AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If \( \frac{1}{(1-2 x)(1+3 x)}=\frac{A}{1-2 x}+\frac{B}{1+3 x} \)
then \( 2 B= \)
\( A \cdot A \)
B. 2A
\( c \cdot 3 A \)
D. -3A
Subject: Physics
Spring scale reads \( 20 N \) as it pulls a
\( 4.0 \mathrm{kg} \) object across a table. What is the
magnitude of the force exerted by object on the spring scale?
A. \( 40 N \)
в. \( 20 N \)
c. \( 4 N \)
D. \( 5 N \)
Subject: Maths
A point \( P \) lies on the line whose end
points are \( \boldsymbol{A}(\mathbf{1}, \mathbf{2}, \mathbf{3}) \) and \( \boldsymbol{B}(\mathbf{2}, \mathbf{1 0}, \mathbf{1}) \)
If \( z \) -co-ordinate of \( P \) is \( 7, \) find sum of its
other co - ordinates.
Subject: Maths
A coin is tossed until a head appears or
it has been tossed 3 times. Given that
head does not appear on the first toss, the probability that the coin is tossed 3 times is
A \( \cdot \frac{1}{4} \)
B. \( \frac{3}{8} \)
\( c \cdot \frac{1}{8} \)
D.
Subject: Maths
Show that the points \( A, B, C \) with position vectors \( \vec{a}=\left(3 i^{-} 4 j^{-} 4 \hat{k}\right), \vec{b}= \)
\( (2 i-j+\hat{k}) \) and \( \vec{c}=(i-3 j-5 \hat{k}) \)
respectively,form the vertices of a rightangled triangle.
Subject: Chemistry
Assertion
In the Contact process, the catalyst mass is heated electrically only initially
Reason
To conserve energy the mixture is heated by exhaust gases from the catalytic converter by heat exchangers.
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 \( \boldsymbol{K}_{s p} \) for \( \boldsymbol{C r}(\boldsymbol{O H})_{3} \) is \( 1.6 \times 10^{-30} \)
The solubility of this compound in water
is:
\( \mathbf{A} \cdot 4 \sqrt{1.6 \times 10^{-30}} \)
в. \( 4 \sqrt{1.6 \times 10^{-30} / 27} \)
c. \( 1.6 \times 10^{-9} \)
D. \( 2 \sqrt{1.6 \times 10^{-30}} \)
Subject: Physics
Derive the relation between object distance (u) and image distance (v) in terms of refractive index of the medium
(n) and the radius of curvature (R) of the spherical surface.
A \( \cdot \frac{\mu_{1}}{\mu_{2}} \)
в. \( \frac{\mu_{2}}{\mu_{1}} \)
c. \( \frac{\mu_{2}}{2} \)
D. \( \frac{\mu_{1}}{2} \)
Subject: Maths
If \( f(x)=\frac{\sin 3 x}{\sin x}, x \neq 0 \) is continuous
\[
=\boldsymbol{K}, \boldsymbol{x}=\mathbf{0}
\]
function, then \( \boldsymbol{K}= \)
A .
B. 3
\( c \cdot \frac{1}{3} \)
D.
Subject: Maths
For matrices \( A \) and \( B ; \) if \( A B=4 I, \) then
\( A^{-1} \) is \( = \)
A \( .4 B \)
в. \( 4 B^{-1} \)
c. \( \frac{1}{4} \)
D. \( \frac{1}{4} B^{-1} \)
Subject: Chemistry
A mother cell disintegrates into 60
identical cells and each daughter cell further disintegrates into 24 smaller cells. The smallest cells are uniform
cylindrical in shape with the diameter
of \( 120 A \) and each cell is \( 6000 A \) long. The density of the smallest cell is 1.12
\( \mathrm{g} / \mathrm{cm}^{3} . \) If the molar mass of the mother cell is \( x \times 10^{10} g, \) find \( x \) (nearest integer).
Subject: Physics
If the moment of inertia of a circular
disc about an axis tangentially and
parallel to its surface be \( I \), then the moment of inertia about the axis
tangential but perpendicular to the surface will be :
A \( \cdot \frac{6}{5} I \)
в. \( \frac{3}{4} I \)
c. \( \frac{3}{2} I \)
D. \( \frac{5}{4} \)
Subject: Physics
Two cells of emf's \( 1.25 \mathrm{V} \) and \( 0.75 \mathrm{V} \) having equal internal resistance are connected in parallel. The effective emf is
A . \( 0.75 v \)
B. 1.25V
c. \( 2.0 v \)
D. 1.0v
E. \( 0.5 v \)
Subject: Chemistry
The solubility product of \( \boldsymbol{C r}(\boldsymbol{O H})_{3} \) at
\( 298 K \) is \( 6.0 \times 10^{-31} . \) The concentration
of hydroxide ions in a saturated
solution of \( \boldsymbol{C r}(\boldsymbol{O H})_{3} \) will be :
A \( \cdot\left(2.22 \times 10^{-31}\right)^{1 / 4} \)
B. \( \left(4.86 \times 10^{-29}\right)^{1 / 4} \)
c. \( \left(18 \times 10^{-31}\right)^{1 / 2} \)
D. \( \left(18 \times 10^{-31}\right)^{1 / 4} \)
Subject: Maths
Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}: \)
\( \boldsymbol{6} \boldsymbol{x}-\boldsymbol{9}+\boldsymbol{8} \boldsymbol{y}=\mathbf{0} \)
Subject: Biology
Assertion : Agricultural output increased several times after introduction of DDT.
Reason: DDT was the first insecticide use
d on a wide scale.
A. If both the assertion and the reason are true and the
reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false
E. If the assertion is false but reason is true
Subject: Chemistry
A gas is expanded from volume \( V_{1} \) to
volume \( V_{2} \) in three processes, shown in
the figure. If \( U_{A}, U_{B} \) and \( U_{C} \) and \( U_{D} \)
represent the internal energies of the
gas in state \( A, B, C \) and \( D \) respectively,
the which of the following is not correct.
A. \( U_{B}-U_{A}>0 \)
B. \( U_{C}-U_{A}=0 \)
c. \( U_{D}-U_{A}<0 \)
D. \( U_{B}=U_{C}=U_{D} \)
Subject: Maths
The sum \( ^{20} C_{0}+^{20} C_{1}+^{20} C_{2}+\ldots . .+^{20} \)
\( C_{10} \) is equal to
A \( \cdot 2^{20}+\frac{20 !}{(10 !)^{2}} \)
В. \( 2^{19}+\frac{1}{2} \cdot \frac{20 !}{(10 !)^{2}} \)
C \( \cdot 2^{19}+^{20} C_{10} \)
D. none of these
Subject: Maths
Sum of the first \( p, q \) and \( r \) terms of an
A.P. are \( a, b \) and \( c, \) respectively. Prove \( \operatorname{that} \frac{\boldsymbol{a}}{\boldsymbol{p}}(\boldsymbol{q}-\boldsymbol{r})+\frac{\boldsymbol{b}}{\boldsymbol{q}}(\boldsymbol{r}-\boldsymbol{p})+ \)
\( \frac{c}{r}(p-q)=0 \)
Subject: Chemistry
Assertion
Molarity of an aqueous solution at \( 0^{\circ} \mathrm{C} \)
is less than the molarity of the same
solution at \( 4^{\circ} \mathrm{C} \)
Reason
Molarity increases with an increase of
temperature
A. Both Assertion and Reason are correct and the Reason is the correct explanation of the Assertion
B. Both Assertion and Reason are correct but the Reason is not the correct explanation of the Assertion
C. The Assertion is correct but the Reason is incorrect
D. The Assertion is incorrect but the Reason is correct
Subject: Chemistry
Few isomers are given below. The correct statement regarding them are:
(i) \( \left[\boldsymbol{C r}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right] \boldsymbol{C l}_{3} \)
(ii) \( \left[\boldsymbol{C r}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{5} \boldsymbol{C l}\right] \boldsymbol{C l}_{2} \cdot \boldsymbol{H}_{2} \boldsymbol{O} \)
\( \left(\text { iii) }\left[\boldsymbol{C r}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{4} \boldsymbol{C l}_{2}\right] \boldsymbol{C l} . \boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O}\right. \)
A. (i),(ii) and (iii) are hydrate isomers
B. (i),(ii) and (iii) are coordination isomers.
\( c . \) (i),(ii) and (iii) are ionisation isomers
D. (i) and (ii) are stereo-isomers
Subject: Physics
The diagram below shows a cathode ray tube in which the arrow indicates a
beam of charged particles approaching
an electric field between the plates \( A \)
and B. State the approximate voltage \( V_{1} \)
used to heat the filament
A . \( 1.5 \mathrm{v} \)
B. 3
\( c \cdot 6 v \)
D. 12
Subject: Chemistry
An organic compound undergoes firstorder decomposition. The time taken for
its decomposition to \( 1 / 8 \) and \( 1 / 10 \) of
its initial concentration are \( t_{1 / 8} \) and
\( t_{1 / 10} \) respectively. What is the value of \( \frac{\left[\boldsymbol{t}_{\mathbf{1} / \mathbf{8}}\right]}{\left[\boldsymbol{t}_{\mathbf{1} / \mathbf{1 0}}\right]} \times \mathbf{1 0} ?\left(\boldsymbol{t a k e} \log _{\mathbf{1 0}} \mathbf{2}=\mathbf{0 . 3}\right) \)
Subject: Maths
The Total Surface Area of a cube in \( c m^{2} \)
is equal to the volume of the cube in
\( c m^{3} \) The edge of the cube is \( _{--}-- \) (in \( \mathrm{cm} \)
\( A \cdot 3 \)
B. 4
\( c \cdot 5 \)
D. 6
Subject: Maths
Find the solution of \( \frac{d y}{d x}=\frac{2 y-x-4}{y-3 x+3} \)
\( \mathbf{A} \cdot\left(\log \left(v^{2}-3 v+1\right)-\frac{1}{2 \frac{\sqrt{21}}{2}} \log \frac{v-\frac{5}{2}-\frac{\sqrt{21}}{2}}{v-\frac{5}{2}+\frac{\sqrt{21}}{2}}\right)= \)
\( -\log \alpha+c \)
\( ^{\mathrm{B}} \cdot\left(\log \left(v^{2}+3 v+1\right)-\frac{1}{2 \frac{\sqrt{21}}{2}} \log \frac{3 v-\frac{5}{2}-\frac{\sqrt{21}}{2}}{v-\frac{5}{2}+\frac{\sqrt{21}}{2}}\right)= \)
\( -\log \alpha+c \)
\( \left(\log \left(v^{2}-5 v+1\right)-\frac{1}{2 \frac{\sqrt{21}}{2}} \log \frac{3 v-\frac{5}{2}-\frac{\sqrt{21}}{2}}{v-\frac{5}{2}+\frac{\sqrt{21}}{2}}\right)= \)
\( -\log \alpha+c \)
\( \left(\log \left(v^{2}-5 v+1\right)-\frac{1}{2 \frac{\sqrt{21}}{2}} \log \frac{v-\frac{5}{2}-\frac{\sqrt{21}}{2}}{v-\frac{5}{2}+\frac{\sqrt{21}}{2}}\right)= \)
\( -\log \alpha+c \)
Subject: Physics
A parallel plate condenser with oil (dielectric constant 2 ) between the
plates has capacitance \( C . \) If the oil is removed, the capacitance of capacitor becomes:
A. \( \sqrt{2 C} \)
B. 2C
c. \( \frac{c}{\sqrt{2}} \)
D. \( \frac{c}{2} \)
Subject: Physics
A particle of mass \( m \) moves on a straight line with its velocity varying with the distance travelled according to the equation \( \boldsymbol{v}=\boldsymbol{\alpha} \sqrt{\boldsymbol{x}}, \) where a is a
constant. Find the total work done by all the forces during a displacement from
\( \boldsymbol{x}=\mathbf{0} \) to \( \boldsymbol{x}=\boldsymbol{d} \)
A \( \cdot \frac{1}{2} m a^{2} b \)
B. \( \frac{1}{4} m a^{2} b \)
\( c \cdot m a^{2} b \)
D. \( 2 m a^{2} b \)
Subject: Physics
Three identical charges, each having a
value \( 1.0 \times 10^{-3} \mathrm{C} \) are placed at the
corners of an equilateral triangle of side \( 20 \mathrm{cm} \) Find the potential at the center of the triangle
\( \mathbf{A} \cdot 2.3 \times 10^{6} \mathbf{V} \)
В. \( 2.3 \times 10^{5} \mathrm{V} \)
c. \( 2.3 \times 10^{4} \mathrm{V} \)
D. \( 2.3 \times 10^{3} \mathrm{V} \)
Subject: Physics
The elements \( A \) and \( B \) combine
together to give two compounds \( A_{2} B_{3} \)
and \( A B_{2} . \) The weight of 0.2 mole of
\( A_{2} B_{3} \) is \( 26 g \mathrm{m} \). The weight of 0.3 mole of
\( A B_{2} \) is \( 24 \mathrm{gm} . \) Then the atomic weights of \( A \) and \( B \) respectively.
A. 15,20
B. 20,25
c. 20,30
D. 25,30
Subject: Chemistry
A compound \( X \) on heating gives a colorless gas. The residue is dissolved
in water to obtain \( Y . \) Excess \( C O_{2} \) is
bubbled through aqueous solution of \( Y \) and \( Z \) is formed. \( Z \) on gentle heating
gives back \( X . \) The \( X \) is:
A \( \cdot C a C O_{3} \)
в. \( C a\left(H C O_{3}\right)_{2} \)
c. \( N a_{2} C O_{3} \)
D. \( N a H C O_{3} \)
Subject: Chemistry
The pair of trihalides of group 15 elements which are not readily
hydrolysed are
A. \( N F_{3} \) and \( N C l_{3} \)
B. \( N F_{3} \) and \( P F_{3} \)
c. \( P C l_{3} \) and \( P F_{3} \)
D. \( N F_{3} \) and \( P C l_{3} \)
Subject: Chemistry
Which of the following statement(s) is/are true?
i. Adding a solute raises the
vapor pressure \& boiling point.
ii. The change in boiling \& freezing point depends on molality.
iii. The number of solute particles in
a solvent is an important factor
in determining the boiling point
elevation.
A. i only
B. ii only
c. i and ii
D. ii and iii
E. i, ii and iii
Subject: Physics
Two identical capacitors are joined in
parallel and charged to a potential \( V \)
Capacitors are separated and then connected in series, i.e., the positive plate of one is connected to the negative plate of other. Identify the correct
option:
A. The charges on the free plates are enhanced.
B. The charges on the free plates decrease.
c. The energy stored in the system increase
D. The potential difference between the free plates is \( 2 V \)
Subject: Chemistry
On passing \( \boldsymbol{H}_{2} \boldsymbol{S} \) into a solution
containing both \( Z n^{2-} \) and \( C u^{2-} \) in
acidic medium, only CuS gets precipitated. This is because:
\( \mathbf{A} \cdot K_{s p} \) of \( C u S<K_{s p} \) of ZnS
B. \( K_{s p} \) of \( C u S=K_{s p} \) of Zns
C. \( K_{s p} \) of \( C u S>K_{s p} \) of ZnS
D. cus is more stable then zns
Subject: Physics
The magnitude of the force between a pair of conductors, each of length
\( 110 \mathrm{cm}, \) carrying a current of \( 10 \mathrm{A} \) each
and separated by a distance of \( 10 \mathrm{cm} \) is \( \left(\mu_{0}=4 \pi \times 10^{-7} H / m\right) \)
\( \mathbf{A} \cdot 55 \times 10^{-5} N \)
В. \( 44 \times 10^{-5} N \)
\( \mathbf{c} \cdot 33 \times 10^{-5} N \)
D. \( 22 \times 10^{-5} N \)
Subject: Chemistry
IUPAC name of \( \boldsymbol{C H}_{3}-\boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)- \)
\( \boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)-\boldsymbol{C H}_{3} \) is:
A. 2,5 dimethyl-3-hexyne
B. 2,5 dimethyl 2- hexyne
c. 3,5 dimethyl- 3 - hexyne
D. 2 - pentane
Subject: Physics
In the space shown a non-uniform
magnetic field \( \overrightarrow{\boldsymbol{B}}=\boldsymbol{B}_{0}(\boldsymbol{1}+\boldsymbol{x})(-\boldsymbol{k}) \)
tesla is present. A closed loop of small resistance, placed in the \( x \) -y plane is
given velocity \( V_{0} . \) The force due to
magnetic field on the loop is
A. zer
B. along + x direction
C. along \( -x \) direction
D. along +y direction
E. none of these
Subject: Maths
Complete the following table if \( \boldsymbol{x} \propto \boldsymbol{y} \)
\[
x
\]
\( \begin{array}{lllll}1 & 2 & 3 & - & 5\end{array} \)
\( 4 \quad 8 \) 16 \( - \) \( y \) 1
Subject: Maths
state-wise teacher-student ratio in
higher secondary schools of India. Find
the mode and mean of this data.
Interpret, the two measures.
A. \( M o d e=43.6 \) and Mean\( =21 . \)
and \( M e a n=24 . \)
B. Mode\( =39.6 \)
c. Mode\( =35.6 \) and Mean \( =27.2 \)
D. \( M o d e=30.6 \) and Mean
Subject: Physics
Determine the distance of 4 th dark
fringe from the left end of air cavity
A \( \cdot \frac{2 L}{6}+\lambda_{0} \)
B. \( _{L_{1}+} \frac{3 L}{4} \)
\( c \cdot \frac{4 L}{7} \)
D. \( \frac{5 L}{7} \)
Subject: Physics
The escape velocity of a projectile from the earth is approximately
A. \( 7 \mathrm{km} / \mathrm{sec} \)
в. \( 112 \mathrm{km} / \mathrm{sec} \)
c. \( 11.2 \mathrm{km} / \mathrm{sec} \)
D. \( 1.1 \mathrm{km} / \mathrm{sec} \)
Subject: Chemistry
Give the electron configuration of the given metal (atom/ions)
\( F e O_{4}^{2-}(\text { ferrate ion }) \)
\( \mathbf{A} \cdot[A r] 3 s^{2} \)
B . \( [A r] 4 s^{2} \)
c. \( [A r] 3 d^{2} \)
D. none of these
Subject: Maths
A survey of people in a given region showed that \( 20 \% \) were smokers. The
probability of death due to lung cancer, given that a person smoked, was 10 times the probability of death due to lung cancer, given that a person did not smoke. If the probability of death due to lung cancer in the region is \( 0.006, \) what is the probability of death due to lung cancer given that a person is a smoker?
A \( \cdot 1 / 140 \)
в. \( 1 / 70 \)
\( c \cdot 3 / 140 \)
D. \( 1 / 10 \)
Subject: Physics
A charge \( Q \) is uniformly distributed over
the surface of two concentric
conducting spheres of radii \( R \) and \( r(R>r) \) Such that surface charge
densities are same for both
spheres.Then potential at common centre of these spheres-
A \( \cdot \frac{K Q(R+r)}{R r} \)
B. \( \frac{K Q(R+r)}{R^{2}+r^{2}} \)
c. \( \frac{K Q}{\sqrt{R^{2}+r^{2}}} \)
\( ^{\mathrm{D}} \cdot \operatorname{KQ}\left(\frac{1}{R}-\frac{1}{r}\right) \)
Subject: Physics
Two skaters P and Q are skating towards each other. Skater P throws a
ball towards Q every 5s such that it always leaves her hand with speed 2
\( m s^{-1} \) with respect to the ground.
Consider two cases:
(i) P runs with speed \( 1 \mathrm{ms}^{-1} \) towards \( \mathrm{Q} \)
while \( Q \) remains stationary
(ii) \( Q \) runs with speed \( 1 m s^{-1} \) towards \( P \) while P remains stationary

Note that irrespective of speed of \( P, \) ball always leaves P's hand with speed 2
\( m s^{-1} \) with respect to the ground. lgnore gravity. Balls will be received by \( Q \)
A. one every 2.5 s in case ( (1) and one every 3.3 s in case (II)
B. One every 2 s in case (I) and one every 4 s in case(ll)
c. one every 3.3 s in case (I) and one every 2.5 s in case (II)
D. one every 2.5 s in case ( (1) and one every 2.5 s in case (I)
Subject: Physics
The emf of a genetator is 12 V and its internal resistance is 1 K\( \Omega .0 \mathrm{m} \)
measuring its emf with a voltmeter of \( 5 K \Omega \) the reading will be:-
A . \( 10 v \)
B. 10 milli v
c. 1 milliv
\( D \cdot 1 v \)
Subject: Maths
f \( z_{1}, z_{2} \) and \( z_{3} \) are complex numbers
such that \( \left|z_{1}\right|=\left|z_{2}\right|=\left|z_{3}\right|= \)
\( \left|\frac{1}{z_{1}}+\frac{1}{z_{2}}+\frac{1}{z_{3}}\right|=1, \) then find the value
of \( \left|z_{1}+z_{2}+z_{3}\right| \)
Subject: Maths
\( \int \cos ^{-1} \sqrt{\frac{1-x}{2}} d x= \)
A. \( \frac{\pi}{2} x-\frac{1}{2} x \cos ^{-1} x+c \)
B. \( \frac{\pi}{2} x-\frac{1}{2} x \cos ^{-1} x+\frac{1}{2} \sqrt{1-x^{2}}+c \)
C \( \cdot \frac{\pi}{2} x-\frac{1}{2} x \cos ^{-1} x-\sqrt{1-x^{2}}+c \)
D. \( \frac{\pi}{2} x+\frac{1}{2} x \cos ^{-1} x+c \)
Subject: Maths
Construct \( \triangle \boldsymbol{A B C} \) with \( \boldsymbol{B C}=\mathbf{6 . 5} \mathrm{cm} \)
\( \boldsymbol{A C}=\mathbf{5} \mathrm{cm} \) and \( \angle \boldsymbol{C}=\mathbf{6 0}^{\circ} . \)
Subject: Chemistry
The initial pressure of the reactant at \( 500 K, \) in the reaction \( C a C O_{3}=C a O+ \)
\( C O_{2} \) is \( 200 m m . \) After \( 20 m \) ins the
pressure is reduced to \( 150 \mathrm{mm} \). Find the
average rate of the reaction?
A . \( 0.33 \times 10^{-6} \) molL \( ^{-1} \) sec \( ^{-1} \)
B . \( 2.33 \times 10^{-6} \) molL \( ^{-1} \) sec \( ^{-1} \)
\( \mathbf{c} \cdot 1.33 \times 10^{-6} \mathrm{molL}^{-1} \mathrm{sec}^{-1} \)
D. \( 3.33 \times 10^{-6} \) molL \( ^{-1} \) sec \( ^{-1} \)
Subject: Chemistry
When sulphur (in the form of \( S_{8} \) ) is
heated at temperature \( T, \) at
equilibrium, the pressure of \( S_{8} \) falls by
\( 30 \% \) from 1.0 atm, because \( S_{8(g)} \) is
partially converted into \( S_{2(g)} \). Find the
value of \( K_{p} \) for this reaction.
A . 0.96
B. 6.14
c. 204.8
D. None of these
Subject: Chemistry
A buffer of \( \mathrm{pH} 8.50 \) is prepared from
0.02 mole of \( K C N . \) The desired volume
of buffer solution is to be 1 litre. How
will you make this buffer using \( \boldsymbol{H} \boldsymbol{C l} \) ? What is the change after addition of \( 0.5 \times 10^{-4} \) mole \( H C l \) to \( 100 c m^{3} \) and
same amount of \( N a O H \) in \( 100 c m^{3} \) of
buffer?
\( \left(\boldsymbol{K}_{\boldsymbol{a}} \boldsymbol{H} \boldsymbol{C} \boldsymbol{N}=\boldsymbol{6} . \boldsymbol{2} \times \mathbf{1 0}^{-10}\right) \)
Subject: Physics
A turn of radius \( 20 \mathrm{m} \) is banked for the
vehicle of mass 200 kg going at a speed of \( 10 \mathrm{m} / \mathrm{s} \). Find the direction and
magnitude of frictional force acting on a vehicle if it moves with a speed \( 5 \mathrm{m} / \mathrm{s} \)
Subject: Physics
In Wheatstone's bridge, three resistors \( P, Q, R \) are connected in three arms in
order and \( 4^{t h} \) arm is formed by two
resistors \( s_{1} \) and \( s_{2} \) connected in
parallel. The condition for bridge to be balanced is \( \frac{P}{Q}= \)
A. \( \frac{R\left(s_{1}+s_{2}\right)}{s_{1} s_{2}} \)
в. \( \frac{s_{1} s_{2}}{R\left(s_{1}+s_{2}\right)} \)
c. \( \frac{R s_{1} s_{2}}{\left(s_{1}+s_{2}\right)} \)
D. \( \frac{\left(s_{1}+s_{2}\right)}{R s_{1} s_{2}} \)
Subject: Physics
A moving body with a mass \( m_{1} \) and velocity u strikes a stationary body of
\( \operatorname{mass} \boldsymbol{m}_{2} . \) The masses \( \boldsymbol{m}_{1} \) and \( \boldsymbol{m}_{2} \)
should be in the ratio \( m_{1} / m_{2} \) so as to decrease the velocity of the first body to
\( 2 u / 3 \) and \( \operatorname{giving} \) a velocity of \( v \) to \( m_{2} \) assuming a perfectly elastic impact.
Then the ratio \( m_{1} / m_{2} \) is :
A. 5
B. 1/5
\( c \cdot 1 / 25 \)
D. 25
Subject: Physics
A \( 1.0 \mathrm{m} \) long metallic rod is rotated with
an angular frequency of 400 rad \( s^{-1} \)
about an axis normal to the rod passing through its one end. The other end of the
rod is in contact with a circular metallic
ring. A constant and uniform magnetic field of 0.5 T parallel to the axis exists everywhere. Calculate the emf developed between the centre and the
ring.
Subject: Maths
If \( \cos \alpha+\cos \beta=0=\sin \alpha+\sin \beta \)
then \( \cos 2 \alpha+\cos 2 \beta \) is equal to
A \( .-2 \sin (\alpha+\beta) \)
B. \( -2 \cos (\alpha+\beta) \)
\( \mathbf{c} \cdot 2 \sin (\alpha+\beta) \)
D. \( 2 \cos (\alpha+\beta) \)
Subject: Physics
The electric charges are distributed in a small volume. The flux of the electric
field through a spherical surface of
radius \( 10 \mathrm{cm} \) surrounding the total charge is \( 20 V \) m. The flux over a
concentric sphere of radius \( 20 \mathrm{cm} \) will
be
A \( .20 \mathrm{V} . \mathrm{m} \)
B. \( 25 V . m \)
c. \( 40 V . m \)
D. 200V.m
Subject: Physics
(a) \( A \) ball of mass \( m \) is thrown vertically upward from the ground with an initial speed \( v, \) its speed decreases continuously till it becomes zero. Thereafter, the ball begins to fall
downward and attains the speed again before striking the ground. It implies that the magnitude of initial and final momentum of the ball are same. Yet, it
is not an example of conservation of momentum. Explain why?
(b) A bullet of mass 20 g is horizontally
fired with a velocity \( 150 m s^{1} \) from a pistol of mass 2 kg. What is the recoil velocity of the pistol?
Subject: Physics
Which of the following phenomena support the wave theory of light?
(a) Scattering
(b) Interference
\( (c) \)
Diffraction
Velocity of light in a denser medium is less
(d) than the velocity of light in the rarer medium.
\( A \cdot A, B, C \)
B. A, B, D
\( c \cdot B, C, D \)
D. \( A, C, \)
Subject: Chemistry
Among the following species which two have a trigonal pyramidal shape?
(I) \( \boldsymbol{N} \boldsymbol{I}_{\mathbf{3}} \)
(II) \( I_{3}^{-} \)
\( (\| I) \boldsymbol{S} \boldsymbol{O}_{3}^{2-} \)
\( (\mathrm{IV}) N O_{3}^{-} \)
A. \( I \) and \( I I I \)
B. III and \( I V \)
c. \( I \) and \( I V \)
D. II and III
Subject: Physics
at a constant temperature of \( \boldsymbol{\theta}_{\boldsymbol{o}} \)
Assume that it obeys Newtons law of
cooling. Its temperature \( \boldsymbol{\theta} \) is plotted
against time ' \( t \). Tangents are drawn to
the curve at the points \( P\left(\theta-\theta_{1}\right) \) and
\( Q\left(\theta-\theta_{2}\right) . \) These tangents meet
the time axis at angles of \( \phi_{2} \) and \( \phi_{1} \) as
shown. Then
A \( \cdot \frac{\tan \phi_{2}}{\tan \phi_{1}}=\frac{\theta_{1}-\theta_{o}}{\theta_{2}-\theta_{o}} \)
B. \( \frac{\tan \phi_{2}}{\tan \phi_{1}}=\frac{\theta_{2}-\theta_{o}}{\theta_{1}-\theta_{o}} \)
\( \mathbf{c} \cdot \frac{\tan \phi_{1}}{\tan \phi_{2}}=\frac{\theta_{1}}{\theta_{2}} \)
D. \( \frac{\tan \phi_{1}}{\tan \phi_{2}}=\frac{\theta_{2}}{\theta_{1}} \)
Subject: Chemistry
Consider the statements \( \$ 1 \) and \( s 2: \)
S1: Conductivity always increases with decrease in the concentration of
electrolyte.
S2: Molar conductivity always increases with decrease in the concentration of
electrolyte.

The correct option among the following is:
A. Both S1 and S2 are correct
B. s1 is wrong and s2 is correct
\( c . \) s1 is correct and s2 is wrong
D. Both S1 and S2 are wrong
Subject: Chemistry
An alpha particle after passing through a potential difference of \( 2 \times 10^{6} \) volt
falls on a silver foil. The atomic number
of silver is \( 47 . \) Calculate \( (I) \) the \( K . E \) of the alpha-particle at the time of falling on the foil. \( (I I) K . E \) of the alpha-
particle at a distance of \( 5 \times 10^{-14} m \)
from the nucleus, \( (I I I) \) the shortest
distance from the nucleus of silver to
which the alpha-particle reaches.