AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
If the de-Broglie wavelength of a particle of mass \( m \) is 100 times its velocity then
its value in terms of its mass \( (m) \) and Planck's constant \( (\boldsymbol{h}) \) is:
A \( \cdot \frac{1}{10} \sqrt{\frac{m}{h}} \)
в. \( 10 \sqrt{\frac{h}{m}} \)
\( c \cdot \frac{1}{10} \sqrt{\frac{h}{m}} \)
D. \( 10 \sqrt{\frac{m}{h}} \)
Subject: Chemistry
\( \boldsymbol{S}^{2-}+\boldsymbol{N} \boldsymbol{a}_{2}\left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{5} \boldsymbol{N} \boldsymbol{O}\right] \longrightarrow \)
Complex is having violet/purple coloration(X)
The total number of possible isomers for complex \( X \) is \( \ldots \ldots . . \) provided the
ambident behavior of \( C N^{-} \) is
not considered
Subject: Maths
Find \( a_{1}+a_{6}+a_{11}+a_{16} \) if it is known
that \( a_{1}, a_{2} \dots \) is an A.P. and \( a_{1}+a_{4}+ \)
\( \boldsymbol{a}_{\boldsymbol{7}}+\ldots+\boldsymbol{a}_{\mathbf{1 6}}=\mathbf{1 4 7} \)
Subject: Chemistry
The basic character of oxides
\( M g O, S r O, K_{2} O, N i O, C s_{2} O \) increase
in the
order:
A \( . M g O>S r O>K_{2} O>N i O>C s_{2} O \)
в. \( C s_{2} O<K_{2} O<M g O<S r O<N i O \)
c. \( N i O<M g O<S r O<K_{2} O<C s_{2} O \)
D. \( K_{2} O<N i O<M g O<S r O<C s_{2} O \)
Subject: Maths
The area bounded by the circle \( x^{2}+ \)
\( y^{2}=8, \) the parabola \( x^{2}=2 y \) and the
line \( y=x \) in \( y \geq 0 \) is
A \( \cdot \frac{2}{3}+2 \pi \)
в. \( \frac{2}{3}-2 \pi \)
c. \( \frac{2}{3}+\pi \)
D. \( \frac{2}{3}-\pi \)
Subject: Maths
The expression \( \cos ^{2}(A-B)+ \)
\( \cos ^{2} B-2 \cos (A-B) \cos A \cos B \)
A. dependent on \( B \) only.
B. dependent on \( A \) and \( B \).
c. dependent on \( A \) only.
D. independent of \( A \) and \( B \).
Subject: Chemistry
Consider the reaction.
\( \left[N i\left(H_{2} O\right)_{6}\right]^{2+}(a q)+3 e n(a q) \rightarrow \)
\( \left[N i(e n)_{3}\right]^{2+}+2 H_{2} O \)
Which of the following property of compound is changed in reaction?
A. Co-ordination number
B. Geometry of complex
c. Hybridization of central atom
D. wavelength of absorbed light
Subject: Maths
If \( A \) and \( B \) are subsets of a set \( X, \) then
what is \( (\boldsymbol{A} \cap(\boldsymbol{X}-\boldsymbol{B})) \cup \boldsymbol{B} \) equal to
\( \mathbf{A} \cdot A \cup B \)
в. \( A \cap B \)
\( c . A \)
D. \( B \)
Subject: Physics
A circuit is shown below.lf \( A \) is an ideal
ammeter, B an ideal Battery of voltae \( V \)
and \( C \) an ideal voltmeter, what will be
reading of the \( \frac{\text { eading of } \boldsymbol{A}}{\text { reading }} \) ?
\( A \)
в. 2 R
\( c \cdot \frac{R}{2} \)
\( D \)
Subject: Maths
For the same signal emitted by a radio antenna, Observer A measures its
intensity to be 16 times the intensity measured by Observer B. The distance of Observer A from the radio antenna is
what fraction of the distance of
Observer B from the radio antenna?
A \( \cdot \frac{1}{4} \)
B. \( \frac{1}{16} \)
c. \( \frac{1}{64} \)
D. \( \frac{1}{256} \)
Subject: Physics
The energy of a particle executing simple harmonic motion is given by the equation \( \boldsymbol{E}=\boldsymbol{A} \boldsymbol{x}^{2}+\boldsymbol{B} \boldsymbol{v}^{2} \) where \( \boldsymbol{x} \) is the
displacement from mean position \( \boldsymbol{x}= \)
0 and \( v \) is the velocity of the particle at
\( x . \) Find the amplitude of \( S . H . M \)
Subject: Chemistry
The mobility of the \( N H_{4}^{+} \) ions is
\( \mathbf{7 . 6 2 3} \times \mathbf{1 0}^{-8} \mathbf{m}^{2} / \boldsymbol{V} \boldsymbol{s} . \) Calculate:
(a) the molar conductivity of \( \boldsymbol{N} \boldsymbol{H}_{\mathbf{4}}^{+} \) ion;
(b) Velocity of the ion of 15 volt are applied across the electrodes \( 25 \mathrm{cm} \)
apart
Subject: Physics
Energy is being emitted from the
surface of black body at \( 127^{\circ} \mathrm{C} \) at the
rate of \( 1.0 \times 10^{6} J / s m^{2} . \) The
temperature of black body at which the rate of energy is \( 16.0 \times 10^{6} J / s m^{2} \) will
be:
\( \mathbf{A} \cdot 754^{\circ} C \)
B. \( 527^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 254^{\circ} C \)
D. \( 508^{\circ} \mathrm{C} \)
Subject: Maths
Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) of \( \boldsymbol{x}^{3}+\boldsymbol{x}^{2} \boldsymbol{y}+\boldsymbol{x} \boldsymbol{y}^{2}+\boldsymbol{y}^{3}=\boldsymbol{8} \mathbf{1} \)
Subject: Chemistry
Which of the following is produced during the following reaction? \( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \frac{575 \boldsymbol{K}}{Z n O, C r_{2} O_{3}} \)
A. Ethanol
B. Ethanal
c. Methanol
D. Methanal
Subject: Maths
The solution of differential equation
\( \boldsymbol{x}^{2} \boldsymbol{y}^{2} \boldsymbol{d} \boldsymbol{y}=\left(1-\boldsymbol{x} \boldsymbol{y}^{3}\right) d \boldsymbol{x} \) is
A \( \cdot x^{3} y^{3}=x^{2}+C \)
B. \( 2 x^{3} y^{3}=3 x^{2}+C \)
c. \( x^{3} y^{3}=x^{2}+x+C \)
D. \( x^{3} y^{3}=3 x^{2}+C \)
Subject: Physics
Sphere (1) moving with velocity \( 4 \mathrm{m} / \mathrm{s} \)
collides another sphere (2) at rest. Find
final velocity of sphere (1) after collision collision perfectly elastic
\( A \cdot 2 \hat{\imath}+\sqrt{3} \hat{\jmath} \)
B . \( 2 \hat{i}-\sqrt{3} \hat{j} \)
\( c \cdot \hat{i}+\sqrt{3} \hat{j} \)
D. \( \hat{i}-\sqrt{3} \hat{j} \)
Subject: Maths
If \( |\vec{a}|=3,|\vec{b}|=4, \) then a value of \( \lambda \) for which \( \vec{a}+\lambda \vec{b} \) is perpendicular to \( \vec{a}- \) \( \lambda \vec{b} \) is
A \( \cdot \frac{9}{16} \)
B. \( \frac{3}{4} \)
\( c \cdot \frac{3}{2} \)
D. \( \frac{4}{3} \)
Subject: Chemistry
When a piece of zinc metal is added to a solution of hydrochloric acid, a reaction occurs. The products are aqueous zinc chloride and hydrogen gas. Which of the following conditions would
result in the fastest rate of reaction
with \( 1.00 g \) of zinc?
\( \mathbf{A} \cdot 0.010 M H C l \) at \( 10^{\circ} C \)
B . \( 0.010 M \) HCl at \( 80^{\circ} \mathrm{C} \)
c. \( 0.10 M \) HCl at \( 10^{\circ} \) C
D. \( 0.10 M H C l \) at \( 80^{\circ} C \)
Subject: Chemistry
The \( K_{s p} \) for \( A g C l \) is \( 2.8 \times 10^{-10} \) at a
given temperature. The solubility of \( A g C l \) in 0.01 molar \( H C l \) solution at
this temperature will be:
A. \( 2.8 \times 10^{-12} \) mol \( L^{-1} \)
-
B . \( 2.8 \times 10^{-8} \mathrm{mol} \mathrm{L}^{-1} \)
c. \( 5.6 \times 10^{-8} \) mol \( L^{-1} \)
D. 2.8 \( \times 10^{-4} \mathrm{mol} \mathrm{L}^{-1} \)
Subject: Physics
A vector \( \vec{p} \) is making \( 45^{\circ} \) and \( 60^{\circ} \) with
+ve \( x \) and \( y \) axes respectively. Then
angle made by this vector with +ve z axis is
A . 255 \( ^{\circ} \)
B . 75
\( c \cdot 30^{0} \)
D. \( 60^{\circ} \)
Subject: Maths
The D.E of simple harmonic motion
whose solution is given by \( \boldsymbol{x}= \) \( A \cos (n t+\alpha) \) is
A \( \cdot \frac{d^{2} x}{d t^{2}}+n x=0 \)
B. \( \frac{d^{2} x}{d t^{2}}+n^{2} x=0 \)
c. \( \frac{d^{2} x}{d t^{2}}-n^{2} x=0 \)
D. \( \frac{d^{2} x}{d t^{2}}+\frac{1}{n^{2}} x=0 \)
Subject: Chemistry
For a first order reaction, to obtain a
positive slope, we need to plot:
\( \{[A] \text { is the concentration of reactant } A\} \)
\( \mathbf{A} \cdot \log _{10}[A] \) vs \( t \)
B. \( -\log _{e}[A] \) vs t
\( \mathbf{C} \cdot \log _{10}[A] \) vs \( \log t \)
D. \( [A] \) vs t
Subject: Physics
For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material
whose refractive index lies between:
\begin{tabular}{ll} 
B. 1 & and \( \sqrt{2} \) \\
\hline
\end{tabular}
\( \begin{array}{lll}c \cdot \sqrt{3} & \text {and} & 2\end{array} \)
\( \begin{array}{lll}\text { D. } \sqrt{5} & \text { and } 2\end{array} \)
Subject: Maths
\( \int \frac{\log x \cdot \sin \left(1+(\log x)^{2}\right)}{x} d x= \)
A. \( -\frac{1}{2} \cos \left(1+(\log x)^{2}\right)+c \)
B. \( \frac{1}{2} \cos \left(1+(\log x)^{2}\right)+c \)
C. \( \frac{1}{2} \sin \left(1+\sin (\log x)^{2}\right)+c \)
D. \( -\frac{1}{2} \sin \left(1+\sin (\log x)^{2}\right)+c \)
Subject: Maths
Find the matrices \( A \) and \( B \) such that \( \boldsymbol{A}+\boldsymbol{B}=\left[\begin{array}{ll}\mathbf{5} & \mathbf{4} \\ \mathbf{7} & \mathbf{3}\end{array}\right] \) and \( \boldsymbol{A}-\boldsymbol{B}= \)
\( \left[\begin{array}{cc}11 & 2 \\ -1 & 7\end{array}\right] \)
Subject: Chemistry
Rutherford's experiment, which established the nuclear model of the
atom, used a beam of:
A. \( \beta \) -particles, which impinged on a metal foil and got absorbed
B. \( \gamma \) -rays, which impinged on a metal foil and ejected electrons
c. helium atoms, which impinged on a metal foil and got scattered
D. helium nuclei, which impinged on a metal foil and got scattered
Subject: Chemistry
Assertion
Chlorine gas turns moist potassium bromide paper red.
Reason
Chlorine gas acts as an oxidising agent.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Physics
A given particle starts at \( x=1 \) on the
potential function \( U(x)=x^{2}-10 x+ \)
\( 25, \) where \( U \) is in Joules and \( x \) is in
meters. It then moves down the
potential gradient to \( x=3 \) where it has
\( 4 J \) of potential energy. If it started at rest, how much kinetic energy does it have as it passes through \( x=3 ? \)
A . 2.5
в. 45
\( c \cdot 8 J \)
D. 12.5
E .16 .5
Subject: Physics
Starting from rest, when a body moves with uniform acceleration, then distances covered after 1 st, 2 nd, \( 3 r d, \)
seconds are in the ratio
A . 1: 2: 3: 4
B . 1:4: ::16.
\( c \cdot 1: 3: 5: 7 \)
D. 2:3: 5:7.
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{cl}\frac{\sin (a+2) x+\sin x}{x} ; & x<0 \\ b ; & x=0 \\ \frac{\left(x+3 x^{2}\right)^{1 / 3}-x^{1 / 3}}{x^{4 / 3}} ; & x>0\end{array}\right. \)
is continuous at \( x=0, \) then \( a+2 b \) is
equal to?
\( A \)
B. -2
\( c \cdot 1 \)
D.
Subject: Maths
\( \lim _{x \rightarrow 0} \frac{(1+x)^{4}-1}{(1+x)^{3}-1}=? \)
A \( \cdot \frac{3}{4} \)
B. \( \frac{9}{16} \)
\( c \cdot \frac{4}{3} \)
D. None of these
Subject: Chemistry
The concentration of the reactant \( R \) at
different times are given below. Find the average rate during different time intervals.
\( t(\sec ) \quad[R](\operatorname{mol} / L) \) )
0.150
10
\[
0.100
\]
20 0.050
A \( . . .005 \mathrm{mol} \mathrm{L}^{-1} \mathrm{s}^{-1}, .005 \mathrm{mol} \mathrm{L}^{-1} \mathrm{s}^{-1} \)
B . .005molL" \( s^{-1}, .0025 \) molL\( ^{-1} s^{-1} \)
c. \( .0025 \mathrm{molL}^{-1} \mathrm{s}^{-1} . .005 \mathrm{molL}^{-1} \mathrm{s}^{-1} \)
D. None of these
Subject: Chemistry
Which is not characteristic of \( \pi \) -bond?
A. \( \pi \) - bond is formed when a sigma bond already formed
B. \( \pi \) - bond are formed from hybrid orbitals
C \( . \pi \) - bond may be formed by the overlapping of \( p \) orbitals
D. \( \pi \) - bond results from lateral overlap of atomic orbitals
Subject: Chemistry
If uncertainty in momentum of electron is three times the uncertainty in position, then uncertainty in velocity of electron would be:
A \( \cdot \frac{1}{4 m} \sqrt{\frac{h}{3 \pi}} \)
в. \( \frac{1}{3 m} \sqrt{\frac{h}{\pi}} \)
c. \( \frac{1}{3 m} \sqrt{\frac{4 \pi}{h}} \)
D. \( \frac{1}{2 m} \sqrt{\frac{3 h}{\pi}} \)
Subject: Physics
Assertion
All the materials always have the same colour, whether viewed by reflected light or through transmitted light.
Reason
The colour of material does not depend
on nature of material.
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
Three point charges, each \( +q \) are placed at the vertices of an equilateral triangle. What charge should be placed at its centroid so that all four charges
are in equilibrium?
A \( \cdot \frac{q}{\sqrt{2}} \)
B. \( \frac{q}{\sqrt{3}} \)
c. \( \frac{\sqrt{3} q}{2} \)
D. \( \frac{2 q}{\sqrt{3}} \)
Subject: Chemistry
What is the most suitable catalyst for reducing vinyl cyanide \( (\boldsymbol{C H}= \) \( \boldsymbol{C H C N} \) to propanenitrile?
A. \( H_{2} / N i \)
в. \( H_{2} / P t \)
C \( \cdot\left(P h_{3} P\right)_{3} R h C l \) (Wilkinson's catalyst)
D. LiAlH\( _{4} \)
Subject: Maths
\[
\text { If } \boldsymbol{f}(\boldsymbol{x}, \boldsymbol{y})=\boldsymbol{x}^{2}+\boldsymbol{y}^{2}-\boldsymbol{2} \boldsymbol{x} \boldsymbol{y},(\boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{R})
\]
and
\( \boldsymbol{A}= \)
\[
\left[\begin{array}{lll}
f\left(x_{1}, y_{1}\right) & f\left(x_{1}, y_{2}\right) & f\left(x_{1}, y_{3}\right) \\
f\left(x_{2}, y_{1}\right) & f\left(x_{2}, y_{2}\right) & f\left(x_{2}, y_{3}\right) \\
f\left(x_{3}, y_{1}\right) & f\left(x_{3}, y_{2}\right) & f\left(x_{3}, y_{3}\right)
\end{array}\right]
\]
such that trace \( (\boldsymbol{A})=\mathbf{0}, \) then which of the following is true (only one option)
A. \( \operatorname{det}(A) \geq 0 \)
в. \( \operatorname{det}(A)=0 \)
\( \mathbf{c} \cdot \operatorname{det}(A) \leq 0 \)
D. \( \operatorname{det}(A)>0 \)
Subject: Chemistry
Indicate the types of isomerism exhibited by the following complex and
draw the structure of this isomer.
\( \boldsymbol{K}\left[\boldsymbol{C r}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{2}\left(\boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)_{2}\right. \)
Subject: Physics
A particle is vibrating in simple harmonic motion with amplitude of \( 4 \mathrm{cm} . \) At what displacement from the equilibrium position is its energy half potential and half kinetic?
A. \( 1 ~ c m \)
B. \( \sqrt{2} \mathrm{cm} \)
\( c \cdot 2 c m \)
D. \( 2 \sqrt{2} \) cm
Subject: Physics
Assertion
The images formed by total internal reflections are much brighter than those formed by mirrors or lenses
Reason

There is no loss of intensity in total
internal reflection.
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
Ampere. A "S" shaped conducting rod AB consisting of two semicircles each of
radius \( r \) is placed in such a way that the
centre \( C \) of the conducting wire is at a
distance \( 2 r \) from the end of the wire.The
rod \( A B \) moves with velocity of \( 5 m s^{-1} \)
along the direction of the current flow as shown in the figure. If the line joining
the ends of the rod makes an angle \( 60^{\circ} \)
with the wire then,
This question has multiple correct options
A. the emf induced between the ends of the rod is \( (\ln 4) \)
\( \mu V \)
B. the end \( A \) is at higher potential than end \( B \).
c. the end \( A \) is at lower potential than end \( B \).
D. the emf induced between the ends of the rod is \( (\ln 3) \)
\( \mu V \)
Subject: Chemistry
When a sample of \( H I \) is warmed to a particular temperature the equilibrium below is established.
\( 2 H I(g) \rightleftharpoons H_{2}(g)+I_{2}(g) \)
At this temperature, it is found that the partial pressure of \( \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \) is 28 times
the partial pressure of \( \boldsymbol{H}_{2}(\boldsymbol{g}) \)
What is the value of \( \boldsymbol{K}_{\boldsymbol{p}} \) at this temperature?
A \( \cdot 1.28 \times 10^{-3} \)
в. 0.035
\( c \cdot 28 \)
D. 784
Subject: Chemistry
Sodium extract is heated with
concentrated \( H N O_{3} \) before testing for halogens because:
A. \( A g_{2} S \) and \( A g C N \) are soluble in acidic medium.
B. silver halides are totally insoluble in nitric acid
c. \( S^{2-} \) and \( C N^{-} \), if present, are decomposed by conc. \( H N O_{3} \) and hence do not interfere in the test.
D. \( A g \) reacts faster with halides in acidic medium.
Subject: Maths
For the function \( f(x)=a(x-h)^{2}+k \)
which of the following statements is
wrong?
A. The value of \( a \) is negative
B. \( f(x) \) is symmetrical across the line \( y=3 \)
c. The function \( g(x)=\frac{2 x}{3} \) intersects \( f(x) \) at its vertex
D. The value of \( h \) is positive
Subject: Maths
If \( \sin \alpha+\sin \beta=\frac{1}{2} \) and \( \cos \alpha+ \)
\( \cos \beta=\frac{\sqrt{3}}{2}, \) then value of \( 3 \alpha+\beta \) is
A \( .90^{\circ} \)
B . \( 0^{\circ} \)
\( c \cdot 120^{\circ} \)
D. \( 60^{\circ} \)
Subject: Chemistry
The two compounds
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{O C H}_{3} \) and
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{O C H}_{2} \boldsymbol{C H}_{3} \) may be
considered as:
A. metamers
B. tautomers
c. functional isomers
D. position isomers
Subject: Chemistry
How are the two atoms \( _{92}^{235} P \) and \( _{92}^{238} P \) similar?
(i) They have the same number of
protons
(ii) They have the same number of
neutrons
(iii) They have the same number of
electrons
A. Only (i)
B. Only (i) and (ii)
c. only (i) and (iii)
D. (i), (ii) and (iii)
Subject: Chemistry
The integral enthalpy of solution in \( \mathrm{kJ} \) of
one mole of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) dissolved in \( \boldsymbol{n} \) mole
of water is given by:
\( \Delta \boldsymbol{H}_{s}=\frac{\mathbf{7 5 . 6} \times \boldsymbol{n}}{\boldsymbol{n}+\mathbf{1 . 8}} \)
Calculate \( \Delta H \) for \( H_{2} S O_{4} \) dissolved in 2
mole of \( \boldsymbol{H}_{2} \boldsymbol{O} \)
\( A \cdot-48.54 \mathrm{kJ} \)
B. 39.79 kJ
c. 48.54 k]
D. \( 75.60 \mathrm{kJ} \)
Subject: Physics
Insulators are materials having an electrical conductivity equal to:
A. Between \( 10^{-8} \mathrm{S} / \mathrm{cm} \) to \( 10^{3} \mathrm{S} / \mathrm{cm} \)
B. \( <10^{-8} \) S/cm
C. Equal to \( 10^{3} \mathrm{S} / \mathrm{cm} \)
\( \mathbf{D} \cdot>10^{3} \mathrm{S} / \mathrm{cm} \)
Subject: Chemistry
The vapour pressure two pure liquids, \( A \) and \( \mathrm{B} \) that form an ideal solution are
300 and 800 torr respectively, at
temperature T.A mixture of the vapour of \( A \) and \( B \) for which the mole fraction of
\( A \) is 0.25 is slowly compressed at temperature T. Calculate
(a) the
composition of the first drop of the
condensate.
Upto two decimal places and multilply the answer by 100
Subject: Maths
What type of a quadrilateral do the
points \( \boldsymbol{A}(\mathbf{2}, \mathbf{2}), \boldsymbol{B}(\mathbf{7}, \mathbf{3}), \boldsymbol{C}(\mathbf{1 1}, \mathbf{1}) \) and
\( D(6,6) \) taken in that order, form?
A. Scalene quadrilateral
B. Square
c. Rectangle
D. Rhombus
Subject: Chemistry
Represent with the help of neat diagrams hydrogen bonding if present
in the molecules of \( \boldsymbol{H} \boldsymbol{F}-\boldsymbol{H}_{2} \boldsymbol{O}, \boldsymbol{H} \boldsymbol{F} \)
\( -N H_{3}, \) aniline \( - \) aniline, \( H_{2} O \)
\( -\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{H}, \boldsymbol{H}_{2} \boldsymbol{O}-\boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{O} \boldsymbol{C} \boldsymbol{H}_{3}, \boldsymbol{H}_{2} \boldsymbol{O} \)
\( -\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}, \boldsymbol{H}_{2} \boldsymbol{O}-\boldsymbol{N} \boldsymbol{a} \boldsymbol{C l} \)
Subject: Maths
If an angle \( a \) is divided into two parts \( A \)
\& \( B \) such
that \( A-B=x \) and \( \tan A: \tan B= \)
\( K: 1, \) then the value of \( \sin x \) is
A \( \cdot \frac{k+1}{k-1} \sin \alpha \)
B. \( \frac{k}{k+1} \sin \alpha \)
c. \( \frac{k-1}{k+1} \sin \alpha \)
D. none of the above
Subject: Physics
Two moles of a gas is expanded to double its volume by two different processors. One is isobaric and the
other is isothermal. If \( w_{1} \) and \( w_{2} \) are the
works done respectively, then
A. \( w_{2}=\frac{w_{1}}{\ln 2} \)
В \( . w_{2}=w_{1} \)
c. \( w_{2}=w_{1} \ln 2 \)
D. \( w_{1}^{2}=w_{2} \ln 2 \)
Subject: Chemistry
Equations of preparation of alcohol from sugar are given:
\( C_{12} H_{22} O_{11}+H_{2} O \stackrel{\text {Invertase}}{\longrightarrow} \)
\( C_{6} H_{12} O_{6}+C_{6} H_{12} O_{6} \)
\( A \)
\( \boldsymbol{C}_{6} \boldsymbol{H}_{12} \boldsymbol{O}_{6} \stackrel{z \text { ymase}}{\longrightarrow} \mathbf{2} \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{H}+\mathbf{2} \boldsymbol{C} \boldsymbol{O}_{2} \)
(a) Write the names of the Compounds
\( A \) and \( B \)
(b) The alcohol obtained here is known
as
(c) How can this alcohol be converted into reflected spirit?
(d) How can power alcohol be prepared?
Subject: Maths
If the transformation \( z=\log \tan \left(\frac{x}{2}\right) \)
reduces the differential equation \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}+\cos \boldsymbol{x} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\mathbf{4} \boldsymbol{y} \operatorname{cosec}^{2} \boldsymbol{x}=\mathbf{0} \) int
\( \frac{d^{2} y}{d x^{2}}+A y=0 \) then the value of \( A \) is
Subject: Physics
A 2 kg mass moving on a smooth frictionless surface with a velocity of \( 10 m s^{-1} \) hits another 2 kg mass kept at rest, in an inelastic collision. After
collision, if they move together,
A. they travel with a velocity of \( 5 m s^{-1} \) in the same direction
B. they travel with a velocity of \( 10 \mathrm{ms}^{-1} \) in the same direction
c. they travel with a velocity of \( 10 m s^{-1} \) in the opposite direction
D. they travel with a velocity of \( 5 m s^{-1} \) in the opposite direction
Subject: Maths
ABCD is a parallelogram, E and F are the mid-points of \( A B \) and \( C D \) respectively. \( \mathrm{GH} \) is any line intersecting \( \mathrm{AD}, \mathrm{EF} \) and BC at G,P and H respectively. Prove that \( \boldsymbol{G} \boldsymbol{P}=\boldsymbol{P} \boldsymbol{H} \)
Subject: Maths
If \( m \) and \( p \) are positive \( (m \geq p) \) and
\( \boldsymbol{\Delta}(\boldsymbol{m}, \boldsymbol{p})= \)
\( \left|\begin{array}{ccc}m & C_{p} & m \\ m+1 & C_{p} \\ m+2 & m+1 & C_{p+1} & m+1 \\ m_{p} & m+2 & m_{p+2} \\ & & m+2\end{array}\right| \) and
\( m_{\boldsymbol{p}}=\mathbf{0} \) if \( \mathbf{m}<\mathbf{p}, \) then
This question has multiple correct options
A \( . \Delta(2,1) / \Delta(1,0)=4 \)
B. \( \Delta(4,3) / \Delta(3,2)=2 \)
\( \mathbf{c} \cdot \Delta(4,3) / \Delta(2,1)=5 \)
D. \( \Delta(4,3) / \Delta(1,0)=10 \)
Subject: Physics
The volume of oil contained in a certain
hydraulic press is \( 0.2 m^{3} . \) The
compressibility of oil is \( 20 \times 10^{-6} \) per
atmosphere. The decrease in volume of the oil when subjected to 200
atmospheres is (1 atmosphere \( = \)
\( \left.1.02 \times 10^{5} N / m^{2}\right) \)
A \( \cdot 4 \times 10^{-4} m^{3} \)
B. \( 8 \times 10^{-4} m^{3} \)
c. \( 16 \times 10^{-4} m^{3} \)
D. \( 2 \times 10^{-4} m^{3} \)
Subject: Chemistry
Which of the following cells can be used to experimentally determine the reduction potential of Zinc?
A \( \cdot Z n(s)\left|Z n^{2+}(a q)\right|\left|H^{+}(a q)\right| H_{2}(g), P t \)
B . \( P t, H_{2}(g)\left|H^{+}(a q)\right||Z n(s)| Z n^{2+}(a q) \)
c. \( Z n(s)\left|Z n^{2+}(a q)\right|\left|C u^{2+}(a q)\right| C u(s) \)
D. any one of these
Subject: Physics
Light of frequency \( v \) is incident on a
metal of threshold frequency \( v_{0} . \) Then work function of metal will be:
A \( . h v \)
в. \( h v_{0} \)
\( \mathbf{c} \cdot h\left(v-v_{0}\right) \)
D. \( h\left(v+v_{0}\right) \)
Subject: Physics
A body of mass \( 0.1 k g \) is moving with a velocity of \( 15 m / s . \) The momentum associated with the ball will be
A. \( 0.5 k g m / s \)
в. \( 1.5 k g m / s \)
c. \( 2.5 k g m / s \)
D. 3.2Ns
Subject: Physics
A beam of unpolarized light is passed first through a tourmaline crystal \( \boldsymbol{A} \) and then through another tourmaline
crystal \( B \) oriented so that its principal
plane is parallel to that of \( A \). The
intensity of final emergent light is \( I \)
The value of the \( I \) is
A \( \cdot \frac{I_{o}}{2} \)
в. \( \frac{I_{o}}{4} \)
c. \( \frac{I_{o}}{8} \)
D. none of these
Subject: Chemistry
According to Bohr's theory, the angular momentum for an electron of 5th orbit
is:
\( \mathbf{A} \cdot 10 h / \pi \)
в. \( 5 h / 2 \pi \)
\( \mathbf{c} \cdot 25 h / \pi \)
D. \( 5 \pi / 2 h \)