AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Four particles of masses in the ratio 1:2:3:4 are rotating in concentric circles of radii proportional to their masses with the same angular velocity. What is the angular momentum of the system
A \( \cdot 4 m w^{2} r \)
B. \( 10 m w^{2} \)
c. \( 30 m w^{2} r \)
D. \( 20 m w^{2} r \)
Subject: Maths
The equation of the curve through \( \left(0, \frac{\pi}{4}\right) \) satisfying the differential
equation. \( e^{x} \tan y d x+(1+ \)
\( \left.e^{x}\right) \sec ^{2} y d y=0 \) is given by
A \( \cdot\left(1+e^{x}\right) \tan y=2 \)
B . \( 1+e^{x}=2 \tan y \)
C \( \cdot 1+e^{x}=2 \sec y \)
D・ \( \left(1+e^{x}\right) \tan y=1 \)
Subject: Chemistry
Compound \( A\left(C_{7} H_{15} B r\right) \) is not \( a \)
primary alkyl bromide. It yield a single alkene (compound B) on being heated with sodium ethoxide in ethanol.
Hydrogenation of compound B yield
\( 2,4- \) dimethylpentane. Identify
compounds \( A \) and \( B \)
A. 3-Bromo-2,4-dimethylpentane and 2,4-Dimethylpent2-ene
B. 2-bromo-2,4-dimethylhexane and 2,4-dimethylhex-2ene
c. 3-bromo-2,4-dimethylhexane and 2,3-dimethylhex-2ene
D. None of these
Subject: Maths
Compute the mean for the following
data:
\( \begin{array}{ll}\text { Marks } & \text { No. of students } \\ \text { Less than 10 } & 0 \\ \text { Less than 30 } & 10 \\ \text { Less than 50 } & 25 \\ \text { Less than 70 } & 43 \\ \text { Less than 90 } & 65 \\ \text { Less than 110 } & 87 \\ \text { Less than 130 } & 96 \\ \text { Less than 150 } & 100\end{array} \) mean is 74.80
f true then enter 1 and if false then
enter
Subject: Maths
\( \boldsymbol{I} \boldsymbol{f} \boldsymbol{I}=\int \boldsymbol{x} \sqrt{\frac{x^{2}+1}{x^{2}-1}} \boldsymbol{d} \boldsymbol{x}, \) then I equals
A \( \cdot \frac{1}{2} \sqrt{x^{4}-1}+\frac{1}{2} \sqrt{x^{4}+1}+c \)
B - \( \frac{1}{2} \sqrt{x^{4}-1}+\frac{1}{2} \operatorname{tn}\left(x^{2}+\sqrt{x^{4}-1}\right)+c \)
c. \( \sqrt{x^{4}-1}+\sin ^{-1}\left(x^{2}\right)+c \)
D. \( \sqrt{x^{4}-1}+2 \sin ^{-1}\left(x^{2}\right)+c \)
Subject: Chemistry
Consider the following species:
(i) \( \left[\boldsymbol{O}_{2}\right]^{2-} \)
(ii) \( [\boldsymbol{C O}]^{+} \)
(iii) \( \left[\boldsymbol{O}_{2}\right]^{+} \)
Among these sigma bond alone is
present in?
A. (i) alone
B. (ii) alone
c. (iii) alone
D. (i) and (ii)
E. (i), (ii) and (iii)
Subject: Chemistry
Complete the following equations:
\( \begin{array}{l}\text { i) } 2 N a O H_{2} \rightarrow \\ \text { cold and dilute }\end{array}+C l_{2} \rightarrow \)
ii) \( 2 F e S O_{4}+H_{2} S O_{4}+C l_{2} \rightarrow \)
iii) \( C l_{2}+3 F_{2} \stackrel{573 K}{\text { excess }} \)
Subject: Maths
The point intersection of the tangents drawn to the curve \( x^{2} y=1-y \) at the
points where it is met by the curve \( x y=1-y \) is given by
A \( .(0,1) \)
в. (1,1)
c. (1,0)
(i) 5
D. \( (0, \infty) \)
Subject: Chemistry
On the basis of the following observations made with aqueous
solutions. assign secondary valences to metals in the following compounds:
Formula
of AgCl precipitated per mole of the compounds with excess AgNO,
\( (i) P d C l_{2} .4 N H_{3} \)
\( (i i) N i C l_{2} .6 H_{2} O \)
\( (\text {iiii}) P t C l_{4} .2 H C l \)
\( (i v) C o C l_{3} .4 N H_{3} \)
\( (v) P t C l_{2} \cdot 2 N H_{3} \)
Subject: Chemistry
Match list I with List II and select the
correct answer using the codes given
below the lists:
List I
(A) Coagulation
(1) Scattering
(B) Lyophilization
(2) Washing of precipitates
(C) Peptization
(3) Purification of colloids
(D) Tyndall
(4) Electrolyte
A. A-4; B-3; C-2; D-1
B. A-2; B-1; C-3; D-4
c. \( A-3 ; B-4 ; C-2 ; D-1 \)
D. A-4; B-3; C-1; D-1 -
Subject: Physics
Assertion
In a Meter Bridge experiment, null point for unknown resistance is measured. Now, the unknown resistance is put
inside an enclosure maintained at a
higher temperature. The null point can be obtained at the same point as before by decreasing the value of the standard resistance. and
Reason
Resistance of a metal increases with
increase in temperature.
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: Maths
For the events \( \boldsymbol{A} \) and \( \boldsymbol{B}, \boldsymbol{P}(\boldsymbol{A})= \)
\( \frac{3}{4}, P(B)=\frac{1}{5}, P(A \cap B)=\frac{1}{20} \) then
\( \boldsymbol{P}(\boldsymbol{A} / \boldsymbol{B})= \)
\( A \cdot \frac{1}{4} \)
B. \( \frac{1}{15} \)
\( c \cdot \frac{3}{4} \)
D.
Subject: Chemistry
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \frac{C a(\boldsymbol{O H})_{2}}{\boldsymbol{\Delta}} \boldsymbol{A} \frac{\boldsymbol{C a}(\boldsymbol{O O C H})_{2}}{\boldsymbol{\lambda}} \)
\( \boldsymbol{B} \stackrel{N H_{2} O \boldsymbol{H}}{\longrightarrow} \boldsymbol{C} \)
Identify the ' \( C^{\prime \prime} \) in the given series
\( \stackrel{\mathrm{H}_{3} \mathrm{C}}{\mathrm{H}_{3} \mathrm{C}} \mathrm{C}=\mathrm{NOH} \)
в. \( C H_{3} C H=N O H \)
\( \mathbf{c} \cdot H_{2} C=N O H \)
D. \( C H_{3} C H_{2} C H=N O H \)
Subject: Physics
A solid sphere of radius \( R \) has moment
of inertia \( I \) about its geometrical axis. If
it is melted into a disc of radius \( r \) and
thickness \( t \). If its moment of inertia
about the tangential axis (which is perpendicular to plane of the disc), is also equal to \( I, \) then the value of \( r \) is
equal to:
A.
B.
c. \( \frac{3}{\sqrt{15}} R \)
\( D \)
Subject: Maths
The chord joining the points where \( x=p \) and \( x=q \) on the curve \( y=a x^{2}+b x+c \)
is parallel to the tangent at the point on the curve whose abscissa is
A. \( \frac{p+q}{2} \)
В. \( \frac{p-q}{2} \)
c. \( \frac{p q}{2} \)
D. \( \frac{p}{q} \)
Subject: Maths
If \( \boldsymbol{y}=\sec ^{-1}\left(\frac{\boldsymbol{x}^{2}+\mathbf{1}}{\boldsymbol{x}^{2}-\mathbf{1}}\right) \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=? \)
A \( \cdot \frac{-2}{\left(1+x^{2}\right)} \)
B. \( \frac{2}{\left(1+x^{2}\right)} \)
c. \( \frac{-1}{\left(1-x^{2}\right)} \)
D. none of these
Subject: Biology
Which of the following situations
correctly describes the similarity between an angiosperm egg and a human egg?
(i) Eggs of both are formed only once in
a lifetime.
(ii) Both the angiosperm egg and human egg are stationary.
(iii) Both the angiosperm egg and human egg are motile transported.
(iv) Syngamy in both results in the formation of zygote.

Choose the correct answer from the
options given below.
\( A \cdot \) (ii) and (iv)
B. (iv) only
c. (iii) and (iv)
D. (i) and (iv)
Subject: Physics
\( A 60 J \) of heat is added to the system, resulting in 15 J of work being done by the system. The remaining 45 J of heat is released. Find out the efficiency of the system?
A. \( 100 \% \)
B. 75 \%
c. \( 45 \% \)
D. 25\%
E . \( 15 \% \)
Subject: Maths
The set of all points of differentiability of the function \( f(x)=\frac{\sqrt{x+1}-1}{\sqrt{x}} \) for
\( x \neq 0 \) and \( f(0)=0 \) is
\( \mathbf{A} \cdot(-\infty, \infty) \)
B. \( [0, \infty) \)
\( c \cdot(0, \infty) \)
\( \mathbf{D} \cdot(-\infty, \infty) \sim\{0\} \)
Subject: Physics
what is the velocity of a monkey running on the roof of the train \( A( \) moving with velocity \( 54 k h / h r) \) against its motion
with a velocity of \( 18 \mathrm{km} h^{-1} \) with respect
to the train \( A \) as observed by a man standing on the ground?
A \( \cdot 5 \mathrm{m} s^{-1} \)
B. \( 10 \mathrm{m} s^{-1} \)
c. \( 15 \mathrm{m} \mathrm{s}^{-1} \)
D. 20 \( \mathrm{m} \mathrm{s}^{-1} \)
Subject: Chemistry
Hardness of water is estimated by the simplest complex formation titration Complex formed by cation in hard water during estimation of hardness is:
\( \mathbf{A} \cdot N a_{2}\left[C a\left(P O_{3}\right)_{6}\right] \)
B . \( N a_{2}[M g(E D T A)] \)
c. \( N a_{2}[P b(E D T A)] \)
D. \( \left[C a\left(S O_{4}\right)_{2}\right]^{2} \)
Subject: Physics
Surface density of charge on a sphere of radius \( R \) in terms of electricity intensity \( E \) at a distance \( r \) in free space
is
\( \left(\epsilon_{0}=\text { permittivity of free space }\right) \)
\( ^{\mathrm{A}} \cdot_{\epsilon_{0} E}\left(\frac{R}{r}\right)^{2} \)
в. \( \frac{\epsilon_{0} E R}{r^{2}} \)
\( ^{\mathbf{C}} \epsilon_{0} E\left(\frac{r}{R}\right)^{2} \)
D. \( \frac{\epsilon_{0} E r}{R^{2}} \)
Subject: Physics
A long curved conductor carrier a current \( \overrightarrow{\boldsymbol{I}}(\overrightarrow{\boldsymbol{I}} \) is a vector). A small current element of length \( d \vec{l} \), on the wire,
induces a magnetic field at a point, away from the current element. If the
position vector between the current
element and the point is \( \vec{r}, \) making an
angle \( \theta \) with current element then, the induced magnetic field density, \( d \vec{B} \) at
the point is \( \left(\mu_{0}= \) permeability of free \right. space
\( \frac{\mu_{o} I(d \vec{l} \times \vec{r})}{4 \pi r^{3}} \) perpendicular to the current element \( d \vec{l} \)
B. \( \frac{\mu_{o} I \times \vec{r} . d \vec{l}}{4 \pi r^{2}} \) perpendicular to the current element \( d \vec{l} \)
\( \frac{\mu_{o} I \times d \vec{l}}{r} \) perpendicular to the plane containing the current element and position vector \( \vec{r} \)
D. \( \frac{\mu_{o} I \times d \vec{l}}{4 \pi r^{2}} \) perpendicular to the plane containing current element and position vector \( \vec{r} \)
Subject: Physics
A circular coil of 16 turns and radius
10cm carrying a current of \( 0.75 A \) rests
with its plane normal to an external
field of magnitude \( 5.0 \times 10^{2} \) T. The coil
is free to turn about an axis in its plane perpendicular to the field direction.
When the coil is turned slightly and released, it oscillates about its stable
equilibrium with a frequency of \( 2 s^{-1} \)
What is the moment of inertia of the
coil about its axis of rotation.?
Subject: Biology
The given statements describe a group
of organisms.
(i) Instead of a cell wall they have a
protein rich pellicle making their body flexible.
(ii) They have 2 flagella, a short and a
long one.
(iii) They show mixotrophic nutrition.
(iv) They are connecting link between
plants and animals. Which of the following groups is
referred to here?
A. Dinoflagellates
B. Slime moulds
c. Desmids and diatoms
D. Euglenoids
Subject: Maths
\( \mathrm{f} \int_{0}^{\pi / 2} \log (\sin \mathrm{x}) \mathrm{d} \mathrm{x}=\mathrm{k} \) then
\( \int_{0}^{\pi / 2} \log (\cos x) d x \)
A \( \cdot \frac{k}{2} \)
B . \( 2 k \)
\( c .-3 k \)
D.
Subject: Chemistry
\( \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \boldsymbol{H}_{3} \boldsymbol{O}^{+}+\boldsymbol{O} \boldsymbol{H}^{-} \)
The above reverse reaction is an
exothermic reaction. What will happen if the temperature is lowered?
A. The \( p H \) will decrease
B. The equilibrium will shift to the right
C. The concentration of \( H_{3} O^{+} \) ions will increase
D. The equilibrium will shift to the left.t.
E. Temperature does not affect equilibrium.
Subject: Maths
\( \Delta A B C \quad \) and \( \Delta D B C \quad \) are two
isosceles triangle on the same base BC
and vertices \( A \) and \( D \) are on the same
side of BC. if AD is extended to intersect
\( \mathrm{BC} \) at \( \mathrm{p}, \) show that AP is the perpendicular bisector of BC
Subject: Chemistry
In the sequence of reaction,the product
B is ?
\( \langle\square\rangle-\mathrm{MgBr}+\mathrm{CH}_{2}-\mathrm{CH}_{2} \longrightarrow \mathrm{A} \frac{\mathrm{H}_{2} \mathrm{O} / \mathrm{H}^{+}}{\mathrm{o}^{\prime}} \)
A. Benzyl alcohol
B. 2-phenyl ethanol
c. 1-phenyl ethanol
D. Quinol
Subject: Maths
Mean deviations of the series \( a, a+ \) \( \boldsymbol{d}, \boldsymbol{a}+\mathbf{2} \boldsymbol{d}, \ldots, \boldsymbol{a}+\boldsymbol{2 n} \boldsymbol{d} \) from its mean is
A \( \cdot \frac{n(n+1) d}{(2 n+1)} \)
в. \( \frac{n d}{2 n+1} \)
c. \( \frac{(n+1) d}{2 n+1} \)
D. \( \frac{(2 n+1) d}{n(n+1)} \)
Subject: Physics
Four identical charges are placed at the points (1,0,0),(0,1,0),(-1,0,0) and \( (0, \)
-1,0)
This question has multiple correct options
A. The potential at the origin is zero.
B. The field at the origin is zero
c. The potential at all points on the z-axis, other than the origin, is zero.
D. The field at all points on the z-axis, other than the origin, acts along the z-axis
Subject: Maths
Arrange the following rational number
in descending order
\( \frac{1}{5}+\frac{1}{-6},\left|-\frac{7}{6}+1\right|,\left(-\frac{1}{2}\right)^{3}, \frac{5}{8} \div \frac{-15}{4} \)
\( \stackrel{1}{5}+\frac{1}{-6},\left(-\frac{1}{2}\right)^{3}, \frac{5}{8} \div \frac{-15}{8},\left|-\frac{7}{6}+1\right| \)
\( \left(-\frac{1}{2}\right)^{3}, \frac{1}{5}+\frac{1}{-6}, \frac{5}{8} \div \frac{-15}{4},\left|-\frac{7}{6}+1\right| \)
\( \mathbf{C} \cdot\left|-\frac{7}{6}+1\right|, \frac{1}{5}+\frac{1}{-6},\left(-\frac{1}{2}\right)^{3}, \frac{5}{8} \div \frac{-15}{4} \)
\( \frac{5}{6} \div \frac{-15}{4},\left|-\frac{7}{6}+1\right|, \frac{1}{5}+\frac{1}{-6},\left(-\frac{1}{2}\right)^{3} \)
Subject: Physics
A storage battery takes \( t_{0} \) time when
DC current \( I_{0} \) is used to charge it. Find
the time taken if a half wave rectifier is
used with \( A C \) mains and effective
current is \( \boldsymbol{I}_{0} \)
A \( \cdot t_{0} \pi \)
в. \( \frac{2 t_{0}}{\pi} \)
c. \( \frac{\pi t_{0}}{2} \)
D. \( t \)
Subject: Physics
Two balls of same mass are dropped from the same height \( h, \) on to the floor. the first ball bounces to a height h/4,
after the collection \( \& \) the second ball to
a height h/16. the impulse applied by
the first \( \& \) second ball on the floor are \( \boldsymbol{I}_{1} \)
and \( I_{2} \) respectively. then
A \( \cdot 5 I_{1}=6 I_{2} \)
B \( .6 I_{1}=5 I_{2} \)
\( \mathbf{c} \cdot 3 I_{1}=2 I_{2} \)
D. \( 2 I_{1}=I_{2} \)
Subject: Physics
The length of a metal wire is \( l_{1} \) when the tension in it is \( F_{1} \) and \( l_{2} \) when the
tension in it is \( F_{2} \). The natural length of
the wire is
A. \( \frac{l_{1} F_{1}+l_{2} F_{2}}{F_{1}+F_{2}} \)
в. \( \frac{l_{2}-l_{1}}{F_{2}-F_{1}} \)
c. \( \frac{l_{1} F_{2}-l_{2} F_{1}}{F_{2}-F_{1}} \)
D. \( \frac{l_{1} F_{1}-l_{2} F_{2}}{F_{2}-F_{1}} \)
Subject: Maths
f \( \omega \) is a cube root of unity, then \( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{\omega} & \boldsymbol{\omega}^{2} \\ \boldsymbol{\omega} & \boldsymbol{\omega}^{2} & \boldsymbol{1} \\ \boldsymbol{\omega}^{2} & \boldsymbol{1} & \boldsymbol{\omega}\end{array}\right| \) is equal to
A .
B. \( \omega \)
\( c \cdot \omega^{2} \)
D.
Subject: Maths
Resolve \( \frac{2 x^{2}-11 x+5}{(x-3)\left(x^{2}+2 x+5\right)} \) into
partial fractions.
A \( \frac{1}{2(x-3)}-\frac{(5 x-5)}{2\left(x^{2}+2 x+5\right)} \)
B. \( \frac{1}{2(x-3)}+\frac{(5 x-5)}{2\left(x^{2}+2 x+5\right)} \)
C \( \frac{1}{(x-3)}+\frac{(5 x-5)}{\left(x^{2}+2 x+5\right)} \)
D \( \frac{1}{2(x+3)}+\frac{(5 x-5)}{2\left(x^{2}+2 x+5\right)} \)
Subject: Chemistry
The oxidation state of the underlined
element in the given compound is:
\( \boldsymbol{N} \boldsymbol{a}_{2}\left[\underline{\boldsymbol{F}} e(\boldsymbol{C} \boldsymbol{N})_{5} \boldsymbol{N} \boldsymbol{O}\right] \)
\( A \cdot-2 \)
\( B .+2 \)
\( c \cdot+3 \)
D. none of these
Subject: Chemistry
Which one of the followings is/are an
example of homogeneous catalysis? This question has multiple correct options
A. Formation of \( S O_{3} \) in the chamber process
B. Formation of \( S O_{3} \) in the contact process
c. Hydrolysis of an ester in the presence of acid.
D. Decomposition of \( K C l O_{3} \) in the presence of \( M n O_{2} \)
Subject: Maths
If \( \boldsymbol{f}\left(\boldsymbol{x}+\frac{1}{x}\right)=\boldsymbol{x}^{3}+\frac{1}{x^{3}}- \)
\( 4\left(x^{2}+\frac{1}{x^{2}}\right)+13 \) then \( f(2+\sqrt{3})= \)
В. \( 19-4 \sqrt{3} \)
c. \( 15-4 \sqrt{3} \)
D. \( 7-4 \sqrt{3} \)
Subject: Physics
If the refractive index of medium \( b \) with
respect to medium \( a \) and that of
medium \( c \) with respect to medium b are given, then the refractive index of a
medium \( c \) with respect to a medium \( a \) can be found by using the relation
\( \boldsymbol{n}_{c a}=\boldsymbol{n}_{b a} \times \ldots \ldots \)
\( \mathbf{A} \cdot n_{d} \)
B. \( n_{a} \)
\( c \cdot n_{a} \)
D. \( n_{b a} \)
Subject: Physics
An object have a velocity \( \overrightarrow{\boldsymbol{v}}=(\hat{\boldsymbol{i}}+ \)
\( \hat{\boldsymbol{j}}) \boldsymbol{m} / \boldsymbol{s} \) at time \( \boldsymbol{t}=\mathbf{0} . \) It undergoes a
constant acceleration \( \boldsymbol{a}=(\hat{\boldsymbol{i}}- \)
\( 2 \hat{j}) m s^{-2} \) for 4 second. The magnitude of
velocity at the end of \( 4 s \) is:
\( \mathbf{A} \cdot \sqrt{74} m / s \)
B. \( \sqrt{80} \mathrm{m} / \mathrm{s} \)
c. \( \sqrt{97} \mathrm{m} / \mathrm{s} \)
D. \( \sqrt{47} \mathrm{m} / \mathrm{s} \)
Subject: Physics
Figure shows a some of the
equipotential surface of the magnetic
scalar potential. The magnetic field at a
point in the region is :
A \( \cdot 2 \times 10^{-5} T \)
B \( \cdot 10^{-5} T \)
\( \mathbf{c} \cdot 10^{-4} T \)
D. \( 2 \times 10^{-4} T \)
Subject: Maths
If \( f(t)=\frac{1+t}{1-t}, \) then \( f(-t) \) is
A \( \cdot \frac{1}{f(t)} \)
в. \( \frac{1}{f(-t)} \)
c. \( f_{t} \frac{1}{t} \)
D. \( f\left(-\frac{1}{t}\right) \)
E. \( 1+f(t) \)
Subject: Physics
Find the value of \( \theta \) such that the
acceleration of \( \boldsymbol{A} \) is \( \boldsymbol{g} / \boldsymbol{6} \) downward
along the incline plane. (All surfaces are
smooth)
A \( \cdot \theta=10^{\circ} \)
B . \( \theta=60^{\circ} \)
\( \mathbf{c} \cdot \theta=45^{\circ} \)
D. \( \theta=53^{\circ} \)
Subject: Maths
Statement-I: The point \( \boldsymbol{A}(\mathbf{3}, \mathbf{1}, \mathbf{6}) \) is the
mirror image of the point \( B(1,3,4) \) in
the plane \( \boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5} \)
Statement-2: The plane \( \boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5} \)
bisects the line segment joining
\( \boldsymbol{A}(\boldsymbol{3}, \mathbf{1}, \boldsymbol{6}) \) and \( \boldsymbol{B}(\mathbf{1}, \boldsymbol{3}, \boldsymbol{4}) \)
A. (1) Statementl is true. Statement-1 is true: Statement
- 2 is a correct explanation for Statement- -
B. (2) Statementl is true, Statement-2 is true: Statement-
9 is not a correct explanation for statement- -
c. (3) Statement-l-lis true, Statement-2 is false.
D. (4) Statementl is false. Statement-2 is true
Subject: Maths
If \( \sin ^{-1}\left(x-\frac{x^{2}}{2}+\frac{x^{3}}{4}-\dots \infty\right)+ \)
\( \cos ^{-1}\left(x^{2}-\frac{x^{4}}{2}+\frac{x^{6}}{4}-\dots \infty\right)=\frac{\pi}{2} \)
and \( 0<x<\sqrt{2}, \) then \( x= \)
A \( \cdot \frac{1}{2} \)
в.
\( c \cdot-\frac{1}{2} \)
D. \( \frac{\sqrt{3}}{2} \)
Subject: Physics
Consider the following two statements A and B and identify the correct answer.
A) The work done in blowing a bubble of
volume \( V \) is \( W \), then the work done in
blowing a soap bubble of volume 2 V will be \( 2^{2 / 3} w \)
B) The excess pressure inside a soap bubble of diameter D and surface
tension \( \mathrm{S} \) is \( \frac{8 S}{D} \)
A. A\&B are false
B. A is false but B is true
C. A is true but B is false
D. A \& B are true
Subject: Chemistry
The chemical equations to represent the most probable outcome in the following is :
\( H g O \stackrel{\Delta}{\rightarrow} ? \)
A \( \cdot 4 \mathrm{HgO} \triangleq 3 \mathrm{Hg}+\mathrm{HgO}_{2}+\mathrm{O}_{2} \)
в. \( 2 \mathrm{HgO} \stackrel{\Delta}{\rightarrow} 2 \mathrm{Hg}+\mathrm{O}_{2} \)
c. No reaction
D. None of these
Subject: Physics
The charge on an electron is:
A . \( 1 \mathrm{c} \)
B \( \cdot+1.6 \times 10^{-19} \mathrm{C} \)
\( \mathrm{c} \ldots 1.6 \times 10^{-19} \mathrm{C} \)
D. 6.25 \( \times 10^{18} \mathrm{C} \)
Subject: Chemistry
The slag formed in the extraction of iron
from haematite in the blast furnace is:
A \( . F e S i O_{3} \)
в. \( \operatorname{casi} O_{3} \)
\( \mathbf{c} \cdot M g S i O_{3} \)
D. \( C a_{3}\left(P O_{4}\right)_{2} \)
Subject: Physics
A car running with a velocity \( 72 \mathrm{kmph} \) on a level road, is stopped after travelling a distance of \( 30 \mathrm{m} \) after
disengaging its engine \( \left(g=10 m s^{-2}\right) \)
The coefficient of friction between the
road and the tyres is.
A. 0.33
B. 4.
c. 0.67
D. 0.8
Subject: Chemistry
The correct structure of \( 7- \)
Hydroxyheptan - 2- one is:
\( \mathbf{A} \cdot H O-C H_{2}-\left(C H_{2}\right)_{4}-C H_{2}-C O C H_{3} \)
B \( \cdot H O-C H_{2}-\left(C H_{2}\right)_{3}-C H_{2}-C O C H_{3} \)
\( \mathbf{c} \cdot H O-C H_{2}-\left(C H_{2}\right)_{3}-C H_{2}-C O C H_{2} C H_{3} \)
\( \mathbf{D} \cdot C H_{3}-C H(O H)-\left(C H_{2}\right)_{3}-C H_{2}-C O C H_{3} \)
Subject: Maths
The D.E. whose solution is \( \boldsymbol{y}=\boldsymbol{c}_{1}+\boldsymbol{c}_{2} \boldsymbol{e}^{\boldsymbol{x}} \)
is:
\( \mathbf{A} \cdot y^{\prime \prime}=y \)
B . \( y^{\prime \prime}=y^{\prime} \)
c. \( y^{\prime \prime}+y=0 \)
D \cdot \( y^{\prime \prime}+y^{\prime}=0 \)
Subject: Chemistry
In Dumas method for estimation of
nitrogen \( 0.30 g \) of an organic compound gave \( 50 m l \) of nitrogen collected at \( 300 K \) and 715 mm of \( H g \) pressure.
What is the percentage composition of nitrogen in the compound if aqueous tension at \( 300 K \) is 15 mm of \( H g ? \)
A . \( 15.23 \% \)
B. \( 17.46 \% \)
c. \( 19.23 \% \)
D . 22\%
Subject: Chemistry
Write the IUPAC names of the following coordination compounds:
(i) \( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{3} \boldsymbol{C l}_{3}\right] \)
(ii) \( \boldsymbol{K}_{\mathbf{3}}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right] \)
(iii) \( \left[\operatorname{CoBr}_{2}(e n)_{2}\right]^{+} \)
Subject: Maths
If \( \boldsymbol{P}\left(\boldsymbol{E}_{\boldsymbol{k}}\right) \propto \boldsymbol{k} \) for \( \boldsymbol{0} \leq \boldsymbol{k} \leq \boldsymbol{n}, \) then
\( \lim _{n \rightarrow \infty} \sum_{k=0}^{n} P\left(E_{k} \mid A\right) \) equals
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( 1 / 2 \)
c. \( 1 / 6 \)
\( D \)
Subject: Physics
When a bullet is fired from a rifle its
momentum become \( 20 \mathrm{kg} \) m/s. If the
velocity of the bullet is \( 1000 m / s \) what
will be its mass?
A . \( 30 g \)
B. \( 5 \mathrm{kg} \)
c. \( 20 g \)
D. \( 500 g \)
Subject: Biology
\( N a^{+}-K^{+} \) pump is found in membranes of many cells, like nerve
cells. It works against electrochemical gradient and involve an integral protein ATPase. For each molecule of ATP used
A. 3 ions of \( N a^{+} \) are pumped out and two \( K^{+} \) are taken in
B. 3 ions of \( N a^{+} \) are taken in and \( 2 K^{+} \) are pumped out
\( \mathrm{c} \cdot 2 \) ions of \( N a^{+} \) are thrown out and \( 3 K^{+} \) are absorbec
D. 3 ions of \( K^{+} \) are absorbed and \( 3 N a^{+} \) are pumped out
Subject: Physics
A string tied on a roof can bear a maximum weight of 50 kg wt. The minimum acceleration that can be
acquired by a man of \( 98 \mathrm{kg} \) to descend will be :
(take \( \mathfrak{g}=9.8 m / s^{2} \)
A. \( 9.8 m / s^{2} \)
В. 4.9 \( m / s^{2} \)
C \( .4 .8 m / s^{2} \)
D. \( 5 m / s^{2} \)
Subject: Chemistry
A black compound of manganese reacts with a halogen acid to give greenishyellow gas. When an excess of this gas
reacts with \( N H_{3} \) an unstable trihalide
is formed. In this process the oxidation state of nitrogen changes from :
\( A \cdot-3 \) to +3
B. - - - to O
\( c .-3 \) to +5
\( D \cdot O \) to -3
Subject: Chemistry
The reaction \( N_{2} O_{5}\left(\text { in } C C l_{4}\right) \rightarrow \)
\( 2 N O_{2}+1 / 2 O_{2}(g) \) is first order in
\( N_{2} O_{5} \) with rate constant \( 6.2 \times 10^{-4} \)
What is the value of rate of reaction
when \( \left[N_{2} O_{5}\right]=1.25 \) mole \( L^{-1} \)
A \( \cdot 7.75 \times 10^{4} \) mol \( L^{-1} S^{-1} \)
B. \( 6.35 \times 10^{3} \) mol \( L^{-1} S^{-1} \)
c. \( 5.15 \times 10^{5} \) mol \( L^{-1} S^{-1} \)
D. \( 3.85 \times 10^{4} \) mol \( L^{-1} S^{-1} \)
Subject: Physics
Calculate the work done by the force of
gravity to pull a \( 10 k g \) box down a \( 30^{\circ} \)
inclined plane of length \( 8.0 m ? \) Note that \( \sin 30^{0}=\cos 60^{0}=0.500 \) and
\( \cos 30^{0}=\sin 60^{0}=0.866 \)
A . \( 40 J \)
B. \( 69 J \)
c. \( 400 J \)
D. \( 690 J \)
E. \( 800 J \)