AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Predict which of the following reactions would proceed spontaneously at \( 298 \mathrm{K} ? \)
Take \( \boldsymbol{E}_{\boldsymbol{F} e^{2+} / \boldsymbol{F} e}^{\boldsymbol{0}}=-\mathbf{0 . 4 4} \boldsymbol{V} \)
This question has multiple correct options
A \( \cdot \operatorname{Co}(s)+F e^{2+}(a q) \rightarrow\left(C o^{2+}(a q)+F e(s)\right. \)
\[
E_{C o^{+2} / C o}^{\ominus}=-0.28 V
\]
B. \( C d^{2+}(a q)+F e(s) \rightarrow C d(s)+F e^{2+}(a q) \)
\[
E_{C d^{2+} / C d}^{\ominus}=0.4 V
\]
c. \( C d(s)+C o^{2+}(a q) \rightarrow C d^{2+}(a q)+C o(s) \)
\[
E_{F e^{2+} / F e}^{\ominus}=-0.44 V
\]
D. \( Z n^{2+}(a q)+H_{2} \rightarrow Z n(s)+2 H^{\oplus} \)
\[
E_{Z n^{2+} / Z n}^{\ominus}=-0.76 V
\]
Subject: Chemistry
Which of the following pairs contains isoelectronic species?
\( \mathbf{A} \cdot B e \) and \( L i^{+} \)
B . \( P^{+} \) and \( S^{-} \)
c. \( N^{2-} \) and \( N e \)
\( D \cdot O^{2-} \) and \( N a^{+} \)
Subject: Physics
What will be the displacement equation of the simple harmonic motion obtained by combining the motions? \( \boldsymbol{x}_{1}=\mathbf{2} \sin \boldsymbol{\omega} \boldsymbol{t}, \quad \boldsymbol{x}_{2}=\boldsymbol{4} \sin \left(\boldsymbol{\omega} \boldsymbol{t}+\frac{\boldsymbol{\pi}}{\boldsymbol{6}}\right) \)
and \( \quad x_{3}=6 \sin \left(\omega t+\frac{\pi}{3}\right) \)
A \( \cdot x=10.25 \sin (\omega t+\phi) \)
B \cdot \( x=10.25 \sin (\omega t-\phi) \)
C \( \cdot x=11.25 \sin (\omega t+\phi) \)
D \( \cdot x=11.25 \sin (\omega t-\phi) \)
Subject: Maths
Choose the correct options:
This question has multiple correct options
A. Remainder obtained on dividing \( p(x)=x^{3}+1 \) by \( (x+ \)
1) is 0
B. \( x=1 \) and \( x=2 \) are zeroes of polynomial \( P(x)= \)
\( 5 x^{5}-20 x^{4}+5 x^{3}+50 x^{2}-20 x-40 \)
C \( \cdot 6 x^{7}-5 x^{4}+2 x+3 \) is a polynomial of degree 7
D. \( x+1 \) and \( 2 x-3 \) are factors of \( 2 x^{3}-9 x^{2}+x+12 \)
Subject: Maths
Find the value of \( \lambda \) if the following equations are consistent \( \boldsymbol{x}+\boldsymbol{y}-\mathbf{3}=\mathbf{0} \)
\( (1+\lambda) x+(2+\lambda) y-8=0 \)
\( \boldsymbol{x}-(\mathbf{1}+\boldsymbol{\lambda}) \boldsymbol{y}+(\boldsymbol{2}+\boldsymbol{\lambda})=\mathbf{0} \)
Subject: Maths
\( \mathrm{IF} \mathrm{A}=\left|\begin{array}{ll}\mathbf{5} & \boldsymbol{x} \\ \boldsymbol{y} & \boldsymbol{6}\end{array}\right| \mathrm{B}=\left|\begin{array}{cc}-\boldsymbol{4} & \boldsymbol{y} \\ -\boldsymbol{4} & -\mathbf{5}\end{array}\right| \) and \( \mathbf{A}+\mathrm{B}=\mathbf{I} \) then
the values of \( x \) and \( y \) respectively are
A \( .-4,4 \)
B. -4,-4
\( c \cdot 4,4 \)
D. 4,-4
Subject: Physics
In forced oscillation of a particle the amplitude is maximum for a frequency
\( \omega_{1} \) of force, while the energy is
maximum for a frequency \( \omega_{2} \) of the force, then:
A. \( \omega_{1}=\omega_{2} \)
В. \( \omega_{1}>\omega_{2} \)
C. \( \omega_{1}<\omega_{2} \) when damping is small and \( \omega_{1}>\omega_{2} \) when damping is large
D. \( \omega_{1}<\omega_{2} \)
Subject: Chemistry
The oxo-acids of \( P_{2} O_{5} \) are
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}, \boldsymbol{H}_{4} \boldsymbol{P}_{2} \boldsymbol{O}_{7}, \boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{3}, \) and \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \)
A. True
B. False
Subject: Maths
On the interval [0,1] the function
\( f(x)=x^{1005}(1-x)^{1002} \) assumes
maximum value equal to.
A \( \cdot \frac{(1005)^{1002}}{(2007)^{2007}} \)
в. \( \frac{(2007)^{2007}}{(1005)^{12055}(1002)^{1002}} \)
c. \( \frac{(2007)^{2007}}{(1005)^{1202}(1002)^{1005}} \)
D. \( \frac{(1005)^{1005}(1002)^{1002}}{(2007)^{2007}} \)
Subject: Chemistry
Complexes formed in the following
methods are:
(1) Mond's process for purification of nicke
(II)Removal of lead poisoning from the
body
(III) Cyanide process for extraction of silver
(IV) Froth floatation process for
separation of \( Z n S \) from galena are by using depressant
\( \begin{array}{llll}\text { A } \cdot \operatorname{Ni}(C O)_{4} & {[P b(E D T A)]^{2-}} & {\left[A g(C N)_{2}\right]} & {\left[Z n(C N)_{2}\right]}\end{array} \)
B. \( N i(C O)_{4} \quad[P b(E D T A)]^{2-} \quad\left[A g(C N)_{2}\right]^{-} \)
\[
\left[Z n(C N)_{4}\right]^{2}
\]
\( \begin{array}{lll}\text { C. } N i(C O)_{6} & {[P b(E D T A)]^{4-}} & {\left[A g(C N)_{2}\right]^{-}\left[Z n(C N)_{6}\right]^{4}}\end{array} \)
\( D \)
\( N i(C O)_{4} \) \( [P b(E D T A)]^{2-} \) \( \left[A g(C N)_{4}\right]^{3-} \) \( \left[Z n(C N)_{4}\right] \)
Subject: Physics
A point source of light, \( \mathrm{S} \) is placed at a distance \( L \) in front of the centre of plane mirror of width d which is hanging vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror, at a distance \( 2 L \) as shown
below. The distance over which the man
can see the image of the light source in the mirror is :
A . \( 3 d \)
B. \( \frac{d}{2} \)
\( c \cdot d \)
D. \( 2 d \)
Subject: Physics
An iron bar (Young's modulus \( = \) \( \left.10^{11} N / m^{2}, \alpha=10^{-6} /^{\circ} C\right) 1 m \) long and
\( 10^{-3} m^{2} \) in area is heated from \( 0^{\circ} C \) to
\( 100^{\circ} \mathrm{C} \) without being allowed to bend
or expand. Find the compressive force in newtons developed inside the bar
Subject: Chemistry
Two reactions \( R_{1} \) and \( R_{2} \) have identical
pre-exponential factors. Actiation
energy of \( R_{1} \) exceeds that of \( R_{2} \) by
\( \mathbf{1 0 k J}^{-1 . \text { If }} \boldsymbol{K}_{1} \) and \( \boldsymbol{K}_{2} \) are rate
constants for reactions \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{1} \)
respectively at \( 300 \mathrm{K}, \) then \( \ln \left(K_{1} / K_{2}\right) \) is
equal to :\( \boldsymbol{R}=\mathbf{8 . 3 1 4} \boldsymbol{J}^{-1} \boldsymbol{K}^{-1} \)
\( A \cdot 8 \)
B. 12
\( c \cdot 6 \)
D. 4
Subject: Physics
A metallic rod undergoes a strain of
\( 0.05 \% . \) The energy stored per unit volume is \( \left(Y=2 \times 10^{11} \mathrm{Nm}^{-2}\right) \)
A \( \cdot 0.5 \times 10^{4} \mathrm{Jm}^{-3} \)
B . \( 0.5 \times 10^{5} \mathrm{Jm}^{-3} \)
c. \( 2.5 \times 10^{5} \mathrm{Jm}^{-3} \)
D. \( 2.5 \times 10^{4} \mathrm{Jm}^{-3} \)
Subject: Maths
If \( \mathbf{f}(\mathbf{x})=\mathbf{x} \cdot \sin \frac{\mathbf{1}}{\boldsymbol{x}} \) for \( \boldsymbol{x} \neq \mathbf{0}, \mathbf{f}(\mathbf{0})=\mathbf{0} \)
then?
A. \( f \) is continuous at \( x=0 \)
B. \( f \) is differentiable at \( x=0 \)
\( \mathrm{c} \cdot f^{\prime}\left(0^{-}\right) \) exists but \( f^{\prime}\left(0^{+}\right) \) does not exist
D. \( f \) is discontinuous at \( x=0 \)
Subject: Physics
A thin oil layer floats on water. A ray of
light making an angle of incidence \( 40^{\circ} \)
shines an oil layer. The angle of refraction of light ray in water is \( \left(\boldsymbol{m} \boldsymbol{u}_{\boldsymbol{o} i l}=\mathbf{1} . \boldsymbol{4} \mathbf{5}, \boldsymbol{\mu}_{\boldsymbol{w} \text {ater}}=\mathbf{1 . 3 3}\right) \)
\( \left[\sin 40^{\circ}=0.6428, \sin 44.5^{\circ}=0.7007\right] \)
\( A \cdot 28.9^{\circ} \)
B . \( 26.5^{\circ} \)
c. \( 44.5^{\circ} \)
\( D \cdot 40^{\circ} \)
Subject: Maths
The value of \( \lim _{x \rightarrow 0} \frac{x}{5}\left[\frac{x}{2}\right] \) (where \( [.] \)
denotes the greatest integer function) is
A \( \cdot \frac{2}{5} \)
в. \( -\frac{2}{5} \)
c. 0
\( D \cdot \infty \)
Subject: Chemistry
Which is not correct relationship
between \( \Delta G^{\ominus} \) and equilibrium
constant \( \boldsymbol{K}_{\boldsymbol{P}} \)
This question has multiple correct options
\( \mathbf{A} \cdot K_{P}=-R T \log \Delta G^{\ominus} \)
В \( . K_{P}=[e / R T]^{\Delta G^{\ominus}} \)
\( \mathbf{C} \cdot K_{P}=-\frac{\Delta G^{\circ}}{R T} \)
\( \mathbf{D} \cdot K_{P}=e^{-\Delta G^{\ominus} / R T} \)
Subject: Maths
If \( 1, \omega, \omega^{2} \) are two cube roots of unity
then \( \Delta=\left|\begin{array}{ccc}1 & \omega^{n} & \omega^{2 n} \\ \omega^{2 n} & 1 & \omega^{n} \\ \omega^{n} \omega^{2 n} & 1\end{array}\right| \) has the value
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot \omega^{2} \)
D.
Subject: Physics
A current flows in a wire of circular
cross section with the free electrons
travelling with drift velocity \( \bar{V} \). If an equal current flows in a wire of same material and twice the radius, the new
drift velocity is:
\( \mathbf{A} \cdot \bar{V} \)
B. \( \frac{\vec{v}}{2} \)
c. \( \frac{\vec{v}}{4} \)
D. 2 \( \bar{V} \)
Subject: Maths
f \( n(A)=4 \) and \( n(B)=6, \) then the
number of surjections from \( \boldsymbol{A} \) to \( \boldsymbol{B} \) is
A \( \cdot 4^{\circ} \)
B. \( 6^{\text {4 }} \)
c. 0
D. 24
Subject: Physics
Two cells of unequal emfs, \( \boldsymbol{E}_{1} \) and \( \boldsymbol{E}_{2} \)
the internal resistance \( r_{1} \) and \( r_{2} \) are
joined as shown. \( V_{A} \) and \( V_{B} \) are the potentials at \( A \) and \( B \) respectively
This question has multiple correct options
A. one cell with continuously supply energy to the other
B. the potential difference across both the cells will be equal
c. the potential difference across one cell will be grater than its emf
D. \( V_{A}-V_{B}=\frac{\left(E_{1} r_{2}-E_{2} r_{1}\right)}{\left(r_{1}+r_{2}\right)} \)
Subject: Maths
The function \( \boldsymbol{f}: \boldsymbol{N} \rightarrow \boldsymbol{N} \) defined by
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}-\mathbf{5}\left[\frac{\boldsymbol{x}}{\mathbf{5}}\right], \) where \( \mathrm{N} \) is the set of
natural numbers and \( [x] \) denotes the
greatest integer less than or equal to \( x \)
is
A. one-one but not onto
B. neither one-one nor onto
c. onto but not one-one
D. one-one and onto
Subject: Physics
To a man walking at the rate of \( 3 k m / h \) the rain appears to fall vertically. When he increases his speed to \( 6 k m / h \) it
appears to meet him at an angle of \( 45^{\circ} \)
with vertical. The speed of rain is
\( \mathbf{A} \cdot 2 \sqrt{2} k m / h \)
B. \( 3 \sqrt{2} \mathrm{km} / \mathrm{h} \)
\( \mathrm{c} \cdot 2 \sqrt{3} \mathrm{km} / \mathrm{h} \)
D. \( 3 \sqrt{3} \mathrm{km} / \mathrm{h} \)
Subject: Physics
Assertion
Magnetic lines forms closed loops in
nature.
Reason
Mono-magnetic pole does not exist in
nature.
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 \( \boldsymbol{y}=(\mathbf{1}+\boldsymbol{x})\left(\mathbf{1}+\boldsymbol{x}^{2}\right)\left(\mathbf{1}+\boldsymbol{x}^{4}\right) \dots . .(\mathbf{1}+ \)
\( \left.x^{2^{n}}\right), \) find \( \frac{d y}{d x} \) at \( x=0 \)
\( \mathbf{A} \cdot 2^{n} \)
B.
\( c .1 \)
D. \( 2 n \)
Subject: Chemistry
Consider the following reaction
sequence,
\( \boldsymbol{C H}_{3} \boldsymbol{C H}(\boldsymbol{O H}) \boldsymbol{C H}_{3} \frac{\operatorname{Conc.H}_{2} \boldsymbol{S O}_{4}}{\boldsymbol{H e a t}} \)
\( \boldsymbol{X} \frac{d i l \cdot \boldsymbol{H}_{2} \boldsymbol{S O}_{4}}{\boldsymbol{H}_{2} \boldsymbol{O}} \boldsymbol{Y} \)
\( x \) and \( Y \) in the reaction respectively are :
A \( \cdot C H_{3} C H=C H_{2}, C H_{3} C H(O H) C H_{3} \)
в. \( C H_{3} C H=C H C H_{3}, C H_{3} C H_{2} C H_{2} O H \)
c. \( C H_{3} C H_{2} C H=C H_{2}, C H_{3} C H_{2} C H_{2} O H \)
D. \( C H_{3} C H_{2} C H_{2} C H_{3}, C H_{3} C H(O H) C H_{2} C H_{3} \)
Subject: Maths
If \( \frac{x^{2}}{f(4 a)}=\frac{y^{2}}{f\left(a^{2}-5\right)} \) respresents and
ellipse with major axis as y-axis and \( \boldsymbol{f} \) is a decreasing function, then
A \( . a \in(-\infty, 1) \)
B . \( a \in(5, \infty) \)
c. \( a \in(1,4) \)
D. \( a \in(-1,5) \)
Subject: Maths
A unit vector \( \vec{a} \) makes angles \( \frac{\pi}{4} \) and \( \frac{\pi}{3} \) with \( \hat{i} \) and \( \hat{j} \) respectively and an acute angle \( \theta \) with \( \hat{k} \). Find the angle \( \theta \) and
components of \( \overrightarrow{\boldsymbol{a}} \)
Subject: Physics
Assertion
In the formula \( P=\frac{2}{3} E, \) the term \( E \)
represents translational kinetic energy
per unit volume of gas.
Reason
In case of monoatomic gas
translational kinetic energy and total
kinetic energy are equal.
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: Physics
A structural steel rod has a radius of
\( 10 m m \) and a length of \( 1.0 m . A 100 k N \)
force stretches it along its length. Calculate (a) stress,
(b) elongation, and
(c) strain on the rod. Young's modulus,
of structural steel is \( 2.0 \times 10^{11} N m^{2} \)
Subject: Maths
The scores on standardized admissions
test are normally distributed with a mean of 500 and a standard deviation
of \( 100 . \) What is the probability that a randomly selected student will score between 400 and 600 on the test?
A. About \( 63 \% \)
B. About \( 65 \% \)
c. About \( 68 \% \)
D. About \( 70 \% \)
Subject: Maths
fthe matrix \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{4}\end{array}\right], \) then \( \boldsymbol{I}+\boldsymbol{A}+ \)
\( A^{2}+\ldots \ldots \ldots . \) upto \( A^{\infty}=\ldots \)
\( \mathbf{A} \cdot\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \)
В. \( \left[\begin{array}{cc}\frac{1}{2} & \frac{1}{3} \\ \frac{1}{-2} & 0\end{array}\right] \)
C. \( \left[\begin{array}{ll}\frac{-1}{2} & \frac{1}{-3} \\ \frac{1}{-2} & 0\end{array}\right] \)
D. \( \left[\begin{array}{cc}\frac{1}{2} & \frac{1}{-3} \\ \frac{1}{-2} & 0\end{array}\right] \)
Subject: Maths
Arrange the following equations in decreasing order of their number of solutions in \( [\mathbf{0}, \mathbf{2} \boldsymbol{\pi}] \)
I) \( 3 \sin ^{2} \theta+4 \cos ^{2} \theta=5 \)
II) \( 4 \sin ^{2} \theta+3 \cos ^{2} \theta=\frac{7}{2} \)
|||| \( 3 \mid \sin ^{2} \theta+4 \cos ^{2} \theta=4 \)
A . ॥,|॥,
B. ।, ॥।, III
c. ॥ा,।, ॥
\( \mathbf{D} \cdot\|\|, \) И,
Subject: Maths
The straight line \( 3 x+4 y-12=0 \)
meets the coordinate axes at \( A \) and \( B \).
An equilateral triangle \( A B C \) is
constructed. The possible coordinates
of vertex \( C \) are
This question has multiple correct options
\( ^{\mathbf{A}} \cdot\left(2\left(1-\frac{3 \sqrt{3}}{4}\right), \frac{3}{2}\left(1-\frac{4}{\sqrt{3}}\right)\right) \)
B \( \cdot\left(-2(1+\sqrt{3}), \frac{3}{2}(1-\sqrt{3})\right) \)
\( \left(2(1+\sqrt{3}), \frac{3}{2}(1+\sqrt{3})\right) \)
\( \left(2\left(1+\frac{3 \sqrt{3}}{4}\right), \frac{3}{2}\left(1+\frac{4}{\sqrt{3}}\right)\right) \)
Subject: Physics
The correct relation between \( S, \theta, L \) and
\( C \) for an optically active solution is:
\( \mathbf{A} \cdot S=\theta L C \)
B. \( \theta=S L C \)
\( \mathbf{c} . L=\theta S C \)
\( \mathbf{D} \cdot C=\theta L S \)
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x} \) then in interval \( (\boldsymbol{0}, \boldsymbol{1}) \)
A. local minima of \( f(x) \) exists
B. local maxima of \( f(x) \) exists
c. Global maxima of \( f(x) \) exists
D. Maxima or minima of \( f(x) \) does not exist
Subject: Maths
\( [(\sqrt{\mathbf{3}}+i)(\sqrt{\mathbf{3}}-i)]^{-\mathbf{3} / 2} \)
\( A \cdot \frac{1}{8} \)
B. \( \left(\frac{1}{8}\right)^{1 / 2} \)
\( c \cdot \frac{1}{4} \)
D.
Subject: Biology
Match the following and pick the correct
combination
\( \begin{array}{lllll} & \text { LIST I } & & \text { LIST II } & \\ \text { A } & \text { Kupffer Cells } & \text { 1 } & \begin{array}{l}\text { Small } \\ \text { intestine }\end{array} \\ \text { B } & \beta \text { cells } & \text { 2 } & \text { PCT } \\ \text { C } & \begin{array}{l}\text { Brush border } \\ \text { cell }\end{array} & \text { 3 } & \begin{array}{l}\text { Liver } \\ \text { sinusoids }\end{array} \\ \text { D } & \text { Paneth cells } & 4 & \text { Pituitary } \\ & \text { 5 } & \begin{array}{l}\text { Islets } \\ \text { Langerhans }\end{array}\end{array} \)
A \( \cdot A-5, B-3, C-2, D- \)
B. A- 3, B- 5, C- 2, D-
C. \( A-2, B-5, C-1, D-3 \)
D. A- \( 1, \) B- \( 2, \) C- \( 3, \) D-
Subject: Chemistry
The two gases making the highest relative contribution to the greenhouse
gases are:
A \( \cdot C O_{2} \) and \( C H_{4} \)
B. \( C H_{4} \) and \( N_{2} O \)
c. \( C F C s \) and \( N_{2} O \)
D. \( C O_{2} \) and \( N_{2} O \)
Subject: Physics
A carbon film resistor has colour code
Green Black Violet Gold. The value of the
resistor is:
A \( .50 M \Omega \)
в. 500 М \( \Omega \)
\( \mathrm{c} .500 \pm 5 \% \) М\( \Omega \)
D. \( 500 \pm 10 \% \) M \( \Omega \)
Subject: Chemistry
Copper reacts with \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) to give \( \boldsymbol{N} \boldsymbol{O} \)
and \( N O_{2} \) in molar ratio of 1: 2
\( \boldsymbol{C u}+\boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \longrightarrow \ldots \ldots+\boldsymbol{N} \boldsymbol{O}+ \)
\( N O_{2}+\dots \dots \)
If true enter 1 , if false enter 0 .
Subject: Maths
What percent to the average sales of
branches \( B_{1} B_{2} \) and \( B_{3} \) in 2007 is the
average sales of branches
\( B_{1}, B_{2}, \) and \( B_{6} \) in \( 2006 ? \)
\( A .75 \% \)
В. \( 77 \% \)
\( c .87 .5 \% \)
D. \( 70 \% \)
Subject: Maths
The domain of \( \boldsymbol{f}(\boldsymbol{x})=\frac{\mathbf{1}}{|\boldsymbol{x}|+\boldsymbol{x}} \) is
\( A \cdot(-\infty, 0) \)
B. \( (0, \infty) \)
\( c \cdot(-\infty, 1) \)
D. (-2,-1)
Subject: Maths
The area bounded by \( \boldsymbol{y}=\boldsymbol{x}^{2}, \boldsymbol{y}=[\boldsymbol{x}+ \)
1], \( x \leq 1 \) and the \( y \) -axis is
A \( \cdot \frac{1}{3} \)
B. \( \frac{2}{3} \)
\( c \cdot 1 \)
D.
Subject: Physics
The reading of \( V_{2} \) is :
\( ^{\mathbf{A}} \cdot \frac{-\pi a^{2} B_{0} R_{1}}{R_{1}+R_{2}} \)
\( ^{\mathbf{B}} \cdot \frac{-\pi a^{2} B_{0} R_{2}}{R_{1}+R_{2}} \)
с. \( \frac{\pi a^{2} B_{0} R_{1}}{R_{1}+R_{2}} \)
D. None of these
Subject: Chemistry
Assertion
NaBO \( _{3} / O H^{-} \) can be used for
oxidation of \( C r^{3+} \) to \( C r^{6}+ \)
Reason
In alkaline medium \( N a B O_{3} \) produces
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
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 gaseous compound A reacts by three independent first-order processes (as shown in the figure) with rate constant
\( 2 \times 10^{3}, 3 \times 10^{3} \) and \( 1.93 \times 10^{3} \) sec \( ^{1} \)
for products \( \mathrm{B}, \mathrm{C} \) and \( \mathrm{D} \) respectively. If
initially pure \( A \) was taken in a closed
container with \( P=8 a t m, \) then the
partial pressure of \( \mathrm{B}(\text { in atm }) \) after 100 sec from the start of experiment:
\( \mathbf{A} \cdot 0.288 \)
B. 0.577
c. 1.154
D. noneofthese
Subject: Physics
Which of the following is/are example(s) of isotones?
\( A \cdot_{6} C^{12} \) and \( _{6} C^{13} \)
B . \( _{11} N a^{23} \) and \( _{12} M g^{23} \)
\( \mathbf{c} \cdot_{14} S i^{30} \) and \( _{16} S^{32} \)
D・ \( _{83} B i^{210} \) and \( _{84} P o^{21} \)
Subject: Chemistry
Assertion
lonic compounds have high melting and boiling points.
Reason
lonic compounds are solids and hard due to strong force of attraction between positive and negative ions in their molecules.
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
An aqueous solution of NaCl on
electrolysis gives \( \boldsymbol{H}_{2(g)^{\prime}}, \boldsymbol{C l}_{2(g)} \) and
NaOH according to the reaction
\( \mathbf{2} C l_{(a q)}^{-}+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \mathbf{2} \boldsymbol{O} \boldsymbol{H}_{(a q)}^{-}+\boldsymbol{H}_{2(g)}+ \)
\( C l_{2(g)} \)
A direct current of 25 amperes with a current efficiency of \( 62 \% \) is passed through 20 liters of NaCl solution (20\% by weight). Write down the reactions taking place at the anode and the cathode. How long will it take to produce \( 1 \mathrm{kg} \) of \( C l_{2} ? \) in hrs. (write the value to the nearest integer).
Subject: Maths
Evaluate and write in standard form:
\( (-3+2 i)^{2}-3(3-i)(-2+2 i), \) where
\( i^{2}=-1 \)
A \( .17+36 \)
B. \( 17-36 i \)
c. \( -17-36 i \)
D. \( -17+36 i \)
Subject: Physics
A car is moving with a speed of 40 \( \mathrm{Km} / \mathrm{hr} . \) If the car engine generates 7 kilowatt power, then the resistance in the path of motion of the car will be- -
A. \( 360 N \)
B. \( 630 N \)
c. zero
D. \( 280 N \)
Subject: Physics
Two copper rods \( P, Q \) of thickness in the ratio 2: 5 taken. If both the rods \( P, Q \) of
lengths \( 10 \mathrm{cm} \) are heated to same temperature rise, then the ratio of the linear expansions of \( P \) to that of rod \( Q \) is:
A .2: 5
B. 5: 2
\( c \cdot 1: 1 \)
\( D \cdot 4: \)
Subject: Chemistry
For the gas phase exothermic reaction,
\( A_{2}+B_{2} \rightleftharpoons C_{2} \) carried out in a closed
vessel, the equilibrium moles of \( A_{2} \) can be increased by:
This question has multiple correct options
A. increasing the temperature
B. decreasing the pressure
c. adding inertgas at constant pressure
D. removing some \( C_{2} \)
Subject: Maths
The line \( \frac{x-2}{3}=\frac{y+1}{2}=\frac{z-1}{-1} \)
intersects the curve \( \boldsymbol{x} \boldsymbol{y}=\boldsymbol{c}^{2}, \boldsymbol{z}=\mathbf{0}, \) if
\( \boldsymbol{c}= \)
A. \( 5 \sqrt{5} \)
B. \( 4 \sqrt{5} \)
c. \( \sqrt{5} \)
D. \( 2 \sqrt{5} \)
Subject: Maths
If \( \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{2}, \boldsymbol{x} \leq \mathbf{0}, \boldsymbol{y} \leq \mathbf{0} \) the point at
which maximum value of \( 3 x+2 y \)
attained will be.
\( \mathbf{A} \cdot(0,0) \)
в. \( \left(\frac{1}{2}, \frac{1}{2}\right) \)
D. (2,0)
Subject: Physics
Consider a parallel plate capacitor
having charge \( Q \). Then
This question has multiple correct options
A. There is no force acting on plates of the capacitor
B. The electric field at outer side of plates is zero
c. The electric field between the plates of the capacitor is \( \frac{\sigma}{i n_{0}} \)
D. The force between the plates is given by \( \frac{Q^{2}}{2 A \epsilon_{0}} \)
Subject: Maths
If \( G \) is centroid of \( \triangle A B C, \) then
A \( \cdot \vec{G}=\vec{a}+\vec{b}+\vec{c} \)
B. \( \vec{G}=\frac{\vec{a}+\vec{b}+\vec{c}}{2} \)
c. \( 3 \vec{G}=\vec{a}+\vec{b}+\vec{c} \)
" \( \quad 3 \vec{G}=\frac{\vec{a}+\vec{b}+\vec{c}}{2} \)
Subject: Maths
If
\( \boldsymbol{a}_{1} \boldsymbol{a}_{2} \ldots \ldots \ldots \ldots \boldsymbol{a}_{\boldsymbol{n}} \boldsymbol{\epsilon} \boldsymbol{R}^{+} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{a}_{1} \boldsymbol{a}_{2} \ldots \ldots \boldsymbol{a}_{n}= \)
1 then the least value of \( \left(1+a_{1}+\right. \)
\( \left.\boldsymbol{a}_{1}^{2}\right)\left(\mathbf{1}+\mathbf{1}_{2}+\boldsymbol{a}_{2}^{2}\right) \ldots \ldots \ldots\left(1+\boldsymbol{a}_{n}+\boldsymbol{a}_{n}^{2}\right) \)
is
\( \mathbf{A} \cdot 3^{n} \)
В . \( n 3^{n} \)
\( c \cdot 3^{3 n} \)
D. Data inadequate
Subject: Maths
Solve the equations \( \frac{\mathbf{1 0}}{\boldsymbol{x}+\boldsymbol{y}}+\frac{\mathbf{2}}{\boldsymbol{x}-\boldsymbol{y}}=4, \frac{\mathbf{1 5}}{\boldsymbol{x}+\boldsymbol{y}}-\frac{\mathbf{5}}{\boldsymbol{x}-\boldsymbol{y}}= \)
-2
Subject: Physics
A particle executes SHM in a straight line. The maximum speed of the particle
during its motion is \( V_{\text {max}} \). Then the average speed of the particle during the SHM is :
A \( \cdot \frac{V_{m}}{\pi} \)
в. \( \frac{V_{m}}{2 \pi} \)
c. \( \frac{2 V_{m}}{\pi} \)
D. \( \frac{3 V_{m}}{\pi} \)