AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
If the equilibrium constant for the
reaction \( 2 X Y \rightleftharpoons X_{2}+Y_{2} \) is 81
what is the value of equilibrium constant for the reaction?
\( \boldsymbol{X} \boldsymbol{Y} \rightleftharpoons \frac{1}{2} \boldsymbol{X}_{2}+\frac{1}{2} \boldsymbol{Y}_{2} \)
\( \mathbf{A} \cdot 81 \)
B. 9
\( c .6561 \)
D. 40.5
Subject: Biology
In birds, males carry two identical sex chromosomes \( (\mathrm{ZZ}) \) and females carry two different sex chromosomes \( (\mathrm{ZW}) . \) A
gene in parakeets called cinnamon is
sex-linked recessive on the \( z \)
chromosome.
If a cinnamon male is crossed with a
normal female, what percentage of the offspring will be cinnamon?
A. All of the males only
B. All of the females only
c. All of the offspring
D. None of the offspring
Subject: Maths
The mode of the following discrete series is:
12 \( \boldsymbol{x}_{i} \quad 1 \quad 3 \quad 5 \quad 6 \)
\( f_{i} \quad 5 \quad 7 \quad 3 \) 8
\( \mathbf{A} \cdot \mathbf{3} \)
B. 12
c. 8
D. 6
Subject: Maths
\( \mathbf{A} \triangle \boldsymbol{A} \boldsymbol{B} \boldsymbol{C} \) in which \( \boldsymbol{A} \boldsymbol{B}= \)
\( \mathbf{5 . 4} \mathbf{c m}, \angle \boldsymbol{C} \boldsymbol{A} \boldsymbol{B}=\mathbf{4 5}^{\circ} \) and \( \boldsymbol{A} \boldsymbol{C}+\boldsymbol{B} \boldsymbol{C}= \)
\( \mathbf{9} \mathrm{cm} . \) Then, perimeter of \( \Delta \boldsymbol{A B C} \) is
A. \( 14.4 \mathrm{cm} \)
B. \( 11.4 \mathrm{cm} \)
\( c .12 .4 \mathrm{cm} \)
D. \( 15.4 \mathrm{cm} \)
Subject: Biology
The formula of Auxin-A is
A. \( \mathrm{C}_{18} \mathrm{H}_{30} \mathrm{O}_{7} \)
the
в. \( \mathrm{c}_{10} \mathrm{H}_{9} \mathrm{NO}_{2} \)
\( \mathbf{c} \cdot \mathbf{c}_{12} \mathbf{H}_{30} \mathbf{O}_{6} \)
D. \( \mathrm{c}_{20} \mathrm{H}_{30} \mathrm{O}_{5} \)
Subject: Maths
In a box containing only purple and green marshmallows, 6 marshmallows
are purple. If the probability of choosing
a purple marshmallow from the box is \( \frac{1}{3}, \) calculate the number of green marshmallows in the box.
\( A \cdot 2 \)
B. 6
c. 9
D. 12
E . 18
Subject: Physics
A student determined to test the law of
gravity for himself walks off a
skyscraper \( 320 m \) high with a stopwatch in hand and starts his free
fall (zero initial velocity). 5 seconds later, superman arrives at the scene
and dives off the roof to save the
student. what must be superman's initial velocity in order that he catches the student just before reaching the ground? [assume that superman's acceleration is that of a free-falling body, \( \left.g=10 m / s^{2}\right] \)
B . \( 25.8 \mathrm{ms}^{-1} \)
c. \( 4.785 \mathrm{ms}^{-1} \)
D. Cannot be determined
Subject: Physics
Assertion (A): With increase of
temperature,elastic property of a substance decreases.

Reason (R) : Elasticity is due to intermolecular forces which decreases
with the increase of intermolecular
distance.
A. Both assertion and reason are true and the reason is correct explanation of the assertion
B. Both assertion and reason are true, but reason is not correct explanation of the assertion
c. Assertion is true, but the reason is false
D. Assertion is false, but the reason is true
Subject: Physics
The temperature of liquid hydrogen is 20 K. What is this temperature on the Fahrenheit scale?
A \( \cdot 495.4^{\circ} \mathrm{F} \)
B . \( -423.4^{\circ} F \)
c \( .-108.56^{\circ} \mathrm{F} \)
D. \( -487.4^{\circ} F \)
Subject: Physics
A homogeneous chain of length \( L \) lies
on a table. Some part of chain is
hanging down the table. The coefficient of friction between the chain and the
table is \( \mu . \) The maximum length which can hangover the table in equilibrium is
A \( \cdot \frac{\mu L}{1+\mu} \)
в. \( \left(\frac{1-\mu}{\mu}\right) L \)
\( ^{C}\left(\frac{1-\mu}{1+\mu}\right)^{2} \)
D. \( \left(\frac{2 \mu}{1+2 \mu}\right) \)
Subject: Chemistry
The same quantity of electricity is passed through \( A l_{2}\left(S O_{4}\right)_{3} \) and \( A g N O_{3} \) solution with platinum electrodes. If \( n \) number of Al atoms are deposited on the cathode, the number of Ag atoms deposited on the cathode will be:
\( A \)
B. 2n
\( c \cdot 3 n \)
D. n/2
Subject: Maths
The volume of hollow sphere is
A \( \cdot \frac{4}{3} \pi \quad\left(R^{3}-r^{3}\right) c m^{3} \)
B・\frac{2 } { 3 } \pi \( \quad\left(R^{3}-r^{3}\right) c m^{3} \)
\( \mathbf{c} \cdot \frac{1}{2} \pi \quad\left(R^{3}-r^{3}\right) c m^{3} \)
Subject: Physics
A converging lens of focal length 6.25 \( \mathrm{cm} \) is used as a magnifying glass. If near point of the observer is \( 25 \mathrm{cm} \) from the eye and the lens is held close to the eye, then the magnification is :
\( A \cdot 4 \)
B. 5
\( c \cdot 8 \)
D. 10
Subject: Maths
If \( \boldsymbol{X}=\{1,2,3,4,5,6,7,8,9,10\} \) is the
universal set and \( \boldsymbol{A}=\{1,2,3,4\}, B= \)
\( \{2,4,6,8\}, C=\{3,4,5,6\} \) verify the
following.
(a) \( \boldsymbol{A} \cup(\boldsymbol{B} \cup \boldsymbol{C})=(\boldsymbol{A} \cup \boldsymbol{B}) \cup \boldsymbol{C} \)
\( (b) A \cap(B \cup C)=(A \cap B) \cup(A \cap C) \)
(c) \( \left(\boldsymbol{A}^{\prime}\right)^{\prime}=\boldsymbol{A} \)
A. Only a is true
B. Only b and c are true
c. only a and b are true
D. All three a, b and c are true.
Subject: Maths
Out of the following numbers, which cannot be represented on a number line? \( \mathbf{0}, \frac{\mathbf{5}}{6}, 1, \frac{2}{4} \)
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{5}{6} \)
c. 1
D. None of these
Subject: Chemistry
The heat capacity at constant volume of a sample of a monoatomic gas is \( \mathbf{3 1 . 8 6 7} J / K . \) Find the internal energy at
\( 300^{\circ} \mathrm{C} \)
A. \( 8.88 k J \)
J
в. \( 9.56 k J \)
\( c .3 .56 k J \)
D. \( 8.96 k J \)
Subject: Maths
Let the sequences \( a_{1}, a_{2}, a_{3}, \dots \dots, a_{n}, \dots \)
from an AP. Then \( a_{1}^{2}-a_{2}^{2}+a_{3}^{2}-a_{4}^{2}+ \)
\( \ldots+a_{2 n-1}^{2}-a_{2 n}^{2} \) is equal to
A \( \cdot \frac{n}{2 n-1}\left(a_{1}^{2}-a_{2 n}^{2}\right) \)
B. \( \frac{2 n}{n-1}\left(a_{2 n}^{2}-a_{1}^{2}\right) \)
c. \( \frac{n}{n+1}\left(a_{1}^{2}+a_{2 n}^{2}\right) \)
D. None of these
Subject: Physics
A can travelling at a speed of \( 20 \mathrm{m} / \mathrm{sec} \) to due north along the highway make it turns on to a side word that has due
east. If takes 50 sec for the ear to comp
lite the 50 sec for the end of 50 sec the
ear has a speed of \( 15 \mathrm{m} / \mathrm{sec} \) along the side road. Determine the magnitude of an acceleration over the 50 sec internal.
Subject: Maths
Suppose \( X \) has a binomial distribution \( B \) of \( 6, \frac{1}{2} . \) Show that \( X=3 \) is the most likely outcome
(Hint \( : P(X=3) \) is the maximum
among all \( \left.\boldsymbol{P}\left(\boldsymbol{x}_{i}\right), \boldsymbol{x}_{i}=\mathbf{0}, \mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}, \boldsymbol{6}\right) \)
Subject: Chemistry
There is change in the type of
hybridisation when:
This question has multiple correct options
\( \mathbf{A} \cdot N H_{3} \) combines with \( H^{+} \)
B. \( A l H_{3} \) combines with \( H^{-} \)
\( \mathbf{C} \cdot N H_{3} \) forms \( N H_{2} \)
D. \( \operatorname{Si} F_{4} \) forms \( \operatorname{Si} F_{4}^{2-} \)
Subject: Physics
The difference between angular speed
of minute hand and second hand of a
clock is
A \( \cdot \frac{59 \pi}{900} \operatorname{rad} / \mathrm{s}^{-1} \)
в. \( \frac{59 \pi}{1800} \mathrm{rad} / \mathrm{s}^{-1} \)
c. \( \frac{59 \pi}{2400} \mathrm{rad} / \mathrm{s}^{1} \)
D. \( \frac{59 \pi}{3600} \mathrm{rad} / \mathrm{s}^{-1} \)
Subject: Maths
\( \left(14 x^{2} y z-28 x^{2} y^{2} z^{3}+32 y^{2} z^{2}\right) \div \)
\( (-4 x y) \)
A. \( \frac{7}{2} y z+7 x y z^{2}+8 x y z \)
B. \( -\frac{7}{2} x z+7 x y z^{3}-\frac{8 y z^{2}}{x} \)
c. \( -\frac{7}{2} x z-7 x y z^{3}+\frac{8 y z^{2}}{x} \)
D. \( \frac{7}{2} x z-7 x y z^{2}-\frac{8 y z^{2}}{x} \)
Subject: Chemistry
What are \( X \) and \( Y \) in the following reaction? \( \boldsymbol{C F}_{2} \boldsymbol{C l}_{2} \stackrel{\boldsymbol{u v}}{\longrightarrow} \boldsymbol{X}+\boldsymbol{Y} \)
\( \mathbf{A} \cdot \dot{C} l C F_{2}, \dot{C l} \)
в. \( C_{2} F_{4}, C l_{2} \)
c. \( C \dot{F} C l_{2}, \dot{F} \)
\( \mathbf{D} \cdot: C C l_{2}, F_{2} \)
Subject: Physics
Three observers \( A, B \) and \( C \) measure the speed of light coming from a source
as \( v_{A}, v_{B} \) and \( v_{C} . \) Observer \( A \) moves
towards the source, \( C \) moves away from source and \( B \) stays stationary. The surrounding medium is water. If \( A \) and C are moving at the same speed, then This question has multiple correct options
A \( \cdot v_{A}>v_{B}>v_{C} \)
в. \( v_{A}<v_{B}<v_{C} \)
c. \( v_{A}=v_{B}=v_{C} \)
D. \( v_{B}=\frac{1}{2}\left(v_{C}+v_{A}\right) \)
Subject: Chemistry
The purpose of stream of air in leaching
process of \( A g_{2} S \) is to?
A. Oxidises \( N a_{2} S \) formed into \( N a_{2} S_{2} O_{3} \)
B. Oxidises \( N a_{2} S \) formed into \( N a_{2} S_{2} O_{4} \)
c. oxidises \( N a_{2} S \) formed into \( N a_{2} O \)
D. Act as catalyst
Subject: Physics
In the figure shown, angle of repose is
\( 45^{0} . \) Find the force of friction, net force
and acceleration of the block when:
\( \boldsymbol{\theta}=\boldsymbol{3} \boldsymbol{0}^{0} \)
2)1) \( \boldsymbol{\theta}=\mathbf{4 5}^{\mathbf{0}} \)
3)1) \( \boldsymbol{\theta}=\mathbf{6 0}^{\mathbf{0}} \)
Subject: Physics
Figure shows a balanced Wheatstone
net. Now, it is disturbed by changing \( \mathrm{P} \)
to \( 11 \omega \).Which of the following steps will
not bring the bridge to balance again?
A. Increasing R by \( 2 \omega \)
B. Increasing S by \( 20 \omega \)
C. Increasing Q by \( 10 \omega \)
D. Making product \( R Q=2200\left(\omega^{2}\right) \)
Subject: Biology
Assertion
Montreal protocol, was signed at Montreal (Canada) in 1987 to control the
emission of ozone depleting substances.
Reason
Kyoto protocol, held in kyoto (Japan) in
\( 1997, \) has specified the commitments of
different countries to mitigate climate
change.
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
The area of the region lying between the
line \( \boldsymbol{x}-\boldsymbol{y}+\mathbf{2}=\mathbf{0} \) and the curve \( \boldsymbol{x}= \)
\( \sqrt{\boldsymbol{y}} \) is
\( \mathbf{A} \cdot \mathbf{9} \)
B. \( \frac{9}{2} \)
c. \( \frac{10}{3} \)
D. none
Subject: Physics
The moment of inertia of a uniform thin
sheet of mass \( M \) of the given shape
about the specified axis is (axis and
sheet both are in the same plane):
A \( \cdot \frac{7}{12} M a^{2} \)
B \( \cdot \frac{5}{12} M a^{2} \)
c. \( \frac{1}{3} M a^{2} \)
D. \( \frac{1}{12} M a^{2} \)
Subject: Maths
If \( \boldsymbol{x}+\boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c}=\boldsymbol{0}, \) then what is the
value of \( \left|\begin{array}{ccc}\boldsymbol{x}+\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{a} & \boldsymbol{x}+\boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{x}+\boldsymbol{c}\end{array}\right| ? \)
\( \mathbf{A} \cdot \mathbf{0} \)
B \( \cdot(A+B+C)^{2} \)
c. \( A^{2}+B^{2}+C^{2} \)
D. \( A+B+C-2 \)
Subject: Maths
n Fig., a circle touches all the four side
of a quadrilateral \( A B C D \) whose sides
\( A B=6 c m, B C=7 c m \) and \( C D= \)
\( 4 \mathrm{cm} . \) Find \( \boldsymbol{A D} \)
\( A \cdot 2 c m \)
B. 5 cm
\( c .3 c m \)
D. \( 4 \mathrm{cm} \)
Subject: Maths
If \( a x^{3}+b x^{2}+c x+d \) is divided by \( x \)
2, then the remainder is equal
A \( . d \)
B. \( a-b+c-d \)
c. \( 8 a+4 b+2 c+d \)
D. \( -8 a+4 b-2 c+d \)
Subject: Physics
A transformer with a \( 110 V \) primary has
a 15: 1 turns ratio. The load resistance,
\( R_{L}, \) is \( 120 . \) What is the approximate voltage across the load?
A . \( 7.3 V \)
B. \( 73 V \)
\( c .88 V \)
D. \( 880 V \)
Subject: Maths
A value of \( C \) for which the conclusion of
Mean Value Theorem holds for the
function \( f(x)=\log _{e} x \) on the interval
[1,3] is
\( \mathbf{A} \cdot 2 \log _{3} e \)
B. \( \frac{1}{2} \log _{3} e \)
\( \mathbf{c} \cdot \log _{3} e \)
D. \( 2 \log _{e} 3 \)
Subject: Physics
An inductive circuit contains
resistance of 10 ohms and an
inductance of \( 20 \mathrm{H} \). If an A.c voltage of 120 volt and frequency \( 60 \mathrm{Hz} \) is applied to this circuit, the current would be
nearly
A. \( 0.16 a m p \)
B. \( 0.3 a m p \)
c. \( 0.48 a m p \)
D. \( 0.80 a m p \)
Subject: Maths
The value of the expression \( ^{47} C_{4}+ \) \( \sum_{j=1}^{5} 52-j C_{3} \) is
\( \mathbf{A} .^{51} C_{4} \)
B. \( ^{52} C_{4} \)
c. \( ^{52} C_{3} \)
D. \( ^{53} C_{4} \)
Subject: Physics
A voltmeter of resistance \( 998 \Omega \) is
connected across a cell of emf \( 2 \mathrm{V} \) and
internal resistance 2\Omega. The potential difference across the voltmeter is?
\( \mathbf{A} \cdot 1.99 \mathrm{v} \)
B. 3.5v
c. \( 5 v \)
D. \( 6 v \)
Subject: Maths
In how many ways can 6 boys and 5 girls can be seated in a row such that no two
girls are together?
A . \( 6 ! 5 \)
в. \( 2 \times 5 ! 5 \)
c. \( 6 ! \times^{7} P_{5} \)
D. \( 6 ! 6 ! \)
Subject: Physics
When an object is placed \( 20 \mathrm{cm} \) from a complex lens then a real image is formed \( 30 \mathrm{cm} \) from the lens. Where
should the object be placed so that a real image of the same size is formed
by the lens.
A. object should be placed \( 24 \mathrm{cm} \) from the lens.
B. object should be placed \( 34 \mathrm{cm} \) from the lens.
c. object should be placed 14 cm from the lens.
D. object should be placed 30 cm from the lens
Subject: Physics
A stationary source is emitting sound
at a fixed frequency \( f_{0}, \) which is reflected by two cars approaching the source. The difference between the
frequencies of sound reflected from the
cars in \( 1.2 \% \) of \( f_{0} . \) What is the
difference in the speed of the cars (in km per hour) to nearest integer? The
cars are moving at constant speeds much smaller that the speed of sound
which is \( 330 m s^{-1} \)
A .2
B. 3
c. 5
D. 7
Subject: Maths
The construction of \( \Delta L M N \) when
\( M N=6 \mathrm{cm} \) and \( m \angle M=45^{\circ} \) is not
possible when difference between \( L M \)
and \( L N \) is equal to:
\( \mathbf{A} \cdot 6.9 \mathrm{cm} \)
B. \( 5.2 \mathrm{cm} \)
\( c .5 \mathrm{cm} \)
D. 4 ст
Subject: Physics
\( A 2 \mathrm{kg} \) disc of radius \( 0.5 \mathrm{m} \) accelerates from rest to 25 rad/s in 5 seconds. The
average power exerted on the disc is
A. 78.1 watts
B. 15.6 Watts
c. 28.1 watts
D. 40.6 watts
Subject: Chemistry
The acidic, basic and amphoteric oxides, respectively, are:
A. \( N_{2} O_{3}, L i_{2} O, A l_{2} O_{3} \)
в. \( M g O, C l_{2} O, A l_{2} O_{3} \)
c. \( N a_{2} O, S O_{3}, A l_{2} O_{3} \)
D. \( C l_{2} O, C a O, P_{4} O_{10} \)
Subject: Chemistry
If \( E_{F e^{2+} / F e}^{0}=-0.441 \mathrm{V} \) and \( E_{F e^{3+} / F e^{2+}}^{0}= \)
\( 0.771 \mathrm{V}, \) the standard \( \boldsymbol{E} \boldsymbol{M} \boldsymbol{F} \) of the
reaction,
\( \boldsymbol{F} \boldsymbol{E}+\mathbf{2} \boldsymbol{F} \boldsymbol{E}^{3+} \rightarrow \mathbf{3} \boldsymbol{F} \boldsymbol{E}^{2+} \) will be:
A \( .0 .330 V \)
\( V \)
B. \( 1.653 V \)
c. \( 1.212 V \)
D. \( 0.111 V \)
Subject: Chemistry
Diols (I-IV) which react with \( C r O_{3} \) in
aqueous \( H_{2} S O_{4} \) and yield products that readily under go dercarboxylation on heating, are:
\( (\mathrm{I}) \)
A. I and \( J \)
B. II and III
c. \( I I \) and \( I V \)
D. \( I \) and \( I V \)
Subject: Maths
If \( P Q R S \) is a square, \( A B \| S Q, A \) is
midpoint of \( S R \) and \( A C=C B, \) which
one is true?
A. \( S A=B Q \)
B. \( P C \) is the bisector of \( \angle S P Q \)
c. \( P C \) if produced will pass through \( R \)
D. All of these
Subject: Chemistry
Name the following reaction.
\( \boldsymbol{H}_{3} \boldsymbol{C}-\boldsymbol{B r}+\boldsymbol{A} \boldsymbol{g} \boldsymbol{F} \rightarrow \boldsymbol{H}_{3} \boldsymbol{C}-\boldsymbol{F}+ \)
\( A g B r \)
Subject: Chemistry
Calculate the de Broglie wavelength for a beam of electron whose energy is \( \mathbf{1 0 0} e V: \)
\( \mathbf{A} \cdot 1 A^{0} \)
B . \( 1.23 A^{\circ} \)
c. \( 2.46 A^{\circ} \)
D. None of these
Subject: Physics
The vector \( \hat{i}+x \hat{j}+3 \hat{k} \) is rotated
through an angle \( \theta \) and doubled in magnitude,then it becomes \( 4 \hat{i}+(4 x- \)
2)\( \hat{j}+2 \hat{k} . \) The value of \( x \) are
A \( \cdot-\frac{2}{3}, 2 \)
в. \( \frac{1}{3}, 2 \)
c. \( \frac{2}{3}, 2 \)
D. zero, 2
Subject: Physics
There is a point charge q located at the centre of a cube. What is the electric
flux of this point charge, through a face of the cube?
A \( \cdot \frac{q}{\epsilon_{0}} \)
в. \( \frac{q}{6 \epsilon_{0}} \)
c. \( \frac{q}{3 \epsilon_{0}} \)
D. It will depend on the size of the cube
Subject: Maths
Calculate the value of the following
determinant:
\( \left|\begin{array}{cccc}\mathbf{1}+\boldsymbol{a} & \mathbf{1} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \mathbf{1}+\boldsymbol{b} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}+\boldsymbol{c} & \mathbf{1} \\ \mathbf{1} & \mathbf{1} & \mathbf{1} & \mathbf{1}+\boldsymbol{d}\end{array}\right| \)
Subject: Physics
The sun subtends an angle of half a
degree at the pole of a concave mirror which has a radius of cutvature of \( 15 m \)
Then the size(diameter) of the image of
the sun formed by the concave mirror is
A \( .7 .5 \mathrm{cm} \)
B. \( 6.55 \mathrm{cm} \)
\( \mathrm{c} .3 .7 \mathrm{cm} \)
D. 13.1cm
Subject: Maths
In a group, if \( 60 \% \) of people drink tea and \( 70 \% \) drink coffee. What is the
maximum possible percentage of people drinking either tea or coffee but
not both?
\( \mathbf{A} \cdot 100 \% \)
B. \( 70 \% \)
\( c .30 \% \)
D. \( 10 \% \)
Subject: Maths
Which of the following options is
INCORRECT?
\( \mathbf{A} \cdot \angle 1=\angle 3 \)
B . \( \angle 1+\angle 4+\angle 5=180^{\circ} \)
\( \mathbf{c} \cdot \angle 8=\angle 6 \)
D. \( \angle 1+\angle 3=180^{\circ} \)
Subject: Chemistry
Total number of methyl group present in
product \( \boldsymbol{A} \) is:
\[
\underset{\mathrm{Me}}{\mathrm{N}}_{\mathrm{O}}^{\mathrm{OMe}}+2 \bigwedge_{\mathrm{Me}} \widehat{\mathrm{MgBr}} \frac{\mathrm{H}_{3} \mathrm{O}^{\oplus}}{\longrightarrow} \mathrm{A}
\]
Subject: Physics
The temperature \( (T) \) of two samples of
the same substance with masses \( \boldsymbol{m}_{1} \)
and \( m_{2} \) and temperatures \( T_{1} \) and \( T_{2} \) when added together is
A. \( \frac{m_{2} T_{1}+m_{1} T_{2}}{m_{1}+m_{2}} \)
в. \( \frac{m_{1} T_{1}+m_{2} T_{2}}{m_{1}+m_{2}} \)
c. \( m_{1} T_{1}+m_{2} T_{2} \)
D. \( m_{1} T_{2}+m_{2} T_{1} \)
Subject: Maths
The vectors \( 3 i+j-5 k \) and \( a i+b j- \)
\( 15 k \) are collinear, if
A \( . a=3, b=1 \)
в. \( a=9, b=1 \)
c. \( a=3, b=3 \)
D. \( a=9, b=3 \)
Subject: Maths
If \( A \) is the area and \( 2 s \) the sum of three
sides of a triangle, then
\( ^{\mathrm{A}} \cdot_{A} \leq \frac{s^{1.5}}{3 \sqrt{3}} \)
в. \( _{A} \leq \frac{s^{1.5}}{2} \)
\( ^{\mathrm{c}} \cdot_{A}>\frac{s^{1.5}}{\sqrt{3}} \)
D. None of these
Subject: Chemistry
\( C O_{2} \) gas along with solid (Y) is obtained when sodium salt (X) is
heated. \( (X) \) is again obtained when \( C O_{2} \)
gas is passed into aqueous solution of
(Y). Identify \( (X) \) and \( (Y) \) respectively.
A. \( N a_{2} C O_{3}, N a_{2} O \)
в. \( N a_{2} C O_{3}, \) NaOH
с. \( N a H C O_{3}, N a_{2} C O_{3} \)
D. \( N a_{2} C O_{3}, N a H C O_{3} \)
Subject: Maths
If two variates \( X \) and \( Y \) are connected
by the relation \( \boldsymbol{Y}=\frac{\boldsymbol{a} \boldsymbol{X}+\boldsymbol{b}}{\boldsymbol{c}}, \) where
\( a, b, c \) are constants such that \( a c<0 \)
then
\( ^{\mathbf{A}} \cdot_{\sigma_{Y}}=_{c}^{a} \sigma_{X} \)
в. \( _{\sigma_{Y}}=-\frac{a}{c} \sigma_{X} \)
c. \( _{\sigma_{Y}}=\frac{a}{c} \sigma_{X}+b \)
D. none of these
Subject: Chemistry
\( \mathbf{A} \)
42 molal solution of sodium chloride
in water causes an elevation in the
boiling point of water by \( 1.88 \mathrm{K} \). What is
the value of Van't Hoff factor? What does
it signify? \( \left[\boldsymbol{K}_{\boldsymbol{b}}=\mathbf{0 . 5 2} \boldsymbol{K} \mathbf{k g} \boldsymbol{m o l}^{-\mathbf{1}}\right] \)
Subject: Physics
Assertion
A point charge \( q \) is placed in front of a
solid conducting sphere. Electric field due to induced charges at the centre of
sphere is zero.
Reason
Electric field at point inside the solid
body of conductor is zero.
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
Pressure (P) exented by liquid on walls of the container when \( h= \) height of the liquid column, \( f= \) density, \( g \) is acceleration due to gravity
A. \( p=h f g \)
в. \( p=\frac{d f}{g} \)
c. \( _{p}=\frac{h g}{f} \)
D. \( p=\frac{d f}{h} \)
Subject: Physics
The arc \( A B \) with the centre \( C \) and the
infinitely long wire having linear charge density \( \lambda \) are lying in the same plane.
The minimum amount of work to be
done to move a point charge \( q_{0} \) from
point \( A \) to \( B \) through a circular path \( A B \)
of radius \( a \) is equal to:
A \( \cdot \frac{q_{0}^{2}}{2 \pi \varepsilon_{0}} \log \left(\frac{2}{3}\right) \)
в. \( \frac{q_{0} \lambda}{2 \pi \varepsilon_{0}} \log \left(\frac{3}{2}\right) \)
c. \( \frac{q_{0} \lambda}{2 \pi \varepsilon_{0}} \log \left(\frac{2}{3}\right) \)
D. \( \frac{q_{0} \lambda}{\sqrt{2} \pi \varepsilon_{0}} \)
Subject: Chemistry
i. \( 0.1 M \) ethanol
ii. \( \mathbf{0 . 1} \boldsymbol{M} \boldsymbol{B} \boldsymbol{a}_{3}\left(\boldsymbol{P} \boldsymbol{O}_{4}\right)_{3} \)
¡¡ii.0.1 \( M N a_{2} S O_{4} \)
Increasing order of freezing point
A \( \cdot(i i)<(i i i)<(i) \)
B. \( (i i i)<(i i)<(i) \)
c. \( (i)<(i i)<(i i i) \)
D. \( (i i)<(i)<(i i i) \)
Subject: Biology
Given below is a diagram of electrostatic precipitator. Identify \( \mathbf{A}, \mathbf{B} \)
\( \mathrm{C} \) and \( \mathrm{D} \) and select the correct option.
A. A- Negatively charged wire, B- Negatively charged dust particles, C- - Discharge corona, D- collection
B. A- Negatively charged wire, B- Discharge corona, CCollection plate, D- Negatively charged dust particles
c. A- Positively charged wire, B- Positively charged dust particles, C- Discharge corona, D- -collection plate
D. A-Positively charged wire, B- Discharge corona, CCollection plate, D- Positively charged dust particles
Subject: Chemistry
Amphoteric oxides of Mn and Cr are:
\( \mathbf{A} \cdot M n O \) and \( C r O \)
B. \( M n_{2} O_{3} \) and \( C r_{2} O_{3} \)
c. \( M n O_{2} \) and \( C r_{2} O_{3} \)
D. \( M n_{2} O_{7} \) and \( C r O_{3} \)
Subject: Maths
Integrate \( \int_{0}^{\pi} \frac{e^{\cos x}}{e^{\cos x}+e^{-\cos x}} d x \)
\( A \cdot \frac{\pi}{12} \)
\( B \cdot \frac{\pi}{3} \)
\( \mathbf{C} \cdot \frac{\pi}{4} \)
D. \( \frac{\pi}{2} \)
Subject: Maths
If \( I \) is the unit matrix of order \( n, \) where
\( k \neq 0 \) is a constant then \( \operatorname{adj}(k I)= \)
A \( \cdot k^{n}(\operatorname{adj} I) \)
B. \( k(\operatorname{adj} I) \)
c. \( k^{2}(\operatorname{adj} I) \)
D. \( k^{n-1}(\text { adj } I) \)
Subject: Maths
If \( \bar{E} \) and \( \overline{\boldsymbol{F}} \) are the complementary
events of events \( \boldsymbol{E} \) and \( \boldsymbol{F} \) respectively
and if \( \mathbf{0}<\boldsymbol{P}(\boldsymbol{F})<\mathbf{1}, \) then:
This question has multiple correct options
\( \mathbf{A} \cdot P(E / F)+P(\bar{E} / F)=1 \)
B \cdot \( P(E / F)+P(E / \bar{F})=1 \)
C \( \cdot P(\bar{E} / F)+P(E / \bar{F})=1 \)
D \( \cdot P(E / \bar{F})+P(\bar{E} / \bar{F})=1 \)
Subject: Physics
ABCD is a square of side \( 100 \mathrm{m} . \) A cyclist
P starts from \( A \) and moves towards \( B \)
with a speed of \( 4 \mathrm{m} / \mathrm{s} \). At the same instant, a second cyclist Q starts from B
and moves towards C with speed of 3
\( \mathrm{m} / \mathrm{s} . \) If the angular velocity of \( \mathrm{Q} \) relative
to \( P \) after \( t \) seconds is \( \frac{4 \sin \theta+n \cos \theta}{\sqrt{(100-4 t)^{2}+n t^{2}}} \)
rad/s, find value of \( n \)