AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A long wire carries a current \( i . \) A rod of
length \( l \) is moved with a velocity \( v \) in a
direction parallel to the wire as shown in figure (a). Find the motional emf induced in the rod:
A \( \cdot \frac{\mu_{0} i}{2 \pi x} l v \)
В \( \cdot \frac{\mu_{0} i}{2 \pi} v \log _{e} \frac{x+l / 2}{x-l / 2} \)
C \( \frac{\mu_{0} i}{2 \pi} v \log _{e} \frac{x-l / 2}{x+l / 2} \)
D. \( \frac{\mu_{0} i v}{2 \pi} \log _{e} \frac{l+x}{x} \)
Subject: Maths
Let \( f(x) \) be a real value function not identically zero satisifes the equation, \( f\left(x+y^{n}\right)=f(x)+f(y)^{n} \) for all real
\( x, y \) and \( f^{\prime}(0) \geq 0 \) where \( n(>1) \) is an odd natural number. \( \boldsymbol{f}(\mathbf{1 0})=\mathbf{1 0 k . F i n d} \)
\( \boldsymbol{k} \) value
Subject: Chemistry
How many grams of magnesium oxide is formed when 4.8 gm of magnesium is combined with \( 3.2 \mathrm{gm} \) of oxygen?
A . \( 4.2 \mathrm{gm} \)
B. 3.2 gm
c. 8 gm
D. \( 16 \mathrm{gm} \)
Subject: Maths
If unit vectors \( \hat{\boldsymbol{i}} \& \hat{\boldsymbol{j}} \) are at right angles to each other and \( \overrightarrow{\boldsymbol{p}}=\mathbf{3} \hat{\boldsymbol{i}}+\boldsymbol{4} \hat{\boldsymbol{j}}, \overrightarrow{\boldsymbol{q}}= \)
\( \mathbf{5} \hat{\mathbf{i}}, \mathbf{4} \overrightarrow{\boldsymbol{r}}=\overrightarrow{\boldsymbol{p}}+\overrightarrow{\boldsymbol{q}} \) and \( \mathbf{2} \overrightarrow{\boldsymbol{s}}=\overrightarrow{\boldsymbol{p}}-\overrightarrow{\boldsymbol{q}} \) then
This question has multiple correct options
A \( \cdot|\vec{r}+k \vec{s}|=|\vec{r}-k \vec{s}| \) for all real \( \mathrm{k} \)
B. \( \vec{r} \) is perpendicular to \( \vec{s} \)
c. \( \vec{r}+\vec{s} \) is perpendicular to \( \vec{r}-\vec{s} \)
D・|\vec| = |\vec| = | \( \vec{p}|=| \vec{q} \)
Subject: Physics
If the work done in turning a magnet of
magnetic moment \( M \) by an angle of \( 90^{\circ} \) from the magnetic meridian is n times the corresponding work done to turn it
through an angle of \( 60^{\circ} \), then the value
of \( n \) is
A . 1
B. 2
\( c \cdot \frac{1}{2} \)
D.
Subject: Physics
A slab of stone of area \( 0.36 m^{2} \) and
thickness 0.1 is exposed on the lower surface to steam at \( 100 C \). A block
of ice at \( 0 C \) rests on the upper surface
of the slab. In one hour \( 4.8 \mathrm{kg} \) of ice is melted. The thermal
conductivity of slab is- (Given latent heat of fusion of ice \( =3.36 \times 10^{5} J k g^{-1} \)
:
A. \( 1.29 \mathrm{J} / \mathrm{m} / \mathrm{s} / \mathrm{C} \)
в. 2.05 \( J / m / s / C \)
c. \( 1.02 \mathrm{J} / \mathrm{m} / \mathrm{s} / \mathrm{C} \)
D. \( 1.24 \mathrm{J} / \mathrm{m} / \mathrm{s} / \mathrm{C} \)
Subject: Physics
In a potentiometer the balancing with a
cell is at length of \( 220 \mathrm{cm} . \) On shunting the cell with a resistance of \( 3 \Omega \) balance
length becomes \( 130 \mathrm{cm} \). What is the internal resistance of this cell?
A. \( 4.5 \Omega \)
B. \( 7.8 \Omega \)
\( c \cdot 6.3 \Omega \)
D. \( 2.08 \Omega \)
Subject: Physics
A wire of length \( 1.0 \mathrm{m} \) and radius \( 10^{-3} \)
\( \mathrm{m} \) is carrying a heavy current and is assumed to radiate as a black body. At
equilibrium its temperature is \( 900 K \)
while that of the surrounding is \( 300 K \) The resistivity of the material of wire at \( 300 K \) is \( \pi^{2} \times 10^{-8} \Omega . m . \) Its
temperature coefficient of resistance is
\( 7.8 \times 10^{-3} /^{0} C . \) Then current in wire will
be (Assume resistivity is linear function of temp.)
\( A \cdot 12 A \)
B. 24 A
c. 36 A
D. 48 A
Subject: Maths
Factorize:
\( 4 x y-x^{2}-4 y^{2}+z^{2} \)
\( \mathbf{A} \cdot(z+x-2 y)(z-x+2 y) \)
B . \( (z-x-2 y)(z-x+2 y) \)
\( \mathbf{c} \cdot(z+x-2 y)(z-x-2 y) \)
D. \( (z+x-2 y)(z-x+y) \)
Subject: Maths
If \( 2 x-7-5 x^{2} \) has maximum value at
\( x=a, \) then \( a=\dots \dots \)
A. \( -1 / 5 \)
в. \( 1 / 5 \)
\( c \cdot 34 / 5 \)
D. \( -34 / 5 \)
Subject: Physics
The focal lengths of the objective and eyepiece of a compound microscope are \( 2 \mathrm{cm} \) and \( 3 \mathrm{cm} \) respectively. The distance between the objective and eyepiece is \( 15 \mathrm{cm} . \) The final image formed is at infinity. The distances in cm of object and image from objective are going to be then:
\( A \cdot 2.4 \) and 12
B. 2.4 and 15
c. 2.3 and 3.0
D. 2.3 and 12
Subject: Physics
Escape velocity for a projectile at
earth's surface is \( v_{e} . \) A body is projected form earth's surface with velocity \( 2_{v_{e}} \)
The velocity of the body when it is at infinite distance from the centre of
the earth is
A \( \cdot v_{e} \)
B. \( 2 v_{e} \)
\( c \cdot \sqrt{2 v} \)
D. \( \sqrt{3} v_{e} \)
Subject: Maths
The point (3,4) is the focus and \( 2 x- \)
\( 3 y+5=0 \) is the directrix of a parabola
Its latus rectum is
A \( \cdot \frac{2}{\sqrt{13}} \)
в. \( \frac{4}{\sqrt{13}} \)
c. \( \frac{1}{\sqrt{13}} \)
D. \( \frac{3}{\sqrt{13}} \)
Subject: Physics
The pendulum of a clock is made of brass. If the clock keeps correct time at \( 20^{\circ} \mathrm{C} \). Calculate how many seconds per
day will it loose at \( 35^{\circ} \mathrm{C} \) ( \( \alpha \) for brass = \( \left.2 \times 10^{-5 o} C\right) \)
A . 12.96
B. 1.29 s
c. \( 129.6 \mathrm{s} \)
D. 8.64
Subject: Physics
The energy supplied to Kolkata by the state electricity board during an average November week day was 40 GWh. If this energy could be obtained by the conservation of matter, how much
mass would have to be annihilated?
A \( .1 .6 g \)
B. \( 2.2 \mathrm{g} \)
c. \( 4.0 \mathrm{g} \)
D. \( 1.6 \mathrm{kg} \)
Subject: Maths
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\boldsymbol{3} \cos \left(\frac{\boldsymbol{\pi}}{\boldsymbol{6}}+\boldsymbol{x}^{0}\right)-\boldsymbol{4} \cos ^{3}\left(\frac{\boldsymbol{\pi}}{\boldsymbol{6}}+\boldsymbol{x}^{0}\right)\right. \)
A \( \cdot \cos \left(3 x^{0}\right) \)
B. \( \frac{\pi}{60} \sin \left(3 x^{0}\right) \)
c. \( \frac{\pi}{60} \cos \left(3 x^{0}\right) \)
D. \( -\frac{\pi}{60} \sin \left(3 x^{0}\right) \)
Subject: Maths
If \( a-b=0.9 \) and \( a b=0.36 ; \) find \( a^{2}- \)
\( \boldsymbol{b}^{2} \)
\( \mathbf{A} \cdot \pm 7.65 \)
B . ±1.35
\( \mathrm{c} .\pm 1.5 \)
D. ±4.5
Subject: Chemistry
Assertion
A small amount of alchohol is added to
chloroform bottles
Reason
Alcohol acts as inhibitor for oxidation of
choloroform.Also it reacts with \( C O C l_{2} \)
to give harmless diethyl carbonate
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 uniform rod of length \( L \) rests on a
frictionless horizontal surface. The rodd
is pivoted about a fixed frictionless axis at one end. The rod is initially at rest. A bullet travelling parallel to the horizontal surface and perpendicular to the rod with speed \( v \) strikes the rod at its centre and becomes embedded in it.
The mass of the bullet is one-sixth the
mass of the rod. What is the final
angular velocity of the rod?
A \( \cdot \omega=\frac{v}{9 L} \)
B. \( \omega=\frac{2 v}{9 L} \)
\( c \cdot \omega=\frac{3 v}{9 L} \)
D. \( \omega=\frac{5 v}{9 L} \)
Subject: Chemistry
Identify the incorrect statement.
\( \mathbf{A} \cdot \operatorname{In} N_{2} O_{4} \) the \( \mathrm{N}-\mathrm{N} \) bond length is longer than the usual N-N single bond distance.
B. \( N O_{2} \) molecule is angular with \( N \) -O distance equal to the intermediate distance between a single and a double bond
\( \mathrm{C} \cdot N_{2} \mathrm{O} \) is a linear molecule and has a small dipole moment.
D. None of the above
Subject: Maths
In a binomial distribution \( B\left(n, p=\frac{1}{4}\right) \) if the probability of at least one success is greater than or equal to \( \frac{9}{10}, \) then \( n \) is greater than
A \( \cdot \frac{1}{\log _{10} 4+\log _{10} 3} \)
В. \( \frac{9}{\log _{10} 4-\log _{10} 3} \)
c. \( \frac{4}{\log _{10} 4-\log _{10} 3} \)
D. \( \frac{1}{\log _{10} 4-\log _{10} 3} \)
Subject: Chemistry
For the reaction: \( 2 H I \rightarrow H_{2}+I_{2} \). the
expression \( \frac{-1}{2} \frac{d(H I)}{d t} \) represents:
A. the rate of formation of \( H I \)
B. the rate of disappearance of \( H I \)
c. the instantaneous rate of the reaction
D. the average rate of reaction
Subject: Physics
A slightly divergent beam of charged particles accelerated by a Potential difference B propagates from a point \( \mathbf{A} \) along the axis of solenoid. The beam is brought into focus at a distance I from the point \( A \) at two successive values of
magnetic induction \( B_{1} \) and \( B_{2} \). If the
specific charge \( \mathrm{q} / \mathrm{m} \) of the particles is \( \frac{\boldsymbol{q}}{\boldsymbol{m}}=\frac{\boldsymbol{x} \boldsymbol{\pi}^{2} \boldsymbol{V}}{\boldsymbol{l}^{2}\left(\boldsymbol{B}_{2}-\boldsymbol{B}_{1}\right)^{2}} \cdot \) Find \( \boldsymbol{x} \)
Subject: Physics
The activity of a radioactive substance
is \( R_{1} \) at time \( t_{1} \) and \( R_{2} \) at time \( t_{2}\left(>t_{1}\right) \)
Its decay constant is \( \lambda \). Then
A \( . R_{1} t_{1} \)
B \( \cdot R_{2}=R_{1} e^{\lambda\left(t_{1}-t_{2}\right)} \)
c. \( \frac{R_{1}-R_{2}}{t_{2}-t_{1}}= \) constant
D. \( R_{2}=R_{1} e^{\lambda\left(t_{2}-t_{1}\right)} \)
Subject: Physics
\( 1 \mathrm{kg} \mathrm{fcm}^{-2} \)
\( \mathrm{Nm}^{-2} \)
A \( \cdot 10^{3} \)
B . \( 10^{5} \)
\( c \cdot 10^{4} \)
\( D \cdot 10^{6} \)
Subject: Chemistry
Choose the correct alternative:
(a) Alloys of metals usually have (greater/less) resistivity than that of their constituent metals.
(b) Alloys usually have much (lower/higher) temperature coefficients
of resistance than pure metals.
(c) The resistivity of the alloy manganin is nearly independent of increases rapidly with increase of
temperature
(d) The resistivity of a typical insulator
(e.g., amber) is greater than that of a metal by a factor of the order of \( \left.\mathbf{1 0}^{\mathbf{2 2}} / \mathbf{1 0}^{\mathbf{3}}\right) \)
Subject: Chemistry
\( \boldsymbol{A} \stackrel{\text {sodalime}}{\longrightarrow} \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{6}} \stackrel{\boldsymbol{C l}_{\boldsymbol{\lambda}}, \boldsymbol{h} \boldsymbol{v}}{\boldsymbol{B}} \)
In this reaction \( A \) and \( B \) are
respectively:
A. Pheno
B. Chlorobenzene
c. Sodium benzoate, Внс
D. \( C_{2} H_{2} \& \) ВНС
Subject: Maths
\( \int \frac{1}{\left(x^{6}-1\right)} d x \)
A \( \cdot 1 / 2\left(\frac{1}{6} \ln \frac{(x-1)^{2}}{x^{2}+x+1}-\frac{1}{\sqrt{3}} \arctan \frac{2 x+1}{\sqrt{3}}-\frac{1}{6} \ln \frac{(x+1)^{2}}{x^{2}-x+1}-\right. \)
\( \left.\quad \frac{1}{\sqrt{3}} \arctan \frac{2 x-1}{\sqrt{3}}\right)+\mathrm{k} \)
B \( \cdot \)
\[
\begin{array}{l}\text { C } \mid / 2\left(\frac{1}{6} \ln \frac{(x+1)^{2}}{x^{2}-x+1}-\frac{1}{\sqrt{3}} \arctan \frac{2 x-1}{\sqrt{3}}-\frac{1}{6} \ln \frac{(x-1)^{2}}{x^{2}+x+1}-\right. \\ \left.\frac{1}{\sqrt{3}} \arctan \frac{2 x+1}{\sqrt{3}}\right)+\mathrm{k}\end{array}
\]
C \( \cdot 1 / 2\left(\frac{1}{6} \ln \frac{(x-1)^{2}}{x^{2}+x+1}-\frac{1}{\sqrt{3}} \operatorname{arccot} \frac{2 x+1}{\sqrt{3}}+\frac{1}{6} \ln \frac{(x+1)^{2}}{x^{2}-x+1}+\right. \)
\( \left.\frac{1}{\sqrt{3}} \operatorname{arccot} \frac{2 x-1}{\sqrt{3}}\right)+\mathrm{k} \)
D \( \cdot 1 / 2\left(\frac{1}{6} \ln \frac{(x-1)^{2}}{x^{2}+x+1}-\frac{1}{\sqrt{3}} \operatorname{arccot} \frac{2 x+1}{\sqrt{3}}-\frac{1}{6} \ln \frac{(x+1)^{2}}{x^{2}-x+1}-\right. \)
\( \left.\frac{1}{\sqrt{3}} \operatorname{arccot} \frac{2 x-1}{\sqrt{3}}\right)+\mathrm{k} \)
Subject: Physics
a poin
is put through a cycle consisting of the following three reversible steps:
(CA): Isothermal compression from 2
atm and 10 litres to 20 atm and 1 litre.
(AB): Isobaric expansion to return the
gas to the original volume of 10 litres
with T going from \( \boldsymbol{T}_{\mathbf{1}} \) to \( \boldsymbol{T}_{\mathbf{2}} \).
(BC): Cooling at constant volume to bring the gas to the original pressure and temperature.

The steps are shown schematically in
the figure given above
(a) Calculate \( T_{1} \) to \( T_{2} \)
(b) Calculate \( \Delta U, q \) and \( w \) in calories,
for each step and for the cycle.
Subject: Physics
If an object is thrown vertically up, with the initial speed \( u \) from the ground, then the time taken by the object to return back to the ground is
\( ^{\mathrm{A}} \cdot \frac{u^{2}}{2 g} \)
в. \( \frac{u^{2}}{g} \)
c. \( \frac{u}{2 g g} \)
D. \( \frac{2 u}{g} \)
Subject: Chemistry
Which of the following has longest \( C-0 \)
bond length? (Free C-O bond length is Co is \( 1.128 \dot{A}) \)
\( \mathbf{A} \cdot N i(C O)_{4} \)
B . \( \left[N i(C O)_{3}\right]^{+} \)
\( \mathrm{c} \cdot\left[\mathrm{Fe}(\mathrm{CO})_{4}\right]^{2-} \)
D・ \( \left[\mathrm{Mn}(\mathrm{C} O)_{6}\right]^{+} \)
Subject: Physics
From point \( A \) located on a highway, one
has to get by a car as soon as possible to point \( B \) located in the field at a
distance \( l \) from point \( D . \) If the car
moves \( n \) times slower in the field, at
what distance \( x \) from \( D \) one must turn
off the highway.
A \( \cdot x=\frac{l}{\sqrt{n^{3}-1}} \)
B. \( x=\frac{l}{\sqrt{n^{2}-1}} \)
c. \( _{x}=\frac{l}{\sqrt{n^{3}-2}} \)
D. \( x=\frac{l}{\sqrt{n^{2}-2}} \)
Subject: Maths
Let \( X \) denote the number of hours you
study during a randomly selected school day. The probability that \( X \) can
take the values of \( x, \) has the following
form, where \( k \) is some constant \( \boldsymbol{P}(\boldsymbol{X}=\boldsymbol{x})=\left\{\begin{array}{ll}\mathbf{0}, \mathbf{1} & \text { if } \boldsymbol{x}=\mathbf{0} \\ \boldsymbol{K} \boldsymbol{x} & \text { if } \boldsymbol{x}=\mathbf{1} \text { or } \mathbf{2} \\ \boldsymbol{K}(\mathbf{5}-\boldsymbol{x}) & \text { if } \boldsymbol{x}=\mathbf{3} \text { or } \mathbf{4} \\ \mathbf{0} & \text { otherwise }\end{array}\right. \)
What is the probability that you study.
For at least two hour.
Subject: Chemistry
While charging the lead storage battery
A. \( P b S O_{4} \) anode is reduced to \( P b \)
B. \( P b S O_{4} \) cathode is reduced to Pb
\( \mathrm{c} \cdot P b S O_{4} \) cathode is oxidised to \( \mathrm{Pb} \)
D. \( P b S O_{4} \) anode is oxidised to \( P b O_{2} \)
Subject: Maths
To get a driver's license, an applicant must pass a written test and a driving
test. Past records show that \( 80 \% \) of the
applicants pass the written test and 60 \( \% \) of those who have passed the written
test pass the driving test. Based on these figures, how many applicants in a random group of 1,000 applicants
would you expect to get driver's licenses?
A . 200
B . 480
c. 600
D. 750
E . 800
Subject: Chemistry
Which of the following represents the given sequence of hybridisation of carbon atoms from left to right :
\( \boldsymbol{s} \boldsymbol{p}^{2}, \boldsymbol{s} \boldsymbol{p}^{2}, \boldsymbol{s} \boldsymbol{p}, \boldsymbol{s} \boldsymbol{p} ? \)
A. \( H_{2} C=C H-C \equiv C H \)
В \( \cdot_{H C} \equiv C-C H=C H_{2} \)
c. \( H_{3} C-C H=C H-C H_{3} \)
D. \( H_{2} C=C H-C H=C H_{2} \)
Subject: Chemistry
When \( 2 g \) of \( A \) gas is introduced into an
evacuated flask kept at \( 25^{\circ} C, \) the pressure is found to be 1 atm. If \( 3 g \) of another gas \( B \) is then added to the
same flask, the total pressure becomes
1.5 atm. The ratio of molecular weights
is:
A . 1: 1
B. 1: 2
\( c \cdot 2: 3 \)
D. none of these
Subject: Maths
In right angled \( \Delta A B C \angle B= \)
\( 90^{\circ} B D \perp A C, A B=b, B D=c, B C= \)
\( \boldsymbol{a}, \boldsymbol{A} \boldsymbol{D}=\boldsymbol{8} \boldsymbol{D} \boldsymbol{C}=\mathbf{1 0} . \) Then find \( ^{\boldsymbol{}} \boldsymbol{b}^{\prime} \)
A \( \cdot \sqrt{5} \)
B. 12
\( c \cdot 6 \sqrt{6} \)
D. \( \sqrt{18} \)
Subject: Chemistry
Intermolecular forces between n-hexane
and n-heptane are nearly same as between hexane and heptane individually. When these two are mixed, which of the following is not true about the solution formed?
A \( \cdot \) It obeys Raoult's law, i.e, \( p_{A}=x_{A} p_{A}^{o} \quad \) and \( p_{B}= \)
\( x_{B} p_{B}^{o} \)
B. \( \Delta H_{\text {mixing }} \) is zero
c. \( \Delta V_{\text {mixing }} \) is zero
D. It forms minimum boiling azeotrope
Subject: Maths
If
(2,4) and (10,10) are the ends of a latus - rectum of an ellipse with eccentricity \( \frac{1}{2}, \) then the length of semi major axis is
A \( \cdot \frac{20}{3} \)
в. \( \frac{15}{3} \)
c. \( \frac{40}{3} \)
D. None of these
Subject: Physics
The Sun delivers \( 10^{3} W / m^{2} \) of electromagnetic flux to the Earth's
surface. The radiation force on the
roof of dimensions \( 8 m \times 20 m \) will be:
A \( \cdot 3.33 \times 10^{-5} N \)
В. \( 5.33 \times 10^{-4} N \)
\( \mathbf{c} \cdot 7.33 \times 10^{-3} N \)
D. \( 9.33 \times 10^{-2} N \)
Subject: Physics
In the circuit shown in figure, \( \boldsymbol{E}_{1}= \)
\( \mathbf{3} \boldsymbol{V}, \boldsymbol{E}_{2}=\mathbf{2} \boldsymbol{V}, \boldsymbol{E}_{3}=\mathbf{1} \boldsymbol{V} \) and \( \boldsymbol{r}_{\mathbf{1}}=\boldsymbol{r}_{\mathbf{2}}= \)
\( r_{3}=1 o h m \)
(a) Find the potential difference
between the points \( A \) and \( B \) and the
currents through each branch.
(b) If \( r_{2} \) is short circuited and the point
\( A \) is connected to point \( B \) through a
resistance \( R, \) find the currents through
\( \boldsymbol{E}_{1}, \boldsymbol{E}_{2}, \boldsymbol{E}_{3} \) and the resistor \( \boldsymbol{R} \)
Subject: Chemistry
\( 0.5 g \) of an organic compound containing nitrogen on kjeldahlising
required \( 29 m l \) of \( N / 5 H_{2} S O_{4} \) for
complete neutralisation of ammonia. The percentage of nitrogen in the compound is :
A. 34.3
B. 16.2
c. 13.6
D. 24.5
Subject: Maths
Solve the following pair of equations:
\( \frac{a}{x}-\frac{b}{y}=0 \)
\( \frac{a b^{2}}{x}+\frac{a^{2} b}{y}=a^{2}+b^{2} \)
A. \( x=a b \) and \( y=b \)
B. \( x=a \) and \( y=b \)
c. \( x=b \) and \( y=a \)
D. \( x=b-a \) and \( y=a b \)
Subject: Chemistry
\( H_{2} O_{2} \) solution used for hair bleaching
is sold as a solution of approximately
\( 5.0 \mathrm{g} H_{2} \mathrm{O}_{2} \) per \( 100 \mathrm{mL} \) of the solution
The molecular mass of \( H_{2} O_{2} \) is \( 34 . \) The
molarity of this solution is approximately:
A \( .0 .15 M \)
B. \( 1.5 M \)
c. \( 3.0 M \)
D. 3.4 \( M \)
Subject: Physics
Four conductors of resistance 4,3,9
and 6 ohm are connected in \( A B, B C, C D \) and DA arms of a Wheatstone bridge. The bridge can be balanced by connecting.
A. \( 1) 6 \) ohm in series with 3 ohm conductor
B. 2) 4 ohm in parallel with 6 ohm conductor
c. 3 ) 3 ohm in series with 3 ohm conductor
D. 4 ) 5 ohm in series with 6 ohm conductor
Subject: Physics
Surface tension of liquid is 70
dyne/cm. Its value in Sl unit is
A . \( 70 \mathrm{N} / \mathrm{m} \)
В. \( 7 \times 10^{-2} N / m \)
C. \( 7 \times 10^{2} N / m \)
D. \( 7 \times 10^{3} N / m \)
Subject: Chemistry
Which of the following is a redox reaction?
A . Reaction of \( H_{2} S O_{4} \) with \( N a O H \)
B. In atmosphere, formation of \( O_{3} \) from \( O_{2} \) by lightening
c. Formation of oxides of nitrogen from nitrogen and oxygen by lightening
D. Evaporation of \( H_{2} O \)
Subject: Physics
Two radio stations broadcast their
programmes at the same amplitude \( \boldsymbol{A} \)
and at slightly different frequencies \( \omega_{1} \)
and \( \omega_{2} \) respectively where \( \omega_{1}-\omega_{2}= \)
1 \( k H z . \) A detector receives the signals
from the two stations simultaneously. It can only detect signals of intensity \( > \) \( 2 A^{2} . \) Find the interval between
successive maxima of the intensity of the signal received by the detector.
A \( \cdot 2 \times 10^{-3} s \)
B. \( 4 \times 10^{-3} s \)
c. \( 1.5 \times 10^{-3} s \)
D. \( 10^{-3} s \)
Subject: Physics
Consider six wires into or out of the
page, all with the same current. Rank the line integral of the magnetic field(from most positive to most
negative) taken counterclock wise around each loop shown as positive in accordance with right hand screw rule.
\( \mathbf{A} \cdot B>C>D>A \)
В . \( B>C=D>A \)
c. \( B>A>C=D \)
D. \( C>B=D>A \)
Subject: Maths
If \( A \) and \( B \) are two events such that
\( \boldsymbol{P}(\boldsymbol{A})=\frac{1}{4}, \boldsymbol{P}(\boldsymbol{B})=\frac{1}{2} \) and \( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})= \)
\( \frac{1}{8} \) find \( P A \cup B \)
Subject: Chemistry
According to Freundlich adsorption isotherm, which of the following is/are
correct?
A \( \cdot \frac{x}{m} \propto p^{1 / 2} \)
в. \( \frac{x}{m} \propto p^{\text {। }} \)
c. \( \frac{x}{m} \propto p^{1 / n} \)
D. All the above
Subject: Physics
An object of mass \( 5 k g \) falls from rest
through a vertical distance of \( 20 m \) and
attains a velocity of \( 10 \mathrm{m} / \mathrm{s} \). How much work is done by the resistance of air on
the object? \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
A . \( 250 J \)
В. \( -650 J \)
c. \( -750 J \)
D. \( 950 J \)
Subject: Chemistry
Which of the following reactions is not a part of Solvay's process for preparation of sodium carbonate?
\( \mathbf{A} \cdot 2 N H_{3}+H_{2} O+C O_{2} \rightarrow\left(N H_{4}\right)_{2} C O_{3} \)
B. \( \left(N H_{4}\right)_{2} C O_{3}+H_{2} O+C O_{2} \rightarrow 2 N H_{4} H C O_{3} \)
c. \( 2 N H_{4} H C O_{3} \rightarrow\left(N H_{4}\right)_{2} C O_{3}+H_{2} O+C O_{2} \)
D. \( N H_{4} H C O_{3}+N a C l \rightarrow N H_{4} C l+N a H C O_{3} \)
Subject: Physics
The coefficient of self induction of a coil
is given by
\( ^{\text {A }} \cdot L=\left(-\frac{d I}{d t}\right) \)
B. \( L=-\frac{e d I}{d t} \)
c. \( _{L}=\frac{d I}{e d t} \)
D. \( L=\frac{d I}{d t} e^{2} \)
Subject: Physics
A transformer having 4000 turns on its primary side and 500 turns on the secondary side. If the input voltage is
\( 240 V, \) find out the output voltage of the secondary side of the transformer?
A . \( 15 ~ V \)
в. \( 30 V \)
c. \( 60 V \)
D. \( 120 V \)
E . \( 240 \mathrm{V} \)
Subject: Physics
A car is travelling along a circular curve that has a radius of \( 50 \mathrm{m} \). If its speed is \( 16 \mathrm{m} / \mathrm{s} \) and is increasing uniformly at \( 8 m / s^{2}, \) determine the magnitude of its acceleration at this instant.
A \( \cdot 9.5 \mathrm{m} / \mathrm{s}^{2} \)
В. \( 9.8 \mathrm{m} / \mathrm{s}^{2} \)
c. \( 8.5 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 7.5 \mathrm{m} / \mathrm{s}^{2} \)
Subject: Chemistry
Select the correct statements regarding
the final product \( (Y) \)
This question has multiple correct options
A. It can be identified with neutral \( F e C l_{3} \) solution
B. On treatment with Zn-dust it yields a product having degree of unsaturation \( =4 \)
C. It undergoes coupling reaction with benzene diazonium chloride at low temperature \( \left(0-5^{\circ} \mathrm{C}\right) \) in slightly basic medium
D. It liberates \( H_{2} \) gas with Na
Subject: Chemistry
The pair whose both species are used in antacid medicinal preparation is:
A. \( \operatorname{NaH} \mathrm{CO}_{3} \) nad \( \mathrm{Mg}(\mathrm{OH})_{2} \)
в. \( N a_{2} C O_{3} \) and \( C a\left(H C O_{3}\right) \)
c. \( C a\left(H C O_{3}\right)_{2} \) and \( M g(O H)_{2} \)
D. \( C a(O H)_{2} \) and \( N a H C O_{3} \)
Subject: Maths
The order, degree of the differential
equation satisfying the relation \( \sqrt{1+x^{2}}+\sqrt{1+y^{2}}=\lambda(x \sqrt{1+y^{2}}) \)
\( \left.y \sqrt{1}+x^{2}\right) \) is
A . 1,1
в. 2,
c. 3,2
D. 0,1
Subject: Chemistry
The volume of helium is \( 44.8 ~ L \) at:
A \( \cdot 100^{\circ} \mathrm{C} \) and 1 atm
B. \( 0^{\circ} \mathrm{C} \) and 1 atm
c. \( 0^{\circ} \mathrm{C} \) and 0.5 atm
D. \( 100^{\circ} \mathrm{C} \) and 0.5 atm
Subject: Chemistry
For the reaction \( N_{2}+3 X_{2} \rightarrow 2 N X_{3} \)
where \( \boldsymbol{X}=\boldsymbol{F}, \boldsymbol{C l} \) (the average bond
energies are \( \boldsymbol{F}-\boldsymbol{F}=\mathbf{1 5 5} \boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1} \)
\( N-F=272 k J m o l^{-1}, C l-C l= \)
\( 242 k J m o l^{-1}, N-C l= \)
\( 200 k J m o l^{-1} \) and \( N \equiv N= \)
\( 941 k J \) mol \( ^{-1} \) ). The heats of formation
of \( N F_{3} \) and \( N C l_{3} \) in \( k J m o l^{-1} \)
respectively, are closest to:
A. -226 and +467
B. +226 and -467
c. -151 and +311
D. +151 and -311