AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Two beads of masses \( m_{1} \) and \( m_{2} \) are
threaded on a smooth circular wire of
radius' \( a^{\prime} \) fixed in a vertical plane. \( B \) is
stationary at the lowest point when \( \boldsymbol{A} \) is
gently dislodged from rest at the
highest point. \( A \) collides with \( B \) at the
lowest point. The impulse given to \( \boldsymbol{B} \)
due to collision is just great enough to
carry it to the level of the centre of the
circle while \( A \) is immediately brought
to rest by the impact. Find \( \boldsymbol{m}_{1}: \boldsymbol{m}_{2} \)
Subject: Maths
The total surface area of cube is
\( 100 \mathrm{cm}^{3} . \) Find its volume.
\( ^{\mathbf{A}} \cdot\left(\frac{100}{6}\right)^{\frac{2}{3}} \)
\( ^{\mathrm{B}}\left(\frac{100}{6}\right)^{\frac{1}{2}} \)
\( ^{\mathrm{C}}\left(\frac{100}{6}\right)^{\frac{3}{2}} \)
D. None
Subject: Chemistry
Which of the following statement is
incorrect?
A. Reducing power in aqueous solution is maximum for lithium metal.
B. Electron affinity order \( O^{+}>O>O^{-}>O^{2-} \)
C. Order of oxidation number of oxygen \( O_{3}>K O_{2}> \)
\( B a O_{2}>K_{2} O \)
D. \( p H \) of aqueous solution \( L i C l>B e C l_{2}>M g C l_{2}> \)
\( A l C l_{3} \)
Subject: Chemistry
The rms speed of hydrogen is \( \sqrt{7} \) times the rms speed of nitrogen. If T is the temperature of the gas, then:
\( \mathbf{A} \cdot T_{H_{2}}=T_{N_{2}} \)
B \( \cdot T_{H_{2}}>T_{N_{2}} \)
\( \mathbf{c} \cdot T_{H_{2}}<T_{N_{2}} \)
D. \( T_{H_{2}}=\sqrt{7} T_{N_{N}} \)
Subject: Chemistry
\( A: A \) mixture of raw rubber and sulphur on heating at \( 373 K-415 K \)
gives vulcanised rubber
\( \mathrm{R}: \mathrm{ZnO} \) decreases the rate of
vulcanisation of rubber.
A. both A and R are correct and R is the correct explanation of the A
B. both A and R are correct but R is not the correct explanation of the \( A \)
C. A is correct but R is incorrect
D. A is incorrect but R is correct
Subject: Maths
Using mathematical induction prove
that:
\[
\frac{\frac{1}{1.2 .3}+\frac{1}{2.3 .4}+\frac{1}{3.4 .5}+\ldots . .+}{n(n+1)(n+2)}=\frac{n(n+3)}{4(n+1)(n+2)}
\]
Subject: Maths
Find the expected value, variance and standard deviation of a random variable
whose \( p . m . f \) is.
\[
\begin{array}{lllll}
\boldsymbol{X}=\boldsymbol{x} & & 1 & 2 & 3 \\
p(X=x) & \frac{1}{5} & \frac{2}{5} & \frac{2}{5} & \frac{2}{5}
\end{array}
\]
Subject: Physics
A battery of emf \( \epsilon_{0}=10 V \) is connected
across a \( 1 \mathrm{m} \) long uniform wire having
resistance \( 10 \Omega / m . \) Two cells of emf
\( \epsilon_{1}=2 V \) and \( \epsilon_{2}=4 V \) having internal
resistances \( 1 \Omega \) and \( 5 \Omega \) respectively are connected as shown in the figure. If
a galvanometer shows no deflection at
the point \( P, \) find the distance of point \( P \)
in cm from the point \( A \). (Round off the
answer to the nearest integer)
Subject: Maths
Solution of differential equation \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}- \)
\( 2 x y=x \) is
A \( \cdot y=C e^{x^{2}}-\frac{1}{2} \)
B. \( y=C e^{x^{2}}+\frac{1}{2} \)
c. \( y=C x^{2}-\frac{1}{2} \)
D. None
Subject: Physics
Assertion
Assertion: The basic laws of
electromagnetism govern all electric and magnetic phenomena.
Reason
Reason: The attempts to unify
fundamental forces of nature reflect the
quest for unification.
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and 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: Physics
What is the equation of motion for the
rocket, if \( m \) is the mass of the rocket at
a given moment, \( \vec{w} \) is its acceleration, and \( \overrightarrow{\boldsymbol{F}} \) is the external force.
\( \mathbf{A} \cdot m \vec{w}=\vec{F}-2 \mu \vec{u} \)
в. \( m \vec{w}=\vec{F}+\mu \vec{u} \)
C \( . m \vec{w}=\vec{F}-3 \mu \vec{u} \)
D \( \cdot m \vec{w}=\vec{F}-\mu \vec{u} \)
Subject: Physics
The Richardson equation is given by \( \boldsymbol{I}=\boldsymbol{A} \boldsymbol{T}^{2} \boldsymbol{e}^{\frac{-B}{k T}} . \) The dimensional formula
for \( A B^{2} \) is same as that for:
A \( \cdot I T^{-2} \)
в. \( k \) Т
\( c \cdot I k^{2} \)
D. \( \frac{I k^{2}}{T} \)
Subject: Physics
If \( \vec{A}=5 \hat{i}+7 \hat{j}-3 \hat{k} \) and \( \vec{B}=2 \hat{i}+2 \hat{j}+ \)
\( a \hat{k} \) are perpendicular vectors then the
value of \( \boldsymbol{a} \) is:
\( A \cdot-2 \)
B. 8
\( c \cdot-7 \)
\( D \cdot-8 \)
Subject: Chemistry
A saturated solution of \( \boldsymbol{C} \boldsymbol{a}_{\boldsymbol{3}}\left(\boldsymbol{P} \boldsymbol{O}_{4}\right)_{2} \)
contains \( 2.0 \times 10^{-8} \mathrm{M} C a^{2+} \) and
\( 1.6 \times 10^{-5} \mathrm{M} P O_{4}^{3-} \) at a certain
temperature. The solubility product
\( \left(K_{s p}\right) \) of \( C a_{3}\left(P O_{4}\right)_{2} \) at that temperature is:
A . \( 2.048 \times 10^{-3} \)
В. \( 2.04 \times 10^{-33} \)
c. \( 3.20 \times 10^{-34} \)
D. \( 8 \times 10^{-34} \)
Subject: Chemistry
If the magnetic moment of a dioxygen species is \( 1.73 \mathrm{BM} \), it may be:
\( A \cdot O_{2} \) or \( O_{2}^{-} \)
B. \( O_{2}^{-} \) or \( O_{2}^{+} \)
\( c \cdot O_{2} \) or \( O_{2}^{+} \)
D. \( O_{2}, O_{2}^{-} \) or \( O_{2}^{+} \)
Subject: Chemistry
By how many times the absolute temperature of a gas would increase
when \( u_{r m s} \) of a gas in a container of fixed volume is increased from \( 5 \times \)
\( 10^{4} \mathrm{cm} \sec ^{-1} \) to \( 10 \times 10^{4} \mathrm{cm} \mathrm{sec}^{-1} ? \)
Subject: Physics
A large cylindrical tank has a hole of area \( A \) at its bottom and water is
poured into the tank through a tube of cross-section area \( \boldsymbol{A} \) ejecting water at
the speed \( v \). Which of the following is
true?
A. Water level in tank keeps on rising
B. No water can be stored in the tank
c. water level will rise to height \( v^{2} / 2 g \) and then stop
D. The water level will be oscillating
Subject: Maths
If \( A \) is a square matrix of order 3 such
that \( A^{2}+A+4 I=0, \) where 0 is the
zero matrix and \( I \) is the unit matrix of
order \( 3, \) then
A. \( A \) is singular and \( A+I \) is non-singular
B. A is non-singular and \( A+I \) is non-singular
c. \( A \) is non-singular and \( A+I \) is singular
D. \( A \) is singular and \( A+I \) is singular
E. \( A \) is non-singular and \( A-I \) is singular
Subject: Maths
Construct \( \triangle A B C \) in which \( B C= \)
\( \mathbf{7} c \boldsymbol{m}, \angle \boldsymbol{B}=\mathbf{7} \mathbf{5}^{\boldsymbol{o}} \) and \( \boldsymbol{A} \boldsymbol{B}+\boldsymbol{A} \boldsymbol{C}= \)
\( 12 \mathrm{cm} \)
Subject: Maths
Statement 1: The variance of first n even
natural numbers is \( \frac{\mathbf{n}^{2}-\mathbf{1}}{\mathbf{4}} \)
Statement 2: The sum of first n natural
numbers is \( \frac{\mathbf{n}(\mathbf{n}+\mathbf{1})}{\mathbf{2}} \) and the sum of
squares of first n natural numbers is \( \frac{\mathbf{n}(\mathbf{n}+\mathbf{1})(\mathbf{2 n}+\mathbf{1})}{\mathbf{6}} \)
A. Statement 1 is true, Statement2 is true,Statement 2 is a correct explanation for Statement 1
B. Statement 1 is true, Statement2 is true;Statement2 is not a correct explanation for statement 1
c. Statement 1 is true, Statement 2 is false
D. Statement 1 is false, Statement 2 is true
Subject: Chemistry
Given
\( \boldsymbol{E}_{\boldsymbol{C r}^{3+} / \boldsymbol{C r}}^{\circ}=-\boldsymbol{0 . 7 4} \boldsymbol{V} ; \boldsymbol{E}_{M n O_{4}^{-} / M n^{2+}}^{\circ}= \)
\( +1.51 V \)
\( \boldsymbol{E}_{C r_{2} O_{7}^{2-} / C r^{3+}}^{\circ}=+\mathbf{1 . 3 3} \boldsymbol{V} ; \boldsymbol{E}_{C l / C l^{-}}^{\circ}= \)
\( +1.36 V \)
based on the data given above, strongest oxidizing agent will
be
A. \( M n^{2+} \)
в. \( M n O_{4}^{-} \)
c. \( C l \)
D. \( C r^{3} \)
Subject: Physics
A spherical uniform planet is rotating about its axis. The velocity of a point on
its equator is \( V \). Due to the rotation of
a planet about its axis the acceleration due to gravity \( g \) at equator is \( \frac{1}{2} \) of \( g \) at
poles. The escape velocity of a particle
on the pole of a planet in terms of \( V \) is
A \( \cdot V_{e}=2 V \)
B. \( V_{e}=V \)
\( \mathrm{c} \cdot_{V_{e}}=\frac{V}{2} \)
D. \( V_{e}=\sqrt{3} V \)
Subject: Maths
Divide the first expression by the
second. Write the quotient and the
remainder.
\( a^{2}-b^{2} ; a-b \)
A. Quotient \( =b \), Remainder \( =0 \)
B. Quotient \( =a+b \), Remainder \( =0 \)
c. Quotient \( =a b \), Remainder \( =a \)
D. Quotient \( =a-b \), Remainder \( =a \)
Subject: Maths
Given that \( \bar{X} \) is the mean and \( \sigma^{2} \) is the
variance of \( n \) observations \( X_{1}, X_{2} \dots X_{n} \)
Prove that the mean and variance of the
observations \( a X_{1}, a X_{2}, a X_{3} \ldots a X_{n} \) are
\( a^{-} x \) and \( a^{2} \sigma^{2} \) respectively \( (a \neq 0) \)
Subject: Chemistry
One mole of a compound AB reacts with one mole of a compound CD according
to the equation \( \boldsymbol{A B}_{(\boldsymbol{g})+} \boldsymbol{C D}_{(g)} \rightleftharpoons \)
\( A D_{(g)}+C B_{(g)} \) When equilibrium had
been established it is was found that
\( 3 / 4 \) mole of reactants \( A B \) and \( C D \) had
been converted to \( A D \) and \( C B \), there is no
change in volume. The equilibrium constant for the reaction is :
A. \( 9 / 16 \)
B . 1/9
\( c \cdot 16 / 9 \)
D. 9
Subject: Chemistry
Write IUPAC name of the following complex compounds
\( (\mathrm{i})\left[\boldsymbol{N} \boldsymbol{i}(\boldsymbol{C} \boldsymbol{O})_{4}\right] \)
(ii) \( \boldsymbol{K}_{\mathbf{2}}\left[\boldsymbol{H} \boldsymbol{g} \boldsymbol{I}_{4}\right] \)
Subject: Maths
\( \int_{0}^{\pi} \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{d} \boldsymbol{x}= \)
A \( \cdot \frac{4}{\pi} \)
в. \( \frac{8}{\pi} \)
\( c \cdot \frac{8}{\pi^{2}} \)
D.
Subject: Physics
In the study of Geiger-Marsdon
experiment on scattering of \( \boldsymbol{\alpha} \) particles by a this foil of gold, draw the
trajectory of \( \boldsymbol{\alpha}- \) particles in the
coulomb field of target nucleus. Explain briefly how one gets the information on the size of the nucleus from this study:
From the relation \( \boldsymbol{R}=\boldsymbol{R}_{0} \boldsymbol{A}^{1 / 3}, \) where \( \boldsymbol{R}_{0} \)
is constant and \( A \) is the mass number
of the nucleus, show that nuclear matter density is independently of \( A \)
Subject: Biology
Assertion: Anterior lobe of pituitary is attached to hypothalamus by a vein
Reason: This attachment is done
through a portal vein
A. If both the assertion and the reason are true and the reason is the correct explanation of the assertion
B. If both the assertion and the reason are true and the reason is not the correct explanation of the assertion
c. If the assertion is true and the reason is false
D. If both the assertion and the reason is false
E. If the assertion is false but the reason is true
Subject: Chemistry
Assertion
Baking powder contains \( N a H C O_{3} \)
\( C a\left(H_{2} P O_{4}\right)_{2}, \) starch and \( N a A l\left(S O_{4}\right)_{2} \)
Reason
\( N a H C O_{3} C a\left(H_{2} P O_{4}\right)_{2} \) is acidic in
aqueous solution. Acidic solution of
\( C a\left(H_{2} P O_{4}\right)_{2} \) liberates \( C O_{2} \) on reaction
with \( \left.N a H C O_{3} \text { Starch }\right] \) as a filter
\( N a A l\left(S O_{4}\right)^{2} \) retarder so that \( C O_{2} \) is given off more slowly while preparing cake or bread.
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 body cools from \( 62^{\circ} \mathrm{C} \) to \( 50^{\circ} \mathrm{C} \) in 10
minutes. If the temperature of the
surroundings is \( 26^{\circ} \mathrm{C} \), then the
temperature of the body after next 10 minutes will be:
A \( \cdot 41^{\circ} \mathrm{C} \)
B . \( 44^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 46^{\circ} C \)
D. \( 48^{\circ} \mathrm{C} \)
Subject: Physics
(a) An iron ring of relative permeability
\( \mu_{r} \) has windings of insulated copper
wire of \( n \) turns per metre. When the
current in the windings is \( I \), find the expression for the magnetic field in the
ring.
(b) The susceptibility of a magnetic material is \( 0.9853 . \) Identify the type of magnetic material. Draw the modification of the field pattern on
keeping a piece of this material in a uniform magnetic field.
Subject: Chemistry
Which of the following complexes is not expected to exhibit isomerism?
\( \mathbf{A} \cdot\left[N i\left(N H_{3}\right)_{4}\left(H_{2} O\right)_{2}\right]^{2+} \)
B. \( \left[P t\left(N H_{3}\right)_{2} C l_{2}\right] \)
\( \mathbf{c} \cdot\left[N i\left(N H_{3}\right)_{2} C l_{2}\right] \)
D. \( \left[N i(e n)_{3}\right]^{2+} \)
Subject: Maths
If \( \boldsymbol{I}_{1}=\int_{0}^{\frac{\pi}{2}} \frac{\cos ^{2} \boldsymbol{x}}{1+\cos ^{2} \boldsymbol{x}} \boldsymbol{d} \boldsymbol{x} \)
\( I_{2}=\int_{0}^{\frac{\pi}{2}} \frac{\sin ^{2} x}{1+\sin ^{2} x} d x \)
\( I_{3}=\int_{0}^{\frac{\pi}{2}} \frac{1+2 \cos ^{2} x \sin ^{2} x}{4+2 \cos ^{2} x \sin ^{2} x} d x, \) then
A \( \cdot I_{1}=I_{2}>I_{3} \)
В . \( I_{3}>I_{1}=I_{2} \)
\( \mathbf{c} \cdot I_{1}=I_{2}=I_{3} \)
D. None of these
Subject: Maths
Mark the correct alternative of the
following. For the function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}+\frac{\mathbf{1}}{\boldsymbol{x}} \)
A. \( x=1 \) is a point of maximum
B. \( x=-1 \) is a point of minimum
c. Maximum value> minimum value
D. Maximum value < minimum value
Subject: Chemistry
The conductivity measurement of a coordination compound of Cobalt (III) shows that it dissociates into 3 ions in
solution. The compound is:
A. Hexaamminecobalt (III) chloride
B. Pentaamminesulphatocobalt (III) chloride
c. Pentaamminechloridocobalt
(III) sulphate
D. Pentaamminechloridocobalt (III) chloride
Subject: Chemistry
For the reaction, \( \boldsymbol{A B}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{A}(\boldsymbol{g})+\boldsymbol{B}(\boldsymbol{g}), \boldsymbol{A B} \) is \( \boldsymbol{3} \boldsymbol{3} \% \)
dissociated at a total pressure of \( \boldsymbol{P} \)
Therefore, \( P \) is related to \( K_{p} \) by one of
the following option:
A \( \cdot P=K_{p} \)
В. \( P=3 K_{p} \)
\( \mathbf{c} \cdot P=4 K_{p} \)
D. \( P=8 K_{p} \)
Subject: Maths
Find the distances between the
following pair of parallel lines:
\( \mathbf{3} \boldsymbol{x}+\mathbf{4} \boldsymbol{y}=\mathbf{1 3}, \mathbf{3} \boldsymbol{x}+\mathbf{4} \boldsymbol{y}=\mathbf{3} \)
Subject: Physics
Two point charges \( q_{1} \) and \( q_{2} \) are placed as shown. Resultant electric field origin is along -y-axis, \( \left(\frac{\boldsymbol{q}_{1}}{\boldsymbol{q}_{2}}\right) \) equals to:
A \( \cdot \frac{1}{\sqrt{2}} \)
B. \( \frac{1}{2 \sqrt{2}} \)
\( c \cdot \sqrt{2} \)
\( D \)
Subject: Maths
Construct quadrilaterals to the given measurements; the order of the letters
in each case is \( A, B, C, D \)
\( A B=4.8 \mathrm{cm}, B C=4.4 \mathrm{cm}, C D=7 \mathrm{cm}, D A= \)
\( 3.4 \mathrm{cm}, \mathrm{BD}=6.2 \mathrm{cm} \)
Subject: Chemistry
Assertion
The equilibrium (given below) attained in a closed vessel remains unaltered by
the addition of \( C a C O_{3}(s) \) \( \boldsymbol{C a} \boldsymbol{C O}_{3}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{C a O}(\boldsymbol{s})+\boldsymbol{C O}_{2}(\boldsymbol{g}) \uparrow \)
Reason
Heterogenous reaction is unaffected by solid and liquid.
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
Let \( A \) be a \( 2 \times 2 \) matrix with non-zero
entries and let \( \mathbf{A}^{2}=\boldsymbol{I}, \) where I is \( \mathbf{2} \times \mathbf{2} \)
identity matrix. Define \( \operatorname{Tr}(\mathbf{A})=\operatorname{sum} \) of diagonal elements of \( A \) and \( |\mathbf{A}|= \) determinant of matrix A.

Statement-1 \( \operatorname{Tr}(\mathrm{A})=0 \) Statement-2:
\( |\mathbf{A}|=\mathbf{1} \)
A. Statement-1 is true, Statement-2 is true; Statement- is not the correct explanation for statement-
B. Statement-1 is true, Statement-2 is false
c. Statement- 1 is false, statement- 2 is true
D. Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-
Subject: Physics
What is the correct definition of
reflectance?
A. Difference between amount of light absorbed by the surface and amount of light reflected.
B. The amount of light reflected by a surface is known as reflectance.
C. The ratio of the amount of the light reflected from a surface to the amount of light falling on the surface is called reflectance.
D. The ratio of amount of light falling on a surface to the amount of light reflected on the surface is called reflectance.
Subject: Maths
The number of solution of the equation \( \boldsymbol{a}^{f(\boldsymbol{x})}+\boldsymbol{g}(\boldsymbol{x})=\mathbf{0}, \) where \( \boldsymbol{a}>\mathbf{0}, \boldsymbol{g}(\boldsymbol{x}) \neq \)
0 and \( g(x) \) has minimum value \( \frac{1}{4}, \) is
A. one
B. two
c. infinitely many
D. zero
Subject: Physics
For the same angle of incidence, the
angles of refraction in media \( \mathrm{P}, \mathrm{Q}, \mathrm{R} \) and
\( \mathrm{S} \) are \( 50^{\circ}, 40^{\circ}, 30^{\circ}, 20^{\circ}, \) respectively. The
speed of light is minimum in medium:
\( A \cdot P \)
B.
\( c \cdot R \)
\( D \cdot s \)
Subject: Physics
A beam of electrons moving with a uniform speed of \( 4 \times 10^{7} m s^{-1} \) is
projected normal to the uniform magnetic field where \( \boldsymbol{B}=\mathbf{1 0}^{-3} \boldsymbol{W} \boldsymbol{b} / \boldsymbol{m}^{2} \)
What is path of the beam in magnetic field?
Subject: Physics
A charged particle with velocity \( 2 \times \) \( 10^{3} m / s \) passes undeflected through
electric and magnetic field. Magnetic field is 1.5 tesla. The electric field
intensity would be
A \( \cdot 2 \times 10^{3} N / C \)
в. \( 1.5 \times 10^{3} N / C \)
c. \( 3 \times 10^{3} N / C \)
\( \mathbf{D} \cdot 4 / 3 \times 10^{-3} N / C \)
Subject: Physics
Two roads intersect at right angle; one
goes along the \( x \) -axis, another along the
y-axis. At any. two cars \( A \) and \( B \) moving
along \( \boldsymbol{y} \) and \( \boldsymbol{x} \) directions; respectively, meet at intersection. Draw the direction
of the motion of car \( A \) as seen from car
\( \boldsymbol{B} \)
Subject: Physics
A particle executes SHM on a straight line. At two positions it's velocity \( u \) and \( \boldsymbol{v} \) while acceleration, \( \boldsymbol{\alpha} \) and \( \boldsymbol{\beta} \)
respectively \( [\beta>\alpha>0] . \) the distance
between the these two positions is
A \( \cdot \frac{u^{2}+v^{2}}{\alpha+\beta} \)
в. \( \frac{u^{2}-v^{2}}{\alpha+\beta} \)
c. \( \frac{u^{2}-v^{2}}{\beta-\alpha} \)
D. \( \frac{u^{2}+v^{2}}{\beta-\alpha} \)
Subject: Physics
If the velocity v of a particle moving
along a straight line decreases linearly
with its displacements from \( 20 m s^{-1} \) to
a value approaching zero at \( s=30 \mathrm{m} \)
then acceleration of the particle at \( s=15 \)
\( m \) is:
A \( \cdot \frac{2}{3} m s^{-2} \)
B. \( -\frac{2}{3} m s^{-2} \)
c. \( \frac{20}{3} m s^{-2} \)
D. \( -\frac{20}{3} m s^{-2} \)
Subject: Physics
An object of mass \( m \) is released from
rest from the top of a smooth inclined
plane of height \( h \). Its speed at the
bottom of the plane is proportional to:
\( \mathbf{A} \cdot m^{0} \)
в. \( m \)
\( c \cdot m^{2} \)
D. \( m^{-1} \)
Subject: Physics
A small mass \( \mathrm{m} \) is attached to the
inside of a rigid ring of the same mass \( \mathrm{m} \) and radius R. The ring rolls without slipping over a horizontal plane. At the moment when the mass m gets into the lowest position, the centre of the ring
moves with velocity \( \boldsymbol{v}_{0} . \) If \( \left(\boldsymbol{v}_{0}\right)_{\max }= \)
\( \sqrt{\mathrm{ngR}}, \) when the ring moves without bouncing, find \( n \)
Subject: Physics
The band gaps of a conductor, semiconductor and insulator are
respectively \( \boldsymbol{E} \boldsymbol{g}_{1}, \boldsymbol{E} \boldsymbol{g}_{2} \) and \( \boldsymbol{E} \boldsymbol{g}_{3} . \) The
relationship between them can be given
as.
A \( . E g_{1}=E g_{2}=E g_{3} \)
в. \( E g_{1}<E g_{2}<E g_{3} \)
c. \( E g_{1}>E g_{2}>E g_{3} \)
D. \( E g_{1}<E g_{2}>E g_{3} \)
Subject: Chemistry
\( \boldsymbol{R}-\boldsymbol{O H} \stackrel{\boldsymbol{P B r}_{3}}{\boldsymbol{A}} \)
\( \boldsymbol{B} \stackrel{\boldsymbol{H C H O}}{\longrightarrow} \boldsymbol{C} \stackrel{\boldsymbol{H}^{+} / \boldsymbol{H}_{2} \boldsymbol{O}}{\longrightarrow} \boldsymbol{D} \)
What are \( A, B, C \& D \) respectively?
\( \mathbf{A} \cdot R-B r, R-B r-M g, R-C H_{2} M g-B r, R- \)
\( C H_{2} C H O \)
B . \( R-B r, R-M g-B r, R-C H_{2}-O-M g-B r, R- \)
\( C H_{2} C H O \)
\( \mathbf{c} \cdot R-B r, R-M g-B r, R-C H_{2}-O-M g-B r, R- \)
\( C H_{2} O H \)
D. \( R-B r, R-M g-B r, R-C H_{2}-B r, R-C H_{2} O H \)
Subject: Chemistry
Which one of the following is the
structure of polyacrylonitrile?
\( \left(\begin{array}{c}C H_{2}-C H \\ _{C l}\end{array}\right) \)
\( \left(\begin{array}{cc}c & c^{l} \\ C H_{2}-c & l \\ & \mid \\ c l\end{array}\right) \)
\( \left(\begin{array}{cc} & C N \\ C H_{2}- & C \\ & _{C O O C H_{3}}\end{array}\right) \)
Subject: Physics
A student while performing an experiment was surprised to find that when two identical cells are either
connected in series or in parallel across
a \( 2 \Omega \) resistor, the same current passes through the resistor. What is the
internal resistance of each cell?
A . \( 2 \Omega \)
B. \( 4 \Omega \)
\( c \cdot 1 \Omega \)
D. 3\Omega
Subject: Maths
If \( \operatorname{Tr}(\mathbf{A})=\mathbf{8}, \operatorname{Tr}(\mathbf{B})=\mathbf{6}, \operatorname{Tr}(\mathbf{A}-\mathbf{2 B})= \)
A . -4
B. 4
\( c \cdot 2 \)
D. 11
Subject: Maths
Which of the following pair of matrices are equal?
A. \( \left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right],\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right] \)
B. \( \left[\begin{array}{ll}4 & 0 \\ 0 & 4\end{array}\right],\left[\begin{array}{ll}4 & 0 \\ 4 & 4\end{array}\right] \)
\( ^{\mathbf{C}} \cdot\left[\begin{array}{ll}4 & 7 \\ 3 & 2\end{array}\right],\left[\begin{array}{cc}3+1 & \sqrt{49} \\ \frac{7-1}{2} & \sqrt{4}\end{array}\right] \)
D. none of the above
Subject: Chemistry
The IUPAC name of the compound:
A. 5-chloro-4-methyl hept-5-en-1-yne
B. 5-chloro-4-methyl hept-1-en-5-yne
c. 3-chloro-4-methyl hept-2-en-6-yne
D. 3-chloro-4-methyl hept-6-en-2-yne
Subject: Physics
A transformer is used to light a \( 120 W \) \( 24 V \) lamp from \( 240 V \) a.c. mains. The
current in the main cable is \( 0.6 A . \) The efficiency of the transformer is
A . \( 48 \% \)
B. \( 63.8 \% \)
c. \( 83.3 \% \)
D. \( 90 \% \)
Subject: Biology
Study the following lists
\begin{tabular}{l|l|l} 
List I & List II \\
A) & Early seed production in conifers & I) & Indole substance \\
\hline B) & Seed development and maturation & II) & Terpene substance \\
C) & Lateral shoot growth & III) & Volatile substance \\
D) & Root hair formation & IV) & Adenine derivative \\
\hline
\end{tabular}
\( \mathbf{A} \)
\( A-\| I, B-I, C-V, D-I \)
B. \( A-11, B-V, C-I V, D-1 \)
C. \( A-11, B-1, C-V, D-I V \)
D. \( A-I V, B-11 I, C-11, D- \)
Subject: Maths
What is the area of the region bounded
by the parabola \( \boldsymbol{y}^{2}=\mathbf{6}(\boldsymbol{x}-\mathbf{1}) \) and
\( \boldsymbol{y}^{2}=\mathbf{3} \boldsymbol{x} \)
A \( \cdot \frac{\sqrt{6}}{3} \)
в. \( \frac{2 \sqrt{6}}{3} \)
c. \( \frac{4 \sqrt{6}}{3} \)
D. \( \frac{5 \sqrt{6}}{3} \)
Subject: Maths
f \( \boldsymbol{y}=\boldsymbol{a} \cos (\sin 2 \boldsymbol{x})+\boldsymbol{b} \sin (\sin 2 \boldsymbol{x}) \)
then \( \boldsymbol{y}^{\prime \prime}+(2 \tan 2 \boldsymbol{x}) \boldsymbol{y}^{\prime}= \)
\( A \)
B \( \cdot 4\left(\cos ^{2} 2 x\right) y \)
c. \( -4\left(\cos ^{2} 2 x\right) y \)
\( D \cdot-\left(\cos ^{2} 2 x\right) y \)