AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Which of the following is a way to
protect your eye, if chemical splatters
into your eye?
A. By slow addition of concentrated acid to water.
B. By slow addition of water to the concentrated acid.
C. By proper replacement of unused or excess chemicals into their properly labelled containers from where they have come.
D. Dispose of chemicals in the proper places following posted procedures. Do not return them to their original containers.
E. Flush eyes with water at the eyewash fountain for at least 15 minutes and then report the accident for further help
Subject: Maths
If 0 is the origin and the coordinates of \( P \) is \( (1,2,-3), \) then find the equation of the plane passing through P and perpendicular to OP.
A. \( x-2 y-3 z=-15 \)
в. \( x+2 y-3 z=14 \)
c. \( x-2 y+3 z=15 \)
D. \( x-2 y-3 z=15 \)
Subject: Physics
For driving current of \( 2 A \) for 6 minute in a circuit. \( 1000 J \) of work is to be done.
The e.m.f. of the source in the circuit is
A . \( 1.38 V \)
в. \( 1.68 V \)
c. \( 2.03 V \)
D. 3.10V
Subject: Chemistry
Most readily hydrolised halide is:
\( \mathbf{A} \cdot C_{6} H_{5} C l \)
В \( \cdot\left(C_{6} H_{5}\right)_{2} C H C l \)
c. \( C_{6} H_{5} C H_{2} C l \)
D \( \cdot\left(C_{6} H_{5}\right)_{3} C C l \)
Subject: Chemistry
The equilibrium constant for the reaction
is:
\( 2 F e^{3+}+3 I^{\ominus} \rightleftharpoons F e^{3+}+C e^{3+} \)
Given :
\( E_{C e^{4+1} C e^{3+}}=1.44 \mathrm{V} \)
\( E_{F e^{3+} 1 F e^{2+}}^{\ominus}=0.68 \mathrm{V} \)
A . \( 7.236 \times 10^{12} \)
B . \( 7.386 \times 10^{12} \)
c. \( 7.158 \times 10^{12} \)
D. None of these
Subject: Physics
Two identical copper spheres carrying chatges \( +Q \) and \( -9 Q \) separated by a certain distance has attractive force \( F \)
If the spheres are allowed to touch eacxh other and moved to distance of
separation 'x'. So that the force between
them becomes \( \frac{4 F}{9} . \) Then \( x \) is equal to
\( A \cdot d \)
B. 2d
\( c \cdot d / 2 \)
D. 4d
Subject: Physics
An open capillary tube contains a drop of water. When the tube is in its vertical
position, the drop forms a column with
a length of 2 \( c m \). The internal diameter
of the capillary tube is 1 mm. Determine the radii of curvature of the upper and
lower meniscus in each case. Consider
the wetting to be complete. Surface tension of water \( =\mathbf{0 . 0 0 7 5} N / \boldsymbol{m} \)
Subject: Physics
resistance \( r \) is connected across a
resistance \( R \) Resistance \( R \) can be
adjusted to any value greater than or equal to zero. A graph is plotted
between the current
\( (i) \) passing
through the resistance and potential
difference \( (V) \) across it. Select the
correct alternative(s).
A. internal resistance of battery is \( 5 \Omega \)
B. emf of the battery is \( 20 V \)
c. maximum current which can be taken from the battery is \( 4 A \)
D. \( V-i \) graph can never be straight line as shown in the
figur
Subject: Physics
In series \( L-R \) circuit, \( X_{L}=R \). Now a
capacitor with \( X_{C}=R \) added in series.
New power factor:
A. Same as initial
B. \( \frac{1}{\sqrt{2}} \) times the initial
c. \( \frac{1}{2} \) times the initial
D. \( \sqrt{2} \) times the initial
Subject: Maths
If \( 0 \leq x \leq 1, \) then \( \sin \left\{\tan ^{-1} \frac{1-x^{2}}{2 x}+\cos ^{-1} \frac{1-x^{2}}{1+x^{2}}\right\} \)
equal to
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c \cdot 0 \)
D. none of these
Subject: Maths
Refer the above figure and find the
value of \( \sec n \)
A \( \cdot \sqrt{5} \)
B. \( 2 \sqrt{5} \)
c. \( \frac{\sqrt{5}}{2} \)
D. \( \frac{\sqrt{5}}{5} \)
E. \( \frac{2 \sqrt{5}}{5} \)
Subject: Chemistry
In the reaction, \( 4 M+8 C N^{-}+ \)
\( \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{O}_{2} \rightarrow \mathbf{4}\left[\boldsymbol{M}(\boldsymbol{C} \boldsymbol{N})_{2}\right]+\mathbf{4} \boldsymbol{O} \boldsymbol{H}^{-} \)
identify the metal \( \mathrm{M} \) as:
A. copper
B. Iron
c. silver
D. zinc
Subject: Maths
The distance between the line \( r=2 \hat{i}- \) \( 2 \hat{j}+3 \hat{k}+\lambda(\hat{i}-\hat{j}+4 \hat{k}) \) and the plane
\( r \cdot(\hat{i}+5 \hat{j}+\hat{k})=5 \) is
A \( \cdot \frac{10}{9} \)
в. \( \frac{10}{3 \sqrt{3}} \)
c. \( \frac{10}{3} \)
D. None of these
Subject: Chemistry
Among the methods for extracting metals from their ores, i.e., 1. roasting a metal sulphide, 2. chemical reduction of a metal oxide, and 3. electrolysis, the
preferred method depends on \( E^{\circ} \) value for the reducing half-reaction:
\( \boldsymbol{M}^{n+}(\boldsymbol{a q})+\boldsymbol{n} \boldsymbol{e}^{-} \rightarrow \boldsymbol{M}(\boldsymbol{s}) \)
What are the criteria of selection of a
good reducing agent for extraction of
metals?
Subject: Physics
A car is moving in a circular horizontal
track of radius \( 10 m \) with a constant
speed of \( 10 m / s . \) A plumb bob is suspended from the roof of the car by a light rigid rod of length 1 m. The angle
made by the rod with track is
A . zero
B . \( 30^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 60^{\circ} \)
Subject: Physics
The temperature of 5 mol of a gas which was held at constant volume was
changed from \( 100^{\circ} \mathrm{C} \) to \( 120^{\circ} \mathrm{C} \). The
change in internal energy was found to
be 80 . \( J \). The total heat capacity of the
gas at constant volume will be equal to
\( \mathbf{A} \cdot 8 J K^{-1} \)
B . \( 0.8 \mathrm{JK}^{-1} \)
\( \mathbf{c} \cdot 4 J K^{-1} \)
D. \( 0.4 \mathrm{JK}^{-1} \)
Subject: Maths
If \( \boldsymbol{k}>\mathbf{0},|\boldsymbol{z}|=|\boldsymbol{w}|=\boldsymbol{k} \) and \( \boldsymbol{\alpha}=\frac{\boldsymbol{z}-\overline{\boldsymbol{w}}}{\boldsymbol{k}^{2}+\boldsymbol{z} \overline{\boldsymbol{w}}} \)
then \( \operatorname{Re}(\alpha) \) equal
A .
B.
\( c . k \)
D. none of these
Subject: Physics
Two vectors \( X \) and \( Y \) are added together.
Which of the following statements
could be true?
I. The resultant magnitude is smaller
than X.
II. The resultant magnitude is larger
than \( Y \)
III. The resultant direction is the same
as either \( X \) or \( Y \)
A. I only
B. II only
C. I and III only
D. II and III only
E . ।, ॥।, and III
Subject: Maths
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left\{\cot ^{-1} \frac{\sqrt{1+\boldsymbol{x}}-\sqrt{1-\boldsymbol{x}}}{\sqrt{1+\boldsymbol{x}}+\sqrt{1-\boldsymbol{x}}}\right\}= \)
\( A \cdot \frac{1}{\sqrt{1-x^{2}}} \)
B \( \cdot \frac{-1}{2 \sqrt{1-x^{2}}} \)
\( \mathbf{C} \cdot \frac{1}{1+x^{2}} \)
D. \( \frac{-1}{2\left(1+x^{2}\right)} \)
Subject: Physics
In the region of space \( \dot{E} \) and \( \dot{B} \) are parallel. A beam of cathode-rays moving in the same direction as \( \dot{E} \) enters the
space. Which of the following conclusions is correct
A. The cathode rays will travel straight
B. The cathode rays wil lbe deflected towards right
c. The speed of cathode ray particles increases
D. The speed of cathode ray particles decreases
Subject: Chemistry
Which of the following is reactions is an example of autoreduction?
A \( \cdot F e_{3} O_{4}+4 C O \rightarrow 3 F e+4 C O_{2} \)
в. \( C u O+C \rightarrow 2 C u+C O \)
c. \( C u_{\left(a_{a}\right)}^{2+}+F e_{(s)} \rightarrow C u_{(s)}+F e_{\left(a_{9}\right)+}^{(2)} \)
D. \( C u_{2} O+\frac{1}{2} C u_{2} S \rightarrow 2 C u+\frac{1}{2} S O_{2} \)
Subject: Maths
If \( S=\frac{1}{1^{2}}+\frac{1}{2^{2}}+\frac{1}{3^{2}}+\frac{1}{4^{2}}+\dots \dots \dots \dots \) to \( \infty \)
then find \( \frac{1}{1^{2}}+\frac{1}{3^{2}}+\frac{1}{5^{2}}+\frac{1}{7^{2}}+\dots \dots \dots \dots \)
\( \infty \) in terms of \( S \)
Subject: Biology
Assertion
Podzol is a highly leached soil and acidic in reaction.
Reason
Excessive moisture content of
podzolized soils promotes leaching of the soil
A. If \( A \) and \( R \) both are true and \( R \) is correct explanation of
\( A \)
B. If A and R both are true but R is not correct explanation of A.
C. If A is correct and R is wrong.
D. If A is wrong and R is true
Subject: Maths
If
\( [x] \) denotes the integral part of \( x, \) then
\( \lim _{x \rightarrow \infty} \frac{1}{n^{3}}\left(\sum_{k=1}^{n}\left[k^{2} x\right]\right) \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{x}{2} \)
c. \( \frac{x}{3} \)
D. \( \frac{x}{6} \)
Subject: Maths
The number of subsets of the \( \operatorname{set} A= \)
\( \left\{a_{1}, a_{2}, \dots \dots \dots a_{n}\right\} \) which contain even
number of elements is
A \( \cdot 2^{n-1} \)
B . \( 2^{n}-1 \)
c. \( 2^{n}-2 \)
D \( \cdot 2^{n} \)
Subject: Maths
Find determinant \( \boldsymbol{D} \boldsymbol{c}=\left|\begin{array}{ccc}\mathbf{1} & \mathbf{1} & -\mathbf{2} \\ \mathbf{1} & -\mathbf{2} & \mathbf{3} \\ \mathbf{2} & -\mathbf{1} & -\mathbf{1}\end{array}\right| \)
Subject: Chemistry
Assertion (A): Internal energy is a state
function and extensive property.
Reason ( \( \mathrm{R} \) ): Internal energy of a
substance depends on gravitational force of attraction.
A. A and R are true and \( \mathrm{R} \) is correct explanation of
B. A and R are true and R is not correct explanation of A
c. A is true, R is false
D. A is false, R is true
Subject: Chemistry
In the following reaction,
\[
\begin{array}{c}
\boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{2}+\boldsymbol{B} \boldsymbol{r} \boldsymbol{O}_{3}^{-}+\boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \boldsymbol{B} \boldsymbol{r} \boldsymbol{O}_{4}^{-}+ \\
\boldsymbol{X} \boldsymbol{e}+\boldsymbol{2} \boldsymbol{H} \boldsymbol{F}:
\end{array}
\]
This question has multiple correct options
A \( . X e F_{2} \) is an oxidising agent
B. \( X e F_{2} \) is an reducing agent
\( \mathrm{C} \cdot B r O_{3}^{-} \) is oxidised to \( B r O_{4}^{-} \)
D. \( X e F_{2} \) is reduced to HF
Subject: Chemistry
Arrange
\( \boldsymbol{N} \boldsymbol{a}^{+}, \boldsymbol{M} \boldsymbol{G}^{2+}, \boldsymbol{O}^{2-}, \boldsymbol{F}^{-} \boldsymbol{A} \boldsymbol{l}^{3+}, \boldsymbol{N}^{3-} \)
(each having 10 electrons) in increasing
ionic radii.
\( \mathbf{A} \cdot A l^{3+}<M g^{2+}<N a^{+}<F^{-}<O^{2-}<N^{3-} \)
B. \( N^{3-}<O^{2}<F^{-}<N a^{+}<M g^{2+}<A l^{3+} \)
C \( \cdot A l^{3+}<M g^{2+}<F^{-}<N a^{+}<O^{2-}<N^{3-} \)
D. None of these
Subject: Physics
The radius of a metal sphere is \( 100 \mathrm{cm} \)
\( \operatorname{at} 0^{\circ} \mathrm{C} \) and \( 101 \mathrm{cm} \) at \( 100^{\circ} \mathrm{C} . \) The
coefficient of volume expansion of metal is :
A \( \cdot 10^{-4} /^{\circ} \mathrm{C} \)
В. \( 3 \times 10^{-4} /^{\circ} \mathrm{C} \)
c. \( 2 \times 10^{-4} /^{\circ} \mathrm{C} \)
D. \( 1.5 \times 10^{-4} /^{\circ} \mathrm{C} \)
Subject: Physics
A thin lens of focal length \( 10 \mathrm{cm} \) is cut
into two equal halves and are kept as
shown in figure. It an object \( \boldsymbol{O} \) is placed
at distance \( 10 \mathrm{cm} \) from the optical
centre of combination. then the
distance of image from object will be
\( A \cdot 5 \mathrm{cm} \)
B. 7.5 \( \mathrm{cm} \)
\( c \cdot 10 \mathrm{cm} \)
D. 20 cm
Subject: Physics
The slope of plate characteristic and mutual characteristic curves of a triode
value is \( 0.02 \mathrm{mA} / \mathrm{V} \) and \( 1 \mathrm{mA} / \mathrm{V} \). The
amplification factor of triode value is:
A \( .2 \times 10^{8} \)
B. 20
c. 50
D. 40
Subject: Biology
Assertion
The process of fusion of a sperm with an ovum is called fertilisation
Reason
Only one sperm can fertilise an ovum.
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
Which of the following is true for a line \( l \) lying in the same plane and
intersecting \( \triangle A B C \) but not perpendicular to \( \overline{B C} ? \)
A. \( l \) intersects \( \overline{A B} \) or \( \overline{A C} \)
B. \( l \) intersects \( \overline{A C} \)
c. \( l \) does not intersects \( \overline{A B} \) or \( \overline{A C} \)
D. \( l \) intersects \( \overline{A B} \)
Subject: Chemistry
The IUPAC name of
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right) \boldsymbol{C H}(\boldsymbol{C H O}) \boldsymbol{C H}_{2} \boldsymbol{C} \)
is:
A. 2-sec-butylbutanal
B. 2,3-diethylbutanal
c. 2-Ethyl-3-methyl-pentanal
D. 3-methyl-2-ethylpentanal
Subject: Physics
In reaching her destination, a backpacker walks with an average velocity of \( 1 m / s, \) due west. This average
velocity results, because she hikes for
\( 6 k m \) with an average velocity of \( 3 m / s \) due west, turns around, and hikes with
an average velocity of \( 0.3 m / s \) due east.How far to east did she walk (in
kilometers)?
A. 1.714
в. 2
\( c .6 \)
D
Subject: Physics
In a regular polygon of \( n \) sides, each corner is at a distance \( r \) from the
centre. Identical charges of magnitude \( q \) are placed at \( (n-1) \) corners. The field
at the centre is
A. \( _{k^{2}} \frac{q}{r^{2}} \)
в. \( _{(n-1) k \frac{q}{r^{2}}} \)
c. \( \frac{n}{n-1} k^{\frac{q}{r^{2}}} \)
D. \( \frac{n-1}{n} k \frac{q}{r^{2}} \)
Subject: Physics
A uniformly tapering conical wire is made from a material of Young's
modulus \( Y \) and has a normal,
unextended length \( L \). The radii, at the upper and lower ends of this conical
wire, have values \( R \) and \( 3 R \)
respectively. The upper end of the wire is fixed to a rigid support and a mass \( M \) is suspended from its lower end. The equilibrium extended length,of this wire, would equal to:
A \( \cdot L\left(1+\frac{1}{3} \frac{M g}{\pi \Upsilon R^{2}}\right) \)
в. \( L\left(1+\frac{2}{9} \frac{M g}{\pi \Upsilon R^{2}}\right) \)
c. \( _{L}\left(1+\frac{1}{9} \frac{M g}{\pi \Upsilon R^{2}}\right) \)
D. \( L\left(1+\frac{2}{3} \frac{M g}{\pi \Upsilon R^{2}}\right) \)
Subject: Physics
The electric potential at a distance of \( 3 m \) on the axis of a short dipole of dipole moment \( 4 \times 10^{-12} \) coulomb-
metre is
A \( \cdot 1.33 \times 10^{-3} V \)
\( V \)
B. \( 4 m V \)
c. \( 12 m V \)
D. \( 27 \mathrm{mV} \)
Subject: Chemistry
One reaction that occurs in producing steel from iron ore is the reduction of
iron ore(II) by carbon monoxide to give iron metal and carbon dioxide. The
equilibrium constant \( \boldsymbol{K}_{\boldsymbol{p}} \) for the
reaction at \( 1000 \mathrm{K} \) is \( 0.259 . F e O+ \)
\( \boldsymbol{C O} \leftrightharpoons \boldsymbol{F} \boldsymbol{e}+\boldsymbol{C O}_{2} . \) If the initial partial
pressure of \( \mathrm{CO} \) and \( C \mathrm{O}_{2} \) are 1 atm and
0.5 atm respectively, the equilibrium
partial pressures of \( \mathrm{CO} \) and \( \boldsymbol{C O}_{2} \) at
1000K are :
A. 1.191 atm, 0.309 atm
B. 0.309 atm, 1.191 atm
c. 1.191 atm for both
D. 0.309 atm for both
Subject: Chemistry
For a given value of the degree of dissociation \( (\alpha), \) which of the following
have correct van't Hoff factor?
This question has multiple correct options
A. \( N a C l ; i=2+\alpha \)
в. \( C a\left(N O_{3}\right)_{2} ; i=1+2 \alpha \)
c. \( K_{4}\left[\left(F e(C N)_{6}\right] ; i=1+4 \alpha\right. \)
D. \( \left(N H_{4}\right)_{3} P O_{4} ; i=3+\alpha \)
Subject: Chemistry
Which of the following has the highest boiling point?
A. \( C_{3} H_{7} C l \)
в. \( C_{4} H_{9} C l \)
c. \( C H_{3} C H\left(C H_{3}\right) C H_{2} C l \)
D. \( \left(C H_{3}\right)_{3} C-C l \)
Subject: Physics
Two forces each of \( 10 \mathrm{N} \) act at an angle
\( 60^{0} \) with each other. The magnitude and direction of the resultant with respect
to one of the vectors is:
A \( \cdot \sqrt{10} \mathrm{N}, 30^{\circ} \)
B . \( 10 \sqrt{3} \mathrm{N}, 30^{\circ} \)
c. \( 20 \mathrm{N}, 120^{\circ} \)
D. \( 10 \sqrt{2} \mathrm{N}, 120^{\circ} \)
Subject: Maths
There are 4 white and 3 black balls in a
box. In another box there are 3 white and
4 black balls. An unbiased dice is rolled.
If it shows a number less than or equal
to
\( 3, \) then a ball is drawn from the first
box, but if it shows a number more than
3 , then a ball is drawn from the second
box. If the ball drawn is black, then the
probability that the ball was drawn from the first box is
A \( \cdot \frac{1}{2} \)
B. \( \frac{6}{7} \)
\( c \cdot \frac{4}{7} \)
D. 3 7
Subject: Physics
A body of mass \( m=3.513 \mathrm{kg} \) is moving
along the \( x \) -axis with a speed of
\( \mathbf{5 . 0 0 m s}^{-1} . \) The magnitude of its momentum is recorded as:
A . 17.56 kgms \( ^{-1} \)
в. 17.57 kgms\( ^{-1} \)
c. \( 17.6 \mathrm{kgms}^{-1} \)
D. 17.565 kgms\( ^{-1} \)
Subject: Physics
A uniform rod of length \( L \) rests against
a smooth wall as shown in figure. Find
the friction coefficient between the
ground and the lower end if the
minimum angle that the rod can make
with the horizontal is \( \theta \)
A \( \cdot \frac{L \cos ^{2} \theta \sin \theta}{2 h-l \cos \theta \sin ^{2} \theta} \)
B. \( \frac{L \cos \theta \sin ^{2} \theta}{2 h-l \operatorname{cs} \theta \sin ^{2} \theta} \)
c. \( \frac{L \cos ^{2} \theta \sin \theta}{2 h-l \cos ^{2} \theta \sin \theta} \)
D. \( \frac{L \cos \theta \sin ^{2} \theta}{2 h-l \cos ^{2} \theta \sin \theta} \)
Subject: Chemistry
Predict which of the following will be coloured in aqueous solution? \( \boldsymbol{T} \boldsymbol{i}^{3+}, \boldsymbol{V}^{3+}, \boldsymbol{C} \boldsymbol{u}^{+}, \boldsymbol{S} \boldsymbol{c}^{3+}, \boldsymbol{M} \boldsymbol{n}^{2+}, \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+} \) and
\( C o^{2+} . \) Give reasons for each
Subject: Maths
\( A B C D \) is a square of length \( a, a \in \)
\( N, a>1 . \) Let \( L_{1}, L_{2}, L_{3} \dots \dots, \) be point on
BC such that \( \boldsymbol{B} \boldsymbol{L}_{1}=\boldsymbol{L}_{1} \boldsymbol{L}_{2}=\boldsymbol{L}_{2} \boldsymbol{L}_{3}= \)
\( \ldots=1 \) and \( M_{1}, M_{2}, M_{3} \ldots \ldots \ldots \) be points
on CD such that \( \boldsymbol{C} \boldsymbol{M}_{\mathbf{1}}=\boldsymbol{M}_{\mathbf{1}} \boldsymbol{M}_{\mathbf{2}}= \)
\( =1 . \) Then \( \sum_{n=1}^{a-1}\left(A L_{2}^{2}+L_{n} M_{n}^{2}\right) \) is
equal to
A \( \cdot \frac{1}{2} a(a-1)^{2} \)
B.
\[
\frac{1}{2}(a-1)(2 a-1)(4 a-1)
\]
c.
\[
\frac{1}{2} a(a-1)(4 a-1)
\]
D. None of these
Subject: Maths
If \( \boldsymbol{y}=\boldsymbol{e}^{-\boldsymbol{x}} \cos \boldsymbol{x}, \) show that \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}= \)
\( 2 e^{-x} \sin x \)
Subject: Maths
\( \mathrm{f} \frac{d y}{d x}+\sqrt{\frac{1-y^{2}}{1-x^{2}}}=0 . \) Prove that,
\( \boldsymbol{x} \sqrt{1-\boldsymbol{y}^{2}}+\boldsymbol{y} \sqrt{1-\boldsymbol{x}^{2}}=\boldsymbol{A} \) where \( \mathbf{A} \) is
constant.
Subject: Maths
A rectangle has two opposite vertices at the points (1,2) and \( (5,5) . \) If the other
vertices lie on the line \( x=3 \), then the
coordinates of the other vertices are
\( \mathbf{A} \cdot(3,-1),(3,-6) \)
в. (3,1),(3,5)
C . (3,2),(3,6)
D. (3,1),(3,6)
Subject: Physics
Geeta placed three objects made of different materials as shown in the
figure. She observed a bright spot of light at (II) but (III) would not get any spot. Then,
A. (I) and (II) are made of transparent materials and (III) is made of opaque material
B. (I) is made of transparent material,
(II) is made of translucent material and (III) is made of opaque material.
c. (।) is made of transparent material
(II) is made of opaque material and (III) is made of either transparent or opaque or translucent material
D. (I) and (II) are made of opaque material and (III) is made of transparent material.
Subject: Physics
A planar structure of length L and width Wis made of two different optical
media of refractive indices \( n_{1}=1.5 \)
and \( n_{2}=1.44 \) as shown in figure. If \( L> \)
\( >W, \) a ray entering from end \( A B \) will
emerge from end \( \mathrm{CD} \) only if the total internal reflection condition is met
inside the structure. For \( \boldsymbol{L}=\mathbf{9 . 6 m}, \) if
the incident angle \( \theta \) is varied, the
maximum time taken by a ray to exit
the plane \( \mathrm{CD} \) is \( t \times 10^{-9} \mathrm{s} \), where \( \mathrm{t} \) is
[Speed of light \( c=3 x \)
\( \left.10^{8} \mathrm{m} / \mathrm{s}\right] \)
Subject: Maths
In a cuboid, if the sum of the lenghth of
edges is represented by \( S \), the total
surface area is represented by \( \boldsymbol{T} \) and the length of diagonal is represented by
\( D, \) then the value of \( D \) is
A \( \cdot \sqrt{\frac{52}{4}-T} \)
В. \( \sqrt{\frac{S^{2}}{14}-T} \)
c. \( \sqrt{\frac{s^{2}}{16}+T} \)
D. \( \sqrt{\frac{S^{2}}{16}-T} \)
Subject: Chemistry
Given: \( C a O+C O_{2} \rightarrow C a C O_{3}+ \)
\( 40 \mathrm{kcal} / \mathrm{mole.} \) If \( 176 \mathrm{g} \) of \( \mathrm{CO}_{2} \) are
consumed, then how many \( k c a l \) of heat
are released?
A. \( 80 \mathrm{kcal} \)
в. 100 kcal
c. 120 kcal
D. 160 kcal
Subject: Chemistry
Increasing strength of H-bonding \( (\boldsymbol{X}- \)
\( --\boldsymbol{H}-\boldsymbol{X}) \) in \( \boldsymbol{S}, \boldsymbol{O}, \boldsymbol{F}, \boldsymbol{C l}, \boldsymbol{N} \) is:
A. \( C l<S<N<O<F \)
в. \( N<C l<S<O<F \)
c. \( S<C l<N<O<F \)
D. \( S<N<C l<O<F \)
Subject: Chemistry
The monomer \( (G=M e \text { or } C l) \) when
treated with Zieglar - Natta catalyst undergo polymerisation as shown in the figure. Which of the following statement is not true considering the process
given above?
\[
\begin{aligned}
\mathrm{n} / \sqrt{\backslash} \frac{\text { Zieglar-Natta }}{\text { Catalyst }} &=[\sqrt{1}]_{\mathrm{n}}=\\
& \text { cis-poly-1,3-butadiene }
\end{aligned}
\]
A. The general class of polymer formed is known as homopolymer
B. The polymer obtained is stereoregular
C. Buna-N can be prepared using above process
D. Synthetic rubber can be formed by above process using 1,3 - butadiene
Subject: Physics
Potential Energy(U) of a body of unit mass moving in a one-dimension conservative force field is given by \( U= \)
\( \left(x^{2}-4 x+3\right) . \) All units are in S.I.
(i) Find the equilibrium positions of the body
(ii) Show that oscillations of the body
about this equilibrium positions is simple harmonic motion \& find its time period.
(iii) Find the amplitude of oscillations if speed of the body at equilibrium position is \( 2 \sqrt{6} \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
Assertion
Sigma bond is stronger than pi bond.
Reason

The strength of a bond depends on the
extent of overlapping.
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
Distance between an object and plane
mirror is \( 100 \mathrm{cm} \). Find the distance
between the object and its image.
\( \mathbf{A} \cdot 50 \mathrm{cm} \)
B. \( 100 \mathrm{cm} \)
c. \( 200 \mathrm{cm} \)
D. \( 300 c m \)
E . \( 400 \mathrm{cm} \)
Subject: Physics
A bullet of mass \( 20 g \) and moving with a
velocity of \( 200 m / s \) strikes a heap of
sand and comes to rest after
penetrating \( 3 c m \) inside it. The force exerted by the sand on the bullet will be:
\( \mathbf{A} \cdot 11.2 \times 10^{8} d y n e \)
B . \( 15.7 \times 10^{8} \) dyne
c. \( 13.3 \times 10^{8} \) dyne
D. \( 18.6 \times 10^{8} \) dyne
Subject: Maths
The value of
\( \tan \left(\sin ^{-1}\left(\cos \left(\sin ^{-1} x\right)\right)\right) \tan \left(\cos ^{-1}(\sin \right. \)
where \( \boldsymbol{x} \boldsymbol{\epsilon}(\boldsymbol{0}, 1), \) is equal to
A .
в.
c. -1
D. none of these
Subject: Maths
The integral \( \int_{0}^{a} \frac{g(x)}{f(x)+f(a-x)} d x \)
vanishes, if
A \( \cdot g(x) \) is odd
B. \( f(x)=f(a-x) \)
c. \( g(x)=-g(a-x) \)
D. \( f(a-x)=-g(x) \)
Subject: Chemistry
To find the standard potential of \( M 3^{+} / M \) electrode, the following cell is constituted :
\( \boldsymbol{P t} / \boldsymbol{M} / \boldsymbol{M}^{3+}\left(\mathbf{0 . 0 0 1 m o l} \boldsymbol{L}^{-1}\right) / \boldsymbol{A} \boldsymbol{g}^{+}(\mathbf{0 . 0 1} \)
The emf of the cell is found to be 0.421
volt at \( 298 \mathrm{K} \) The standard potential of
half reaction \( M^{3}+3 e^{-} \rightarrow M \) at \( 298 \mathrm{K} \)
will be :
(Given \( \boldsymbol{E}_{A g^{+} / A g}^{e} \) at \( 298 \mathrm{K}=0.80 \) Volt
A. 0.32 volt
B. 0.66 Volt
c. 1.28 volt
D. 0.38 Volt