AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Let \( \left\{a_{n}\right\} \) and \( \left\{b_{n}\right\} \) are two sequences
given by \( a_{n}=(x)^{1 / 2^{n}}+ \)
\( (\boldsymbol{y})^{1 / 2^{n}} \) and \( \boldsymbol{b}_{n}=(\boldsymbol{x})^{1 / 2^{n}}-(\boldsymbol{y})^{1 / 2^{n}} \) for
all \( n \epsilon \) N. The value of \( a_{1} a_{2} a_{3} \dots a_{n} \) is equal to
\( A \cdot x-y \)
в. \( \frac{x+y}{b_{n}} \)
c. \( \frac{x-y}{b_{n}} \)
D. \( \frac{x y}{b_{n}} \)
Subject: Maths
\( \int\left[\log (1+\cos x)-x \tan \left(\frac{x}{2}\right)\right] d x \)
A \( \cdot x \log (1+\tan x) \)
B \( \cdot x \log (1+\sin x) \)
\( \mathbf{C} \cdot \log (1+\sin x) \)
D. \( x \log (1+\cos x) \)
Subject: Chemistry
In the hardening stage of plaster of paris, the compound formed is :
A. \( \operatorname{CaSO}_{4} \)
B. orthorhombic \( C a S O_{4} .2 H_{2} O \)
\( \mathrm{c} \cdot \mathrm{CaSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. monoclinic \( C a S O_{4} .2 H_{2} O \)
Subject: Physics
An experiment is performed to
determine the \( I-V \) characteristics of
a Zener diode, which has a protective
resistance of \( R=100 \Omega \), and a
maximum power of dissipation rating
of \( 1 W . \) The minimum voltage range of
the DC source in the circuit is
A. \( 0-24 V \)
В. \( 0-5 V \)
\( \begin{array}{ll}c-12 V & V \\ V V & -0.12\end{array}-12 \)
D. \( 0-8 V \)
Subject: Chemistry
Assertion
In the reaction below, the final product
will be a meso diacid
Reason
The initial step of rection is \( S_{N} 2 \)
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Physics
Two vibrating strings of the same
material but length \( L \) and \( 2 L \) have radii
\( 2 r \) and \( r \) respectively. They are
stretched under the same tension. Both
the string vibrate in their fundamental
modes, the one of length \( L \) with
frequency \( v_{1} \) and other with frequency
\( \boldsymbol{v}_{2} . \) The ratio \( \boldsymbol{v}_{1} / \boldsymbol{v}_{2} \) is given by
A . 2
B. 4
c. 8
D.
Subject: Maths
The sides of a triangle with positive area have lengths 5,7 and \( a . \) The sides of a second triangle with positive area
have lengths 5,7 and \( b \) Which of the following is NOT a possible
value of \( |\boldsymbol{a}-\boldsymbol{b}| ? \)
A . 3
B. 5
\( c \cdot 7 \)
D. 10
Subject: Maths
In the figure above, three lines intersect
at a point.
If \( \boldsymbol{f}=\mathbf{8 5}^{\boldsymbol{o}} \) and \( \boldsymbol{c}=\mathbf{2 5}^{\boldsymbol{o}}, \) what is the
value of \( a ? \)
Note : Figure not drawn to scale
A \( \cdot 60^{\circ} \)
B. \( 65^{\circ} \)
\( c \cdot 70^{\circ} \)
D. \( 75^{\circ} \)
Subject: Physics
A resistance 'R' draws power'P' when connected to an AC source. If an
inductance is now placed in series with the resistance, such that the
impedance of the circuit becomes 'Z',
the power drawn will be
\( \mathbf{A} \cdot P\left(\frac{R}{Z}\right) \)
в. \( P \)
c. \( P\left(\frac{R}{Z}\right)^{2} \)
D. \( P \sqrt{\frac{R}{Z}} \)
Subject: Physics
For the given situation irrespective of the magnitude of charge and their
separation it is found that total energy of the system (i.e. electric potential energy and their K.E.) is related to K.E. by the equation total energy = -kinetic energy \( (k) \) Which of the following gives the correct value of potential energy of the system?
A \( \cdot \frac{q^{2}}{4 \pi \varepsilon_{0} R} \)
В. \( \frac{q^{2}}{8 \pi \varepsilon_{0} R} \)
\( ^{\mathbf{C}}-\frac{q^{2}}{4 \pi \varepsilon_{0} R} \)
\( ^{\mathrm{D}}-\frac{q^{2}}{8 \pi \varepsilon_{0} R} \)
Subject: Maths
Diagonals \( \boldsymbol{A C} \) and \( \boldsymbol{B D} \) of a
trapezium \( \boldsymbol{A B C D} \) with \( \boldsymbol{A B} \| \boldsymbol{D C} \)
intersect each other at \( O . \) Prove that
\( \boldsymbol{a} \boldsymbol{r}(\boldsymbol{A O D})=\boldsymbol{a r}(\boldsymbol{B O C}) \)
Subject: Physics
A metallic rod of \( ^{\prime} \boldsymbol{L}^{\prime} \) length is rotated
with angular frequency of \( ^{\prime} \omega^{\prime} \) with one
end hinged at the centre and the other
end at the circumference of a circular
metallic ring of radius \( L \) about an axis
passing through the centre and perpendicular to the plane of the ring. \( \mathbf{A} \)
constant and uniform magnetic field \( \boldsymbol{B} \) parallel to the axis is present
everywhere. Deduce the expression for
the emf between the centre and the
metallic ring.
(a)
\( (b) \)
Subject: Maths
A survey conducted on 600 students of
B. A part I classes of a collage gave the
following report. Out of 600 students,
307 took economics, 198 took history,
230 took sociology, 65 took history and
economics, 45 took economics and sociology, 31 took sociology and history and 10 took all the three subjects. The report sounded very impressive, but the surveyor was fired. Why?
Subject: Maths
The area bounded by curves \( 3 x^{2}+ \)
\( \mathbf{5} \boldsymbol{y}=\mathbf{3} 2 \) and \( \boldsymbol{y}=|\boldsymbol{x}-\mathbf{2}| \) is
A . 25
B. 17/2
c. \( 33 / 2 \)
D. 33
Subject: Chemistry
Assertion: The standard potential of
\( \boldsymbol{C l}^{\ominus}|\boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}| \boldsymbol{A} \boldsymbol{g} \) half cell is related to that
of \( \boldsymbol{A} \boldsymbol{g}^{\ominus} \mid \boldsymbol{A} \boldsymbol{g} \)
Reason:
\( \boldsymbol{E}_{\boldsymbol{A} \boldsymbol{g}^{\ominus} \mid \boldsymbol{A} \boldsymbol{g}}^{\ominus}=\boldsymbol{E}_{C l^{\ominus}|A \boldsymbol{g} C l| \boldsymbol{A} \boldsymbol{g}}^{\ominus}+\frac{\boldsymbol{R} \boldsymbol{T}}{\boldsymbol{F}} \ln \boldsymbol{K}_{s p} \)
\( (A g C \mid) \)
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false
Subject: Maths
The equation of the plane that passes through the points (1,0,2),(-1,1,2),(5,0,3) is
A. \( x+2 y-4 z+7=0 \)
B. \( x+2 y-3 z+7=0 \)
c. \( x-2 y+4 z+7=0 \)
D. \( 2 y-4 z-7+x=0 \)
Subject: Physics
The velocity of a particle increases from u to v in a time t during which it covers a distances S. If the particle has a uniform acceleration, which one of the following equations does not apply to the motion?
A \( .2 \mathrm{S}=(\mathrm{v}+\mathrm{u}) \)
B. \( a=\frac{v-u}{t} \)
c. \( v^{2}=u^{2}-2 a S \)
D. \( s=\left[u+\frac{1}{2} a t\right] \)
Subject: Physics
A surface \( d s=10 \hat{j} \) is kept in an electric field \( \overrightarrow{\boldsymbol{E}}=\mathbf{2} \hat{\boldsymbol{i}}+\boldsymbol{4} \hat{\boldsymbol{j}}+7 \hat{\boldsymbol{k}} . \) How much
electric flux will come out through the surface?
A . 40 unit
B. 50 unit
c. 30unit
D. 20 unit
Subject: Physics
The potential energy of a rocket of mass \( 100 k g \) at height \( 10^{7} m \) from earth surface is \( 4 \times 10^{9} \) Joule. The weight of
the rocket at height \( 10^{9} \) will be
\( \mathbf{A} \cdot 4 \times 10^{-2} N \)
В . \( 4 \times 10^{-3} N \)
c. \( 8 \times 10^{-2} N \)
D. \( 8 \times 10^{-3} N \)
Subject: Chemistry
The reduction potential of hydrogen
half-cell will be negative if:
\( \mathbf{A} \cdot \mathrm{p}\left(\mathrm{H}_{2}\right)=1 \) atom and \( \left[\mathrm{H}^{+}\right]=2.0 \mathrm{M} \)
\( \mathbf{B} \cdot \mathbf{p}\left(\mathbf{H}_{2}\right)=1 \) atm and \( \left[\mathrm{H}^{+}\right]=1.0 \mathrm{M} \)
\( \mathbf{C} \cdot \mathrm{p}\left(\mathrm{H}_{2}\right)=2 \mathrm{atm} \) and \( \left[\mathrm{H}^{+}\right]=1.0 \mathrm{M} \)
\( \mathbf{D} \cdot \mathrm{p}\left(\mathrm{H}_{2}\right)=2 \mathrm{atm} \) and \( \left[\mathrm{H}^{+}\right]=2.0 \mathrm{M} \)
Subject: Physics
The ratio of maximum to minimum
intensity due to superposition of two waves is \( \frac{49}{9} . \) Then the ratio of the intensity of component waves is :
A \( \cdot \frac{25}{4} \)
в. \( \frac{16}{25} \)
c. \( \frac{4}{49} \)
D. \( \frac{9}{49} \)
Subject: Maths
If \( \frac{\cos \left(\theta_{1}-\theta_{2}\right)}{\cos \left(\theta_{1}+\theta_{2}\right)}+\frac{\cos \left(\theta_{3}+\theta_{4}\right)}{\cos \left(\theta_{3}-\theta_{4}\right)}=0 \)
then \( \tan \theta_{1} \tan \theta_{2} \tan \theta_{3} \tan \theta_{4} \) is equal
to
A . -1
B.
\( c \cdot 2 \)
\( D \)
Subject: Maths
If the points \( \boldsymbol{A}(\overline{\boldsymbol{a}}), \boldsymbol{B}(\overline{\boldsymbol{b}}), \boldsymbol{C}(\overline{\boldsymbol{c}}) \) satisfy
the relation \( 3 \bar{a}-8 \bar{b}+5 \bar{c}=0 \) then the
points are
A. vertices of an equilateral triangle
B. collinear
c. vertices of a right angled triangle
D. vertices of an isosceles triangle
Subject: Physics
A wheel of radius 0.5 m rolls without sliding on a horizontal surface, starting from rest, the wheel moves with
constant acceleration \( 6 ~ r a d / s^{2} \). The distance travelled by the centre of the wheel from \( t=0 \) to \( t=3 s \) is:
A . 27 m
в. \( 13.5 \mathrm{m} \)
\( c .18 m \)
D. zero
Subject: Physics
A particle of mass m moving with velocity u makes an elastic one dimensional collision with a stationary
particle of mass m. They are in contact for a short time T. Their force of
interaction increases from zero to \( F_{0} \)
linearly in time \( \frac{T}{2} \) and decreases inearly to zero in further time \( \frac{T}{2} \) (shown in figure)
The magnitude of \( F_{0} \) is :
A . \( m u / 2 T \)
в. \( m u / T \)
\( \mathrm{c} .2 \mathrm{mu} / \mathrm{T} \)
D. None of these
Subject: Chemistry
\( 500 m L \) of a hydrocarbon gas, burnt in
excess og oxygen, yields \( 2500 m L C O_{2} \)
and 3 liters of water vapour, all volumes
being mesured at the same temperature and pressure, what is the formula of the hydrocarbon?
A \( \cdot C_{4} H_{8} \)
B. \( C_{5} H_{12} \)
c. \( C_{5} H_{1} \)
D. \( C_{2} H_{6} \)
Subject: Chemistry
\( 10.0 g m s \) of \( C a C O_{3} \) on heating gave
\( 4.4 g m s \) of \( C O_{2} \) and \( 5.6 g m s \) of \( C a O \) This observation is in agreement with
the:
A. law of constant composition
B. law of multiple proportion
c. law of reciprocal proportion
D. law of conservation of mass
Subject: Physics
A straight conductor of uniform cross
section carries a current i. Let \( \mathrm{S} \) be the
specific charge on an electron. The momentum of all the free electrons per
unit length of the conductor due to their drift velocity only is
\( ^{A} \cdot \frac{i}{S} \)
B. \( i \) S
\( ^{c} \cdot\left(\frac{i}{S}\right)^{2} \)
D. \( \sqrt{\frac{i}{s}} \)
Subject: Maths
If \( \vec{a} \) and \( \vec{b} \) two collinear vectors then
which of the following are incorrect
A \( \cdot \vec{b}=\lambda \vec{a} \) for some scalar
B \( \cdot \vec{a}=\pm \vec{b} \)
C. The respective components of \( \vec{a} \) and \( \vec{b} \) are proportional
D. Both the vectors \( \vec{a} \) and \( \vec{b} \) have same direction, but different magnitude.
Subject: Physics
A A ratery is cumectuatuss AD as
shown in the figure. The value of the current supplied by the battery when in one case, battery's positive terminal is connected to A and in other case when
positive terminal of battery is connected to B will respectively be
в. \( 0.1 A \) and \( 0.2 A \)
c. 0.2 A and 0.4 A
D. \( 0.4 \mathrm{A} \) and \( 0.2 \mathrm{A} \)
Subject: Chemistry
Van't Hoff factor of \( \boldsymbol{H} \boldsymbol{g}_{2} \boldsymbol{C l}_{2} \) in its
aqueous solution will be \( \left(H g_{2} C l_{2} \) is \right. \( 80 \% \) ionized in the solution):
A . 1.6
B . 2.
\( c .3 .6 \)
D. 4.6
Subject: Physics
Two identical bodies are made of a
material for which the heat
capacity increases with temperature.
One of these is at \( 100^{\circ} \mathrm{C}, \) while the
other one is at \( 0^{0} \mathrm{C} \). If the two bodies
are brought into contact, then
assuming no heat loss, the find common temperature is
\( \mathbf{A} \cdot 0^{\circ} C \)
B. \( 550^{\circ} \mathrm{C} \)
c. more than \( 50^{\circ} \mathrm{C} \)
D. Less than \( 50^{\circ} \mathrm{C} \) but greater than \( 0^{\circ} \mathrm{C} \)
Subject: Maths
\( \lim _{x \rightarrow a} \frac{\sqrt{a+2 x}-\sqrt{3 x}}{\sqrt{3 a+x}-2 \sqrt{x}} \) is equal to
A \( \cdot \frac{2}{\sqrt{3}} \)
B. \( -\frac{1}{\sqrt{3}} \)
\( c \cdot \frac{2}{3 \sqrt{3}} \)
D. \( \frac{1}{\sqrt{3}} \)
Subject: Physics
In a ripple tank, 10 full ripples/s are produced. The distance between peaks of consecutive trough and crest is 15 \( c m \). Calculate the velocity of the
ripples.
\( A \cdot 2 m / s \)
в. \( 3 m / s \)
c. \( 4 m / s \)
D. \( 6 m / s \)
Subject: Physics
A very long cylindrical wire of radius \( \mathrm{R} \)
carries a current \( \boldsymbol{I}_{\mathbf{0}} \) uniformly
distributed across the cross-section of
the wire, calculate the magnetic flux
through a rectangle that has one side of length w s running down the centre of the wire and another side of length \( R \),
shown in figure
A \( \cdot \frac{\mu_{0} I_{0} \times w R}{4 \pi} \)
B. \( \frac{\mu_{0} I_{0} w}{4 \pi} \)
с. \( \frac{\mu_{0} I_{0} R}{4 \pi w} \)
D. None of these
Subject: Chemistry
Name the type of isomerism exhibited by the following isomers:
\( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]\left[\boldsymbol{C o}\left(\boldsymbol{C N}_{6}\right)\right] \) and
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]\left[\boldsymbol{C r}(\boldsymbol{C N})_{6}\right] \)
Subject: Physics
Two parallel rails with negligible
resistance are \( 10.0 \mathrm{cm} \) apart and are
connected by a \( 5.00 \Omega \) resistor. The
circuit also contains two metal rods
having resistance of \( 10.0 \Omega \) and \( 15.0 \Omega \)
sliding along the rails. The rods are
pulled away from the resistor at a
constant speeds \( 8.00 m / s \) and \( 4.00 m / s \) respectively. A uniform magnetic field
\( 0.010 T \) is applied perpendicular to the
plane of the rails. Determine the current
in the \( 5.00 \Omega \) resistor.
Subject: Maths
A function \( f(x) \) is defined as \( f(x)= \)
\( \boldsymbol{x}^{2}+\mathbf{3} . \) Find \( \boldsymbol{f}(\mathbf{0}), \boldsymbol{f}(\mathbf{1}), \boldsymbol{f}\left(\boldsymbol{x}^{2}\right), \boldsymbol{f}(\boldsymbol{x}+\mathbf{1}) \)
and \( \boldsymbol{f}(\boldsymbol{f}(\mathbf{1})) \)
Subject: Maths
If \( \mathrm{E} \& \mathrm{F} \) are events with \( \boldsymbol{P}(\boldsymbol{E}) \leq \boldsymbol{P}(\boldsymbol{F}) \& \)
\( \boldsymbol{P}(\boldsymbol{E} \cap \boldsymbol{F})>0, \) then
A. occurrence of \( E \Rightarrow \) occurrence of \( F \)
B. occurrence of F\Rightarrow occurrence of E
c. non occurrence of \( E \Rightarrow \) non occurrence of \( F \)
D. none of the above implications holds
Subject: Physics
The amount of heat required to convert 1 g of ice (specific 0.5 cal at \( g^{-1 o} C^{-1} \) ) at
\( -10^{0} C \) to steam at \( 100^{\circ} \mathrm{C} \)
is
Given: Latent heat of ice is \( 80 \mathrm{Cal} / \mathrm{gm} \)
Latent heat of steam is \( 540 \mathrm{Cal} / \mathrm{gm} \) Specific heat of water is \( 1 C a l / g m / C] \)
A . 725 cal
B. 636 cal
c. 716 cal
D. None of these
Subject: Physics
Match the following:
Section A \( \quad \) Section B
\( P . \) Converts electric energy in to
1. Fuse \( \quad \) mechanical energy
2 Electric
\( Q . \) Heating effect of electric current generator
3. Electric
\( R . \) Converts mechanical energy in motor \( \quad \) to electrical energy
\( \mathbf{A} \cdot 1-Q, 2-R, 3-P \)
B \( .1-Q, 2-P, 3-R \)
\( \mathbf{c} \cdot 1-P, 2-Q, 3-R \)
D. \( 1-P, 2-R, 3-Q \)
Subject: Chemistry
Which mineral has been
named incorrectly?
A. Bauxite \( : A l_{2} O_{3} \cdot 2 H_{2} O \)
B. Corundum: \( A l_{2} O_{3} \)
C . Cryolite \( : 3 \mathrm{NaF} \cdot \mathrm{AlF}_{3} \)
D. Feldspar: \( B e_{3} A l_{2} S i_{5} O_{18} \)
Subject: Chemistry
The structure of isoprene is:
\( \mathbf{A} \cdot C H_{2}=C\left(C_{2} H_{5}\right)-C H=C H_{2} \)
B. \( C H_{2}=C\left(O C O H_{3}\right)-C H=C H_{2} \)
\( \mathbf{c} \cdot C H_{2}=C\left(C H_{3}\right)-C H=C H_{3} \)
\( \mathbf{D} \cdot C H_{2}=C H-C=C H \)
Subject: Physics
Read the assertion and reason carefully
to mark the correct option out of the
options given below:
Assertion: At height \( h \) from ground and
at depth \( h \) below ground, where \( h \)
is approximately equal to \( 0.62 R \)
the value of \( g \) acceleration due to
gravity is same.

Reason: Value of \( g \) decreases both
sides, in going up and down.
A. If both assertion and reason are true and the reason is the correct explanation of the assertion
B. If both assertion and reason are true but reason is not the correct explanation of the assertion
c. If assertion is true but reason is false
D. If assertion is false but reason is true
Subject: Physics
Let \( n_{r} \) and \( n_{b} \) be respectively the number of photons emitted by a red bulb and a blue bulb of equal power in a given time, then:
A \( \cdot n_{r}=n_{b} \)
в. \( n_{r}<n_{b} \)
\( \mathrm{c} \cdot n_{r}>n_{b} \)
D. data insufficient
Subject: Maths
If \( \cos (\beta-\gamma)+\cos (\gamma-\alpha)+\cos (\alpha- \)
\( \beta)=-\frac{3}{2}, \) then
This question has multiple correct options
A. \( \sum \cos \alpha=0 \)
B. \( \sum \sin \alpha=0 \)
c. \( \sum \cos \alpha \sin \alpha=0 \)
D. \( \sum(\cos \alpha+\sin \alpha)=0 \)
Subject: Chemistry
The standard reducation potentials of \( Z n^{2+}\left|Z n, C u^{2+}\right| C u \) and \( A g^{+} \mid A g \)
are respectively -0.76,0.34 and \( 0.8 \mathrm{V} \). The following cells were constructed.
a) \( Z n\left|Z n^{2+}\right|\left|C u^{2+}\right| C u \)
b) \( Z n\left|Z n^{2+} \| A g^{+}\right| A g \)
c) \( C u\left|C u^{2+}\right|\left|A g^{+}\right| A g \)
What is the correct order \( E_{\text {cell }}^{0} \) of these cells?
\( A \cdot \) b>c \( >a \)
B. b>a>c
\( c \cdot a>b>c \)
D. c>asb
Subject: Maths
\( \left|\begin{array}{cc}\sin ^{2} \theta & \cos ^{2} \theta \\ -\cos ^{2} \theta & \sin ^{2} \theta\end{array}\right|= \)
\( \mathbf{A} \cdot \cos 2 \theta \)
в. \( \frac{1}{2}\left(1+\cos ^{2} 2 \theta\right) \)
c. \( \frac{1}{2}\left(1-\sin ^{2} 2 \theta\right) \)
D. \( \frac{1}{2} \sin ^{2} 2 \theta \)
Subject: Maths
\[
f(x)=\left\{\begin{array}{ll}
\frac{1-\sin ^{2} x}{3 \cos ^{2} x}, & x<\frac{\pi}{2} \\
a, & x=\frac{\pi}{2} \\
\frac{b(1-\sin x)}{(\pi-2 x)^{2}} & x>\frac{\pi}{2}
\end{array}\right.
\]
then \( f(x) \) is continuous at \( x=\frac{\pi}{2} \)
Subject: Maths
The largest sphere is carved out of a cube of edge \( 14 \mathrm{cm} . \) Then the volume of the sphere is
A \( . \) 1370 \( c m^{3} \)
B . \( 1800 \mathrm{cm}^{3} \)
c. \( 1437 \mathrm{cm}^{3} \)
D. \( 1734 \mathrm{cm}^{3} \)
Subject: Physics
Which of the following is not correct
about cyclotron.?
A. It is a machine to accelerate charged particles or ions to high energies.
B. Cyclotron uses both electric and magnetic fields in combination to increase the energy of charged particles.
C. The operation of the cyclotron is based on the fact that the time for one revolution of an ion is independent of its speed or radius of its orbit
D. The charged particles and ions in cyclotron can move on any arbitary path
Subject: Chemistry
The standard free energy change (in kJ) for the reaction,
\[
\begin{array}{c}
\mathbf{3} \boldsymbol{F} \boldsymbol{e}^{2+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{C r}(\boldsymbol{s})=\boldsymbol{2} \boldsymbol{C r}^{3+}(\boldsymbol{a} \boldsymbol{q})+ \\
\boldsymbol{3} \boldsymbol{F} \boldsymbol{e}(\boldsymbol{s})
\end{array}
\]
\( \operatorname{given} E_{F e^{2+} / F e}^{o}=-0.44 \mathrm{V} \) and
\[
\boldsymbol{E}_{C r^{3+} / \boldsymbol{C r}}^{o}=-\mathbf{0 . 7 4 V} \text { is }(\boldsymbol{F}=\mathbf{9 6 5 0 0 C})
\]
A .57,900
В. -57,900
c. -173,700
D. 173,700
Subject: Physics
For a material \( \boldsymbol{Y}=\mathbf{6 . 6} \times \mathbf{1 0}^{\mathbf{1 0}} \boldsymbol{N} / \boldsymbol{m}^{2} \)
and bulk modulus \( K 11 \times 10^{10} N / m^{2} \) then its Poisson's ratio is:
A . 0.8
B. 0.35
\( c .0 .7 \)
D. 0.4
Subject: Chemistry
The wave number of the radiation whose
quantum 1 erg is:
A. \( 5 \times 10^{15} \mathrm{cm}^{-1} \)
B. \( 15 \times 10^{5} \mathrm{cm}^{-1} \)
c. \( 1.5 \times 10^{15} \mathrm{cm}^{-1} \)
D. \( 5 \times 10^{5} \mathrm{cm}^{-1} \)
Subject: Maths
\( \frac{3+2 i \sin \theta}{1-2 i \sin \theta} \) will be purely imaginary, if
\( \boldsymbol{\theta}= \)
A \( \cdot 2 n \pi-\frac{\pi}{3} \)
в. \( n \pi+\frac{\pi}{3} \)
c. \( n \pi-\frac{\pi}{3} \)
D. None of these
Subject: Chemistry
lonisation constant of \( \boldsymbol{C H}_{3} \) COOH is
\( 1.7 \times 10^{-5} \) and concentration of \( H^{+} \)
ions is \( 3.4 \times 10^{-4} \). Then find out initial
concentration of \( \boldsymbol{C H}_{3} \) COOH molecule.
A. \( 3.4 \times 10^{-4} \)
В. \( 3.4 \times 10^{-3} \)
c. \( 6.8 \times 10^{-4} \)
Subject: Physics
A \( 100 N \) force makes an angle of \( \theta \) with
the \( x \) -axis and has a y-component of
\( 30 N . \) Then the \( x \) -component of the force
is:-
В. \( 95.39 N \)
c. \( 104.4 N \)
D. \( 0 N \)
Subject: Physics
The value of \( A \) in the following reaction
is
\( _{4} \mathrm{Be}^{9}+_{2} \mathrm{He}^{4}=_{6} \mathrm{C}^{A}+_{0} \mathrm{n}^{1} \)
A . 14
B. 10
c. 12
D. 16
Subject: Chemistry
Consider the structure pictured above,
including the accompanying ligand.
Which of the following CORRECTLY
identifies the pictured compound by
name, and identifies the bonding
involved in its structure?
A. The compound is ammonium dichromate. It contains both ionic and covalent bonds.
B. The compound in diammonium chromate. It contains both ionic and covalent bonds.
C. The compound is ammonium dichromate. It contains only ionic bonds.
D. The compound is ammonium chromate. It contains ionic bond.
Subject: Physics
A \( 200 H z \) wave with amplitude 1 mm
travels on a long string of linear mass of density \( 6 g m^{-1} \) kept under a tension of
\( 60 N . \) The average power transmitted across a given point in the string is
A. \( 0.53 \mathrm{W} \)
Wh
в. \( 0.83 \mathrm{W} \)
c. \( 0.47 W \)
D. \( 0.89 W \)
Subject: Maths
\[
\text { If } \boldsymbol{A}=\left[\begin{array}{cc}
\mathbf{2} & \mathbf{2} \\
\mathbf{- 3} & \mathbf{1} \\
\mathbf{4} & \mathbf{0}
\end{array}\right], \boldsymbol{B}=\left[\begin{array}{cc}
\mathbf{6} & \mathbf{2} \\
\mathbf{1} & \mathbf{3} \\
\mathbf{0} & \mathbf{4}
\end{array}\right], \text { find }
\]
matrix \( C \) such that \( A+B+C=0 \)
where \( \boldsymbol{O} \) is the zero matrix.
Subject: Physics
the potential energy of interaction between two particles with the distance
separating them \( r \)
1. \( \mathrm{B} \) and \( \mathrm{D} \) are equilibrium points.
2. \( C \) is a point of stable equilibrium.
3. The force of interaction between the
two particles is attractive between points \( C \) and \( D \) and repulsive between \( D \)
and E.
4. The force of interaction between
particles is repulsive between points \( \mathrm{E} \)
and F.
Which of the above statements are
correct?
A. 1 and 2
B. 1 and 4
c. 2,3 and 4
D. 2 and 4
Subject: Chemistry
Which of the following compound gives \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) by the addition of \( \boldsymbol{H}_{2} \boldsymbol{O} ? \)
A \( \cdot C O\left(N H_{2}\right)_{2} \cdot H_{2} O_{2} \)
в. \( N a_{2} H P O_{4} . H_{2} O_{2} \)
\( \mathrm{c} \cdot\left(N H_{4}\right)_{2} S O_{4} \cdot H_{2} O_{2} \)
D. All of the above
Subject: Chemistry
Law of constant proportion states that:
\( \mathbf{A} \cdot \) a chemical compound always contains exactly the same proportion of elements by mass.
B. mass can neither be created nor destroyed in a chemical reaction.
C. when two elements combine with each other to form
two or more than two compounds, the masses of one the element which combines with the fixed mass of
the other, bears a simple whole number ratio.
D. total mass of products is always equal to the total mass of reactants.
Subject: Chemistry
The bond energies in \( \mathrm{NO}, N O^{+} \) and
\( N O^{-} \) follow the order:
A \( \cdot N O^{+}>N O>N O^{-} \)
В. \( N O>N O^{+}>N O^{-} \)
c. \( N O^{-}>N O>N O^{+} \)
D. \( N O^{+}>N O^{+}>N O \)