AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Let \( \boldsymbol{f}:\{\mathbf{1}, \mathbf{3}, \mathbf{4}\} \rightarrow\{\mathbf{1}, \mathbf{2}, \mathbf{5}\} \) and \( \boldsymbol{g}: \)
\( \{1, \mathbf{2}, \mathbf{5}\} \rightarrow\{1,3\} \) be given \( \boldsymbol{f}= \)
\( \{(\mathbf{1}, \mathbf{2}),(\mathbf{3}, \mathbf{5}),(\mathbf{4}, \mathbf{1})\} \) and \( \boldsymbol{g}= \)
\( \{(\mathbf{1}, \mathbf{3}),(\mathbf{2}, \mathbf{3}),(\mathbf{5}, \mathbf{1})\} . \) Write down \( \boldsymbol{g} \boldsymbol{o} \boldsymbol{f} \)
Subject: Chemistry
Which of the following changes will
increase the EMF of the cell:
\( \boldsymbol{C o}(\boldsymbol{s})\left|\boldsymbol{C o C l}_{2}\left(\boldsymbol{M}_{1}\right) \| \boldsymbol{H} \boldsymbol{C l}\left(\boldsymbol{M}_{2}\right)\right|\left(\boldsymbol{H}_{2}, \boldsymbol{g}\right) \)
This question has multiple correct options
A. Increase the volume of \( C o C l_{2} \) solution from \( 100 \mathrm{mL} \) to
200 mL.
B. Increase \( M_{2} \) from 0.01 M to 0.50 M.
C. Increase the pressure of the \( H_{2}(g) \) from 1.0 to 2.0 atm.
D. Increase \( M_{1} \) from 0.01 M to 0.50 \( \mathrm{M} \)
Subject: Physics
A body weighs \( 160 \mathrm{N} \) on the earth. Find
its weight on the other planet whose:
(a) mass is \( \frac{1}{4} \) times the mass of earth and radius \( \frac{1}{3} \) times that of the earth.
(b) mass is \( \frac{5}{2} \) times the mass of earth and radius \( \frac{4}{5} \) times that of the earth.
Subject: Physics
Assertion
In a small segment of string carrying sinusoidal wave, total energy is conserved if system is isolated.
Reason

Every small part moves in SHM.
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
Consider the two idealised systems
(i) a parallel plate capacitor with large plates and small separation and
(ii) a long solenoid of length \( L>>R \)
radius of cross - section.
In
(i) \( \bar{E} \) is ideally treated as a constant between plates and zero outside. In (ii) magnetic field is constant inside the solenoid and zero outside. These
idealised assumptions, however, contradict fundamental laws as below.
A. case (i) contradicts Gauss's law for electrostatic fields
B. case
(ii) contradicts Gauss's law for electrostatic field
\( c \cdot \) case
(i) agrees with \( \oint \bar{E} . \overline{d l}=0 \)
D. case
(ii) contradicts \( \oint \bar{H} . \overline{d l}=I_{e m} \)
Subject: Chemistry
The difference in height of the mercury column in two arms of a U tube
manometer in arrangement-lis \( \boldsymbol{h}_{\mathbf{1}}= \)
\( 660 \mathrm{mm} . \) In another arrangement -II at the same temperature, 222 gm of
\( \mathrm{CaCl}_{2} \) is dissolved in \( 324 \mathrm{gm} \) of water and the difference in height of mercury
column in two arms is found to be \( h_{2}= \)
\( 680 \mathrm{mm} . \) If the value of degree of
dissociation for \( C a C l_{2} \) in arrangement
-II is \( \alpha, \) then the value of \( 64 \alpha \) is:
[Atmospheric pressure \( =1 \text { atm }] \)
\( : \mathbb{1} \)
Subject: Maths
State true or false:
Rational number from following real
numbers \( -8.0, \sqrt{5}, \frac{5}{7},-\sqrt{18}, \sqrt{32}, 4.28, \pi, 3, \frac{8}{15} \)
\( \operatorname{are}-8.0 . \frac{5}{7}, 4.28,3, \frac{8}{15}, 0.075 \)
A. True
B. False
Subject: Maths
The value of \( 144^{\circ} \) in circular measure is
A \( \cdot \frac{3 \pi^{c}}{4} \)
B. \( \frac{2 \pi^{c}}{3} \)
c. \( \frac{4 \pi^{c}}{5} \)
D. \( \frac{5 \pi^{c}}{6} \)
Subject: Physics
The masses and radii of the earth and
the Moon are \( M_{1}, R_{1} \) and \( M_{2}, R_{2} \)
respectively. Their centres are at distance d apart. The minimum speed with which a particle of mass m should be projected from a point midway the two centres so as to escape to infinity is?
A \( \cdot \sqrt{\frac{2 G\left(M_{1}+M_{2}\right)}{d}} \)
B. \( \sqrt{\frac{4 G\left(M_{1}+M_{2}\right)}{d}} \)
c. \( \sqrt{\frac{4 G M_{1} M_{2}}{d}} \)
D. \( \sqrt{\frac{G\left(M_{1}+M_{2}\right)}{d}} \)
Subject: Maths
\( \operatorname{Given} \boldsymbol{A}=\left[\begin{array}{ccc}1 & \mathbf{2} & -\mathbf{3} \\ \mathbf{5} & \mathbf{0} & \mathbf{2} \\ \mathbf{1} & \mathbf{- 1} & \mathbf{1}\end{array}\right] \) and \( \boldsymbol{B}= \)
\( \left[\begin{array}{ccc}3 & -1 & 2 \\ 4 & 2 & 5 \\ 2 & 0 & 3\end{array}\right] \)
Find the matrix \( C \) such that \( A+2 C= \)
\( \boldsymbol{B} \)
If \( C=\left[\begin{array}{ccc}1 & \frac{-3}{2} & a \\ \frac{-1}{2} & 1 & b \\ \frac{1}{2} & \frac{1}{2} & 1\end{array}\right] \)
Find the value of \( a+b ? \)
Subject: Maths
If \( 0.6 x+0.8=0.28 x+1.16, \) then \( x= \)
A \( \cdot x=\frac{6}{7} \)
в. \( x=\frac{9}{8} \)
c. \( x=\frac{11}{2} \)
D. \( x=\frac{13}{5} \)
Subject: Physics
A convex glass lens \( \left(\mu_{g}=1.5\right) \) has a
focal length of \( 8 \mathrm{cm} \) when placed in air. What is the focal length lens when it is immersed in water? \( \left(\mu_{\omega}=\frac{4}{3}\right) \)
\( \mathbf{A} \cdot 32 \mathrm{cm} \)
B. \( 60 \mathrm{cm} \)
c. \( 16 \mathrm{cm} \)
D. \( 30 \mathrm{cm} \)
Subject: Physics
A stretched rope having linear mass density \( 5 \times 10^{-2} k g m^{-1} \) is under a
tension of \( 80 N . \) The power that has to be supplied to the rope to generate harmonic waves at a frequency of \( 60 H z \)
and an amplitude of \( 6 \mathrm{cm} \) is
\( \mathbf{A} \cdot 215 W \)
B. \( 251 W \)
\( \mathbf{c} .512 W \)
D. \( 521 W \)
Subject: Maths
If \( a, b, c \) are in A.P., then value of the
expression \( a^{3}+c^{3}-8 b^{3} \) is equal to
A . \( 2 a b c \)
B. \( 6 a b c \)
c. \( 4 a b c \)
D. \( -6 a b c \)
Subject: Physics
A ball falling in a lake of depth \( 200 \mathrm{m} \) show \( 0.1 \% \) decrease in its volume at the
bottom. What is the bulk modulus of the
material of the ball:-
A \( \cdot 19.6 \times 10^{8} N / m^{2} \)
B . \( 19.6 \times 10^{-10} \mathrm{N} / \mathrm{m}^{2} \)
C. \( 19.6 \times 10^{10} N / m^{2} \)
D. \( 19.6 \times 10^{-8} N / m^{2} \)
Subject: Physics
The maximum kinetic energy of a particle of mass 100 g and time period lpi secs, executing SHM at its mean position is given as 50 J. The amplitude of oscillation is
A \( . A=50 \sqrt{10} \mathrm{m} \)
В. \( A=5 \sqrt{10} m \)
c. \( A=50 m \)
D. \( A=25 m \)
Subject: Maths
Find the value of \( \theta \) for attaining a max
value of \( \sin ^{p} \theta \cos ^{q} \theta \) is
A \( \cdot \tan ^{-1} \frac{p}{q} \)
B. \( \tan ^{-1} \frac{\sqrt{p}}{\sqrt{q}} \)
c. \( \tan ^{-1}(p+q) \)
\( \mathbf{D} \cdot \tan ^{-1} q \)
Subject: Physics
A radioactive substance has density \( \rho \)
volume \( V \) and decay constant \( \lambda \). If the molecular weight of the substance is
\( M, \) and Avogadro's number is \( N_{a}, \) then the radioactivity of the substance after
time \( ^{\prime} \boldsymbol{t}^{\prime} \) is:
\( ^{\mathbf{A}} \cdot\left(\frac{\lambda V \rho N_{a}}{M}\right)\left(1-e^{\lambda t}\right) \)
B. \( \left(\frac{t N_{a} V}{\rho M}\right) e^{\lambda t / 2} \)
c. \( \frac{\lambda N_{a}}{V \rho M} e^{-\lambda t} \)
D. \( \frac{\lambda V \rho N_{a} e^{-\lambda t}}{M} \)
Subject: Chemistry
Identify the reaction that does not take place in a blast furnace.
A. \( C a C O_{3} \rightarrow C a O+C O_{2} \)
в. \( C a O+S i O_{2} \rightarrow C a S i O_{3} \)
\( \mathbf{c} \cdot 2 F e_{2} O_{3}+3 C \rightarrow 4 F e+3 C O_{2} \)
D. \( C O_{2}+C \rightarrow 2 C O \)
Subject: Maths
Let \( A \) and \( B \) be events such that \( \boldsymbol{P}(\overline{\boldsymbol{A}})=\frac{4}{5}, \boldsymbol{P}(\boldsymbol{B})=\frac{1}{3}, \boldsymbol{P}\left(\frac{\boldsymbol{A}}{\boldsymbol{B}}\right)=\frac{1}{6} \)
then:
A \( . P(A \cap B) \)
в. \( P(A \cup B) \)
\( ^{\mathrm{c}} \cdot_{P}\left(\frac{B}{A}\right) \)
D. Are \( A \) and \( B \) independent
Subject: Maths
Let \( A \) and \( B \) be two symmetric matrices
of order 3
Statement-1:
\( \boldsymbol{A}(\boldsymbol{B} \boldsymbol{A}) \) and \( (\boldsymbol{A B}) \boldsymbol{A} \) are symmetric
matrices.
Statement-2:
\( A B \) is symmetric matrix if matrix
multiplication of \( \boldsymbol{A} \) and \( \boldsymbol{B} \) is
commutative.
A. Statement-1 is true, Statement-2 is true; Statement-2 is correct explanation for Statement-1.
B. Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement- 1 .
c. Statement-1 is true, Statement-2 is false
D. Statement-1 is false, Statement-2 is true.
Subject: Maths
The value of \( \int \sqrt{1+\sec x} d x \) is
\( A \cdot \sin ^{-1}(\sqrt{2} \sin x)+C \)
B \( \cdot 2 \sin ^{-1}\left(\sqrt{2} \sin \frac{x}{2}\right)+C \)
c. \( 2 \sin ^{-1}(\sqrt{2} \sin x)+C \)
D \( \cdot \sin ^{-1}\left(\sqrt{2} \sin \frac{x}{2}\right)+C \)
Subject: Physics
A green light is incident from the water
to the air - water interface at the critical
angle ( \( \theta \) ). Select the correct statement.
A. The spectrum of visible light whose frequency is more than that of green light will come out to the air medium
B. The entire spectrum of visible light will come out of the water at various angles to the normal
C. The entire spectrum of visible light will come out of the water at an angle of \( 90^{\circ} \) to the normal.
D. The spectrum of visible light whose frequency is less than that of green light will come out to the air medium.
Subject: Maths
Let \( S \) be the set of all functions \( f: \)
\( [0,1] \rightarrow R, \) which are continuous on
[0,1] and differentiable on \( (0,1) . \) Then
for every \( f \) in \( S, \) there exists \( a c \in(0,1) \)
depending on \( f, \) such that
\( ^{\text {A } \cdot \frac{f(1)-f(c)}{1-c}=f^{\prime}(c)} \)
B \cdot \( |f(c)-f(1)|<(1-c)\left|f^{\prime}(c)\right| \)
c. \( |f(c)+f(1)|<(1+c)\left|f^{\prime}(c)\right| \)
D \( \cdot|f(c)-f(1)|<\mid f^{\prime}(c) \)
Subject: Maths
The differential equation corresponding
to the family of circles given by
\( (x-a)^{2}+(y-b)^{2}=4 \) where a and
are parameters, is
A \( \cdot 4 \frac{d^{2} y}{d x^{2}}+9 y=0 \)
\( 4\left(\frac{d^{2} y}{d x^{2}}\right)^{2}=\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{3} \)
\( ^{\mathbf{C}} 4 \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}=6 y \)
\( 4\left(\frac{d^{2} y}{a x^{2}}\right)^{2}+\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{2}=0 \)
Subject: Chemistry
Identify \( (A) \) and \( (B) \) in the following
sequence of reactions.
\( \boldsymbol{S} \boldsymbol{n} \boldsymbol{C l}_{2}+\boldsymbol{2} \boldsymbol{N} \boldsymbol{a} \boldsymbol{O} \boldsymbol{H} \rightarrow \)
\( (\boldsymbol{A})(\boldsymbol{w} \boldsymbol{h} i \boldsymbol{t} e \boldsymbol{p} \boldsymbol{p} \boldsymbol{t}) \frac{N a O \boldsymbol{H}}{(e x c e s s)}(\boldsymbol{B}) \)
A \( \cdot \operatorname{Sn}(O H)_{2}, N a_{2} \operatorname{Sn} O_{3} \)
B. \( \operatorname{Sn}(O H)_{2}, N a_{2} S n O_{2} \)
c. \( \operatorname{Sn}(O H)_{2}, N a_{2} \operatorname{Sn}(O H)_{6} \)
D. \( \operatorname{Sn}(O H)_{2} \), no effect
Subject: Physics
The graph shows the variation of
magnification \( m \) produced by convex
lens with image distance \( \vartheta \). The focal
length of the lens used is:
\( A \cdot b \)
в. \( \frac{b}{c a} \)
\( c \cdot \frac{b c}{a} \)
\( D \cdot \frac{c}{b} \)
Subject: Maths
If the \( p^{t h} \) term of the series of positive numbers \( 25,22 \frac{3}{5}, 20 \frac{1}{2}, 18 \frac{1}{4}, \dots \) is
numerically the smallest, then the \( p^{t h} \)
is.
A \( \cdot \frac{1}{4} \)
B.
c. \( \frac{1}{3} \)
D.
Subject: Chemistry
Vapour pressure of a pure liquid \( X \) is 2 \( \operatorname{atm} \) at \( 300 \mathrm{K} \). It is lowered to 1 atm on
dissolving 1 g of \( Y \) in \( 20 g \) of liquid \( X \). If
molar mass of \( X \) is 200 , what is the
molar mass of \( Y ? \)
A . 20
B. 10
c. 100
D. 30
Subject: Chemistry
Which of the following statements
about molecular and empirical formulas is lare false?
I. \( A \) given compound can have the same, molecular and empirical formula.
II. The molecular formula is a whole
number multiple of the empirical
formula.
III. \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) represents the empirical formula of hydrogen peroxide.
A. III only
B. I and II only
c. Il and III only
D. I, II an III
E. I only
Subject: Physics
A smooth ball of mass \( m \) strikes a
horizontal surface with a velocity \( v \) in a
direction making an angle \( 30^{\circ} \) with the
normal to the surface as shown in
figure. If the coefficient of restitution for
the collision between the ball and the
surface is \( e \) and the ball was in contact
with the surface for a small time \( \Delta t, \) the
average force acting on the ball during
collision is
\( \mathbf{A} \cdot m g \)
B. \( \frac{m v(1+e)}{2 \Delta t} \)
c. \( \sqrt{3} \frac{m v(1-e)}{2 \Delta t} \)
D. \( \sqrt{3} \frac{m v(1+e)}{2 \Delta t} \)
Subject: Physics
A transistor having \( \alpha=0.99 \) is used in
common base amplifier. If the load resistance is \( 0.45 M \Omega \) and the dynamic resistance of the emitter junction is
\( \mathbf{5 0} \mathbf{\Omega}, \) the voltage gain of the amplifier will be
A .7910
0
в. 8910
\( c .9910 \)
D. 6910
Subject: Maths
If the position vectors of three consecutive vertex of any parallelogram \( \operatorname{are} \) respectively \( \hat{i}+\hat{j}+\hat{k}, \hat{i}+3 \hat{j}+ \)
\( \mathbf{5} \hat{\boldsymbol{k}}, \mathbf{7} \hat{\boldsymbol{i}}+\mathbf{9} \hat{\boldsymbol{j}}+\mathbf{1 1} \hat{\boldsymbol{k}} \) then the position
vector of its fourth vertex is:
A \( \cdot 6(\hat{i}+\hat{j}+\hat{k}) \)
в. \( 7(\hat{i}+\hat{j}+\hat{k}) \)
c. \( 2 \hat{j}-4 \hat{k} \)
D. \( 6 \hat{i}+8 \hat{j}+1 \hat{0} k \)
Subject: Physics
An air bubble inside water oscillates
due to some explosion with period T. If
\( T \propto P^{a} d^{b} E^{c} \) then determine the values
of \( a, b \) and \( c . \) Here \( P, d \) and \( E \) are the static pressure, density and total energy of explosion of water, respectively.
A \( \cdot a=\frac{5}{6}, b=1, c=\frac{1}{3} \)
B. \( a=-\frac{5}{6}, b=\frac{1}{2}, c=\frac{1}{3} \)
c. \( a=1, b=1, c=1 \)
D. \( a=0, b=0, c=1 \)
Subject: Physics
A flat coil, \( C \) of \( n \) turn, area \( A \) and
resistance \( R \), is placed in a uniform
magnetic field of magnitude \( B \). The plane of the coil is initially perpendicular to \( B \). The coil is rotated by an angle \( \theta \) about a diameter and
charge of amount \( Q \) flows through it. Choose the correct alternatives.
This question has multiple correct options
A \( \cdot \theta=90^{\circ}, Q=(B A n / R) \)
B . \( \theta=180^{\circ}, Q=(2 B A n / R) \)
c. \( \theta=180^{\circ}, Q=0 \)
Subject: Physics
In a regular polygon of \( n \) sides, each corner is at a distance \( r \) from the centre. Identical charges are placed at \( (n-1) \) corners. At the centre, the magnitude of intensity is \( \mathrm{E} \) and the potential is V.The ratio V/E is
\( A \cdot r n \)
B. \( r(n-1) \)
\( c \cdot(n-1) / r \)
\( D \cdot r(n-1) / n \)
Subject: Chemistry
The electrode potentials for \( \boldsymbol{C u}^{2+}(\boldsymbol{a q})+\boldsymbol{e}^{-} \rightarrow \)
\( \boldsymbol{C u}^{+}(\boldsymbol{a q}) \) and \( \boldsymbol{C u}^{+}(\boldsymbol{a q})+\boldsymbol{e}^{-} \rightarrow \boldsymbol{C u}(\boldsymbol{s}) \)
are \( +0.15 \mathrm{V} \) and +0.50 respectively. The value of \( \boldsymbol{E}^{0} \boldsymbol{C u}^{2+} \mid \boldsymbol{C u} \) will be :
A . \( 0.500 \mathrm{v} \)
B. 0.325
\( c .0 .650 v \)
D. 0.150
Subject: Physics
A particle executes SHM given by the equation \( \boldsymbol{x}=\mathbf{4} \sin (\mathbf{2} \boldsymbol{\pi} \boldsymbol{t}+\boldsymbol{\pi} / \mathbf{4}), \) what
will be the velocity of the particle at \( t= \) (1/8)th sec;
A. velocity = 0
B. velocity = maximum
c. velocity = minimum
D. The particle's speed cannot be determined
Subject: Maths
If \( S_{n} \) denotes the sum of \( n \) terms of a
G.P. whose common ratio is \( r, \) then \( (r-1) \frac{d S_{n}}{d r} \) is equal to
A \( \cdot(n-1) S_{n}+n S_{n-1} \)
B . \( (n-1) S_{n}-n S_{n-1} \)
\( \mathbf{c} \cdot(n-1) S_{n} \)
D. None of these
Subject: Maths
The vectors \( \bar{a}, \bar{b}, \bar{c} \) are of the same length and taken pair wise, they form equal angles. If \( \bar{a}=\bar{i}+\bar{j} \) and \( \bar{b}=\bar{j}+\bar{k} \)
then the components of \( \bar{c} \) are?
A. (1,0,1)
в. (1,2,3)
c. (-1,1,2)
D. (-1,4,1)
Subject: Maths
If \( a_{1}, a_{2}, a_{3}, \dots \dots \dots \) be in \( A . P . \) such that
\( \boldsymbol{a}_{1}+\boldsymbol{a}_{5}+\boldsymbol{a}_{10}+\boldsymbol{a}_{15}+\boldsymbol{a}_{20}+\boldsymbol{a}_{24}=\mathbf{2 2 5} \)
then the sum of first 24 terms of the
A.P is
Subject: Maths
Find the equation of the plane passing through the point (2,-1,1) and through the line of intersection of the planes \( \vec{r} \). \( (2 \hat{i}-3 \hat{j}+\hat{k})=3 \) and \( \vec{r} \cdot(\hat{i}+5 \hat{j}- \)
\( \hat{\boldsymbol{k}})=\mathbf{4 . 4} \)
Subject: Biology
Most of the vertebrates have jaws with teeth. The mode of arrangement of teeth
on the jaws is called dentition.
The various types of teeth seen in mammals are incisors (I) canines (C)
premolars (P) and molars(M). They are used for biting, tearing, chewing and grinding respectively. Canines, the tearing teeth are welldeveloped in carnivores and illdeveloped or absent in herbivores.
Now answer the following:
(i) In frogs, all the teeth in the upper jaw look alike, whereas in human beings
they are different. The type of dentition in man can be called
(a) Homodont
(b) Isodont \( (c) \)
Heterodont
(d) Acrodont
(ii) The dental formula of a mammal is
written as ICPM=2023/1023. The teeth
missing in it are
(a) incisors
(b) canines
(c) premolars
(d) molars
Subject: Chemistry
The standard reduction potentials \( \boldsymbol{E}^{\mathbf{C}} \)
for the half reactions are follows:
\( \boldsymbol{Z} \boldsymbol{n} \rightarrow \boldsymbol{Z} \boldsymbol{n}^{2+}+\boldsymbol{2} \boldsymbol{e}^{-} ; \quad \boldsymbol{E}^{\ominus}= \)
\( +0.76 V \)
\( \boldsymbol{F e} \rightarrow \boldsymbol{F} \boldsymbol{e}^{2+}+\boldsymbol{2} \boldsymbol{e}^{-} ; \quad \boldsymbol{E}^{\ominus}=\mathbf{0 . 4 1} \boldsymbol{V} \)
The EMF for the cell reaction
\( \boldsymbol{F} \boldsymbol{e}^{2+} \boldsymbol{Z} \boldsymbol{n} \rightarrow \boldsymbol{Z} \boldsymbol{n}^{2+}+\boldsymbol{F} \boldsymbol{e} \) is:
A . \( -0.35 V \)
в. \( +0.35 V \)
c. \( +1.17 v \)
D. -1.17V
Subject: Chemistry
\( A t 817, K_{p} \) for the reaction between
\( C O_{2}(g) \) and excess hot graphite \( (s) \) is
10 atm.
(a) The sum of equilibrium
concentration of the gases at \( 817^{\circ} \mathrm{C} \) is
\( X M \) and a total pressure of 5 atm.
(b) At \( Y \) atm total pressure, the gas
contains \( 5 \% C O_{2} \) by volume.
The value of \( 1000(X+Y) \) is
Subject: Maths
If \( \boldsymbol{x}=\tan \boldsymbol{\theta}+\cot \boldsymbol{\theta}, \boldsymbol{y}=\cos \boldsymbol{\theta}-\sin \theta \)
then
A. \( x=y \)
B. \( \frac{1-y^{2}}{2}=\frac{1}{x} \)
\( ^{\mathbf{c}} \cdot \frac{y^{2}-1}{2}=\frac{1}{x} \)
D. \( \frac{1+y^{2}}{2}=\frac{1}{x} \)
Subject: Chemistry
\( \boldsymbol{O} \)
\( \boldsymbol{P h}-\hat{\boldsymbol{C}}-\boldsymbol{O}-\boldsymbol{C P h}_{3} \frac{\boldsymbol{H}_{3}^{18} \boldsymbol{O} \oplus}{\longrightarrow} \)
Product of this reaction is:
B. \( o^{18} \)
\( P h-C-O H+P h_{3} C-O H \)
c. \( _{\text {I }}^{o} \)
Ph \( -C-O H+P h_{3} C-O H \)
D.
\[
P h-C-O H+P h_{3} C-O H
\]
Subject: Maths
A dairy produces a 500 -gram pack of butter in the shape of a cylinder. The radius of the circular end of the pack is \( 3.9 \mathrm{cm} . \) and the length of the pack is 10.5 cm. The volume of the pack of the butter
is \( x \mathrm{cm}^{3} . \) The 500 gm pack is redesigned. It is now produced in the shape of a cuboid with a square end of side \( 6.5 \mathrm{cm} . \) The length of the redesigned pack f butter is y cm. Now
choose the correct options. This question has multiple correct options
A. \( x=405 \)
в. \( y=11.9 \)
c. \( x=502 \)
D. \( y=13.9 \)
Subject: Biology
Assertion
In tropical rainforest 0 horizon and \( A \) horizon of soil profile are shallow and
nutrient poor
Reason
Excessive growth of micro organism in soil depletes its organic content
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
Find the particular solution of the differential equation:
\( \boldsymbol{y}(\mathbf{1}+\log \boldsymbol{x}) \frac{\boldsymbol{d} \boldsymbol{x}}{\boldsymbol{d} \boldsymbol{y}}-\boldsymbol{x} \log \boldsymbol{x}=\mathbf{0} \)
when \( y=e^{2} \) and \( x=e \)
Subject: Maths
Find the values of \( a \) and \( b \) such that the
function defined by
\( f(x)=\left\{\begin{array}{l}5, \text { if } x \leq 2 \\ a x+b, \text { if } 2<x<10 \text { is a } \\ 21, \text { if } x \geq 10\end{array}\right. \)
continuous function.
Subject: Physics
Assertion
Width of the beam is increased in going from in air to water.
Reason
Rays of light diverge when they go from one medium to another.
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
The standard electrode potential \( \left(\boldsymbol{E}^{\ominus}\right) \) for \( \boldsymbol{O C l}^{-} \mid \boldsymbol{C l}^{-} \) and \( \boldsymbol{C l}^{-} \mid \frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{C l}_{2} \)
respectively are \( 0.94 \mathrm{V} \) and \( -1.36 \mathrm{V} \). The
\( \boldsymbol{E}^{\ominus} \) value of \( \boldsymbol{O} \boldsymbol{C l}^{-} \mid \frac{\boldsymbol{1}}{\boldsymbol{2}} \boldsymbol{C l}_{2} \) will be:
A. \( -0.42 \mathrm{v} \)
в. \( -2.20 \mathrm{v} \)
c. \( 0.52 \mathrm{v} \)
D . 1.04
Subject: Chemistry
\( H_{2} O_{2} \) turns blackened lead paintings to white colour. In this reaction it oxidizes
PbS to \( P b S O_{4} \). The number of moles of
\( H_{2} O_{2} \) needed to oxidize 0.1 moles of
\( P b S \) is:
A . 1 mole
B. 0.1 mole
c. 0.5 mole
D. 0.4 mole
Subject: Physics
A parallel-plate air condenser of plate
area \( A \) and separation d is charged to
potential \( V \) and then the battery is
removed. Now a slab of dielectric
constant \( k \) is introduced between the
plates. If \( Q, E \) and \( W \) denote respectively the magnitude of charge on each plate, the electric field between the plates
(after introduction of dielectric slab)
and work done on the system in the process of introducing the slab, then This question has multiple correct options
A \( \cdot W=\frac{\varepsilon_{0} A V h^{2}}{2 d}(1-1 / k) \)
\( ^{\mathbf{B}} \cdot Q=\frac{\varepsilon_{0} K A V}{d} \)
\( ^{\mathbf{C}} \cdot Q=\frac{\varepsilon_{0} A V}{d} \)
D. \( \quad E=\frac{V}{k d} \)
Subject: Chemistry
According to Freundlich adsorption isotherm, which of the following is
correct?
A \( \cdot \frac{x}{m} \propto P^{o} \)
B. \( \frac{x}{m} \propto P^{1} \)
c. \( \frac{x}{m} \propto P^{1 / n} \)
D. All of the above are correct for different ranges of pressure
Subject: Maths
For a quadratic function in standard
form, \( \boldsymbol{y}=\boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{c}, \) Find the axis of
symmetry.
A \( \cdot y=\frac{-b}{2 a} \)
в. \( x=\frac{-b}{2 a} \)
c. \( y=\frac{b^{2}-4 a c}{2 a} \)
D. None of these
Subject: Chemistry
The equilibrium concentration of \( \boldsymbol{X}, \boldsymbol{Y} \)
and \( Y X_{2} \) are 4,2 and 2 moles respectively for the equilibrium \( 2 X+ \)
\( \boldsymbol{Y} \rightleftharpoons \boldsymbol{Y} \boldsymbol{X}_{2} . \) The value of \( \boldsymbol{K}_{c} \) is:
A. 0.625
B. 0.0625
c. 6.25
D. 0.00625
Subject: Chemistry
Q Type your question
(a) \( \mathbf{B r}_{\mathbf{2}} / \mathbf{r} \boldsymbol{e} \)
\( (b) B r_{2} / C C l_{4} \)
\( (c) \prod B B \)
(d) \( \boldsymbol{H} \boldsymbol{B} \boldsymbol{r} \)
This question has multiple correct options
\( \mathbf{A} \)
(a) and para
\( B \)
(b)
\( c \)
\( (c) \)
D. \( (1,2-\mathrm{H} \) shift gives more stable benzylic carbocation)
\( (d) \)