AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Assertion: The heat of vaporization of
water and the heat of fusion of water is
numerically different. Reason: When water freezes or
vaporizes, its chemical composition remains unchanged.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
E. Both Assertion and Reason are incorrect
Subject: Maths
Left hand derivative and right hand
derivative of a function \( f(x) \) at a point \( x=a \) are defined as
\( f^{\prime}\left(a^{-}\right)=\lim _{h \rightarrow 0^{+}} \frac{f(a)-f(a-h)}{h}= \)
\( \lim _{h \rightarrow 0^{-}} \frac{f(a)-f(a-h)}{h}= \)
\( \lim _{x \rightarrow a^{+}} \frac{f(a)-f(x)}{a-x} \) respectively
Let \( f \) be a twice differentiable function.
We also know that derivative of an even
function is odd function and derivative
of an odd function is even function.
If \( f \) is even, which of the following is
Right hand derivative of \( \boldsymbol{f}^{\prime} \) at \( \boldsymbol{x}=\boldsymbol{a} \)
A. \( \lim _{h \rightarrow 0^{-}} \frac{f^{\prime}(a)+f^{\prime}(-a+h)}{h} \)
B. \( \lim _{h \rightarrow+} \frac{f^{\prime}(a)+f^{\prime}(-a-h)}{h} \)
c. \( \lim _{h \rightarrow 0} \frac{-f^{\prime}(a)+f^{\prime}(-a+h)}{-h} \)
D. \( \lim _{h \rightarrow 0^{+}} \frac{f^{\prime}(a)+f^{\prime}(-a+h)}{h} \)
Subject: Maths
If \( \int \frac{f(x)}{1-x^{3}} d x= \)
\( \log \left|\frac{x^{2}+x+1}{x-1}\right| \frac{A}{948 \sqrt{3}} \tan ^{-1} \frac{2 x+1}{\sqrt{3}}+ \)
\( C \) then \( A=_{-}- \)
where \( f(x) \) is a polynomial of second
degree in \( x \) such that \( f(0)=f(1)= \)
\( \mathbf{3} f(\mathbf{2})=\mathbf{3} \)
Subject: Maths
If \( f(x)=12 x^{5} \) and \( g(x)=-3 x^{2} \)
determine \( (\boldsymbol{f} \cdot \boldsymbol{g})(-1) \)
\( [\text {Given }:(\boldsymbol{f} \cdot \boldsymbol{g})(\boldsymbol{x})=\boldsymbol{f}(\boldsymbol{x}) \cdot \boldsymbol{g}(\boldsymbol{x})] \)
A . 36
B . 42
\( c \cdot 32 \)
D. -36
Subject: Chemistry
Which of the following is a true
statement?
A. Among the carbonyl compounds, ketones have slightly higher boiling points than the isomeric aldehydes. This is due to the presence of two electron releasing groups around the carbonyl carbon which makes them more polar.
B. Among the carbonyl compounds, ketones have slightly lower boiling points than the isomeric aldehydes. This is due to the presence of two electron releasing groups around the carbonyl carbon which makes them more polar.
C. Among the carbonyl compounds, ketones have slightly lower boiling points than the isomeric aldehydes. This is due to the presence of two electron releasing groups around the carbonyl carbon which makes them less polar.
D. Among the carbonyl compounds, ketones have slightly higher boiling points than the isomeric aldehydes. This is due to the presence of two electron releasing groups around the carbonyl carbon which makes them less polar.
Subject: Chemistry
The reaction \( \mathbf{2} \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{O}_{2} \stackrel{N O(\boldsymbol{g})}{\boldsymbol{\lambda}} \boldsymbol{2} \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) \)
A. Heterogeneous catalysiss
B. Homogegenous catalysiss
c. Enzyme catalysis
D. None of them
Subject: Physics
The equation of a stationary wave is
\( \boldsymbol{Y}=\mathbf{1 0} \sin \frac{\boldsymbol{\pi} \boldsymbol{x}}{\boldsymbol{4}} \cos 20 \boldsymbol{\pi} \boldsymbol{t} . \) The distance
between two consecutive nodes in
meters is -
\( A \cdot 4 \)
B. 2
\( c \cdot 5 \)
D. 8
Subject: Chemistry
Q Type your question-
\( x \)
ethanoate.
Melting \( \quad \) Boiling Compound Formula point / \( \quad \) point
0
\[
\text { methyl } \quad C_{3} H_{6} O_{2} \quad-98
\]
ethanoate
\[
\text { ethyl } \quad C_{4} H_{8} O_{2} \quad-84
\]
ethanoate
A student wished to separate a mixture
of methyl ethanoate and ethy
ethanoate which are miscible with one
another. The easiest method of
separating the two would be by:
A. placing the mixture in a separating funnel, allowing the denser liquid to settle to the bottom, and collecting this liquid from the funnel in the normal way
B. performing a fractional distillation, and collecting two liquids in different vessels
C. freezing the mixture, then allowing this solid to sublime the more volatile substance would be
collected first
D. adding the mixture to water and allowing the more soluble compound to dissolve, The other compound could then the removed by filtration
Subject: Maths
Decide whether sets \( A \) and \( B \) are equal
sets or not. \( \boldsymbol{A}=\mathbf{2}, \mathbf{4}, \mathbf{6}, \mathbf{8}, \boldsymbol{B}=\{\mathbf{x} \mid \mathbf{x} \) is a
positive even natural number less than
9
Subject: Maths
If \( a, b, c \) and \( d \) are real numbers such that and if \( \boldsymbol{A}=\left|\begin{array}{cc}\boldsymbol{a}+\boldsymbol{i b} & \boldsymbol{c}+\boldsymbol{i d} \\ -\boldsymbol{c}+\boldsymbol{i d} & \boldsymbol{a}-\boldsymbol{i b}\end{array}\right| \) then
\( A^{-1}= \)
\( \mathbf{A} \cdot\left|\begin{array}{ll}a+i b & -c-i d \\ c-i d & a-i b\end{array}\right| \)
B. \( \left|\begin{array}{ll}a-i b & c+i d \\ -c+i d & a+i b\end{array}\right| \)
c. \( \left|\begin{array}{cc}a-i b & -c-i d \\ c-i d & a+i b\end{array}\right| \)
D. \( \left|\begin{array}{ll}a+i b & c+i d \\ c-i d & a-i b\end{array}\right| \)
Subject: Maths
In the system of equations \( \boldsymbol{x}+\boldsymbol{y}=\mathbf{4} \boldsymbol{x} \boldsymbol{y} \)
and \( \frac{1}{x}+\frac{2}{y}=10, \) the value of \( x \) and \( y \)
will be
A \( \cdot-\frac{1}{3} \) and \( \frac{1}{6} \)
B \( \cdot \frac{1}{5} \) and \( \frac{1}{6} \)
c. \( -\frac{1}{2} \) and \( \frac{1}{6} \)
D. \( +\frac{1}{3} \) and \( -\frac{1}{2} \)
Subject: Physics
\( \mathbf{A} \)
\( 4 \Omega(\text { or } 4 \text { ohm }) \) wire and \( a 2 \Omega \) (or 2
ohm)wire are connected in parallel. \( \mathbf{A} \)
current of \( 3 A \) passes through the wires. How much current passes through the 2
\( \Omega(\text { or } 2 \text { ohm }) \) wire?
\( A \cdot 2 A \)
B. 4A
\( c \cdot 6 A \)
D. 8A
Subject: Maths
If \( \boldsymbol{B}=\left\{\boldsymbol{y} \mid \boldsymbol{y}^{2}=\boldsymbol{3} \boldsymbol{6}\right\} \) then the \( \operatorname{set} \boldsymbol{B} \) is a
set.
A. Empty
B. singleton
c. Infinite
D. None of the above
Subject: Physics
Assertion
Ratio of isothermal bulk modulus and
adiabatic bulk modulus for a
monoatomic gas at a glven pressure is \( \frac{3}{5} \)
Reason This ratio is equal to \( \gamma=\frac{C_{p}}{C_{v}} \)
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
Assertion
For practical purposes, the earth is
used as a reference at zero potential in
electrical circuits.
Reason
The electric potential of a sphere of
radius \( R \) with charge \( Q \) uniformly distributed on the surface is given by
\( \frac{Q}{4 \pi \varepsilon_{0} R} \)
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 and Reason are correct
Subject: Physics
uniformly distributed charge \( Q \). The rod
has been bent in a \( 120^{\circ} \) circular arc of
radius \( r . \) In terms of \( Q \) and \( r, \) what is
the electric field \( \vec{E} \) due to the rod at
point \( \boldsymbol{P} ? \)
A \( \quad \vec{E}=\frac{3 \sqrt{3} \lambda}{8 \pi^{2} \epsilon_{0} r^{2}} \hat{i} \) where \( \lambda=\frac{2 Q}{3 \pi r} \)
B \( \quad \vec{E}=\frac{3 \sqrt{3} \lambda}{8 \pi^{2} \epsilon_{0} r^{2}} \hat{i} \) where \( \lambda=\frac{3 Q}{2 \pi r} \)
C \( \quad \vec{E}=\frac{3 \sqrt{3} \lambda}{8 \pi^{2} \epsilon_{0} r^{2}} \hat{j} \) where \( \lambda=\frac{2 Q}{3 \pi r} \)
D \( \quad \vec{E}=\frac{3 \sqrt{3} \lambda}{8 \pi^{2} \epsilon_{0} r^{2}} \hat{j} \) where \( \lambda=\frac{3 Q}{2 \pi r} \)
Subject: Maths
Observe the following lists Let \( f(x) \) be
any function
List - I
A) \( f^{\prime}(\mathrm{a})=0 \) and
I) \( f(x) \) is increasing at \( x=a \)
\[
f^{\prime \prime}(\mathrm{a})<0 \text { then }
\]
B) \( f^{\prime}(\mathrm{a})=0 \) and
2) \( f(x) \) has maximum value
\[
f^{\prime \prime}(\mathrm{a})>0 \text { then } \quad \text { at } x=a
\]
3) \( f(x) \) has
C) \( f^{\prime}(a) \neq 0 \) then neither maximum nor minimum
D) \( f^{\prime}(a)>0 \)
4) \( f(x) \) has minimum value at \( x=a \)
5) \( f(x) \) is decreasing at \( x=a \)
\( A \cdot A-4, B-2, C-3, D-5 \)
B. A -2,B -4, C -3, D -1
C. \( A-2, B-4, C-3, D-5 \)
D. A -2,B -4, C -5, D-1
Subject: Physics
A point mass \( M \) moving with a certain velocity collides with a stationary point mass \( \frac{M}{2} . \) The collision is elastic and
one dimension. Let the ratio of the final velocities of \( M \) and \( \frac{M}{2} \) be \( x \). The value of \( x \) is :
\( A \cdot 2 \)
B. 3
\( c \cdot \frac{1}{2} \)
D.
Subject: Chemistry
If \( \mathrm{E} \) is the energy of the combining
atomic orbitals, \( E_{1} \) and \( E_{2} \) are the
energies of molecular orbitals formed,
then:
A. \( E-E_{1}>E_{2}-E \)
B. \( E-E_{1}<E_{2}-E \)
c. \( E-E_{1}=E_{2}-E \)
D. Any one of the above
Subject: Physics
A fielder on the ground throws a ball at an angle of \( 15^{\circ} \) to the horizontal with
velocity \( V_{A} \) at the wicket to dismiss the
batsman. Had he thrown the ball at \( 45^{\circ} \)
with a speed \( V_{B} \) to hit the wicket, then \( \frac{V_{B}}{V_{A}} \) is
\( ^{A} \cdot \frac{1}{\sqrt{3}} \)
в. \( \sqrt{2} \)
c. \( \sqrt{3} \)
D. \( \frac{1}{\sqrt{2}} \)
Subject: Chemistry
Which of the following is NOT
calcination?
\( \mathbf{A} \cdot F e(O H)_{3} \cdot x H_{2} O \rightarrow F e_{2} O_{3}+H_{2} O \)
B. \( C u C O_{3} \cdot C u(O H)_{2} \rightarrow^{2} C u O+C O_{2}+H_{2} O \)
\( \mathbf{c} \cdot C a C O_{3} \rightarrow^{C} a O+C O_{2} \)
D. \( \left(N H_{4}\right)_{2} C O_{3} \rightarrow^{2} N H_{3}+C O_{2}+H_{2} O \)
Subject: Chemistry
Assertion
\( X e F_{6} \) can be used as an oxidising
agent.
Reason
Oxidation state of \( \mathrm{Xe} \) in \( X e F_{6} \) is +6
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 true but Reason is false
D. Assertion is false but Reason is true
Subject: Chemistry
Two isothermals are shown in figure at
temperature \( T_{1} \) and \( T_{2} . \) Which of the
following relations is correct?
A \( \cdot T_{1}>T_{2} \)
в. \( T_{1}<T_{2} \)
\( c \cdot T_{1}=T_{2} \)
\( T_{1}=(1 / 2) T_{2} \)
Subject: Physics
The number of electrons to be removed
from a glass rod in order that it acquires a charge of \( 1 \mu C \) is:
A. \( 6.25 \times 10^{12} \)
B. \( 10^{12} \)
c. \( 6.25 \times 10^{13} \)
D. \( 10^{13} \)
Subject: Physics
From a uniform disc of radius \( R, \) a
circular disc of radius \( \boldsymbol{R} / 2 \) is cut out. The centre of the hole is at \( R / 2 \) from the centre of the original disc. Locate the centre of gravity of the resultant flat body.
A \( \cdot \frac{R}{6} \) from the centre
в. \( \frac{R}{15} \) from the centre
c. \( -\frac{R}{5} \) from the centre
D. \( \frac{R}{20} \) from the centre
Subject: Chemistry
Infrared lamps are used in restaurants to keep the food warm. The infrared
radiation is strongly absorbed by water, raising its temperature and that of the food. If the wavelength of infrared
radiation is assumed to be \( 1500 n m \)
then the number of photons per second of infrared radiation produced by an infrared lamp, that consumes energy at
the rate of \( 100 W \) and is \( 12 \% \) efficient
only, is \( \left(x \times 10^{19}\right) . \) The value of \( x \) is:
\( \left[\text { Given: } \boldsymbol{h}=\mathbf{6 . 6 2 5} \times \mathbf{1 0}^{-\mathbf{3 4}} \boldsymbol{J}-\boldsymbol{s}\right] \)
Subject: Chemistry
What is the oxidation state of \( C r \) in
\( \left[\boldsymbol{C r}\left(\boldsymbol{O}_{2}\right)_{4}\right]^{3-} ? \)
\( A \cdot+3 \)
\( B \cdot+4 \)
\( c \cdot+5 \)
\( D \cdot+6 \)
Subject: Physics
Assertion: For a charged particle moving from point \( P \) to point \( Q, \) the net work done by an electrostatic field on the particle is independent of the path connecting point \( P \) to point \( Q \) Reason: The net work done by a
conservative force on an object moving along a closed loop is zero.
A. If both Assertion arid Reason are correct and Reason the correct explanation of Assertion
B. If both Assertion and Reason are correct, but Rea not the correct explanation of Assertion.
c. If Assertion is correct but Reason is incorrect.
D. If Assertion is incorrect but Reason is correct.
Subject: Maths
The angle which the tangent to a curve at any point \( (x, y) \) on it makes with axis
of \( x \) is \( \tan ^{-1}\left(x^{2}-2 x\right) \) for all values of \( x \)
and it passes through the point (2,0) Determine the point on it whose
ordinate is maximum.
A \( .(2,8 / 3) \)
в. \( (0,4 / 3) \)
c. \( (1,2 / 3) \)
D. \( (-1,4 / 3) \)
Subject: Physics
A ball collides with a smooth fixed wall
with a velocity \( 10 \mathrm{m} / \mathrm{s} \) and returns with
a velocity 6 m/s. Considering oblique
collision, the coefficient of restitution \( e \)
can not be:
A . 0.8
B. 0.6
c. 0.5
D. 0.4
Subject: Maths
\( \operatorname{Let} \mathbf{f}(\mathbf{x})=\mathbf{x}+\tan ^{-1} \mathbf{x}, \mathbf{g}(\mathbf{x})= \)
\( \frac{x}{1+x^{2}}(x>0) \) Then
A \( \cdot \mathrm{f}(\mathrm{x})<\mathrm{g}(\mathrm{x}), \mathrm{x}>0 \)
B. \( f(x)>g(x), x>0 \)
c. \( f(x)<g(x) \) in \( [1, \infty) \)
D. None of these
Subject: Chemistry
A reaction mixture containing \( \boldsymbol{H}_{2}, \boldsymbol{N}_{2} \)
and \( N H_{3} \) has partial pressure
2 atm, 1 atm and 3 atm respectively at
\( 725 K . \) If the value of \( K_{P} \) for reaction
\( N_{2}+3 H_{2} \rightleftharpoons 2 N H_{3} \) is \( 4.28 \times \)
\( 10^{-5} a t m^{-2} \) at \( 725 K \), in which direction
the net reaction will go :
A. Forward
B. Backward
c. No net reaction
D. Direction of reaction cannot be predicted
Subject: Physics
The centripetal force \( \boldsymbol{F} \) acting on a particle moving uniformly in a circle may depend upon mass \( (\boldsymbol{m}), \) velocity
\( (v) \) and radius \( (r) \) of the circle. Derive
the formula for \( \boldsymbol{F} \) using the method of dimensions.
\( \left.^{\mathrm{A}} \cdot_{F}=\frac{m v^{2}}{r} \text { (where } k=1\right) \)
B . \( F=m v^{2} \times r \) (where \( k=1 \) )
C \( \cdot F=m v^{3} \times r \) (where \( k=1 \) )
D. \( F=\frac{m v^{3}}{r} \) (where \( k=1 \) )
Subject: Maths
If \( \vec{a}+\vec{b}+\vec{c}=\overrightarrow{0} \) such that \( |\vec{a}|=3,|\vec{b}|= \)
\( \mathbf{5} \) and \( |\overrightarrow{\boldsymbol{c}}|=\mathbf{7} \)
What is \( \vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a} \) equal to.
A . -83
B. \( \frac{-83}{2} \)
c. 75
D. \( \frac{-75}{2} \)
Subject: Maths
The straight line passing through the point of intersection of the straight lines
\( \boldsymbol{x}-\mathbf{3} \boldsymbol{y}+\mathbf{1}=\mathbf{0} \) and \( \mathbf{2} \boldsymbol{x}+\mathbf{5} \boldsymbol{y}-\mathbf{9}=\mathbf{0} \)
and having infinite slope and and at a distance 2 units from the origin has the
equation
\( \mathbf{A} \cdot x=2 \)
В. \( 3 x+y-1=0 \)
\( \mathbf{c} \cdot y=1 \)
D. None of these
Subject: Physics
A system is shown in the figure. Block \( \boldsymbol{A} \)
moves with velocity \( 10 m / s . \) The speed
of the mass \( B \) will be: \( \left(\sin 15^{\circ}=\right. \)
\( \left.\frac{\sqrt{3}-1}{2 \sqrt{2}}\right) \)
A. \( 10 \sqrt{2} \mathrm{m} / \mathrm{s} \)
в. \( 5 \sqrt{3} \) m/
c. \( \frac{20}{\sqrt{3}} m / s \)
D. \( 10 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
Which one of the following electronic configuration corresponds to the element with maximum electopositive
character?
A \( \cdot[K r] 5 s^{1} \)
в. \( [N e] 3 s^{1} \)
c. \( [A r] 4 s^{1} \)
D. \( [X e] 6 s^{1} \)
Subject: Chemistry
Assertion
Statement-I: Enthalpy of atomization is the heat of reaction \( \boldsymbol{H}_{2} \boldsymbol{O}(\mathrm{I}) \longrightarrow \boldsymbol{H}_{2} \boldsymbol{O} \)
\( (g) \)
Reason
Statement-II : Gaseous molecules are
far apart of each other due to less
attraction.
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
Which of the statements about the
reaction below are incorrect?
\( 2 P b O(s)+C(s) \rightarrow 2 P b(s)+C O_{2}(g) \)
(a) Lead is getting reduced.
(b) Carbon dioxide is getting oxidised
(c) Carbon is getting oxidised.
(d) Lead oxide is getting reduced
A \( \cdot(a) \) and \( (b) \)
B. (a) and (c)
\( c \cdot(a),(b) \) and \( (c) \)
D. All
Subject: Maths
For \( \boldsymbol{X} \rightarrow \boldsymbol{B}(\boldsymbol{n}, \boldsymbol{p}), \) if \( \boldsymbol{n}=\mathbf{2 5}, \boldsymbol{E}(\boldsymbol{x})=\mathbf{1 0} \)
then \( S . D .(x)= \)
A \( .2 \sqrt{6} \)
B. 2.4
c. \( 2 \sqrt{10} \)
D. \( \sqrt{2.4} \)
Subject: Physics
Assume that life has existed on the
surface of the moon, without changing its present acceleration due to gravity
i.e., one sixth that on the surface of the
moon. If 5 kg weight of sugar is purchased on the Earth and the Moon,
how many cups of tea can be made out
of it on the Earth and the Moon
respectively? Note, From 100 g of sugar 10 cups of tea can be mode on the earth. \( \left(g=10 \mathrm{m} \mathrm{s}^{-2}\right) \)
Subject: Chemistry
Given \( : \boldsymbol{H}_{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{O}_{2}+\boldsymbol{2} \boldsymbol{H}^{\oplus}+\boldsymbol{2} \boldsymbol{e}^{-} \)
\( \boldsymbol{e}^{\oplus}=-\mathbf{0 . 6 9} \boldsymbol{V} \)
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2}+\boldsymbol{2} \boldsymbol{H}^{\oplus}+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O} \)
\( \boldsymbol{E}^{\oplus}=\mathbf{1} . \mathbf{7 7} \boldsymbol{V} \)
\( \mathbf{2} \boldsymbol{I}^{\ominus} \rightarrow \boldsymbol{I}_{\mathbf{2}}+\mathbf{2} \boldsymbol{e}^{-} \)
\( \boldsymbol{E}^{\ominus}=-\mathbf{0 . 5 3 5} \boldsymbol{V} \)
Assertion: \( H_{2} O_{2} \) acts as an oxidizing
agent for \( \boldsymbol{I}^{\ominus} \)
Reason: \( \boldsymbol{E}^{\ominus} \) is positive.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Assertion is false but Reason is true Both Assertion and Reason are false
Subject: Physics
If it is assumed that \( _{92}^{235} U \) decays only by emitting \( \alpha- \) and \( \beta \) -particles, the possible product of the decay is
A \( \cdot \frac{225}{89} \mathrm{Ac} \)
B . \( \frac{297}{A c} \)
\( \mathbf{C} \cdot_{89}^{230} A c \)
D・ \( _{89}^{23} A C \)
Subject: Chemistry
Which of the following statements are
true about the alkali metals?
This question has multiple correct options
A. All alkali-metal salts impart a characteristic colour to the Bunsen flame.
B. Among LiOH, CsOH, KOH, and RbOH, CsOH has the highest solubility in water.
C. Among the alkali metals, cesium is the most reactive.
D. The reducing character of the alkali metal hydrides follow the order: \( L i H>N a H>K H>R b H>C s H \)
Subject: Chemistry
Ordinary gasoline (petrol) that is used as fuel cars, scooters and automobiles
contain many different chemicals that
are added in small quantities, each performing an important role. Some of these are mentioned here. Which of the
option is false?
A. Soaps used for removing particles of grease from petrol tanks ensure a free flow of petrol
B. Anti-icing agents are used for depressing the freezing point of particles of ice
C. Anti-rust agents are used for protecting against corrosion by water
sticking on the walls of the carbureter
Subject: Physics
When the current in a wire is \( 1 A \), the
drift velocity is \( 1.2 \times 10^{-4} \mathrm{ms}^{-1} . \) The
drift velocity when current becomes 5 A
is
A \( \cdot 1.2 \times 10^{-4} \mathrm{ms}^{-1} \)
В. \( 3.6 \times 10^{-4} \mathrm{ms}^{-1} \)
\( \mathbf{c} \cdot 6 \times 10^{-4} m s^{-1} \)
D. \( 4.8 \times 10^{-4} \mathrm{ms}^{-1} \)
Subject: Maths
\( \sqrt{\mathbf{2}}+\sqrt{\mathbf{2}}+\sqrt{\mathbf{2}}+\ldots+\boldsymbol{n} \) terms
\( \mathbf{2} \cos \frac{\boldsymbol{\pi}}{\mathbf{2}^{n+1}}, \boldsymbol{n} \boldsymbol{\epsilon} \boldsymbol{N} \)
Subject: Physics
What type of curve do we get, if \( x^{2} \) and
\( v^{2} \) are plotted for a particle executing \( \mathrm{SHM}, \mathrm{x} \) and \( \mathrm{v} \) are the position and velocity of the particle:
A . Circle
B. Straight line
c. Ellipse
D. Rectangle
Subject: Physics
Two rings of the same radius \( R \) and
mass \( M \) are placed such that their centres coincide and their planes are perpendicular to each other. The moment of inertia of the system
about an axis passing through the common centre and perpendicular to the plane of one of the rings is:
\( ^{A} \cdot \frac{M R^{2}}{2} \)
в. \( M R^{2} \)
c. \( \frac{3 M R^{2}}{2} \)
D. \( 2 M R^{2} \)
Subject: Chemistry
Calculate the percentage ionization of
\( 0.01 \mathrm{M} \) acetic acid in \( 0.1 \mathrm{M} \) HCl. \( \boldsymbol{K}_{\boldsymbol{a}} \) of
acetic acid is \( 1.8 \times 10^{-5} \)
A . \( 0.18 \% \)
B. 0.018\%
c. \( 1.8 \% \)
D. 18\%
Subject: Physics
\( \boldsymbol{y}(\boldsymbol{x}, \boldsymbol{t})=\mathbf{0 . 8} /\left[(\boldsymbol{4} \boldsymbol{x}+\boldsymbol{5} \boldsymbol{t})^{2}+\mathbf{5}\right] \)
represents a moving pulse, where \( x \) and
\( y \) are in meter and \( t \) in second. Then
This question has multiple correct options
A. pulse is moving in \( +x \) direction
B. in \( 2 s \) it will travel a distance of 2.5 m
c. its maximum displacement is 0.16 m
D. it is symmetric pulse
Subject: Chemistry
The electron configuration for the noble gas with the highest first ionization
energy is:
A \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{3} 3 p^{6} \)
B . \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{1} \)
c. \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} \)
D. \( 1 s^{2} \)
E \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 p^{1} \)
Subject: Maths
Calculate the probability that a number selected at random from the set \{ \( \mathbf{2}, \mathbf{3}, \mathbf{7}, \mathbf{1 2}, \mathbf{1 5}, \mathbf{2 2}, \mathbf{7 2}, \mathbf{1 0 8}\} \) will be
divisible by both 2 and 3
A
в. \( \frac{3}{8} \)
\( c \cdot \frac{3}{5} \)
D.
\( E \cdot 7 \)
8
Subject: Maths
Prove that \( \boldsymbol{x}^{4}+\boldsymbol{4}=(\boldsymbol{x}+\mathbf{1}+\boldsymbol{i})(\boldsymbol{x}+ \)
\( \mathbf{1}-\boldsymbol{i})(\boldsymbol{x}-\mathbf{1}+\boldsymbol{i})(\boldsymbol{x}-\mathbf{1}-\boldsymbol{i}) \)
Subject: Physics
In a Geiger-Marsden experiment, calculate the distance of closest
approach to the nucleus of \( Z=80 \)
when \( \alpha \) -particle of \( 8 M e V \) energy
impinges on it before it comes momentarily to rest and reverses its direction. How will the distance of
closest approach be affected when the
kinetic energy of the \( \alpha \) -particle is doubled?
Subject: Maths
\( \boldsymbol{p}: \) He is hard working.
\( \boldsymbol{q}: \) He will win
The symbolic form of "He is hard working then he will win", is
A \( . p \vee q \)
в. \( p \wedge q \)
\( \mathbf{c} \cdot p \Rightarrow q \)
D. \( q \Rightarrow p \)
Subject: Maths
Find \( F(x) \) from the \( \operatorname{given} F^{\prime}(x) \) \( F^{\prime}(x)=2 \sin 5 x+3 \cos (x / 2) \) which is
zero for \( \boldsymbol{x}=\boldsymbol{\pi} / \mathbf{3} \)
Subject: Chemistry
Complete the following nuclear
equation:
\( _{26}^{69} \mathrm{Fe} \rightarrow \beta+_{-}- \)
\( \mathbf{A} \cdot_{25}^{58} \mathrm{Mn} \)
B . \( \frac{58}{27} \mathrm{Co} \)
\( \mathbf{C} \cdot_{25}^{59} \mathrm{Mn} \)
\( D \cdot \frac{59}{27} \mathrm{Co} \)
E \( . \begin{array}{c}60 \mathrm{Mn} \\ 25\end{array} \)