AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Assertion
If \( \boldsymbol{H}_{2} \) and \( \boldsymbol{C l}_{2} \) enclosed separately in the
same vessel exert pressure of 100 and
200 mm respectively, their mixture in
the same vessel at the same
temperature will exert a pressure of
\( 300 m m \)
Reason
Dalton's law of partial pressures states that total pressure is the sum of partial
pressures.
Read the above assertion and reason
and choose the correct option regarding
¡t.
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: Chemistry
Number of \( \boldsymbol{H} \boldsymbol{C O}_{3}^{-} \) ions joined by \( \boldsymbol{H}- \)
bonding in \( \boldsymbol{K} \boldsymbol{H} \boldsymbol{C O}_{3} \) is:
A. 5
B.
\( c \cdot 3 \)
D.
Subject: Maths
Three vertical poles of heights \( h_{1}, h_{2} \)
and \( h_{3} \) at the vertices \( A, B \) and \( C \) of \( a \)
\( \triangle A B C \) subtend angles \( \alpha, \beta, \gamma \)
respectively at the circumcentre of the triangle. If \( \cot \alpha, \cot \beta, \cot \gamma \) are in \( A P \)
then \( h_{1}, h_{2}, h_{3} \) are in
\( A \cdot A P \)
в. GР
c. нр
D. None of these
Subject: Maths
\( x=t \cos t, y=t+\sin t . \) Then \( \frac{d^{2} x}{d y^{2}} \) at
\( t=\frac{\pi}{2} \) is
A \( \cdot \frac{\pi+4}{2} \)
в. \( -\frac{\pi+4}{2} \)
c. -2
D. none of these
Subject: Chemistry
Q Type your question
\( 2 H_{2} O_{2} \rightarrow 2 H_{2} O+O_{2}(g) \Delta H= \)
\( -99 k j / \) mole \( , \Delta s=+69 J K^{-1} \) mole \( ^{-1} \)
Addition of solution of KI causes \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
to decompose very rapidly as well
Step -1 (slow) \( \boldsymbol{H}_{2} \boldsymbol{O}_{2}+\boldsymbol{l} \rightarrow \boldsymbol{l} \boldsymbol{O}+\boldsymbol{H}_{2} \boldsymbol{O} \)
Step -2 (fast)
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2}+\boldsymbol{l} \boldsymbol{O} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{r}+\boldsymbol{O}_{2}(\boldsymbol{g}) \)
Overall reaction:
\( 2 H_{2} O_{2} \rightarrow H_{2} O+O_{2}(g) \)
The above experiment causes a big fluff of foam to spiral out of the beaker Elephant toothpaste reaction) Identify the wrong statement.
rhis question has multiple correct options
A \( \cdot H_{2} O_{2} \) is thermodynamically and kinetically unstable
B. LO (aq) is the reaction intemediate
c. the elephant tooth paste is hot to toch
D. a glowing splint if plunged into the elephant toothpaste will catch fire
Subject: Physics
Assertion
An object from a greater height reaches a steady terminal velocity.
Reason
The viscous forces on a body depends upon its velocity. The greater the velocity the greater is the viscous force.
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
From the observation of Ohm's law \( 1 \rightarrow \) V
graph is drawn here.

From that which points are concluded?
\( P: I \rightarrow V \) graph is a straight line.
Q: Ratio of V and I remains constant
every time.
R: The electric current in a conductor
increases in same proportion with the increase in voltage
A. Statements P, Q and R are all true
B. Statements Q and R are true
c. Statements P and R are true
D. Statements P and Q are true
Subject: Physics
The distance between two parallel wires carrying current of \( 1 A \) is 1 m. The force per unit length between the conductors
is
A \( \cdot 2 \times 10^{7} N m^{-1} \)
В. \( 2 \times 10^{-7} \mathrm{Nm}^{-1} \)
c. \( 4 \times 10^{7} N m^{-1} \)
D. \( 4 \times 10^{-7} \mathrm{Nm}^{-1} \)
Subject: Chemistry
Find the number of pi bonding
molecular orbital from the following set if z the internuclear axis :
\( \boldsymbol{p}_{z} \) and \( \boldsymbol{d}_{z^{2}}, \boldsymbol{p}_{\boldsymbol{x}} \) and \( \boldsymbol{d}_{\boldsymbol{x} z}, \boldsymbol{d}_{\boldsymbol{x} z} \) or \( \boldsymbol{d}_{\boldsymbol{y} z}, \boldsymbol{d}_{\boldsymbol{x} \boldsymbol{z}} \)
and \( \boldsymbol{d}_{\boldsymbol{y} \boldsymbol{z}} \)
Subject: Maths
If \( \boldsymbol{A}=\left(\begin{array}{ll}\mathbf{3} & \mathbf{5} \\ \mathbf{7} & \mathbf{9}\end{array}\right) \) is written as \( \boldsymbol{A}=\boldsymbol{P}+\boldsymbol{Q} \)
where \( \boldsymbol{P} \) is a symmetric matrix and \( \boldsymbol{Q} \) is skew-symmetric matrix, then write the \( \operatorname{matrix} \boldsymbol{P} \)
Subject: Maths
There are two candidates Bhiku and
Mhatre for an election. Bhiku gets \( 65 \% \) of the total valid votes. If the total votes
were \( 6000, \) what is the number of valid votes that the other candidate Mhatre
gets if \( 25 \% \) of the total votes were
declared invalid?
A. 1575
в. 1625
\( c .1675 \)
D. 1525
Subject: Maths
If \( A=\{a, b, c, d, e\}, B=\{a, c, e, g\} \) and \( C= \)
\( \{b, d, e, g\} \) then which of the following is
true?
A \( \cdot C \subset(A \cup B) \)
B . \( C \subset(A \cap B) \)
c. \( A \cup B=A \cup C \)
D. Both(1) and (3)
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 \( (\boldsymbol{Y}) \cdot(\boldsymbol{X}) \) and \( (\boldsymbol{Y}) \)
respectively are:
A \( . N a_{2} C O_{3} \) and \( N a_{2} O \)
в. \( N a_{2} C O_{3} \) and \( N a O H \)
c. \( N a H C O_{3} \) and \( N a_{2} C O_{3} \)
D. \( N a_{2} C O_{3} \) and \( N a H C O_{3} \)
Subject: Maths
If \( f(x)=\left(x^{2}-x+2\right)\left(x^{2}-4\right) \) then the
\( \operatorname{set}\{x \mid f(x)>0, x \in R\} \) is equal to
\( \mathbf{A} \cdot(-\infty,-2) \)
в. \( (2,+\infty) \)
c. (-2,2)
D \( \cdot(-\infty,-2) \cup(2,+\infty) \)
Subject: Chemistry
Which of these are the characteristics
of wave function \( \mathbf{\Psi} ? \)
This question has multiple correct options
A. \( \Psi \) must be single valued
в. \( \int_{-\infty}^{+\infty} \Psi^{2} d x d y d z=1 \)
c. \( \Psi \) must be finite and continous
D. \( \Psi \) represents a standing wave
Subject: Physics
The binding energy per nucleon of deuteron \( \left(_{1} H^{2}\right) \) and helium \( \left(_{2} H e^{4}\right) \) are
1.1 \( M e V \) and \( 7.0 \mathrm{MeV} \), respectively. The energy released when two deuterons fuse to form a helium
nucleus is
A. \( 36.2 \mathrm{MeV} \)
B. 23.6 MeV
c. \( 47.2 \mathrm{MeV} \)
D. \( 11.8 \mathrm{MeV} \)
E. \( 9.31 \mathrm{MeV} \)
Subject: Chemistry
\[
\begin{array}{c}
\text { Given: } S+\frac{3}{2} O_{2} \longrightarrow S O_{3}+2 x k c a l \\
S O_{2}+\frac{1}{2} O_{2} \longrightarrow S O_{3}+y k c a l
\end{array}
\]
With the help of the above reactions,
find out the heat of formation of \( \boldsymbol{S O}_{2} \)
A \( \cdot(2 x-y) \)
B . \( (x+y) \)
\( \mathbf{c} \cdot(2 x+y) \)
D \( \cdot(2 x / y) \)
Subject: Physics
A transformer has 500 primary turns and 10 secondary turns. If the secondary has resistive load of \( 15 \Omega \), the currents
in the primary and secondary respectively, are:
B. 3.2 \( \times 10^{-3} A, \) 0.16 \( A \)
c. 0.16 А, 0.16 А
D. 3.2 \( \times 10^{-3} A, 3.2 \times 10^{-3} A \)
Subject: Chemistry
\( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{C O O H}+\boldsymbol{C H}_{3} \boldsymbol{M} \boldsymbol{g} \boldsymbol{I} \rightarrow ? \)
\( \mathbf{A} \cdot C_{6} H_{5} C O O M g I \)
в. \( C H_{4} \)
c. Both a and \( b \)
D. none
Subject: Maths
In the set of all \( 3 \times 3 \) real matrices a
relation is defined as follows. A matrix
\( A \) is related to a matrix \( B \), if and only
there is a non-singular \( 3 \times 3 \) matrix \( P \)
such that \( B=P^{-1} A P . \) This relation is
A. reflexive,symmetric but not transitive
B. reflexive, transitive but not symmetric
c. symmetric, transitive but not reflexive
D. an equivalence relation
Subject: Physics
The fractional change in the value of free-fall acceleration \( g \) for a particle when it is lifted from the surface to an
elevation \( \boldsymbol{h}(\boldsymbol{h}<<\boldsymbol{R}) \) is :
A \( \cdot \frac{h}{R} \)
в. \( \frac{2 h}{R} \)
\( c \cdot-\frac{2 h}{R} \)
D. \( -\frac{h}{R} \)
Subject: Maths
Calculate the scalar product of the following vectors. The vector \( x \) satisfies the following conditions: \( (a) x \) is collinear with the
vector \( \boldsymbol{a}=\mathbf{6} \boldsymbol{i}-\boldsymbol{8} \boldsymbol{j}-\mathbf{7 . 5 k} ;(\boldsymbol{b}) \boldsymbol{x} \)
makes an acute angle with the Oz axis; \( (c)|x|=50 . \) Find the
coordinates of the vector \( x \)
Subject: Maths
If \( \vec{x} \) and \( \vec{y} \) are two non-collinear vectors and \( A B C \) is a triangle with sides \( a, b, c \) satisfying \( (20 a-15 b) \vec{x}+(15 b- \)
\( 12 c) \vec{y}+(12 c-20 a)(\vec{x} \times \vec{y})=\overrightarrow{0}, \) then
the triangle \( A B C \) is
A. An acute angle triangle
B. An obtuse angle triangle
c. A right angle triangle
D. An isosceles triangle
Subject: Chemistry
A balloon contains \( 14.0 L \) of air at
760 torr.. What will be the volume of
the balloon when it is taken to a depth
of \( 10 f t \) in a swimming pool? Assume that the temperature of the air and water are equal (density: \( \boldsymbol{H} \boldsymbol{g}= \) \( \mathbf{1 3 . 6} \boldsymbol{g} / \boldsymbol{m} \boldsymbol{L} \)
A . 11.0
в. 11.3
c. 10
D. 10.8
Subject: Chemistry
Available chlorine can be liberated from
bleaching powder by the reaction with:
This question has multiple correct options
A \( \cdot \) conc. \( H_{2} S O_{4} \)
в. \( d i l . H_{2} S O_{4} \)
\( c \cdot C O_{2} \)
D. \( d i l . H N O_{3} \)
Subject: Biology
Match column -I with column-II and
select the correct answer using the codes given below:
Column-I Colum -
\( \| \)
(A) Global warming Eutrophication
(B) Algal bloom
\( (q) C O \)
\( \mathbf{C O}_{\mathbf{2}} \)
(C) Nitrogen fixation Rhizobium
(D) Pseudomonas
(s) Fossil
Fuel
(E) Non-renewable resource
Denitrification
\( A \cdot(A)-p,(B)-q,(C)-r,(D)-t,(E)-s \)
B. (A)- q, (B)- \( p,(C)-r,(D)-t,(E)-s \)
C. \( (A)-q,(B)-p,(C)-r,(D)-s,(E)-s \)
D. \( (A)-q,(B)-p,(C)-s,(D)-r,(E)-t \)
Subject: Maths
Let \( [x] \) denote the greatest integer less than or equal to \( x \)
If \( f(x)=[x \sin \pi x], \) then \( f(x) \) is
This question has multiple correct options
A. continuous at \( x=0 \)
B. continuous in (-1,0)
c. differentiable at \( x=1 \)
D. differentiable in (-1,1)
E. none of these
Subject: Maths
A man on a wharf \( 12 \mathrm{mt} \) above the water
level pulls in a rope to which a boat is
attached at the rate of 1 mt per second.
At what rate is the boat approaching the shore, when there is still 13 mt rope out
?
\( \mathbf{A} \cdot 2.6 \mathrm{m} / \mathrm{sec} \)
B . \( 2 \mathrm{m} / \mathrm{sec} \)
c. \( 5 \mathrm{m} / \mathrm{sec} \)
D. \( 6.5 \mathrm{m} / \mathrm{sec} \)
Subject: Chemistry
Which of the following statement(s)
is/are false?
This question has multiple correct options
\( \mathbf{A} \cdot \Delta_{r} S \) for \( \frac{1}{2} C l_{2}(g) \rightarrow C l(g) \) is positive
B. \( \Delta E<0 \) for combustion of \( C H_{4}(g) \) in a sealed
container with rigid adiabatic system
C. \( \Delta G \) is always zero for a reversible process in a closed
system
D. \( \Delta G^{0} \) for an ideal gas reaction is a function of pressure
Subject: Chemistry
Nitrogen dioxide \( \left(N O_{2}\right) \) dissociates
into nitric oxide \( (N O) \) and oxygen \( \left(O_{2}\right) \)
as follows:
\( 2 N O_{2} \rightarrow 2 N O+O_{2} \)
If the rate of decrease of concentration
of \( N O_{2} \) is \( 6.0 \times 10^{-12} \) mol \( L^{-1} s^{-1} \)
What will be the rate of increase of
concentration of \( O_{2} ? \)
В. \( 6 \times 10^{-12} \) mol \( L^{-1} s^{-1} \)
D. \( 1.5 \times 10^{-12} \) mol \( L^{-1} s^{-1} \)
Subject: Maths
Factorize:
\( 4 a^{2}-12 a+9-49 b^{2} \)
A \( \cdot(2 a+7 b-3)(8 a-7 b-3) \)
в. \( (2 a-7 b-3)(8 a-7 b+3) \)
c. \( (2 a-7 b-3)(2 a-7 b+3) \)
D. \( (2 a+7 b-3)(2 a-7 b-3) \)
Subject: Maths
\( \left[\begin{array}{ccc}1 & 0 & 2 \\ -1 & 1 & -2 \\ 0 & 2 & 1\end{array}\right]+\left[\begin{array}{ccc}5 & 1 & -2 \\ 1 & 1 & 0 \\ -2 & -2 & 1\end{array}\right] \)
What will be the sum of the diagonal
elements of the resultant matrix.
A . 10
B. 6
\( c \)
\( D \)
Subject: Chemistry
Which of the reactions defines \( \Delta \boldsymbol{H}_{\boldsymbol{f}}^{o} \) ?
A. \( C_{\text {diamond}}+O_{2}(g) \longrightarrow C O_{2}(g) \)
B \( \cdot \frac{1}{2} H_{2}(g)+\frac{1}{2} F_{2}(g) \rightarrow H F(g) \)
C. \( N_{2}(l)+3 H_{2}(g) \longrightarrow 2 N H_{3}(g) \)
\( ^{\mathrm{D}} \cdot \operatorname{CO}(g)+\frac{1}{2} O_{2}(g) \rightarrow C O_{2}(g) \)
Subject: Physics
Two magnetic poles of pole strengths \( 324 m A-m \) and \( 400 m A-m \) are kept at
a distance of \( 10 \mathrm{cm} \) in air. The null point will be at a distance of
on the line joining the two poles, from the weak pole if they are like poles:
A. 4.73
B. 5
\( c .6 .2 \)
D. 5.27
Subject: Physics
A transverse harmonic wave on a string is described by
\( \boldsymbol{y}(\boldsymbol{x}, \boldsymbol{t})=\mathbf{3} \cdot \mathbf{0} \sin (\mathbf{3 6} \boldsymbol{t}+\mathbf{0 . 0 1 8} \boldsymbol{x}+\boldsymbol{\pi} / \mathbf{4}) \)
where \( x \) and \( y \) are in \( c m \) and \( t \) in s. The
positive direction of \( x \) is from left to
right.
(a) Is this a travelling wave or a stationary wave? If it is travelling what are the speed and direction of its propagation?
(b) What are its amplitude and
frequency?
(c) What is the initial phase at the
origin?
(d) What is the least distance between
two successive crests in the wave?
Subject: Maths
The statement \( P(n) " 1 \times 1 !+2 \times 2 !+ \)
\( \mathbf{3} \times \mathbf{3} !+\ldots+\boldsymbol{n} \times \boldsymbol{n} !=(\boldsymbol{n}+\mathbf{1}) ! \mathbf{1} " \)
A. True for all \( n>1 \)
B. Not true for any \( n \)
c. True for all \( n \epsilon N \)
D. None of these
Subject: Chemistry
The equilibrium constant for the reaction:
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{B} \boldsymbol{r}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{2} \boldsymbol{H} \boldsymbol{B} \boldsymbol{r}(\boldsymbol{g}) \)
is 67.8 at \( 300 K . \) The equilibrium
constant for the dissociation of \( \boldsymbol{H} \boldsymbol{B} \boldsymbol{r} \) is:
A . 0.0147
B. 67.8
c. 33.90
D. 8.349
Subject: Chemistry
The colour of \( C u C r_{2} O_{7} \) solution in
water is green because
A \( \cdot C u^{2+} \) ion is green
в. \( C r_{2} O_{7}^{2} \)
c. both the ions are green
D. \( C u^{2+} \) ion is blue and \( C r_{2} O_{7}^{2-} \) ion is yellow
Subject: Physics
The acceleration of a particle as
observed from two different frames \( S_{1} \)
and \( S_{2} \) have equal magnitudes of 2
\( m s^{-2} \)
This question has multiple correct options
A. The relative acceleration of the frame may either be zero or \( 4 \mathrm{ms}^{-2} \)
B. Their relative acceleration may have any value between zero to \( 4 \mathrm{ms}^{-2} \)
C. Both the frames may be stationary with respect to the earth
D. The frames may be moving with same acceleration in same direction
Subject: Physics
The figure shows a metre-bridge circuit, with \( A B=100 c m, X=12 \Omega \) and \( R= \)
\( 18 \Omega, \) and the jockey \( J \) in the position of
balance. If \( R \) is now made \( 8 \Omega \), through
what distance will \( J \) have to be moved
to obtain balance?
A . \( 10 \mathrm{cm} \)
B. 20 cm
\( c .30 \mathrm{cm} \)
D. \( 40 \mathrm{cm} \)
Subject: Maths
Let \( \mathrm{p}, \mathrm{q}, \mathrm{r} \in \boldsymbol{R}^{+} \) and \( 27 p q r \geq(p+q+ \)
\( r)^{3} \) and \( 3 p+4 q+5 r=12 \) then \( p^{3}+ \)
\( \boldsymbol{q}^{4}+\boldsymbol{r}^{\boldsymbol{5}} \) is equal to
\( A \cdot 2 \)
B. 6
\( c \cdot 3 \)
D. None of these
Subject: Physics
Three bulbs \( A, B \) and \( C \) are connected
as shown in figure. The bulbs \( B \) and \( C \)
are identical. If the bulb \( C \) is fused,
then:
A. Brightness of both bulbs \( A \) and \( B \) will increase
B. Brightness of both bulbs \( A \) and \( B \) will decrease
c. Brightness of the bulb \( A \) decrease and that of bulb \( B \) ncreases
D. None of the bulbs will glow
Subject: Chemistry
Match the column with types of polymer
in list I with their examples in list II.
List -
List - II
A) Natural Polymer
1) PVC
B) Ehene Polymer
2) Nylon - 6,6
C) Polyamide polymer
3) Silk
D) Vinylchloride polymer
4) Polyethylene
A. \( A-2, B-3, C-4, D-1 \)
в. \( A-3, B-2, C-1, D-4 \)
c. \( A-3, B-4, C-2, D-1 \)
D. \( A-3, B-2, C-4, D-1 \)
Subject: Physics
A conducting circular loop is placed in a uniform magnetic field, \( B=.025 \) T with its plane perpendicular to the loop The radius of the loop is made to shrink at a
constant rate of \( 1 \mathrm{mms}^{-1} \). The induced
e.m.f. when the radius is \( 2 \mathrm{cm} \), is
\( \mathbf{A} \cdot 2 \pi \mu V \)
в. \( \pi \mu V \)
c. \( \frac{\pi}{2} \mu V \)
D. \( 2 \mu V \)
Subject: Chemistry
f pressure increases then its effect on given equilibrium
\( \boldsymbol{C}(s)+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C} \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \)
It is shifted in:
A. forward direction
B. backward direction
c. no effect
D. none of these
Subject: Maths
Sonali pounded a stake into the ground, when she attached a rope to both the stake and her dog's collar, the dog could reach 9 feet from the stake in any direction. Find the approximate area of the lawn, in square feet, the dog could
reach from the stake. \( (\pi=3.14) \)
A . 28
B. 57
\( c .113 \)
D. 254
Subject: Maths
Solve: \( \cot \left(\cos e c^{-1} \frac{5}{3}+\tan ^{-1} \frac{2}{3}\right) \)
A \( \cdot \frac{6}{17} \)
в. \( \frac{3}{17} \)
c. \( \frac{4}{17} \)
D. \( \frac{5}{17} \)
Subject: Maths
The area lying in the first quadrant between the curves \( x^{2}+y^{2}=\pi^{2} \) and
\( y=\sin x \) and \( y- \) axis is
\( ^{A} \cdot \frac{\pi^{3}-8}{4} \) sq. units
B. \( \frac{\pi^{3}+8}{4} \) sq. units
c. \( 4\left(\pi^{3}-8\right) \) sq. units
D. \( \frac{\pi-8}{4} \) sq. units
Subject: Physics
A ball dropped from a point \( P \) crosses a
point \( Q \) in \( t \) second. if \( R \) and \( S \) are
points such that, \( P Q=Q R=R S \), the
time taken by the ball to travel from \( \boldsymbol{R} \)
to \( S \) is:
A. \( (\sqrt{2}-1) t \)
B . \( (\sqrt{3}-\sqrt{2}) t \)
c. \( \sqrt{3} t \)
D. \( (\sqrt{3}-1) t \)
Subject: Physics
Assume 100 pm \( X \) -ray beam is passed through YDSE. Interference pattern is observed on a photographic plate placed \( 40 \mathrm{cm} \) away from the slits. What should be the separation between the slits so that the separation between two successive maxima is \( 0.1 \mathrm{mm} \)
A \( .4 \mu m \)
в. \( 0.4 \mu m \)
\( c .4 n m \)
D. \( 40 \mu m \)
Subject: Maths
The ratio of the total surface area and
the lateral surface area of a right cone is 4: 3 and its height is \( 8 \mathrm{m}, \) then its base area is approx
A \( \cdot 24 m^{2} \)
B. \( 33 m^{2} \)
\( \mathbf{c} \cdot 21 m^{2} \)
D. \( 27 m^{2} \)
Subject: Maths
The mean of \( x_{1}, x_{2} \dots x_{50} \) is \( M, \) if every
\( \boldsymbol{x}_{i},=1,2 \ldots 50 \) is replaced by \( \boldsymbol{x}_{i} / \mathbf{5 0} \) then
the mean is
A.
в. \( _{M+\frac{1}{50}} \)
c. \( \frac{50}{M} \)
D. \( \frac{M}{50} \)
Subject: Physics
Find the difference of air pressure between the inside and outside of a
soap bubble \( 5 m m \) in diameter, if the
surface tension is \( 1.6 N / m \)
A \( \cdot 2560 N / m^{2} \)
В. \( 3720 N / m^{2} \)
\( \mathrm{c} \cdot 1208 \mathrm{N} / \mathrm{m}^{2} \)
D. \( 950 N / m^{2} \)
Subject: Physics
The angle between \( \overrightarrow{\boldsymbol{R}}=\mathbf{2} \hat{\mathbf{i}}+\mathbf{3} \hat{\boldsymbol{j}}-\mathbf{4} \hat{\boldsymbol{k}} \)
and y-axis is
\( ^{\mathrm{A}} \cdot \cos ^{-1}\left(\frac{2}{\sqrt{29}}\right) \)
в. \( \cos ^{-1}\left(\frac{3}{\sqrt{29}}\right) \)
\( ^{\mathrm{c}} \cdot \sin ^{-1}\left(\frac{3}{\sqrt{29}}\right) \)
D \( \cdot \tan ^{-1}\left(\frac{3}{\sqrt{29}}\right) \)
Subject: Chemistry
The rate of a reaction expressed in terms of change in concentration of products at two different times, that is the average rate in terms of product, can be written as ?
This question has multiple correct options
A \( \cdot \frac{x_{2}-x_{1}}{t_{2}-t_{1}} \)
B. \( +\Delta x / \Delta t \)
c. \( -\frac{x_{2}-x_{1}}{t_{2}-t_{1}} \)
D. \( -\Delta x / \Delta t \)
Subject: Chemistry
Consider the following statements and arrange in the order of true/false as given in the codes. \( S_{1}: \) Long form of periodic table completely helps in predicting the
oxidation state of elements.
\( S_{2}: \) Metallic and covalent radii of potassium are 203 pm and 230 pm respectively.
\( \boldsymbol{S}_{3}: \) Formation of \( \boldsymbol{S} \boldsymbol{e}^{2-} \) and \( \boldsymbol{A} \boldsymbol{r}^{-}, \) both
the absorption of energy.
A . FFT
в. गाग
c. \( \pi \mathrm{F} \)
D. TFT
Subject: Chemistry
Assertion
Vapor in its natural state is a solid or
liquid at room temperature.
Reason
Gas in its natural state at room
temperature would still be a 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. Both Assertion and Reason are incorrect
Subject: Physics
A short linear object of length \( b \) lies along the axis of a concave mirror of
focal length \( f \) at a distance u from the pole of the mirror. The size of the image is approximately equal to
\( A \)
\[
^{b}\left(\frac{u-f}{f}\right)^{\frac{1}{2}}
\]
в.
\[
b\left(\frac{b}{u-f}\right)^{\frac{1}{2}}
\]
\( c \)
\[
b\left(\frac{u-f}{f}\right)
\]
\( D \)
\[
b\left(\frac{f}{u-f}\right)^{2}
\]
Subject: Physics
A diminished image of an object is to be obtained on a screen \( 1.0 \mathrm{m} \) from it. This
can be achieved by appropriately placing
A. a concave mirror of suitable focal length
B. a convex mirror of suitable focal length
c. a convex lens of focal length less than \( 0.25 \mathrm{m} \)
D. a concave lens of suitable focal length
Subject: Maths
The sides of an \( 8 \times 8 \) square are cut by
certain points into pieces of length and 7,2 and 6,3 and 5 and 4 and 4 as
shown in the figure above. The area of
the quadrilateral determined by these
four points are
\( A \cdot 28 \)
в. 36
\( c \cdot 48 \)
\( D \)
Subject: Chemistry
The rate equation for the reaction \( \boldsymbol{A}+ \)
\( 2 B \rightarrow \) Products is given as rate\( = \)
\( \boldsymbol{K}[\boldsymbol{A}][\boldsymbol{B}]^{2} . \) If the volume of the vessel is
decreased to half of the initial volume,
then the reaction rate bears the
following relation to the original rate as:
A. \( 1 / 2 \) times
B. 2 times
c. 4 times
D. 8 times
Subject: Physics
Four similar particles of mass \( \mathrm{m} \) are orbiting in a circle of radius \( r \) in the
same angular direction because of their
mutual gravitational attractive force.
Velocity of a particle is given by
\( A \)
B. \( \sqrt{\frac{G m}{r}} \)
c. \( \sqrt{\frac{G m}{2}(1+2 \sqrt{2})} \)
\( \frac{1}{2}\left[\frac{G m}{r}\left(\frac{1+2 \sqrt{2}}{2}\right)\right]^{\frac{1}{2}} \)
Subject: Maths
If \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}\}, \boldsymbol{B}=\{\mathbf{3}, \mathbf{4}\} \)
find \( (A \times B) \cup(B \times A) \)
\( \mathbf{A} \)
\[
\{(1,3),(2,3),(3,3),(1,4),(2,4),(3,4),(3,1),(4,1),(3,2)
\]
B.
\[
\{(2,3),(3,3),(1,4),(2,4),(3,4),(3,1),(4,1),(3,2),(4,2)
\]
\( \mathbf{c} \)
\{(1,3),(2,3),(3,3),(1,4),(2,4),(3,4),(3,1),(4,1),(4,2)
D. None of these
Subject: Maths
The function \( f(x)= \) \( \frac{\log (1+a x)-\log (1-b x)}{x} \) is not
defined at \( x=0 . \) The value of which
should be assigned to \( f \) at \( x=0 \), is
\( \mathbf{A} \cdot a-b \)
B. \( a+b \)
\( \mathbf{c} \cdot \log a+\log b \)
D. None of these
Subject: Chemistry
The freezing point of equimolal aqueous solution will be highest for:
A. \( C_{6} H_{5} N H_{3}^{+} C l^{-} \)
в. \( \quad C a\left(N O_{3}\right)_{2} \)
c. \( _{L a}\left(N O_{3}\right)_{2} \)
D. \( C_{6} H_{12} O_{6} \)