AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
After watching a programme on TV about the adverse effects of junk food and soft drinks on the health of school
children, Sonali, a student of Class XII,
discussed the issue with the school
principal. The principal immediately instructed the canteen contractor
to replace the fast food with the fiber and vitamins rich food like sprouts, salad, fruits etc. This decision was welcomed by
the parents and the students. After
reading the above passage, answer the following questions:
(a) What values are expressed by Sonali and the Principal of the school?
(b) Give two examples of water-soluble
vitamins.
Subject: Chemistry
Outline the reaction sequence for the
conversion of ethene to ethyne (the number of steps should not be more
than two
A. \( A: H O C l \) в: кон
B. A: Bromine water B: Diethyl amine
c. \( A: \mathrm{Cl}_{2}, h \nu \mathrm{B}: \mathrm{Ca}(\mathrm{OH})_{2} \)
D. A: Bromine water \( B: K O H \)
Subject: Maths
Solution of differential equation \( (x \cos x-\sin x) d x=\frac{x}{y} \sin x d y \) is
\( \mathbf{A} \cdot \sin x=\ln |x y|+c \)
B. \( \ln \left|\frac{\sin x}{x}\right|=y+c \)
\( c \cdot\left|\frac{\sin x}{x y}\right|=c \)
D. None of these
Subject: Maths
If \( \bar{a}, \bar{b} \) and \( \bar{c} \) are non-coplanar vectors and If \( \bar{d} \) is such that \( \overline{\boldsymbol{d}}=\frac{\mathbf{1}}{\boldsymbol{x}}(\overline{\boldsymbol{a}}+\overline{\boldsymbol{b}}+\overline{\boldsymbol{c}}) \)
and \( \bar{a}=\frac{1}{y}(\bar{b}+\bar{c}+\bar{d}) \) where \( x \) and \( y \) are
non-zero real numbers, then \( \frac{1}{x y}(\bar{a}+ \) \( \overrightarrow{\boldsymbol{b}}+\overline{\boldsymbol{c}}+\overline{\boldsymbol{d}})= \)
A . \( 3 \bar{c} \bar{c} \bar{c} \)
в. \( -\bar{a} \)
c. \( \overline{0} \)
D. \( 2 \bar{a} \bar{a} \bar{a} \)
Subject: Physics
A beam of light consisting of two wavelengths \( 65000 \mathrm{A} \) and \( 5200 \mathrm{A} \), is used to obtain interference fringes in Youngs double slit experiment. Suppose the mth bright fringe due to \( 6500 \mathrm{A} \) coincides with nth bright fringe due to \( 5200 \mathrm{A} \) at a minimum distance from
the central maximum. Then
A \( . m=4 ; n=5 \)
B. \( m=5 ; n=4 \)
c. \( m=8 ; n=10 \)
D. \( m=10 ; n=8 \)
Subject: Physics
A \( 3.0 k g \) lump of clay is moving to the
left at \( 4.0 m / s . \) It collides in a perfectly inelastic collision with a \( 6.0 k g \) lump of
clay moving to the right at \( 2.0 m / s \) What is the total kinetic energy after
the collision?
\( A \cdot 62 J \)
в. \( 36 J \)
c. \( 25 J \)
D. \( 12 . J \)
E . \( 0 . J \)
Subject: Maths
\( \cos ^{-1}(\sqrt{\frac{\boldsymbol{a}-\boldsymbol{x}}{\boldsymbol{a}-\boldsymbol{b}}})=\sin ^{-1}(\sqrt{\frac{\boldsymbol{x}-\boldsymbol{b}}{\boldsymbol{a}-\boldsymbol{b}}}) \)
possible if
A \( . a>x>b \) or \( a<x<b \)
В. \( a=x=b \)
C. \( a>b \) and \( x \) takes any value
D. \( a<b \) and \( x \) takes any value
Subject: Physics
A stationary ball weighing \( 0.25 \mathrm{kg} \) acquires a speed of \( 10 \mathrm{m} / \mathrm{s} \) when hit by a hockey stick. The impulse imparted to the ball is :
A . 2.5 Ns
B. 2.0Ns
c. \( 1.5 \mathrm{Ns} \)
D. 0.5Ns
Subject: Maths
The parallel sides of a trapezium are 20 \( \mathrm{m} \) and \( 30 \mathrm{m} \) and its non parallel sides are \( 6 \mathrm{m} \) and \( 8 \mathrm{m} \). Find the area of the trapezium.
A \( \cdot 96 m^{2} \)
в. \( 82 m^{2} \)
c. \( 100 \mathrm{m}^{2} \)
D. \( 120 m^{2} \)
Subject: Chemistry
If dichloromethane \( (D C M) \) and water
\( \left(H_{2} O\right) \) are used for differential extraction, which one of the following statements is correct?
A. \( D C M \) and \( H_{2} O \) would stay as lower and upper layer respectively in the S.F.
B. \( D C M \) and \( H_{2} O \) will be miscible clearly
c. \( D C M \) and \( H_{2} O \) would stay as upper and lower layer respectively in the separating funnel (S.F.)
D. \( D C M \) and \( H_{2} O \) will make trubid/colloidal mixtur
Subject: Maths
If two vertices of an isosceles triangle \( \operatorname{are}(2,0) \) and (2,5) and length of the equal sides is 3 then the third vertex is
A \( .(2,6) \&(-5,3) \)
B. (8,3)\( \&(5,1) \)
\( ^{\mathbf{C}} \cdot\left(2 \pm \frac{\sqrt{11}}{2}, \frac{5}{2}\right) \)
D. \( \left(3 \pm \frac{\sqrt{14}}{2}, \frac{7}{2}\right) \)
Subject: Chemistry
\( N a+C l \rightarrow N a^{+}+C l^{-} \rightarrow N a^{+} C l^{-} \)
(2,8,1)(2,8,7)(2,8)(2,8,8)
The above equation represents the
formation of sodium chloride. Observe
the equation and answer the following:
a) How many electrons are transferred
from \( N a \) to \( C l ? \)
b) Name the force acting between \( N a^{+} \)
and \( C l^{-} \)
c) Name the nearest noble gas to \( C l^{-} \)
d) Name the bond between \( N a^{+} \) and
\( \boldsymbol{C l}^{-} \)
e) How many electrons are present in
\( N a^{+} \) ion?
Subject: Chemistry
The \( C r O_{3} \) on reaction with \( H C l \) and
NaOH(aq) gives, respectively:
A \( \cdot C r O_{2} C l_{2}, C r O_{4}^{2} \)
B. \( \operatorname{Cr}(O H)_{2}, C r O_{4}^{2} \)
c. \( C l_{2}, C r_{2} O_{7}^{2-} \)
D. \( C l_{2}, C r(O H)_{3} \)
Subject: Physics
The average kinetic energy \( E \) of a gas
molecule is given by the equation \( \boldsymbol{E}= \)
\( \frac{3}{2} k T \)
where \( T \) is the absolute (kelvin
temperature)

What are the SI base units if \( k \) ?
A \( \cdot k g^{-1} m^{-1} s^{2} K \)
B. \( k g^{-1} m^{-2} s^{2} K \)
c. \( k g m s^{-2} K^{-1} \)
D. \( \operatorname{kgm}^{2} s^{-2} K^{-1} \)
Subject: Maths
The equation of the circle which touches the lines \( x=0, y=0 \) and
\( 4 x+3 y=12 \) is
A \( \cdot x^{2}+y^{2}-2 x-2 y-1=0 \)
В . \( x^{2}+y^{2}-2 x-2 y+3=0 \)
c. \( x^{2}+y^{2}-2 x-2 y+2=0 \)
D. \( x^{2}+y^{2}-2 x-2 y+1=0 \)
E . \( x^{2}+y^{2}-2 x-2 y-3=0 \)
Subject: Maths
From mean value theorem, \( \boldsymbol{f}(\boldsymbol{b})- \) \( \boldsymbol{f}(\boldsymbol{a})=(\boldsymbol{b}-\boldsymbol{a}) \boldsymbol{f}^{1}\left(\boldsymbol{x}_{1}\right) ; \boldsymbol{a}<\boldsymbol{x}_{1}< \)
bif \( f(x)=\frac{1}{x} \) then \( x_{1}= \)
\( A \cdot \sqrt{a b} \)
B. \( \frac{a+b}{2} \)
c. \( \frac{a b}{a+b} \)
D・ \( \frac{a-b}{b-a-a-b} \)
Subject: Maths
The value of \( \sin ^{-1}\left(\cos \frac{33 \pi}{5}\right) \) is
A \( \cdot \frac{3 \pi}{5} \)
в. \( \frac{7 \pi}{5} \)
c. \( \frac{\pi}{10} \)
D. \( -\frac{\pi}{10} \)
Subject: Physics
A cylınder ot nelght \( n \) thled with water
and is kept on lock of height h/2. The
level of water in the cylinder is kept constant. Four holes numbered 1,2,3
and 4 are at the side of the cylinder and
at height \( 0, \) h/4, h/2 and \( 3 h / 4 \)
respectively. When all four holes are opened together, the hole from which
water will reach farthest distance on
the plane PQ is the hole number.
\( A \)
\( B .2 \)
\( c \cdot 3 \)
D.
Subject: Physics
A conducting circular loop is placed in a uniform magnetic field \( \mathrm{B}=0.025 \mathrm{T} \) with its plane perpendicular to the magnetic field. The radius of the loop starts
shrinking at \( 1 \mathrm{mm} \mathrm{s}^{-1} \). The induced emf
in the loop when the radius is \( 2 \mathrm{cm} \) is:
A. \( 2 \pi \mu V \)
в. \( \pi \mu V \)
c. \( \frac{\pi}{2} \mu V \)
D. \( 3.2 \pi \mu V \)
Subject: Maths
The angle between any two diagonals of
cube are:
A \( \cdot \cos ^{-1}\left(\frac{1}{2}\right) \)
B. \( \cos ^{-1}\left(\frac{1}{3}\right) \)
\( ^{\mathbf{C}} \cdot \cos ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
\( \mathrm{D} \cdot \cos ^{-1}\left(\frac{1}{\sqrt{2}}\right) \)
Subject: Chemistry
Figure depicts the charge in conc. of species \( x \& y \) for reaction \( 2 x \rightarrow y, \) as a
function of time the point of inter
section of two curves represents?
\( A \cdot t_{1 / 2} \)
В \( \cdot t_{1 / 3} \)
\( c \cdot t_{1 / 4} \)
\( \mathbf{D} \cdot t_{2} \)
Subject: Maths
In figure (ii) given below, \( \boldsymbol{A B} \| \boldsymbol{D} \boldsymbol{E} \) and
\( \boldsymbol{B} \boldsymbol{D} \| \boldsymbol{E} \boldsymbol{F} . \) Prove that \( \boldsymbol{D} \boldsymbol{C}^{2}=\boldsymbol{C} \boldsymbol{F} \times \boldsymbol{A} \boldsymbol{C} \)
Subject: Maths
Minimize \( z=6 x+2 y, \) Subject to \( x+ \)
\( 2 y \geq 3, x+4 y \geq 4,3 x+y \geq 3, x \geq \)
\( \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \)
Subject: Physics
If the force is given by \( \boldsymbol{F}=\boldsymbol{a} \boldsymbol{t}+\boldsymbol{b} \boldsymbol{t}^{2} \) with \( \boldsymbol{t} \)
as time. The dimensions of a and b are:
\( \mathbf{A} \cdot\left[M L T^{-4}\right],\left[M L T^{-2}\right. \)
B . \( \left[M L T^{-3}\right],\left[M L T^{-4}\right] \)
C \( \cdot\left[M L^{2} T^{-3}\right],\left[M L^{2} T^{-2}\right] \)
D \cdot \( \left[M L^{2} T^{-3}\right],\left[M L^{3} T^{-4}\right] \)
Subject: Chemistry
Match the following and write the order
for ABCD.
List List - II
1) Conc
A) Decarboxylating agent
\[
H_{2} S O_{4} / 170^{0} C
\]
B) Dehydrohalogenating
2) \( \mathrm{NaOH}+\mathrm{CaO} \)
agent
C) Dehalogenating agent
3) \( Z n \) dust
D) Dehydrating agent
4) aq \( K O H \)
5) alcoholic \( K O H \)
A . 1234
B. 2 4 31
\( c \cdot 2531 \)
D. 1534
Subject: Maths
Verify the following
(i) (0,7,-10),(1,6,-6) and (4,9,-6) are the vertices of an isosceles triangle
(ii) (0,7,10),(-1,6,6) and (-4,9,6) are the vertices of a right angled triangle
(iii) (-1,2,1),(1,-2,5),(4,-7,8) and (2,-3,4) are the vertices of a parallelogram
Subject: Physics
The surface tension of soap solution is
\( 0.05 N m^{-1} . \) If the diameter of the soap
bubble is \( 4 \mathrm{cm} . \) The excess pressure
inside the soap bubble over that of outside is .................. Pascal:
A . 10
в. 1.0
c. \( 0 . \)
D. 0.25
Subject: Physics
A wire of uniform cross-section has a
resistance of \( \boldsymbol{R} \) \Omega. What would be the
resistance of a similar wire, made of the
same material, but twice as long and of
twice the diameter?
A \( \cdot \frac{3}{2} R \)
в. \( \frac{5}{2} R \)
c. \( \frac{1}{2} R \)
D. \( \frac{1}{4} R \)
Subject: Chemistry
A substance reacts with initial concentration of \( a \) mol \( d m^{-3} \) according
to zero order kinetics. The time it takes
for the completion of the reaction is:
\( k= \) rate constant
A \( \cdot \frac{k}{a} \)
в. \( \frac{a}{2 k} \)
c. \( \frac{a}{k} \)
D. \( \frac{2 k}{a} \)
Subject: Maths
Calculate mean deviation about mean
for the given data.
Score \( (x) \quad 6 \quad 20 \) 3. 8
11 Frequency
\( \begin{array}{ll}\text { (f) } & \text { (f) } 7\end{array} \) 27
A. 3.117
B. 3.217
c. 4.212
D. 6.21
Subject: Physics
toppr 'ОGा
Q Type your question_
but represents path from each of the
two slits to the third "bright fringe"
formed as part of the interference
pattern.
In the diagram how much longer is path
1 than path \( 2 ? \)
\( \mathbf{A} .400 n m \)
B. \( 1200 n m \)
\( \mathbf{c} \cdot 1600 n m \)
D. \( 1000 n m \)
E . \( 600 n m \)
Subject: Chemistry
A certain liquid mixture of two liquids \( A \) and B (behaving ideally) has a vapour
pressure 70 torr \( (1 \text { torr }=1 \mathrm{mm}) \) at \( 25^{\circ} \mathrm{C} \) for a certain mole fraction \( X \) of \( A \). For the same mole fraction \( X \) for \( B \) in the
mixture, the vapour pressure of mixture
is 90 torr at \( 25^{\circ} \mathrm{C} . \) If \( \boldsymbol{P}_{A}^{0}-\boldsymbol{P}_{B}^{0}=\mathbf{4 0} \) torr
calculate \( P_{A}^{0}, P_{B}^{0} \) and \( X \)
A . 100 torr, 60 torr, 0.25
B. 120 torr, 80 torr, 0.25
c. 200 torr, 160 torr, 0.25
D. 220 torr, 180 torr, 0.25
Subject: Physics
A body moves along circular path of radius \( 10 \mathrm{m} \) and the coefficient of friction is \( 0.5 . \) What should be its
angular velocity in rad/s if it is not to
slip from the surface? \( \left(\boldsymbol{g}=\mathbf{9 . 8 m} / \boldsymbol{s}^{2}\right) \)
A . 0.7
B. 0.28
c. 0.27
D. 2.7
Subject: Chemistry
The monomer for the given compound
is:
\[
\left[\begin{array}{l}
\mathrm{CH}_{3} \\
\mathrm{I} \\
\mathrm{fH}_{3}
\end{array}\right]_{n_{2}}
\]
A. 2-methylpropene
B. Styrene
c. Propylene
D. Ethene
Subject: Physics
Assertion(A): The possibility of an electric bulb fusing is higher at the time of switching on and off
Reason(R): Inductive effects produce a large current at the time of switch-on
and switch-off.
A. Both A and R are individually true and R is the correct explanation of A
B. Both A and R are individually true but R is not the correct explanation of \( A \)
c. A is true but R is false
D. Both A and R are false
Subject: Physics
A \( 4 \mu F \) capacitor is charged to \( 400 V . \) If its plates are joined through a resistance \( 2 k \Omega, \) then heat produced in the resistance is
\( \mathbf{A} \cdot 0.16 J \)
в. \( 0.32 J \)
c. \( 0.64 J \)
D. \( 1.28 J \)
Subject: Physics
A ball is dropped from a height of \( 1 m \) The coefficient of restitution between the ground and the ball is \( 1 / 3 . \) The height to which the ball will rebound after two collisions with ground is :
A. \( 9 m \)
в. \( 1 / 9 m \)
c. \( 1 / 81 m \)
D. \( 81 m \)
Subject: Maths
The value of
\( \frac{(\sqrt{\mathbf{2}}+\mathbf{1}) \mathbf{1 9 8}}{\boldsymbol{\pi}} \int_{\boldsymbol{\pi} / 4}^{\boldsymbol{3} \boldsymbol{\pi} / \boldsymbol{4}} \frac{\boldsymbol{\phi}}{\mathbf{1}+\sin \phi} \boldsymbol{d} \boldsymbol{\phi} \) is
Subject: Maths
Which of the following function is one-
one?
A \( . f: R \rightarrow R \) given by \( f(x)=|x-1| \) for all \( x \in R \)
B. \( g:\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \rightarrow R \) given by \( g(x)=|\sin x| \) for all \( x \in \)
\( \left[\frac{-\pi}{2}, \frac{\pi}{2}\right] \)
\( \mathbf{c} \cdot_{h}:\left[\frac{-\pi}{2}, \frac{\pi}{2}\right] \in R \operatorname{given} \operatorname{by} h(x)=\sin x \) for all \( x \in \)
\( \left[\frac{-\pi}{2}, \frac{\pi}{2}\right] \)
\( \mathbf{D} \cdot \phi: R \rightarrow R \) given by \( f(x)=x^{2}-4 \) for all \( x \in R \)
Subject: Chemistry
Assertion
Among isomeric alkanes, branching increases the boiling points.
Reason
branching lowers the intermolecular van der waals force of attraction.
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 wrong but Reason is correct.
Subject: Chemistry
Q Type your question
made to reaci with anute nul tads r is
evolved in the reaction which is made to
pass through the delivery tube into test
tube 2 having solution \( Z \) and a milky
solution is obtained What are \( X, Y \) and \( Z \)
respectively?
A. \( N a O H, C O_{2}, N a_{2} C O_{3} \)
в. \( \operatorname{Ca}(O H)_{2}, H_{2}, C a\left(H C O_{3}\right)_{2} \)
c \( \cdot \operatorname{ca}(O H)_{2}, C O_{2}, C a C O_{3} \)
D \( \cdot \) \( _{C a} \) a \( C \) O \( _{3}, \) C \( O_{2}, C a(O H)_{2} \)
Subject: Maths
There are two balls in an urn whose
colors are not known ( ball can be either
white or black). A white ball is put into
the urn. A ball is then drawn from the
urn. The probability that it is white is
A \( \cdot \frac{1}{4} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{2}{3} \)
D.
Subject: Maths
\( P \) is point in the interior of an equilateral triangle with side a units. If \( P_{1}, P_{2} \) and \( P_{3} \) are the distance of \( P \) from
the three sides of the triangle, then
\( \boldsymbol{P}_{1},+\boldsymbol{P}_{2}+\boldsymbol{P}_{3} \) is?
A \( \cdot \) equals \( \frac{2 a}{3} \) units
в. \( _{\text {equals }} \frac{a \sqrt{3}}{2} \)
\( c . \) is more than a unit
D. cannot be determined unless the location of P is specified.
Subject: Physics
A particle in a certain conservative force field has a potential energy given by \( U=\frac{20 x y}{z} . \) The force exerted on it is?
A \( \cdot\left(\frac{20 y}{z}\right) \hat{i}+\left(\frac{20 x}{z}\right) \hat{j}+\left(\frac{20 x y}{z^{2}}\right) \hat{k} \)
B. \( -\left(\frac{20 y}{z}\right) \hat{i}-\left(\frac{20 x}{z}\right) \hat{j}+\left(\frac{20 x y}{z^{2}}\right) \hat{k} \)
\( ^{\mathrm{c}} \cdot\left(\frac{20 y}{z}\right) \hat{i}-\left(\frac{20 x}{z}\right) \hat{j}-\left(\frac{20 x y}{z^{2}}\right) \hat{k} \)
D \( \cdot\left(\frac{20 y}{z}\right) \hat{i}+\left(\frac{20 x}{z}\right) \hat{j}-\left(\frac{20 x y}{z^{2}}\right) \hat{k} \)
Subject: Physics
Electric field intensity at a point due to a charge \( Q \) is \( 24 \mathrm{N} / \mathrm{C} \) and electric potential at \( A^{\prime} \) due to charge \( Q \) is \( =12 \mathrm{j} / \mathrm{C} \) The distance between the charges and magnitude of \( Q \) are
A \( \cdot 0.4 m, 0.667 \times 10^{-9} \mathrm{C} \)
B . \( 0.4 m, 6.67 \times 10^{-4} \mathrm{C} \)
c. \( 0.5 m, 2.67 \times 10^{-9} \mathrm{C} \)
D. \( 0.5 m, 7.66 \times 10^{-9} \mathrm{C} \)
Subject: Physics
Two satellites \( A \) and \( B \) of masses \( m_{1} \)
and \( m_{2}\left(m_{1}=2 m_{2}\right) \) are moving in
circular orbits of radii \( r_{1} \) and
\( r_{2}\left(r_{1}=4 r_{2}\right), \) respectively, around the
earth. If their periods are \( T_{A} \) and \( T_{B} \)
then the ratio \( T_{A} / T_{B} \) is
A .4
B . 16
\( c \cdot 2 \)
D. 8
Subject: Physics
A dense sphere of mass \( M \) is placed at
the centre of a circle of radius \( R \). Find
the work done, when a particle of mass
\( m \) is brought from \( A \) to \( B \) along a circle
as shown in the figure.
A . zer
в. \( \frac{G M m}{R} \)
c. \( -\frac{G M m}{R} \)
D. \( \frac{2 G M m}{B} \)
Subject: Physics
A particle of mass \( m \) and carrying a charge \( e \) is fired perpendicular to a uniform magnetic induction \( B \) with a
velocity \( v . \) The time period of revolution for the subsequent motion is given by
A \( \cdot \frac{2 \pi B}{m e} \)
в. \( \frac{2 \pi e}{B} \)
с. \( \frac{2 \pi m}{B e} \)
D. \( \frac{\pi B e}{m} \)
Subject: Maths
The slope of the tangent to the curve
\( \boldsymbol{x}=\boldsymbol{t}^{2}+\boldsymbol{3} \boldsymbol{t}-\mathbf{8}, \boldsymbol{y}=\boldsymbol{2} \boldsymbol{t}^{2}-\boldsymbol{2} \boldsymbol{t}-\mathbf{5} \) at the
point (2,-1) is
A \( \cdot \frac{22}{7} \)
B. \( \frac{6}{7} \)
\( c \cdot \frac{7}{6} \)
D. \( -\frac{6}{7} \)
Subject: Maths
Consider the following groups \( A \) and B.A \( : 3,4,5, \dots \dots \dots \dots \) pto n terms
\( B: 15,19,23, \dots \dots \dots \) pto \( n \) terms
If means deviations of groups \( A \) and \( B \) about their means are \( \alpha \) and \( \beta \)
respectively then
A \( . \beta=5 \alpha \)
в. \( \beta=4 \alpha+3 \)
c. \( \beta=4 \alpha \)
D. None
Subject: Chemistry
A quantity of \( 0.62 g \) of \( N a_{2} C O_{3} . H_{2} O \) is
added to \( 100 \mathrm{ml} \) of \( 0.1 N-H_{2} S O_{4} \)
solution. The resulting solution would be
A . acidic
B. alkaline
c. neutral
D. buffer
Subject: Physics
Two point charge \( Q \) and \( -3 Q \) are placed at some distance apart. If the electric field at the location of \( Q \) is \( \vec{E} \), the field at the location of \( -3 Q \) is:
A. \( \vec{E} \)
в. \( -\vec{E} \)
c. \( +\frac{\vec{E}}{3} \)
D. \( -\frac{\vec{E}}{3} \)
Subject: Maths
Evaluate \( \int \frac{1+x^{-2 / 3}}{1+x} d x \)
The ans is \( =\frac{1}{2}\left[\log (t+1)^{4}\left(t^{2}-t+\right.\right. \)
1) \( ]+\sqrt{3} \cdot \tan ^{-1} \frac{2 t-1}{\sqrt{(3))}} \)
then \( t=? \)
\( \mathbf{A} \cdot x^{1 / 3} \)
B . \( x^{1 / 2} \)
\( c \)
\( \mathbf{D} \cdot x^{3} \)
Subject: Physics
Current of \( 2 A \) passing through a coil of
100 turns gives rise to a magnetic flux of \( 5 \times 10^{-3} W b \) per turn. The magnetic energy associated with coil is
\( \mathbf{A} \cdot 5 \times 10^{-3} J \)
B. 5.5
c. \( 0.5 \times 10^{-3} J \)
D. \( 0.5 J \)
Subject: Physics
A point 0 is placed midway between the
two converging mirror of focal length \( \boldsymbol{f} \)
each. find \( d \) so that object and image
coincide:
A \( .2 f, 4 f \)
B. \( 2 f, 3 f \)
\( c \cdot 4 f \)
D. \( 2 f, f \)
Subject: Maths
For the values \( x_{1}, x_{2} \dots \dots x_{101} \) of a
distribution \( x_{1}<x_{2}<x_{3}<\dots . .< \)
\( x_{100}<x_{101} . \) The mean deviation of this
distribution with respect to a number will be minimum when k is equal to
A. \( x_{1} \)
в. \( x_{5} \)
c. \( x_{50} \)
D. \( \frac{x_{1}+x_{2}+\ldots . .+x_{101}}{101} \)
Subject: Physics
Three fuse wires \( A, B \) and \( C \) tinned
copper having identical cross section and length \( 8 \mathrm{cm}, 12 \mathrm{cm} \) and \( 16 \mathrm{cm} \) are
used as fuses. For the same value of
current
A. fuse A will melt first
B. fuse B will melt first
c. fuse C will melt first
D. all fuse will melt for same current
Subject: Physics
The focal length of a convex lens of
glass \( (\mu=1.5) \) is \( 2 c m . \) The focal length of the lens when immersed in a liquid of
refractive index 1.25 will be :
A \( .5 \mathrm{cm} \)
B. \( 2.4 \mathrm{cm} \)
\( c .1 c m \)
D. \( 4 c m \)
Subject: Maths
The surface area of three conterminous
faces of a furniture is \( 5,10,20 \mathrm{q} . \mathrm{cm} \) respectively. Find the volume of the
cuboid.
A \( \cdot 2 \sqrt{10} \mathrm{cm}^{3} \)
B . \( 20 \sqrt{10} \mathrm{cm}^{3} \)
c. \( 40 \sqrt{10} \mathrm{cm}^{3} \)
D. \( 10 \sqrt{10} \mathrm{cm}^{3} \)
Subject: Maths
Number of intersecting points of the
\( \operatorname{conic} 4 x^{2}+9 y^{2}=1 \) and \( 4 x^{2}+y^{2}=4 \)
is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. 0 (zero)
Subject: Physics
The potential difference between point B
and \( \mathrm{C} \) of the circuit is
A \( \cdot \frac{\left(C_{2}-C_{1}\right)}{V} \)
B. \( \frac{\left(C_{4}-C_{3}\right)}{V} \)
c. \( \frac{\left(C_{2} C_{3}-C_{1} C_{4}\right)}{\left(C_{1}+C_{2}+C_{3}+C_{4}\right)} \cdot V \)
D. \( \frac{C_{1} C_{4}-C_{2} C_{3}}{\left(C_{1}+C_{2}\right) \times\left(C_{3}+C_{4}\right)} \cdot V \)
Subject: Maths
Find the value of \( y-x \) from the
following equation \( \mathbf{2}\left[\begin{array}{cc}\boldsymbol{x} & \mathbf{5} \\ \mathbf{7} & \boldsymbol{y}-\mathbf{3}\end{array}\right]+\left[\begin{array}{cc}\mathbf{3} & \mathbf{- 4} \\ \mathbf{1} & \mathbf{2}\end{array}\right]=\left[\begin{array}{cc}\mathbf{7} & \mathbf{6} \\ \mathbf{1 5} & \mathbf{1 4}\end{array}\right] \)
Subject: Maths
\( \int \frac{x+\sin x}{1+\cos x} d x= \)
A \( \cdot x \tan \frac{x}{2}+c \)
B. \( x \cot \frac{x}{2}+c \)
c. \( x \sin \frac{x}{2}+c \)
D. \( x \cos \frac{x}{2}+c \)
Subject: Physics
A radioactive material is in the form of
a sphere whose radius is \( 9 \times 10^{-3} \) m. If
\( 6.25 \times 10^{12} \beta^{-} \) particles are emitted per
second by it then in how much time will a potential of 1 volt be produced on the
sphere if it is isolated?
A . \( 1.1 \mathrm{ms} \)
B . \( 10^{-8} \mathrm{ms} \)
c. \( 1.0 \mu s \)
D. 11 \mus
Subject: Physics
Two block \( A \) and \( B \) are arranged as
shown in the figure. The mass of block \( A \) is 10 kg. The coefficient of friction
between the block \( A \) and the horizontal
plane is \( 0.2 . \) The minimum mass of block \( B \) to start motion will be
A . \( 0.2 \mathrm{kg} \)
в. \( 10 \mathrm{kg} \)
\( c .5 k g \)
D. \( 2 k g \)
Subject: Chemistry
How many moles of electrons will weigh
one kilogram?
\( \mathbf{A} \cdot 6.023 \times 10^{23} \)
B. \( \frac{1}{9.108} \times 10^{31} \)
C \( \cdot \frac{6.023}{9.108} \times 10^{54} \)
D. \( \frac{1}{9.108 \times 6.023} \times 10^{8} \)
Subject: Chemistry
\( 50 \mathrm{mL} \) aqueous solution of \( \mathrm{Fe} \boldsymbol{S O}_{4} \)
required 12 mL of 0.2 M \( K M n O_{4} \) in
acidic medium for complete oxidation. Calculate the molarity of ferrous sulphate solution. The reaction is:
\( M n O_{4}^{-}+5 F e^{2+}+8 H^{+} \rightarrow M n^{2+}+ \)
\( \mathbf{5} \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}+\mathbf{4} \boldsymbol{H}_{2} \boldsymbol{O} \)
A. 0.024
B. 0.24
c. 2.4
D. \( 2.4 \times 10^{-3} \)
Subject: Physics
A cell supplies a current of \( 0.9 \mathrm{A} \) through a \( 2 \Omega \) resistor and a current of
\( 0.3 \mathrm{A} \) through a \( 7 \Omega \) resistor. The internal resistance of the cell is :-
A . \( 1.0 \Omega \)
в. \( 0.5 \Omega \)
c. \( 2.0 \Omega \)
D. \( 1.2 \Omega \)
Subject: Chemistry
Consider the following reactions in equilibrium with initial concentration of \( 0.01 \mathrm{M} \) of every species (assuming the same equilibrium constant same)
\( (\mid) P C l_{5}(g) \rightleftharpoons P C l_{3}(g)+C l_{2}(g) \)
\( (\|) 2 \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \)
\( (\| I) N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \)
Arrange these reactions in the order of the extent to which it takes place.
A \( . \) ।>॥>
c. ॥<॥ा《