject: Physics
An object is placed \( 0.40 \mathrm{m} \) from one of
the two lenses \( L_{1} \) and \( L_{2} \) of focal
lengths \( 0.20 \mathrm{m} \) and \( 0.10 \mathrm{m} \) respectively as depicted in the figure. The separation between the lenses is 0.30
"

The final image formed by this two lens
system is at
A. \( 0.13 \mathrm{m} \) to the rignt of the second lens
B . . 05 rn to the right of the second lens
c. \( 0.13 \mathrm{m} \) to the left of the second lens
D. Infinity
Subject: Chemistry
The line spectrum is noticed during the transition of an electron from higher
excited state to lower one in \( \boldsymbol{H} \) -atom
only when an electron falls from:
A . \( 2 s \) -orbital to \( 1 s \) -orbital
B. 2p-orbital to 1s-orbital
c. \( 3 s \) -orbital to \( 2 p \) -orbital
D. \( 4 p \) -orbital to \( 2 p \) -orbital
Subject: Maths
\( \left|\begin{array}{ccc}x^{2}+x & x+1 & x+2 \\ x^{2}+3 x-1 & 3 x & 3 x-3 \\ x^{2}+2 x+3 & 2 x-1 & 2 x-1\end{array}\right|= \)
\( A x+B \) where \( A \) and \( B \) are
determinants of order \( 3 . \) Then \( A+2 B \) is
equal to
Subject: Chemistry
The ionic enthalpy of hydrogen atom is \( 1.312 \times 10^{6} J \) mol \( ^{-1} . \) The energy
required to excite the electron in the
atom from \( n_{1}=1 \) to \( n_{2}=2 \) is:
A . \( 8.51 \times 10^{5} \mathrm{Jmol}^{-1} \)
B. \( 6.56 \times 10^{5} \mathrm{Jmol}^{-1} \)
c. \( 7.56 \times 10^{5} \mathrm{Jmol}^{-1} \)
D. \( 9.84 \times 10^{5} \mathrm{Jmol}^{-1} \)
Subject: Physics
A submarine that is not moving sends out a sonar sound wave travelling at \( 200 \mathrm{m} / \mathrm{s}, \) which reflects off a boat back
to the submarine. The sonar crew
detects the reflected wave 8 s after it
was send out. how far away is the boat from the submarine?
A. \( 8000 m \)
в. \( 80 m \)
c. \( 800 m \)
D. \( 9000 m \)
Subject: Maths
If \( \sqrt{\boldsymbol{y}+\boldsymbol{x}}+\sqrt{\boldsymbol{y}-\boldsymbol{x}}=\boldsymbol{c} \text { (where } \boldsymbol{c} \neq \mathbf{0}) \)
then \( \frac{d y}{d x} \) has the value equal to
This question has multiple correct options
A \( \cdot \frac{2 x}{c^{2}} \)
в. \( \frac{x}{y+\sqrt{y^{2}-x^{2}}} \)
c. \( \frac{y-\sqrt{y^{2}-x^{2}}}{x} \)
D. \( \frac{c^{2}}{2 y} \)
Subject: Maths
The area of the region bounded by the curves \( \boldsymbol{y}=\boldsymbol{x}^{2} \) and \( \boldsymbol{x}=\boldsymbol{y}^{2} \) is
A \( \cdot \frac{1}{3} \)
в. \( \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
D. 3
Subject: Physics
If \( \vec{a}+\vec{b}+\vec{c}=0,|\vec{a}|=3,|\vec{b}|=5,|\vec{c}|=7 \)
then the angle between \( \vec{a} \& \vec{b} \) is?
A \( \cdot \frac{\pi}{6} \)
в. \( \frac{2 \pi}{3} \)
\( c \cdot \frac{5 \pi}{3} \)
D.
Subject: Physics
A force \( \overrightarrow{\boldsymbol{F}}=\boldsymbol{x} \hat{\boldsymbol{i}}+\boldsymbol{2} \boldsymbol{y} \hat{\boldsymbol{j}} \) is applied on a
particle. Find out work done by \( \boldsymbol{F} \) to
move the particle from point \( \boldsymbol{A} \) to \( \boldsymbol{B} \)
A . \( -3.5 ~ J \)
в. \( -2.5 \mathrm{J} \)
c. \( -4.5 J \)
D. -45
Subject: Physics
The average translational kinetic energy of air molecules is \( 0.040 e V \)
\( \mathbf{1} e V=\mathbf{1 . 6} \times \mathbf{1 0}^{-19} \mathbf{J} \) ). Calculate the
temperature of the air. Boltzman's
constant \( k=1.38 \times 10^{-23} J K^{-1} \)
Subject: Chemistry
Which compound of oxygen is most likely to contain an \( \boldsymbol{O}-\boldsymbol{O} \) bond?
A \( \cdot C O_{2} \)
в. \( N O_{2} \)
\( c \cdot s O_{2} \)
D. \( H_{2} O_{2} \)
E \( . T i O_{2} \)
Subject: Physics
fixed resistors of resistance \( 2.0 \Omega \) and
\( 4.0 \Omega \) connected in series with a \( 3.0 \Omega \)
resistor fitted with a sliding contact.
These are connected across a battery of
e.m.f \( 9.0 \mathrm{V} \) and zero internal resistance,
as shown
What are the maximum and the
minimum output voltages of this
potential divider circuit?
A. maximum voltage/V : \( 4.0 ; \) minimum voltage \( / V: 2.0 \)
B. maximum voltage/V : 5.0 ; minimum voltage/V : 2.0
C. maximum voltage/V : \( 9.0 ; \) minimum voltage \( / V: 0 \)
D. maximum voltage/V : 9.0 ; minimum voltage/ \( V: 2.0 \)
Subject: Physics
Calculate the means free path of
nitrogen molecule at \( 27^{\circ} \mathrm{C} \) when pressure is 1.0 atm. Given, diameter of nitrogen molecule \( =1.5 \stackrel{o}{A}, k_{B}= \)
\( 1.38 \times 10^{-23} J K^{-1} . \) If the average speed
of nitrogen molecule is \( 675 m s^{-1} \). The time taken by the molecule between two successive collisions is?
A. 0.6 ns
B. \( 0.4 \mathrm{ns} \)
c. \( 0.8 \mathrm{ns} \)
D. 0.3 ns
Subject: Maths
If \( \vec{a} \) and \( \vec{b} \) are unit vectors, then angle between \( \vec{a} \) and \( \vec{b} \) for \( \sqrt{3} \vec{a}-\vec{b} \) to be unit
vector is
A \( .60^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 45 \)
D. 30
Subject: Physics
A particle executes \( \boldsymbol{S H} \boldsymbol{M} \) on a line
\( 8 c m \) long. Its \( K . E \) and \( P . E \) will be equal
when its distance from the mean
position is:
A. \( 4 \mathrm{cm} \)
B. 2 cm
\( \mathrm{c} \cdot 2 \sqrt{2} \mathrm{cm} \)
D. \( \sqrt{2} \) cm
Subject: Maths
Eccentricity of the ellipse \( 4 x^{2}+y^{2}-8 y-8=0 \) is
A \( \frac{\sqrt{3}}{2} \)
в. \( \frac{\sqrt{3}}{4} \)
\( c \cdot \frac{\sqrt{3}}{\sqrt{2}} \)
D. \( \frac{\sqrt{3}}{8} \)
E \( \cdot \frac{\sqrt{3}}{16} \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{cc}2 & 3 \\ \mathbf{5} & -2\end{array}\right] \) be such that \( \boldsymbol{A}^{-1}=\boldsymbol{k} \boldsymbol{A} \)
then find the value of \( k \)
Subject: Chemistry
Reaction by which Benzaldehyde cannot
be prepared is:
\( \mathbf{A} \)
in \( \mathrm{CS}_{2} \) followed by \( \mathrm{H}_{3} \mathrm{O}^{-} \)
\( B \)
in presence of Pd-BaSO
\( \mathbf{C} \)
presence of anhydrous AlCl
D.
and conc. HCl
Subject: Physics
Find the terminal voltage across \( \boldsymbol{E}_{1} \) and
\( \boldsymbol{E}_{2} \) in fig :
A. \( 3.6 V, 7.8 V \)
B. \( 2.4 V, 7.8 V \)
c. \( 3.6 V, 10 V \)
D. \( 2.4 V, 10.2 V \)
Subject: Physics
Three masses \( 2 \mathrm{kg}, 3 \mathrm{kg} \) and \( 4 \mathrm{kg} \) are lying at the corners of an equilateral triangle of side a. The \( x \) coordinate of
the centre of mass is :
\( ^{A} \cdot \frac{7}{12} a \)
\( B \cdot \frac{5}{2} a \)
\( \frac{7 \sqrt{2}}{9} a \)
D
Subject: Physics
A brass rod has a length of \( 0.2 m, \) area of
cross section \( 1.0 \mathrm{cm}^{2} \) and young's
modulus \( 10^{11} \mathrm{Nm}^{-2} . \) If it is compressed
by \( 5 k g \) weight along its length, then the change in its energy will be :
A. an increase of \( 2.4 \times 10^{-5} \) j
B. a decrease of \( 2.4 \times 10^{-5} \mathrm{J} \)
c. an increase of \( 2.4 \times 10^{7} \) J
D. a decrease of \( 2.4 \times 10^{7} \) j
Subject: Maths
In the given figure, \( A M \perp B C \) and \( A N \)
is the bisector of \( \angle A \). Then \( \angle M A N \) is
A \( \cdot 32 \frac{1}{2} \)
B . \( 16 \frac{1}{2} \)
\( c \cdot 16^{0} \)
\( D \cdot 32^{0} \)
Subject: Maths
If the value of the determinant
\( \left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{1} & \boldsymbol{1} \\ \boldsymbol{1} & \boldsymbol{b} & \boldsymbol{1} \\ \boldsymbol{1} & \boldsymbol{1} & \boldsymbol{c}\end{array}\right| \) is positive, then
A \( . a b c>1 \)
B . \( a b c>-8 \)
c. \( a b c<-8 \)
D. \( a b c>-2 \)
Subject: Maths
Based on equations reducible to linear equations Solve for \( x \) and \( y: \frac{16}{x+3}+\frac{3}{y-2}= \) \( \mathbf{5} ; \frac{\mathbf{8}}{\boldsymbol{x}+\mathbf{3}}-\frac{\mathbf{1}}{\boldsymbol{y}-\mathbf{2}}=\mathbf{0} \)
A. \( x=5, y=3 \)
В. \( x=7, y=2 \)
c. \( x=1, y=5 \)
D. None of these
Subject: Physics
A dielectric with a dielectric constant of
\( k \) is inserted between the plates of the
capacitor of capacitance \( C \) having
a potential difference of \( \Delta V \) between
the two plates. Calculate the energy
stored in the capacitor?
A \( \cdot \frac{1}{2}(C / k)(\Delta V)^{2} \)
B \( \cdot \frac{1}{2}(k / C)(\Delta V)^{2} \)
\( ^{\mathrm{c}} \cdot \frac{1}{2} k C(\Delta V)^{2} \)
D. \( \frac{1}{2} k C \Delta V \)
E \( \cdot \frac{1}{2}(C / k) \Delta V \)
Subject: Physics
A stone is dropped into a well of depth
\( h " . \) The splash is heard after time " \( \boldsymbol{t} " \) If " \( C " \) be the velocity of sound, then -
A \( \cdot t=\sqrt{\frac{g c}{2 h}} \)
B. \( t=c+g h \)
c. \( t=c-v \)
D. \( t=\frac{h}{c}+\sqrt{\frac{2 h}{g}} \)
Subject: Chemistry
On adding \( 0.1 M \) solution each of
\( \left[\boldsymbol{A} \boldsymbol{g}^{+}\right],\left[\boldsymbol{B} \boldsymbol{a}^{2+}\right],\left[\boldsymbol{C} \boldsymbol{a}^{2+}\right] \) in \( \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
solution, species first precipitated is:
\( \left[\boldsymbol{K}_{s p}\left(\boldsymbol{B} \boldsymbol{a} \boldsymbol{S} \boldsymbol{O}_{4}\right)=\mathbf{1 0}^{-11}, \boldsymbol{K}_{s p}\left(\boldsymbol{C a} \boldsymbol{S O}_{4}\right)=\right. \)
A \( \cdot A g_{2} S O_{4} \)
в. Ва а S О\( _{4} \)
\( c \cdot \operatorname{cas} O_{4} \)
D. All of these
Subject: Maths
n the figure \( \Delta A B C, D E \| \) \( B C, A(\Delta A D E)=48 \) sq.cm., \( \frac{A D}{D B}=\frac{4}{5} \)
Find the area of \( \Delta B E C \)
A . 60 sq.cm
B. 95 sq.cm
c. 108 sq.cm
D. 135 sa.cm
Subject: Chemistry
The molecular weight of an organic compound is 58.0 g/mol. Compute the boiling point of a solution containing \( 24.0 \mathrm{g} \) of the solute and \( 600 \mathrm{g} \) of water when the barometric pressure is such that pure water boils at
\( 99.725^{\circ} \mathrm{C} .\left(K_{6} \text { forwater } 0.513^{\circ} \mathrm{C} / \mathrm{m}\right) \)
\( \mathbf{A} \cdot 50^{\circ} C \)
B . \( 100.08^{\circ} \mathrm{C} \)
\( c \cdot 150.1^{\circ} C \)
D. \( 180.34^{\circ} \mathrm{C} \)
Subject: Maths
The contents of 100 match boxes were
checked to determine the number of
matches they contained.
No. of \( \quad 35 \quad 36 \)
37
matches
No. of match
\( \begin{array}{ll}\text { 12 } & \text { 15 }\end{array} \)
boxes
Calculate the mean number of matches
per box
A . 38
B. 42
c. 67
D. 51
Subject: Chemistry
How many atoms are contained in a
mole of acetic acid?
A \( \cdot 8 \times 6.02 \times 10^{23} \) atom \( \mathrm{mol}^{-1} \)
B . \( 4 \times 6.02 \times 10^{23} \) atom \( \mathrm{mol}^{-1} \)
C. \( 6 \times 6.02 \times 10^{23} \) atom \( \mathrm{mol}^{-1} \)
D. None of the above
Subject: Chemistry
For the reaction, \( 2 N O+C l_{2} \longrightarrow \)
\( 2 N O C l, \) the following mechanism has
been proposed:
\( N O+C l_{2} \rightleftharpoons N O C l_{2} \)
\( N O C l_{2}+N O \longrightarrow 2 N O C l \)
(slow)
The rate law for the reaction is:
A \( \cdot \) Rate \( =k[N O]^{2}\left[C l_{2}\right] \)
B・Rate \( =k[N O]\left[C l_{2}\right]^{2} \)
c. Rate \( =k\left[N O C l_{2}\right] \)
D・Rate \( =k[N O C l]^{2} \)