AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
\( f(x) \) is a function defined on the set of
Real Numbers \( \boldsymbol{f}(\mathbf{1})=\mathbf{1} \)

Also, \( f(x+5) \geq f(x)+5 \) for all \( x \epsilon R \)
and \( f(x+1) \leq f(x)+1 \)
If \( , g(x)=(f(x))^{2}-f(x) \)
This question has multiple correct options
A \( \cdot g(2019)>(2019)^{2} \)
B . \( g(2019)<(2019)^{2} \)
C \( \cdot g(2019)=(2019)^{2} \)
D. \( g(2019)=2019 \times 2018 \)
Subject: Chemistry
During discharging of a lead storage
battery, which of the following is/are
true?
This question has multiple correct options
\( \mathbf{A} \cdot H_{2} S O_{4} \) is produced
B. \( H_{2} O \) is consumed
\( \mathrm{C} \cdot P b S O_{4} \) is formed at both electrodes
D. Density of electrolytic solution decreases
Subject: Physics
which is free to rotate about the smooth
vertical hinge passing through the center and perpendicular to the plate, is lying on a smooth horizontal surface. A
particle of mass \( m \) moving with speed
\( u^{\prime} \) collides with the plate and sticks to
it as shown in figure. The angular velocity of the plate after collision will
be:
\( A \cdot \frac{12}{5} \)
B. \( \frac{12}{19} \)
c. \( \frac{3}{-} \underline{u} \)
\( 2 a \)
D. \( \frac{3}{5} \)
Subject: Physics
From the understanding of cartesian sign convention for reflection by spherical mirror, students took part in group discussion for FA - 1 in classroom.
Who is wrong in the group discussion? Alpesh : All the distances are measured
from the pole of a mirror parallel to the
principal axis. Beena: The distances measured in the
direction of incident ray are taken
positive. Chamak: The height measured upward
and perpendicular to principal axis is taken negative.
Daksha : The height measured downward and perpendicular to principal axis is taken as positive.
A. Champak and Daksha
B. Only Champak
c. Alpesh and Beena
D. only Daksha
Subject: Chemistry
When \( N O \) and \( N O_{2} \) are mixed, the
following equilibrium are readily obtained, \( 2 N O_{2} \rightleftharpoons N_{2} O_{4}, K_{p}= \)
\( 6.8 a t m^{-1} \) and \( N O+N O_{2} \rightleftharpoons N_{2} O_{3} . \) In
an experiment when \( N O \) and \( N O_{2} \) are
mixed in the ratio of \( 1: 2, \) the final total
pressure was 5.05 at \( m \) and the partial
pressure of \( N_{2} O_{4} \) was \( 1.7 a t m \)
Calculate
(a) the equilibrium partial pressure of \( N O,(b) K_{p} \) for: \( N O+ \)
\( N O_{2} \rightleftharpoons N_{2} O_{3} \)
A \( .3 .43 a t m^{-1} \)
B. \( 5.63 a t m^{-1} \)
c. \( 7.43 a t m^{-1} \)
D. None of these
Subject: Physics
Two coherent point sources \( S_{1} \) and \( S_{2} \) vibrating in phase emit light of wavelength \( \lambda \). The separation between the sources is \( 2 \lambda \). Consider a line
passing through \( S_{2} \) and perpendicular
to the line \( S_{1} S_{2} \). What is the smallest
distance from \( S_{2} \) where a minimum of
intensity occurs?
Subject: Maths
In a triangle \( A B C \), a straight line parallel to \( B C \) intersects \( A B \) and \( A C \)
at point \( D \) and \( E \) respectively. If the
area of \( A D E \) is one-fifth of the area of
\( A B C \) and \( B C=10 \mathrm{cm}, \) then \( D E \)
equals
A . \( 2 \mathrm{cm} \)
в. \( 2 \sqrt{5} \) ст
\( c .4 \mathrm{cm} \)
D. \( 4 \sqrt{5} \mathrm{cm} \)
Subject: Physics
What is the reason to operate the
photodiodes in reverse bias?
A. fractional change due to the photo-effects on the majority carrier dominated forward bias current is more easily measurable than the fractional change in the reverse bias current.
B. reverse bias is more efficient than forward bias.
C. fractional change due to the photo-effects on the minority carrier dominated reverse bias current is more easily measurable than the fractional change in the forward bias current.
D. reverse bias configuration result in larger amount of current \( (\operatorname{in} \mu A) \)
Subject: Chemistry
\( \Delta_{f} G^{o} \) at \( 500 K \) for substance 'S' in liquid state and gaseous state are \( +100.7 k c a l \) mol \( ^{-1} \) and
\( +103 k c a l m o l^{-1}, \) respectively
Vapour pressure of liquid 'S' at \( 500 K \)
is approximately equal to: \( (\boldsymbol{R}= \)
\( \left.2 \operatorname{cal} K^{-1} m o l^{-1}\right) \)
A. 100 atm
B. 1 atm
c. 10 atm
D. 0.1 atm
Subject: Physics
Find a vector in thedirection of \( 5 \hat{i}-\widehat{j}+ \)
\( 2 \widehat{k} \) which has magnitude 8 units.
A \( \cdot \frac{8}{\sqrt{30}} \hat{i}-\frac{40}{\sqrt{30}} \hat{j}+\frac{16}{\sqrt{30}} \widehat{k} \)
B. \( \frac{16}{\sqrt{30}} \hat{i}+\frac{8}{\sqrt{30}} \hat{j}-\frac{40}{\sqrt{30}} \widehat{k} \)
c. \( \frac{40}{\sqrt{30}} \hat{i}-\frac{8}{\sqrt{30}} \hat{j}+\frac{16}{\sqrt{30}} \widehat{k} \)
D. None
Subject: Maths
The coefficient of \( x^{n} \) in the expansion of \( \frac{1}{(1-x)(1-2 x)(1-3 x)} \) is
A \( \cdot \frac{1}{2}\left(2^{n+2}-3^{n+3}+1\right) \)
B. \( \frac{1}{2}\left(3^{n+2}-2^{n+3}+1\right) \)
c. \( \frac{1}{2}\left(2^{n+3}-3^{n+2}+1\right) \)
D. none of these
Subject: Physics
A rigid diatomic ideal gas undergoes an adiabatic process at room temperature,. The relation between
temperature and volume of this process
is \( \boldsymbol{T} \boldsymbol{V}^{\boldsymbol{x}}= \) constant, then \( \boldsymbol{x} \) is :
A \( \cdot \frac{5}{3} \)
B. \( \frac{2}{5} \)
\( c \cdot \frac{2}{3} \)
D. \( \frac{3}{5} \)
Subject: Maths
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be given by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( x^{2}+3 . \) Find \( (\text { a })\{x: f(x)=28\} \)
the pre-images of 39 and 2 under
Subject: Chemistry
For a reversible reaction, \( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{C}+ \)
\( D, \) the graph for rate of reaction with
time is given below. Mark the terms \( (p),(q) \) and \( (r) \)
A \( \cdot(p)- \) rate of backward reaction
(q) - rate of forward reaction
(r) - equilibrium
B. (p) - rate of forward reaction,
(q) - rate of backward reaction, (r) - equilibrium
c. (p) - concentration of products
(q) - concentration of reactants, (r) - rate of reaction
D. (p) - instantaneous rate of reaction,
(q) - variation of rate, (r) - average rate of reaction
Subject: Physics
In a smooth stationary cart of length \( d \)
a small block is projected along it's length with velocity v towards front.
Coefficient of restitution for each
collision is e. The cart rests on a smooth
ground and can move freely. The time taken by block to come to rest w,r.t cart
is
\( A \)
B. \( \frac{e d}{(l+e) v} \)
\( c \cdot d \)
D. infinite
Subject: Chemistry
According to Charles's law:
This question has multiple correct options
\( \mathbf{A} \cdot(d V / d T)_{P}=K \)
\( \mathbf{B} \cdot(d V / d T)_{P}=-K \)
\( \mathbf{C} \cdot(d V / d T)_{P}=-K / T \)
D. \( V \propto T \)
Subject: Physics
Ashokbhai goes to an electric shop to buy an electric bulb to obtain light in a small room of his home. Which of the
following statement is scientifically
correct
A. Give bulb of \( 60 \mathrm{V} \)
B. Give bulb of \( 60 \mathrm{J} / \mathrm{s} \)
c. Give bulb of \( 60 A \)
D. Give bulb of \( 60 \mathrm{W} \)
Subject: Physics
A particle is released from rest from a
tower of height 3 h.The ratio of times to
fall equal height h,i.e., \( t_{1}: t_{2}: t_{3} \) is
\( \mathbf{A} \cdot \sqrt{3}: \sqrt{2}: 1 \)
B. 3: 2: 1
\( \mathbf{C} \cdot 9: 4: 1 \)
D. \( 1:(\sqrt{2}-1):(\sqrt{3}-\sqrt{2}-1) \)
Subject: Physics
A radioactive nucleus can decay by two different processes. The mean value
period for the first process is \( t_{1} \) and that
for the second process is \( t_{2} \). The effective mean value period for the two
processes is
A \( \cdot \frac{t_{1}+t_{2}}{2} \)
B . \( t_{1}+t_{2} \)
c. \( \sqrt{t_{1} t_{2}} \)
D. \( \frac{t_{1} t_{2}}{t_{1}+t_{2}} \)
Subject: Maths
If \( \boldsymbol{A}=\{\mathbf{0}, \mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}\} \) and relation \( \boldsymbol{R} \)
defined by \( a R b \) such that \( 2 a+b=10 \)
then \( R^{-1} \) equals
A \( \cdot\{(4,3),(2,4),(5,0)\} \)
B - \{(3,4),(4,2),(5,0)\}
c. \{(4,3),(2,4),(0,5)\}
D \( \cdot\{(4,3),(4,2),(5,0)\} \)
Subject: Biology
Which of the following statements is or are not true?
1. Cork cambium is otherwise called as
phellogen.
2. Cork is otherwise called as phellem.
3. Secondary cortex is otherwise called
as periderm.
4. Cork cambium, cork and secondarycortex are collectively called as phelloderm
\( A \cdot 3 \) and 4 only
B . 1 and 2 only
c. 2 and 3 only
D. 2 and 4 only
Subject: Maths
If \( f(x)=\frac{x^{2}}{2}, 0 \leq x<1 \) and \( f(x)= \)
\( \frac{2 x^{2}-2 x+3}{2} ; 1 \leq x \leq 2, \) then
\( \lim _{x \rightarrow 1} f(x)= \)
A \( \cdot \frac{1}{2} \)
B. \( \frac{3}{2} \)
c. does not exist
D. \( -\frac{1}{2} \)
Subject: Physics
Assertion: gases are characterised with
two coefficients of expansion
Reason: when heated both volume and
pressure increase with the rise in
temperature
A. Both assertion (A) and reason (R) are correct and \( \mathrm{R} \) gives the correct explanation
B. Both assertion (A) and reason (R) are correct but R doesnt give the correct explanation
c. \( A \) is true but \( R \) is false
D. A is false but R is true
Subject: Physics
The radius of a planet is \( R_{1} \) and \( a \)
satellite revolves around it in a radius \( \mathrm{R} \)
2
Time period of revolution is \( T . \) Find the
acceleration due to gravity.
\( ^{\mathbf{A}} \cdot \frac{4 \pi^{2} R_{2}^{3}}{R_{1}^{2} T^{2}} \)
B. \( \frac{4 \pi^{2} R_{2}^{2}}{R_{1} T^{2}} \)
\( ^{\mathrm{c}} \cdot \frac{2 \pi^{2} R_{2}^{3}}{R_{1} T^{2}} \)
D. \( \frac{4 \pi^{2} R_{2}}{T^{2}} \)
Subject: Physics
The figure shows the various positions (labelled by subscripts) of small
magnetised needles \( P \) and \( Q \). The arrows
show the direction of their magnetic
movement.configuration corresponds to
the lowest potential energy among all
the configurations shown
A . \( P Q_{3} \)
в. \( P Q_{4} \)
\( c \cdot P Q_{5} \)
D. \( P Q_{6} \)
Subject: Physics
A block of mass \( m \) containing a net positive charges \( q \) is placed on a smooth horizontal table which
terminates in a ventricles wall as shown
in figure \( (29 . E 2) . \) The distance of the
block from the wall is \( d . \) A horizontal
electric field \( E \) towards right is
switched on. Assuming elastic collisions ( if any) find the time periods of the resulting oscillatory motion. Is it a simple harmonic motion?
Subject: Physics
Photoelectric effect supports quantum
nature of light because
This question has multiple correct options
A. there is a maximum frequency of light below which no photoelectrons are emitted
B. the maximum kinetic energy of photoelectrons depends only on the frequency of light and not on its intensity
C. even when the metal surface is faintly illuminated, the photoelectrons leave the surface immediately
D. electric charge of the photoelectrons is quantized
Subject: Physics
Two wires \( X \) and \( Y \) are made of different
metals. The Young modulus of wire \( X \) is
twice that of wire Y. The diameter of
wire \( X \) is half that of wire \( Y \).

The wires are extended with the same
strain and obey Hooke's law.
What is the ratio
A \( \cdot \frac{1}{8} \)
B. \( \frac{1}{2} \)
\( c \cdot 1 \)
D.
Subject: Maths
If \( f(x)=\frac{x+1}{x-1} ; \) then \( f\left(\frac{1}{2}\right)= \)
A \( \cdot \frac{1}{2} \)
B. \( -\frac{1}{2} \)
\( c \cdot \frac{3}{2} \)
D. -
Subject: Maths
\( \operatorname{Let} U=\{1,2,3,4,5,6,7,8,9\}, A= \)
\( \{1,2,3,4\}, B=\{2,4,6,8\} \) and \( C= \)
\( \{3,4,5,6\} . \) Find (i) \( A^{\prime}(\text { ii }) B^{\prime}(\text { iii) }(A \cup \)
\( C)^{\prime}(\text { iv })(A \cup B)^{\prime}(v)\left(A^{\prime}\right)^{\prime}\left(\text { vi) }(B-C)^{\prime}\right. \)
Subject: Maths
If the d.rs of \( O A \) and \( O B \) are 1,-1,-1
and \( 2,-1,1, \) then the d.cs of the line perpendicular to both \( \boldsymbol{O} \boldsymbol{A} \) and \( \boldsymbol{O B} \) are
в. -2,-3,1
c. \( \frac{-2}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{1}{\sqrt{14}} \)
D. \( \frac{2}{\sqrt{41}}, \frac{3}{\sqrt{41}}, \frac{-1}{\sqrt{41}} \)
Subject: Physics
A ballon filled with air at \( 47^{\circ} \mathrm{C} \) has volume
of 3 litre. If ballon is kept in a room its
volume becomes 2.7 litre, the
temperature of the room is :
\( \mathbf{A} \cdot 5^{\circ} \mathbf{C} \)
B. \( 10^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot 15^{\circ} \mathrm{C} \)
D. \( 20^{\circ} \mathrm{C} \)
Subject: Physics
A composite wire consits of a steel wire of length \( 1.5 ~ m \) and a copper wire of
length \( 2.0 m, \) with a uniform cross-
sectional area of \( 2.5 \times 10^{-5} m^{2} . \) It is
loaded with a mass of 200 kg. Find the
extension produced. Young's modulus of copper is \( 1.0 \times 10^{11} N m^{-2} \) and that of
steel is \( 2.0 \times 10^{11} N m^{-2} \)
Take \( \boldsymbol{g}=\mathbf{9 . 8} \boldsymbol{m} \boldsymbol{s}^{-2} \)
Subject: Chemistry
The hybridization of iodine in \( \mathbf{I F}_{5} \) is :
\( A \cdot s p^{3} d \)
B \( \cdot \operatorname{sp}^{3} \mathrm{d}^{2} \)
\( \mathbf{c} \cdot \mathbf{s p}^{3} \mathrm{d}^{3} \)
\( D \cdot s p^{3} \)
Subject: Chemistry
\( X e F_{4} \) reacts with water \( a t-80^{\circ} C \) to
give:
A \( . \quad X e O F_{2} \)
в. \( X e O F_{4} \)
\( \mathbf{c} \cdot X e O_{3} \)
D. \( X e O_{2} F_{2} \)
Subject: Physics
Marbles, each of mass \( 1 \mathrm{g} \) are dropped from a height of \( 10 \mathrm{m} \) on to a horizontal
smooth metal surface at the rate of 50
per second. Find the force on the surface. If the surface were inclined to
the horizontal at an angle of \( 60^{\circ}, \) what would be force on it be? Assume
collisions to be elastic. \( g=9.8 m / s^{2} \)
A. \( 1.2 N ; 0.7 N \)
в. \( 1.4 N ; 0.5 N \)
c. \( 1.4 N ; 0.7 N \)
D. \( 0.4 N ; 0.4 N \)
Subject: Physics
A point charge \( q \) is at centre of an
unchanged spherical conducting shell
of inner radius \( a \) and outer radius \( b \)
Work needed to move the charge out to
infinity will be
\( ^{\mathbf{A}} \cdot \frac{q^{2}}{4 \pi \varepsilon_{0}}\left(\frac{1}{a}-\frac{1}{b}\right) \)
B. \( \frac{1}{8 \pi \epsilon_{0}} \frac{q^{2}}{a} \)
\( ^{\mathbf{c}} \cdot \frac{q^{2}}{8 \pi \epsilon_{0}}\left[\frac{1}{b}-\frac{1}{a}\right] \)
\( ^{\mathrm{D}} \cdot \frac{q^{2}}{8 \pi \epsilon_{0}}\left[\frac{1}{a}-\frac{1}{b}\right] \)
Subject: Physics
A voltmeter and an ammeter are joined
in series to an ideal cell, giving readings \( \mathrm{V} \) and \( \mathrm{A} \) respectively. If \( \mathrm{a} \)
resistance equal to the resistance of the ammeter if now joined in parallel to
the ammeter
This question has multiple correct options
A. V will no change
B. V will increase slightly
c. A will become exactly half of its initial vale
D. A will become slightly more than half of its initial value
Subject: Physics
A student wishes to demonstrate
electromagnetic induction. He has a magnet and connecting wires.
Which other apparatus does he need? \( \boldsymbol{\gamma}=\boldsymbol{n e e d e d}, \quad \boldsymbol{X}=\boldsymbol{n o t n e e d e d} \)
A. Voltmeter - \( \gamma \), battery -
B. Voltmeter - , battery - \( X \)
c. voltmeter - \( X \), battery -
D. voltmeter - \( X \), battery \( -X \)
Subject: Chemistry
Name the types of isomerism shown by the following pairs of compounds:
(i) \( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]\left[\boldsymbol{P t} \boldsymbol{C l}_{4}\right] \) and
\( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]\left[\boldsymbol{C u} \boldsymbol{C l}_{4}\right] \)
(ii) \( \left[\boldsymbol{C o}(\boldsymbol{P n})_{2} \boldsymbol{C l}_{2}\right]^{+} \) and \( \left[\boldsymbol{C o}(\boldsymbol{t n})_{2} \boldsymbol{C l}_{2}\right]^{+} \)
Subject: Physics
A wire of radius \( 1 \mathrm{mm} \) is bent in the
form of a circle of radius \( 10 \mathrm{cm} . \) The
bending moment will be \( (Y=2 \times \) \( \left.\mathbf{1 0}^{\mathbf{1 1}} \mathbf{N} / \boldsymbol{m}^{\mathbf{2}}\right) \)
\( A \cdot 3.14 \mathrm{N} / \mathrm{m} \)
B. \( 6.28 \mathrm{N} / \mathrm{m} \)
c. \( 1.57 \mathrm{N} / \mathrm{m} \)
D. 15.7 N/m
Subject: Maths
If \( I^{2}+\mathbf{m}^{2}=1, \) then the max values of
\( \boldsymbol{I}+\mathbf{m} \) is
\( A \cdot 1 \)
B. \( \sqrt{2} \)
c. \( \frac{1}{\sqrt{2}} \)
D. 2
Subject: Chemistry
One mole of \( N_{2} O_{5}(g) \) at \( 300 \mathrm{K} \) is left in a closed container under one atm. It is
heated to \( 600 \mathrm{K} \) when \( 20 \% \) by mass of
\( N_{2} O_{5}(g) \) decomposes to \( N O_{2}(g) . \) The resultant pressure is:
A . 1.2 atm
B. 2.4 atm
c. 2.0 atm
D. 1.0 atm
Subject: Chemistry
Calculate the wavelength and energy of radiation emitted for the electronic
transition from infinite to stationary
state of hydrogen atom. (Given, \( \boldsymbol{R}= \) \( \mathbf{1} . \mathbf{0} \mathbf{9 6 7} \mathbf{8} \times \mathbf{1 0}^{\mathbf{7}} \mathbf{m}^{-\mathbf{1}}, \mathbf{h}=\mathbf{6 . 6 2 5 6} \times \)
\( 10^{-34} J-s \) and \( c=2.9979 \times 10^{8} m s^{-1} \)
)
Subject: Chemistry
Assertion
Chloride ions, \( C l^{-}, \) can be oxidized to
produce chlorine gas.
Reason
Two chloride ions gives up an electron
to form \( C l_{2} \)
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: Physics
A brass disc and a carbon disc of same
radius are assembled alternatively to make a cylindrical conductor. The resistance of the cylinder is independent of the temperature. The ratio of thickness of the brass disc to
that of the carbon disc is \( \alpha \) is
temperature coefficient of resistance \( \& \)
Neglect linear expansion
A \( \cdot \frac{\alpha_{C} \rho_{C}}{\alpha_{B} \rho_{B}} \)
в. \( \frac{\alpha_{C} \rho_{B}}{\alpha_{B} \rho_{C}} \)
c. \( \frac{\alpha_{B} \rho_{C}}{\alpha_{C} \rho_{B}} \)
D. \( \frac{\alpha_{B} \rho_{B}}{\alpha_{C} \rho_{C}} \)
Subject: Chemistry
Select the correct statement(s) about
NHE.
This question has multiple correct options
\( \mathbf{A} \cdot E^{\ominus} \) of \( \mathrm{NHE} \) is arbitrarilly assumed to be zero.
B. \( E^{\ominus} \) of NHE is equal to zero.
\( \mathbf{C} \cdot \) NHE refers as \( P t, H_{2}(g) \mid H_{a=1}^{\oplus}(a q) \) at \( 25^{\circ} C \)
D. NHE is very susceptible to dissolved \( O_{2}, H_{2} S \), and all other reducing agents.
Subject: Chemistry
\( B e^{+3} \) and a proton are accelerated by the same potential,their de-Broglie wavelengths have the ratio:
(Assume mass of proton = mass of
neutron)
\( ^{A} \cdot \frac{1}{2 \sqrt{2}} \)
B. 1: 4
c. 1: 1
D. \( 1: 3 \sqrt{3} \)
Subject: Chemistry
Lindane can be obtained by the reaction
of benzene with:
\( \mathbf{A} \cdot C H_{3} C l / \) anhy. \( A l C l_{3} \)
B. \( C l_{2} \) /sunlight
c. \( C_{2} H_{5} \) Ilanhy. \( A l C l_{3} \)
D. \( C H_{3} C O C l / A l C l_{3} \)
Subject: Chemistry
Calculate the amount of oxygen at 0.20 atm dissolved in 1 kg of water at 293 K. The Henry's law constant for oxygen is
\( 4.58 \times 10^{4} \) atmosphere at \( 293 \mathrm{K} \)
\( \mathbf{A} \cdot 7.07 \times 10^{-6} \mathrm{kg} \)
В. \( 7.27 \times 10^{-6} \mathrm{kg} \)
C \( .7 .57 \times 10^{-6} \mathrm{kg} \)
D. \( 7.77 \times 10^{-6} \mathrm{kg} \)
Subject: Physics
When a mass is suspended from the end of a wire the top end of which is attached to the roof of the lift, the
extension is \( e \) when the lift
is stationary. If the lift moves up with a constant acceleration \( \boldsymbol{g} / \mathbf{2}, \) the
extension of the wire would be
A \( \cdot \frac{2 e}{3} \)
в. \( \frac{3 e}{2} \)
\( c \cdot 2 e \)
D. \( 3 e \)
Subject: Chemistry
Determine the equilibrium constant of the following reaction at \( 298 K: \) \( 2 F e^{3+}+S n^{2+} \rightarrow 2 F e^{2+}+S n^{4+} \)
(Given: \( \boldsymbol{E}_{\boldsymbol{S n}^{4+} / \boldsymbol{S n}^{2+}}^{\circ}= \)
\( \mathbf{0 . 1 5} \)volt; \( \boldsymbol{E}_{\boldsymbol{F} e^{3+} / \mathbf{F e}^{2+}}^{\circ}=\mathbf{0 . 7 7 1} \mathbf{v o l t} \mathbf{t} \)
Subject: Chemistry
Assertion
Solubility product of \( B a F_{2} \) will increase
on dilution.
Reason
Solubility of \( B a F_{2} \) will not change in
changing temperature
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 \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{0} & \mathbf{1} \\ \mathbf{1} & \mathbf{0}\end{array}\right], \) then \( \boldsymbol{A}^{4}= \)
A. \( \left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \)
в. \( \left[\begin{array}{ll}1 & 1 \\ 0 & 0\end{array}\right] \)
c. \( \left[\begin{array}{ll}0 & 0 \\ 1 & 1\end{array}\right] \)
D. \( \left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right] \)
Subject: Physics
The maximum refractive index of a
prism which permits passage of the light through it when the refracting
angle of the prism is \( 90^{\circ}, \) is :
A. \( 1 / \sqrt{2} \)
B. \( \sqrt{2} \)
c. \( \sqrt{\frac{3}{2}} \)
D. \( \frac{3}{2} \)
Subject: Maths
Find inverse proportionaly constant if \( x \) and \( y \) are in inverse proportion.
\[
\boldsymbol{x} \quad \mathbf{9} \quad \boldsymbol{6} \quad \boldsymbol{3} \quad \boldsymbol{1}
\]
\begin{tabular}{l}
6 \\
\hline
\end{tabular} \( y \quad 2 \quad 3 \)
\( \mathbf{A} \cdot \mathbf{9} \)
B. 18
c. 27
D. 30
Subject: Physics
Six identical particles each of mass \( \boldsymbol{m} \)
are arranged at the corners of a regular hexagon of side length \( L \). If the mass of one of the particle is doubled, the shift in the centre of mass is:
A.
в. \( \frac{6 \mathrm{L}}{7} \)
\( c \cdot \frac{L}{7} \)
D. \( \frac{\mathrm{L}}{\sqrt{3}} \)
Subject: Maths
In a class, there are 18 girls and 16 boys. The class teacher wants to choose
one pupil for class monitor. What she does, she writes the name of each pupil on a card and puts them into a basket and mixes thoroughly. A child is asked to pick one card from the basket. What
is the probability that the name written on the card is:
(i) the name of a girl
(ii) the name of a
boy
Subject: Physics
The moment of inertia of a fly-wheel is \( 4 k g m^{2} . \) A torque of 10 Newton-meter is
applied on it. The angular acceleration produced will be :
A .25 radians \( / \mathrm{sec}^{2} \)
B. 0.25 radians \( / \) sec \( ^{2} \)
c. 2.5 radians \( / \) sec \( ^{2} \)
D. Zero
Subject: Physics
Assertion
The net magnetic force on a current loop in a uniform magnetic field is zero but torque may or may not be zero
Reason
Torque on a current carrying coil in a magnetic field is given by \( \bar{\tau}= \) \( \boldsymbol{n} \boldsymbol{I}(\overline{\boldsymbol{A}} \boldsymbol{X} \overline{\boldsymbol{B}}) \)
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
The value of \( \int_{-\pi}^{\pi} \frac{\sin ^{2} x}{1+7^{x}} d x \) is
A \( \cdot 7^{x} \)
B. \( \pi \)
\( c \cdot \frac{\pi}{2} \)
\( D \cdot 2^{\pi} \)
E . \( 7 \pi \)
Subject: Physics
What is the mass of one curie of \( U^{234} ? \)
A . \( 3.7 \times 10^{10} g \)
B. \( 3.7 \times 10^{-10} g \)
c. \( 6.25 \times 10^{-34} g \)
D. \( 1.438 \times 10^{-11} g \)
Subject: Physics
The potential energy of a particle of mass \( 5 \mathrm{kg} \) moving in the \( \mathrm{x} \) -y plane is given by the equation, \( U=-7 x+24 y \)
Joule. Here \( x \) and \( y \) are in the meter at \( t=0, \) the particle is at the origin and moving with velocity \( (2 \hat{i}+3 \hat{j}) m / s . \) The
magnitude of acceleration of particle is
\( \mathbf{A} \cdot 3 m / s^{2} \)
B . \( 5 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 15 \mathrm{m} / \mathrm{s}^{2} \)
Subject: Maths
Two tangents are drawn to a circle from
an external point \( A \), touching the circle at the points \( P \) and \( Q . A \) third tangent
intersects segment \( \boldsymbol{A P} \) at \( \boldsymbol{B} \) and
segment \( A Q \) at \( C \) and touches the
circle at \( R \) If \( A Q=10 \) units, then the
perimeter of \( \Delta A B C \) is
A . 22.0
в. 20.5
\( c .20 .0 \)
D. 40.0