AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
An iron ball at \( 40^{\circ} \mathrm{C} \) is dropped in a mug
containing water at \( 40^{\circ} \mathrm{C} \)
The heat will
A. flow from iron ball to water
B. not flow from iron ball to water or from water to iron ball
c. flow from water to iron ball.
D. increase the temperature of both
Subject: Physics
(a) Six lead-acid type of secondary cells
each of emf \( 2.0 \mathrm{V} \) and
internal resistance \( 0.015 \Omega \) are joined in series to provide a supply to a resistance of \( 8.5 \Omega . \) What are the
current drawn from the supply and its terminal voltage?
(b) A secondary cell after long use has an emf of \( 1.9 \mathrm{V} \) and a large internal resistance of \( 380 \Omega . \) What maximum
current can be drawn from the cell?
Could the cell drive the starting motor of a car?
Subject: Maths
\( \operatorname{Let} A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right], a, b, c, d \neq 0, \) then
\( \boldsymbol{B}=\boldsymbol{A} \boldsymbol{A}^{\prime}-\boldsymbol{A}^{\prime} \boldsymbol{A} \) equals
A. \( (a d-b c) I \)
в. \( (a c-b d) I \)
c.
D. none of these
Subject: Physics
Change in internal energy of the gas in the isobaric process is:
A \( .2 .5 \times 10^{4} J \)
В. \( 1.2 \times 10^{6} J \)
c. \( 3 \times 10^{5} J \)
D. \( 0.5 \times 10^{3} J \)
Subject: Physics
A bar magnet is placed with its North pole pointing North. Neutral point is at a distance 'd' from the center of magnet.
The net magnetic induction at the same
distance on the axial line of the magnet.
A \( \cdot 2 B_{H} \)
в. \( 3 B_{H} \)
\( c . B_{H} \)
D. \( 7 B \) н
Subject: Chemistry
The standard electrode potential \( \boldsymbol{E}_{l_{2} / r}^{o}, \quad \boldsymbol{E}_{B r^{-} / B r_{2}}^{0} \quad \) and \( \quad \boldsymbol{E}_{\boldsymbol{F} e / F e^{2+}}^{0} \) are
respectively \( +0.54 \mathrm{V},-1.09 \mathrm{V} \) and \( 0.44 \mathrm{V} . \) On
the basis of above data which of the
following process is non spontaneous?
\( \mathbf{A} \cdot B r_{2}+2 I^{1} \rightarrow 2 B r+I_{2} \)
B. \( F e+B r_{2} \longrightarrow F e^{2+}+2 B r \)
C. \( F e+I_{2} \longrightarrow F e^{2+}+2 I^{-} \)
D. \( I_{2}+B r \longrightarrow 2 I^{-}+B r_{2} \)
Subject: Physics
A very long, straight, then wires carries \( -3.60 n C m^{-1} \) of fixed negative charge. The wire is to be surrounded by a uniform cylinder of positive charge, radius \( 1.50 \mathrm{cm} \), coaxial with the wire.
The volume charge density \( \rho \) of the cylinder is to be selected so that the net electric field outside the cylinder is zero. Calculate the required positive charge density \( \rho\left(\operatorname{in} \mu C m^{-3}\right) \)
\( A \)
в. 7
\( c .5 \)
\( D \)
Subject: Physics
A car is to be hoisted by elevator to the fourth floor of a parking garage, which is 14 m above the ground. If the elevator
can have maximum acceleration of \( \mathbf{0 . 2} \)
\( m / s^{2} \) and maximum deceleration of 0.1 \( m / s^{2} \) and can reach a maximum speed of \( 2.5 m / s, \) the shortest time to make
the lift, starting form rest and ending at
rest is \( K \). The value of \( 2 K \) will be
Subject: Maths
Find all possible integers whose
geometric mean is 16
A \( .(1,256),(2,128),(4,64),(8,32),(16,16) \)
B . (1,256),(2,128),(4,64),(16,1),(1,16)
C \( .(1,256),(4,4),(4,64),(8,32),(16,16) \)
D. (1,256),(2,128),(1,4),(8,32),(16,16)
Subject: Chemistry
Assertion
Heat added to a system at lower temperature causes greater randomness than when the same
quantity of heat is added to it at higher
temperature
Reason
Entropy is a measure of the degree of randomness or disorder in the system.
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 \( f^{\prime \prime}(x)<0, \forall x \epsilon(a, b), \) and \( (c, f(c)) \) is
point of maxima, where \( c \epsilon(a, b), \) then
\( f^{\prime}(c) \) is
A \( \cdot \frac{f(b)-f(a)}{b-a} \)
в. \( \left[\frac{f(b)-f(a)}{b-a}\right] \)
c. \( 2\left[\frac{f(b)-f(a)}{b-a}\right] \)
D.
Subject: Physics
A satellite is launched into a circular
orbit of radius r around the earth. \( \mathbf{A} \)
second satellite is launched into an
orbit of radius \( 1.01 \mathrm{r} \). The period of the second satellite is larger than that of
first one by approximately.
\( A \cdot 0.5 \% \)
B . 1.0 \%
c. \( 1.5 \% \)
D. 3.0 \%
Subject: Chemistry
Formation of polyethylene from calcium carbide taken place as follows:
\( \boldsymbol{C a C}_{2}+\mathbf{2 H _ { 2 }} \boldsymbol{O} \rightarrow \boldsymbol{C a}(\boldsymbol{O H})_{2}+\boldsymbol{C}_{2} \boldsymbol{H}_{2} \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{2}+\boldsymbol{H}_{2} \rightarrow \boldsymbol{C}_{2} \boldsymbol{H}_{4} \)
\( \boldsymbol{n} \boldsymbol{C}_{2} \boldsymbol{H}_{4} \rightarrow\left(\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{C} \boldsymbol{H}_{2}\right) \boldsymbol{n} \)
The amount of polyethylene obtained from \( 64.0 \mathrm{kg} \) of \( \mathrm{CaC}_{2} \) is:
\( A \cdot 27 \mathrm{kg} \)
в. \( 24 \mathrm{kg} \)
c. \( 22 \mathrm{kg} \)
D. \( 28 \mathrm{kg} \)
Subject: Maths
Let \( \boldsymbol{f}:[\mathbf{1}, \infty] \rightarrow[\mathbf{2}, \infty] \) if \( \boldsymbol{f}(\mathbf{1})=\mathbf{2} . \) be
differentiable function such that
\( 6 \int_{1}^{x} f(t) d t=3 x f(x)-x^{3} \) then the
value of \( \boldsymbol{f}(\mathbf{2}) \) is....
Subject: Maths
\( \boldsymbol{S}_{\boldsymbol{n}}=\boldsymbol{2} \boldsymbol{n}^{2}+\boldsymbol{3} \boldsymbol{n} ; \) then \( \boldsymbol{d}=\ldots \)
A . 13
B. 4
\( c .9 \)
D. -2
Subject: Physics
An electron (mass \( \boldsymbol{m} \) ) with initial
velocity \( \vec{v}=v_{0} \hat{i}+v_{0} \hat{j} \) is an electric
field \( \vec{E}=-E_{0} \hat{k} . \) If \( \lambda_{0} \) is initial de-
Broglie wave length at time \( t \) is given by
\( A \)
\[
\frac{\lambda_{0}}{\sqrt{1+\frac{e^{2} E^{2} t^{2}}{2 m^{2} v_{0}^{2}}}}
\]
в.
\[
\frac{\lambda_{0} \sqrt{2}}{\sqrt{1+\frac{e^{2} E^{2} t^{2}}{m^{2} v_{0}^{2}}}}
\]
c.
\[
\frac{\lambda_{0}}{\sqrt{2+\frac{e^{2} E^{2} t^{2}}{m^{2} v_{0}^{2}}}}
\]
D.
\[
\frac{\lambda_{0}}{\sqrt{1+\frac{e^{2} E_{0}^{2} t^{2}}{m^{2} v_{0}^{2}}}}
\]
Subject: Chemistry
The specific rate constant of the
decomposition of \( N_{2} O_{5} \) is \( 0.008 m i n^{-1} \)
The volume of \( O_{2} \) collected after 20
minute is \( 16 \mathrm{mL} \). The volume in \( \mathrm{ml} \) that
would be collected at the end of
reaction. \( N O_{2} \) formed is dissolved in
\( \boldsymbol{C C l}_{4} \) is
Subject: Physics
The velocity of sound in a gas in which two waves of wavelengths \( 50 \mathrm{cm} \) and
\( 50.5 \mathrm{cm} \) produces 6 beats per second is?
A. \( 303 \mathrm{m} / \mathrm{s} \)
B. \( 332 \mathrm{m} / \mathrm{s} \)
c. \( 296 \mathrm{m} / \mathrm{s} \)
D. \( 228 \mathrm{m} / \mathrm{s} \)
Subject: Maths
If \( O A B C \) is a tetrahedron such that the
\( \boldsymbol{O} \boldsymbol{A}^{2}+\boldsymbol{B} \boldsymbol{C}^{2}=\boldsymbol{O} \boldsymbol{B}^{2}+\boldsymbol{C} \boldsymbol{A}^{2}=\boldsymbol{O} \boldsymbol{C}^{2}+ \)
\( A B^{2}, \) then which of the following is/are
correct
A. \( A B \perp O C \)
в. \( O B \neq C A \)
c. \( O C=A B \)
D. \( A B \perp B C \)
Subject: Chemistry
The solubility of \( C a F_{2}(K=3.4 \times \)
\( \mathbf{1 0}^{-11} \) ) in \( 0.1 M \) solution of \( N a F \) would
be:
A \( \cdot 3.4 \times 10^{-12} M \)
В. \( 3.4 \times 10^{-10} M \)
c. \( 3.4 \times 10^{-9} M \)
D. \( 3.4 \times 10^{-13} M \)
Subject: Physics
The temperature co-efficient of
resistance of a wire is \( 0.0012 /^{\circ} \mathrm{C} \). Its
resistance is \( 1 \Omega \) at \( 300 K . \) At what
temperature, its resistance will be \( 2 \Omega ? \)
A . \( 1133 K \)
B. \( 854 K \)
c. \( 1217 K \)
D. \( 1154 K \)
Subject: Physics
stands at the end of diving board, as
shown. The board is uniform, massive
and solid. There is no vibration or
motion of any kind. The board is firmly
attached to two supports at point \( \boldsymbol{P}_{1} \)
and \( P_{2} . \) The professor now begins to walk slowly in (right) from the end of
the board towards \( P_{1} . \) While he is
walking, how should you describe the force on the board by the support at
point \( P_{2} ? \) (i.e. Over at the far right hand
end)
A. upwards and increasing magnitude.
B. upwards and decreasing magnitude
c. downwards and increasing magnitude.
D. downwards and decreasing magnitude
Subject: Maths
The equation of the circle passing
through (3,6) and whose centre is (2,-1) is
A \( \cdot x^{2}+y^{2}-4 x+2 y=45 \)
B . \( x^{2}+y^{2}-2 y+45=0 \)
c. \( x^{2}+y^{2}+4 x-2 y=45 \)
D. \( x^{2}+y^{2}+2 y+45=0 \)
Subject: Physics
8
the magnetic field changes at the rate
of \( d B / d t . A B=B C . \) Calculate the
induced emf between the ends of length
\( A B, \) if \( A C \) and \( B C \) were removed from
the circuit.
\( ^{\mathbf{A}} \cdot R^{2}\left(\frac{d B}{d t}\right) \)
\( ^{\mathbf{B}} \cdot 4 R^{2}\left(\frac{d B}{d t}\right) \)
\( ^{\mathbf{C}} \cdot \frac{1}{2} R^{2}\left(\frac{d B}{d t}\right) \)
\( ^{\mathrm{D}} 2 R^{2}\left(\frac{d B}{d t}\right) \)
E. None of the above
Subject: Chemistry
Which of the following is true about a solution that has \( [\boldsymbol{O H}]=\mathbf{1 . 0} \times \mathbf{1 0}^{-\mathbf{8}} \)
M?
A. The pHis 8 and the solution is acidic
B. The \( \left[H^{+}\right]=1.0 \times 10^{-8} \mathrm{M} \) and the solution is basic
c. The pHis 6 and the solution is acidic
D. The \( \left[H^{+}\right]=1.0 \times 10^{-6} \mathrm{M} \) and the solution is basic
E . The \( \left[H^{+}\right]=1.0 \times 10^{-14} \mathrm{M} \) and the solution is neutral
Subject: Physics
Which of the following options, which describe the dependence of drift
velocity \( v_{d} \) on electric field \( E, \) obeys
Ohm's law?
A \( \cdot v_{d} \propto E \)
В \( \cdot v_{d} \propto E^{2} \)
\( \mathbf{c} \cdot v_{d} \propto \sqrt{E} \)
D. \( v_{d}= \) constant
Subject: Chemistry
A sample of H-atoms containing all the
atoms in some excited state is
irradiated with light of wavelength \( \lambda \) and the atoms get re-excited to further
higher orbit. On removing the light source, atoms de-excite to ground state
with emission of radiations. The
emission spectrum thus obtained
consists of ten spectral lines corresponding to ten different wavelengths. Out of the ten spectral lines, seven lines have the wavelength
smaller than the incident llambda,
while only two of them have
wavelengths longer than the incident wavelength. The orbit number in which electrons were present initially is:
A. 3
B. 4
\( c \cdot 5 \)
\( D .6 \)
Subject: Physics
Which of the following nuclear reactions
is not possible?
A \( \cdot \frac{12}{6} C+_{6}^{12} C \longrightarrow_{10}^{20} N e+_{2}^{4} H e \)
B . \( _{4}^{9} B e+_{1}^{1} H \rightarrow_{3}^{6} L i+_{2}^{4} H e \)
C \( \cdot \frac{11}{5} B e+_{1}^{1} H \rightarrow_{4}^{9} B e+_{2}^{4} H e \)
D. \( _{3}^{7} L i+_{2}^{4} H e \longrightarrow_{1}^{1} H+_{4}^{10} B \)
Subject: Physics
\( \ln \operatorname{an} \alpha \) -decay the kinetic energy of \( \alpha \) particle is \( 48 \mathrm{MeV} \) and \( Q \) -value of the
reaction is \( 50 ~ M e V \). The mass number
of the molecular nucleus is \( X \). Find
value of \( \boldsymbol{X} / \mathbf{2 5} \)
(Assume that daughter nucleus is in ground state.)
A .2
B. 4
\( c \cdot 6 \)
D. 8
Subject: Maths
Calculate the scalar product of the following vectors. Two points \( A \) and \( B \) are given in the rectangular Cartesian system of coordinates Oxy on the curve \( \boldsymbol{y}=\mathbf{2}^{\boldsymbol{x}+\mathbf{2}} \)
the points being such that \( \overrightarrow{\boldsymbol{O A}} \cdot \boldsymbol{i}= \)
-1 and \( \overrightarrow{O B} \cdot i=2, \) where 1 is a unit
vector of the \( 0 x \) axis. Find the length of the vector \( \overline{-4 O A}+\overrightarrow{O B} \)
Subject: Physics
A person climbs up a stalled escalator in \( 60 s . \) If standing on the same but escalator running with constant velocity he takes 40 s. How much time
is takne by the person to walk up the
moving escalator?
\( \mathbf{A} \cdot 37 s \)
в. \( 27 s \)
c. \( 24 s \)
D. \( 45 s \)
Subject: Chemistry
In the extraction of copper from its sulphide ore, the metal is finally
obtained by the reduction of cuprous oxide with:
A. Copper (I) sulphide \( \left(C u_{2} S\right) \)
B. Sulphur dioxide \( \left(S O_{2}\right) \)
c. Iron sulphide (Fes)
D. Carbon monoxide (CO)
Subject: Chemistry
Which of the following bond is nonpolar
covalent?
A. \( S i \) Si bond in \( C l_{3} \) sisicla
B. \( S i C l \) bond in \( C l_{3} \) sisiCla
c. \( C a F \) bond in \( C a F_{3} \)
D. \( N H \) bond in \( N H_{3} \)
Subject: Chemistry
A : tetracyanomrthane
B : carbon
dioxide
C: benzene \( \quad \) D : 1, 3-bute-di-
ene
Ratio of \( \sigma \) and \( \pi \) bonds is in order:
A. \( A=B<C<D \)
в. \( A=B<D<C \)
c. \( A=B=C=D \)
Subject: Physics
What length of German silver wire, diameter \( 0.050 \mathrm{cm}, \) is needed to make a
28 resistor, if the resistivity of German silver is \( 2.2 \times 10^{-7} m ? \)
A . \( 20 m \)
B. \( 25 m \)
\( c .30 m \)
D. 35 m
Subject: Biology
Following are the misconceptions about
root hydrotropism. State whether they
are correct or not.
i. The greater growth of roots in moist
soil zones than in dry soil zones is not
usually a result of hydrotropism. Hydrotropism requires a root to bend
from a drier to a wetter soil zone. Roots
require water to grow so roots that happen to be in moist soil will grow and branch much more than those in dry
soil.
ii. Roots cannot sense water inside
intact pipes via hydrotropism and break the pipes to obtain the water.
iii. Roots cannot sense water several
feet away via hydrotropism and grow toward it. At best hydrotropism probably
operates over distances of a couple millimeters.
A. (i) and (iii) are correct.
B. (i) and
(ii) are correct
C. All are correct.
D. None of the above are correct.
Subject: Maths
The value of \( \lim _{\boldsymbol{x} \rightarrow \boldsymbol{\pi} / 2} \frac{\sin (\boldsymbol{x} \cos \boldsymbol{x})}{\cos (\boldsymbol{x} \sin \boldsymbol{x})} \) is
equal to
A . 0
в. \( \frac{\pi}{2} \)
\( c . \pi \)
D . 2 \( \pi \)
Subject: Chemistry
Number of faradays required to convert 1 mole of \( \boldsymbol{C r}_{2} \boldsymbol{O}_{\mathbf{7}}^{2-} \) into \( \boldsymbol{C r}^{\mathbf{3}+} \) ions is
\( A \cdot 6 \)
B. 4
\( c \cdot 3 \)
D. none of these
Subject: Maths
To eliminate \( x \) from equations \( x+y+ \)
\( 3 x=12 \rightarrow \ldots . . \) (1) \( \& 8 x+3 y=17 \rightarrow \ldots \)
(2), equation (2) is to be multiplied by
\( A \cdot 8 \)
в. \( -\frac{1}{2} \)
\( c \cdot \frac{1}{2} \)
D. 3
Subject: Maths
The integral \( \int_{0}^{\pi} x f(\sin x) d x \) is equal to
This question has multiple correct options
\( \mathbf{A} \cdot \frac{\pi}{2} \int_{0}^{\pi} f(\sin x) d x \)
B \( \cdot \frac{\pi}{4} \int_{0}^{\pi} f(\sin x) d x \)
\( ^{\mathbf{C}} \pi \int_{0}^{\pi / 2} f(\sin x) d x \)
\( ^{\mathrm{D}} \pi \int_{0}^{\pi / 2} f(\cos x) d x \)
Subject: Physics
For the given experimental setup, the oscillation frequency of the mass is
\( \boldsymbol{f} \cdot \boldsymbol{S}_{1} \) and \( \boldsymbol{S}_{2} \) are identical springs. One
spring is now removed, then frequency
will become.
A . \( 2 f \)
B. \( \frac{f}{\sqrt{2}} \)
c. \( \frac{f}{\sqrt{3}} \)
D. \( \sqrt{2} f \)
Subject: Physics
Five resistance are connected as shown
in figure. If total current flowing is \( 0.5 A \)
then the potential difference \( \boldsymbol{V}_{\boldsymbol{A}}-\boldsymbol{A}_{\boldsymbol{B}} \)
is:
\( A \cdot 8 V \)
в. \( 6 V \)
\( c \cdot 2 V \)
D. \( 4 V \)
Subject: Physics
\( \mathbf{A} \)
girl throws a ball with velocity at an
inclination of \( 45^{\circ} \). The ball strikes the
smooth vertical wall at a horizontal
distance d from the girl and after reboundig returns to her hand. What is the coefficient o restitution between
wall fand the ball.
A \( \cdot v^{2}-g d \)
в. \( \frac{g d}{v^{2}-g d} \)
c. \( \frac{g d}{v^{2}} \)
D. \( \frac{v^{2}}{g d} \)
Subject: Maths
If \( A \) and \( B \) are two events in a sample
space \( S \) such that \( P(A) \neq 0, \) then
\( P\left(\frac{B}{A}\right)= \)
A \( \cdot P(A) \cdot P(B) \)
в. \( \frac{P(A \cap B)}{P(B)} \)
c. \( \frac{P(A \cap B)}{P(A)} \)
D \( \cdot P(B) \)
Subject: Physics
A golfer swings a golf club so that the end of the club is moving \( 30 \mathrm{m} / \mathrm{s} \) when it strikes the ball. The radius of the
circular path for the end of the club (which includes the club and the
golfer's arms ) is \( 1.8 \mathrm{m} \)
What is the centripetal acceleration of
the end of the club as it strikes the
ball?
\( \mathbf{A} \cdot 500 m / s^{2} \)
B. \( 1.7 \mathrm{m} / \mathrm{s}^{2} \)
\( \mathbf{c} \cdot 0.06 m / s^{2} \)
D. \( 54 \mathrm{m} / \mathrm{s}^{2} \)
E . \( 0 \mathrm{m} / \mathrm{s}^{2} \)
Subject: Physics
An ammeter has a resistance of \( G \)
ohms and range of \( I \) amperes. The value of resistance required in parallel to
convert it into an ammeter of range \( \boldsymbol{n} \boldsymbol{I} \)
is
A \( . n G \)
в. \( (n-1) G \)
c. \( G /(n-1) \)
D. \( G / n \)
Subject: Physics
A force \( F=-6 x^{3} \) is acting on a block
moving along x-axis. Work done by this
force is:
This question has multiple correct options
A. Positive in displacing the block from \( x=3 \) to \( x=1 \)
B. Positive in displacing the block from \( x=-3 \) to \( x=-1 \)
c. Negative in displacing the block from \( x=0 \) to \( x=4 \)
D. zero in displacing the block from \( x=-2 \) to \( x=+2 \)
Subject: Maths
The positive value of \( k \) for which \( \mathbf{k e}^{\mathbf{x}}- \)
\( \mathbf{x}=\mathbf{0} \) has only one root is
A . \( 1 / e \)
B. 1
\( c \)
D. \( \log _{\mathrm{e}} 2 \)
Subject: Chemistry
In the following reaction \( X \) and \( Y \) are respectively, \( C_{2} H_{2} \stackrel{X}{\rightarrow} C_{6} H_{6} \stackrel{Y}{\longrightarrow} \)
\( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{S} \boldsymbol{O}_{\boldsymbol{3}} \boldsymbol{H} \)
A. iron tube, heating \( N a_{2} S O_{4} \)
B. zn, conc. \( H_{2} S O_{4} \)
c. red hot iron tube, fusing \( H_{2} S O_{4} \)
D. \( H_{2} / P d, B a S O_{4} d i l . H_{2} S O_{4} \)
Subject: Chemistry
About alkali metal - liquid \( \boldsymbol{N} \boldsymbol{H}_{3} \)
solution which of the following statement is not true?
A. Blue colour due to ammoniated electrons
B. Blue colour changes to bronze on dilution due to formation of metal clusters
c. with increse in concentration of alkali metals paramagnetic nature decreases due to electron electron combination
D. on heating blue colour becomes colourless due to formation of metal amide and \( H_{2} \) gas
Subject: Physics
If a disc slides from top to bottom of an
inclined plane, it takes time \( t_{1} . \) If it rolls, it takes time \( t_{2} . \) Now \( \frac{t_{2}^{2}}{t_{1}^{2}} \) is
A \( \cdot \frac{1}{2} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{3}{2} \)
D. \( \frac{2}{5} \)
Subject: Maths
If two cubes each of side \( 12 \mathrm{cm} \) are
joined end to end then the surface area of the resulting cuboid is
A \( \cdot 1728 \mathrm{cm}^{2} \)
B . \( 1440 \mathrm{cm}^{2} \)
c. \( 1445 \mathrm{cm}^{2} \)
D. \( 1450 \mathrm{cm}^{2} \)
Subject: Maths
\( \mathbf{f}\left|\begin{array}{ccc}\boldsymbol{a}+\boldsymbol{b} & \boldsymbol{b}+\boldsymbol{c} & \boldsymbol{c}+\boldsymbol{a} \\ \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{b}+\boldsymbol{c} \\ \boldsymbol{b}+\boldsymbol{c} & \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b}\end{array}\right|=\boldsymbol{t} \times \operatorname{det} \) of
circulant matrix whose elements of first
column are \( a, b, c \)
then 't' equals
A . 5
B. 6
\( c \cdot-2 \)
\( D \)
Subject: Chemistry
The cell in which the following reaction
occurs:
\( 2 F e^{3+}(a q)+2 I^{-}(a q) \rightarrow 2 F e^{2+}(a q)+ \)
\( \boldsymbol{I}_{2}(\boldsymbol{s}) \)
has \( E_{c e l l}^{\circ}=0.236 V \) at \( 298 K . \) Calculate
the standard Gibbs energy of the cell
reaction. (Given : \( 1 \boldsymbol{F}= \)
\( \left.\mathbf{9 6}, \mathbf{5 0 0} \boldsymbol{C} \boldsymbol{m o l}^{-\mathbf{1}}\right) \)
Subject: Maths
Find the arithmetic mean of the series:
\( \mathbf{1}, \mathbf{3}, \mathbf{5} \dots \dots \dots \dots(\mathbf{2 n}-\mathbf{1}) \)
\( A \cdot n \)
B. \( 2 n \)
\( c \cdot \frac{n}{2} \)
D. \( n-1 \)
Subject: Physics
A circular disc is rotating about its own
axis at constant angular acceleration. If its angular velocity increases from
210 rpm to 420 rpm during 21 rotations then the angular acceleration of disc is :
A. \( 5.5 \mathrm{rad} / \mathrm{s}^{2} \)
B. 11 rad / \( s^{2} \)
c. \( 16.5 \mathrm{rad} / \mathrm{s}^{2} \)
D. 22 rad / \( s^{2} \)
Subject: Chemistry
A nucleus, kept at rest in free space, break up into two smaller nuclei of
masses \( m \) and \( 2 m . \) Total energy
generated in this fission is E. The bigger part is radioactive, emits five gamma ray photons in the direction opposite to its velocity, and finally comes to rest. Now, answer the following questions:
\( \left(\operatorname{given} ; h=6.6 \times 10^{-34} ; m=1.00 \times\right. \)
\( \mathbf{1 0}^{-\mathbf{2 6}} \mathbf{k g}, \boldsymbol{E}=\mathbf{3 . 6 3} \times \mathbf{1 0}^{-\mathbf{8}} \mathbf{m s}^{-\mathbf{1}} \)
The wavelength of the gamma ray is?
\( \begin{array}{l}\text { A } \cdot 0.02 A^{0} \\ ^{0}\end{array}^{0} \cdot 0.0 A A^{0} \)
B. \( 0.03 A^{\circ} \)
c. \( 0.04 A^{\circ} \)
D. \( 0.05 A^{\circ} \)
Subject: Physics
In an experiment to determine the focal length \( (f) \) of a concave mirror by the
\( u-v \) method, a student places the
object pin \( A \) on the principal axis at a distance \( x \) from the pole \( P . \) The student
looks at the pin and its inverted image from a distance keeping the eye in line with \( P A . \) When the student shifts the
eye towards left, the image appears to
the right of the object pin. Then:
A. \( x<f \)
B. \( f<x<2 f \)
c. \( x=2 f \)
D. \( x>2 f \)
Subject: Physics
Figure shows a fixed square frame of
wire having a total resistance r placed
coplartarly with a long, straight wire
The wire carries a current i given by \( i= \)
\( i_{2} \cos (2 \pi t / T), \) Find \( (a) \) the flux of the
magnetic field through the square frame
(b) the emf induced in
the frame and
(c) the heat developed in the frame in the time interval 0 to 10 T.
Subject: Maths
Find the value of the following determinant:
\( \left|\begin{array}{cc}-4 & \frac{-6}{35} \\ 7 & \frac{35}{5} \\ 5 & 5\end{array}\right| \)
A \( \cdot \frac{15}{34} \)
в. \( \frac{32}{45} \)
c. \( \frac{25}{33} \)
D. \( \frac{38}{35} \)
Subject: Chemistry
Rate of formation of \( \boldsymbol{S} \boldsymbol{O}_{3} \) according to
the reaction \( 2 S O_{2}+O_{2} \rightarrow \)
\( \mathbf{2 S O}_{3} \quad \) is \( \quad \mathbf{1 . 6} \times \mathbf{1 0}^{-\mathbf{3}} \mathbf{k g} \quad \mathbf{m i n}^{-\mathbf{1}} \)
Hence rate at which \( S O_{2} \) reacts is:
A . \( 1.6 \times 10^{-3} \mathrm{kg} \) min \( ^{-1} \)
В. \( 8.0 \times 10^{-4} k g \) min\( ^{-1} \)
c. \( 3.2 \times 10^{-3} k g \) min\( ^{-1} \)
D. \( 1.28 \times 10^{-3} \mathrm{kg} \) min\( ^{-1} \)
Subject: Maths
Prove the following by using the principle of mathematical induction for
all \( \boldsymbol{n} \in \boldsymbol{N} \)
\( \left(1+\frac{3}{1}\right)\left(1+\frac{5}{4}\right)\left(1+\frac{7}{9}\right) \dots \dots(1+ \)
\( (n+1)^{2} \)
Subject: Physics
A thin tube of uniform cross-section is
sealed at both ends. It lies horizontally,
the middle \( 5 \mathrm{cm} \) containing mercury and
the two equal ends containing air at the
same pressure \( P_{o} . \) When the tube is held
at an angle \( 60^{\circ} \) with the vertical, the
lengths of the air column above and
below the mercury are 46 and \( 44.5 \mathrm{cm} \)
respectively. The pressure \( P_{o} \) in \( \mathrm{cm} \) of \( \mathrm{Hg} \)
is: (The temperature of the system is left at \( 30 \mathrm{K} \)
A. 80 cm of \( H g \)
B. \( 75.4 \mathrm{cm} \) of \( \mathrm{Hg} \)
c. 70 cm of \( H g \)
D. 90 cm of \( H g \)
Subject: Chemistry
For the reaction
\[
\boldsymbol{P C l}_{3(g)}+\boldsymbol{C l}_{2(g)} \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{5(g)}
\]
the value of \( \boldsymbol{K}_{c} \) at \( 250^{\circ} \mathrm{C} \) is \( 26 . \) The
value of \( K_{p} \) a this temperature will be
A . 0.61
B. 0.57
c. 0.83
D. 0.46