AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
The azeotropic mixture of water (boiling
point \( =100^{\circ} \mathrm{C} \) ) and \( H C l \) (boiling point
\( \left.=85^{\circ} \mathrm{C}\right) \) boils at about \( 110^{\circ} \mathrm{C} . \) During
distillation of this mixture, it is
possible to obtain:
A. pure \( H C l \)
B. pure \( H_{2} O \)
c. pure \( H C l \) as well as \( H_{2} O \)
D. neither pure \( H_{2} O \) nor pure \( H C l \)
Subject: Maths
Show that the function \( \boldsymbol{y}=\boldsymbol{A} \cos \boldsymbol{x}+ \)
\( B \sin x \) is a solution of the differential
equation \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}+\boldsymbol{y}=\mathbf{0} \)
Subject: Physics
A container is divided into two equal
parts I and II by a partition with a small
hole of diameter d. The two partitions are filled with same ideal gas, but held
at temperatures \( \boldsymbol{T}_{\boldsymbol{I}}=\mathbf{1 5 0 K} \) and \( \boldsymbol{T}_{\boldsymbol{I I}}= \)
\( 300 K \) by connecting to heat reservoirs.
Let \( \lambda_{I} \) and \( \lambda_{I I} \) be the mean free paths of the gas particles in the two parts such
that \( \boldsymbol{d}>>\boldsymbol{\lambda}_{\boldsymbol{I}} \) and \( \boldsymbol{d}>>\boldsymbol{\lambda}_{\boldsymbol{I} I} . \) Then
\( \boldsymbol{\lambda}_{I} / \boldsymbol{\lambda}_{I I} \) is close to.
\( \mathbf{A} \cdot 0.25 \)
B. 0.5
c. 0.7
D. 1.0
Subject: Maths
If \( \quad A=\left(\begin{array}{ll}1 & 3 \\ 4 & 5\end{array}\right) \) then \( A^{-1} \) equals
\( ^{\mathrm{A}} \cdot \frac{1}{7}(A+6 I) \)
в. \( \frac{1}{7}(A-6 I) \)
c. \( \frac{1}{7}(6 I-A) \)
D. None of these
Subject: Maths
Given \( \boldsymbol{A}=\{\mathbf{2}, \mathbf{3}, \mathbf{5}\} \) and \( \boldsymbol{B}= \)
\{6,10,14,18\}\( ; \) find the number of elements in relation \( R \) such that \( R= \)
\( \left\{(x, y) \in A \times B, x<y \text { and } \frac{y}{x} \epsilon N\right\} \)
Subject: Physics
Consider the circular loop having
current \( i \) and with central point \( O . \) The
magnetic field at the central point \( \boldsymbol{O} \) is
A \( \cdot \frac{2 \mu_{0} i}{3 \pi R} \) acting downward
B. \( \frac{5 \mu_{0} i}{12 R} \) acting downwaro
c. \( \frac{6 \mu_{0} i}{11 R} \) acting downwar
D. \( \frac{3 \mu_{0} i}{7 R} \) acting downwar
Subject: Physics
A cell of emf \( E \) volts with no internal
resistance is connected to a wire of
uneven cross-sectional area. The wire
has three sections of equal length. The radius of the middle section is \( a \)
and the other are \( 2 a \). The ratio of the
potential difference across the middle section to any other section is
A .2: 1
B . 4: 1
c. 1: 2
D. 1: 4
Subject: Chemistry
\( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g)+ \) heat
For the reaction above, what is the effect
on the equilibrium position when the pressure is decreased?
A. Increased production of products
B. Increased production of reactants
c. Fluctuations in the amounts of reactants and products
D. No impact on the equilibrium
E. Cannot be determined
Subject: Chemistry
The oxidation state of copper changes
when aqueous copper (II) ions react with:
\( (I) N a O H(a q) \)
\( (I I) F e(s) \)
\( (I I I) K I(a q) \)
A. \( I, I I, I I I \)
B. II only
c. \( I I, I I I \)
D. I only
Subject: Biology
unplece the given labıe about absorption of nutrients through small intestine by selecting the correct option.
Process Nutrients
Active transport and II Fructose and
II
Simple Diffusion

IV and \( v \)
A. \( I \) -Amino Acids
\[
I I-C a^{2+}
\]
\( I I I- \) Passive transport, \( I V- \) Glycerol \( V \) -Fatty Acids
B. I-Galactose,
\( I I- \) Amino Acids \( I I I- \) Passive transport \( I V-V \) itamin \( -C \)
\( V \) - water
c. \( I \) - Glucose, \( I I- \) Galactose
III-Facilitated diffusion,
\( I V- \) Glycerol \( V \) - water
D. \( I \) -Glucose,
\( I I- \) Short chain fatty acids,
III - Facilitated diffusion, \( I V- \) Water
\( V \) - Vitamin-B complex
Subject: Chemistry
The cation responsible for turning moist neutral litmus red on reaction with dil
\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) is
A . \( H^{+} \)
B. \( N H_{4}^{+} \)
\( c \cdot O^{-} \)
D. \( O_{3}^{+} \)
Subject: Maths
Find the sum of \( n \) terms of \( 1^{2}+ \)
\( \left(1^{2}+2^{2}\right)+\left(1^{2}+2^{2}+3^{2}\right)+ \)
\( \left(1^{2}+2^{2}+3^{2}+4^{2}\right)+\ldots \) from that find
the sum of the first 10 terms
Subject: Maths
A cylindrical tank of radius \( 10 m \) is being filled with wheat at the rate of 314
cubic metre per hour. then the depth of the wheat is increasing at the rate of
A \( \cdot 1 m^{3} / h \)
B. \( 0.1 m^{3} / h \)
\( \mathbf{c} \cdot 1.1 m^{3} / h \)
D. \( 0.5 m^{3} / h \)
E. None of these
Subject: Maths
\( \int \frac{1}{\sqrt{\sin ^{3} x \sin (x+a)}} d x \) is equal to
A \( \cdot 2 \cos e c \alpha \sqrt{\cos \alpha+\sin \alpha \tan x}+c \)
B. \( -2 \cos e c \alpha \sqrt{\cos \alpha+\sin \alpha \cot x}+c \)
\( \mathbf{c} \cdot \cos e c \alpha \sqrt{\cos \alpha+\sin \alpha \tan x}+c \)
D. \( -\cos e c \alpha \sqrt{\cos \alpha+\sin \alpha \tan x}+c \)
Subject: Physics
The order of size of nucleus and Bohr's
radius of an atom respectively are:
\( \mathbf{A} \cdot 10^{-14} m, 10^{-10} m \)
В. \( 10^{-10} m, 10^{-8} m \)
c. \( 10^{-20} m, 10^{-16} m \)
D. \( 10^{-8} m, 10^{-6} m \)
Subject: Maths
In a series of 3 independent trials, the probability of exactly 2 success is 12 times as large as the probability of 3 successes. The probability of a success in each trail is
A \( \cdot \frac{1}{5} \)
B. \( \frac{2}{5} \)
\( c \cdot \frac{3}{5} \)
D. \( \frac{4}{5} \)
Subject: Physics
To parallel rail track an north south.
Train \( A \) moves north with a speed of
\( \mathbf{5 4} k \boldsymbol{m} / \boldsymbol{h} \) and train \( \boldsymbol{B} \) moves south with
a speed of \( 90 \mathrm{km} / \mathrm{h} \). What is the Velocity of \( B \) with respect to capital \( A ? \)
Velocity of ground with respect to \( B \) ?
Velocity of monkey running on the roof
of train \( A \) against its motion with a velocity of \( 18 \mathrm{km} / \mathrm{h} \) with respect to the \( \operatorname{train} A \) as observe by man standing on
the ground?
Subject: Chemistry
If the de Broglie wavelength of the
electron in \( n^{t h} \) Bohr orbit in a
hydrogenic atom is equal to \( 1.5 \pi a_{0}\left(a_{0}\right. \)
is Bohr radius), then the value of \( n / z \) is:
A . 1.0
в. 0.75
c. 0.40
D. 1.50
Subject: Maths
If \( f(x)=x^{2}, g(x)=x^{2}-5 x+6, \) then
\( \boldsymbol{g}(\mathbf{2})+\boldsymbol{g}(\mathbf{3})+\boldsymbol{g}(\mathbf{0})-\boldsymbol{f}(\mathbf{0})-\boldsymbol{f}(\mathbf{1})- \)
\( \boldsymbol{f}(-2) \)
A . 2
B.
\( c \cdot \frac{5}{6} \)
\( D \)
Subject: Physics
The pressure on a square plate is measured by measuring the force on the plate. If the maximum error in the measurement of force and length are respectively \( 4 \% \) and \( 2 \% \), then the maximum error in the measurement of
pressure is :
A . \( 1 \% \)
B. 2\%
c. \( 4 \% \)
D. \( 8 \% \)
Subject: Physics
The length of metallic wire is \( l_{1} \) when
the tension is \( T_{1} \) and \( l_{2} \) when the
tension is \( T_{1} . \) The original length of the wire is
A \( \cdot \frac{l_{1}+l_{2}}{2} \)
в. \( \frac{l_{1} T_{2}+l_{2} T_{1}}{T_{1}+T_{2}} \)
c. \( \frac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}} \)
D. \( \sqrt{T_{1} T_{2} l_{1} l_{2}} \)
Subject: Chemistry
The elevation in boiling point of a
solution of 13.44 g of \( C u C l_{2} \) (Molar mass 134.4 ) in \( 1 \mathrm{kg} \) water is:
\( \left[\boldsymbol{K}_{\boldsymbol{b}}=\mathbf{0 . 5 2} \mathrm{K} \text { molality }^{-1}\right] \)
A . 0.16
B. 0.05
c. \( 0 . \)
D. 0.2
Subject: Physics
A fighter plane flying horizontally at an altitude of \( 1.5 k m \) with speed \( 720 k m / h \) passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for
the shell with muzzle speed 600 ms\( ^{-1} \) to hit the plane ? At what minimum altitude should the pilot fly the plane to avoid being hit ? Take \( g=10 m s^{-2} \)
Subject: Physics
A small piece of wire bent into L shape such that the upright and horizontal portions are of equal length. It is placed with the horizontal portion along the
axis of concave mirror of radius of
curvature \( 20 \mathrm{cm} \). If the bend is \( 40 \mathrm{cm} \) from the pole of the mirror, then the ratio of the length of the images of the upright and horizontal portions of the wire is
A \( \cdot 1: 9 \)
в. 1: 3
\( c \cdot 3: \)
\( D \cdot 2: \)
Subject: Physics
Two identical parallel plate capacitors are connected in series and then joined
with a battery of \( 100 ~ V . A \) sheet of
dielectric constant 4.0 is inserted
between the plates of second capacitor. The potential difference across the
capacitors will be respectively.
\( \mathbf{A} \cdot 50 V, 50 V \)
B . \( 80 \mathrm{V}, 20 \mathrm{V} \)
c. \( 20 V, 80 V \)
D. \( 75 V, 25 V \)
Subject: Physics
The electric potential decreases uniformly from \( 120 \mathrm{V} \) to \( 80 \mathrm{V} \) as one
moves on the X-axis from \( x=-1 c m \) to
\( \boldsymbol{x}=+1 \mathrm{cm} . \) The electric field at the
origin.
A. must be equal to \( 20 V / c m \)
B. must be equal to \( 2.0 \mathrm{V} / \mathrm{cm} \)
c. must be greater than \( 20 V / \mathrm{cm} \)
D. must be less than \( 20 \mathrm{V} / \mathrm{cm} \)
Subject: Chemistry
Assertion
\( C_{P}-C_{V}=R \) for ideal gas.
Reason
\( R \) is the work done when temperature of
one mole of an ideal gas is increased by
\( \mathbf{1}^{o} \)
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
Q Type your question
at the bottom.lnitially the holes are closed and water is filled into
the container. Now the container is
rotated about its axis with an angular velocity \( \omega=\sqrt{12} r a d / s e c . \) As seen from
the rotating frame of the container. The initial velocity of efflux after opening
the holes will be: \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}, \boldsymbol{h}=\right. \)
\( 5 m) \)
A \( \cdot 10 \frac{m}{s} \)
В \( \cdot 10 \sqrt{2} \frac{m}{s} \)
\( \mathrm{c} \cdot_{20} \frac{m}{s} \)
D. \( 20 \sqrt{2} \frac{m}{s} \)
Subject: Maths
Sum the series:
\( \mathbf{2}^{1 / 4} \cdot \mathbf{4}^{\mathbf{1} / 8} \cdot \mathbf{8}^{\mathbf{1} / \mathbf{1 6}} \cdot \mathbf{1 6}^{\mathbf{1} / 32} \ldots . \) is equal
Subject: Maths
The mean of given data is
\( \begin{array}{cccccc}\mathbf{x} & 2 & 4 & 6 & 8 & 10 \\ f & 7 & 4 & 5 & 5 & 4\end{array} \)
\( \mathbf{A} \cdot 5.6 \)
B . 6.4
\( c \cdot 6 \)
D. None of these
Subject: Physics
Flux associated with coil of unit area
placed int he magnetic field of
induction \( B \) is doubled in \( 0.2 s . \) The emf
induced in the coil is:
A . \( 5 V \)
B. \( 10 B V \)
\( \mathrm{c} .5 B V \)
D. \( 10 V \)
Subject: Physics
The electric field of an electromagnetic
wave in free space is given by \( \vec{E} 10 \cos \left(10^{7} t ! k x\right) \hat{j} V / m \) where \( t \) and \( x \)
are in seconds and metres respectively. It can be iferred that
(i) the wavelength \( \% \) is \( 188.4 \mathrm{m} \)
(ii) the wave number \( k \) is 0.33 rad/m
(iii) the wave amplitude is \( 10 \mathrm{V} / \mathrm{m} \)
(iv) the wave is propagating along \( +x \) direction
Which one of the following pairs of
statements is correct?
A . (iii) and (iv)
B. (i) and (ii)
c. (ii) and (iii)
D. (i) and (iii)
Subject: Physics
Assertion The angle between the two vectors \( (\hat{i}+ \)
\( \hat{\boldsymbol{j}}) \) and \( (\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}) \) is \( \frac{\pi}{3} \) radian
Reason
Angle between two vectors \( \vec{A} \) and \( \vec{B} \) given by \( \boldsymbol{\theta}=\cos ^{-1}\left(\frac{\vec{A} \cdot \vec{B}}{A B}\right) \)
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: Chemistry
Assertion
The catalytic converter in the car's exhaust system converts polluting exhaust gases into non-toxic gases.
Reason
Catalytic converter contains a mixture of transition metals and their oxides
embedded in the inner support.
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
If \( \sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2} \)
then the value of \( x^{9}+y^{9}+z^{9}-\frac{1}{x^{9} y^{9} z^{9}} \)
is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D.
Subject: Physics
Assertion
The change in kinetic energy of a particle is equal to the work done on it by the net force.
Reason
Change in kinetic energy of particle is equal to the work done only in case of a system of one particle.
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
A body of mass \( m \) is released from a
height equal to the radius \( R \) of the Earth. The velocity with which it will
strike the Earth's surface is
A \( \cdot \sqrt{2 g R} \)
в. \( \sqrt{g R} \)
\( \mathbf{c} \cdot \sqrt{2 m g R} \)
D. \( \sqrt{m g R} \)
E \( . m \sqrt{g R} \)
Subject: Chemistry
At \( 10^{\circ} \mathrm{C}, \) the osmotic pressure of urea
solution is 500 mm. The solution is
diluted and the temperature is raised to
\( 25^{\circ} C, \) when the osmotic pressure is
found to be 105.3 mm. Determine
extent of dilution?
A. Sol. \( \left(V_{\text {final}}=5 V_{\text {original}}\right) \)
B. Sol. ( \( \left.V_{\text {final}}=7 V_{\text {original}}\right) \)
c. sol. \( \left(V_{\text {final}}=3 V_{\text {original}}\right) \)
D. None of the above
Subject: Physics
An aluminium wire carrying a current has diameter \( 0.84 \mathrm{mm} \). The electric
field in the wire is \( 0.49 V / m . \) What is,
(a) the current carried by the wire?
(b) the potential difference between two points in the wire 12.0 m apart?
(c) the resistance of a \( 12.0 \mathrm{m} \) length of this wire?
Specific resistance of aluminum is \( 2.75 \times 10^{8} \Omega-m \)
Subject: Physics
In a car a rear view mirror having a
radius of curvature \( 1.50 \mathrm{m} \) forms a
virtual image of a bus located \( 10.0 \mathrm{m} \)
from the mirror. The factor by which the mirror magnifies the size of the bus is
close to
A . 0.06
B. 0.07
\( c \cdot 0.08 \)
D. 0.09
Subject: Maths
Find the values of the following determinant, where \( \boldsymbol{i}=\sqrt{-1} \) \( \left|\begin{array}{cc}\mathbf{2} \boldsymbol{i} & -\mathbf{3} i \\ \boldsymbol{i}^{\mathbf{3}} & -\mathbf{2} \boldsymbol{i}^{5}\end{array}\right| \)
Subject: Physics
The minimum horizontal acceleration of
the container, so that the pressure at
point \( A \) of the container becomes
atmospheric is (the tank is of sufficient
height) ?
\( 4 \frac{2}{3} g \)
B. \( \frac{4}{3} g \)
\( c \cdot \underline{4}_{0} \)
59
D. \( \frac{3}{-g} \)
Subject: Chemistry
Assertion
Metals like Na, K, Ca and Mg are never
found in their free state in nature.
Reason
Metals are very reactive elements. So, it
combine with other non metal to
complete its octet. Metals like \( \mathrm{Na}, \mathrm{K}, \mathrm{Ca} \) and Mg are never found in their free state in nature.
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
A ball dropped from one metre above the top of a window, crosses the window in
\( t_{1} s . \) If the same ball is dropped from \( 2 m \) above the top of the same window,
time taken by it to cross the window is
\( t_{2} s . \) Then
\( \mathbf{A} \cdot t_{2}=t_{1} \)
в. \( t_{2}=2 t \)
c. \( t_{2}>t_{1} \)
D \( \cdot t_{2}<t_{1} \)
Subject: Maths
Draw a circle with centre \( C \) and radius
\( 3 \mathrm{cm} . \) Take a point \( \boldsymbol{P} \) outside the circle
such that \( C P=6 \mathrm{cm} . \) Construct
tangents \( \boldsymbol{P} \boldsymbol{A} \) and \( \boldsymbol{P} \boldsymbol{B} \) from this point to
the circle, where \( A \) and \( B \) are the
intersection points of the tangents. Then \( \boldsymbol{m} \angle \boldsymbol{A} \boldsymbol{C B}=? \)
\( \mathbf{A} \cdot 60 \)
B. \( 120^{\circ} \)
\( c \cdot 30^{\circ} \)
D. \( 90^{\circ} \)
Subject: Physics
State Kirchoff's rules. Use these rules to
find the values of current \( \boldsymbol{I}_{1}, \boldsymbol{I}_{2}, \boldsymbol{I}_{3} \) in
the circuit diagram given
\begin{tabular}{|l|l|}
\hline\( I_{1} \) & \( 1 / 2 V \) & \( \gamma_{1}=4 \Omega \) \\
& \\
\( \vdots \) & 11 \\
\hline\( I_{2} \) & \\
\( I_{3} \) & \( 4 V \) & \( \gamma_{3}=3 \Omega \) \\
\hline
\end{tabular}
Subject: Physics
\( \ln \) an \( L C \) circuit the capacitor has
maximum charge \( q_{0} . \) The value of \( \left(\frac{d I}{d t}\right)_{\max }, \) where \( I \) is current in the circuit and \( t \) is time, is
\( ^{A} \cdot \frac{q_{0}}{L C} \)
в. \( \frac{q_{0}}{\sqrt{L C}} \)
c. \( \frac{q_{0}}{L C}-1 \)
D. \( \frac{q_{0}}{L C}+1 \)
Subject: Physics
A centrifuge starts rotating from rest
and reaches a rotational speed of 8,000 radians/sec in 25 seconds. Calculate
the angular acceleration of the
centrifuge?
A. 160 radians \( / \)sec\( ^{2} \)
B. 320radians/sec^
c. 640 radians / sec \( ^{2} \)
D. 10,000 radians \( / \)sec\( ^{2} \)
E .20,000 radians / sec \( ^{2} \)
Subject: Chemistry
a) Draw labelled diagram of Standard Hydrogen Electrode (SHE).

Write its half cell reaction of \( \boldsymbol{E}^{o} \) value
b) Calculate \( \triangle r G^{\ominus} \) for the following
reaction:
\( \boldsymbol{F} \boldsymbol{e}_{(\boldsymbol{a q})}^{+\mathbf{2}}+\boldsymbol{A} \boldsymbol{g}_{(\boldsymbol{a q})}^{+} \rightarrow \boldsymbol{F e}_{(\boldsymbol{a q})}^{+\mathbf{3}}+\boldsymbol{A} \boldsymbol{g}_{(s)} \)
\( \left(\text { Given }: \boldsymbol{E}_{\text {Cell }}^{0}=+\mathbf{0 . 0 3} \boldsymbol{V}, \boldsymbol{F}=\mathbf{9 6 5 0 0} \boldsymbol{C}\right) \)
Subject: Maths
Let \( f(x) \) be a non-constant twice differentiable function defined on
\( (-\infty, \infty) \) such that \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{f}(\mathbf{1}-\boldsymbol{x}) \)
and \( f^{\prime}\left(\frac{1}{4}\right)=0 . \) Then
This question has multiple correct options
A \( \cdot f^{\prime}(x) \) vanishes at least twice on [0,1]
B \( ^{\prime} f^{\prime}\left(\frac{1}{2}\right)=0 \)
\( ^{\mathrm{c}} \int_{-1 / 2}^{1 / 2} f\left(x+\frac{1}{2}\right) \sin x d x=0 \)
D \( \cdot \int_{0}^{1 / 2} f(t) e^{\sin \pi t} d t=\int_{1 / 2}^{1} f(1-t) e^{\sin \pi t} d t \)
Subject: Physics
The frequency of radio waves corresponding to a wavelength of \( 10 \mathrm{m} \)
is
\( \mathbf{A} \cdot 3 \times 10^{7} H z \)
B \( .3 .3 \times 10^{8} \mathrm{Hz} \)
\( \mathbf{C} \cdot 3 \times 10^{9} H z \)
D. \( 3 \times 10^{-7} \mathrm{Hz} \)
Subject: Physics
The bulk modulus of a liquid of density
\( 8000 k g m^{-3} \) is \( 2 \times 10^{9} N m^{-2} . \) The
speed of sound in that liquid is (in
\( \left.m s^{-1}\right) \)
A . 200
B. 250
\( c \cdot 100 \)
D. 350
E. 500
Subject: Physics
A horizontal straight wire \( 10 \mathrm{m} \) long extending from east to west is falling
with a speed of \( 5.0 m s^{-1}, \) at right angles
to the horizontal component of the
earth's magnetic field 0.30 \( \times 10^{-4} W B m^{-2} . \) (a) What is the
instantaneous value of the emf induced
in the wire?(b) What is the direction of
the emf?(c) Which end of the wire is at
the higher electrical potential?
Subject: Physics
The parallel combination of two air filled parallel plate capacitors of capacitance \( \mathrm{C} \) and \( \mathrm{NC} \) is connected to a battery of
voltage, \( V \). When the capacitors are fully charged, the battery is removed and after that a dielectric material of
dielectric constant \( \mathrm{K} \) is placed between the two plates of the first capacitor. The new potential difference of the combined system is?
A \( \cdot \frac{V}{K+n} \)
в. \( V \)
c. \( \frac{(n+1) V}{(K+n)} \)
D. \( \frac{n V}{K+n} \)
Subject: Maths
\( P \) is a point in the interior of \( a \)
parallelogram \( A B C D . \) Show that
\( \boldsymbol{a r}(\triangle \boldsymbol{A P B})+\boldsymbol{a r}(\triangle \boldsymbol{P C D})= \)
\( \frac{1}{2} a r(A B C D) \)
Subject: Maths
A man \( 160 \mathrm{cm} \) tall, walks away from a source of light situated at the top of a
pole \( 6 \mathrm{m} \) high, at the rate of \( 1.1 \mathrm{m} / \mathrm{sec} \)
How fast is the length of his shadow increasing when he is \( 1 \mathrm{m} \) away from the pole?
Subject: Chemistry
If \( 9 \mathrm{gm} H_{2} O \) is electrolysed completely with the current of \( 50 \% \) efficiency then?
A. 96500 charge is required
B. \( 2 \times 96500 \) C charge is required
\( \mathrm{c} \cdot 5.6 \mathrm{L} \) of \( \mathrm{O}_{2} \) at STP will be formed
D. 11.2 Lof \( O_{2} \) at STP will be formed
Subject: Chemistry
Arrange the following compounds in the increasing order of their boiling points.
\( \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H} \boldsymbol{O}, \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H} \)
\( \boldsymbol{O}-\boldsymbol{C}_{2} \boldsymbol{H}_{5}, \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C}_{2} \boldsymbol{H}_{5} \)
A \( \cdot C H_{3} C H_{2} C H_{2} C H_{2} C H_{3}<H_{5} C_{2}-O-C_{2} H_{5}< \)
\( C H_{3} C H_{2} C H_{2} C H O<C H_{3} C H_{2} C H_{2} C H_{2} O H \)
в. \( C H_{3} C H_{2} C H_{2} C H_{2} C H_{3}>H_{5} C_{2}-O-C_{2} H_{5}> \)
\( C H_{3} C H_{2} C H_{2} C H O<C H_{3} C H_{2} C H_{2} C H_{2} O H \)
c. \( C H_{3} C H_{2} C H_{2} C H_{2} C H_{3}<H_{5} C_{2}-O-C_{2} H_{5}< \)
\( C H_{3} C H_{2} C H_{2} C H O>C H_{3} C H_{2} C H_{2} C H_{2} O H \)
D. \( C H_{3} C H_{2} C H_{2} C H_{2} C H_{3}>H_{5} C_{2}-O-C_{2} H_{5}< \)
\( C H_{3} C H_{2} C H_{2} C H O>C H_{3} C H_{2} C H_{2} C H_{2} O H \)
Subject: Chemistry
The rate of certain hypothetical reaction \( A+B+C \rightarrow \) products is given by \( \boldsymbol{r}=-\frac{\mathbf{d}[\boldsymbol{A}]}{\mathbf{d} \boldsymbol{t}}=\boldsymbol{K}[\boldsymbol{A}]^{1 / 2} \boldsymbol{K}[\boldsymbol{B}]^{1 / 3} \boldsymbol{K}[\boldsymbol{C}]^{1 / 4} \)
The order of the reaction:
\( A \)
в. \( \frac{1}{2} \)
\( c \cdot 2 \)
D. \( \frac{13}{12} \)
Subject: Chemistry
For the equilibrium, an increase of temperature will,
\[
\mathbf{2} N \boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{N}_{2} \boldsymbol{O}_{4}(\boldsymbol{g})+\mathbf{1 4 . 6} \boldsymbol{k} c \boldsymbol{a} \boldsymbol{l}
\]
A . favour the formation of \( N_{2} O_{4} \)
B. favour the decomposition of \( N_{2} O_{4} \)
c. not affect the equilibriumm
D. stop the reaction
Subject: Physics
A planet is revolving in an elliptical orbit around the sun. Its closest
distance from the sun is \( r \) and the
farthest distance is \( R \). If the velocity of
the planet nearest to the sun be \( v \) and
that farthest away from the sun be \( V \)
then \( \boldsymbol{v} / \boldsymbol{V} \) is :
A \( \cdot R^{2} / r^{2} \)
B . \( r^{2} / R^{2} \)
c. \( R / r \)
D. \( r / R \)
Subject: Chemistry
The normality of a solution of a mixture containing \( \boldsymbol{H} \boldsymbol{C l} \) and \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is \( \boldsymbol{N} / \mathbf{5} \)
Twenty millilitres of this solution reacts
with an excess of \( A g N O_{3} \) solution to
give \( 0.287 g \) of silver chloride. The
percentage of \( H C l \) in the mixture by
mass, is \( (A g=108) \)
A . \( 42.69 \% \)
B. \( 57.31 \% \)
c. \( 50 \% \)
D. 25\%