AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
A solution of sucrose (molar mass \( =342 \)
\( \left.g m o l^{-1}\right) \) has been prepared by dissolving 68.5 g of sucrose in 1000 g of water. The freezing point of the solution obtained will be:
\( \left[\mathrm{K}_{f} \text { for water }=1.86 \mathrm{K} \mathrm{kg} \mathrm{mol}^{-1}\right] \)
A . - \( 0.372 \mathrm{c} \)
B. 0.520C
c. \( +0.372 c \)
D. 0.570C
Subject: Physics
Two charges are at a distance \( d \) apart. If
\( \boldsymbol{d} \)
a copper plate of thickness \( \frac{u}{2} \) is kept
between them, the effective force will be
A. \( F / 2 \)
B. zero
\( c \cdot 2 F \)
D. \( \sqrt{2} F \)
Subject: Maths
\( \lim _{n \rightarrow \infty} \frac{\left(1^{2}+2^{2}+3^{2}+\ldots+n^{2}\right)\left(1^{3}+2^{3}+\right.}{\left(1^{6}+2^{6}+3^{6}+\ldots+n^{6}\right)} \)
\( ? \)
A \( \cdot \frac{1}{6} \)
B. \( \frac{1}{12} \)
c. \( \frac{7}{12} \)
D. \( \frac{1}{7} \)
Subject: Physics
Six point charges are kept at the
vertices of a regular hexagon of side \( \boldsymbol{L} \)
and centre \( O \), as shown in the figure. Given that \( K=\frac{1}{4 \pi \epsilon_{0}} \frac{q}{L^{2}}, \) which of the following statement(s) is(are) correct?
This question has multiple correct options
A. The electric field at \( O \) is \( 6 K \) along \( O D \)
B. The potential at \( O \) is zero
c. The potential at all points on the line \( P R \) is same
D. The potential at all points on the line \( S T \) is same
Subject: Chemistry
\( (\boldsymbol{x}) \boldsymbol{C} \boldsymbol{H}_{3}-\underset{\prod_{0}^{M}-\boldsymbol{S}}{\|} \boldsymbol{O}-\boldsymbol{H} \)
\( (\boldsymbol{y}) \boldsymbol{C H}_{3}- \)
14 \( \begin{array}{ll}0 \\ \stackrel{1}{C}-O-H & (z) C H_{3}-O H\end{array} \)
Set the following in increasing order of
their \( p K_{a} \) values.
A. \( y<x<z \)
в. \( x<y<z \)
\( \mathbf{c} \cdot y<z<x \)
D. \( x<z<y \)
Subject: Maths
Evaluate:
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left\{\tan ^{-1} \frac{\boldsymbol{x}}{\mathbf{1}+\boldsymbol{x}^{2}}+\tan ^{-1} \frac{\mathbf{1}+\boldsymbol{x}^{2}}{\boldsymbol{x}}\right\} \)
\( A \)
в.
\( c \cdot \frac{1}{2} \)
\( D \)
Subject: Physics
A proton and an \( \alpha \) -particle, accelerated through the same potential difference, enter a region of uniform magnetic field normally. If the radius of the proton orbit is \( 10 c m, \) the radius of \( \alpha \) -orbit is
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
в. \( 10 \sqrt{2} \mathrm{cm} \)
\( c \cdot 20 c m \)
\( D .5 \sqrt{2} c m \)
Subject: Physics
A planet of mass \( 3 \times 10^{29} \mathrm{gm} \) moves
around a star with a constant speed of
\( 2 \times 10^{8} m s^{-1} \) in a circle of radii \( 1.5 \times \)
\( 10^{12} \mathrm{m} . \) The gravitational force exerted
on the planet by the star is
A \( .6 .67 \times 10^{22} \) dyne
B . \( 6.67 \times 10^{26} \) N
c. \( 8 \times 10^{26} \mathrm{N} \)
D. \( 8 \times 10^{27} \) dyne
Subject: Maths
If \( p \rightarrow(q \vee r) \) is false, then the truth
values of \( p, q, r \) are respectively
\( \mathbf{A} \cdot \mathbf{T}, \mathbf{F}, \mathbf{F} \)
B. F, F, F
c. F, T, T
D. Т, т, \( F \)
Subject: Physics
The resistance of the meter bridge \( A B \)
is given figure is 4 \Omega. With a cell of emf
\( \varepsilon=0.5 V \) and rheostat resistance
\( R h=2 \Omega \) the null point is obtained at
some point \( J . \) When the cell is replaced
by another one of emf \( \varepsilon=\varepsilon_{2} \) the same
null point \( J \) is found for \( R_{h}=6 \Omega \). The
emf \( \varepsilon \) is
A \( .0 .6 ~ V \)
B. \( 0.5 V \)
c. \( 0.3 V \)
D. \( 0.4 V \)
Subject: Physics
The wavelength \( \lambda_{e} \) of an electron and \( \lambda_{p} \)
of a photon of same energy \( \boldsymbol{E} \) are
related by:
\( A \cdot \lambda_{p} \propto \lambda_{e} \)
B. \( \lambda_{p} \propto \sqrt{\lambda_{e}} \)
c. \( \lambda_{p} \propto \frac{1}{\sqrt{\lambda_{e}}} \)
D. \( \lambda_{p} \propto \lambda_{e}^{2} \)
Subject: Physics
A conducting rod of length I and mass \( \mathrm{m} \) is moving down a smooth inclined plane of inclination \( \boldsymbol{\theta} \) with constant
velocity \( v . \) A current \( i \) is flowing in the
conductor in a direction perpendicular to paper inward. A vertically upward magnetic field \( \vec{B} \) exists in space. Then,
magnitude of magnetic field \( \vec{B} \) is:
A \( \cdot \frac{m g}{i l} \sin \theta \)
B. \( \frac{m g}{i l} \tan \theta \)
c. \( \frac{m g \cos \theta}{i l} \tan \theta \)
D. \( \frac{m g}{\text {ilsint}} \)
Subject: Physics
A simple harmonic motion has an
amplitude \( A \) and time period \( T . \) The
time required by it to travel \( x=A \) to
\( \boldsymbol{x}=\frac{\boldsymbol{A}}{2} \) is:
A. \( T / 6 \)
в. \( T / 4 \)
c. \( T / 3 \)
D. \( T / 2 \)
Subject: Chemistry
Assertion: All chemical added to food
items are called food preservatives.
Reason: All the chemicals increase the
nutritive value of the food.
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. Both Assertion and Reason are incorrect
D. Assertion is correct but Reason is incorrect
E. Assertion is incorrect but Reason is correct
Subject: Physics
If \( g \) on the surface of the Earth is 9.8
\( m s^{-2}, \) then it's value at a depth of 3200
\( k m \) (Radius of the earth \( =6400 \mathrm{km} \) ) is
\( \mathbf{A} \cdot 9.8 m s^{-2} \)
в. zero
C \( .4 .9 \mathrm{ms}^{-2} \)
D. \( 2.45 \mathrm{ms}^{-2} \)
Subject: Biology
Some organisms and their type of reproductions are given below. Find the correct alternative showing the correct
pair-
(a) Paramecium
(1) Spore formation
(b) Hydra
(2) Budding
(c) Mucor
(3) Fission
(d) Spirogyra
(4) Fragmentation
A. \( a-1, b-2, c-3, d-4 \)
4
B. a- 3, b- 4, c- 2, d-1
c. a- \( 2, b-3, c-4, d-1 \)
D. a- 3, b- 2, c-1, d-4
Subject: Biology
Assertion
BOD(Biological oxygen demand) is a
device that is used to measure quality
of water.
Reason
High BOD is observed in highly polluted
water
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
In the given figure \( D C=C B=4 \mathrm{cm} \)
and \( A E=2 \mathrm{cm} . \) Calculate the area of
shaded portion, if \( D C \| A B \)
\( 4 \cdot 8 c m^{2} \)
3. \( 8.44 \mathrm{cm}^{2} \)
\( \therefore 7 \mathrm{cm}^{2} \)
) \( 7.44 \mathrm{cm}^{2} \)
Subject: Chemistry
Which of the following can convert
acidified \( C r_{2} O_{7}^{2-} \) to green product?
\( \mathbf{A} \cdot S O_{2}, H_{2} S O_{3} \) and \( H_{2} S O_{4} \)
B. \( S O_{2}, H_{2} S \) and \( H_{2} S O_{3} \)
\( \mathbf{c} \cdot S O_{3}, H_{2} S \) and \( F e^{3+} \)
D. \( S O_{3}^{-}, H_{2} S \) and \( F e^{+2} \)
Subject: Physics
\( \ln \) an \( A C \) circuit, voltage \( V=V_{0} \sin \omega t \)
and inductor L is connected across the
circuit.Then the instantaneous power
will be
\( ^{\mathrm{A}} \cdot \frac{V_{0}^{2}}{2 \omega L} \sin \omega t \)
B. \( \frac{-V_{-}^{2}}{2 \omega L} \) sinwt
c. \( \frac{-V_{0}^{2}}{2 \omega L} \sin 2 \omega t \)
D. \( \frac{V_{0}^{2}}{\omega L} \sin 2 \omega t \)
Subject: Maths
Let \( S=\{1,2,3, \dots \dots n\} \) and \( A= \)
\( \{(a, b) \mid 1 \geq a, b \geq n\}=S \times S . A \)
subset \( B \) of \( A \) is said to be a good subset if \( (x, x) \in B \) for every \( x \in S \)
Then the number of good subsets of \( \boldsymbol{A} \)
is
\( A \cdot 1 \)
B. \( 2^{n} \)
\( c \cdot 2^{n(n-1)} \)
D. \( 2^{n^{2}} \)
Subject: Maths
\( \lim _{n \rightarrow \infty}\left[\frac{1}{2 n}+\frac{1}{\sqrt{4 n^{2}-1}}+\frac{1}{\sqrt{4 n^{2}-4}}+. .\right. \)
is equal to
A \( \cdot \frac{\pi}{4} \)
в. \( \frac{\pi}{2} \)
c.
D.
Subject: Maths
\( \int \frac{1}{1-\cos ^{4} x} d x=-\frac{1}{2 \tan x}+ \)
\( \frac{k}{\sqrt{2}} \tan ^{-1}\left(\frac{\tan x}{\sqrt{2}}\right)+C, \) where \( k= \)
A \( \frac{1}{2} \)
B. \( -\frac{1}{2} \)
\( c \cdot-1 \)
D.
Subject: Physics
Two capacitators having capacitances
\( C_{1} \) and \( C_{2} \) are charged with \( 120 V \) and
\( 200 V \) batteries respectively. When they
are connected in parallel now, it is found that the potential on each one of them is zero. Then:
A \( \cdot 8 C_{1}=5 C_{2} \)
В. \( 9 C_{1}=5 C_{2} \)
\( \mathbf{c} \cdot 3 C_{1}=5 C_{2} \)
D. \( 5 C_{1}=3 C_{2} \)
Subject: Maths
STATEMENT 1: In a \( \Delta A B C, \) if \( A, B, C \)
are in \( A . P . \) and triangle is equilateral,
then \( \cos A+2 \cos B+\cos C=2 \)
STATEMENT 2: In a \( \Delta A B C, \) if \( A, B, C \)
\( \operatorname{are} \operatorname{in} A \cdot P \cdot \) and \( \cos A+\cos B+ \)
\( \cos C=2, \) then the triangle
is isosceles.
A. Statement-1 is true, Statement-2 is true, Statementis correct explanation of Statement-
B. statement-1 is true, statement-2 is true, statement- is not correct explanation for Statement-
c. statement-1 is true, statement-2 is false
D. statement-1 is false, Statement-2 is true
Subject: Maths
If \( \frac{1+3 p}{3}, \frac{1-p}{4} \) and \( \frac{1-2 p}{2} \) are mutually exclusive events. Then, range
of \( p \) is
A \( \cdot \frac{1}{3} \leq p \leq \frac{1}{2} \)
в. \( \frac{1}{2} \leq p \leq \frac{1}{2} \)
c. \( \frac{1}{3} \leq p \leq \frac{2}{3} \)
D. \( \frac{1}{3} \leq p \leq \frac{2}{5} \)
Subject: Chemistry
The sodium extract of an organic
compound on boiling with \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) and
on subsequent treatment with ammonium molybdate solution gives a yellow precipitate. Which of the following elements may be present in the compound?
A. Nitrogen
B. Sulphur
c. Phosphorus
D. Halogen
Subject: Biology
Correct sequence of layers of bacterial
cell envelope from outward to inward is
A. Cell wall \( \rightarrow \) Glycocalyx \( \rightarrow \) Cell membrane
B. Cell membrane \( \rightarrow \) Glycocalyx \( \rightarrow \) Cell wall
c. Glycocalyx \( \rightarrow \) Cellwall \( \rightarrow \) Cell membrane
D. Glycocalyx \( \rightarrow \) Cell membrane \( \rightarrow \) Cell wall
Subject: Chemistry
Which of the following orders is correct regarding basicity of indicated molecules?
A. N, N - Dimethyltoluidine > p - toluidine >aniline > p nitroaniline
B. Aniline > N, N - dimethyl- p - toluidine > p - toluidine > aniline
c. p - Toluidine > N, N - dimethyl - p - toluidine > aniline
- nitroaniline
D. N, N-Dimethyltoluidine > aniline > p -toluidine > p nitroaniline
Subject: Chemistry
Assertion
\( \boldsymbol{I}_{2}+\boldsymbol{I}^{-} \longrightarrow \boldsymbol{I}_{\boldsymbol{3}} \)
In above reaction, \( \boldsymbol{I}_{2} \) is Lewis base.
Reason

Electron pair acceptor is Lewis base.
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
Two parallel wires \( 2 \mathrm{m} \) apart carry currents of 2 A and 5 A respectively in the same direction, the force per unit
length acting between these two wires is:
A \( \cdot 2 \times 10^{-6} \mathrm{N} \mathrm{m}^{-1} \)
В. 3 \( \times 10^{-6} \mathrm{N} \mathrm{m}^{-1} \)
c. \( 1 \times 10^{-6} \mathrm{N} \mathrm{m}^{-1} \)
D. \( 4 \times 10^{-6} \mathrm{N} \mathrm{m}^{-1} \)
Subject: Chemistry
The structural formulae of some
organic compounds are given below:
i. \( C H_{3}-C H_{2}-C O-C H_{3} \)
ii. \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C H O} \)
iii. \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{O H} \)
¡v. \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{3} \)
a. Which of these is an alkane?
b. Write the structural formula of the
position isomer of the third compound.
c. Which of the given compounds are functional isomers?
d. Write the structural formula of the
chain isomer of the fourth compound.
Subject: Maths
\( \operatorname{Let} f(x)=\left\{\begin{array}{ll}x^{n} \sin \frac{1}{x}, & x \neq 0 \\ 0, & x=0\end{array}, \) then \right.
\( f(x) \) is continuous but not differentiable
at \( x=0 \) if
A \( . n \in(0,1] \)
B. \( \mathrm{n} \in[1, \infty) \)
c. \( n \in(-\infty, 0) \)
\( \mathbf{D} \cdot \mathbf{n}=0 \)
Subject: Physics
Along the \( X \) -axis, three charges \( \frac{q}{2},-q \) and \( \frac{q}{2} \) are placed at \( x=0, x=a \) and \( x=2 a \) respectively. The resultant electric potential at \( x=a+r(\text { if }, a<r) \) is :
\( \left(\epsilon_{0} \) is the permittivity of free space) \right.
A \( \cdot \frac{q a}{4 \pi \epsilon_{0} r^{2}} \)
в. \( \frac{q a^{2}}{4 \pi \epsilon_{0} r^{3}} \)
\( ^{\mathbf{C}} \cdot \frac{q\left(a^{2} / 4\right)}{4 \pi \epsilon_{0} r^{3}} \)
D. \( \frac{q}{4 \pi \epsilon_{0} r} \)
Subject: Maths
Let \( \overrightarrow{\boldsymbol{a}}=\boldsymbol{a}_{1} \hat{\boldsymbol{i}}+\boldsymbol{a}_{2} \hat{\boldsymbol{j}}+\boldsymbol{a}_{3} \hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{b}}=\boldsymbol{b}_{1} \hat{\boldsymbol{i}}+ \)
\( \boldsymbol{b}_{2} \hat{\boldsymbol{j}}+\boldsymbol{b}_{3} \hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{c}}=\boldsymbol{c}_{1} \hat{\boldsymbol{i}}+\boldsymbol{c}_{2} \hat{\boldsymbol{j}}+\boldsymbol{c}_{3} \hat{\boldsymbol{k}} . \).If \( |\overrightarrow{\boldsymbol{c}}|= \)
1 and \( (\vec{a} \times \vec{b}) \times \vec{c}=0 \) then
\( \left|\begin{array}{lll}\boldsymbol{a}_{1} & \boldsymbol{a}_{2} & \boldsymbol{a}_{3} \\ \boldsymbol{b}_{1} & \boldsymbol{b}_{2} & \boldsymbol{b}_{3} \\ \boldsymbol{c}_{1} & \boldsymbol{c}_{2} & \boldsymbol{c}_{3}\end{array}\right|^{2}= \)
A . 0
в.
c. \( |\vec{a}|^{2}|\vec{b}|^{2} \)
D. \( |\vec{a} \times \vec{b}|^{2} \)
Subject: Physics
Two samples \( A \) and \( B \) of a gas initially at the same pressure and temperature are compressed from volume \( V \) to \( \frac{V}{2}(A \) isothermally and \( B \) adiabatically). The
final pressure of \( \boldsymbol{A} \) is
A. greater than the final pressure of \( B \)
B. equal to the final pressure of \( B \)
c. less than the final pressure of \( B \)
D. twice the final pressure of \( B \)
Subject: Chemistry
\( \boldsymbol{P}_{4}+\boldsymbol{6} \boldsymbol{C l}_{2} \rightarrow \)
A \( \cdot 2 P_{2} C l_{2} \)
B. \( 4 P C l_{3} \)
c. \( P C l_{6} \)
D. \( P_{2} C l_{5} \)
Subject: Maths
\( \mathbf{f} A=\left[\begin{array}{cc}\cos \boldsymbol{x} & -\sin \boldsymbol{x} \\ \sin \boldsymbol{x} & \cos \boldsymbol{x}\end{array}\right], \) then find \( \boldsymbol{A} \boldsymbol{A}^{\boldsymbol{T}} \)
Subject: Physics
A block slides down on an incline of angle \( 30^{\circ} \) with an acceleration \( \frac{g}{4} . \) Find the coefficient of kinetic friction.
A \( \cdot \frac{1}{2 \sqrt{2}} \)
B. 0.6
c. \( \frac{1}{2 \sqrt{3}} \)
D. \( \frac{1}{\sqrt{2}} \)
Subject: Chemistry
Find the over voltage if electrolysis of brine solution requires \( 2.19 \mathrm{V} \) to produce
\( \mathrm{H}_{2} \) and \( \mathrm{Cl}_{2} . \) (Write your answer upto two
decimal places)
Given: \( \boldsymbol{E}_{\boldsymbol{H}^{+} / \boldsymbol{H}}^{\boldsymbol{o}}=\mathbf{0} \) and \( \boldsymbol{E}_{C l^{-} / C l_{2}}^{o}= \)
\( -1.36 V \)
Subject: Chemistry
The formula of
dichlorobis(urea)copper(II) is:
A \( \cdot\left[C u\left(O=C\left(N H_{2}\right)_{2}\right)_{2}\right] C l_{2} \)
в. \( \left[C u C l_{2}\left(O=C\left(N H_{2}\right)_{2}\right)_{2}\right] \)
c. \( \left[C u\left(O=C\left(N H_{2}\right)_{2}\right)\right] C l \)
D \( \cdot\left[C u C l_{2}\left(O=C\left(N H_{2}\right)_{2}\right) H_{2}\right] \)
Subject: Physics
When light shines on a \( \boldsymbol{p}-\boldsymbol{n} \) junction
diode, the current \( (I) v s . \) voltage \( (V) \) is observed as in the figure below:
In which quadrant(s) does the diode generate power, so that it can be used
as a solar cell?
A . Quad 1 only
c. Quad 4 only
D. Quad 1 and 4 onl
Subject: Physics
n the circuit shown below emf of each
batter y is 5V; and has an internal
resistance of \( 1.0 \Omega . \) The current in the
circuit \( \left(I_{0}\right) \) and the reading in an ideal
voltmeter (V) are
A \( \cdot I_{0}=1 A, V=0 \)
В . \( I_{0}=5 A, V=0 \)
c. \( I_{0}=1 A, V=1 \)
D . \( I_{0}=5 A . V=1 \)
Subject: Maths
If \( C_{r} \) denotes the binomial coefficient
\( ^{n} C_{r} \) then \( (-1) C_{0}^{2}+2 C_{1}^{2}+5 C_{2}^{2}+ \)
\( \ldots(3 n-1) C_{n}^{2}= \)
A \( \cdot(3 n-2)^{2 n} C_{n} \)
\( ^{\text {В }} \cdot\left(\frac{3 n-2}{2}\right)^{2 n} C_{n} \)
c. \( (5+3 n)^{2 n} C_{n} \)
D \( \cdot\left(\frac{3 n-5}{2}\right)^{2 n} C_{n+1} \)
Subject: Physics
A slab of stone area \( 3500 \mathrm{cm}^{2} \) and
thickness \( 10 \mathrm{cm} \) is exposed on the lower
surface to steam at \( 100^{\circ} \mathrm{C} \). A block of
ice at \( 0^{\circ} C \) rests on upper surface of the slab. In one hour \( 4.8 k g \) of ice of melted.
The thermal conductivity of the stone is \( J s^{-1} m^{-1} k_{-1} \) is
(Latent heat of ice \( =\mathbf{3 . 3 6} \times \mathbf{1 0}^{\mathbf{5}} \mathbf{J} / \mathbf{k g} \) )
A . 12.0
B. 10.5
c. 1.02
D. 1.24
Subject: Maths
The probability of happening of an event
\( A \) is 0.5 and that of \( B \) is \( 0.3 . \) If \( A \) and \( B \)
are mutually exclusive events, then the probability of neither A nor B is?
A . 0.4
B. 0.5
\( c .0 .2 \)
D. 0.9
Subject: Physics
If pressure \( P, \) Velocity \( V, \) and time \( T \) are taken as fundamental physical quantities, then the
dimensional formula for force is:
A \( \cdot P V^{2} T^{2} \)
B . \( P^{-1} V^{2} T^{-1} \)
c. \( P V T^{2} \)
D. \( P^{-1} V T^{2} \)
Subject: Maths
If
\( \sin ^{-1} \frac{2 x}{1+x^{2}} ; \cos ^{-1} \frac{1-x^{2}}{1+x^{2}} ; \tan ^{-1} \frac{2 x}{1-x^{2}} \)
each is equal to \( 2 \tan ^{-1} x . \),then show that \( \int 2 \tan ^{-1} x= \)
\( 2\left[x \tan ^{-1} x-\frac{1}{2} \log \left(1+x^{2}\right)\right] \)
Subject: Physics
In displacement method, the distance
between object and screen is 96 cm.
The ratio of lengths of two images
formed by a converging lens placed
between them is \( 4 . \) Then
This question has multiple correct options
A. Ratio of the length of object to the length of shorter image is 2
B. Distance between the two positions of the lens is \( 32 \mathrm{cm} \)
C. Focal length of the lens is \( 64 / 3 \mathrm{cm} \)
D. When the shorter image is formed on screen, distance of the lens from the screen is \( 32 \mathrm{cm} \)
Subject: Maths
Find derivative of \( \sin ^{-1}\left(x^{2}\right) \) using first
principle.
A \( \cdot \frac{2 x}{\sqrt{1-x^{2}}} \)
в. \( \frac{2 x}{\sqrt{1-x}} \)
c. \( \frac{2 x}{\sqrt{1-x^{4}}} \)
D. \( \frac{x}{\sqrt{1-x^{4}}} \)
Subject: Maths
Let \( \boldsymbol{A}=\{-1,1\}, \) Then discuss whether
the given functions from \( A \) to itself are one-one onto or bijective:
(i) \( f(x)=\frac{x}{2} \)
(ii) \( g(x)=|x| \)
(iii) \( h(x)=X^{2} \)
Subject: Physics
A vertical cylindrical vessel separated in two parts by a frictionless piston free to move along the length of a vessel. The length of vessel is \( 90 \mathrm{cm} \) and the piston divides the cylinder in the ratio \( 2: 1 . \) Each
of the two parts contain 0.1 mole of
an ideal gas. The temperature of the gas
is \( 27^{\circ} \mathrm{C} \) in each part. The mass of the
piston is
A. \( 41.5 \mathrm{kg} \)
B. \( 8.97 \mathrm{kg} \)
c. \( 9.57 \mathrm{kg} \)
D. 11.57 kg
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 B with respect to A.
\( \mathbf{A} \)
A. \( -22 \mathrm{m} / \mathrm{s} \)
в. \( 22 \mathrm{m} / \mathrm{s} \)
c. \( -40 m / s \)
D. \( 17 \mathrm{m} / \mathrm{s} \)
Subject: Maths
For two data sets, each of size 5 , the
variances are given to be 4 and 5 and the corresponding means are given to
be 2 and \( 4, \) respectively. The variance of the combined data set is
A \( \cdot \frac{11}{2} \)
B. 6
c. \( \frac{13}{2} \)
D.
Subject: Maths
\( A_{3 * 3} \) is a non - singular matrix \( \Rightarrow \)
\( \boldsymbol{A}^{2}(\boldsymbol{A} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A})= \)
\( \mathbf{A} \cdot|A| A \)
B. \( I \)
c. \( |A| \)
D・ \( |A|^{2} I \)
Subject: Physics
In the given circuit, the voltage across
the voltage across the load is
maintained at \( 12 \mathrm{V} \). The current in the
zener diode varies from 0-50 mA. What
is the maximum watage of the diode?
\( A \cdot 12 W \)
B. 6 w
c. \( 0.6 w \)
D. \( 1.2 \mathrm{w} \)
Subject: Maths
If \( \tan \theta=\frac{4}{7}, \) then \( \frac{7 \sin \theta-3 \cos \theta}{7 \sin \theta+3 \cos \theta}= \)
A \( \cdot \frac{1}{7} \)
в.
\( c \cdot \frac{3}{7} \)
D. \( \frac{5}{14} \)
Subject: Chemistry
The freezing point of a solution containing 5.85 g of \( N a C l \) in \( 100 g \) of
water is \( -3.348^{\circ} \mathrm{C} . \) Calculate van't Hoff
factor 'i' for this solution. What will be
the experimental molecular weight of NaCl?
\( \left(K_{f} \text { for water }=1.86 K k g m o l^{-1}, \) at. wt. \right. \( \mathrm{Na}=23, \mathrm{Cl}=35.5) \)
Subject: Maths
\( \mathbf{A}=\left[\begin{array}{cc}\cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha\end{array}\right] \) then \( \mathbf{A} . \mathbf{A}^{\mathbf{T}} \)
A. Null matrix
в. А
\( c \cdot I \)
D. A
Subject: Physics
When a uniform wire of radius r is
stretched by a \( 2 k g \) weight, the increase
in its length is 2.00 mm. If the radius of
the wire is \( r / 2 \) and other conditions
remain in the same, increase in
its length is
A. \( 2.00 \mathrm{mm} \)
в. \( 4.00 \mathrm{mm} \)
c. \( 6.00 m m \)
D. \( 8.00 m m \)
Subject: Chemistry
Balance the following equations:
\( \boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{2-}+\boldsymbol{I}^{-}+\boldsymbol{H}^{+} \rightarrow \boldsymbol{C r}^{3+}+\boldsymbol{I}_{2}+ \)
\( H_{2} O \)
\( \mathbf{A} \cdot C r_{2} O_{7}^{2-}+6 I^{-}+14 H^{+} \rightarrow 2 C r^{3+}+3 I_{2}+7 H_{2} O \)
B. \( C r_{2} O_{7}^{2-}+I^{-}+14 H^{+} \rightarrow 2 C r^{3+}+3 I_{2}+7 H_{2} O \)
\( \mathbf{c} \cdot C r_{2} O_{7}^{2-}+6 I^{-}+7 H^{+} \rightarrow 2 C r^{3+}+I_{2}+7 H_{2} O \)
D. None of these
Subject: Chemistry
Assertion
The presence of \( C O_{2} \) in the air
accelerates corrosion.
Reason
\( C O_{2} \) is a poisonous gas.
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
The converse of the contrapositive of the
conditional \( \boldsymbol{p} \rightarrow \sim \boldsymbol{q} \) is :
A \( . p \rightarrow q \)
в. \( p \rightarrow \sim q \)
\( \mathbf{c} . \sim q \rightarrow p \)
\( \mathbf{D} \cdot \sim p \rightarrow q \)
Subject: Physics
Assertion
Two point coherent sources of light \( \boldsymbol{S}_{1} \)
and \( S_{2} \) are placed on a line as shown in
figure. \( P \) and \( Q \) are two points on that
line. If at point \( \boldsymbol{P} \) maximum intensity is observed, then maximum intensity should also be observed at \( Q \)
Reason
In the figure, the distance \( \left|\boldsymbol{S}_{1} \boldsymbol{P}-\boldsymbol{S}_{2} \boldsymbol{P}\right| \)
is equal to distance \( \left|\boldsymbol{S}_{1} \boldsymbol{Q}-\boldsymbol{S}_{2} \boldsymbol{Q}\right| \)
\[
\vec{Q} \quad \overrightarrow{s_{1}} \quad \dot{S_{2}} \quad \dot{P}
\]
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: Physics
The incident intensity on a horizontal surface at sea level from the sun is
about \( 1 k W m^{-2} . \) Assuming that 50 per cent of this intensity is reflected and 50 per cent is absorbed, determine the
radiation pressure on this horizontal surface (in pascals).
A \( .8 .2 \times 10^{-2} \)
В . \( 5 \times 10^{-6} \)
c. \( 3 \times 10^{-5} \)
D. \( 6 \times 10^{-5} \)