AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
It cost Rs 4020 to paint the inner curved surface area of hemisphere of radius
8 \( m \). If it is painted at rate of Rs.
10 per \( m^{2} \). Find inner curved surface.
A. \( 402 m^{2} \)
в. \( 400 \mathrm{m}^{2} \)
c. \( 200 m^{2} \)
D. \( 201 m^{2} \)
Subject: Physics
A cylindrical tube of uniform crosssectional area A is filled with two air
tight frictionless pistons. The pistons are connected to each other by a
metallic wire. Initially, the pressure of
the gas is \( p_{o} \) and temperature is \( T_{o} \)
atmospheric pressure is also \( p_{o} \$ . \) Now, the temperature of the gas is increased
to \( 2 T_{0}, \) the tension of wire will be.
A \( \cdot 2 p_{o} \)
в. \( p_{o} A \)
c. \( \frac{p_{o} A}{2} \)
D. \( 4 p_{o} A \)
Subject: Maths
Suppose \( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{- 1} & \mathbf{5} \\ \mathbf{4} & \mathbf{3} & \mathbf{7}\end{array}\right] \) find \( \mathbf{4} \boldsymbol{A} \)
Subject: Chemistry
The pH of a neutral water is \( 6.5 . \) Then
the temperature of water:
\( A \cdot \operatorname{ls} 25^{\circ} C \)
B. Is more than \( 25^{\circ} \mathrm{C} \)
c. Is less than \( 25^{\circ} \mathrm{C} \)
D. can be more or less than \( 25^{\circ} \mathrm{C} \)
E. Cannot be predicted
Subject: Chemistry
Sulphuric acid reacts with sodium hydroxide as follows
\( H_{2} S O_{4}+2 N a O H \rightarrow N a_{2} S O_{4}+2 H_{2} O \)
When 1 L of 0.1 M sulphuric acid solution is allowed to react with 1 L of \( 0.1 \mathrm{M} \)
sodium hydroxide solution, the amount of sodium sulphate formed and its molarity in the solution obtained is ?
A. \( 0.1 \mathrm{molL}^{-1} \)
B. \( 7.10 g \)
c. 0.025 mol \( L^{-1} \)
D. \( 3.55 g \)
Subject: Chemistry
If the molar concentration of \( \boldsymbol{P b I}_{2} \) is
\( 1.5 \times 10^{-3} \) mol \( L^{-1}, \) then the
concentration of iodide ions in \( g \) ion \( L^{-1} \)
is:
A. \( 3.0 \times 10^{-3} \)
В. \( 6.0 \times 10^{-3} \)
D. \( 0.6 \times 10^{-6} \)
Subject: Physics
A thin diamagnetic rod is placed vertically between the poles of an electromagnet. When the current in the electromagnet is switched on, then the diamagnetic rod is pushed up, out of the horizontal magnetic field. Hence the rod gains gravitational potential energy. The work required to do this comes
from
A. The lattice structure of the material of the rod
B. The current source
c. The induced electric field due to the changing magnetic field
D. The magnetic field
Subject: Maths
Evaluate: \( \int_{0}^{\frac{\pi}{4}}\left(\tan ^{4} x+\tan ^{2} x\right) d x \)
\( \mathbf{A} \cdot \mathbf{1} \)
в. \( 1 / 2 \)
c. \( 1 / 3 \)
D. \( 1 / 4 \)
Subject: Physics
A wire in the shape of an equilateral
triangle with sides of length \( 1.00 m \) is
kept in a magnetic field of \( 2.00 T \)
pointing to the right. Find out the magnitude of the magnetic flux passing through the triangle?
A. \( 0 W b \)
в. \( 1.00 \mathrm{Wb} \)
c. \( 1.73 W b \)
D. 2.00Wb
E. \( 3.46 W b \)
Subject: Chemistry
Lithopone is mixture of :
A. \( Z n C O_{3}, B a C O_{3} \)
в. \( Z n S, N a_{2} S O_{4} \)
\( \mathrm{c} \cdot Z n S O_{4}, B a S O_{4} \)
D. \( Z n S, \) BaSO\( _{4} \)
Subject: Maths
For two events \( A \) and \( B, P(A \cap B) \) is
This question has multiple correct options
\( \mathbf{A} \cdot \) not less than \( P(A)+P(B)-1 \)
B. not greater than \( P(A)+P(B) \)
C . equal to \( P(A)+P(B)-P(A \cup B) \)
D・equal to \( P(A)+P(B)+P(A \cup B) \)
Subject: Maths
Evaluate \( \int \frac{\boldsymbol{x}^{2}}{\mathbf{9}+\mathbf{1 6 x}^{\mathbf{6}}} \boldsymbol{d} \boldsymbol{x} \)
A \( \frac{1}{16} \tan ^{-1}\left(\frac{4 x^{3}}{3}\right)+c \)
в. \( \frac{1}{36} \tan ^{-1}\left(\frac{3 x^{3}}{4}\right)+c \)
c. \( \frac{1}{16} \tan ^{-1}\left(\frac{3 x^{3}}{4}\right)+c \)
D. \( \frac{1}{36} \tan ^{-1}\left(\frac{4 x^{3}}{3}\right)+c \)
Subject: Maths
The number of solutions of
\( \sin ^{-1}\left(1+b+b^{2}+\cdots \infty\right)+ \)
\( \cos ^{-1}\left(a-\frac{a^{2}}{3}+\frac{a^{2}}{9} \cdots \infty\right)=\frac{\pi}{2} \) is
\( A \)
B. 2
\( c .3 \)
\( D \)
Subject: Physics
The relation between internal energy U, pressure \( P \) and volume \( V \) of a gas in an adiabatic process is \( U=a+b P V, \) where a and b are positive constants. What is the value of \( \gamma \) ?
A. \( \frac{a}{b} \)
B. \( \frac{b+1}{b} \)
c. \( \frac{a+1}{a} \)
D.
Subject: Maths
In the figure, \( M N S \) is tangent to the
circle with centre \( O \) at \( N \)
\( A B \) is chord parallel to \( M N S . \) find
\( \angle A N C \)
A . 50
B. \( 90^{\circ} \)
\( c \cdot 40 \)
D. 20
Subject: Chemistry
\( 9.2 \mathrm{g} N_{2} \mathrm{O}_{4} \) is heated in a \( 1 \mathrm{L} \) vessel till equilibrium state is established
\( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \)
In equilibrium state \( 50 \% N_{2} O_{4} \) was dissociated, equilibrium constant will be
A . \( 0 . \)
B. 0.4
\( c .0 .3 \)
D. 0.2
Subject: Physics
Three lenses in contact have a
combined focal length of \( 12 \mathrm{cm} \). When the third lens is removed the combined
focal length becomes \( 60 \mathrm{cm} \). The third
lens is :
A. a converging lens of focal length 30 cm
B. a converging lens of focal length 60 cm
c. a diverging lens of focal length 30 cm
D. a diverging lens of focal length 60 cm
Subject: Chemistry
Arrange the following compounds in the increasing order of their reactivity
towards HCN.
I. Acetaldehyde
II. Acetone
III. Methyl-tert-butyl ketone
IV. Di-tert-butyl ketone
A. III <II<IV <
B. II \( |<|<\mid V<\| \)
c. \( \mid V<\|<\|<1 \)
D. II<IV <I<III
Subject: Physics
Four identical solid spheres each of
mass \( M \) and radius \( R \) are fixed at four
corners of a light square frame of side length \( 4 R \) such that centres of spheres coincide with corners of square.
The moment of inertia of 4 spheres about an axis perpendicular to the plane of frame and passing through its centre is:
A \( \cdot \frac{21 M R^{2}}{5} \)
в. \( \frac{42 M R^{2}}{5} \)
c. \( \frac{84 M R^{2}}{5} \)
D. \( \frac{168 M R^{2}}{5} \)
Subject: Chemistry
sweetener \( A, B, C \) and \( D . \) To identify
these samples, he performed certain experiments and noted the following observations.
(i) \( A \) and \( D \) both form a blue-violet
colour with ninhydrin.
(ii) Lassaigne extract of \( \mathrm{C} \) gives positive
\( A g N O_{3} \) test and negative
\( \boldsymbol{F} \boldsymbol{e}_{4}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right]_{3} \) test.
(iii) Lassaigne extract of \( \mathrm{B} \) and \( \mathrm{D} \) gives positive sodium nitroprusside test.
Based on these observations which
option is correct?
A. A: Alitame; B: Saccharin;
C: Aspartame; D: Sucralose
B. A: Aspartame; B: Saccharine;
C: Sucralose; D: Alitame
C. A: Aspartame; B: Alitame;
c: Saccharin; D: Sucralose
D. A: Saccharin; B: Alitame;
C: Sucralose; D: Aspartame
Subject: Physics
Two particles having the same momentum enter at right angles into same magnetic field and travel in circular paths of radius \( r_{1} \) and \( r_{2} \). The
ratio of their charges is:
A \( \cdot \frac{r_{1}}{r_{2}} \)
B. \( \left(\frac{r_{1}}{r_{2}}\right)^{1 / 2} \)
\( ^{c} \cdot\left(\frac{r_{1}}{r_{2}}\right)^{2} \)
D. \( \left(\frac{r_{1}}{r_{2}}\right)^{-1} \)
Subject: Chemistry
A hydrogen-like atom(atomic number
Z) is in a higher excited state of quantum number n. This excited atom can make a transition to the first state
by successively emitting two photons of energies \( 10.20 \mathrm{eV} \) and \( 17.00 \mathrm{eV} \)
Alternatively, the atom from the same excited state can make a transition to
the energy 4.24 eV and 5.95 eV. If the
excited level for second transition is
3.The value of atomic number(z)
is
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D. 3
Subject: Maths
Assertion
In the shop there are five types of ice-
creams available, a child buys six ice-
creams.
Reason
The number of different ways the child
can buy the six ice-creams is \( ^{10} C_{3} \)
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
Identify the incorrect statement in
respect of two square matrices \( A \) and \( B \) conformable for sum and product
A \( \cdot t_{r}(A+B)=t_{r}(A)+t_{r}(B) \)
B . \( t_{r}(\alpha A)=\alpha t_{r}(A), \quad \alpha \epsilon R \)
\( \mathbf{c} \cdot t_{r}\left(A^{T}\right)=t_{r}(A) \)
D. none of these
Subject: Physics
A diverging meniscus lens of 1.5 refractive index has concave surface of
radii 3 and 4 cm.The position of the
image, if an object is placed \( 12 \mathrm{cm} \) in front of the lens, is
A. \( 7 \mathrm{cm} \)
B. - 8 cm
\( c .9 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)
Subject: Physics
Assertion (A): More the turns more is
the
resistance
Reason(R): Impedance of primary and secondary in a transformer is directly proportional
to number
of turns in the coils.
A. Both Assertion and Reason are true and Reason is the correct explanation for Assertion
B. Assertion and Reason are true but Reason is not the correct explanation for Assertion
C. Assertion is true, Reason is false
D. Assertion is false, Reason is true
Subject: Chemistry
Which of the following is a representation of Gay-Lussac's law?
A \( \cdot P_{1} T_{1}=P_{2} T_{2} \)
B . \( P_{1} T_{2}=P_{2} T_{1} \)
c. \( P_{1} V_{1}=P_{2} V_{2} \)
D. \( V_{1} T_{2}=V_{2} T_{1} \)
Subject: Chemistry
Give IUPAC name of the following compounds:
(a) \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{O H} \)
(b) \( \boldsymbol{H} \boldsymbol{C O O H} \)
(c) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C H}_{3} \)
Subject: Maths
Find the inverse of the following \( \operatorname{matrices} \boldsymbol{A}=\left(\begin{array}{ccc}2 & \mathbf{0} & \mathbf{1} \\ \mathbf{1} & \mathbf{2} & \mathbf{3} \\ \mathbf{3} & \mathbf{1} & \mathbf{1}\end{array}\right) \)
Subject: Maths
Sneh buys \( X \) eggs to resell them at a profit of \( 10 \% \) but loses \( 10 \% \) of the eggs. By how much should she mark up the selling price in order to retain \( 10 \% \) profit
A. 30\%
в. 33.33 \%
c. 22.1 \%
D. 25 \%
Subject: Physics
The ratio of acceleration due to gravity at a depth \( h \) below the surface of earth
and at a height \( h \) above the surface for \( \boldsymbol{h}<<\boldsymbol{R} \)
A. constants only when \( h<<R \)
B. increases linearly with \( h \)
C. increases parabolically with \( h \)
D. decreases
Subject: Maths
\( \operatorname{Let} \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{0} \\ \mathbf{1} & \mathbf{1}\end{array}\right], \) and \( \boldsymbol{I}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{0} \\ \mathbf{0} & \mathbf{1}\end{array}\right] \) then
prove that \( \boldsymbol{A}^{n}=\boldsymbol{n} \boldsymbol{A}-(\boldsymbol{n}-\mathbf{1}) \boldsymbol{I}, \boldsymbol{n} \geq 1 \)
Subject: Maths
The range of the function \( f(x)= \)
\( \left(8^{x}+4^{x}+8^{-x}+4^{-x}+5\right) \) is
\( A \cdot\left(\frac{7}{4}, \infty\right) \)
B. \( \left[\frac{7}{4}, \infty\right) \)
c. \( (9, \infty) \)
D \( \cdot[9, \infty) \)
Subject: Chemistry
I. Agitation and stirring will increase
the rate at which salt dissolves in water
\( I I . \) Increased movement of water
molecules allow sodium ions and
chloride ions to be pulled apart as
shells of hydration are formed.
A. Statement I is true, Statement \( I I \) is true and is a correct explanation of the phenomena described in \( I \)
B. Statement I is true, Statement II is false
c. statement \( I \) is false, statement \( I I \) is true
D. Statement I is false, Statement II is false
Subject: Biology
Assertion
Enzyme differ from man-made catalysts as the enzymes affect fewer substrates
Reason
Enterokinase is activator for pepsin.
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
Find the area of triangle having vertices \( \operatorname{are} \boldsymbol{A}(\mathbf{3}, \mathbf{1}), \boldsymbol{B}(\mathbf{1} \mathbf{2}, \mathbf{2}) \) and \( \boldsymbol{C}(\mathbf{0}, \mathbf{2}) \)
A . 4
B. 6
c. 12
D. 18
Subject: Maths
Let \( P \) and \( Q \) be two sets then what is
\( \left(\boldsymbol{P} \cap \boldsymbol{Q}^{\prime}\right) \cup(\boldsymbol{P} \cup \boldsymbol{Q})^{\prime} \) equal to \( ? \)
A \( \cdot\left(P \cap Q^{\prime}\right) \cup(P \cup Q)^{\prime}=\xi \cap Q^{\prime}=\xi \cap Q^{\prime}=\xi \)
B . \( \left(P \cup Q^{\prime}\right) \cup(P \cup Q)^{\prime}=\xi \cap Q^{\prime}=\xi \cap Q^{\prime}=\xi \)
C \( \cdot\left(P \cap Q^{\prime}\right) \cup(P \cap Q)^{\prime}=\xi \cap Q^{\prime}=\xi \cap Q^{\prime}=\xi \)
D. none of the above
Subject: Maths
Which of the following number has same unit digit as its cube?
\( \begin{array}{l}\text { A } \cdot 122^{3} \\ ^{3}\end{array}^{1}^{32} \)
B. \( 168^{3} \)
\( \mathbf{c} \cdot 137^{3} \)
D. \( 184^{3} \)
Subject: Maths
\( \int \frac{\ln (\cos x+\sqrt{\cos 2 x})}{\sin ^{2} x} d x= \)
\( \frac{\sqrt{\cos 2 x}}{\sin x}-x+\cot x \times \ln [e(\cos x+\sqrt{\cos 2 x})]+c \)
\( \frac{\sqrt{\cos 2 x}}{\sin x}+x-\cot x \times \ln [e(\cos x+\sqrt{\cos 2 x})]+c \)
\( \frac{\sqrt{\cos 2 x}}{\sin x}+x+\cot x \times \ln [e(\cos x+\sqrt{\cos 2 x})]+c \)
Subject: Chemistry
Fill in the blanks by putting appropriate choices.During adsorption there is \( _{-}- \) -in enthalpy and in the
entropy of a system but adsorption is a
spontaneous process and thus AG must be \( \quad \) Rate of
physisorption with increase in
pressure.
A. decrease, decrease, negative, increases
B. increase, increase, positive, decreases
c. decrease, increase, negative, decreases
D. increase, decrease, positive, increases
Subject: Physics
A ball collides with a smooth and fixed
inclined plane of inclination \( \boldsymbol{\theta} \) after falling vertically through a distance h. If it moves horizontally just after impact, the coefficient of restitution is
\( \mathbf{A} \cdot \tan ^{2} \theta \)
B \( \cdot \cot ^{2} \theta \)
\( c . \tan \theta \)
D. \( \cot \theta \)
Subject: Physics
A superconductor has \( T_{C}(0)=100 K \)
When a magnetic field of 7.5 Tesla is
applied, its \( T_{c} \) decreases to 75 K. For this material one can definitely say that
when
A \( \cdot B=5 \) Tesla, \( T_{c}(B)=80 K \)
B. \( B=5 \) Tesla, \( 75 K<T_{c}(B)<100 K \)
c. \( B=10 \) Tesla, \( 75 K<T_{c}<100 K \)
D. \( B=10 \) Tesla, \( T_{c}=70 K \)
Subject: Chemistry
The decreasing order of bond dissociation energies of \( \boldsymbol{C}-\boldsymbol{C}, \boldsymbol{C}-\boldsymbol{H} \)
and \( H-H \) bonds is:
A. \( H-H>C-H>C-C \)
в. \( C-C>C-H>H-H \)
c. \( C-H->C-C>H-H \)
D. \( C-C>H-H>C-H \)
Subject: Chemistry
Gaseous \( N_{2} O_{4} \) dissociates into
gaseous \( N O_{2} \) according to the reaction
\( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \) at \( 300 \mathrm{K} \) and 1
atm pressure, the degree of
dissociation of \( N_{2} O_{4} \) is \( 0.2 . \) If one mole
of \( N_{2} O_{4} \) gas is contained in a vessel then the density of the equilibrium mixture is :
A. \( 3.11 \mathrm{g} / \mathrm{L} \)
B. 4.56 g/L
c. \( 1.56 g / L \)
D. \( 6.22 \mathrm{g} / \mathrm{L} \)
Subject: Biology
Select the option that correctly
identifies \( A \) to \( E \) in the given flow chart.
\( \mathbf{A} \cdot A-\alpha, B-\beta, C-G|u c a g o n, D-H y p e r g| y c a e m i a, E- \)
Hypoglycaemia
B. A- \( \beta \), B- \( \alpha \), C-Cortisol, D-Hypoglycaemia, EHyperglycaemia
C \( . A-\beta, B-\alpha, C \) -Cortisol, D-Hyperglycaemia, EHypoglycaemia
D. \( A-\beta, B-\alpha, C \) -Glucagon, D-Hypoglycaemia, EHyperglycaemia
Subject: Maths
A rectangle ABCD is inscribed in a circle
with centre 0. If AC is the diagonal and
\( \angle B A C=30^{\circ}, \) then radius of the circle
will be equal to
A \( \cdot \frac{\sqrt{3}}{2} B C \)
B. BC
\( c \cdot \sqrt{3} B C \)
D. 2BC
Subject: Chemistry
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{O}_{2}, \) is an
example of disproportionation because:
A. oxidation number of oxygen only decreases
B. oxidation number of oxygen only increases
c. oxidation number of oxygen decreases as well as increase
D. oxidation number of oxygen neither decreases nor increases
Subject: Physics
The rigid conducting thin wire frame carries an electric current \( I \) and this
frame is inside a uniform magnetic field \( \vec{B} \) as shown in fig. Then
A. the net magnetic force on the frame is zero but the torque is not zero
B. the net magnetic force on the frame and the torque due to magnetic field are both zero
c. the net magnetic force on the frame is not zero and the torque is also not zero
D. none of these
Subject: Physics
The north pole of a magnet is moved
into a coil through the end \( \boldsymbol{A} \) Simultaneously the north pole of another magnet is moved into the coil through the end \( B \) as shown in the
figure. The direction of induced emf will:
A. Be in the anticlockwise direction as seen through the end \( A \)
B. Be in the clockwise direction as seen through the end \( B \)
c. Depend on the speed with which the two magnets are moved
D. Depend on the speed with which the magnets are moved and the strengths of the magnets
Subject: Chemistry
When a compound X reacts with ozone in aqueous medium,a compound Y is produced.Ozone also reacts with Y and
produces compound \( z, z \) acts as an oxidising agent,then \( \mathrm{X}, \mathrm{Y} \) and \( \mathrm{Z} \) will be :
A \( \cdot X=H I, Y=I_{2} \) and \( Z=H I O_{3} \)
B. \( X=K I, Y=I_{2} \) and \( Z=H I O_{3} \)
C. \( X=K I, Y=I_{2} \) and \( Z=H I O_{4} \)
D. \( X=H I, Y=I_{2} \) and \( Z=H I O_{4} \)
Subject: Chemistry
Given below are few mixtures formed by mixing two components. Which of the following binary mixtures will have same composition in liquid and vapour phase?
(i) Ethanol \( + \) Chloroform
(ii) Nitric acid + Water
(iii) Benzene + Toluene
(iv) Ethyl chloride \( + \) Ethyl bromide
A. (i) and (iii)
B. (i) and (ii)
c. (i), (ii) and (iii)
D. (iii) and (iv)
Subject: Chemistry
Given the equilibrium constants:\( \boldsymbol{C I}^{-}+\boldsymbol{H} \boldsymbol{g} \boldsymbol{C I}^{+} \rightleftharpoons \boldsymbol{H} \boldsymbol{g} \boldsymbol{C I}_{2} \)
\( \boldsymbol{K}_{\mathbf{1}}=\mathbf{3} \times \mathbf{1 0}^{\mathbf{6}} \)
\( \boldsymbol{H} \boldsymbol{g} \boldsymbol{C} \boldsymbol{I}_{2}+\boldsymbol{C} \boldsymbol{I}^{-} \rightleftharpoons \boldsymbol{H} \boldsymbol{g} \boldsymbol{C} \boldsymbol{I}_{3}^{-} ; \boldsymbol{K}_{2}=\boldsymbol{8} . \boldsymbol{9} \)
The equilibrium constants for the disproportionation equilibrium
\( 2 H g C I_{2} \rightleftharpoons H g C I^{+} H g C I_{3}^{-} \) is :
\( \mathbf{A} \cdot 3 \times 10^{-6} \)
В. \( 4 \times 10^{-6} \)
c. \( 3.5 \times 10^{-6} \)
D. \( 4.5 \times 10^{-6} \)
Subject: Biology
Match the following
Dominant
gametophytic
generation
a. Bog
moss
2
True moss
Riccia fluitans .
b. Moss
3. Aquatic
3. Riccia fluitans
4. Show heterospory
d. Aryophyte
A. \( 1-a, 2-c, 3-d, 4-b \)
B. \( 1-d, 2-a, 3-c, 4-b \)
C. \( 1-b, 2-c, 3-a, 4-d \)
D. \( 1-a, 2-d, 3-c, 4-b \)
Subject: Maths
Three numbers are chosen at random
without replacement from \( 1,2, \ldots .10 . \) The probability that the minimum of the
chosen numbers is 3 , or their maximum
is \( 7, \) is
A \( \cdot \frac{7}{40} \)
B. \( \frac{5}{40} \)
c. \( \frac{11}{40} \)
D. None of these
Subject: Chemistry
In which of the following solvents, KI has highest solubility? The dielectric
constant \( (\epsilon) \) of each liquid is given in
parentheses.
A \( \cdot C_{6} H_{6}(\epsilon=0) \)
B. \( \left(C H_{3}\right)_{2} C O(\epsilon=21) \)
c. \( C H_{3} O H(\epsilon=32) \)
D. \( C C l_{4}(\epsilon=0) \)
Subject: Physics
The emissivity of tungsten is \( 0.4 . \) A tungsten sphere with a radius of \( 4.0 \mathrm{cm} \) is suspended within a large evacuated
enclosures whose walls are 300 K. What
power input is required to maintain the
sphere at a temperature is \( 3000 \mathrm{K} \) if heat conduction along supports is neglected ? Take \( \sigma=5.6 \times \) \( \mathbf{1 0}^{-6} \boldsymbol{W} / \boldsymbol{m}^{2}-\boldsymbol{K}^{4} \)
\( \mathbf{A} \cdot 3.7 \times 10^{4} W \)
в. \( 3.7 \times 10^{5} W \)
c. \( 3.7 \times 10^{6} W \)
D. \( 3.7 \times 10^{7} W \)
Subject: Physics
The average depth of Indian ocean
is about 3000 m. The value of fractional
compression \( \frac{\Delta V}{V} \) of water at the
bottom of the ocean is:
[Given that the bulk modulus of water
is \( 2.2 \times 10^{9} N m^{-2}, g=9.8 m s^{-2} \) and
\( \left.\rho_{H_{2}} O=1000 k g . m^{-3}\right] \)
A. \( 3.4 \times 10^{-2} \)
B . \( 1.34 \times 10^{-2} \)
c. \( 4.13 \times 10^{-2} \)
D. \( 13.4 \times 10^{-2} \)
Subject: Physics
The upper portion of an inclined plane of
inclination \( \alpha \) is smooth and the lower
portion is rough. A particle slides down
from rest from the top and just comes to rest at the foot. If the ratio of smooth
Iength to rough length is \( m: n \), find the
coefficient of friction.
A \( \cdot \mu=\left(\frac{m-n}{n}\right) \tan \alpha \)
B \( \cdot \mu=\left(\frac{m+n}{m}\right) \tan \alpha \)
\( \mathbf{c} \cdot_{\mu}=\left(\frac{m-n}{m}\right) \tan \alpha \)
D. \( \mu=\left(\frac{m+n}{n}\right) \tan \alpha \)
Subject: Physics
The graph below shows the "x-direction"
position of a charged particle flying
around in space and accelerating due
only to some electric field.

During which time interval is the force
on the particle in the x-direction
greatest?
\( \mathbf{A} \cdot 5 \) to 6 seconds
B. 6 to 7 seconds
\( c .7 \) to 8 seconds
D. 8 to 9 seconds
E. 10 to 11 seconds
Subject: Chemistry
The magnitude of charge present on one azide ion in coulombs is:
\( \mathbf{A} \cdot 96500 \)
B . \( 4.8 \times 10^{19} \)
c. \( 4.8 \times 10^{-19} \)
D. \( 1.6 \times 10^{-19} \)
Subject: Biology
Assertion
Archaebacteria are able to survive in
harsh habitats.
Reason
Presence of peptidoglycan in cell wall
help archaebacteria to survive in extreme conditions.
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
c. If assertion is true but reason is false.
D. If both assertion and reason are false
Subject: Physics
A liquid drop placed on a horizontal plane has a near spherical shape (slightly flattened due to gravity). Let \( \boldsymbol{R} \) be the radius of its largest horizontal section. A small disturbance causes the
drop to vibrate with frequency \( v \) about
its equilibrium shape. By dimensional analysis the ratio \( \frac{v}{\sqrt{\frac{\sigma}{\rho R^{3}}}} \) can be (Here
\( \sigma \) is surface tension, \( \rho \) is density, \( g \) is
acceleration due to gravity, and \( k \) is an arbitrary dimensionless constant).
\( ^{\mathrm{A}} \cdot \frac{k \rho g R^{2}}{\sigma} \)
в. \( \frac{k \rho R^{2}}{g \sigma} \)
c. \( \frac{k \rho R^{3}}{g \sigma} \)
D. \( \frac{k \rho}{g \sigma} \)
Subject: Chemistry
The type of isomerism shown by
\( \left[\boldsymbol{C o}(\boldsymbol{e n})_{2}(\boldsymbol{N} \boldsymbol{C S})_{2}\right] \boldsymbol{C l} \) and
\( \left[\boldsymbol{C o}(\boldsymbol{e n})_{2}(\boldsymbol{N} \boldsymbol{C S})\right] \boldsymbol{C l} \) is :
A. ionization
B. cordination
c. linkage
D. all of these
Subject: Physics
A vessel of volume \( 0.2 m^{3} \) contains
hydrogen gas at temperature \( 300 K \) and pressure 1 bar. Find the heat required to raise the temperature to \( 400 K . \) The molar heat capacity of hydrogen at constant volume is
\( \mathbf{5} \) cal / molK.
A \( \cdot(\Delta Q)_{v}=2.1 k c a l \)
B . \( (\Delta Q)_{v}=4.2 \mathrm{kcal} \)
C \( \cdot(\Delta Q)_{v}=2 k c a l \)
D. \( (\Delta Q)_{v}=4 k c a l \)