AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Assertion
If in a \( \triangle A B C, \) a line \( D E \| B C \)
intersects \( A B \) in \( D \) and \( A C \) in \( E, \) then \( \frac{A B}{A D}=\frac{A C}{A E} \)
Reason
If a line is drawn parallel to one side of a triangle intersecting the other two sides, then the other two sides are
divided in the same ratio.
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
For a particular reversible reaction at
temperature \( T, \Delta H \) and \( \Delta S \) were found
to be both +ve. If \( T_{e} \) is the temperature at equilibrium, the reaction would be
spontaneous when:
A \( \cdot T_{e}>T \)
в. \( T>T_{e} \)
\( \mathbf{c} \cdot T_{e} \) is 5 times \( T \)
D. \( T=T_{e} \)
Subject: Physics
The work done in blowing a soap bubble slowly from a radius of \( 5 \mathrm{cm} \) to a radius of \( 10 \mathrm{cm} \) is...................... Joule (given the
surface tension of water is \( 3.5 \times 10^{-2} \mathrm{N} \)
\( \left.m^{-1}\right) \)
\( A \cdot 6.6 \times 10^{-3} \)
B. 2.2 \( \times 10^{-3} \)
c. \( 4.4 \times 10^{-3} \)
D. 8.8 \( \times 10^{-3} \)
Subject: Physics
Assertion
A body having the uniform density has
same point, as centre of gravity and
centre of buoyancy
Reason
While formulating the equation for positioning centre of mass and centre of buoyancy,has difference of the term
of uniform density only.
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: Physics
The addition of two numbers \( 6.75 \times 10^{3} \)
\( \mathrm{cm} \) and \( 4.52 \times 10^{2} \mathrm{cm} \) with regard to
significant figures is:
A \( \cdot 7.20 \times 10^{3} \mathrm{cm} \)
В. \( 7.20 \times 10^{3} \mathrm{mm} \)
c. \( 7.20 \times 10^{4} \mathrm{cm} \)
D. None of these
Subject: Chemistry
toppr
Q Type your question
\( \operatorname{than} \boldsymbol{X} \boldsymbol{e} \boldsymbol{C l}_{2} \)
Reason
\( \boldsymbol{\Delta} \boldsymbol{H} \)
\( \boldsymbol{X} \boldsymbol{e}(\boldsymbol{g}) \longrightarrow \boldsymbol{X} \boldsymbol{e}^{+}(\boldsymbol{g})+\boldsymbol{e}^{-} ; \boldsymbol{I} \) (ionisation
energy
\( \boldsymbol{X}_{2}(\boldsymbol{g}) \longrightarrow 2 \boldsymbol{X}(\boldsymbol{g}) ; \boldsymbol{D}(\text { Bond energy }) \)
\( \mathbf{2} \boldsymbol{X}(\boldsymbol{g})+\boldsymbol{2} \boldsymbol{e}^{-} \longrightarrow \mathbf{2} \boldsymbol{X}^{-}(\boldsymbol{g}) ; \mathbf{2} \boldsymbol{E} \)
(electron affinity)
\( \boldsymbol{X} \boldsymbol{e}^{+}(\boldsymbol{g})+\boldsymbol{2} \boldsymbol{X}^{-}(\boldsymbol{g}) \longrightarrow \boldsymbol{X} \boldsymbol{e} \boldsymbol{X}_{2}(\boldsymbol{g}) ;-\boldsymbol{U} \)
(lattice energy)
\( \boldsymbol{X} \boldsymbol{e}(\boldsymbol{g})+\boldsymbol{X}_{2}(\boldsymbol{g})+\boldsymbol{X} \boldsymbol{e} \boldsymbol{X}_{2}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}_{f}= \)
\( \boldsymbol{I}+\boldsymbol{D}+\boldsymbol{2} \boldsymbol{F}-\boldsymbol{U} \)
By taking values of \( I, D, E \) and \( U, \) we
find that \( \Delta H_{f}^{\circ}\left(X e F_{2}\right) \) is more negative than that of \( X e C l_{2} . \) Thus \( X e F_{2} \) is much
more stable.
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: Physics
A ray of light undergoes deviation of \( 30^{\circ} \) when incident on an equilateral prism of refractive index \( \sqrt{2} \). The angle made
by the ray inside the prism with the base of the prism is then
A \( \cdot 30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. zero
Subject: Biology
Q Type your question
nú, kangaroo rat, showing the relative size
of cortex and medulla. Coypu is found in
freshwater and is never of short of water
to drink. Brown rats are able to go some
days without drinking. Kangaroo rats are able to live in deserts without
drinking at all. Which kidney belongs to
which animal?
A. Brown rat
coypu Kangaroo rat
B. Brown rat Kangaroo rat coypu
c. Kangaroo rat Brown rat coypu
D. Kangaroo rat coypu Brown
Subject: Physics
An aluminium container of mass 100
\( \mathrm{gm} \) contains \( 200 \mathrm{gm} \) of ice at \( -20^{0} \mathrm{C} \) Heat is added to the systeam at the rate of 100 cal/s. Find the temperature of the system after 4 minutes (specific heat of ice \( =0.5 \) and \( L=80 \) cal/gm, specific heat of \( \left.A l=0.2 c a l / g m^{0} C\right) \)
Subject: Chemistry
Ethylamine \( \left(C_{2} H_{5} N H_{2}\right) \) can be obtained from N-ethylphthalimide on treatment with:
A . \( N a B H_{4} \)
в. \( C a H_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. \( N H_{2} N H_{2} \)
Subject: Maths
If \( \boldsymbol{A}=\{1,2,3\}, B=\{1,4,6,9\} \) and \( R \)
is a relation from \( A \) to \( B \) defined by \( x \) is
greater than \( y \). The range of \( R \) is
\( \mathbf{A} \cdot\{1,4,6,9\} \)
в. \{4,6,9\}
\( c \cdot\{1\} \)
D. none of these
Subject: Maths
If the ratio of sum of \( n \) terms in two A.P's
is \( 2 n: n+1, \) then the ratio of \( 8^{t h} \) terms
is
\( \mathbf{A} \cdot 15: 8 \)
B. 8: 133
\( \mathbf{c} .5: 17 \)
D. none
Subject: Maths
The value of \( \lim _{n \rightarrow \infty} \frac{1}{n} \Sigma_{r=0}^{n-1} 4 \cdot \frac{r}{n}=? \)
\( ^{\mathrm{A}} \cdot \int_{1}^{5} 4 d x \)
в. \( \int_{0}^{4} 5 d x \)
\( ^{\mathrm{c}} \int_{0}^{1} 4 x d x \)
D. \( \int_{0}^{1} 4 d x \)
Subject: Physics
Assertion
Power of the lens is larger if its focal length is smaller.
Reason
Power of the lens measures the ability to converge or diverge the refracted
rays.
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: Physics
A resistance of \( \boldsymbol{R} \) draws the current
form of the potentiometer. The
potentiometer wire, \( A B, \) has a total
resistance of \( \boldsymbol{R}_{0} . \) A voltage \( \boldsymbol{V} \) is
supplied to the perpendicular. Derive an
expression for the voltage across \( \boldsymbol{R} \)
when the sliding contact is in the middle of potentiometer wire.
Subject: Physics
Two radioactive materials \( A \) and \( B \) have
decay constants 5 \lambda and \( \lambda \) respectively. Initially both \( A \) and \( B \) have the same number of nuclei. The ratio of the
number of nuclei of \( A \) to that of \( B \) will be
\( \frac{1}{e} \) after a time
A \( \cdot \frac{1}{5 \lambda} \)
в. \( \frac{1}{4 \lambda} \)
\( c \cdot \frac{5}{4 \lambda} \)
D. \( \frac{4}{5 \lambda} \)
Subject: Maths
The probability that \( A \) can solve a problem is \( \frac{2}{3} \) and that \( B \) can solve is \( \frac{3}{4} \) If both of them attempt the problem. What is probability that the problem act solved?
A \( \cdot \frac{11}{12} \)
в. \( \frac{7}{12} \)
c. \( \frac{5}{12} \)
D. \( \frac{9}{12} \)
Subject: Chemistry
Bone ash mainly contains:
A. \( \mathrm{CaO} \)
в. \( \mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2} \)
\( \mathrm{c} \cdot \mathrm{CaCl}_{2} \)
D. \( \mathrm{NH}_{2} \mathrm{NH}_{2} \)
Subject: Chemistry
Which of the following compounds would have significant intermolecular hydrogen bonding?
\( \boldsymbol{H} \boldsymbol{F}, \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{O} \boldsymbol{H}, \boldsymbol{N}_{2} \boldsymbol{H}_{4}, \boldsymbol{C} \boldsymbol{H}_{4} \)
This question has multiple correct options
A. \( H F, N_{2} H_{4} \)
в. \( H F, C H_{4}, C H_{3} O H \)
\( \mathbf{c} \cdot H F, C H_{3} O H \)
D. \( C H_{3} O H, C H_{4} \)
Subject: Chemistry
Give the formula of each of the following
coordination entities:
(i) \( C o^{3+} \) ion is bound to one \( C l^{-} \), one
\( N H_{3} \) molecule and two bidentate
ethylene diamine (en) molecule.
(ii) \( N i^{2+} \) ion is bound to two water
molecules and two oxalate ions.
Write the name and magnetic behavior of each of the above coordination entities. (At. no.: \( \mathrm{Co}=27, \mathrm{Ni}=28 \) )
Subject: Physics
Let \( E_{1}(r), E_{2}(r) \) and \( E_{3}(r) \) be the
respective electric fields at a distance from a point charge \( Q, \) an infinitely long wire with constant linear charge density \( \lambda, \) and an infinite plane with uniform
surface charge density \( \sigma . \) If \( \mathrm{E}_{1}\left(r_{0}\right)= \)
\( E_{2}\left(r_{0}\right)=E_{3}\left(r_{0}\right) \) at a given distance \( r_{0} \)
then :
A \( \cdot Q=4 \sigma \pi r_{0}^{2} \)
B . \( r_{0}=\frac{\lambda}{2 \pi \sigma} \)
c. \( E_{1}\left(r_{0} / 2\right)=2 E_{2}\left(r_{0} / 2\right) \)
D. \( E_{2}\left(r_{0} / 2\right)=4 E_{3}\left(r_{0} / 2\right) \)
Subject: Physics
The resistance of a galvanometer is \( 50 \Omega \) and the current required to give full-scale deflection is \( 100 \mu A \). In order
to convert it into an ammeter, reading upto \( 10 A, \) it is necessary to put
resistance of:
\( \mathbf{A} \cdot 5 \times 10^{-3} \Omega \) in parallel
B. \( 5 \times 10^{-4} \Omega \) in parallel
\( \mathrm{c} \cdot 10^{5} \Omega \) in series
D. \( 99950 \Omega \) in series
Subject: Maths
If \( \alpha, \beta \) be straight lines in a plane, then
check \( R_{1} \) and \( R_{2} \) for being reflexive,
symmetric and transitive \( \boldsymbol{\alpha} \boldsymbol{R}_{1} \boldsymbol{\beta} \boldsymbol{i} \boldsymbol{f} \boldsymbol{\alpha} \perp \)
\( \boldsymbol{\beta} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{\alpha} \boldsymbol{R}_{2} \boldsymbol{\beta} \boldsymbol{i} \boldsymbol{f} \boldsymbol{\alpha} \)
Subject: Maths
\( \frac{x^{2}+x+1}{(x-1)(x-2)(x-3)}=\frac{A}{x-1}+ \)
\( \frac{B}{x-2}+\frac{C}{x-3} \)
\( \Rightarrow \boldsymbol{A}+\boldsymbol{C}= \)
\( A \cdot 4 \)
B. 5
\( c \cdot 6 \)
D.
Subject: Physics
The expansion of an ideal gas of mass \( \mathrm{m} \) at a constant pressure \( \mathrm{P} \) is given by
the straight line B. Then, the expanasion of the same ideal gas of mass \( 2 \mathrm{m} \) at a
pressure \( 2 P \) is given by the straight line
A.
B. A
\( c \cdot B \)
D. data insufficient
Subject: Physics
A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant 'b', the correct equivalence would be :
A. \( L \leftrightarrow m, C \leftrightarrow k, R \leftrightarrow b \)
в. \( L \leftrightarrow \frac{1}{b}, C \leftrightarrow \frac{1}{m}, R \leftrightarrow \frac{1}{k} \)
c. \( L \leftrightarrow k, C \leftrightarrow b, R \leftrightarrow m \)
D \( \cdot L \leftrightarrow m, C \leftrightarrow \frac{1}{k}, R \leftrightarrow b \)
Subject: Maths
If the radius of a sphere is measured as
\( 9 \mathrm{cm} \) with an error of \( 0.03 \mathrm{cm} \) then, find
the approximate error in calculating its volume
A. \( 9.72 \pi \mathrm{cm}^{3} \)
B . \( 7.92 \pi \mathrm{cm}^{3} \)
c. \( 8.72 \pi \mathrm{cm}^{3} \)
D. None of these
Subject: Physics
A linear charge having linear charge
density \( \lambda \), penetrates a cube diagonally
and then it penetrate a sphere diametrically as shown. What will be the ration of flux coming out of cube and
sphere.
\( ^{A} \cdot \frac{1}{2} \)
в. \( \frac{2}{\sqrt{3}} \)
c. \( \frac{\sqrt{3}}{2} \)
\( D \)
Subject: Maths
\( \boldsymbol{f}: \boldsymbol{R} \longrightarrow \boldsymbol{R} \operatorname{are} \boldsymbol{g}: \boldsymbol{R} \longrightarrow \boldsymbol{R} \) are defined
by \( f(x)=2 x+3 \) and \( g(x)=x^{2}+7 \)
then the values of \( x \) for which \( f[g(x)]= \)
25 are
\( A \cdot \pm 1 \)
в. ±2
\( c .\pm 3 \)
\( \mathrm{D} \cdot \pm 4 \)
Subject: Physics
The potential energy of a certain spring
when stretched through a distance \( ^{\prime} S^{\prime} \)
is 10 joule. The amount of work (joule) that must be done on this spring to stretch it through an additional
distance \( ^{\prime} \boldsymbol{S}^{\prime} \) will be
A . 30
B. 40
c. 10
D. 20
Subject: Physics
Calculate the force required to lift a load of \( 60 N, \) placed at a distance of
\( 3 m, \) from the fulcrum if the effort force
is applied at a distance of \( 6 \mathrm{cm} \) from
the fulcrum.
\( A .300 N \)
в. \( 3000 N \)
c. \( 1500 N \)
D. 30 \( N \)
Subject: Chemistry
Two vessels each of volume \( V \) have air at
pressure \( \boldsymbol{P}_{1} \) and temperature \( \boldsymbol{T}_{1} \). They are connected through a narrow tube and in one of the vessel the temperature
changes from \( T_{1} \) to \( T_{2} \) keeping the
other at \( T_{1} \). Find the pressure of the gas.Assume the volume of gas is negligible.
A \( \cdot \frac{2 P_{1} T_{1}}{T_{1}+T_{2}} \)
в. \( \frac{2 P_{1}}{T_{1}+T_{2}} \)
c. \( \frac{2 P_{1} T_{2}}{T_{1}+T_{2}} \)
D. None of these
Subject: Physics
A catapult with a basket of mass \( 50 \mathrm{kg} \) launches a \( 200 \mathrm{kg} \) rock by swinging around from a horizontal to a
vertical position with an angular velocity of 2.0 rad/s. Assuming the rest of the catapult is massless and the catapult arm is \( 10 \mathrm{m} \) long, what is the velocity of the rock as it leaves the catapult?
\( A \cdot 10 \mathrm{m} / \mathrm{s} \)
B. 20 \( \mathrm{m} / \mathrm{s} \)
\( c \cdot 25 m / s \)
D. \( 50 \mathrm{m} / \mathrm{s} \)
E. \( 100 \mathrm{m} / \mathrm{s} \)
Subject: Maths
The harmonic conjugate of (2,3,4) with respect to the points (3,-2,2) and (6,-17,-4) is
\( ^{\mathbf{A}} \cdot\left(\frac{18}{5},-5, \frac{4}{5}\right) \)
в. (11,-16,2)
c. \( \left(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}\right) \)
D. (0,0,0)
Subject: Chemistry
What is the minimum mass of
\( C a C O_{3}(s), \) below which it decomposes completely, required to established equilibrium in a 6.50 litre container for
the reaction:
\( \boldsymbol{C a C O}_{3}(s) \rightleftharpoons \boldsymbol{C a O}(\boldsymbol{s})+ \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g}) ; \boldsymbol{K}_{c}=\mathbf{0 . 0 0 5} \) mole / litre
A. \( 3.25 g \)
в. \( 24.6 g \)
c. \( 40.9 g \)
D. \( 8.0 g \)
Subject: Maths
The minimum value of \( f(x)=x^{2}+ \)
\( \mathbf{2} \boldsymbol{x}+\mathbf{3}, \boldsymbol{x} \in \boldsymbol{R} \) is equal to
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
\( D \)
Subject: Chemistry
\( 20 \mathrm{ml} \) of \( 1 \mathrm{M} \mathrm{BaCl}_{2} \) solution and \( 25 \mathrm{m} \)
of \( 0.1 \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4} \) are mixed to form
\( B a S O_{4} . \) The amount of \( B a S O_{4} \)
precipitated are:
A . 2.5 g
B. 2.5 moles
c. 2.5 millimoles
D. 0.05 millimoles
Subject: Physics
A conducting rod of length \( \boldsymbol{L}=\mathbf{0 . 1 m} \) is
moving with a uniform speed \( \boldsymbol{v}= \)
\( 0.2 m / s \) on conducting rails in a
magnetic field \( B=0.5 T \) as shown. On
one side, the end of the rails is
connected to a capacitor of capacitance \( C=20 \mu F . \) Then the charges on the
capacitor plates are :
A \( \cdot q_{A}=0=q_{B} \)
B \( \cdot q_{A}=+20 \mu C \) and \( q_{B}=-20 \mu C \)
\( \mathbf{c} \cdot q_{A}=+0.2 \mu C \) and \( q_{B}=-0.2 \mu C \)
\( \mathbf{D} \cdot q_{A}=-0.2 \mu C \) and \( q_{B}=-0.2 \mu C \)
Subject: Chemistry
Which of the following is a dispropprtonation reaction?
A \( \cdot C a C O_{3}+2 H^{+} \rightarrow C a^{2+}+C O_{2} \)
B \( \cdot 2 C r O_{4}^{2-}+\rightarrow C r_{2} O_{7}^{2+} H_{2} O \)
c. \( C r_{2} O_{4}^{2-}+\rightarrow 2 C r O_{4}^{2-}+H_{2} O \)
D. \( C u_{2} O+2 H^{+} \rightarrow C u^{2+}+H_{2} O \)
Subject: Physics
A ray of light strikes a transparent rectangular slab of refractive index \( \sqrt{2} \) at an angle of incidence of \( 45^{\circ} . \) The angle between the reflected and refracted rays is:
\( A \cdot 75^{\circ} \)
B. \( 90^{\circ} \)
\( \mathrm{c} \cdot 105^{\circ} \)
D. \( 120^{\circ} \)
Subject: Chemistry
Equilibrium constant for two complexes
are:
\( \boldsymbol{A}: \boldsymbol{K}_{4}\left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{6}\right] \quad ; \quad \boldsymbol{2} . \boldsymbol{6} \times 10^{37}( \) for
dissociation)
\( \boldsymbol{B}: \boldsymbol{K}_{3}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \quad ; \quad \mathbf{1 . 9} \times \mathbf{1 0}^{17} \) (for
dissociation)
A. \( A \) and \( B \) are equally stable
B. \( A \) is more stable than \( B \)
\( \mathrm{c} . B \) is more stable than \( A \)
D. The predictable stability
Subject: Chemistry
The molality of an aqueous dilute solution containing non-volatile solute is 0.1 m. What is the boiling
temperature (in \( ^{\circ} \boldsymbol{C} \) ) of solution?
(Boiling point elevation constant, \( \boldsymbol{K}_{\boldsymbol{b}}= \) \( 0.52 k g m o l^{-1} K ; \) boiling temperature
of water \( =100^{\circ} \mathrm{C} \) )
A. 100.0052
в. 100.052
c. 100.0
D. 100.52
Subject: Physics
A body of mass \( 0.2 \mathrm{kg} \) dropped from a height '6 m'. If \( e=\frac{1}{\sqrt{6}} \) then K.E. lost
during its first bounce from the ground
is
\( \mathbf{A} \cdot 1.96 J \)
B. \( 9.8 J \)
c. 19.6 .5
D. zero
Subject: Physics
Two metallic spheres \( S_{1} \) and \( S_{2} \) are
made of the same material and have
identical surface finish. The mass of \( S_{1} \)
is three times to that of \( S_{2} \). Both
the spheres are heated to the same high temperature and placed in the same room having lower temperature but are thermally insulated from each other. The ratio of the initial rate of cooling of
\( S_{1} \) to that \( S_{2} \) is :
A \( \cdot \frac{1}{3} \)
в. \( \left(\frac{1}{3}\right)^{\frac{1}{3}} \)
c. \( \frac{1}{\sqrt{3}} \)
D. \( \frac{\sqrt{3}}{1} \)
Subject: Maths
A lot contains 20 articles. The
probability that the lot contains exactly 2 defective articles is 0.4 and the
probability that the lot contains exactly 3 defective articles is \( 0.6 . \) Articles are
drawn from the lot at random one by one without replacement and tested till all the defective articles are found. The
probability that the testing procedure ends at the twelfth testing \( \frac{100-k}{1900} \) Find the value of \( k \)
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{2}^{100} \boldsymbol{x}+\mathbf{1} \)
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{3}^{100} \boldsymbol{x}+\mathbf{1} \)
Then the set of real numbers x such that
\( \boldsymbol{f}(\boldsymbol{g}(\boldsymbol{x}))=\boldsymbol{x} \) is
A. Empty
B. A singleton
c. A finite se with more than one element
D. Infinite
Subject: Chemistry
\( 0.16 \mathrm{g} \) of methane was subjected to combustion at \( 27^{\circ} \mathrm{C} \) in a bomb
Calorimeter. The temperature of
calorimeter system (including water)
was found to rise by \( 0.5^{\circ} \) C. The heat of combustion of methane at :
(i) constant volume and ( ii ) constant
pressure.
[Given: The thermal capacity of
calorimeter system is \( 17.7 \mathrm{kJ} K^{-1} \)
\( \left.\left(\boldsymbol{R}=\mathbf{8 . 3 1 4} \boldsymbol{J} \boldsymbol{m o l}^{-\mathbf{1}} \boldsymbol{K}^{-1}\right)\right] \)
B. (i) -785 kJ / mol ( ii) - 859.95 kJ / mol
c. (i) -587kJ / mol ( ii) -789.95 kJ / mol
D. (i) -985 kJ/ mol ( ii ) - 999.95 kJ / mol
Subject: Chemistry
Write chemical equations for metallurgical processes to represent roasting of Galena \( (\boldsymbol{P b S}) \)
A. \( 2 P b S+3 O_{2} \rightarrow P b_{2} O_{2}+2 S O_{2} \)
в. \( P b S+2 O_{2} \rightarrow P b O+S O_{3} \)
\( \mathrm{c} \cdot 2 P b S+3 O_{2} \rightarrow 2 P b O+2 S O_{2} \)
D. None of these
Subject: Chemistry
The uncertainty in position and velocity of the particle are \( 0.1 n m \) and \( 5.27 \times \)
\( 10^{-24} m s^{-1} \) respectively then find the
mass of the particle \( (\boldsymbol{h}=\mathbf{6 . 6 2 5} \times \) \( 10^{-34} J s^{-1} \)
Subject: Physics
In the arrangement shown in figure,
dielectric constant \( k_{1}=2 \) and \( K_{2}=3 . \) If
the capacitance across \( \mathrm{P} \) and \( \mathrm{Q} \) are \( C_{1} \) and \( C_{2} \) respectively, then \( \frac{C_{1}}{C_{2}} \) will be (the gaps shown are negligible)
A . 1:
B. 2:
\( c .9: 5 \)
D. 25: 24
Subject: Physics
what is the angular momentum of an electron of de-broglie wavelength \( \lambda ? \)
given \( r \) is the radius of orbit
\( A \cdot \frac{r h}{\lambda} \)
B. \( \frac{2 r h}{\lambda} \)
\( c \cdot \frac{3 r h}{\lambda} \)
D. \( \frac{4 r h}{\lambda} \)
Subject: Physics
The required kinetic energy of an object of mass \( \mathrm{m}, \) so that it may escape, will
be
\( \mathbf{A} \cdot \frac{1}{4} m g R \)
B . \( \frac{1}{2} m g R \)
c. \( \mathrm{mg} \) R
D. 2 mgR
Subject: Maths
Calculate the scalar product of the following vectors.

Resolve the vector \( d=\{1,1,1\} \) into
components with respect to three
noncoplanar vectors \( \boldsymbol{a}= \)
\( \{1,1,-2\}, b=\{1,-1,0\}, \) and \( c= \)
\{0,2,3\}
Subject: Maths
Solve \( \int \frac{d x}{\sqrt{5 x^{2}-2 x}} \)
\( \mathbf{A} \cdot_{I}=\frac{1}{\sqrt{5}} \log \left|x-\frac{1}{5}-\frac{1}{\sqrt{5}} \sqrt{5 x^{2}-2 x}\right|+c \)
B. \( I=-\frac{1}{\sqrt{5}} \log \left|x-\frac{1}{5}+\frac{1}{\sqrt{5}} \sqrt{5 x^{2}-2 x}\right|+c \)
\( ^{\mathbf{C}} I=\frac{1}{\sqrt{5}} \log \left|x-\frac{1}{5}+\frac{1}{\sqrt{5}} \sqrt{5 x^{2}-2 x}\right|+c \)
D. None of these
Subject: Chemistry
\( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}}\left(\boldsymbol{C} \boldsymbol{H}_{2}\right)_{\boldsymbol{2}} \boldsymbol{C} \boldsymbol{d}+ \)
\( \boldsymbol{2} \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C o C l} \stackrel{d r y}{\operatorname{ether}} \)
Subject: Physics
A particle of charge \( q \) and mass \( m \)
moves in a circular path of radius \( r \) in a
uniform magnetic field \( B \).

The particle is replaced with a particle
of identical charge and mass \( \frac{1}{2} m \) The radius of the new circular path the
particle makes is:
A \( \cdot \frac{1}{4} r \)
в. \( \frac{1}{2} r \)
c. \( r \)
D. \( 2 r \)
E . \( 4 r \)
Subject: Physics
A toroid of n turns, mean radius R and
cross-sectional radius a carries current
I. It is placed on a horizontal table taken as \( x-y \) plane. Its magnetic moment
\( \bar{M} \) is
A. is non-zero and points in the z-direction by symmetry
B. points along the axis of the toroid \( (\bar{M}=M \phi) \)
c. is zero, otherwise there would be field falling as \( \frac{1}{r^{3}} \) at large distances outside the toroid
D. is pointing radially outwards
Subject: Chemistry
A person drinks 200 g of \( 3 \% \) glucose solution (molecular wt. \( =180 \) ) after
aerobic exercise. The number of carbon
atoms consumed by him is :
\( \begin{array}{ll}\text { A } & \text { . } 3.01 \times 10^{2}\end{array} \)
В. \( 1.0 \times 10^{22} \)
C. \( 2.01 \times 10^{22} \)
D. \( 1.20 \times 10^{23} \)
Subject: Maths
A straight line \( r=a+\lambda b \) meets the
plane \( r . n=0 \) in \( P . \) The position vector
of \( \boldsymbol{P} \) is
A \( \cdot a+\frac{a \cdot n}{b \cdot n} b \)
B. \( a+\frac{b . n}{a . n} b \)
c. \( _{a-} \frac{a . n}{b . n} b \)
D. None of these
Subject: Chemistry
The activation energy for most of the
reaction is approximately \( 50 \mathrm{kJ} \) mol \( ^{-1} \)
The rate for temperature coefficient for
such reaction will be:
\( \mathbf{A} \cdot \approx 2 \)
в. \( \approx 3 \)
\( c \cdot<1 \)
\( D \ldots 4 \)
Subject: Chemistry
At \( 298 \mathrm{K} \) temperature, \( A \) hydrogen gas electrode is made by dipping platinum wire in a solution of HCl of \( \mathrm{pH}=10 \) and
by passing hydrogen gas around the platinum were at one atm pressure. The potential of electrode would be?
\( \mathbf{A} \cdot 0.59 \mathrm{V} \)
B. \( 0.118 v \)
c. \( 1.18 v \)
D. \( 0.059 \mathrm{V} \)
Subject: Physics
In the given arrangement, the loop is moved with constant velocity v in a
uniform magnetic field B in a restricted region of width a. The time for which the
emf is induced in the circuit is?
A \( \cdot \frac{2 b}{v} \)
B. \( \frac{2 a}{v} \)
c. \( \frac{(a+b)}{v} \)
D. \( \frac{2(a-b)}{v} \)