AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A lens forms a real image of an object
on a screen placed at a distance of 100
\( \mathrm{cm} \) from the screen. If the lens is moved
by \( 20 \mathrm{cm} \) towards the screen, another image of the object is formed on the screen. The focal length of the lens is:
\( A \cdot 12 \mathrm{cm} \)
B. 24 \( \mathrm{cm} \)
\( c \cdot 36 \mathrm{cm} \)
D. \( 48 \mathrm{cm} \)
Subject: Chemistry
For the following equilibrium, \( N_{2} O_{4} \rightleftharpoons \)
\( 2 N O_{2} \) in gaseous phase, \( N O_{2} \) is \( 50 \% \) of
the total volume when equilibrium is
set up. Hence, percent of dissociation of
\( N_{2} O_{4} \) is:
A . 50\%
B. 25\%
c. \( 66.66 \% \)
D. 33.33\%
Subject: Physics
Find out the missing particle in the following nuclear reaction?
\( _{1}^{2} \boldsymbol{H}+_{29}^{63} \boldsymbol{C u} \rightarrow_{30}^{64} \boldsymbol{Z} \boldsymbol{n}+(?) \)
A. Proton
B. Neutron
c. Electron
D. Positron
E . Deuteron
Subject: Maths
In a building programme the event that all the materials will be delivered at the
correct time is \( M \) and the event that
the building programme will be completed on time is \( F . \) Given that \( \boldsymbol{P}(M)=\mathbf{0 . 8} \) and \( \boldsymbol{P}(\boldsymbol{M} \cap \boldsymbol{F})=\mathbf{0 . 6 5} \)
find \( \boldsymbol{P}(\boldsymbol{F} / \boldsymbol{M}) . \) If \( \boldsymbol{P}(\boldsymbol{F})=\mathbf{0 . 7}, \) find the
probability that the building programme will be completed on time if all the materials are not delivered at the
correct time.
\( ^{\mathbf{A}} \cdot P(F / M)=\frac{11}{16} ; P(F / \bar{M})=\frac{1}{6} \)
B. \( P(F / M)=\frac{15}{16} ; P(F / \bar{M})=\frac{1}{8} \)
\( ^{\mathbf{c}} \cdot P(F / M)=\frac{13}{16} ; P(F / \bar{M})=\frac{1}{4} \)
D. None of these
Subject: Physics
A solid sphere rolls without slipping on
a rough horizontal floor, moving with a
speed \( \boldsymbol{v} . \) It makes an elastic collision
with a smooth vertical wall. After
impact,

This question has multiple correct options
A. it will move with a speed \( v \) initially.
B. its motion will be rolling without slipping
C. its motion will be rolling with slipping initially and its rotational motion will stop momentarily at some instant.
D. its motion will be rolling without slipping only after some time.
Subject: Chemistry
Benzoic acid undergoes dimerisation
in benzene solution.The vant Hoff factor
is related to the degree of association
\( \alpha^{\prime} \) of the acid as :
A \( . i=1-\alpha \)
B . \( i=1+\alpha \)
C \( i=1-\frac{\alpha}{2} \)
D. \( i=1+\frac{\alpha}{2} \)
Subject: Maths
Find the area of the region bounded by
the curves \( y=\log _{e} x, y=\sin ^{4} \pi x, x= \)
\( \mathbf{0} \)
A \( \cdot \frac{11}{8} \) sq.units
B. \( \frac{9}{8} \) sq.units
c. \( \frac{13}{8} \) sq.units
D. \( \frac{15}{8} \) sq.units
Subject: Maths
Calculate all solutions of \( |z-1| \times \mid z- \)
\( \mathbf{1} \mid=\mathbf{1} \)
A. intersecting straight line passing through (1,0)
B. solutions are exactly the points of the circle with center (1,0) and radius 1
c. solutions are exactly the points of the circle with center (1,0) and radius \( \sqrt{2} \)
D. none of these
Subject: Maths
Construct a cyclic quadrilateral EFGH
with \( \mathrm{EF}=5.2 \mathrm{cm}, \angle \mathrm{GEF}=50^{\circ}, \mathrm{FG}=6 \mathrm{cm} \)
and \( \angle \mathrm{EGH}=40^{\circ} \)
Subject: Maths
The given graph represent the how much consumers would be willing to
pay for store brand and brand name
products. If a consumer is chosen at
random, then the probability that the
consumer is will to pay at least \( \$ 8 \) for
the product is \( \frac{u}{b}, \) where \( a, b \) are \( c 0 \)
primes. Find the value of \( b-a ? \)

Store Brand \( \square \) Brand Name
Subject: Chemistry
Which of the following is an endothermic
reaction
\( \mathbf{A} \cdot N_{2}(g)+3 H_{2}(g)-92 k J \rightarrow 2 N H_{3}(g) \)
B \( \cdot N_{2}(g)+O_{2}(g)+180.8 k J \rightarrow 2 N O(g) \)
\( \mathbf{c} \cdot H_{2}(g)+C l_{2}(g) \rightarrow 2 H C l(g)+184.6 k J \)
\( \mathbf{D} \cdot C(g r)+2 H_{2}(g) \rightarrow C H_{4}(g)+74.8 k J \)
Subject: Physics
A constant force acting on a body of mass \( 3.0 \mathrm{kg} \) changes its speed from \( 2.0 \mathrm{ms}^{-1} \) to \( 3.5 \mathrm{ms}^{-1} \) in \( 25 \mathrm{s} \). The
direction of the motion of the body
remains unchanged. What is the magnitude of the force (in newton)?
A . 0.18
в. 0.36
c. 0.72
D. 0.24
Subject: Maths
If \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma}, \boldsymbol{\delta} \) are the smallest \( + \) ive angles
in ascending order of magnitude which have their sines equal to a +ive quantity \( \lambda \) then the value of \( 4 \sin \frac{\alpha}{2}+ \) \( 3 \sin \frac{\beta}{2}+2 \sin \frac{\gamma}{2}+\sin \frac{\delta}{2}= \)
A \( \cdot 2 \sqrt{1-\lambda} \)
B. \( 2 \sqrt{1+\lambda} \)
c. \( 2 \sqrt{\lambda} \)
D. \( 2 \sqrt{\lambda+2} \)
Subject: Chemistry
Which of the following have identical bond order?
(I) \( \boldsymbol{C} \boldsymbol{N}^{-} \)
(II) \( \boldsymbol{O}_{\mathbf{2}}^{-} \)
\( (\|\|) N O^{+} \)
\( (\mid V) C N^{+} \)
A . ।, ॥
B. ॥, IV
c. ।, ॥।, ॥।
D. I, IV
Subject: Physics
A card sheet divided into squares each
of size \( 1 \mathrm{mm}^{2} \) is being viewed at a
distance of \( 9 \mathrm{cm} \) through a magnifying glass (a converging lens of focal length
\( 9 c m \) ) held close to the eye and the
magnifying glass if the virtual image of each square is to have an area of
\( 6.25 m m^{2} . \) Would you be able to see
the squares distinctly with your eyes very close to the magnifier?
Subject: Biology
Assertion
Forest influences local air circulation
and may thus retain solid suspensions and gaseous elements.
Reason
Forests control the wind velocity and air
flows.
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 one of the following is the differential equation that represents the family of curves \( y=\frac{1}{2 x^{2}-c} \) where
\( c \) is an arbitrary constant?
A \( \cdot \frac{d y}{d x}=4 x y^{2} \)
B. \( \frac{d y}{d x}=\frac{1}{y} \)
c. \( \frac{d y}{d x}=x^{2} y \)
D. \( \frac{d y}{d x}=-4 x y^{2} \)
Subject: Maths
If \( \boldsymbol{x}=\boldsymbol{a} \cos \boldsymbol{\theta} ; \boldsymbol{y}=\boldsymbol{b} \sin \theta, \) then find \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}} \)
Subject: Maths
f \( \boldsymbol{A}=\{\mathbf{5}, \boldsymbol{6}, \boldsymbol{7}, \boldsymbol{8}\} \) and \( \boldsymbol{B}=\{\boldsymbol{6}, \boldsymbol{8}, \boldsymbol{1} \boldsymbol{0}\} \)
find total elements in \( (\boldsymbol{A} \cup \boldsymbol{B}) \times(\boldsymbol{A} \cap \)
\( B) \)
Subject: Physics
A trolley is under the action of a
constant force \( F \). The sand contained by
it is poured out through a hole in the
floor at the rate of \( m \) per second.lf initial
mass of sand and trolley was \( M \) and
initial speed was \( u, \) the acceleration of
trolley at time \( t \) is given by
\( A \)
в.
c. \( \frac{F}{M-m} \)
D. \( \frac{F}{M+m} \)
Subject: Physics
The missing particle in the reaction:
\( \underset{99}{253} \boldsymbol{E} \boldsymbol{s}+_{2}^{4} \boldsymbol{H} \boldsymbol{e} \rightarrow_{101}^{256} \boldsymbol{M} \boldsymbol{d}+ \)
A. deuteron
B. proton
c. neutron
D. \( \beta \) - particle
Subject: Chemistry
Q Type your question
to
X). Assume that \( Y \) and \( Z \) are on the
same horizontal line, and \( z \) and \( X \) are on
the same vertical line. The area inside
the shape \( \boldsymbol{X}-\boldsymbol{Y}-\boldsymbol{Z}-\boldsymbol{X} \) is \( \mathbf{1 0 0 0} \boldsymbol{J} \)
If the heat absorbed by the gas during
process \( X-Y \) is \( 2000 J \) and the heat
released by the gas during process \( Y \)
\( Z \) is \( 3000 J \), how much heat is lost or
gained during process \( Z-X ? \)
A \( .2000 J \) is gained
B. \( 2000 \mathrm{J} \) is lost
c. \( 1000 J \) is gained
D. \( 1000 \mathrm{J} \) is lost
E. \( 5000 \mathrm{J} \) is gainec
Subject: Chemistry
Among \( \boldsymbol{B F}_{3}, \boldsymbol{N}\left(\boldsymbol{S} \boldsymbol{i} \boldsymbol{H}_{3}\right)_{3}, \boldsymbol{N}\left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{3}, \boldsymbol{O}\left(\boldsymbol{S} \boldsymbol{i} \boldsymbol{H}_{3}\right)_{2} \)
the number of molecules or molecular
ions which have back bonding is:
A . 1
B. 3
\( c \cdot 4 \)
D. all \( l \)
Subject: Physics
Three simple harmonic motions in the
same direction having the same amplitude a and same period are superposed. If each differs in phase
from the next by \( 45^{\circ}, \) then :
This question has multiple correct options
A. The resultant amplitude is \( (1+\sqrt{2}) a \)
B. The phase of the resultant motion relative to the first is \( 90^{\circ} \)
c. The energy associated with the resulting motion is \( (3+2 \sqrt{2}) \) times the energy associated with any single motion
D. The resulting motion is not simple harmonic
Subject: Chemistry
When hydrogen sulphide is reacted with sulphuric acid, which products are formed?
This question has multiple correct options
A . \( S \)
в. \( S O_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O} \)
\( \mathrm{D} \cdot \mathrm{SO}_{3} \)
Subject: Physics
Assertion: Virtual object can't be seen
by human eye. Reason: Virtual object is formed by
converging rays.
A. Both assertion and reason are correct and reason is
the correct explanation of the assertion
B. Both assertion and reason are correct, but reason is not the correct explanation of the assertion
C. Assertion is correct but reason is incorrect
D. Assertion is incorrect but Reason is correct
E. Both assertion and reason are incorrect
Subject: Maths
If \( a_{1}, a_{2}, a_{3} \dots \) are in A.P.with common
difference 'd',then
\( \tan \left\{\tan ^{-1}\left(\frac{d}{1+a_{1} a_{2}}\right)+\tan ^{-1}\left(\frac{d}{1+a_{2} a_{3}}\right)+\right. \)
is equal to
A \( \cdot \frac{(n-1) d}{a_{1}+a_{n}} \)
B \( \cdot \frac{(n-1) d}{1+a a_{n}} \)
c. \( \frac{(n-1) d}{1+a a a_{n}} \)
D. \( \frac{a_{n}-a_{1}}{a_{n}+a_{1}} \)
Subject: Maths
Let \( A \) and \( B \) be two events such that \( P(\overline{A \cup B})=\frac{1}{6}, P(A \cap B)=\frac{1}{4} \) and
\( P(\bar{A})=\frac{1}{4}, \) then events \( A \) and \( B \) are
A. equally likely, but not independent
B. equally likely and mutually exclusive
c. mutually exclusive and independent
D. independent but not equally likely
Subject: Physics
A train of length \( 100 m \) is moving in a
hilly region. At what speed must it approach a tunnel of length \( 80 m \) so that
a person at rest with respect to the tunnel will see that the entire train is in
the tunnel at one time?
A. \( 1.25 c \)
B. \( 0.8 c \)
c. \( 0.64 c \)
D. \( 0.6 c \)
E \( .0 .36 c \)
Subject: Chemistry
Which of the following statement(s)
is/are correct about the modern
periodic table?

This question has multiple correct options
A. It consists of \( s, p, d \) and \( f \) blocks
B. The energy levels filling order in 6 th period is \( 6 s, 4 f, 5 d \) and \( 6 p \)
C . III \( B \) group does not contain maximum number of elements
D. It consists only metals
Subject: Maths
If the roots of \( \frac{1}{x+a}+\frac{a}{x+b}=\frac{1}{c}, \) are equal in magnitude and opposite in sign, then the product of the roots is :
A \( \cdot-\frac{1}{2}\left(a^{2}+b^{2}\right) \)
B. \( \frac{1}{2}\left(a^{2}+b^{2}\right) \)
c. \( -\frac{3}{2}\left(a^{2}+b^{2}\right) \)
D. None
Subject: Maths
In a meeting, \( 70 \% \) of the members favour and \( 30 \% \) oppose a certain proposal. A member is selected at
random and we take \( \boldsymbol{X}=\mathbf{0} \) if he
opposed, and \( X=1 \) if he is in favour.
Find \( \boldsymbol{E}(\boldsymbol{X}) \) and \( \boldsymbol{V} \boldsymbol{a} \boldsymbol{r}(\boldsymbol{X}) \)
Subject: Chemistry
Label the hydrophilic and hydrophobic parts in the following compounds.
(i) \( \boldsymbol{C H}_{3}\left(\boldsymbol{C H}_{2}\right)_{10} \boldsymbol{C H}_{2} \boldsymbol{O} \boldsymbol{S} \overline{\boldsymbol{O}_{3}} \stackrel{+}{\boldsymbol{N} \boldsymbol{a}} \)
(ii) \( \boldsymbol{C H}_{3}\left(\boldsymbol{C H}_{2}\right)_{15} \stackrel{+}{\boldsymbol{N}}\left(\boldsymbol{C H}_{3}\right)_{3} \overline{\boldsymbol{B}} \boldsymbol{r} \)
(iii)
\( \boldsymbol{C H}_{3}\left(\boldsymbol{C H}_{2}\right)_{16} \boldsymbol{C O O}\left(\boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{O}\right)_{n} \boldsymbol{C H}_{2} \boldsymbol{C} \)
Subject: Maths
\( f-1+\cos 56^{\circ}+\cos 58^{\circ}+\cos 66^{\circ}= \)
\( k \sin 28^{\circ} \sin 29^{\circ} \sin 33^{\circ}, \) then the value
of k is
A . 1
B. 3
\( c \cdot 4 \)
D. 5
Subject: Chemistry
The correct IUPAC name of the following
hydrocarbon is :
A. 4,5 -diisopropyl-3-methylheptane
B. 3-methyl-4,5-diisopropylheptane
C. 5 -ethyl-4-isopropyl-3,6-dimethylheptane
D. 3-Ethyl-4-isopropyl-2,5-dimethylheptane
Subject: Physics
Assertion
At a point in space, the electric field points towards north. In the region,
surrounding this point the rate of
change of potential will be zero along
the east and west
Reason
Electric field due to a charge is in the
space around the charge
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
Assertion
Assertion: A solution of \( N H_{4} C l \) in
water is acidic in nature.
Reason
Reason : Ammoniun ions undergo
hydrolysis to form \( N H_{4} O H \)
A. If both the assertion and reason are true and reason is the correct explanation of assertion.
B. If both the assertion and reason are true but reason is not the correct explanation of assertion
c. If assertion is true but reason is false
D. If both assertion and reason are false
Subject: Chemistry
\( \begin{array}{ll}\text { List-I } & \text { List-II } \\ \text { (A) } O_{3}+C_{2} N_{2} & \text { (1) Black colour } \\ \text { (B) } H_{2} O_{2}+O_{3} & \text { (2) Rocket fuel } \\ \text { (C) } A g+O_{3} & \text { (3) Tailing } \\ \text { (D) } O_{3}+H g & \text { (4) } O_{2}+H_{2} O\end{array} \) The correct match is:
A. A-1, B-3, C-2, D-4
B. A-2, B-4, C-1, D-3
C. \( A-3, B-2, C-3, D-1 \)
D. \( A-4, B-1, C-4, D-2 \)
Subject: Maths
A function
\( f:[3,7) \rightarrow R \) is defined as
follows
\( f(x)=\left\{\begin{array}{cc}4 x^{2}-1 ; & -3 \leq x<2 \\ 3 x-2 ; & 2 \leq x \leq 4 \\ 2 x-3 ; & 4<x<7\end{array}\right. \)
Find \( \boldsymbol{f}(-\mathbf{2})-\boldsymbol{f}(\mathbf{4}) \)
Subject: Chemistry
The run of cyanamide \( N H_{2} C N \) with dioxygen was carried out in a bomb
calorie meter and \( \Delta u \) was found to be
\( -742.7 k J / m o l \)
Calculate the enthalpy for the reaction at \( 298 \mathrm{K} \)
\( N H_{2} C N(s)+\frac{3}{2} O_{2} \rightarrow N_{2}+C O_{2}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \)
Subject: Maths
If \( 1+\sin x+\sin ^{2} x+\sin ^{3} x+\ldots \infty \) is
equal to \( 4+2 \sqrt{3}, 0<x<\pi, \) then \( x \) is
equal to
\( ^{A} \cdot \frac{\pi}{6} \)
в.
c. \( \frac{\pi}{3} \) or \( \frac{\pi}{6} \)
D. \( \frac{\pi}{3} \) or \( \frac{2 \pi}{3} \)
Subject: Physics
Assertion (A): According to Newton's third law sum of action and reaction is
not equal to zero Reason (R) : The forces
action and reaction acts on different
bodies.
A. A and R are correct and R is the correct
explanation of
B. A and R are correct and R is not the correct
explanation A
c. \( A \) is true and \( R \) is false
D. A is false and R is true
Subject: Chemistry
Match the List I (Equations) with the List II (Type of Processes).

List I \( \quad \) List II (Type of processes) (Equations)
(а) \( K_{p}>Q \)
(i) Non-spontaneous
(b) \( \Delta G^{o}< \)
(ii) Equilibrium \( R T \log _{e} Q \)
(iii) Spontaneous and
(c) \( K_{p}=Q \quad \) endothermic
\[
\text { (d) } T>\frac{\Delta H}{\Delta S}
\]
(iv) Spontaneous
Select the correct matching code.
\( \mathbf{A} \cdot a \rightarrow i ; b \rightarrow i i ; c \rightarrow i i i ; d \rightarrow i v \)
в. \( a \rightarrow i v ; b \rightarrow i i i ; c \rightarrow i i ; d \rightarrow i \)
\( \mathbf{c} \cdot a \rightarrow i v ; b \rightarrow i ; c \rightarrow i i ; d \rightarrow i v \)
D. \( a \rightarrow i i ; b \rightarrow i ; c \rightarrow i i i ; d \rightarrow i v \)
Subject: Biology
A novel species with double stranded genetic material consists of 5 bases
namely P.Q. R. S. T. with percentages
given below.
Percentage 22
\( 28 \quad 22 \)
Based on the above information, which
ONE of the following infrences is NOT supported by the observation?
A. S- base pairs with T, and Q base pairs with R
B. S base pairs with \( Q \),and T base pairs with \( Q \)
C. P base pairs with \( R \), and \( S \) base pairs with \( Q \)
D. P base pairs with \( \mathrm{R} \), and T base pairs with \( \mathrm{Q} \)
Subject: Physics
A rubber ball of mass \( 4 \mathrm{kg} \) has the same diameter as a plastic ball of mass 0.5
kg. Both the balls are dropped simultaneously from the roof of a building.When they are \( 8 \mathrm{m} \) above the ground,they have the same
A. Kinetic energy
B. Potential energy
c. Momentum
D. Acceleration
Subject: Maths
The remainder when the determinant
\( \left|\begin{array}{lll}2014^{2014} & 2015^{2015} & 2016^{2016} \\ 2017^{2017} & 2018^{2018} & 2019^{2019} \\ 2020^{2020} & 2021^{2021} & 2022^{2022}\end{array}\right| \)
is divided by 5 is.
A . 1
B . 2
\( c \cdot 4 \)
\( D \)
Subject: Maths
The order and degree of the differential
equation. \( \left(\frac{d^{2} y}{d x^{2}}\right)^{3}+\left(\frac{d y}{d x}\right)=\int y d x \) are
respectively.
A . 2 and 3
B. 2 and 2
\( c .3 \) and 1
D. 3 and 2
Subject: Maths
Prove the following by using the principle of mathematical induction for
all \( \boldsymbol{n} \in \boldsymbol{N}: \mathbf{1 . 2}+\mathbf{2 . 2}^{\mathbf{2}}+\mathbf{3 . 2}^{\mathbf{2}}+\ldots \ldots . \)
\( \boldsymbol{n} \cdot \boldsymbol{2}^{n}=(\boldsymbol{n}-\mathbf{1}) \mathbf{2}^{n+\mathbf{1}}+\mathbf{2} \)
Subject: Maths
Find the derivative of \( \frac{2^{x} \cot x}{\sqrt{x}} \)
A \( \cdot \frac{2^{x}}{\sqrt{x}}\left\{\log 2 \cot x-\csc ^{2} x-\frac{\cot x}{2 x}\right\} \)
B. \( \frac{2(x+1)}{\sqrt{x}}\left\{\log 2 \cot x-\csc ^{2} x-\frac{\cot x}{2 x}\right\} \)
C \( \frac{2^{x}}{\sqrt{x}}\left\{\log 2 \cot x-\csc ^{2} x-\frac{\cot x}{x^{2}}\right\} \)
D. None of these
Subject: Physics
Two charged balls of the same radius and weight suspended on threads of equal length are immersed into a liquid having density of \( d_{1} \) and a dielectric constant \( K \)
The density \( d \) of the material of the balls for the angles of divergence of the
threads in the air and in the dielectric to
be the same is:
A \( \cdot \frac{K d}{K-1} \)
B. \( \frac{K-1}{K d} \)
C. \( \frac{d}{K-1} \)
D. \( \frac{K-1}{d} \)
Subject: Physics
A substance of mass \( m_{1} \) with specific
heat capacity \( s_{1} \) and initial
temperature \( \theta_{1} \) is mixed with another
substance of mass \( m_{2}, \) specific heat
capacity \( s_{2} \) and initial temperature \( \theta_{2} \) respectively. Then, their equilibrium
temperature is \( \left.\ldots \ldots \text { (take } \boldsymbol{\theta}_{1}>\boldsymbol{\theta}_{2}\right) \)
A \( \cdot \frac{m_{1} s_{1} \theta_{1}-m_{2} s_{2} \theta_{2}}{m_{1} s_{1}-m_{2} s_{2}} \)
В \( \cdot \frac{m_{1} s_{1} \theta_{1}-m_{2} s_{2} \theta_{2}}{m_{1} s_{1}+m_{2} s_{2}} \)
c. \( \frac{m_{2} s_{2} \theta_{2}-m_{1} s_{1} \theta_{1}}{m_{1}+m_{2}} \)
D. \( \frac{m_{1} s_{1} \theta_{1}+m_{2} s_{2} \theta_{2}}{m_{1} s_{1}+m_{2} s_{2}} \)
Subject: Maths
In the figure, an equilateral triangle of side \( 6 \mathrm{cm} \) and its circumcircle is shown
Find the area of shaded portion. Take \( (\boldsymbol{\pi}=\mathbf{3 . 1 4}, \sqrt{\mathbf{3}}=\mathbf{1 . 7 3}) \)
A. \( 22.11 \mathrm{cm}^{2} \)
B. \( 22 \mathrm{cm}^{2} \)
c. \( 21.11 \mathrm{cm}^{2} \)
D. \( 23.11 \mathrm{cm}^{2} \)
Subject: Physics
A body in a laboratory takes 4 minutes
to cool from \( 61^{\circ} \mathrm{C} \) and \( 59^{\circ} \mathrm{C} \). If the
laboratory temperature is \( 30^{\circ} C \) then
the time taken by it to cool from \( 51^{\circ} \mathrm{C} \) to
\( 49^{\circ} C \) will be:
\( A \cdot 8 \min \)
B. 6 min
\( c .5 \mathrm{min} \)
D. 4 min
Subject: Physics
The excess temperature of a body falls
from \( 12^{\circ} \mathrm{C} \) to \( 6^{\circ} \mathrm{C} \) in 5 minutes, then the
time to fall the excess temperature
from \( 6^{\circ} \mathrm{C} \) to \( 3^{\circ} \mathrm{C} \) is (assume the
Newton's cooling is valid)
A . 10 minutes
B. 7.5 minutes
c. 5 minutes
D. 2.5 minutes
Subject: Maths
The area between the curves \( x^{2}=4 y \)
and line \( \boldsymbol{x}+\mathbf{2}=\mathbf{4} \boldsymbol{y} \) is
A \( \cdot \frac{9}{8} \)
в. \( \frac{9}{4} \)
\( c \cdot \frac{9}{2} \)
D.
Subject: Maths
The angle between the lines \( 3 x+y- \)
\( \mathbf{7}=\mathbf{0} \) and \( \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\mathbf{9}=\mathbf{0} \) is
A \( \cdot \frac{\pi}{3} \)
в.
\( c \cdot \frac{\pi}{2} \)
D.
Subject: Chemistry
Write the balanced chemical equation for the last step of oxidation test of
sulphur.
A \( . B a C l_{2}+N a_{2} S O_{4} \rightarrow B a S O_{4}+2 N a C l \)
в. \( H C l+N a_{2} S O_{4} \rightarrow N a H S O_{4}+N a C l \)
c. \( B a C l_{2}+2 H C l \rightarrow 2 C l_{2}+B a+H_{2} \)
D. None of the above
Subject: Maths
\( f(x)=\lim _{n \rightarrow \infty} \sum_{k=1}^{n} \frac{n}{n^{2}+k^{2} x^{2}}, x>0 \) is
equal to
\( \mathbf{A} \cdot x \tan ^{-1}(x) \)
B \( \cdot \tan ^{-1}(x) \)
c. \( \frac{\tan ^{-1}(x)}{x} \)
D. none of the above
Subject: Maths
\( \ln \Delta A B C, B C=A B \) and \( \angle B=80^{\circ} \)
Then \( \angle A \) is equal to
A . \( 80^{\circ} \)
В . \( 40^{\circ} \)
\( c .50^{\circ} \)
D. \( 100^{\circ} \)
Subject: Maths
Find the solution of
\( (3 x+4 y-5)^{2} \frac{d y}{d x}=a^{2} \)
A \( \quad 4 y+\lambda=\frac{2 a}{\sqrt{3}} \tan ^{-1} \frac{(3 x+4 y-5) \sqrt{3}}{2 a} \)
B. \( 2 y+\lambda=\frac{5 a}{\sqrt{3}} \tan ^{-1} \frac{(3 x+4 y-5) \sqrt{3}}{2 a} \)
c. \( \quad 2 y+\lambda=\frac{2 a}{\sqrt{3}} \tan ^{-1} \frac{(3 x+4 y-5) \sqrt{3}}{2 a} \)
D. \( 4 y+\lambda=\frac{5 a}{\sqrt{3}} \tan ^{-1} \frac{(3 x+4 y-5) \sqrt{3}}{2 a} \)
Subject: Chemistry
Match the column:
Postulates Theory
p) Atoms are divisible into three
i. Dalton's subatomic particles \( \quad \) atomic theory
q) Discovery of the nucleus
i. Modern central positive charge) atomic theory
r) Atoms are indivisible
iii. Rutherford
s) Position of the electron
¡v. Neils Bohr
\( \mathbf{A} \cdot p \rightarrow i i, q \rightarrow i i i, r \rightarrow i, s \rightarrow i v \)
B \( \cdot p \rightarrow i, q \rightarrow i i, r \rightarrow i, s \rightarrow i i \)
\( \mathbf{c} \cdot p \rightarrow i i, q \rightarrow i, r \rightarrow i, s \rightarrow i i \)
D. \( p-i i i, q-i v, r-i i, s-i \)
Subject: Chemistry
\( \mathrm{R}, \mathrm{S} \) and \( \mathrm{T}, \) respectively are?
\( \mathbf{A} \cdot S O_{2} C l_{2}, P C l_{5} \) and \( H_{3} P O_{4} \)
B. \( S O_{2} C l_{2}, P C l_{3} \) and \( H_{3} P O_{3} \)
\( \mathbf{c} \cdot S O C l_{2}, P C l_{3} \) and \( H_{3} P O_{2} \)
D \( \cdot S O C l_{2}, P C l_{5} \) and \( H_{3} P O_{4} \)
Subject: Physics
Charged particle (charge= \( q ; \) mass \( = \)
\( \boldsymbol{m} \) ) is rotating in a circle of radius \( \boldsymbol{R} \)
with uniform speed \( V \), Ratio of its magnetic moment \( (\mu) \) to the angular
momentum \( (L) \) is
\( ^{\mathrm{A}} \cdot \frac{q}{2 m} \)
в. \( \frac{q}{m} \)
c. \( \frac{q}{4 m} \)
D. \( \frac{2 q}{m} \)
Subject: Physics
A wheel moves in the xy plane such that
the location of its center is given by
equations
\( \mathbf{x}_{\mathbf{0}}=\mathbf{1 2 t}^{3}, \mathbf{y}_{\mathbf{0}}=\mathbf{R}=\mathbf{2}, \) where \( \mathbf{x}_{o} \) and \( \mathbf{y}_{o} \)
are measured in metre and \( t \) in
seconds.
The angular displacement of a radial
line measured from a vertical reference
line is \( \Theta=8 t^{4}, \) where \( \Theta \) is in radians
(given \( v_{o} \) is the velocity of center of
wheel