AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Charge passing through a conductor of \( \operatorname{cross} \operatorname{section} \operatorname{area} A=0.3 m^{2} \) is given
by \( \boldsymbol{q}=\mathbf{3} \boldsymbol{t}^{2}+\mathbf{5} \boldsymbol{t}+\mathbf{2} \) in coulomb, when \( \boldsymbol{t} \)
is in second. What is the value of drift
velocity at \( t=2 s ?(\text { Given, } n=2 x \)
\( \mathbf{1 0}^{\mathbf{2 5}} / \boldsymbol{m}^{\mathbf{3}} \mathbf{)} \)
A \( \cdot 0.77 \times 10^{-5} \mathrm{m} / \mathrm{s} \)
B . \( 1.77 \times 10^{-5} \mathrm{m} / \mathrm{s} \)
C \( .2 .08 \times 10^{-5} \mathrm{m} / \mathrm{s} \)
D. \( 0.57 \times 10^{-5} \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
Which of the following give the correct increasing order of the atomic radii of
\( \boldsymbol{O}, \boldsymbol{F}, \boldsymbol{a} \boldsymbol{n} \boldsymbol{N} ? \)
A. \( O, F, N \)
в. \( N, F, O \)
c. \( O, N, F \)
D. \( F, O, N \)
Subject: Biology
Select the correct statement from the
following.
A. Activated sludge-sediment in settlement tanks of sewage treatment plant is a rich source of aerobic bacteria
B. Biogas is produced by the activity of aerobic bacteria on animal waste.
C. Methanobacterium is an aerobic bacterium found in
rumen of cattle.
D. Biogas, commonly called as gobar gas, is pure methane.
Subject: Chemistry
For the reaction shown, which best
describes the elementary reaction?
\( \mathbf{2} N_{2} \boldsymbol{O}_{\mathbf{5}} \leftrightarrow \mathbf{4} \boldsymbol{N} \boldsymbol{O}_{\mathbf{2}}+\boldsymbol{O}_{\mathbf{2}} \)
A. First order unimolecular
B. Second order unimolecular
c. Second order bimolecular
D. First order bimolecular
Subject: Maths
In a right-angled, triangle the area of the square drawn on the Hypotenuse is \( 289 c m^{2} \) and the area of the
square drawn on the Base is \( 225 \mathrm{cm}^{2} \)
What will be the area of the square
drawn on the Height of the triangle in
\( c m^{2} ? \)
Subject: Maths
Show that if \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{B} \) and \( \boldsymbol{g}: \boldsymbol{B} \rightarrow \boldsymbol{C} \)
are one-one, then \( g \circ f: A \rightarrow C \) is also
one-one.
Subject: Physics
Two conducting concentric, hollow spheres \( A \) and \( B \) have radii a and \( b \) respectively, with A inside B.Their common potentials is \( V \). A is now given some charge such that its potential becomes zero. The potential of B will
now be :
A. 0
B. \( V(1-a / b) \)
c. \( v \) a/b
D. v b/a
Subject: Physics
A stone thrown upward with a speed 'u' from the top of the tower reaches the ground with a velocity '3u'. The height of
the tower is :-
A \( \cdot \frac{3 u^{2}}{g} \)
в. \( \frac{4 u^{2}}{g} \)
c. \( \frac{6 u^{2}}{g} \)
D. \( \frac{9 u^{2}}{g} \)
Subject: Chemistry
The percentage of isomers formed during monobromination of \( 2,3- \) dimethyl butane at room temperature
relative to \( 1,2,3 \mathrm{H} \) atoms to chlorination is \( (1.0: 3.8: 5.0) \)
A . 81\%
B. 56\%
c. 15\%
D. 22\%
Subject: Maths
Is it true to say that area of a segment of a circle is less than the area of its
corresponding sector? Why?
A. yes, it is true for minor segment since ar.minor segment = ar.sector-triangle made by the radii and the chord of the segment.
B. Yes, it is only true for major segment since ar.minor segment = - ar.sector-triangle made by the radii and the chord of the segment
C. No, it is only true for major segment since ar.minor segment
=ar.sector-triangle made by the radii and the chord of the segment.
D. No, it is only true for minor segment since ar.minor segment
=ar.sector-triangle made by the radii and the chord of the segment.
Subject: Maths
Assertion
Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{m} \boldsymbol{i} \boldsymbol{n} \cdot(\boldsymbol{x}+1, \sqrt{1-\boldsymbol{x}}), \) then
area bounded by \( y=f(X) \& x \) -axis is
\( \mathbf{7} \)
\( \overline{6} \) square units.
Reason
\( \min \) of \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}x+1 & \text { for }-1 \leq x<0 \\ \sqrt{1-x} & , 0<x \leq 1\end{array}\right. \)
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: Chemistry
Assertion
\( C e^{4+} \) is good analytical reagent.
Reason
\( C e^{4+} \) has the tendency to change to
\( C e^{3+} \)
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: Chemistry
Match the column I with column II and
mark the appropriate choice.

Column I
(A)
Metals used as \( \quad \) (i) \( \quad \) Aluminium semiconductors
Electrolytic Zone
(B) reduction \( \quad \) refining
(ii)
Dressing
(C) \( \quad \) Cyanide process \( \quad \) (iii) \( \quad \) of \( Z n S \)
Froth floatation \( \quad, \ldots \) Extraction
(D) \( \quad \) process \( \quad \) (iv) \( \quad \) of \( A g \)
\( \mathbf{A} \cdot(A) \rightarrow(i),(B) \rightarrow(i i i),(C) \rightarrow(i i),(D) \rightarrow(i v) \)
B. \( (A) \rightarrow(\text { iii), }(B) \rightarrow(i v),(C) \rightarrow(i \text { i) },(D) \rightarrow(i) \)
C \( .(A) \rightarrow(\text { iv ) },(B) \rightarrow(\text { ii }),(C) \rightarrow(\text { iii }),(D) \rightarrow(i) \)
\( \mathbf{D} \cdot(A) \rightarrow(i i),(B) \rightarrow(i),(C) \rightarrow(i v),(D) \rightarrow(i i i) \)
Subject: Physics
During collision
a) There is a change in momenta of individual bodies
b) The change in total momentum of the system of colliding particle is zero
c) The change in total energy is zero
d) The law of conservation of
momentum is not valid
A. only a \( \& \) b are true
B. only b \& c are true
\( c \cdot a, b \& c \) are true
D. b, c \& d are true
Subject: Physics
A ring of mass kept on a horizontal
rough A force \( F \) is applied tangentially
at its rim as shown. The coefficient of
frictionless between the ring and the
surface is \( \mu \) Then
A. Friction will act in the forward direction
B. Friction will act in the backward direction
c. Friction force will not act
D. Frictional force will be \( \mu g \)
Subject: Physics
Imagine a new planet having the same density as that of the earth but it is 3
times bigger than the earth in size. If
the acceleration due to gravity on the
surface of the earth is \( g \) and that on the
new planet is \( g^{\prime} \), then what is the value of \( \frac{\boldsymbol{g}^{\prime}}{\boldsymbol{g}} \)
Subject: Chemistry
Which of the following statements
is/are true?
This question has multiple correct options
A. The standard molar enthalpy of formation of \( C O_{2} \) is equal to the standard molar enthalpy of combustion of carbon (graphite).
B. Molar heat capacity of water in equilibrium with ice at constant pressure is infinity.
C. A reaction is impossible at any temperature if \( \Delta H> \) \( 0, \Delta S<0 \)
D. The heat of neutralization of strong acid and strong base in solution is equal to the \( \Delta H \) of the reaction
\( H_{2} O+H^{+} \rightleftharpoons H_{3} O^{+} \)
Subject: Chemistry
When \( H_{2} S \) is passed into aqueous \( S O_{2} \)
\( \mathbf{A} \cdot H_{2} S \) is converted to yellow precipitate of sulphur
B. \( S O_{2} \) is converted to yellow precipitate of sulphur
C \( . \) a clear solution of \( H_{2} S O_{4} \) is formed
D. \( S O_{2} \) as well as \( H_{2} S \) are converted into a yellow precipitate of sulphur
Subject: Maths
\( \boldsymbol{C}_{\mathbf{1}}+\mathbf{2} \boldsymbol{C}_{\mathbf{2}}+\mathbf{3} \boldsymbol{C}_{\mathbf{3}}+\ldots \ldots+\boldsymbol{n} \boldsymbol{C}_{\boldsymbol{n}} \) is equal
to
A \( \cdot 2^{n-1} \)
B . \( 2^{n+1} \)
c. \( n .2^{n-1} \)
D \( \cdot n \cdot 2^{n+1} \)
Subject: Chemistry
The reaction between \( A \) and \( B \) is first
order with respect to A and zero order with respect to B. Fill in the blanks in
the following table:
\( \begin{array}{lll}\text { Experiment } & {[\boldsymbol{A}] / \boldsymbol{m o l} \boldsymbol{L}^{-1}} & \boldsymbol{B}] / \boldsymbol{m o l} \boldsymbol{L}^{-1} \\ 1 & 0.1 & 0.1 \\ 11 & - & 0.2 \\ 111 & 0.4 & 0.4 \\ & & \\ & & \\ & & \\ & & \\ & & \end{array} \)
Subject: Maths
If \( \boldsymbol{\alpha}, \boldsymbol{\beta}(\boldsymbol{\alpha}<\boldsymbol{\beta}) \) are the roots of the
equation \( 6 x^{2}+11 x+3=0 \) then which
of the following are real? This question has multiple correct options
\( A \cdot \cos ^{-1} \alpha \)
B. \( \sin ^{-1} \beta \)
\( \mathbf{c} \cdot \operatorname{cosec}^{-1} \alpha \)
D. Both \( \cot ^{-1} \alpha \) and \( \cot ^{-1} \beta \)
Subject: Maths
Solve the following inequality and show
it graphically:
\( \frac{\boldsymbol{x}+\mathbf{4}}{\boldsymbol{x}-\mathbf{3}}>\mathbf{0}, \boldsymbol{x} \in \boldsymbol{W} \)
\( ^{A} \cdot \underbrace{0}_{-3-2-1} \cdot 1,0 \)
в.
\( c_{1}+ \)\begin{tabular}{ccccccc}
\hline-5 & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4
\end{tabular}
Subject: Chemistry
The ammonia evolved from the
treatment of \( 1.50 \mathrm{g} \) of an organic compound for the estimation
of nitrogen was passed in \( 100 \mathrm{ml} \) of 0.5 M sodium hydroxide solution for complete neutralization.
The organic compound is:
A. thiourea
B. benzamide
c. urea
D. acetamide
Subject: Chemistry
Peptization of \( S n O_{2} \) by \( N a O H \) gives:
\( \mathbf{A} \cdot\left[\operatorname{Sn} O_{2}\right] \operatorname{Sn} O_{3}^{2-}: 2 N a^{+} \)
B \( \cdot\left[\operatorname{Sn} O_{2}\right] S n^{4+}: O^{2} \)
\( \mathbf{c} \cdot\left[\operatorname{Sn} O_{2}\right] N a: O H^{-} \)
D・ \( \left[\operatorname{Sn} O_{2}\right] S n^{4+}: O H^{-} \)
Subject: Maths
If \( p(x)=x^{2}-4, q(x)=x^{3}-8, r(x)= \)
\( (x+2) \) and \( s(x)=\left(x^{2}+2 x+4\right) \) then
choose the correct options -
A \( \cdot p(x) \cdot s(x)=q(x) \cdot r(x) \)
B . \( p(x) . s(x) \neq q(x) . r(x) \)
c. \( p(x) . q(x)=s(x) . r(x) \)
D. None of these
Subject: Biology
Assertion
Excess nitrate in drinking water causes
blue baby' syndrome.
Reason
The maximum limit of nitrate in
drinking water is 50 ppb.
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: Chemistry
a. Calculate e.m.f of cell for the reaction:
\( M g_{(s)}+C u^{2+}(0.0001 M) \rightarrow \)
\( M g^{2+}(0.001 M)+C u_{(s)} \)
Given that: \( E_{M g^{2+} / M g}^{o}=-2.37 \mathrm{V} \)
\( E_{C u^{2+} / C u}^{o}=+0.34 v \)
b. i) State Kohlrausch law.
ii) What is meant by limiting molar
conductance.
Subject: Chemistry
Assertion
Law of conservation of mass holds good
for nuclear reactions.
Reason
Law states that mass can be neither
created nor destroyed in a chemical
reaction.
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: Maths
The value of \( x \) in the expression
\( \left(x+x^{\log _{10} x}\right)^{5}, \) if the third term in the
expansion is \( 10,00,000, \) is This question has multiple correct options
A \( \cdot 10^{-1} \)
B . \( 10^{\text {। }} \)
\( \mathbf{c} \cdot 10^{-5 / 2} \)
D. \( 10^{5 / 2} \)
Subject: Physics
A capacitor of capacitance \( C_{1} \) charged
at a certain potential v. It is connected
with another uncharged capacitor \( C_{2} \) What is the final p.d. of this new system.
A \( \cdot \frac{C_{2} V}{C_{1} C_{2}} \)
в. \( \frac{C_{1} V}{C_{1} C_{2}} \)
c. \( \left(1+\frac{C_{2}}{C_{1}}\right) \)
D. \( D\left(1-\frac{C_{2}}{C_{1}}\right) V \)
Subject: Physics
The ratio of the energy required to set up in cube of side \( 10 \mathrm{cm} \) uniform magnetic field of \( 4 W b / m^{2} \) and a
uniform electric field of \( 10^{6} V / m \) is:
A \( \cdot 1.4 x 10^{7} \)
B. \( 1.4 x 10^{5} \)
c. \( 1.4 x 10^{6} \)
D. \( 1.4 x 10^{3} \)
Subject: Chemistry
\( \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{S}+\boldsymbol{N} \boldsymbol{a} \boldsymbol{C} \boldsymbol{N} \longrightarrow(\boldsymbol{A}),(\boldsymbol{A})+ \)
\( \boldsymbol{Z} \boldsymbol{n} \longrightarrow(\boldsymbol{B}) \)
(B) is a metal. Hence (A) and (B) are:
A \( \cdot \operatorname{Na}_{2}\left[\operatorname{Zn}(C N)_{4}\right], Z n \)
B . \( N a_{2}\left[A g(C N)_{2}\right], A g \)
c. \( N a_{2}\left[A g(C N)_{4}\right], A g \)
D. \( N a_{3}\left[A g(C N)_{4}\right], A g \)
Subject: Maths
The arrangement of the following conics in the ascending order of their eccentricities is
A) \( r(4+\cos \theta)=8 \)
B) \( \frac{1}{r}=\frac{3}{5}-\frac{3 \cos \theta}{5} \)
C) \( 8=r(1+3 \cos \theta) \)
A. \( B, C, A \)
в. \( B, A, C \)
c. \( A, B, C \)
D. \( A, C, B \)
Subject: Physics
A body is hanging from a rigid support by an extensible string of length \( L \). It is struck inelastically by an identical body of mass \( m \) with horizontal velocity \( v= \)
\( \sqrt{2 g l}, \) the tension in the string
increases just after striking by:
A . \( m g \)
в. \( 3 m g \)
c. \( 2 m g \)
D. None of these
Subject: Maths
If a plane has \( X \) -intercept \( l, Y \) -intercept
\( m \) and \( z \) -intercept \( n, \) and perpendicular
distance of plane from origin is \( k, \) then \( ? \)
A \( \cdot l^{2}+m^{2}+n^{2}=\frac{1}{k^{2}} \)
B. \( \frac{1}{l^{2}}+\frac{1}{m^{2}}+\frac{1}{n^{2}}=\frac{1}{k^{2}} \)
c. \( l^{2}+m^{2}+n^{2}=k^{2} \)
D. \( \frac{1}{l^{2}}+\frac{1}{m^{2}}+\frac{1}{n^{2}}=k^{2} \)
Subject: Maths
Find the values of \( x \) which satisfy \( \left|\frac{x^{2}}{x-1}\right| \leq 1 \)
\( ^{\mathbf{A}} \cdot_{x} \in\left[\frac{-1-\sqrt{3}}{2}, \frac{-1+\sqrt{3}}{2}\right] \)
в. \( _{x} \in\left[\frac{-1-\sqrt{5}}{2}, \frac{-1+\sqrt{5}}{2}\right] \)
\( ^{\mathbf{c}} \cdot_{x} \in\left[\frac{-1-\sqrt{7}}{3}, \frac{-1+\sqrt{7}}{3}\right] \)
D. None of these
Subject: Chemistry
sewage ettluent on the levels of oxygen concentration, bacterial population and
algal growth in a fresh water stream.
The given graph is plotted based on his
findings.
select the correct statement regarding
the given graph.
A. There is a fall in oxygen concentration between point and \( 4 \mathrm{km} \) downstream because it is utilized by algae for respiration during day
B. There is a rise in oxygen concentration between \( 4 \mathrm{km} \) and \( 8 \mathrm{km} \) downstream because of oxygen for respiration is lower
C. Bacterial population never recovers from 8 km onwards because all the oxygen is used by algae
D. There is decrease in the level of bacteria between \( 5 \mathrm{km} \) and \( 7 \mathrm{km} \) downstream because all the oxygen and organic matter has been used up by algal population
Subject: Maths
\( \int_{0}^{2 \pi} \cos m x \cdot \sin n x d x \) where \( m, n \) are
integers \( = \)
\( A \cdot O \)
B . \( \pi \)
\( \mathbf{c} \cdot \pi / 2 \)
D. \( 2 \pi \)
Subject: Physics
A solid sphere is placed on a smooth
horizontal plane. A horizontal impluse \( I \) is applied at a distance \( h \) above the
central line as shown in the figure. Soon
after giving the impulse the sphere starts rolling.
The ratio \( h / R \) would be
A . 1 2
B. 2 5
\( c \cdot \frac{1}{4} \)
D. 1
Subject: Maths
The domain of \( \frac{1}{\sqrt{x-x^{2}}}+ \) \( \sqrt{3 x-1-2 x^{2}} \) is
\( ^{\mathbf{A}} \cdot\left(\frac{1}{2}, 11\right) \)
в. \( \left(\frac{1}{2}, 31\right) \)
c. \( \left(\frac{1}{2}, 17\right) \)
D \( \cdot\left(\frac{1}{2}, 41\right) \)
Subject: Chemistry
Select the correct order of \( \mathrm{C} \) - \( \mathrm{O} \) bond
Iength:
\( \mathbf{A} \cdot\left[M(C O)_{3}\left(P F_{3}\right)\right]<\left[M(C O)_{3}\left(P C l_{3}\right)\right]< \)
\( \left[M(C O)_{3}\left(P M e_{3}\right)\right] \)
\( \mathbf{B} \cdot\left[M(C O)_{3}\left(P F_{3}\right)\right]>\left[M(C O)_{3}\left(P C l_{3}\right)\right]> \)
\( \left[M(C O)_{3}\left(P M e_{3}\right)\right] \)
\( \mathbf{c} \cdot\left[M(C O)_{3}\left(P F_{3}\right)\right]=\left[M(C O)_{3}\left(P C l_{3}\right)\right]= \)
\( \left[M(C O)_{3}\left(P M e_{3}\right)\right. \)
\( \mathbf{D} \cdot\left[M(C O)_{3}\left(P F_{3}\right)\right]=\left[M(C O)_{3}\left(P C l_{3}\right)\right]> \)
\( \left[M(C O)_{3}\left(P M e_{3}\right)\right] \)
Subject: Physics
Three resistances are connected to form
a \( T \) -shape as shown in the figure. Then
the current in the \( 4 \mathrm{K} \) resistor is :
A. \( 0.93 \mathrm{mA} \)
B. \( 1.42 \mathrm{mA} \)
c. \( 2.5 \mathrm{mA} \)
D. 1.57 m
Subject: Chemistry
Aluminate ion in aqueous solution actually exists as:
\( \mathbf{A} \cdot\left[A l(O H)_{6}\right]^{3} \)
в. \( \left[A l(O H)_{4}\left(H_{2} O\right)_{2}\right]^{-} \)
\( \mathbf{c} \cdot\left[A l(O H)_{3}\left(H_{2} O\right)_{3}\right. \)
D・ \( \left[A l(O H)_{5} H_{2} O\right]^{-2} \)
Subject: Physics
A carbon filament has resistance of 120
\( \Omega \) at \( 0^{0} C . \) The resistance of a copper
filament connected in series with
carbon so that the combination has
same resistance at all temperatures
must be
\( \alpha \) of carbon \( =-7 \times 10^{-4} /^{0} C ; \alpha \) of
\( \operatorname{copper}=4 \times 10^{-3} /^{0} C \)
A . \( 120 \Omega \)
B. 21\Omega
\( c \cdot 60 \Omega \)
D. 210\Omega
Subject: Physics
Six capacitors each of capacitance of
\( 2 \mu F \) are connected as shown in the
figure. The effective capacitance
between \( A \) and \( B \) is:
\( \mathbf{A} \cdot 12 \mu F \)
в. \( \frac{8}{3} \mu F \)
\( c .6 \mu F \)
D \( \frac{2}{3} \mu F \)
Subject: Maths
Find the quadratic function \( \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{i} \boldsymbol{f} \boldsymbol{f}(\boldsymbol{0})=\mathbf{1}, \boldsymbol{f}(1)=\mathbf{0}, \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{f}(\boldsymbol{3})= \)
\( \mathbf{5} \)
Subject: Physics
The stress along the length of a rod(with rectangular cross section) is \( 1 \% \) of the Young's modulus of its material. What is the approximate percentage of change of its volume? (Poisson's ratio of
the material of the rod is 0.3 ).
A . \( 3 \% \)
B. 1\%
\( c .0 .7 \% \)
D. \( 0.4 \% \)
Subject: Maths
In a triangle \( \triangle A B C, 3 \sin A+ \)
\( 4 \cos B=6 \) and \( 4 \sin B+3 \cos A=1 \)
then the angle \( C \) is
A \( .150^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 30^{\circ} \)
Subject: Maths
The equation of motion of a rocket are:
\( \boldsymbol{x}=\mathbf{2} \boldsymbol{t}, \boldsymbol{y}=-\boldsymbol{4} \boldsymbol{t}, \boldsymbol{z}=\boldsymbol{4} \boldsymbol{t}, \) where the time
\( t \) is given in seconds and the coordinate
of a moving point in kilometers. At what distance will the rocket be from the
starting point \( O(0,0,0) \) in 10 seconds?
\( \mathbf{A} \cdot 60 \mathrm{km} \)
B. \( 30 \mathrm{km} \)
c. \( 45 \mathrm{km} \)
D. None of these
Subject: Physics
A uniform thin bar of mass \( 6 \mathrm{m} \) and length 12L is bent to make a regular hexagon. Its moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of a hexagon is
A \( .20 m L^{2} \)
\( \mathbf{B} \cdot 6 m L^{2} \)
c. \( \frac{12}{5} m L^{2} \)
D. \( 30 m L^{2} \)
Subject: Chemistry
The density of 3 M solution of NaCl is 1.2 \( \mathrm{g} m L^{-1} . \) The molality of the solution is?
A. 2.79 \( \mathrm{m} \)
B. 1.79 \( m \)
c. \( 3.5 \mathrm{m} \)
D. 5.58 m
Subject: Chemistry
The free energy for a reaction having \( \Delta H=31400 \mathrm{cal}, \Delta S= \)
32 cal \( K^{-1} \) mol \( ^{-1} \) at \( 1000^{\circ} \mathrm{C} \) is:
\( \mathbf{A} \cdot-9336 \mathrm{cal} \)
в. -7386 са\( l \)
\( \mathbf{c} .-1936 \mathrm{cal} \)
D. +9336 cal
Subject: Maths
Binary operation \( ^{*} \) on \( \mathrm{R}-\{-1\} \) defined by \( \boldsymbol{a} * \boldsymbol{b}=\frac{\boldsymbol{a}}{\boldsymbol{b}+\mathbf{1}} \) is
\( A .^{*} \) is associative and cummutative
B. \( ^{*} \) is neither associative nor commutative
c. \( ^{*} \) is commutative but not associative
D. \( ^{*} \) is associative but not commutative
Subject: Maths
f \( \boldsymbol{y}=\log [\boldsymbol{x}+\sqrt{\boldsymbol{x}^{2}+\boldsymbol{a}^{2}}], \) show that
\( \left(x^{2}+a^{2}\right) \frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}=0 \)
Subject: Physics
A system consists of a uniformly charged sphere of radius \( \boldsymbol{R} \) and \( \mathbf{a} \) surrounding medium filled by a charge
with the volume density \( \rho=\frac{\alpha}{r}, \) where
\( \alpha \) is a positive constant and \( r \) is the
distance from the centre of the sphere.
Find the charge of the sphere for which the electric field intensity \( \boldsymbol{E} \) outside the
sphere is independent of \( \boldsymbol{R} \)
\( ^{\mathrm{A}} \cdot \frac{\alpha}{2 \varepsilon_{0}} \)
в. \( \frac{2}{\alpha \varepsilon_{0}} \)
\( c \cdot 2 \pi \alpha R^{2} \)
D. None of these
Subject: Physics
Match the following
List I List 1
a. frictional force \( \quad \) e. reduction of friction
b. rolling friction
f. causes wear and tear
c. ball bearing less than kinetic friction g.
d. trading of surface \( \quad \) h. increase of friction
The correct match is
\( \mathbf{A} \cdot a \rightarrow i ; b \rightarrow e ; c \rightarrow h ; d \rightarrow f \)
B \( \cdot a \rightarrow f ; b \rightarrow f ; c \rightarrow e ; d \rightarrow g \)
\( \mathbf{c} \cdot a \rightarrow f ; b \rightarrow g ; c \rightarrow e ; d \rightarrow h \)
D \( . a \rightarrow i ; b \rightarrow f ; c \rightarrow h ; d \rightarrow e \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}(\mathbf{1}+|\sin \boldsymbol{x}|)^{\frac{a}{|\sin |}}, & -\boldsymbol{\pi} / \boldsymbol{6}<\boldsymbol{x}<\mathbf{0} \\ \boldsymbol{b}, & \boldsymbol{x}=\mathbf{0} \\ \boldsymbol{e}^{\frac{\tan 2 x}{\tan x}}, & \boldsymbol{0}<\boldsymbol{x}<\boldsymbol{\pi} / \boldsymbol{6}\end{array}\right. \)
continuous at \( x=0, \) find the values of
\( a \) and \( b \)
A \( \cdot \frac{3}{2}, e^{3 / 2} \)
B. \( \frac{-2}{3}, e^{-3 / 2} \)
c. \( \frac{2}{3}, e^{2 / 3} \)
D. None of these
Subject: Physics
Assertion
When two coils are wound on each
other, the mutual induction between
the coils is maximum.
Reason
Mutual induction does not depend on
the orientation of the coils.
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
\( \boldsymbol{A}(\boldsymbol{3}, \boldsymbol{2}, \boldsymbol{0}), \boldsymbol{B}(\boldsymbol{5}, \boldsymbol{3}, \boldsymbol{2}), \boldsymbol{C}(-\boldsymbol{9}, \boldsymbol{6},-\boldsymbol{3}) \) are
three points forming a triangle. If \( \boldsymbol{A} \boldsymbol{D} \)
the bisector of \( \angle B A C \) meets \( B C \) in \( D \)
then coordinates of \( D \) are
\( ^{\mathrm{A}} \cdot\left(-\frac{19}{8}, \frac{57}{16}, \frac{17}{16}\right) \)
В \( \cdot\left(\frac{19}{8},-\frac{57}{16}, \frac{17}{16}\right) \)
\( ^{\mathrm{C}} \cdot\left(\frac{19}{8}, \frac{57}{16}, \frac{17}{16}\right) \)
D. None of these
Subject: Maths
If \( x y- \) plane and \( y z- \) plane divides the line segment joining \( A(2,4,5) \) and \( B(3,5,-4) \) in the ratio \( a: b \) and \( p: q \) respectively then value of \( \left(\frac{a}{b}+\frac{p}{q}\right) \) may be
A \( \cdot \frac{23}{12} \)
в. \( \frac{7}{5} \)
\( c \cdot \frac{7}{12} \)
D. \( \frac{21}{10} \)
Subject: Chemistry
This environmental pollutant belongs to a group of dangerous chemicals known as persistent organic pollutants. The
chemical name for this pollutant is
\( \mathbf{2}, \mathbf{3}, \mathbf{7}, \mathbf{8}-\boldsymbol{T} \boldsymbol{C} \boldsymbol{D} \boldsymbol{D} . \) Name it
A. Dibenzofurans
B. Biphenyls
c. Dioxin
D. Aldrin
Subject: Physics
Two equal positive charges \( Q \) are fixed at points \( (a, 0) \) and \( (-a, 0) \) on the \( x \) axis. An opposite charge \( -q \) at rest is released from point \( (0, a) \) on the \( y \) -axis.
The charge \( -\boldsymbol{q} \) will
A. move to infinity
B. Move to origin and rest there
c. Undergo SHM about the origin
D. Execute oscillatory periodic motion but not SHM