AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Match the following:
Biodegradable \( \mathbf{F} \)
(i) \( \quad(p) \quad \) Hydroxybuta B
p polymer poing
(ii) Phenol
2-chlorobuta-1
(ii) Bakelite
(ig) Phenol
Neoprene
(iv) Glyptal
(r) 2-chlore
diene
(iii) 2-chlo
diene
\( \mathbf{A} \cdot i-p, i i-q, i i i-r, i v-s \)
B \( . i-q, i i-p, i i i-r, i v-s \)
\( \mathbf{c} \cdot i-p, i i-q, i i i-s, i v-r \)
D. \( i-s, i i-r, \) ii \( i-p, i v-q \)
Subject: Maths
Factorize :
\( a^{4}+4 b^{4}+3 a^{2} b^{2} \)
\( \mathbf{A} \cdot\left(a^{2}+a+2 b^{2}\right)\left(a^{3}-a b+2 b^{3}\right) \)
B \( \cdot\left(a^{2}-a b-2 b^{2}\right)\left(a^{2}-a b+2 b^{2}\right) \)
\( \mathbf{C} \cdot\left(a^{3}+b+2 b^{3}\right)\left(a^{2}-a b+2 b^{2}\right) \)
D \( \cdot\left(a^{2}+a b+2 b^{2}\right)\left(a^{2}-a b+2 b^{2}\right) \)
Subject: Chemistry
Allyl bromide is:
\( \mathbf{A} \cdot C H_{2}=C H-C H_{2}-B r \)
B \( \cdot C H_{2}=C H_{2}-B r \)
\( \mathbf{c} \cdot C H_{3}-C H=C H-B r \)
\( \mathbf{D} \cdot C H_{3}-C H_{2}-C H_{2}-B r \)
Subject: Maths
Find the term of the expansion of \( (\sqrt[3]{x^{-2}}+x)^{7} \) containing \( x \) in the
second power
\( \mathbf{A} \cdot T_{4} \)
в. \( T_{5} \)
c. \( T_{6} \)
\( \mathbf{D} \cdot T_{7} \)
Subject: Maths
If \( C_{1}: x^{2}+y^{2}-20 x+64=0 \) and
\( C_{2}: x^{2}+y^{2}+30 x+144=0 . \) Then the
length of the shortest line segment \( \boldsymbol{P Q} \)
which touches \( C_{1} \) at \( P \) and to \( C_{2} \) at \( Q \)
is
A . 10
B. 15
\( c \cdot 22 \)
D. 27
Subject: Maths
A man travelled \( 72 \mathrm{km} \) to the North of
Hubballi and then \( 121 \mathrm{km} \) to the south
of it. How far from Hubballi was he
finally.
\( \mathbf{A} \cdot 49 \mathrm{km} \)
B. 9 кт
c. \( 49 \mathrm{m} \)
D. \( 4 \mathrm{km} \)
Subject: Physics
A rubber cord of length \( 40 \mathrm{cm} \) and area
of cross section \( 4 \times 10^{-6} \mathrm{m}^{2} \) is extended
by 10cm. If the energy gained is 20 joule young's modulus of rubber is
\( \mathbf{A} \cdot 10^{8} N m^{-2} \)
B . \( 2 \times 10^{8} \mathrm{Nm}^{-2} \)
\( \mathbf{c} \cdot 4 \times 10^{8} \mathrm{Nm}^{-2} \)
D. \( 1.5 \times 10^{6} N m^{-2} \)
Subject: Maths
Find one rational number between the
following pairs of rational numbers
(i) \( \frac{4}{3} \) and \( \frac{2}{5} \)
(ii) \( \frac{-2}{7} \) and \( \frac{5}{6} \)
(iii) \( \frac{5}{11} \) and \( \frac{7}{8} \)
(iv) \( \frac{7}{4} \) and \( \frac{8}{3} \)
Subject: Physics
A snap bubble is being blown on a tube
of radius \( 1 \mathrm{cm} \). the surface tension of the
soap solution is \( 0.05 \mathrm{N} / \mathrm{m} \) and the
bubble makes an angle of \( 60^{\circ} \) with the
tube as shown. The excess of pressure
over the atmospheric pressure in the
tube is:
\( A \cdot 5 P a \)
B. 1 Pa
c. \( 10 \mathrm{Pa} \)
D. 20 Pa
Subject: Maths
Assertion
Let \( f \) and \( g \) be increasing and
decreasing functions respectively from \( [0, \infty] \) to \( [0, \infty] . \operatorname{Let} h(x)=f(g(x)) . \) If
\( h(0)=0, \) then \( h(x) \) is always zero
Reason
\( h(x) \) is an increasing function of \( x \)
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 charge/size ratio of a cation determines its polarizing power. Which one of the following sequences represents the increasing order of the polarizing power of the cationic species,
\( \mathrm{K}^{+}, \mathrm{Ca}^{2+}, \mathrm{Mg}^{2+}, \mathrm{Be}^{2+} ? \)
\( A \cdot M g^{2+}<B e^{2+}<K^{+}<C a^{2+} \)
B. \( B e^{2+}<K^{+}<C a^{2+}<M g^{2} \)
C \( \cdot \mathrm{k}^{+}<\mathrm{Ca}^{2+}<\mathrm{Mg}^{2+}<\mathrm{Be}^{2+} \)
D. \( \mathrm{Ca}^{2+}<\mathrm{Mg}^{2+}<\mathrm{Be}^{2+}<\mathrm{K}^{+} \)
Subject: Chemistry
The action of concentrated sulphuric
acid on urea \( \left(N H_{2} C O N H_{2}\right) \) results in
the production of a white crystalline solid \( X \) of formula \( H_{3} N O_{3} S . \) This is a
monobasic acid. On treatment with
sodium nitrate and dilute hydrochloride
acid at \( 0^{\circ} \mathrm{C}, \) it liberates 1 mole of \( N_{2} \) per
mol of \( X \) and on addition of aqueous
barium chloride, the resulting solution
yields 1 mole of \( B a S O_{4} \) per mole of \( X \) taken
Deduce the structure of \( \boldsymbol{X} \)
Subject: Physics
A swimmer is capable of swimming
\( 1.65 m s^{-1} \) in still water. If she swims
directly across a \( 180 \mathrm{m} \) wide river whose current is \( 0.85 \mathrm{m} / \mathrm{s} \), how far downstream(from a point opposite her standing point) will she reach?
\( \mathbf{A} .92 .7 \mathrm{m} \)
в. \( 40 \mathrm{m} \)
c. 48 m
D. 20
Subject: Maths
The real part of
\( \left[\mathbf{1}+\cos \left(\frac{\pi}{5}\right)+i \sin \left(\frac{\pi}{5}\right)\right]^{-1} \) is
A .
в. \( \frac{1}{2} \)
c. \( \frac{1}{2} \cos \left(\frac{\pi}{10}\right) \)
D. \( \frac{1}{2} \cos \left(\frac{\pi}{5}\right) \)
Subject: Physics
Which formula is used to calculate the
coefficient of viscosity of a given liquid in the laboratory (symbols have their usual meanings)?
A \( \cdot_{\eta}=\frac{9}{2}(\rho-\sigma) g \frac{r^{2}}{v} \)
в. \( \frac{2}{9}(\rho-\sigma) g \frac{r^{2}}{v} \)
\( ^{\mathrm{c}} \cdot \frac{2}{9}(\rho-\sigma) g \frac{r^{2}}{v g} \)
\( ^{\mathrm{D}} \cdot \frac{2}{9}(\rho-\sigma) g \frac{v g}{r^{2}} \)
Subject: Chemistry
Consider the following reaction.
\[
\left.\right|_{\mathbf{C H O}} ^{\mathbf{C H O}}+\left.\mathbf{O H}^{-} \longrightarrow\right|_{\mathbf{C H}_{2} \mathbf{O H}} ^{\mathbf{O O}^{-}}
\]
A. It is not a disproportionation reaction
B. It is intramolecular redox reaction
C. \( O H^{-} \) is reducing as well as oxidising agent
D. \( (C H O)_{2} \) is a reducing as well as oxidising agent
Subject: Maths
The centre of a square is at the origin
and vertex is \( A(2,1) . \) Find the \( c 0 \)
ordinates of other vertices of the square
A. \( B(1,-2), C(-2,-1), D(-1,-2) \)
B. \( B(-1,-2), C(-2,-1), D(-1,-2) \)
c. \( B(-1,2), C(-2,-1), D(1,-2) \)
D. \( (-1,-2), C(-2,-1), D(1,2) \)
Subject: Physics
A bi-convex lens is formed with two thin
plano-convex lenses as shown in the figure. The refractive index n of the first
lens is 1.5 and that of the second lens is
1.2 Both the curved surfaces are of the
same radius of curvature \( \boldsymbol{R}=\mathbf{1 4 c m} \)
For this bi-convex lens, for an object
distance of \( 40 \mathrm{cm}, \) the image distance
will be
\( \mathbf{A} \cdot-280.0 \mathrm{cm} \)
в. \( 40.0 \mathrm{cm} \)
c. \( 21.5 \mathrm{cm} \)
D. \( 13.3 \mathrm{cm} \)
Subject: Chemistry
The process of separation of an organic
compound from its aqueous solution
by shaking with a suitable solvent is termed solvent extraction or differential
extraction.
The organic compound present in
aqueous layer moves to the organic
solvent because:
A. the organic substance is more soluble in the organic solvent
B. organic compound being lighter moves in the upper layer
c. organic solvent is insoluble in water hence organic compound moves up
D. from the supersaturated aqueous solution the solute starts diffusing
Subject: Maths
If \( A^{\prime} \) is the transpose of a square matrix
A, then
A \( \cdot|A| \neq \mid A^{\prime} \)
B \( \cdot|A|=\left|A^{\prime}\right| \)
c \( \cdot|A|+\left|A^{\prime}\right|=0 \)
D \cdot \( |A|=\left|A^{\prime}\right| \) only when A is symmetric
Subject: Chemistry
What is the correct relationship between the following compound?
\[
\begin{array}{l}
\boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\underset{C H_{3}}{\boldsymbol{C}} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{C} \boldsymbol{H}_{3} \\
\boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\underset{C H_{3}}{\boldsymbol{C}} \boldsymbol{H}_{2}
\end{array}
\]
Subject: Physics
If the position vector of the vertices of a triangle are \( \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\boldsymbol{2} \hat{\boldsymbol{k}} ; \boldsymbol{2} \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \boldsymbol{\&} \)
\( \mathbf{3} \hat{\mathbf{i}}-\hat{\boldsymbol{j}}+\mathbf{2} \hat{\boldsymbol{k}}, \) then find the area of the
triangle.
A. \( \sqrt{5} m^{2} \)
B. \( 5 m^{2} \)
\( c \cdot 25 m^{2} \)
D. \( 2 m^{2} \)
Subject: Chemistry
When pure ammonium chloride is dissolved in pure water, the \( p H \) of the resulting solution is not \( 7 . \) This is
because:
A. ammonium ions accept protons from water molecules leaving free \( O H^{-} \) ions in the solution
B. ammonium ions donate protons to water molecules forming \( H_{3} O^{+} \) ions in the solution
c. ammonium ions combine with water molecules to give the weak base, ammonium hydroxide
D. chloride ion make the solution acidic
Subject: Maths
The area(in sq. units) of the smaller portion enclosed between the curves, \( x^{2}+y^{2}=4 \) and \( y^{2}=3 x, \) is
A \( \cdot \frac{1}{\sqrt{3}}+\frac{4 \pi}{3} \)
в. \( \frac{1}{2 \sqrt{3}}+\frac{\pi}{3} \)
c. \( \frac{1}{2 \sqrt{3}}+\frac{2 \pi}{3} \)
D. \( \frac{1}{\sqrt{3}}+\frac{2 \pi}{3} \)
Subject: Physics
Calculate the electric flux through ring shown in figure is:
\( ^{A} \cdot \frac{q}{2 \varepsilon_{0}}\left[1+\frac{L}{\sqrt{R^{2}+L^{2}}}\right. \)
в. \( \frac{q}{2 \varepsilon_{0}}\left[1-\frac{L}{\sqrt{R^{2}+L^{2}}}\right. \)
c. \( \frac{q}{\varepsilon_{0}}\left[1-\frac{L}{\sqrt{R^{2}+L^{2}}}\right. \)
D. zero
Subject: Chemistry
An excess of \( A g_{2} C r O_{4}(s) \) is added to a
\( \mathbf{5} \times \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{M} \boldsymbol{K}_{\mathbf{2}} \boldsymbol{C r} \boldsymbol{O}_{\mathbf{4}} \) solution. The
concentration of \( A g^{+} \) in the solution is closest to.[Solubility product for \( \left.A g_{2} C r O_{4}=1.1 \times 10^{-12}\right] \)
B . \( 1.5 \times 10^{-5} \) М
c. \( 1.0 \times 10^{-6} \mathrm{M} \)
D. \( 5.0 \times 10^{-3} \) М
Subject: Maths
If \( \boldsymbol{R}=\left\{(\boldsymbol{x}, \boldsymbol{y}): \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{Z}, \boldsymbol{x}^{2}+\boldsymbol{y}^{2} \leq \mathbf{4}\right\} \)
is a relation in \( Z \) then domain \( D \) is
\( \mathbf{A} \cdot\{-2,-1,0,1,2\} \)
B \( \cdot\{-2,-1,0\} \)
c. \{0,1,2\}
D. None of these
Subject: Physics
An isolated conducting sphere whose radius \( R=1 m \) has a charge \( q=\frac{1}{9} n C \)
The energy density at the surface of the
sphere is:
A \( \cdot \frac{\varepsilon_{0}}{2} J / m^{3} \)
B . \( \varepsilon_{0} J / m^{3} \)
\( \mathbf{c} \cdot 2 \varepsilon_{0} J / m^{3} \)
D. \( \frac{\varepsilon_{0}}{3} J / m^{3} \)
Subject: Physics
Two particles of different masses \( m_{1} \)
and \( m_{2}, \) different charges \( Q_{1} \) and \( Q_{2} \)
are accelerated through the same potential difference and then enter a
uniform magnetic field in a direction perpendicular to the field. If they trace circular paths of same radius, then the
ratio of their masses \( \left(m_{1} / m_{2}\right) \) must be
A \( \cdot Q_{2} / Q_{1} \)
в. \( Q_{1} / Q_{2} \)
c. \( \left(Q_{1} / Q_{2}\right)^{1 / 2} \)
the
D. \( \left(Q_{2} / Q_{1}\right)^{1 / 2} \)
Subject: Biology
Thermococcus, Methanococcus and
Methanobacterium exemplify
A. Bacteria that contain a cytoskeleton and ribosomes
B. Archaebacteria that contain protein homologous to eukaryotic core histones
C. Archaebacteria that lack any histones resembling those found in eukaryotes but whose DNA is negatively supercoiled
D. Bacteria whose DNA is relaxed or positively supercoiled but which have a cytoskeleton as well as mitochondria
Subject: Chemistry
\( \boldsymbol{K}_{s p} \) of a salt \( \boldsymbol{N} \boldsymbol{i}(\boldsymbol{O} \boldsymbol{H})_{2} \) is \( \boldsymbol{2} \times \mathbf{1 0}^{-15} \)
then molar solubility of \( N i(O H)_{2} \) in
\( \mathbf{0 . 0 1} \boldsymbol{M} \mathbf{N a O H} \mathbf{~ i s : ~} \)
A \( \cdot 2 \times 10^{-15} \mathrm{M} \)
B . \( 2^{-1 / 3} \times 10^{-5} M \)
c. \( 2 \times 10^{-11} M \)
D. \( 10^{-7} M \)
Subject: Physics
The maximum value attained by the tension in the string of a swinging pendulum is four times the minimum value it attains. There is no slack in the
string. The angular amplitude of the pendulum is?
A \( \cdot 90^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 30^{\circ} \)
Subject: Maths
The value of the sum \( \sum_{n=1}^{13}\left(i^{n}+i^{n+1}\right) \)
where \( \boldsymbol{i}=\sqrt{-\mathbf{1}} \) is:
\( \mathbf{A} \cdot i \)
B. \( -i \)
\( c \cdot 0 \)
D. \( i-1 \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{cc}\cos \boldsymbol{x} & \sin \boldsymbol{x} \\ -\sin \boldsymbol{x} & \cos \boldsymbol{x}\end{array}\right], \) show that
\( A^{2}= \)
\( \left[\begin{array}{cc}\cos 2 x & \sin 2 x \\ -\sin 2 x & \cos 2 x\end{array}\right] \) and \( A^{\prime} A=I \)
Subject: Physics
At a harbour, a boat is standing and wind is blowing at a speed of \( \sqrt{2} \mathrm{m} / \mathrm{sec} \) due to which, the flag on the boat flutters along northeast. Now the boat enters in to river, which is flowing with a velocity of \( 2 \mathrm{m} / \mathrm{sec} \). due north. The boat
starts with zero velocity relative to the river and its constant acceleration
relative to the river is \( 0.2 m / s e c^{2} \) due east. In which direction will the flag
flutter at 10 seconds?
A. south-east
B. south-west
c. \( 30^{\circ} \) south of west
D. west
Subject: Maths
Let in \( \Delta A B C, \angle A=\frac{\pi}{2} . \) Then value of \( \tan ^{-1} \frac{b}{a+c}+\tan ^{-1} \frac{c}{a+b} \) equals
A \( \cdot \frac{\pi}{2} \)
в.
\( c \cdot \frac{\pi}{3} \)
D. None of these
Subject: Physics
The distance between the two charges
\( +q \) and \( -q \) of a dipole is \( r . \) The
intensity at a point on the axial line at a
distance \( x \) from the centre of dipole is
proportional to
A \( \cdot \frac{q}{x^{2}} \)
в. \( \frac{q r}{x^{2}} \)
c. \( \frac{q}{x^{3}} \)
D. \( \frac{q r}{x^{3} r} \)
Subject: Maths
A bag contains \( a \) white and \( b \) black
balls. Two players, \( A \) and \( B \) alternately
draw a ball from the bag, replacing the
ball each time after the draw till on of
them draws a white ball and win the
game. \( A \) begins the game. If the
probability of \( \boldsymbol{A} \) winning the game is
three times that of \( B \), the ratio \( a: b \) is
A . 1: 1
B. 1: 2
\( c \cdot 2: 1 \)
D. None of these
Subject: Chemistry
Which of the following shows positive deviation from Raoult's law?
A. \( C_{6} H_{6} \) and \( C_{6} H_{5} C H_{3} \)
B . \( C_{6} H_{6} \) and \( C C l_{4} \)
c. \( C H C l_{3} \) and \( C_{2} H_{5} O H \)
D. \( C H C_{3} \) and \( C H_{3} C O C H_{3} \)
Subject: Physics
Assertion
Ultrasonic waves are longitudinal
waves of frequency greater than 20,000 \( \mathrm{Hz} \)
Reason
The maximum frequency of audible sound waves is \( 20,000 \mathrm{Hz} \)
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 net force \( \sum F_{x}(t)=A+B t^{2} \) in the \( +x \)
direction is applied to a girl of mass \( \mathrm{m} \) The force starts at \( t=0 \) and continues
until time t.
This question has multiple correct options
A. Impulse of the force is \( 2 B t \)
B. Her speed at time t is \( \frac{A}{m} t+\left(\frac{B}{3 m}\right) t^{3} \)
C. Impulse of the force is \( A t+\left(\frac{B}{3}\right) t^{3} \)
D. Her speed at time tis \( \left(\frac{2 B}{m}\right) t \)
Subject: Chemistry
Assertion
In atomic form hydrogen consists one proton and one electron.
Reason
In elemental form hydrogen exists as a diatomic molecule and is called
dihydrogen.
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
A first order reaction follows the
expression:
A \( \cdot C_{t} e^{k_{1} t}=C_{0} \)
B. \( C_{t}=C_{t} e^{k_{1} t} \)
\( \mathbf{c} \cdot \ln \frac{C_{o}}{C_{t}}=-k_{1} t \)
\( \mathbf{D} \cdot \ln \frac{C_{t}}{C_{o}}=k_{1} t \)
Subject: Chemistry
The density of an equilibrium mixture of \( N_{2} O_{4} \) and \( N O_{2} \) at \( 101.32 K P_{a} \) is 3.62
\( g d m^{3} \) at \( 288 \mathrm{K} \) and \( 1.84 \mathrm{g} d m^{3} \) at \( 348 \mathrm{K} \)
What is the heat of the reaction for the
following reaction?
\( N_{2} O_{4} \rightleftharpoons 2 N O_{2}(g) \)
B. \( \Delta_{r} H=75.68 \) kJ \( \mathrm{mol}^{-1} \)
C . \( \Delta_{r} H=95.7 \) kJ \( \mathrm{mol}^{-1} \)
D. \( \Delta_{r} H=151.3 \) kJ \( \mathrm{mol}^{-1} \)
Subject: Maths
Verify whether the function \( \boldsymbol{f}: \mathrm{AB} \) where \( \boldsymbol{A}=\boldsymbol{R}-\{\mathbf{3}\} \) and \( \boldsymbol{B}= \)
\( \boldsymbol{R}-\{1\}, \) defined by \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}-\boldsymbol{2}}{\boldsymbol{x}-\boldsymbol{3}} \) is
one-one and on-to or not. Give reason.
Subject: Physics
If \( \vec{A}=4 \hat{i}+6 \widehat{j} \) and \( \vec{B}=2 \hat{i}+3 \hat{j} \).Then :
\( \mathbf{A} \cdot \vec{A} \cdot \vec{B}=29 \)
в . \( \vec{A} \times \vec{B}=0 \)
\( ^{\mathbf{c}} \cdot \frac{|\vec{A}|}{|\vec{B}|}=\frac{2}{1} \)
D. angles between \( \vec{A} \) and \( \vec{B} \) is 30
Subject: Maths
Equation of a straight line on which length of perpendicular from the origin is four units and the line makes an
angle of \( 120^{\circ} \) with \( x- \) axis is
A \( . x \sqrt{3}+y+8=0 \)
в. \( x+\sqrt{3} y=8 \)
c. \( x \sqrt{3}-y=8 \)
D. \( x-\sqrt{3} y+8=0 \)
Subject: Chemistry
Chlorobenzene can be prepared by
reacting aniline with:
A \( . \) Hydrochloric acid \( (H C l) \)
B. Cuprous chloride \( \left(C u_{2} C l_{2}\right) \)
C. Chlorine in the presence of anhydrous aluminium chloric
D. Nitrous acid followed by heating with cuprous chloride(c
Subject: Physics
A dipole of dipole moment \( \overrightarrow{\boldsymbol{p}} \) is kept along an electric field \( \overrightarrow{\boldsymbol{E}} \) such that \( \overrightarrow{\boldsymbol{E}} \) and \( \vec{p} \) are in the same direction. Find the work done in rotating the dipole by an angle \( \pi \)
A. \( W=3 E p \)
в. \( W=2 E p \)
c. \( W=4 \) Ер.
D. \( W=5 E p \)
Subject: Maths
\( \boldsymbol{y}=\cos ^{-1}\left\{\frac{2 \boldsymbol{x}-\boldsymbol{3} \sqrt{1-\boldsymbol{x}^{2}}}{\sqrt{\mathbf{1 3}}}\right\}, \) find \( \frac{\boldsymbol{d} \boldsymbol{2}}{\boldsymbol{d}} \)
Subject: Chemistry
What is the oxidation state of Co in the
complex \( \left[\text { Co} C l_{2}(e n)_{2}\right]^{+} ? \)
[Note: Ethylenediamine \( (e n)=H_{2} N- \)
\( \left.\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{N} \boldsymbol{H}_{2}\right] \)
Subject: Physics
carrying current \( i_{0} \) lies in the \( x \) -y plane as shown in the figure. It is hinged at \( y^{-} \)
axis so that it can freely route about it. Moment of inertia of the loop about an
axis through its c.m. and normal to its
plane is equal to \( \gamma M a^{2} . A t t=0, \) an
external magnetic field of induction B is applied along +ve x axis. The initial angular acceleration of the loop is equal
to
A \( \cdot \frac{4 i_{0} B}{M(2 \gamma+1)} \)
В. \( \frac{i_{0} B}{M \gamma} \)
c. \( \frac{4 i_{0} \pi B}{M(2 \gamma+1)} \)
D. \( \frac{4 i_{0} B}{(2 \gamma+1)} \)
Subject: Maths
The D.E whose solution is \( y=A \cos x+ \)
\( \sin x \) is:
A \( \cdot \frac{d y}{d x}+y \tan x=\sec x \)
в. \( \frac{d y}{d x}+y \sin x=\cos x \)
c. \( \frac{d y}{d x}+y \sec x=\tan x \)
D. \( \frac{d y}{d x}+y \cot x=\csc x \)
Subject: Physics
A uniform copper wire carries a current
\( \boldsymbol{i} \) amperes and has \( \boldsymbol{p} \) carriers per metre.
The length of the wire is \( l \) metres and its
cross-section area is s metre. If the
charge on a carrier is \( q \) coulombs, the
drift velocity in \( m s^{-1} \) is given by
\( \mathbf{A} \cdot i / l s q \)
\( \mathbf{B} \cdot i / p s q \)
\( \mathbf{c} \cdot p s q / i \)
\( \mathbf{D} \cdot i / p s l q \)
Subject: Physics
A travelling wave has an equation of the form \( \boldsymbol{A}(\boldsymbol{x}, \boldsymbol{t})=\boldsymbol{f}(\boldsymbol{x}+\boldsymbol{v} \boldsymbol{t}) . \) The relation
connecting positional derivative with
time derivative of the function is:
A \( \cdot \frac{d A}{d t}=\pm v^{2} \frac{d A}{d x} \)
в. \( \frac{d A}{d t}=\pm v \frac{d A}{d x} \)
c. \( \left.\frac{d A}{d t}=\pm \sqrt{(} v\right) \frac{d A}{d x} \)
D. \( \frac{d A}{d t}=(2 \pi v / \lambda) \frac{d A}{d x} \)
Subject: Physics
Identify the energy changes in the following two cases -
\( A: A \) car moving up a hill
B : Photographic film is exposed to sun-
light
A. In 'A' mechanical energy in moving car is converted to potential energy and in 'B' potential energy is converted to chemical energy
B. In'A' potential energy in moving car is converted to kinetic energy and in 'B' chemical energy is converted to light energy.
C. In'A' kinetic energy in moving car is converted to potential energy and in 'B' potential energy is converted to light energy.
D. In'A' kinetic energy is moving car is converted to potential energy and in 'B' light energy is converted to chemical energy.
Subject: Physics
In an LCR circuit the potential
difference between the terminal of the
inductance is \( 60 V \), between the
terminals of the capacitor is \( 30 V \) and
that between the terminals of the
resistance is \( 40 \mathrm{V} \). The supply voltage
will be equal to:
\( \mathbf{A} \cdot 130 V \)
в. \( 10 V \)
\( c .50 V \)
D. \( 70 V \)
Subject: Physics
A ballon starts rising from the ground with an acceleration of \( 1.25 \mathrm{m} / \mathrm{s}^{2} \). After
\( 8 s \) a stone is released from the balloon.
The stone will (take \( \left.g=10 m / s^{2}\right) \)
A. have a displacement of \( 50 \mathrm{m} \)
B. cover a distance of 40 \( \mathrm{m} \) in reaching the ground
c. reach the ground in 4 s
D. reach the ground in 16 s
Subject: Chemistry
Match the name of vitamins in column
with their sources in column II and
mark the appropriate choice.
Column I Column II
(A) Vitamin
\( B_{1} \)
(i) Milk, yeast, cereals
(B) Vitamin
(ii) Meat, fish, egg
\( B_{12} \)
(C) Vitamin
(iii) Carrots, butter, papaya
(D) Vitami
(iv) Citrus fruits, amla, green leafy
\( \mathrm{C} \quad \) vegetables
\( \mathbf{A} \cdot(A) \rightarrow(\text { iii) },(B) \rightarrow(i v),(C) \rightarrow(i),(D) \rightarrow(\text { ii }) \)
B. \( (A) \rightarrow(\text { ii) },(B) \rightarrow(i),(C) \rightarrow(i \text { i) },(D) \rightarrow(i v) \)
C \( \cdot(A) \rightarrow(\text { iv ) },(B) \rightarrow(\text { iii) },(C) \rightarrow(\text { ii }),(D) \rightarrow(i) \)
D. (A) \( \rightarrow \) (i), (B) \( \rightarrow \) (ii), (C) \( \rightarrow \) (ii), (D) \( \rightarrow \) (iv)
Subject: Maths
If \( y=\sqrt{\frac{1+\tan x}{1-\tan x}} \) then \( \frac{d y}{d x} \) is equal to
A \( \cdot \frac{1}{2} \sqrt{\frac{1-\tan x}{1+\tan x}} \sec ^{2}\left(\frac{\pi}{4}+x\right) \)
в. \( \sqrt{\frac{1-\tan x}{1+\tan x}} \sec ^{2}\left(\frac{\pi}{4}+x\right) \)
c. \( \frac{1}{2} \sqrt{\frac{1-\tan x}{1+\tan x}} \sec \left(\frac{\pi}{4}+x\right) \)
D. None of these
Subject: Chemistry
(a) Draw the molecular structoms of
following compounds:
(i) \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\boldsymbol{6}} \)
(ii) \( \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{8} \)
(b) Explain the following observations:
(i) The molecules \( N H_{3} \) and \( N F_{3} \)
have dipole moments which are of opposite direction.
(ii) All the bonds of \( P C l_{5} \) molecule
are not equivalent.
(iii) Sulphur in vapour state exhibits paramagnetism.
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{cl}\boldsymbol{x}^{a} \cos (\mathbf{1} / \boldsymbol{x}), & \text { if } \quad \boldsymbol{x} \neq \mathbf{0} \\ \text { 0, } & \text { if } \quad \boldsymbol{x}=\mathbf{0}\end{array}\right. \)
continuous at \( x=0 \) then
\( \mathbf{A} \cdot \alpha<0 \)
B \( . \alpha>0 \)
\( \mathbf{c} \cdot \alpha=0 \)
D. \( \alpha \geq 0 \)