AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Two resistance \( R_{1} \) and \( R_{2} \) are made of
different materials. The temperature
coefficient of the material of \( \boldsymbol{R}_{1} \) is \( \boldsymbol{\alpha} \)
and of the material of \( \boldsymbol{R}_{2} \) is \( -\boldsymbol{\beta} \). The
resistance of the series combination of
\( R_{1} \) and \( R_{2} \) will not change with temp.
then ratio of resistance of two wire will
be :-
A \( \cdot \frac{\alpha}{\beta} \)
B. \( \frac{\alpha+\beta}{\alpha-\beta} \)
\( ^{\mathbf{C}} \cdot \frac{\alpha^{2}+\beta^{2}}{\alpha \beta} \)
D. \( \frac{\beta}{\alpha} \)
Subject: Chemistry
\( C H_{3} C O O H \) is titrated with NaOH
solution. Which of the following
statement is true?
A. conductance increases upto equivalence point, after which it decreases.
B. Conductance decreases upto equivalence point, after which it increases.
c. conductance first increases (but not rapidly) upto equivalence point and then increases rapidly after equivalence point.
D. none
Subject: Chemistry
Methyl amine reacts with acetyl chloride to form:
A. \( C H_{3} N H_{2} \)
B. \( C H_{3} N H N a \)
c. \( C H_{3} N H C O C H_{3} \)
D. \( \left(C H_{3}\right)_{2} N C O C H_{3} \)
Subject: Physics
An unpolarized beam of intensity \( 2 a^{2} \) passes through a thin Polaroid. Assuming zero absorption in the Polaroid, the intensity of emergent planes polarized light will be
\( \mathbf{A} \cdot 2 a^{2} \)
в. \( a^{2} \)
\( c \cdot \sqrt{2} a \)
D. \( \frac{a^{2}}{\sqrt{2}} \)
Subject: Physics
In the adjoining figure \( A, B, \) and \( C \) represents three progressive waves.
Which of the following statement about the waves is correct?
A \( \cdot \) wave \( \mathrm{C} \) lags behind in phase by \( \frac{\pi}{2} \) from \( \mathrm{A} \) and \( \mathrm{B} \) leads
by \( \frac{\pi}{2} \)
B. Wave C leads in phase by \( \pi \) from \( A \) and \( B \) lags behind by \( \pi \)
C. wave C leads in phase by \( \frac{\pi}{2} \) from A and lags behind by
\( \frac{\pi}{2} \)
D. Wave C lags behind in phase by \( \pi \) from \( \mathrm{A} \) and \( \mathrm{B} \) leads by \( \pi \)
Subject: Maths
A biased coin with probability \( P,(0<p< \)
1) of heads is tossed until a head
appear for the first time. If the
probability that the number of tosses
required is even is \( \frac{2}{5} \) then \( P= \)
\( A \cdot \frac{2}{5} \)
B.
\( c \cdot \frac{2}{3} \)
\( D \cdot \frac{1}{3} \)
Subject: Chemistry
In the above cell cathodic cell reaction
and number of electrons involved are:
A \( \cdot 2 A g^{+}+2 e^{-} \rightarrow 2 A g, 2 e^{-} \)
B. \( A g^{+}+e^{-} \rightarrow A g, 1 e^{-} \)
\( \mathbf{c} \cdot 2 H^{+}+2 e^{-} \rightarrow H_{2}, 2 e^{-} \)
D. \( H^{+}+e^{-} \rightarrow \frac{1}{2} H_{2}, e^{-} \)
Subject: Maths
\( \left|\begin{array}{ccc}\frac{1}{a} & a^{2} & b c \\ \frac{1}{b} & b^{2} & c a \\ \frac{1}{c} & c^{2} & a b\end{array}\right|= \)
A \( \cdot \) abc
B. \( a+b+c \)
\( c \cdot 0 \)
D. \( 4 a b c \)
Subject: Maths
Which of the following is true about \( \boldsymbol{f}(\boldsymbol{x}) ? \)
A. \( f(x) \) decreases for \( x \epsilon[2 n \pi,(2 n+1) \pi], n \epsilon Z \)
в.
\( f(x) \) decreases for \( x \epsilon\left[(2 n-1) \frac{\pi}{2},(2 n+1) \frac{\pi}{2}\right], n \epsilon Z \)
c. \( f(x) \) is non-monotonic function.
D. \( f(x) \) increases for \( x \in R \)
Subject: Chemistry
The correct increasing order of trans-
effect of the following species is:
A \( \cdot B r^{-}>C N^{-}>N H_{3}>C_{6} H_{5} \)
B . \( C N^{-}>B r^{-}>C_{6} H_{5}^{-}>N H_{3} \)
c. \( N H_{3}>C N^{-}>B r^{-}>C_{6} H_{5} \)
D. \( C N^{-}>C_{6} H_{5}^{-}>B r^{-}>N H_{3} \)
Subject: Physics
An Ideal gas undergoes an isobaric
process. If its heat capacity is \( C_{v} \) at
constant volume and number of mole \( n \)
then the ratio of work done by gas to heat given to gas when temperature of gas changes by \( \Delta \boldsymbol{T} \) is:
\( ^{A} \cdot\left(\frac{n R}{c_{v}+R}\right) \)
в. \( \left(\frac{R}{c_{v}+R}\right) \)
\( ^{\mathrm{c}} \cdot\left(\frac{n R}{c_{v}-R}\right) \)
\( ^{D \cdot}\left(\frac{R}{c_{v}-R}\right) \)
Subject: Physics
A bus shuttles between two places
connected by a straight road with uniform speed of \( 36 k m p h \). If it stops at
each place for 15 minutes and the
distance between the two places is
\( 60 k m, \) then what is average value of
velocity?
A. \( 28.5 k m p h \)
в. 28 втрь
c. \( 27.5 k m p h \)
D. \( 29.5 k m p h \)
Subject: Physics
The line of action of a force \( \overrightarrow{\boldsymbol{F}}= \)
\( (-3 \hat{i}+\hat{j}+5 \hat{k}) N \) passes through \( a \)
point \( (7,3,1) . \) The moment of force \( (\vec{\tau}=\vec{r} \times \vec{F}) \) about the origin is given by
\( \mathbf{A} \cdot 14 \hat{i}+38 \hat{j}+16 \hat{k} \)
B . \( 14 \hat{i}+38 \hat{j}-16 \hat{k} \)
c. \( 14 \hat{i}-38 \hat{j}+16 \hat{k} \)
D. \( 14 \hat{i}-38 \hat{j}-16 \hat{k} \)
Subject: Chemistry
The average velocity of an ideal gas
molecule at \( 27^{\circ} \mathrm{C} \) is \( 0.3 m s^{-1} . \) The
average velocity at \( 927^{\circ} \mathrm{C} \) will
be
Write numerical value (upto 2 digit only) after decimal point only as for 0.19 write \( 19) \)
Subject: Maths
The value of the determinant
\( \left|\begin{array}{ccc}5 & 5 & 14 \\ ^{5} C_{1} & ^{5} C_{4} & 1 \\ ^{5} C_{2} & ^{5} C_{5} & 1\end{array}\right| \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. -576
c. 80
D. none of these
Subject: Maths
\( \int \frac{x}{\left(x^{2}-a^{2}\right)\left(x^{2}-b^{2}\right)} d x \) is equal to
\( \frac{1}{k\left(b^{2}-a^{2}\right)} \ln \frac{\left(x^{2}-b^{2}\right)}{\left(x^{2}-a^{2}\right)} \cdot \) Find \( k \)
Subject: Biology
Given below are four statements (i)-(iv).
Which two of the following statements
are correct?
(i) It is estimated that more than 70
percent of the world livestock
population is in India and China.
(ii) Stringent cleanliness and hygiene (both of the cattle and the handlers) are
of paramount importance while milking, storage and transport of the milk and its products.
(iii) Out-breeding is the breeding between animals of the same breed
only.
(iv) Crosses between different breeds is
called inbreeding.
A \( \cdot \) (i) and (ii)
B. (iii) and (iv)
c. (i) and (iv)
D. (ii) and (iii)
Subject: Physics
A steel wire of original length \( 1 \mathrm{m} \) and
cross-sectional area \( 4.00 \mathrm{mm}^{2} \) is
clamped at the two ends so that it lies horizontally and without tension. If a load of \( 2.16 \mathrm{kg} \) is suspended from the middle point of the wire, what would be
its vertical depression?Y of the steel \( = \) \( \mathbf{2 . 0} \times \mathbf{1 0}^{1 \mathbf{1}} \mathbf{N m}^{-\mathbf{2}} \)
take \( \mathfrak{g}=10 m s^{-2} \)
Subject: Physics
A ball is dropped from a bridge \( 122.5 \mathrm{m} \) above a river. After the ball has been
falling for \( 2 s, \) a second ball is thrown straight down after it. What must the initial velocity of the second ball be so that both hit the water at the same
time?
A. \( 40 \mathrm{m} / \mathrm{s} \)
В. \( 55.5 \mathrm{m} / \mathrm{s} \)
c. \( 26.1 \mathrm{m} / \mathrm{s} \)
D. \( 9.6 \mathrm{m} / \mathrm{s} \)
Subject: Physics
A person with myopic vision see objects only up to a distance of \( 0.25 \mathrm{m} . \) To be able to read a book placed at the distance of \( 0.50 \mathrm{m} \) from the eyes, the
spectacles needed by this person have
power of
A . -1.00
B . -1.5
c. - 2.0 \( D \)
D. +2.00
Subject: Maths
PQR is a triangle. S is a point on the side
QR of \( \Delta \) PQR such that \( \angle \mathrm{PSR}=\angle \mathrm{QPR} / \)
Given \( \boldsymbol{Q} \boldsymbol{P}=\mathbf{8 c m}, P \mathrm{R}=\mathbf{6 c m} \) and \( \mathbf{S R}=\mathbf{3} \)
\( \mathrm{cm} \)
(I) Prove \( \Delta \mathrm{PQR} \sim \Delta \) SPR
(II) Find the length of QR and PS
areaof \( \Delta P Q R \)
(III) \( \frac{d r e a o f \Delta S P R}{a r e a o f} \)
Subject: Chemistry
Name the following compounds.
(i)
(ii)
(iii) \( \mathrm{H}_{3} \mathrm{C}-\mathrm{C}=\mathrm{CH} \)
(iv)
(v) \( \mathrm{H}_{6} \mathrm{C}-\mathrm{C} \equiv \mathrm{C}-\mathrm{CH} \)
Subject: Chemistry
Increase in temperature favors the
forward reaction in:
A \( \cdot 2 S O_{2}(g)+O_{2}(g) \leftrightharpoons 2 S O_{3}(g) \)
в. \( 203 \leftrightharpoons 302(g) \)
c. \( C(\text { graphite }) \leftrightharpoons C(\text { diamond }) \)
D \( \cdot H_{2}(g)+\frac{1}{2} O_{2}(g) \leftrightharpoons H_{2} O(g) \)
Subject: Maths
The degree of \( \frac{d^{2} y}{d x^{2}}+ \)
\( \left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{3 / 2}=0 \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D.
Subject: Physics
Some magnetic flux is changed in a coil
of resistance 10 ohm. As a result an
induced current is developed in it,
which varies with time as shown in
figure. The magnitude of change in flux
through the coil in Webers is (Neglect
self inductance of the coil)
\( A \cdot 2 \)
\( B .4 \)
\( c \cdot 6 \)
\( D \)
Subject: Chemistry
Hydrogentaion of vegetable ghee at
\( 25^{\circ} C \) reduces the pressure of \( H_{2} \) from 2 atm to 1.2 atm in 50 minute. The rate of
reaction in terms of change of molarity per second is:
A \( \cdot 1.09 \times 10^{-5} \) mollitre \( ^{-1} \sec ^{-1} \)
B. \( 2.90 \times 10^{-5} \) mollitre \( ^{-1} \) sec \( ^{-1} \)
c. \( 3.29 \times 10^{-5} \) mollitre \( ^{-1} \) sec \( ^{-1} \)
D. None of these
Subject: Biology
Given: \( 1= \) Natural selection; \( 2= \)
Variations and their inheritance; \( 3= \)
Survival of the fittest; \( 4= \) Struggle for existence.

According to Darwinism, which of the following represents the correct sequence of events in the origin of new
species?
A .3,4,1,2
в. 2,3,1,4
c. 1,2,3,4
D. 4,2,3,1
Subject: Chemistry
\( X, Y \) and \( Z \) in the given graph are?
\( \mathbf{x}_{2}=(\mathbf{Y}) \quad \) Mole fraction \( \longrightarrow \quad \mathbf{y}_{2}=(\mathbf{Z}) \)
A. \( X=p_{1}+p_{2}, Y=1, Z=0 \)
B . \( X=p_{1}+p_{2}, Y=0, Z=0 \)
C \( \cdot X=p_{1} \times p_{2}, Y=0, Z=0 \)
D. \( X=p_{1}-p_{2}, Y=1, Z=0 \)
Subject: Physics
A cubical vessel of height \( 2 \mathrm{m} \) is full of water. The work done in pumping the water out of the vessel is?
A . \( 72.3 \mathrm{kJ} \)
B. \( 78.4 \mathrm{kJ} \)
c. \( 64.5 \mathrm{kJ} \)
D. \( 57.9 \mathrm{kJ} \)
Subject: Physics
Identical charges -q each are placed at 8 corners of a cube of each side \( b \)
Electrostatic potential energy of a charge +q which is placed at the centre of cube will be :
\( ^{\mathbf{A}} \cdot \frac{-4 \sqrt{2} q^{2}}{\pi \epsilon_{0} b} \)
B. \( \frac{-8 \sqrt{3} q^{2}}{\pi \epsilon_{6} b} \)
\( ^{\mathrm{c}} \cdot \frac{-4 q^{2}}{\sqrt{3} \pi \epsilon_{0} b} \)
D. \( \frac{-8 \sqrt{2} q^{2}}{\pi \epsilon_{0} b} \)
Subject: Maths
No. of permutations of 25 dissimilar things taken more than 15 at a time when repetitions are allowed is
A \( \cdot \frac{25}{24}\left(25^{25}-25^{15}\right) \)
В \( \cdot \frac{25}{24}\left(25^{25}-25^{10}\right) \)
c. \( \frac{25}{24}\left(25^{25}+25^{15}\right) \)
D. \( \frac{25}{24}\left(25^{25}+25^{10}\right) \)
Subject: Chemistry
\( \boldsymbol{K}_{s p} \) of \( Z e_{3}\left(P O_{4}\right)_{4} \) in terms of solubility
\( (S) \) is:
\( \mathbf{A} \cdot 108 S^{7} \)
B . \( 4 S^{3} \)
\( \mathrm{c} \cdot 6912 S^{7} \)
D. none of these
Subject: Physics
Two particles \( A \) and \( B \) are moving with
constant velocities \( v_{1} \) and \( v_{2} \cdot A t t=0, v_{1} \)
makes an angle \( \theta_{1} \) with the line joining
\( A \) and \( B \) and \( v_{2} \) makes an angle \( \theta_{2} \) with
the line joining \( A \) and \( B \). Find their
velocity of approach
Subject: Physics
A helicopter flies horizontally with
constant velocity in a direction \( \boldsymbol{\theta} \) east of
north between two points \( \boldsymbol{A} \) and \( \boldsymbol{B}, \) at distance d apart. Wind is blowing from south with constant speed u; the speed of helicopter relative to air is nu, where
\( \mathbf{n}>1 . \) Find the speed of the helicopter along AB. The helicopter returns from B
to A with same speed nu relative to air in same wind. Find the total time for the
journeys.
Subject: Maths
Let \( \boldsymbol{y}=\boldsymbol{y}(\boldsymbol{x}) \) be the solution of the
differential equation, \( \left(x^{2}+1\right)^{2} \frac{d y}{d x}+ \)
\( 2 x\left(x^{2}+1\right) y=1 \) such that \( y(0)=0 \)
\( \sqrt{\boldsymbol{a} \boldsymbol{y}}(1)=\frac{\boldsymbol{\pi}}{\mathbf{3 2}}, \) then the value of 'a' is:
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{16} \)
\( c \cdot \frac{1}{4} \)
D.
Subject: Maths
Let \( p \in I R \) then the differential
equation of the family of curves \( y= \)
\( (\alpha+\beta x) e^{p x}, \) where \( \alpha, \beta \) are arbitrary
constants, is:
A \( \cdot y^{\prime \prime}+4 p y^{\prime}+p^{2} y=0 \)
в. \( y^{\prime \prime}-2 p y^{\prime}+p^{2} y=0 \)
c. \( y^{\prime \prime}+2 p y^{\prime}-p^{2} y=0 \)
D. \( y^{\prime \prime}+2 p y^{\prime}+p^{2} y=0 \)
Subject: Chemistry
If \( \boldsymbol{H}_{2}, \boldsymbol{H} e, \boldsymbol{O}_{2} \) and \( \boldsymbol{N}_{2} \) tarvel with same
velocity then the longest de-Brogile wavelength should be associated with:
A \( . H_{2} \)
в. \( H e \)
\( c \cdot O_{2} \)
D. \( N_{2} \)
Subject: Physics
A circular coil of wire is connected to a battery of negligible internal resistance and has magnetic induction \( B \) at its centre. If the coil is unwound and
rewound to have double the number of
turns, and is connected to the same
battery, then the magnetic induction at
the center is :
\( \mathbf{A} \cdot 2 B \)
в. \( 4 B \)
\( c . B \)
D. \( 0.5 B \)
Subject: Chemistry
What is the solution used for the
preparation of hydrogen peroxide by electrolytic procedure?
A \( .0 .2 N N a O H \)
в. \( 50 \% \) Н \( _{2} \) S \( O_{4} \)
c. \( 20 \% \) NaOH
D. \( 5 \% \) NaCl
Subject: Physics
Two cars \( A \) and \( B \) approach stationary observer from opposite sides as shown in fig. Observer hears no beats. If the frequency of the horn of the \( \operatorname{car} B \) is \( 504 H z, \) the frequency
of horn of car \( A \) will be :
A \( .529 .2 \mathrm{Hz} \)
в. \( 295.2 \mathrm{Hz} \)
с. \( 440.5 \mathrm{H} \)
D. none of these
Subject: Chemistry
Which of the following reactions will not
produce \( H_{2} \) gas?
(a) Fe+dil. HCI
(b) \( \mathrm{Zn}+ \) dil. HCl
(c) \( \mathrm{Cu}+ \) dil. \( \mathrm{HCl} \)
(d) \( A g+d i l . H C l \)
\( A \cdot a, c, d \)
B. \( c, d \)
\( c \cdot a, d \)
\( D \cdot b, d \)
Subject: Physics
In air, a charged soap bubble of radius 'r' is in equilibrium having outside and inside pressures being equal. The charge on the bubble is
\( (\epsilon= \) permittivity of free space Tesurface tension of soap solution)
A \( \cdot 4 \pi r^{2} \sqrt{\frac{2 T \epsilon_{0}}{r}} \)
В. \( 4 \pi r^{2} \sqrt{\frac{4 T \epsilon_{0}}{r}} \)
c. \( _{4 \pi r^{2}} \sqrt{\frac{6 T \epsilon_{0}}{r}} \)
D. \( 4 \pi r^{2} \sqrt{\frac{8 T \epsilon_{0}}{r}} \)
Subject: Maths
If \( l, m, n \) are three parallel lines and the
transversal \( t_{1} \) and \( t_{2} \) cut the lines \( l, m, n \)
at the points \( A, B, C \) and \( P, O, R \) as
shown in the figure, then
A \( \cdot \frac{A B}{B C}=\frac{P O}{O R} \)
B. \( \frac{A B}{O R}=\frac{B C}{P O} \)
c. \( \frac{A P}{B O}=\frac{B O}{C R} \)
D. \( \frac{A B}{P O}=\frac{A P}{B O} \)
Subject: Maths
If \( \alpha \) is a real number for which \( f(x)= \)
\( \cos ^{-1} x \) is defined then a possible value
of \( [\alpha] \) is (where \( [.] \) denotes greatest
integer function)
This question has multiple correct options
\( A \cdot 2 \)
B.
\( c \cdot-1 \)
\( D \cdot-2 \)
Subject: Maths
If \( \theta \leq x \leq \pi ; \) then the area bounded by
the curve \( \boldsymbol{y}=\boldsymbol{x} \) and \( \boldsymbol{y}=\boldsymbol{x}+\sin \boldsymbol{x} \) is
A . 2
B. 4
\( c \cdot 2 \pi \)
D. \( 4 \pi \)
Subject: Maths
Find the area of a sector with an arc
length of \( 20 c m \) and a radius of \( 6 \mathrm{cm} \)
\( \mathbf{A} \cdot 20 \mathrm{cm}^{2} \)
B. \( 40 \mathrm{cm}^{2} \)
\( c \cdot 60 c m^{2} \)
D. \( 80 \mathrm{cm}^{2} \)
Subject: Physics
The wavelength of \( H_{\alpha} \) line in hydrogen
spectrum was found to be \( 6563 A \) in the laboratory. If the wavelength of same line in the spectrum of a milky way is \( \boldsymbol{O} \)
observed to be \( 6568 A \), then recession velocity of milky way will be
A. \( 105 \mathrm{m} / \mathrm{s} \)
В. \( 1.05 \times 10^{6} \mathrm{m} / \mathrm{s} \)
c. \( 10.5 \times 10^{6} \mathrm{m} / \mathrm{s} \)
D. \( 0.105 \times 10^{6} \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
Balance the following equation by ion electron method.
\( \boldsymbol{P}_{4}+\boldsymbol{O H}^{-}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{2}^{-}+\boldsymbol{P H}_{3} \)
Subject: Chemistry
In the 'ring test' of \( N O_{3}^{-} \) ion, there is
formation of brown colour ring. What is
its formula?
\( \mathbf{A} \cdot\left[F e\left(H_{2} O\right)_{5} N O_{3}\right]^{2} \)
B . \( \left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4} \mathrm{NOSO}_{4}\right]^{2+} \)
c. \( \left[F e\left(H_{2} O\right)_{5} N O\right]^{2+} \)
D. None of these
Subject: Maths
\( \boldsymbol{y}=\sqrt{\frac{\boldsymbol{1}-\boldsymbol{x}}{\mathbf{1}+\boldsymbol{x}}} \)
Prove that \( \left(\mathbf{1}-\boldsymbol{x}^{2}\right) \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\boldsymbol{y}=\mathbf{0} \)
Subject: Chemistry
Consider the following equations for a cell reaction, then:
\( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{C}+\boldsymbol{D}, \quad \boldsymbol{E}^{o}=\boldsymbol{x} \) volt, \( \boldsymbol{K}_{e q}= \)
\( \boldsymbol{K}_{\mathbf{1}} \)
\( \mathbf{2 A}+\mathbf{2 B} \rightleftharpoons \mathbf{2 C}+\mathbf{2 D}, \quad \boldsymbol{E}^{o}=\boldsymbol{y} \) volt
\( \boldsymbol{K}_{e q}=\boldsymbol{K}_{2} \)
A \( \cdot x=y, K_{1}=K_{2} \)
B . \( x=2 y, K_{1}=2 K_{2} \)
C \( . x=y, K_{1}^{2}=K_{2} \)
D. \( x^{2}=y, K_{1}^{2}=K_{2} \)
Subject: Physics
Identify which of the following best
describe the Mutual inductance?
A. the ability of a current carrying conductor to induce a voltage in another conductor through a mutual magnetic field.
B. the ability of current carrying conductor to produce a changing magnetic field.
C. the ability of a conductor to induce a magnetic field in another current carrying conductor
D. the ability of a current carrying conductor to induce a current in another conductor through a mutual magnetic field.
E. the ability of a magnetic field to induce a voltage in a current carrying conductor.
Subject: Chemistry
The production of dihydrogen gas via water gas shift reaction
\( \boldsymbol{C O}_{(\boldsymbol{g})}+\boldsymbol{H}_{2} \boldsymbol{O}_{(\boldsymbol{g})} \stackrel{\Delta}{\longrightarrow} \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2(\boldsymbol{g})} \)
The \( C O_{2} \) gas is removed by scrubbing with solution of?
A. sodium arsenite
B. Calcium oxide
c. Sodium phosphate
D. aluminium oxide
Subject: Maths
'X' speaks truth in \( 60 \% \) of the cases and
'Y' in \( 50 \% \) of the cases. The probability that they contradict each other while narrating the some incident, is
A \( \cdot \frac{1}{2} \)
B. \( \frac{3}{4} \)
\( c \cdot \frac{3}{5} \)
D. None of these
Subject: Physics
A ray of light is incident on the surface
of a glass plate at an angle of incidence equal to Brewster's angle \( \phi \). If \( \mu \) represents the refractive index of glass with respect to air, then the angle between the reflected and the refracted
rays is
\( A \cdot 90^{\circ}+\phi \)
B . \( \sin ^{-1}(\mu \cos \phi) \)
c. \( 90^{\circ} \)
D. \( 90-\sin ^{-1}\left(\frac{\sin \phi}{\mu}\right) \)
Subject: Physics
Two balls of equal mass are projected upwards simultaneously, one from the ground with initial velocity \( 50 m s^{-1} \)
and the other from a 40 m tower with
initial velocity of \( 30 m s^{-1} \). The
maximum height attained by their centre of mass will be:
\( A .80 m \)
B. \( 60 m \)
c. \( 100 m \)
D. \( 120 m \)
Subject: Maths
It is desired to construct a cylindrical
vessel of capacity 500 cubic metres open at the top.What should be the dimensions of the vessel so that the
material need is minimum, given that the thickness of the material used is 2
\( \mathrm{cm} \)
\( ^{\mathbf{A}} \cdot \quad r=\left(\frac{100}{\pi}\right)^{1 / 3}, h=5\left(\frac{100}{\pi}\right)^{1 / 3} \)
B. \( _{r}=\left(\frac{500}{\pi}\right)^{1 / 3}=h \)
\( r=\left(\frac{1000}{\pi}\right)^{1 / 3}, h=\left(\frac{125}{\pi}\right)^{1 / 3} \)
\( r=\left(\frac{20}{\pi}\right)^{1 / 3}, h=\left(\frac{100}{\pi}\right)^{1 / 3} \)
Subject: Chemistry
The hydrophilic end of synthetic
detergent is:
A. \( C H_{3}\left(C H_{2}\right)_{10}-C H_{2}- \)
в. \( -C H_{3} \)
\( \mathrm{c} .-C H_{2}-C H_{3} \)
D. \( -C O O^{-} N a^{+} \)
Subject: Physics
The balls, having linear momenta \( \overrightarrow{\mathbf{p}}_{1}= \) \( \mathbf{p} \hat{\mathbf{i}} \) and \( \overrightarrow{\mathbf{p}}_{2}=-\mathbf{p} \hat{\mathbf{i}}, \) undergo a collision in
free space. There is no extemal force
acting on the balls. Let \( \overrightarrow{\mathbf{p}}_{1} \) and \( \overrightarrow{\mathbf{p}}_{2} \) be
their final momenta. The following option(s) is (are) NOT ALLOWED for any
non-zero value of \( \mathbf{p}, \mathbf{a}_{1}, \mathbf{a}_{2}, \mathbf{b}_{1}, \mathbf{b}_{2}, \mathbf{c}_{1} \)
and \( \mathbf{c}_{2} \)
This question has multiple correct options
\( \mathbf{A} \cdot \overrightarrow{\mathbf{p}}_{1}=\mathbf{a}_{1} \hat{i}+\mathbf{b}_{1} \hat{\mathbf{j}}+\mathbf{c}_{1} \hat{\mathbf{k}} \)
\[
\overrightarrow{\mathrm{p}}_{2}=\mathrm{a}_{2} \mathrm{i}+\mathrm{b}_{2}
\]
B \( \cdot \overrightarrow{\mathrm{p}}_{1}=\mathrm{c}_{1} \hat{\mathrm{k}} \)
\[
\overrightarrow{\mathrm{p}}_{2}=\mathrm{c}_{2} \hat{\mathrm{k}}
\]
C \( \cdot \overrightarrow{\mathrm{p}}_{1}=\mathrm{a}_{1} \mathrm{i}+\mathrm{b}_{1} \hat{\mathrm{j}}+\mathrm{c}_{1} \hat{\mathrm{k}} \)
\[
\overrightarrow{\mathrm{p}}_{2}=\mathrm{a}_{2} \hat{\mathrm{i}}+\mathrm{b}_{2} \hat{\mathrm{j}}-\mathrm{c}_{1} \hat{\mathrm{k}}
\]
D \( \cdot \overrightarrow{\mathrm{p}}_{1}=\mathrm{a}_{1} \hat{\mathrm{i}}+\mathrm{b}_{1} \hat{\mathrm{j}} \)
\[
\overrightarrow{\mathrm{p}}_{2}=\mathrm{a}_{2} \mathrm{i}+\mathrm{b}_{1} \hat{\mathrm{j}}
\]
Subject: Physics
A piece of ice of mass \( 40 g \) is dropped
into \( 200 g \) of water at \( 50^{\circ} \mathrm{C} \). Calculate the final temperature of the water after all the ice has melted. Specific heat
capacity of water \( =4200 J k g^{-1} K^{-1} \)
Specific latent heat of fusion of ice \( = \)
\( 336 \times 10^{3} J k g^{-1} \)
Subject: Chemistry
\( \sqrt{V} \) on two particles \( A \) and \( B \) are plotted against de-broglie wavelengths. Where V is the potential on the particles. Which of the following relation is correct about the mass of particles?
A \( \cdot m_{A}=m_{B} \)
в. \( m_{A}>m_{B} \)
\( \mathbf{c} \cdot m_{A}<m_{B} \)
D \( . m_{A} \leq m_{B} \)
Subject: Maths
The larger area bounded between the
curve \( |\boldsymbol{x}|^{2}+|\boldsymbol{y}|^{2}=\mathbf{1} \) and the line \( \boldsymbol{x}+ \)
\( y=1 \) is
\( ^{\mathrm{A}} \cdot\left(\frac{\pi}{4}-\frac{1}{2}\right) \) sq. unit
B. \( \left(\frac{\pi}{4}+1\right) \) sq. unit
c. \( \left(\frac{3 \pi}{4}+\frac{1}{2}\right) \) sq. unit
D \( \cdot\left(\frac{3 \pi}{4}-\frac{1}{2}\right) \) sq. unit
Subject: Physics
A dancer is rotating on smooth horizontal floor with an angular
momentum \( L \). The dancer folds her
hands so that her momentof inertia
decreases by \( 25 \% \). The new angular momentum is.
A \( \cdot \frac{3 L}{4} \)
в. \( \frac{L}{4} \)
c. \( \frac{L}{2} \)
D. \( L \)
Subject: Physics
A particle moves in \( x y \) plane. The position vector at any time \( t \) is \( \vec{r}= \) \( \left\{(2 t) \hat{i}+\left(2 t^{2}\right) \hat{j}\right\} m . \) The rate of change of \( \theta \) at time \( t=2 \) second (where \( \theta \) is an
angle which its velocity vector makes
with positive \( x-a x i s) \) is:
A \( \cdot \frac{2}{17} \operatorname{rad} / s \)
в. \( \frac{1}{14} r a d / s \)
c. \( \frac{4}{7} \) rad \( / \) s
D. \( \frac{6}{5} \) rad \( / \) s
Subject: Chemistry
\( \boldsymbol{C H}_{2}=\boldsymbol{C}=\boldsymbol{C H}_{2} \stackrel{\boldsymbol{H}_{3} \boldsymbol{O}^{+}}{\longrightarrow} ? \)
Select the correct statement(s)
regarding the (major) product formed in the above reaction:
A. it reduces Fehling's solution
B. it is oxidised by Tollen's reagent
c. it decolourises \( B r_{2}-C C l_{4} \)
D. it gives iodoform test