AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Two charged spheres of radii \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2} \)
have equal surface charge density. The ratio of their potential at an equidistant external point is
A \( \cdot \frac{R_{2}}{R_{1}} \)
в. \( \left(\frac{R_{2}}{R_{1}}\right)^{2} \)
\( ^{\mathbf{c}} \cdot\left(\frac{R_{1}}{R_{2}}\right)^{2} \)
D. \( \frac{R_{1}}{R_{2}} \)
Subject: Maths
One angle of a seven sided polygon is
\( 108^{\circ} \) and each of the other six angles is
\( x^{\circ} . \) The value of \( x \) is
\( \mathbf{A} \cdot 114^{\circ} \)
B. \( 121^{\circ} \)
\( \mathrm{c} \cdot 131^{\circ} \)
D. \( 132^{\circ} \)
Subject: Chemistry
Which is an incorrect order of basic
strength?
A \( \cdot N H_{2}^{-}>P H_{2} \)
B \( . H_{2} O>H_{2} \)
\( c \)
\( D \)
\( \mathrm{E} \cdot \mathrm{CO}_{3}^{2-}>\mathrm{HCO}_{3}^{-} \)
Subject: Chemistry
Specific volume of cylindrical virus particles is \( 6.02 \quad \times 10^{-2} \) cc/gm whose radius and length are \( 7, \dot{A} \) and \( 10 A \) respectively. If \( N_{A}=6.02 \times 10^{23} \) find
molecular weight of virus.
A. \( 15.4 \mathrm{kg} / \mathrm{mol} \)
B . \( 1.54 \times 10^{4} \mathrm{kg} / \mathrm{mol} \)
\( \begin{array}{lll}\text { C. } 3.08 & \times 10^{4} \mathrm{kg} / \mathrm{mol}\end{array} \)
D. \( 1.54 \times 10^{3} \mathrm{kg} / \mathrm{mol} \)
Subject: Physics
One of the two forces is double and the
other resultant is equal to the greater force. The angle between then is
\( \mathbf{A} \cdot \cos ^{-1}(1 / 2) \)
B . \( \cos ^{-1}(-1 / 2) \)
c. \( \cos ^{-1}(1 / 4) \)
D. \( \cos ^{-1}(-1 / 4) \)
Subject: Chemistry
Which of the following compound cannot be thermally decomposed even
at high temperature?
A. \( C s H C O_{3} \)
в. \( R b_{2} C O_{3} \)
\( \mathrm{c} \cdot L i_{2} \mathrm{CO}_{3} \)
D. \( \left(N H_{4}\right)_{2} C O_{3} \)
Subject: Biology
The weather forecast in a week has
been summarised as above.
Based on the above information answer
the questions A school wants to arrange a picnic for its students. What is the best day for
that?
\begin{tabular}{|l|l|l|l|}
\hline Day & Max. & Min. & Forecast \\
\hline Sun & \( 36^{\circ} \mathrm{C} \) & \( 24^{\circ} \mathrm{C} \) & Sunny and hot \\
Mon & \( 34^{\circ} \mathrm{C} \) & \( 22^{\circ} \mathrm{C} \) & Sunny \\
Tue & \( 30^{\circ} \mathrm{C} \) & \( 20^{\circ} \mathrm{C} \) & Dry and cloudy \\
Wed & \( 32^{\circ} \mathrm{C} \) & \( 21^{\circ} \mathrm{C} \) & Cloudy \\
Thu & \( 27^{\circ} \mathrm{C} \) & \( 16^{\circ} \mathrm{C} \) & Rain \\
Fri & \( 30^{\circ} \mathrm{C} \) & \( 20^{\circ} \mathrm{C} \) & Light showers \\
Sat & \( 32^{\circ} \mathrm{C} \) & \( 21^{\circ} \mathrm{C} \) & Cloudy \\
\hline
\end{tabular}
A. Monday
B. Tuesday
c. Thursday
D. Friday
Subject: Maths
Observe the given multiplies of 37
\( 37 \times 3=111 \)
\( 37 \times 6=222 \)
\( 37 \times 9=333 \)
\( 37 \times 12=444 \)
Find the product of \( 37 \times 27 ? \)
A . 999
B. Greatest 3 digit number
c. Either A or B
D. Smallest 3-digit number
Subject: Chemistry
Thomas slag is:
A \( \cdot C a_{3}\left(P O_{4}\right)_{2} \cdot 2 H_{2} O \)
в. \( C a_{3}\left(P O_{4}\right)_{2} \cdot \) Са \( \operatorname{Si} O_{3} \)
\( \mathbf{c} \cdot M g S i O_{3} \)
D. \( \operatorname{casi} O_{3} \)
Subject: Physics
Find the angle in degrees through which the photon is scattered in the scattering event described.
\( \mathbf{A} \cdot\left(3 \times 10^{-3}\right) \)
B \( \cdot\left(3 \times 10^{-5}\right) \)
C \( \cdot\left(3 \times 10^{-7}\right) \)
D. \( \left(3 \times 10^{-9}\right) \)
Subject: Chemistry
A Science teacher wrote 3 statements
about rancidity:
(i) When fats and oils are reduced, they become rancid
(ii) In chips packet, rancidity is
prevented by oxygen
(iii) Rancidity is prevented by adding antioxidants.
Selects the correct option.
A. (i)
B. (ii) and (iii)
c. (iii)
D. (i), (ii) and (iii)
Subject: Chemistry
When \( H_{2} O_{2} \) is added to ice cold
solution of acidified potassium
dichromate in ether and the contents
are shaken and allowed to stand?
A. A blue colour is obtained in ether due to formation of \( C r_{2}\left(S O_{4}\right)_{3} \)
B. A blue colour is obtained in ether due to formation of \( C r O_{5} \)
c. A blue colour is obtained in ether due to formation of \( C r O_{3} \)
D. Chromyl chloride is formed.
Subject: Physics
For the path \( P Q R \) in a conservative
force field, the amount of work done in
carrying a body from \( P \) to \( Q \& \) from \( Q \) to
\( R \) are \( 5 J \& 2 J \) respectively. The work
done in carrying the body from \( \boldsymbol{P} \) to \( \boldsymbol{R} \)
will be-
в. 3 J
c. \( \sqrt{21} J \)
D. Zer
Subject: Maths
Assertion
\( \tan x\left(2+\sin ^{2} x\right)>6 x \forall x \in\left[0, \frac{\pi}{4}\right] \)
Reason
If \( f(x) \) and \( g(x) \) are continuous in \( [a, b] \) differentiable in \( (\boldsymbol{a}, \boldsymbol{b}), \boldsymbol{f}(\boldsymbol{a})= \)
\( \boldsymbol{g}(\boldsymbol{a}) \) and \( \boldsymbol{f}^{\prime}(\boldsymbol{x})<\boldsymbol{g}^{\prime}(\boldsymbol{x}) \forall \boldsymbol{x} \in(\boldsymbol{a}, \boldsymbol{b}) \)
\( \operatorname{then} f(x)<g(x) \forall x \in(a, b) \)
A. Assertion and Reason are correct and the Reason is the correct explanation for the Assertion
B. Assertion and Reason are correct and the Reason is Not the correct explanation for the Assertion
c. Assertion is correct while the Reason is incorrect
D. Assertion is incorrect while the Reason is correct
Subject: Physics
A pebble is thrown vertically upwards from a bridge with an initial velocity of \( 4.9 m s^{-1} . \) It strikes the water after \( 2 s \)
Height of the bridge is:
A . \( 19.6 \mathrm{m} \)
в. \( 14.7 \mathrm{m} \)
c. \( 9.8 \mathrm{m} \)
D. \( 4.9 \mathrm{m} \)
Subject: Physics
A particle of mass \( M \) is executing oscillations about the origin on the \( x \)
axis. Its potential energy is \( |\boldsymbol{U}|=\boldsymbol{K}\left|\boldsymbol{x}^{2}\right| \)
where \( K \) is a positive constant. If the
amplitude of oscillations is \( a \), then its
period \( \boldsymbol{T} \) is
A. proportional to \( 1 / \sqrt{a} \)
B. independent of \( a \)
c. proportional to \( \sqrt{a} \)
D. proportional to \( a^{1 / 2} / 2 \) poorional
Subject: Physics
An object of height \( 10 \mathrm{cm} \) is placed at a distance of \( 100 \mathrm{cm} \) before the convex
mirror perpendicular below the
principal axis. If the focal length of the mirror is \( 10 \mathrm{cm}, \) on applying the Cartesian sign convention, find the object distance
A . -100cm
B. \( +100 \mathrm{cm} \)
c. \( 50 \mathrm{cm} \)
D. -50 cm
Subject: Maths
Show that the points \( \boldsymbol{A}(\mathbf{0}, \mathbf{1}, \mathbf{2}), \boldsymbol{B}(\mathbf{2},-\mathbf{1}, \mathbf{3}) \) and \( \boldsymbol{C}(\mathbf{1},-\mathbf{3}, \mathbf{1}) \)
are vertices of an isosceles right-angled triangle.
Subject: Physics
A body is thrown vertically upwards and rises to a height of \( 10 \mathrm{m} \). The velocity with which the body was thrown
upwards is \( \left(\boldsymbol{g}=\mathbf{9 . 8} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
\( A \cdot 16 \mathrm{m} / \mathrm{s} \)
B. \( 15 \mathrm{m} / \mathrm{s} \)
\( c \cdot 14 m / s \)
D. \( 12 \mathrm{m} / \mathrm{s} \)
Subject: Physics
The number of electrons present in \( 1 C \) of charge is
A \( \cdot 4.25 \times 10^{18} \)
B. \( 6.25 \times 10^{18} \)
c. \( 3.25 \times 10^{18} \)
D. \( 2.25 \times 10^{18} \)
Subject: Chemistry
Consider the following transformations
\( \boldsymbol{I} \cdot \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6}+\boldsymbol{N} \boldsymbol{a} \boldsymbol{F} \longrightarrow \boldsymbol{N} \boldsymbol{a}^{+}\left[\boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{7}\right]^{-} \)
\( \boldsymbol{I} \boldsymbol{I} \cdot \boldsymbol{2} \boldsymbol{P} \boldsymbol{C l}_{5}(\boldsymbol{s}) \longrightarrow\left[\boldsymbol{P} \boldsymbol{C l}_{4}\right]^{+}\left[\boldsymbol{P} \boldsymbol{C l}_{6}\right]^{-} \)
\( \boldsymbol{I I I} \cdot\left[A l\left(H_{2} O\right)_{6}\right]^{3+}+H_{2} O \longrightarrow \)
\( \left[A l\left(H_{2} O\right)_{5} O H\right]^{2+}+H_{3} O^{+} \)
Possible transformations are:
A. \( I, I I, I I I \)
В. \( I, I I I \)
c. \( I, I I \)
D. II, III
Subject: Physics
A fan of moment of inertia \( I \) is set into
rotation at time \( t=0 \) with constant
power \( P . \) Then
A. The angular speed of the fan is proportional to \( t \)
B. The angular acceleration of the fan remains constant
c. The magnitude of the angular displacement is proportional to \( t^{2} \)
D. The magnitude of the torque is proportional to \( t^{-1 / 2} / 2 \) -
Subject: Physics
A steel cylindrical rod of length \( l \) and
radius \( r \) is suspended by its end from the ceiling. Find the elastic deformation
energy \( U \) of the rod.
A \( \cdot U=\frac{1}{6} \pi r^{2} \rho^{2} g^{2} \frac{l^{3}}{E} \)
B. \( U=\frac{5}{6} \pi r^{2} \rho^{2} g^{2} \frac{l^{3}}{E} \)
\( ^{\mathrm{C}} U=\frac{1}{6} \pi r^{2} \rho^{2} g^{2} \frac{2 l^{3}}{E} \)
D. \( U=\frac{5}{6} \pi r^{2} \rho^{2} g^{2} \frac{2 l^{3}}{E} \)
Subject: Maths
\( A \) and \( B \) are two independent events. The probability that both \( A \) and \( B \) occur is \( \frac{1}{6} \) and the probability that neither of them occur is \( \frac{1}{3} \). Then \( P(A) \) is equal to
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{5}{6} \)
D. \( \frac{1}{2} \) or \( \frac{1}{3} \)
Subject: Physics
The galvanometer resistance is \( 30 \Omega \) and it is connected to 2 V battery along with a resistance \( 2000 \Omega \) in series. \( A \)
full scale deflection of 25 divisions is
obtained. In order to reduce this
deflection to 20 divisions, the resistance in series should be
A. 2507 \( \Omega \)
в. 2320 \( \Omega \)
c. \( 2180 \Omega \)
D. 2210 \( \Omega \)
Subject: Maths
The following data gives the amount of loans (in crores of rupees) disbursed by
a bank during some years:
Year \( \begin{array}{lll}1992 & 1993 & 1994 \\ 4 & 19999\end{array} \)
Loan
in
crores 28
55
of rupees
Represent the above data with the help of a bar graph.
Subject: Chemistry
Calculate the heat of combustion (kJ) of
propane, \( C_{3} H_{8} \) using the listed standard enthalpy of reaction data:
\[
\begin{array}{c}
C_{3} H_{8}(g)+\mathbf{5} O_{2}(g) \longrightarrow \\
\mathbf{3} C O_{2}(g)+4 H_{2} O(g) \\
\mathbf{3} C(s)+4 H_{2}(g) \longrightarrow \\
C_{3} H_{8}(g) \Delta H / k J=-103.8 \\
C(s)+O_{2}(g) \longrightarrow C O_{2}(g) \Delta H / k J= \\
-393.5 \\
H_{2}(g)+1 / 2 O_{2}(g) \longrightarrow \\
H_{2} O(g) \Delta H / k J=-241.8
\end{array}
\]
A . - 2043.9
B. -1532.9
c. -1021.9
D. -739.
Subject: Chemistry
For a number of years, it was not clear whether mercury (I) ion existed in solution as \( H g^{\oplus} \) or as \( H g_{2}^{2+} . \) To distinguish between these two possibilities, the following set up was
made:

Hg(I) I Solution A II Solution B I Hg(I) where solution A contained 0.263 g mercury
(I) nitrate per liter and solution B contained 2.63 g mercury
(I) nitrate per litre. If the measured EMF of such a
cell is \( 0.0289 \mathrm{V} \) at \( 18^{\circ} \mathrm{C} \), then mercury
(I) ions exist in the form of \( \boldsymbol{H} \boldsymbol{g}_{2}^{2+} \)
f true enter 1 , else enter 0
Subject: Maths
The statement \( \boldsymbol{p} \rightarrow(\boldsymbol{q} \rightarrow \boldsymbol{p}) \) is
equivalent to
A \( \cdot p \rightarrow(p \wedge q) \)
в. \( p \rightarrow(p \leftrightarrow q) \)
c. \( p \rightarrow(p \rightarrow q) \)
D. \( p \rightarrow(p \vee q) \)
Subject: Chemistry
The maximum tendency to form unipositive ion is for the element which has the following electronic configuration:
A \( \cdot 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2} \)
B . \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 3 p^{1} \)
c. \( 1 s^{2}, 2 s^{2}, 2 p^{6} \)
D. \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 3 p^{3} \)
Subject: Physics
White light is normally incidents on a soap film. The thickness of the film is \( 0.5 \mu m \) and its refractive index is 1.33 Which wave length will be reflected maximum in the visible region?
A \( .26600 A^{\circ} \)
B . \( 8860 A^{\circ} \)
\( \mathrm{c} .5320 A^{\circ} \)
D. \( 3800 A^{\circ} \)
Subject: Physics
Three man \( A, B, C \) of mass \( 40 \mathrm{kg}, 50 \mathrm{kg} \)
\( \& 60 \mathrm{kg} \) are standing on a plank of mass \( 90 \mathrm{kg}, \) which is kept on a smooth
horizontal plane. If \( A \& C \) exchange their
positions then mass B will shift
\( \mathbf{A} \cdot 1 / 3 \mathrm{m} \) towards left
B. 1/3 m towards right
c. will not move w.r.t. ground
D. \( 5 / 3 \) m toward left
Subject: Maths
Differentiate \( \boldsymbol{f}(\boldsymbol{x}) \) with respect to \( \boldsymbol{g}(\boldsymbol{x}) \)
for the following.
\( \boldsymbol{f}(\boldsymbol{x})=\log _{e} \boldsymbol{x}, \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{e}^{\boldsymbol{x}} \)
Subject: Physics
The equation of a wave disturbance is
given as : \( \boldsymbol{y}= \) \( 0.02 \cos \left(\frac{\pi}{2}+50 \pi t\right) \cos (10 \pi x), \) where
\( x \) and \( y \) are in meters and \( t \) in seconds.
Choose the wrong statement:
A. Antinode occurs at \( X=0.3 m \)
B. The wavelength is \( 0.2 \mathrm{m} \).
c. The speed of the constituent waves is \( 4 m / s \)
D. Node occurs at \( X=0.15 \mathrm{m} \)
Subject: Maths
Given that \( a(a+b)=36 \) and \( b(a+ \)
\( b)=64, \) where \( a \) and \( b \) are positive,
\( (a-b) \) equals:
A . 2.8
B. 3.2
\( c .-2.8 \)
D. - 2.5
Subject: Chemistry
The rate constant for the forward
reaction \( \boldsymbol{A}(\boldsymbol{g}) \rightleftharpoons 2 \boldsymbol{B}(\boldsymbol{g}) \) is \( 1.5 \times \)
\( 10^{-3} s^{-1} \) at \( 100 \mathrm{K} \). If \( 10^{-5} \) moles of \( \mathrm{A} \) and
100 moles of \( \mathrm{B} \) are present in a 10 litre vessel at equilibrium then rate constant for the backward reaction at
this temperature is:
A. \( 1.50 \times 10^{4} L \) mol \( ^{-1} s^{-1} \)
B . \( 1.5 \times 10^{11} L \) mol \( ^{-1} s^{-1} \)
c. \( 1.5 \times 10^{10} L m o l^{-1} s^{-1} \)
D. \( 1.5 \times 10^{-11} L \) mol \( ^{-1} s^{-1} \)
Subject: Chemistry
Assertion
The mobility of sodium ion is lower than that of potassium ion.
Reason
The ionic mobilities depend on the effective radius of the ion.
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
If \( \boldsymbol{f}=\{(\boldsymbol{6}, \boldsymbol{3}),(\boldsymbol{8}, \boldsymbol{9}),(\boldsymbol{5}, \boldsymbol{3}),(-\mathbf{1}, \boldsymbol{6})\} \)
then the pre-images of 3 are
A. 5 and -1
B. 6 and 8
c. 8 and -1
D. 6 and 5
Subject: Maths
If \( \boldsymbol{A}=\{\boldsymbol{x}: \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{W}, \boldsymbol{3} \leq \boldsymbol{x}<\mathbf{6}\}, \boldsymbol{B}= \)
\{3,5,7\} and \( C=\{2,4\} \)
find \( : \boldsymbol{A} \times(\boldsymbol{B}-\boldsymbol{C}) \)
Find the number of elements in such a
set.
Subject: Physics
One litre of helium under a pressure of 2 atm and at \( 27^{\circ} \mathrm{cis} \) heated until its
pressure and volume are doubled. The
final temperature attained by the gas is
\( A \cdot 927 K \)
B . \( 927^{\circ} \mathrm{C} \)
\( c \cdot 1200^{0} c \)
D. None
Subject: Chemistry
While studying the saponification reaction, what do you observe when you mix an equal amount of colourless vegetable oil and \( 20 \% \) aqueous solution of \( N a O H \) in a beaker?
A. The colour of the mixture has become dark brown
B. A brisk effervescence is taking place in the beaker
c. The outer surface of the beaker has become hot
D. The outer surface of the beaker has become cold
Subject: Physics
Five cells each of internal resistance
\( 0.2 \Omega \) and \( \mathrm{emf} 2 V \) are connected in
series with a resistance of \( 4 \Omega \).The
current through the external resistance
is
A. \( 4 A \)
в. \( 2 A \)
\( c \cdot 1 A \)
D. \( 0.5 A \)
Subject: Maths
The value of \( \lim _{x \rightarrow 1}\left(\frac{x^{n}+x^{n-1}+x^{n-2}+\ldots .+x^{2}+x}{x-1}\right. \)
is
A \( \cdot \frac{n(n+1)}{2} \)
B.
\( c \cdot 1 \)
\( D \)
Subject: Chemistry
The relation between the slope of
isothermal curve and slope of adiabatic
Curve:
A. Slope of adiabatic curve \( =\gamma \) times slope of isothermal
curve
B. Slope of isothermal curve \( =\gamma \) times slope of adiabatic
curve
C. Slope of adiabatic curve \( =\gamma^{2} \) times slope of isothermal curve
D. Slope of isothermal curve \( =\gamma^{2} \) times slope of adiabatic curve
Subject: Physics
A particle moves along a parabolic path
\( \boldsymbol{y}=\mathbf{9} \boldsymbol{x}^{2} \) in such a way that the \( \boldsymbol{x} \)
component of velocity remains constant and has a value \( 0.333 m / s . \) The magnitude of acceleration of the particle is:
A . 1
B. 2
\( c \cdot 3 \)
D.
Subject: Maths
For what value of \( x, \) is the matrix \( A= \) \( \left[\begin{array}{ccc}\mathbf{0} & \mathbf{1} & \mathbf{- 1} \\ -\mathbf{1} & \mathbf{0} & \mathbf{3} \\ \boldsymbol{x} & \mathbf{- 3} & \mathbf{0}\end{array}\right] \) a skew symmetric
matrix?
Subject: Physics
cm carrying a current \( I \) of 12 A is placed
in different orientations as shown in the
figure below.
If there is a uniform magnetic field of
\( 0.3 T \) in the positive z-direction, in which
orientations the loop would be in (i)
stable equilibrium and (ii) unstable
equilibrium:
(1)
(2)
(3)
(4)
A \( \cdot(2) \) and \( (4), \) respectively
B. (2) and
\( (3), \) respectively
C. () 1 and \( (2), \) respectively
D. () 1 and
\( (3), \) respectively
Subject: Physics
If the displacement of a particle varies
with time as \( \sqrt{x}=t+7, \) which of the
following statements is(are) true?
This question has multiple correct options
A. Velocity of the particle is inversely proportional to \( t \).
B. Velocity of the particle is proportional to \( t \)
C. Velocity of the particle is proportional to \( \sqrt{t} \)
D. The particle moves with a constant accelera
Subject: Physics
In a series \( L C R \) circuit, the voltage across the resistance, capacitance and
inductance is \( 10 V \) each. If the
capacitance is short circuited, the voltage across the inductance will be :
A. \( 10 V \)
B. \( \frac{10}{\sqrt{2}} V \)
c. \( \frac{10}{3} V \)
D. 20 \( V \)
Subject: Maths
The angle between the line \( x+y=3 \) and the line joining the points (1,1) and (-3,4) is
A \( \cdot \tan ^{-1}(7) \)
B \( \cdot \tan ^{-1}(-1 / 7) \)
\( \mathbf{c} \cdot \tan ^{-1}(1 / 7) \)
D. None of these
Subject: Chemistry
The energy of an electron in the first
Bohr orbit of H-atom is -13.6 eV. The
possible energy value(s) of the excited state(s) for electrons in Bohr orbits of
hydrogen is:
A. \( -3.4 e V \)
в. \( -4.2 e V \)
c. \( -6.8 e V \)
D. \( +6.8 e V \)
Subject: Physics
A planet is moving in an elliptical orbit If \( T, U, E \) and \( L \) are its kinetic energy,
potential energy, total energy and magnitude of angular momentum respectively, then which of the following
statement is true.
\( \mathbf{A} \cdot T \) is conserved
B. \( U \) is always positive
c. \( E \) is always negative
D. \( L \) is conserved but the direction of vector \( \vec{L} \) will continuously change
Subject: Maths
The domain of the function \( \mathbf{f}(\boldsymbol{x})=\sqrt{\frac{\boldsymbol{x}-\mathbf{2}}{\boldsymbol{x}+\mathbf{2}}}+\sqrt{\frac{\mathbf{1}-\boldsymbol{x}}{\mathbf{1}+\boldsymbol{x}}} \) is
A. \( R \)
B. [-2,2]
c. [-1,1]
D.
Subject: Maths
\( \frac{\mathbf{2} \boldsymbol{x}+\mathbf{1}}{(\boldsymbol{x}-\mathbf{1})\left(\boldsymbol{x}^{2}+\mathbf{1}\right)}=\frac{\boldsymbol{A}}{\boldsymbol{x}-\mathbf{1}}+\frac{\boldsymbol{B} \boldsymbol{x}+\boldsymbol{c}}{\boldsymbol{x}^{2}+\mathbf{1}} \Rightarrow \frac{\boldsymbol{A}-\boldsymbol{B}}{\boldsymbol{C}}= \)
\( A \cdot 8 \)
B. 6
\( c \cdot 4 \)
D. 2
Subject: Physics
A solid metallic sphere of radius \( r \) is
allowed to fall freely through air. If the frictional resistance due to air is
proportional to the cross-sectional area and to the square of the velocity, then the terminal velocity of the sphere is proportional to which of the following?
A \( \cdot r^{2} \)
B.
\( c \cdot r^{3 / 2} \)
D. \( r^{1 / 2} \)
Subject: Physics
Shown in the figure below is a meter-
bridge set up with null deflection in the
galvanometer

The value of the unknown resistor \( \boldsymbol{R} \) is
A. \( 13.75 \Omega \)
B. \( 220 \Omega \)
\( c \cdot 110 \Omega \)
D. \( 55 \Omega \)
Subject: Maths
Eight players \( \boldsymbol{P}_{1}, \boldsymbol{P}_{2}, \ldots \ldots \boldsymbol{P}_{8} \) play a
knock-out tournament. It is known that
whenever the players \( P_{i} \) and \( P_{j} \) play,
the player \( \boldsymbol{P}_{i} \) will win if \( i<j \). Assuming
that the players are paired at random in each round, the probability that the
player \( \boldsymbol{P}_{4} \) reaches the final is \( \boldsymbol{k} / \mathbf{7} \) 0. Find
\( \boldsymbol{k} \)
Subject: Physics
In a given region a charge particle is moving under the effect of electric and magnetic field with uniform velocity \( \vec{v}=(\hat{i}+\hat{j}-\hat{k}) \mathrm{m} / \mathrm{s} \) and magnetic field
is given as \( \vec{B}=(2 \hat{i}+\hat{j}-2 k) \) T. The
electric field is given as?
\( \mathbf{A} \cdot(i+j-k) \mathrm{V} / \mathrm{m} \)
B. \( (i-j+k) \vee / m \)
c. \( (i+k) \vee / m \)
D. \( (-i-k) \vee / \) m
Subject: Physics
A magnetising field of 1500 A \( m^{-1} \)
produces flux of \( 2.4 \times 10^{-5} \) weber in a
iron bar of the cross-sectional area of
\( 0.5 c m^{2} . \) The permeability of the iron bar is?
A . 245
в. 250
c. 252
D. 255 55
Subject: Physics
The ratio of the radii of gyration of the disc about its axis and about a tangent perpendicular to its plane will be:
A \( \cdot \frac{1}{\sqrt{3}} \)
в. \( \sqrt{\frac{3}{2}} \)
c. \( \frac{1}{\sqrt{2}} \)
D. \( \sqrt{\frac{5}{3}} \)
Subject: Maths
If foci are points (0,1)(0,-1) and minor axis is of length \( 1, \) then equation of ellipse is
A \( \cdot \frac{x^{2}}{1 / 4}+\frac{y^{2}}{5 / 4}=1 \)
В. \( \frac{x^{2}}{5 / 4}+\frac{y^{2}}{1 / 4}=1 \)
c. \( \frac{x^{2}}{3 / 4}+\frac{y^{2}}{1 / 4}=1 \)
D. \( \frac{x^{2}}{1 / 4}+\frac{y^{2}}{3 / 4}=1 \)
Subject: Chemistry
The critical density of the \( \operatorname{gas} C O_{2} \) is \( 0.44 g c m^{-3} \) at a certain temperature. If
\( r \) is the radius of the molecule, \( r^{3} \) in
\( c m^{3} \) is approximate:
[N is Avogadro number]
A \( \frac{25}{\pi N} \)
в. \( \frac{100}{\pi N} \)
c. \( \frac{6}{\pi N} \)
D. \( \frac{25}{4 N \pi} \)
Subject: Maths
n the matrix \( \boldsymbol{A}=\left|\begin{array}{cccc}\mathbf{2} & \mathbf{5} & \mathbf{1 9} & -\mathbf{7} \\ \mathbf{3 5} & -\mathbf{2} & \frac{\mathbf{5}}{\mathbf{2}} & \mathbf{1 2} \\ \sqrt{\mathbf{3}} & -\mathbf{1} & \mathbf{- 5} & \mathbf{1 7}\end{array}\right| \)
write.
Order of matrix.
Subject: Maths
What must be the matrix \( \boldsymbol{X} \) if \( 2 \boldsymbol{X}+ \) \( \left[\begin{array}{l}12 \\ 34\end{array}\right]=\left[\begin{array}{l}38 \\ 72\end{array}\right] ? \)
A \( \cdot\left[\begin{array}{l}13 \\ 2-1\end{array}\right] \)
в. \( \left[\begin{array}{l}1-3 \\ 2-1\end{array}\right] \)
c. \( \left[\begin{array}{l}26 \\ 4-2\end{array}\right] \)
D. \( \left[\begin{array}{l}2-6 \\ 4-2\end{array}\right] \)
Subject: Chemistry
Which of the following ether is not cleaved by HI even at \( 525 \mathrm{K} \) ?
A. \( C_{6} H_{5}-O-C H_{3} \)
в. \( C_{6} H_{5}-O-C_{6} H_{5} \)
c. \( C_{6} H_{5}-O-C_{3} H_{7} \)
D.
Subject: Maths
If \( f(x)=\int_{-1}^{1} \frac{\sin x}{1+t^{2}} d t \) then \( f^{\prime}\left(\frac{\pi}{3}\right) \) is
A. nonexistent
в. \( \pi / 4 \)
c. \( \pi \sqrt{3 / 4} \)
D. none of these
Subject: Chemistry
Column II gives method to separate phases mentioned in column I. Match
them and select the correct answer
from the codes given below.
Column Column I
(a) Miscible liquids
(p) Distillation
\( (q) \)
(b) Immiscible liquids \( \quad \) Crystallization
(c) Pure copper sulphate from
\( (r) \)
an impure sample Sublimation
(s) Separating
(d) Salt and ammonium chloride funnel
\( A \cdot(a)-(q),(b)-(s),(c)-(p),(d)-(r) \)
B. \( (a)-(p),(b)-(s),(c)-(q),(d)-(r) \)
\( c \cdot(a)-(r),(b)-(s),(c)-(p),(d)-(q) \)
D. (a) - (r), (b) - (s), (c) - (q), (d) - (p)