AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Which among the following oxoacids of phosphorus shows a tendency of disproportionation?
A. Phosphinic aicd \( \left(H_{3} P O_{2}\right) \)
B. orthophosphoric acid (H \( _{3} P O_{4} \) )
c. Phosphonic acid \( \left(H_{3} P O_{3}\right) \)
D. Pyrophosphoric acid \( \left(H_{4} P_{2} O_{7}\right) \)
Subject: Chemistry
The chemical that changes its colour
when it is left open in sunlight is:
\( \mathbf{A} \cdot \operatorname{Fe} S O_{4}(s) \)
B . \( P b\left(N O_{3}\right)_{2}(s) \)
c. \( A g C l(s) \)
D. \( B a C l_{2}(a q) \)
Subject: Maths
If \( \left(1+x^{2}\right) \frac{d y}{d x}=x(1-y), y(0)=\frac{4}{3} \)
then the value of \( y(\sqrt{8})+\frac{8}{9} i s \)
\( A \cdot 4 \)
B. 2
\( c \cdot 3 \)
D.
Subject: Physics
A bicycle can go up a gentle incline with
constant speed where the frictional force of ground pushing the rear whee
is \( F_{2}=4 N . \) With what force \( F_{1} \) must
the chain pull on the socket wheel if
\( R_{1}=5 \mathrm{cm} \) and \( R_{2}=30 \mathrm{cm} ? \)
\( A \cdot 4 N \)
В. 24 .
\( c .140 N \)
D. \( \frac{35}{4} \) N
Subject: Physics
A ray of light is incident on a plane
mirror and the angle of reflection is \( 50^{\circ} \)
Calculate the angle between the incident ray and the reflected ray.
A \( .50^{\circ} \)
B . \( 25^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 100^{\circ} \)
Subject: Maths
Use synthetic division to find the quotient \( Q \) and remainder \( R \) when dividing \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{5}+\boldsymbol{x}^{4}+\boldsymbol{x}^{3}+\boldsymbol{2} \boldsymbol{x}-\boldsymbol{5} \) by \( \boldsymbol{x}+\boldsymbol{i} \)
\( (i=\sqrt{(}-1) \text { imaginary unit }) \)
Subject: Chemistry
Select the wrong relation(s).
This question has multiple correct options
\( \Delta S=\left(\frac{\partial E}{\partial T}\right)_{p} \times n F \)
\( \mathbf{B} \cdot-\Delta S=(\partial E \partial T)_{p} \times n F \)
\( \left(\frac{\partial E}{\partial T}\right)_{p}=\left(\frac{\partial \Delta S}{\partial T}\right) \)
\( ^{\mathbf{D}} \cdot\left(\frac{\partial E}{\partial T}\right)_{p}=\frac{\Delta H+n E F}{T} \)
Subject: Physics
The supply voltage to room is 120 \( V \). The
resistance of the lead wires is \( 6 \Omega . \) A
\( 60 W \) bulb is already switched on. What
is the decrease of voltage across the bulb, when a \( 240 W \) heater is switched
on in parallel to the bulb?
A . zero
в. 2.9 volt
c. 13.3 volt
D. 10.04 Volt
Subject: Physics
A force \( F \) is applied on a lawn mower at
an angle of \( 60^{\circ} \) with the horizontal. If it
moves through a distance \( x \) in horizontal direction, the work done by
the force is:
A \( \cdot \frac{F x}{2} \)
в. \( \frac{\sqrt{3} F x}{2} \)
c. \( 2 F x \)
D. None of the above
Subject: Chemistry
Ethanol is converted into ethoxy ethane:
A. by heating excess of ethanol with conc. \( H_{2} S O_{4} \) at \( 140^{\circ} \) \( c \)
B. by heating Ethanol with excess of conc. \( H_{2} S O_{4} \) at 413 \( k \)
C. by treating with conc. \( H_{2} S O_{4} \) at room temperature
D. by treating with conc. \( H_{2} S O_{4} \) at \( 273 \mathrm{K} \)
Subject: Maths
An arc of a bridge is semi- elliptical with major axis horizontal. The length of
the base is 9 meter and the highest part of the bridge is 3 meter from the horizontal. The best approximation of the pillar 2 meter form the center of the base is
A \( \cdot \frac{11}{4} m \)
в. \( \frac{8}{3} m \)
c. \( \frac{7}{2} m \)
D. \( 2 m \)
Subject: Maths
Prove that:
\[
\tan ^{-1}\left[\frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}\right]=\frac{\pi}{4}-
\]
\( \frac{1}{2} \cos ^{-1} x,-\frac{1}{\sqrt{2}} \leq x \leq 1 \)
Subject: Chemistry
The total number of electrons in 4.2 g of \( N^{3-} \) ion is: \( \left(N_{A} \) is the Avogadro's \right.
number
A \( \cdot 2.1 N_{A} \)
в. \( 4.2 N_{A} \)
\( c \cdot 3 N_{A} \)
D. \( 3.2 N_{A} \)
Subject: Maths
Resolve into partial fractions \( \frac{x^{2}+2}{(x+1)^{3}(x-2)} \)
A \( \cdot \frac{6}{(x+2)}+\frac{6}{(x+1)}-\frac{5}{(x+1)^{2}}+\frac{3}{(x+1)^{3}} \)
B. \( -\frac{6}{(x+2)}+\frac{6}{(x+1)}-\frac{5}{(x+1)^{2}}+\frac{3}{(x+1)^{3}} \)
C \( \cdot-\frac{6}{(x+2)}+\frac{3}{(x+1)}-\frac{5}{(x+1)^{2}}+\frac{3}{(x+1)^{3}} \)
D \( \cdot-\frac{3}{(x+2)}-\frac{3}{(x+1)}-\frac{5}{(x+1)^{2}}+\frac{3}{(x+1)^{3}} \)
Subject: Maths
The value of the determinant
\( \left|\begin{array}{lll}a_{1} & m a_{1} & b_{1} \\ a_{2} & m a_{2} & b_{2} \\ a_{3} & m a_{3} & b_{3}\end{array}\right| \) is
\( \mathbf{A} \cdot \mathbf{0} \)
В. \( m a_{1} a_{2} a_{3} \)
\( \mathrm{c} \cdot m a_{1} b_{2} a_{2} \)
D. \( m b_{1} b_{2} b_{3} \)
Subject: Maths
The differential equation of the family of hyperbolas having centres at the origin and whose axes are the co-ordinate
axes is
A \( \cdot x y y_{2}+x y_{1}^{2}+y y_{1}=0 \)
B. \( x y y_{2}-x y_{1}^{2}-y y_{1}=0 \)
c. \( x y y_{2}+x y_{1}^{2}-y y_{1}=0 \)
D. \( x y y_{2}+x y_{1}-y y_{1}=0 \)
Subject: Maths
From a variable point of an ellipse \( \frac{x^{2}}{d^{2}}+ \) \( \frac{\boldsymbol{y}^{2}}{\boldsymbol{b}^{2}}=1 \) normal is drawn to the ellipse.
Find the maximum distance of the
normal from the centre of the ellipse.
\( \mathbf{A} \cdot a+b \)
B. \( a-b \)
c. \( a^{2}-b^{2} \)
D. \( -a+b \)
Subject: Physics
Calculate the de Broglie wavelength of an electron having kinetic energy of
\( 1.6 \times 10^{-6} \) erg \( \left(m_{e}=9.11 \times\right. \)
\( \mathbf{1 0}^{-\mathbf{2 8}} \boldsymbol{g}, \boldsymbol{h}=\mathbf{6 . 6 2} \times \mathbf{1 0}^{-\mathbf{2 7}} \mathbf{e r g}-\boldsymbol{s e c} \)
B . \( 0.00029 A^{\circ} \)
c. \( 0.0122 A^{\circ} \)
D. \( 1.29 A^{\circ} \)
Subject: Chemistry
Magnetic moment of \( \boldsymbol{C r}(\boldsymbol{Z}= \) \( \mathbf{2 4}), \boldsymbol{M n}^{+}(\boldsymbol{Z}=\mathbf{2 5}) \) and \( \boldsymbol{F} \boldsymbol{e}^{\mathbf{2}+}(\boldsymbol{Z}=\mathbf{2 6}) \)
are \( x, y, z . \) They are in order:
A. \( x<y<z \)
в. \( x=y<z \)
c. \( z<x=y \)
D. \( x=y=z \)
Subject: Physics
On the axis of a transparent sphere of
refractive index \( (\boldsymbol{n}=\mathbf{2}) \& \) radius \( \mathbf{8 c m} \)
an object is kept at the distance \( 8 \mathrm{cm} \) from the surface of the sphere. Find the
minimum distance of the image after all possible refraction from the surface
of the sphere in cm.
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{x} & \boldsymbol{y} & \boldsymbol{z} \\ \boldsymbol{p} & \boldsymbol{q} & \boldsymbol{r}\end{array}\right], \boldsymbol{B}= \)
\( \left[\begin{array}{ccc}\boldsymbol{q} & -\boldsymbol{b} & \boldsymbol{y} \\ -\boldsymbol{p} & \boldsymbol{a} & -\boldsymbol{x} \\ \boldsymbol{r} & \boldsymbol{-} \boldsymbol{c} & \boldsymbol{z}\end{array}\right] \) then
This question has multiple correct options
B . \( |A|=-\mid B \)
c. \( |A|=2|B| \)
D. \( A \) is invertible if and only if \( B \) is invertible
Subject: Physics
Two bodies of masres \( 1 k g \) and \( 3 k g \) have position vectors \( \hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) and \( -\boldsymbol{3} \boldsymbol{i}- \)
\( 2 \hat{j}+\hat{k} \) respectively. The centre of mass
of this system has a position vector
B . \( -2 \hat{i}-1 \hat{j}+\hat{k} \)
c. \( 2 \hat{i}-\hat{j}-2 \hat{k} \)
D. \( -\hat{i}+\hat{j}+\hat{k} \)
Subject: Physics
A mass \( m \) rests at height \( 2 h \) above the floor, while a mass \( 2 m \) rests at a height of \( 3 h . \) How much more gravitational
potential energy does \( 2 m \) have
compared to \( m \) if the gravitational field is uniform?
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( m g h \)
c. \( 2 m g h \)
D. \( 3 m g h \)
E . \( 4 m g h \)
Subject: Maths
The arrangement of the following sets in the proper order is
A. Domain of \( \frac{|\boldsymbol{x}|}{\boldsymbol{x}} \)
B. Range of \( \operatorname{cosec} x \)
C. Range of cot \( x \)
D. Domain of \( \sqrt{x^{2}-4} \)
A. \( C \subset A \subset B \subset D \)
в. \( D \subset B \subset C \subset A \)
c. \( C \subset A \subset D \subset B \)
D. \( D \subset B \subset A \subset C \)
Subject: Physics
The escape velocity of a projectile from the earth's surface is approximately.
A. \( 7 \mathrm{km} / \mathrm{s} \)
В. \( 112 \mathrm{km} / \mathrm{s} \)
c. \( 11.2 \mathrm{km} / \mathrm{s} \)
D. \( 1.1 \mathrm{km} / \mathrm{s} \)
Subject: Maths
If \( \boldsymbol{P}\left(\boldsymbol{E}_{\boldsymbol{k}}\right)=\boldsymbol{C} \) for \( \mathbf{0} \leq \boldsymbol{k} \leq \boldsymbol{n}, \) then \( \boldsymbol{P}(\boldsymbol{A}) \)
equals
A \( \cdot 1 / 2 \)
в. \( 2 / 3 \)
\( c \cdot 1 / 6 \)
D. \( 1 /(n+1) \)
Subject: Maths
The unit vector perpendicular to both the vectors \( \vec{a}=\vec{i}+\vec{j}+\vec{k} \) and \( \vec{b}=2 \vec{i}- \)
\( \vec{j}+3 \vec{k} \) and making an acute angle with the vector \( \vec{k} \) is
A \( \cdot-\frac{1}{\sqrt{26}}(4 \vec{i}-\vec{j}-3 \vec{k}) \)
B. \( \frac{1}{\sqrt{26}}(4 \vec{i}-\vec{j}-3 \vec{k}) \)
c. \( \frac{1}{\sqrt{26}}(4 \vec{i}-\vec{j}+3 \vec{k}) \)
D. None of these
Subject: Maths
What is the value of mode for the
following data:
\( \begin{array}{ll}\text { Class interval } & \text { Frequency } \\ 350-369 & 15 \\ 370-389 & 27 \\ 390-409 & 31 \\ 410-429 & 19 \\ 430-449 & 13 \\ 450-469 & 6\end{array} \)
\( A . \quad 390 \)
B . 394.50
\( c .394 \)
D. 400
Subject: Chemistry
The equilibrium constant \( \boldsymbol{K}_{\boldsymbol{p}} \) for the
reaction \( \boldsymbol{P} \boldsymbol{C l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \)
is \( 3.81 \times 10^{2} \) at \( 600 \mathrm{K} \) and \( 2.69 \times 10^{3} \)
at 700 K. Calculate \( \Delta_{r} H \)
\( A \cdot 68.248 \mathrm{kJ} \)
B. 69.04 kJ
c. 71.89 k
D. 80.09 kJ
Subject: Chemistry
Which of the following statement is
correct?
\( \mathbf{A} \cdot S-S \) bond is present in \( H_{2} S_{2} O_{6} \)
B. In peroxosulphuric acid \( \left(H_{2} S O_{5}\right) \) sulphur is in +8 oxidation state
C. Copper powder along with \( A l_{2} O_{3} \) and \( K_{2} O \) is used as a
catalyst in the preparation of \( N H_{3} \) by Haber's process
D. Change in enthalpy is positive for the preparation of \( S O_{3} \) by catalytic oxidation of \( S O_{2} \)
Subject: Physics
The volume of a vessel is V. The volume of
the barrel of pump is \( \mathrm{v} \). After \( n \) strokes of
the exhaust pump, what the pressure of
air inside the vessel if the original
pressure inside the vessel is \( \mathrm{P}_{0} \) ?
A \( \cdot P_{0}\left(\frac{V}{V+v}\right)^{n} \)
B \( \cdot P_{0}\left(\frac{V+v}{V}\right)^{n} \)
\( \mathbf{c} \cdot \frac{P_{0} V}{V+v} \)
D. \( \frac{P_{0}(V+v)}{v} \)
Subject: Physics
How much energy is released when a \( \mathrm{s} \mathrm{O}^{16} \) nucleus is completely converted
into energy?

The binding energy per nucleon of \( _{8} O^{16} \)
is \( 7.97 M e V \) and \( m_{p}=1.0078 u \) and
\( \boldsymbol{m}_{\boldsymbol{n}}=\mathbf{1 . 0 0 8 7 u} \)
A . \( 14899.438 \mathrm{MeV} \)
в. 148.99 Ме \( V \)
c. 4489.73 Ме \( V \)
D. 448.973 MeV
Subject: Physics
Resistance of a wire at \( 20^{\circ} C \) is \( 20 \Omega \) and
at \( 500^{\circ} \mathrm{C} \) is \( 60 \Omega . \) At what temperature
its resistance is \( 25 \Omega \)
\( \mathbf{A} \cdot 160^{\circ} C \)
B. \( 250^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 100^{\circ} \mathrm{C} \)
D. \( 80^{\circ} \mathrm{C} \)
Subject: Physics
Match the following
\( \begin{array}{lllll}\text { List I } & & \text { List II } & \\ \text { Adjustment } & & & \\ \text { of focal } & \text { a } & \text { Accommodation } \\ \text { length } & & & \\ \text { 2 } & \begin{array}{l}\text { distance of } \\ \text { distinct vision }\end{array} & \text { b } & \text { Infinity } \\ \text { 3 } & \begin{array}{l}\text { Farthest point } \\ \text { of visibility }\end{array} & \text { c } & \text { 25 cm } \\ \text { 4 } & \begin{array}{l}\text { Vision } \\ \text { impairment }\end{array} & \text { d } & \text { Cataract }\end{array} \)
A . \( 1-b, 2-c, 3-a, 4-d \)
B. 1-d, 2-c, 3-b, 4-a
c. \( 1- \) a, \( 2-c, 3-b, 4-d \)
D. 1-c, 2-a, 3-d, 4-b
Subject: Biology
Which of the following statements is
not true?
The partial pressure of
A. Oxygen in deoxygenated blood is \( 40 \mathrm{mm} \) Hg
B. Oxygen in deoxygenated blood is \( 95 \mathrm{mm} \) Hg
c. oxygen in alveolar air is \( 104 \mathrm{mm} \) Hg
D. Carbon dioxide in the alveolar air is 40 \( \mathrm{mm} \) Hg
Subject: Chemistry
The overall reaction of a hydrogen-
oxygen fuel cell is:
A \( \cdot 2 H_{2(g)}+O_{2(g)} \rightarrow 2 H_{2} O_{(l)} \)
B \( \cdot 2 H_{2(g)}+4 O H_{(a q)}^{-} \rightarrow 4 H_{2} O_{(l)}+4 e^{-} \)
c. \( O_{2(g)}+2 H_{2} O_{(l)}+4 e^{-} \rightarrow 4 O H_{(a q)}^{-} \)
D. \( 4 O H_{(a q)}^{-}+4 e^{-} \rightarrow 2 H_{2} O_{(l)} \)
Subject: Maths
Differentiate the following function with
respect to \( x \)
\( \left(2 x^{2}-3\right) \sin x \)
A \( \cdot 4 x \sin x-\left(2 x^{2}-3\right) \cos x \)
B. \( 4 x \sin x+\left(2 x^{2}+3\right) \cos x \)
c. \( 4 x \sin x+\left(2 x^{2}-3\right) \cos x \)
D. None of the above
Subject: Chemistry
Assertion
In a Daniell cell, if the concentration of
\( C u^{2+} \) and \( Z n^{2+} \) ions are doubled, the
EMF of the cell will be doubled.
Reason
f the concentration of ions in contact
with metals is doubled, the electrode
potential is doubled.
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 \( f(x)=x e^{x(1-x)}, \) then \( f(x) \) is
A \( \cdot \) increasing on \( \left[-\frac{1}{2}, 1\right] \)
B. decreasing on R
C. increasing on R
D. decreasing on \( \left[-\frac{1}{2}, 1\right] \)
Subject: Maths
STATEMENT-1: If \( a b^{2} c^{3}, a^{2} b^{3} c^{4}, a^{3} b^{4} c^{5} \)
are in A.P.
\( (a, b, c>0), \) then the minimum value of
\( a+b+c \) is 3
STATEMENT-2: Arithmetic mean of any
two numbers is greater than geometric
mean of the numbers.
A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is the correct explanation for STATEMENT-1
B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C . STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True
Subject: Maths
ff \( \left(x_{1}, y_{1}, z_{1}\right) \) and \( B\left(x_{2}, y_{2}, z_{2}\right) \) are
two points such that the direction \( \operatorname{cosines} \) of \( A B \) are \( l, m, n \) then
\( l=\frac{x_{2}-x_{1}}{|A B|}, m=\frac{y_{2}-y_{1}}{|A B|}, n=\frac{z_{2}-z_{1}}{|A B|} \)
Subject: Chemistry
The \( p H \) of a saturated solution of
\( M g(O H)_{2} \) in water will be :
\( \left(K_{s p}=4 \times 10^{-12}\right) \)
A. \( 4-\log 2 \)
B. \( 10-\log 2 \)
c. \( 4+\log 2 \)
D. \( 10+\log 2 \)
Subject: Chemistry
Assertion
Aldehyde have lower boiling point than
ether.
Reason
Aldehydes are less polar than ether.
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
Shobos mothers present age is six times Shobos present age. Shobos age five years from now will be one third of
his mothers present age. What are their resent ages?
A. Shobos age: 5 years; Shobos mothers age: 30 years
B. Shobos age: 4 years; Shobos mothers age: 24 years
c. Shobos age: 10 years; shobos mothers age: 60 years
D. Shobos age: 1 years; shobos mothers age: 6 years
Subject: Physics
A man weighing \( 80 \mathrm{kg} \) is standing at the centre of a flat boat and he is \( 20 m \)
from the shore. He walks \( 8 m \) on the
boat towards the shore and then halts.
The boat weight 200 kg. How far is he
from the shore at the end of this time?
A . \( 11.2 m \)
в. \( 13.8 \mathrm{m} \)
c. 14.3 m
D. \( 15.4 \mathrm{m} \)
Subject: Physics
State the uses of dimensional analysis
using dimensions, show that 1 joule \( = \) \( \mathbf{1 0}^{\mathbf{7}} \) erg
OR
Explain different types of errors in
measurement.

An object was weighed by a physical balance and following readings were obtained
\( 5.04 g, 5.06 g, 4.17 g, 5 g m, 4.93 g m \)
Find
1.) Mean absolute error
2.) percentage error
Subject: Physics
The distance between the plates of a
condenser is reduced to \( \frac{1}{4} t h \) and the
space between the plates is filled up by a medium of dielectric constant \( \mathrm{K}(2.8) \). The
capacity is increased by :
A. 5.6times
B. 11.2times
c. 22.4 times
D. 44.8 times
Subject: Physics
If the magnitude of mass is 1 kg that of time is 1 minute and that of
acceleration due to gravity is \( 10 \mathrm{ms}^{-2} \) the magnitude of energy injoule
A \( .3 .6 \times 10^{5} \)
В. \( 3.6 \times 10^{-5} \)
c. \( 3.6 \times 10^{2} \)
D. 10
Subject: Maths
The area of a triangle, whose vertices \( \operatorname{are}(3,2),(5,2) \) and the point of intersection of the lines \( \boldsymbol{x}=\boldsymbol{a} \) and \( \boldsymbol{y}= \)
\( 5, \) is 3 square units. What is the value of
\( \boldsymbol{a} ? \)
A . 2
B. 3
\( c \cdot 4 \)
D. 5
Subject: Chemistry
A metal X on heating in nitrogen gas
gives Y. Y on treatment with \( \boldsymbol{H}_{2} \boldsymbol{O} \) gives a colourless gas which when passed
through \( C u S O_{4} \) solution gives a blue colour.Y is :
A \( \cdot \operatorname{Mg}\left(\mathrm{NO}_{3}\right)_{2} \)
B . \( \mathrm{Mg}_{3} \mathrm{N}_{2} \)
c. \( \mathrm{NH}_{3} \)
D. \( \mathrm{MgO} \)
Subject: Chemistry
The relationship between the value of
Osmotic pressure \( (\pi) \) of the solution
obtained by dissolving \( 6 g . \mathrm{L}^{-1} \) of acetic
\( \operatorname{acid}\left(\pi_{1}\right) \) and 7.45 g.L \( ^{-1} \) of \( \mathrm{KCl}\left(\pi_{2}\right) \) is :
A \( \cdot \pi_{1}<\pi_{2} \)
В. \( \pi_{1}>\pi_{2} \)
\( \mathbf{c} \cdot \pi_{1}=\pi_{2} \)
D. \( \frac{\pi_{1}}{\pi_{1}+\pi_{2}}=\frac{\pi_{2}}{\pi_{1}+\pi_{2}} \)
Subject: Physics
\( 1 g \) of ice at \( 0^{0} C \) is converted to steam
at \( 100^{0} C . \) The amount of heat required
will be:
\( \left(L_{\text {steam}}=536 c a l / g\right) \)
A . 756 call \( l \)
B. 12000 cal
c. 716 call \( l \)
D. 450 call \( l \) and
Subject: Physics
The length of a thin wire require to
manufacture a solenoid of length \( l= \) \( 100 \mathrm{cm} \) and inductance \( L=1 m H, \) if
the solenoid's cross-sectional diameter
is considerably less than its length is:
A. \( 1 k m \)
в. \( 0.10 \mathrm{km} \)
c. \( 0.010 \mathrm{km} \)
D. \( 10 \mathrm{km} \)
Subject: Physics
There are two non conducting spheres
having uniform volume charge
densities \( \rho \) and \( -\rho . \) Both spheres have
equal radius R. The spheres are now laid
down such that they overlap as shown in the figure. The electric field \( \overrightarrow{\boldsymbol{E}} \) in the
overlap region is :
A. non uniform
B. zero
c. \( \frac{\rho}{3 \epsilon_{0}} \vec{d} \)
Subject: Physics
lce at \( -20^{\circ} \mathrm{C} \) is dropped into \( 0.25 \mathrm{kg} \) of
the water at \( 20^{\circ} \mathrm{C} \). The final
temperature of the system is \( 0^{\circ} C \)
when all the ice is melted. Find
approximate mass of ice in the water in kg. (Specificheat of ice = \( \mathbf{2 0 0 0} \boldsymbol{J} \boldsymbol{k g}^{-1} \boldsymbol{K}^{-1}, \boldsymbol{L}=\mathbf{3 3 . 4} \times \mathbf{4} \boldsymbol{J} \boldsymbol{k g}^{-1} \)
A . 0.06
B. 6
\( c \cdot 60 \)
D.
Subject: Chemistry
A system absorbs \( 10^{3} \) cal of heat and
the system does \( 1677.3 J \) work. The
internal energy of the system increases by \( 2515 . J . \) The value of J is
A. \( 4.19 \mathrm{J} / \mathrm{cal} \)
в. 4.18 cal \( / J \)
c. \( 42 J / \) cal \( l \)
D. \( 420 J / c a l \)
Subject: Physics
Assertion
Pressure applied to an enclosed fluid is transmitted undiminished to every
portion of the fluid and the walls of the
containing vessel.
Reason
Fluids cannot distribute the external
pressure equally to all portions.
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: Chemistry
The resistance of a \( \frac{N}{10} K C l \) aqueous solution is \( 245 \Omega \). If the electrodes in the
cell are \( 4 \mathrm{cm} \) apart and area having
\( 77 \mathrm{cm}^{2} \) each, the molar conductance of
the solution will be:
A . 233
B. 2.12
c. 23.32
D. 0.233
Subject: Chemistry
Which of the assumptions of the kinetic-molecular theory best explains the observations that a gas can be
compressed?
A. Gas molecules move at random with no attractive forces between them
B. The velocity of gas molecules is proportional to their kelvin temperature
c. The amount of space occupied by a gas is much greater than the space occupied by the actual gas molecules
D. In collisions with the walls of the container or with other molecules, energy is conservedd
Subject: Chemistry
The exothermic formation of \( C l F_{3} \) is
represented by the equation: \( C l_{2}(g)+ \)
\( \mathbf{3} F_{2}(\boldsymbol{g}) \rightleftharpoons 2 \boldsymbol{C l} \boldsymbol{F}_{3}(\boldsymbol{g}), \boldsymbol{\Delta} \boldsymbol{H}=-\mathbf{3 2 9} \mathbf{k J} \)
Which of the following will increase the
quantity of \( C l F_{3} \) in an equilibrium
mixture of \( C l_{2}, F_{2} \) and \( C l F_{3} ? \)
A. Increasing the temperature
B. Removing \( C l_{2} \)
c. Increasing the volume of container
D. Adding \( F_{2} \)
Subject: Physics
One end of a uniform rod of mass \( \boldsymbol{M} \)
and cross-sectional area \( \boldsymbol{A} \) is
suspended from the other end. The stress at the mid-point of the rod will be
A \( \cdot \frac{2 M g}{A} \)
в. \( \frac{3 M g}{2 A} \)
c. \( \frac{M g}{A} \)
D. zero
Subject: Physics
A circular coil of \( n \) turns is kept in a uniform magnetic field such that the plane of the coil is perpendicular to the field. The magnetic flux associated with
the coil is now \( \phi . \) Now the coil is opened
and made into another circular coil
of twice the radius of the previous coil and kept in the same field such that the plane of the coil is perpendicular to the field. The magnetic flux associated with this coil now is:
\( A \cdot \phi \)
B. 2
\( c \cdot \frac{\phi}{4} \)
D. \( \frac{\phi}{2} \)
Subject: Physics
The centre of mass of the shaded
portion of the disc is (The mass is
uniformly distributed in the shaded
portion):
\( A \cdot \frac{R}{20} \) to the left of \( A \)
B. \( \frac{R}{12} \) to the left of \( A \)
C. \( \frac{R}{40} \) to the right of \( A \)
D. \( \frac{R}{12} \) to the right of \( A \)
Subject: Maths
Discuss the continuity of the following
function at \( x=0 . \) If the function has a
removable discontinuity, redefine the
function so as to remove the
discontinuity
\( f(x)=\left\{\begin{array}{ll}\frac{4^{x}-e^{x}}{6^{x}}-1 & \text { for } x \neq 0 \\ \log \left(\frac{2}{3}\right) & \text { for } x=0\end{array}\right. \)
Subject: Physics
A thin bar of mass \( M \) and length \( L \) is
free to rotate about a fixed horizontal
axis through a point at its end. The bar
is brought to a horizontal position and then released. The axis is perpendicular
to the rod. The angular velocity when it
reaches the lowest point is This question has multiple correct options
A. directly proportional to its length and inversely proportional to its mass
B. independent of mass and inversely proportional to the square root of its length
C. dependent only upon the acceleration due to gravity and the length of the bar
D. directly proportional to its length and inversely proportional to the acceleration due to gravity
Subject: Physics
The equation of the progressive wave, where \( t \) is the time in second, \( x \) is the distance in metre is \( y=A \cos 240(t- \) \( \left.\frac{x}{12}\right) . \) The phase difference (in Sl units) between two positions0.5m apart is
A . 40
B. 20
c. 10
D. 5
Subject: Maths
If \( f(x)=\frac{a x+b}{c x+d} \) and \( (f o f)(x)=x \)
then
This question has multiple correct options
A \( \cdot a^{2}+b c=1 \)
B . \( d^{2}+b c=1 \)
\( \mathbf{c} \cdot a+d=0 \)
D. none of these