AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
(a) Obtain a relation for equivalent capacitance of the series combination
of capacitors. Draw a circuit diagram
(b) 10 capacitors each of capacity \( 10 \mu F \) are joined first in series and then
in parallel. Write the value of product of equivalent capacitances.
(c) What will be the value of
capacitance of a \( 4 \mu F \) capacitor if a
dielectric of dielectric constant 2 is
inserted fully between the plates of parallel plate capacitor.
Subject: Maths
\( f(x)=\left\{\begin{array}{l}x-5 ; x \leq 1 \\ 4 x^{2}-9 ; 1<x \leq 2 \\ 3 x^{2}+4 ; x>2\end{array}\right. \)
Then \( \boldsymbol{f}\left(\boldsymbol{2}^{+}\right)-\boldsymbol{f}\left(\boldsymbol{2}^{-}\right)= \)
\( A \)
B. 2
\( c \)
\( D \)
Subject: Maths
Indicate the relation which can hold in
their respective domain for infinite
values of \( x \)
This question has multiple correct options
\( \mathbf{A} \cdot \tan \left|\tan ^{-1} x\right|=|x| \)
B \cdot \( \cot \left|\cot ^{-1} x\right|=|x| \)
C \( \cdot \tan ^{-1}|\tan x|=|x| \)
D \( \cdot \sin \left|\sin ^{-1} x\right|=|x| \)
Subject: Physics
Identify what happens to a stream of \( \alpha \)
particles that is shoot at a thin sheet of gold foil in a rutherford experiment?
A. All of the particles pass straight through
B. A few of the particles bounce back at \( 180^{\circ} \)
C. All of the particles bounce back at \( 180^{\circ} \)
D. Most of the particles are absorbed by the foil
E. None of the particles are deflected by more than \( 45^{\circ} \)
Subject: Maths
The focus of a conic is the origin and its
corresponding directrix is \( 7 x-y- \)
\( \mathbf{1 0}=\mathbf{0 .} \) If length of its latus rectum is 2
then its eccentricity is:
A \( \cdot \sqrt{2} \)
B. 1
c. \( \frac{1}{\sqrt{2}} \)
D. \( \frac{1}{2} \)
Subject: Chemistry
Consider the reaction at 300 K.
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \rightarrow 2 \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}^{o}= \)
\( -185 k J \)
If 2 mole of \( H_{2} \) completely react with 2
mole of \( C l_{2} \) to form HCl. What is \( \Delta U^{\circ} \)
for the reaction?
\( \mathbf{A} \cdot \mathbf{0} \)
B . -185 kJ
c. 370 k.
D. None of these
Subject: Maths
\( \boldsymbol{A}=(\mathbf{1},-\mathbf{2}, \mathbf{3}), \boldsymbol{B}=(2,1,3), \boldsymbol{C}=(4,2, \)
1) and \( G=(-1,3,5) \) is the centroid of
the tetrahedron \( A B C D . \) Then the fourth
coordinate is
A. (11,11,13)
В. (-11,11,45)
c. (-11,11,13)
D. (11,13,11)
Subject: Maths
If \( \boldsymbol{P}=\left[\begin{array}{cc}\frac{\sqrt{\mathbf{3}}}{\mathbf{2}} & \frac{\mathbf{1}}{2} \\ -\frac{\mathbf{1}}{\mathbf{2}} & \frac{\sqrt{\mathbf{3}}}{\mathbf{2}}\end{array}\right], \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{1} \\ \mathbf{0} & \mathbf{1}\end{array}\right] \) and
\( Q=P A P^{T} \) then \( P\left(Q^{2005}\right) P^{T} \) equal to
\begin{tabular}{l} 
A. \( \left[\begin{array}{cc}1 & 2005 \\
0 & 1\end{array}\right] \) \\
\hline
\end{tabular}
B. \( \left[\begin{array}{cc}\sqrt{3} / 2 & 2005 \\ 1 & 0\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{cc}1 & 2005 \\ \sqrt{3} / 2 & 1\end{array}\right] \)
D. \( \left[\begin{array}{ll}1 & \sqrt{3} / 2 \\ 0 & 2005\end{array}\right] \)
Subject: Physics
A solenoid is connected to a source of
constant e.m.f. for a long time. A soft iron piece is inserted into it. Then, which of the following is/are correct? This question has multiple correct options
A. Self-inductance of the solenoid gets increased
B. Flux linked with the solenoid increases; hence, steady state current gets decreased
C. Energy stored in the solenoid gets increased
D. Magnetic moment of the solenoid gets increased
Subject: Physics
An electric dipole has a pair of equa and opposite point charges \( +\mathrm{Q} \) and \( \mathrm{Q} \) separated by a distance 2x. The axis of the dipole is defined as
A. the line joining positive charge to -ve charge
B. the line making angle of \( 45^{\circ} \) with line joining two charges
c. perpendicular to the line joining the two charges drawn at the centre and pointing upward direction
D. perpendicular to the line joining the two charges drawn at the centre and pointing downward direction
Subject: Maths
The simplification of \( \cos (A+ \)
\( B) \cos (A-B) \) is equivalent to:
A \( \cdot \sin ^{2} A-\sin ^{2} B \)
B. \( \cos ^{2} B-\sin ^{2} A \)
\( \mathbf{c} \cdot \cos ^{2} A-\cos ^{2} B \)
D. \( \cos 2 A \cdot \sin 2 B \)
Subject: Maths
\( \mathbf{f}_{\mathbf{1}}=\left|\begin{array}{ccc}\mathbf{7} & \boldsymbol{x} & \mathbf{2} \\ -\mathbf{5} & \boldsymbol{x}+\mathbf{1} & \mathbf{3} \\ \mathbf{4} & \boldsymbol{x} & \mathbf{7}\end{array}\right|, \boldsymbol{\Delta}_{2}= \)
\( \left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{2} & \boldsymbol{7} \\ \boldsymbol{x}+\boldsymbol{1} & \boldsymbol{3} & -\boldsymbol{5} \\ \boldsymbol{x} & \boldsymbol{7} & \boldsymbol{4}\end{array}\right| \) then \( \boldsymbol{\Delta}_{1}-\boldsymbol{\Delta}_{2}=\boldsymbol{0} \) for
\( \mathbf{A} \cdot x=2 \)
B. all real \( x \)
c. \( x=0 \)
D. none of these
Subject: Physics
\( 1 \mathrm{cc} \) of water is taken from the surface
to the bottom of a lake having depth 100m. If bulk modulus of water is \( 2.2 \times \)
\( 10^{9} N / m^{2} \) then decrease in the volume
of the water will be
A \( .4 .5 \times 10^{-4} c c \)
B. \( 8.8 \times 10^{-4} c c \)
c. \( 2.2 \times 10^{-4} c c \)
D. \( 1.1 \times 10^{-4} c c \)
Subject: Physics
If the resistances of values \( R_{1} \) and \( R_{2} \)
are connected on both ends as shown in
figure, current \( I, \) flowing through
resistance \( R_{1} \) is given by
\( A \)
\[
\frac{B l R_{2}\left(v_{1} r_{2}-v_{2} r_{1}\right)}{R_{1} R_{2}\left(r_{1}+r_{2}\right)+r_{2} r_{1}\left(R_{1}+R_{2}\right)}
\]
B.
\[
\frac{B l R_{2}\left(v_{1} r_{2}+v_{2} r_{1}\right)}{R_{1} R_{2}\left(r_{1}+r_{2}\right)+r_{2} r_{1}\left(R_{1}+R_{2}\right)}
\]
\( c \)
\[
\frac{B l R_{2}\left(v_{1} r_{2}-v_{2} r_{1}\right)}{R_{1} R_{2}\left(r_{1}-r_{2}\right)+r_{2} r_{1}\left(R_{1}+R_{2}\right)}
\]
D.
\[
\frac{B l R_{2}\left(v_{1} r_{2}-v_{2} r_{1}\right)}{R_{1} R_{2}\left(r_{1}+r_{2}\right)-r_{2} r_{1}\left(R_{1}+R_{2}\right)}
\]
E . nont
Subject: Chemistry
To make the following reduction process
spontaneous, temperature should be:
\( Z n O+C \longrightarrow Z n+C O \)
A \( \cdot 1000^{\circ} \mathrm{C} \)
В. \( >1000^{\circ} \mathrm{C} \)
\( c \cdot<500^{\circ} C \)
D. \( <1000^{\circ} \mathrm{C} \)
Subject: Maths
If \( \alpha, \beta \) are roots of the equation \( x^{2}+ \) \( \mathbf{2} \boldsymbol{x}+\mathbf{5}=\mathbf{0} \) and \( \overrightarrow{\boldsymbol{a}}=(\boldsymbol{\alpha}+\boldsymbol{\beta}) \hat{\mathbf{i}}+ \)
\( \boldsymbol{\alpha} \boldsymbol{\beta} \hat{\boldsymbol{j}} \overrightarrow{\boldsymbol{b}}=\boldsymbol{\alpha} \boldsymbol{\beta} \hat{\boldsymbol{i}}+(\boldsymbol{\alpha}+\boldsymbol{\beta}) \hat{\boldsymbol{j}}+\left(\boldsymbol{\alpha}^{2}+\boldsymbol{\beta}^{2}\right) \hat{\boldsymbol{k}} \)
\( \operatorname{then} \vec{a} \times \vec{b}= \)
A \( . \hat{i}+12 \hat{j}+12 \hat{k} \)
B . \( -30 \hat{i}+12 \hat{j}-4 \hat{k} \)
c. \( -30 \hat{i}-12 \hat{j}-21 \hat{k} \)
D. \( \hat{i}-12 \hat{j}+29 \hat{k} \)
Subject: Chemistry
Consider the following metallurgical
processes:
1) Heating impure metal with \( \mathrm{CO} \) and distilling the resulting volatile carbonyl
(b.pt. \( \left.43^{\circ} \mathrm{C}\right) \) and finally decomposing at
\( 150^{\circ} \mathrm{C} \) to \( 230^{\circ} \mathrm{C} \) to get the pure metal.
2) Heating the sulphide ore in the air until a part is converted to oxide and
then further heating in the absence of
air to let the oxide react with
unchanged sulphide.
3) Electrolyzing the molten electrolyte
containing \( C a C l_{2} \) to obtain the metal.
The processes used for obtaining sodium, nickel and copper are,
respectively:
A. 1,2 and 3
B. 2, 3 and 1
c. 3,1 and 2
D. 2,1 and 3
Subject: Maths
A n insurance company insured 2000 scoo terdrivers. 4000 car drivers and
6000 truck drivers, 7 he probeblitey of an accident involving a scooter. a and truck is \( \frac{1}{100}, \frac{3}{100} \) and \( \frac{3}{20} \) respectively. one
of the insured persons meets with an accident. what is the probability that he is a scooter driver?
Subject: Physics
Two blocks of masses 400 g and 200 g are connected through a light string going over a pulley which is free to rotate about is axis. The pulley has a moment of inertia \( 1.6 \times 10^{-4} k g-m^{2} \)
and a radius \( 2.0 \mathrm{cm} . \) Find the speed of the blocks at this instant.
Subject: Physics
The approximate depth of an ocean is
\( 2700 m . \) The compressibility of water is
\( 45.4 \times 10^{-11} P a^{-1} \) and density of water
is \( 10^{3} k g / m^{3} . \) What fractional compression of water will be obtained at the bottom of the ocean?(Take \( g= \)
\( 10 m s^{-2} \)
A \( \cdot 1.2 \times 10^{-2} \)
В. \( 1.4 \times 10^{-2} \)
C \( .0 .8 \times 10^{-2} \)
D. \( 1.0 \times 10^{-2} \)
Subject: Chemistry
A \( 500 \mathrm{mL} \) solution is prepared by dissolving 20 g sodium hydroxide in water. This is mixed in another \( 200 \mathrm{mL} \)
solution of \( N a O H \) having molarity 0.2
M. The molarity of resulting solution is:
A. 0.66 M
в. 0.77 М
c. \( 1.80 \mathrm{M} \)
D. 1.97 М
Subject: Chemistry
The hybridization of carbon in diamond, graphite and acetylene is respectively:
В \( . s p, s p^{2}, s p^{3} \)
\( \mathbf{c} \cdot s p^{3}, s p^{2}, s p \)
\( \mathbf{D} \cdot s p^{2}, s p^{3}, s p \)
Subject: Maths
The sum of all the solutions of the
equation \( \cos \theta \cos \left(\frac{\pi}{3}+\theta\right) \cos \left(\frac{\pi}{3}-\theta\right)= \)
\( \frac{1}{4}, \theta \epsilon[0,6 \pi] \)
A. \( 15 \pi \)
в. \( 30 \pi \)
c. \( \frac{100 \pi}{3} \)
D. None of these
Subject: Chemistry
In laboratory, \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) is prepared by the
action of:
A \( \cdot \) cold \( H_{2} S O_{4} \) and \( B a O_{2} \)
B. aqueous alkali on \( N a_{2} O_{2} \)
c. \( M n O_{2} \) and cold \( H_{2} S O_{4} \)
D. dilute \( H C l \) and \( M n O_{2} \)
Subject: Physics
In the given figure a block of weight
\( 10 N \) is resting on a horizontal surface.
The coefficient of static friction
between the block and the surface is
\( \mu_{s}=0.4 . \) A force of \( 3.5 N \) will keep the
block in uniform motion, once it has
been set in motion. A horizontal force of
\( \mathbf{3} N \) is applied to the block, then the
block will
A. move over the surface with constant velocity
B. move having accelerated motion over the surface.
c. will not move.
D. first it will move with a constant velocity for some time and then it will have an accelerated motion
Subject: Physics
The coefficient of linear expansion of a crystalline substance in one direction is
\( 2 \times 10^{-4} /^{0} \mathrm{C} \) and in every direction
perpendicular to it is \( 3 \times 10^{-4} /^{0} \mathrm{C} \). The coefficient of cubical expansion of crystal is equal to
A. \( 5 \times 10^{-4} /^{0} \mathrm{C} \)
B. \( 4 \times 10^{-4} /^{0} \mathrm{C} \)
c. \( 8 \times 10^{-4} /^{0} \mathrm{C} \)
D. \( 7 \times 10^{-4} /^{0} \mathrm{C} \)
Subject: Maths
A bag contains 6 red, 4 white and 8 blue balls. If three ball are drawn at random,
find the probability that:
(i) All the three balls are red.
(ii) All the three balls are blue.
\( A \)
(i) \( \frac{5}{204}, \) (ii) \( \frac{7}{102} \)
в.
(i) \( \frac{9}{204}, \) (ii) \( \frac{7}{102} \)
\( c \)
(i) \( \frac{7}{204}, \) (ii) \( \frac{5}{102} \)
D. None of these
Subject: Chemistry
Assertion
\( E_{c e l l}^{0}=0 \) for a chloride ion concentration cell.
Reason
For this concentration cell: \( \boldsymbol{E}_{\boldsymbol{c e l l}}= \) \( \frac{\boldsymbol{R} \boldsymbol{T}}{\boldsymbol{n} \boldsymbol{F}} \boldsymbol{l} \boldsymbol{n} \frac{\left[\boldsymbol{C l}^{-}\right]_{L H S}}{\left[\boldsymbol{C l}^{-}\right]_{R H S}} \)
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
Of 30 applicants for a job, 14 had at least 4 years'experience, 18 had degrees, and 3 had less than 4 years experience and did not have a degree. How many of the applicants had at least
4 years' experience and a degree?
A . 14
B. 13
c. 9
\( D .7 \)
E. 5
Subject: Maths
The inverse proposition of \( (\boldsymbol{p} \wedge \sim \boldsymbol{q}) \Rightarrow \boldsymbol{r} \)
is
\( A \cdot \sim r \Rightarrow \sim p \vee q \)
в. \( p \vee q \Rightarrow \sim r \)
\( \mathbf{c} \cdot r \Rightarrow p \wedge \sim q \)
D. none of these.
Subject: Chemistry
Which solution would have a \( \boldsymbol{p} \boldsymbol{H} \)
greater than \( 7.0 ? \)
A. \( 1.0 M \) HCl
в. \( 0.5 M \) NH\( _{4} \) С \( l \) l
c. \( 0.1 M K C N \)
D. \( 1.0 M H_{2} S O_{4} \)
E. \( 0.25 M \) НС \( N \)
Subject: Physics
toppr oGın
Q Type your question
position \( x=12 \mathrm{m} \) on the line.
A proton placed at any point on the line
between the two charges will
experience a net force due to the two
charges. The net force acting on the
proton is shown as a function of
position in the graph, where positive
values of force represent rightward
force.

What is the sign of each charge, and
which charge is stronger?
A. Charge 1 is positive, Charge 2 is positive, and the stronger charge is Charge 2 .
B. Charge 1 is negative, Charge 2 is positive, and the stronger charge is Charge 1
c. Charge 1 is positive, Charge 2 is negative, and the stronger charge is Charge 1.
D. Charge 1 is negative, Charge 2 is positive, and the stronger charge is Charge 2 .
E. Charge 1 is negative, Charge 2 is negative, and the stronger charge is Charge 1.
Subject: Chemistry
On the basis of Werner's theory explain,
why cobalt amine complex,
\( \mathrm{CoCl}_{3} 4 \mathrm{NH}_{3} \) when treated with
\( A g N O_{3} \) solution precipitates only one
\( C l^{-} \) ion even though there are three
\( C l^{-} \) ions?
Subject: Chemistry
An element \( ^{\prime} A^{\prime} \) forms a chloride \( A C l_{4} \)
The number of electrons in the valence
shell of \( ^{\prime} \boldsymbol{A}^{\prime} \) is:
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c .3 \)
D.
Subject: Chemistry
A solution containing \( 4 g \) of a non-
volatile organic solute per \( 100 m L \) was found to have an osmotic pressure
equal to \( 500 \mathrm{cm} \) of mercury at \( 27^{\circ} \mathrm{C} \) The molecular weight of solute is:
A .14 .97
B. 149.7
\( c .1697 \)
D. 1.497
Subject: Chemistry
Identyfy oxidation and reduction process for the reaction-
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{s})+\boldsymbol{F}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{H} \boldsymbol{F}(\boldsymbol{g})+\boldsymbol{H} \boldsymbol{O} \boldsymbol{F}(\boldsymbol{g}) \)
Subject: Maths
When the temperature of medium is
\( 20^{\circ} \mathrm{C} \) a certain substance cools from
\( 100^{\circ} \mathrm{C} \) to \( 60^{\circ} \mathrm{C} \) in 10 minutes. Its
temperature after 40 minutes from the beginning is
A \( \cdot 15^{\circ} \mathrm{C} \)
B . \( 20^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 25^{\circ} C \)
D. \( 30^{\circ} \mathrm{C} \)
Subject: Physics
The resultant amplitude, when two
waves of same frequency but with
amplitudes \( a_{1} \) and \( a_{2} \) superimpose with a phase difference of \( \pi / 2 \) will be
A \( \cdot a_{1}^{2}+a_{2}^{2} \)
B \( \cdot \sqrt{a_{1}^{2}+a_{2}^{2}} \)
c \( \cdot a_{1}-a_{2} \)
D. \( a_{1}+a_{2} \)
Subject: Chemistry
The mass percentage composition of the elements in nitric acid are \( \boldsymbol{H}= \) \( \mathbf{1 . 5 9 \%}, \boldsymbol{N}=\mathbf{2 2 . 2 2 \%}, \boldsymbol{O}=\mathbf{7 6 . 1 9 \%} \)
respectively. \( (\boldsymbol{H}=\mathbf{1}, \boldsymbol{N}=\mathbf{1 4}, \boldsymbol{O}=\mathbf{1 6}) \)
A. True
B. False
Subject: Maths
The sum of \( n \) terms of the series \( 1^{2}- \)
\( \mathbf{2}^{2}+\mathbf{3}^{2}-\mathbf{4}^{2}+\mathbf{5}^{2}-\mathbf{6}^{2}+\ldots \) is
This question has multiple correct options
A \( \cdot \frac{-n(n+1)}{2} \) if \( n \) is ever
B. \( \frac{n(n+1)}{2} \) if \( n \) is od
c. \( -n(n+1) \) if \( n \) is even
D. \( \frac{n(n+1)(2 n+1)}{6} \) if \( n \) is odd
Subject: Maths
A sphere is inscribed in a cubical box
such that the sphere is tangent to all six faces of the box, What is the ratio of
the volume of the cubical box to the
volume of sphere?
A . \( 6 \pi \)
в. \( 36 \pi \)
c. \( \frac{4 \pi}{3} \)
D. \( \frac{6}{\pi} \)
Subject: Maths
The position vectors of two points \( A \) and \( \mathrm{B} \) are \( i+j-k \) and \( 2 i-j+k \)
respectively. Then \( |\boldsymbol{A} \boldsymbol{B}|= \)
\( A \cdot 2 \)
B. 4
\( c .3 \)
D. 5
Subject: Physics
Suppose Earth has a volume 'V' and surface area 'A'; then its becomes a
large capacitor having the value of capacitance as
A \( \cdot 12 \pi \in_{0} \frac{V}{A} \)
в. \( _{4 \pi \in_{0}} \frac{V}{A} \)
c. \( _{4 \pi \in_{0}} \frac{A}{V} \)
D. \( _{12 \pi \in_{0}} \frac{A}{V} \)
Subject: Chemistry
\( \boldsymbol{C O C l}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) ; \boldsymbol{K}_{1}= \)
\( \mathbf{0 . 3 2 9} \)
\( \mathbf{2} \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) ; \boldsymbol{K}_{2}= \)
\( 2.24 \times 10^{22} \)
Calculate the equilibrium constant for the reaction given below from the data
given above at \( 1000 K \)
\( \mathbf{2} \boldsymbol{C O C l}_{2}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{2} \boldsymbol{C O}_{2}(\boldsymbol{g})+ \)
\( \boldsymbol{C l}_{2}(\boldsymbol{g}) \)
Subject: Maths
A bag contains some white and some black balls, all combinations of balls
being equally likely. The total number of
balls in the bag is \( 10 . \) If three balls are drawn at random without replacement and all of them are found to be black,
the probability that the bag contains 1
white and 9 black balls is
A \( \cdot \frac{14}{55} \)
B. \( \frac{12}{55} \)
\( c \cdot \frac{2}{55} \)
D. \( \frac{8}{55} \)
Subject: Maths
The curve amongst the family of curves, represented by the differential
equation, \( \left(x^{2}-y^{2}\right) d x+2 x y d y=0 \)
which passes through (1,1) is :
A. A circle with centre on the y-axis
B. A circle with centre on the x-axis
c. An ellipse with major axis along the y-axis
D. A hyperbola with transverse axis along the x-axis
Subject: Physics
Zeroth law of thermodynamics is not
valid for which one of the following?
A \( \cdot 50 \) ml of water at \( 25^{\circ} \mathrm{C} \) is mixed with \( 150 \mathrm{ml} \) of water at
\( 25^{\circ} \mathrm{C} \)
B. \( 500 \mathrm{ml} \) of milk at \( 15^{\circ} \mathrm{C} \) is mixed with \( 100 \mathrm{ml} \) of water at
\( 15^{\circ} \mathrm{C} \)
\( \mathrm{c} .5 \mathrm{kg} \) of wet steam at \( 100^{\circ} \mathrm{C} \) is mixed with \( 50 \mathrm{kg} \) of dry and saturated steam
D. \( 10 \mathrm{ml} \) of water at \( 20^{\circ} \mathrm{C} \) is mixed with \( 10 \mathrm{ml} \) of Sulfuric acid at \( 20^{\circ} \mathrm{C} \)
Subject: Physics
A condenser of capacity \( 0.2 \mu F \) is
charged to a potential of 600 V. The battery is now disconnected and the
condenser of capacity \( 1 \mu F \) is connected across it. The potential of the condenser will reduce to
\( \mathbf{A} \cdot 600 V \)
B. \( 300 V \)
c. \( 100 V \)
D. \( 120 V \)
Subject: Physics
A ship sends a longitudinal wave towards the bottom of the sea. The wave
returns from the bottom of the sea after
\( \mathbf{2 . 0} s . \) The bulk modulus of the sea water
is \( 2.2 \times 10^{9} N m^{-2} \) and the density of
water is \( 1.1 \mathrm{g} \mathrm{cm}^{-3} . \) The depth of the sea is about
A . \( 2200 m \)
в. 2000 \( m \)
c. \( 1400 m \)
D. \( 1100 m \)
Subject: Maths
The line passing through the points \( (5,1, a) \) and \( (3, b, 1) \) crosses the \( y z \) plane at the point \( \left(0, \frac{17}{2}, \frac{-13}{2}\right) . \) Then
A \( \cdot a=2, b=8 \)
В. \( a=4, b=6 \)
c. \( a=6, b=4 \)
D. \( a=8, b=2 \)
2
Subject: Maths
The lines \( p\left(p^{2}+1\right) x-y+q=0 \) and
\( \left(p^{2}+1\right)^{2} x+\left(p^{2}+1\right) y+2 q=0 \) are
perpendicular to a common line for:
A. exactly one value of
B. exactly two values of \( \mathrm{p} \)
C. more than two values of \( \mathrm{p} \)
D. no value of
Subject: Chemistry
Based on the first law of
thermodynamics, which one of the following is correct?
A. For an isochoric process, \( \mathrm{E}=-\mathrm{C} \)
B. For an adiabatic process, E = -Q
c. For an isothermal process, \( \mathrm{E}=-\mathrm{Q} \)
D. For an cyclic process, \( \mathrm{W}=-\mathrm{Q} \)
Subject: Maths
Find the limits of
\[
\begin{array}{l}
\frac{\sqrt{\boldsymbol{a}^{2}+\boldsymbol{a} \boldsymbol{x}+\boldsymbol{x}^{2}}-\sqrt{\boldsymbol{a}^{2}-\boldsymbol{a} \boldsymbol{x}+\boldsymbol{x}^{2}}}{\sqrt{\boldsymbol{a}+\boldsymbol{x}}-\sqrt{\boldsymbol{a}-\boldsymbol{x}}}, \text { when } \\
\boldsymbol{x}=\mathbf{0}
\end{array}
\]
Subject: Physics
A brass rod of length \( 30 \mathrm{cm} \) is joined to
a copper rod of length \( 60 \mathrm{cm} \). The two rods are of the same thickness and at
initial temperature of \( 20^{\circ} \mathrm{C} \). What is the change in length of the combined rod,
when the same is heated to \( 160^{\circ} \mathrm{C} \)

Coefficients of linear expansion of brass
and copper are \( 1.9 \times 10^{-5}^{\circ} C^{-1} \) and
\( 1.7 \times 10^{-5}^{\circ} C^{-1} \) respectively
Subject: Physics
A rigid body of mass m rotates with angular velocity \( \omega \) about an axis at a
distance a from the centre of mass \( C \).
The radius of gyration about \( C \) is \( K \) Then, kinetic energy of rotation of the body about new parallel axis is :
A \( \cdot \frac{1}{2} m K^{2} \omega^{2} \)
B \( \cdot \frac{1}{2} m a^{2} \omega^{2} \)
c. \( \frac{1}{2} m\left(a+K^{2}\right) \omega^{2} \)
D. \( \frac{1}{2} m\left(a^{2}+K^{2}\right) \omega^{2} \)
Subject: Maths
\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{1} /\left(\mathbf{1}-\boldsymbol{e}^{-\mathbf{1} / \boldsymbol{x}}\right), \boldsymbol{x} \neq \mathbf{0} \) If \( \mathbf{f} \) is
continuous at \( x=0 \) then, Find \( f(0) \)
Subject: Physics
If \( \frac{\boldsymbol{I}_{1}}{\boldsymbol{I}_{2}}=\frac{\boldsymbol{9}}{\mathbf{1}} \) then \( \frac{\boldsymbol{I}_{\boldsymbol{m a x}}}{\boldsymbol{I}_{\boldsymbol{m i n}}}=? \)
A. 100: 64
в. 64: 100
c. 4: 1
D. 1: 4
Subject: Physics
A car travels first \( 30 k m \) with a uniform
speed of \( 60 k m p h \) and then next \( 30 k m \)
with a uniform speed of \( 40 k m p h \). Find
the average speed of the car.
A. \( 24 \mathrm{kmph} \)
B. \( 48 \mathrm{kmph} \)
c. 72 kmph
D. \( 96 \mathrm{kmph} \)
Subject: Physics
A force \( f_{1} \) pushes on an object of mass
\( 10 \mathrm{kg} \) with a force of \( 5 \mathrm{N} \) to the right. \( \mathrm{A} \) force pushes on the same object with a
force \( f_{2} \) of \( 15 \mathrm{N} \) to the left. What is the
acceleration of the object?
A \( \cdot 0.3 \mathrm{m} / \mathrm{s}^{2} \) to the left
B. \( 0.5 \mathrm{m} / \mathrm{s}^{2} \) to the left
C. \( 1 \mathrm{m} / \mathrm{s}^{2} \) to the left
D. \( 1.5 \mathrm{m} / \mathrm{s}^{2} \) to the left
E \( \cdot 10 m / s^{2} \) to the left
Subject: Physics
Two cells, having the same emf are connected in series through an external
resistance \( R \) Cells have internal
resistance \( r_{1} \) and \( r_{2}\left(r_{1}>r_{2}\right) \)
respectively. When the circuit is closed, the potential difference across the first
cell is zero, The value of \( \boldsymbol{R} \) is
\( \mathbf{A} \cdot r_{1}+r_{2} \)
В. \( r_{1}-r_{2} \)
c. \( \frac{r_{1}+r_{2}}{2} \)
D. \( \frac{r_{1}-r_{2}}{2} \)
Subject: Physics
A block of mass \( m \) slides down an
inclined right angled trough. If the
coefficient of kinetic friction between
the block and the trough is \( \mu_{k} \)
acceleration of the block down the plane
is:
\( \mathbf{A} \cdot g\left(\sin \theta-2 \mu_{k} \cos \theta\right) \)
B \( \cdot g\left(\sin \theta+2 \mu_{k} \cos \theta\right) \)
\( \mathbf{c} \cdot g\left(\sin \theta-\sqrt{2} \mu_{k} \cos \theta\right) \)
\( \mathbf{D} \cdot g\left(\sin \theta-\mu_{k} \cos \theta\right) \)