AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
In a triangle \( A B C, D \) divides BC in the ratio 3: 2 and \( E \) divides \( C A \) in the ratio 1:
3. The lines \( A D \) and \( B E \) meet at \( H \) and \( C H \)
meets \( A B \) in \( F \). Find the ratio in which \( F \)
divides AB.
A. \( A F: F B=2: 1 \)
B. \( A F: F B=1: 2 \)
c. \( A F: F B=2: 3 \)
D. \( A F: F B=3: 2 \)
Subject: Physics
Consider the following nuclear reactions:
\( 1 . \frac{14}{7} N+_{2}^{4} H e \longrightarrow_{8}^{17} O+_{1}^{1} H \)
2. \( _{4}^{9} B e+_{1}^{1} H \longrightarrow_{3}^{9} L i+_{2}^{4} H e \)
3. \( _{\mathbf{1 2}}^{24} \boldsymbol{M} \boldsymbol{g}+_{\mathbf{2}}^{\mathbf{4}} \boldsymbol{H} \boldsymbol{e} \longrightarrow_{\mathbf{1 4}}^{\mathbf{2 7}} \boldsymbol{S} \boldsymbol{i}+_{\mathbf{0}}^{\mathbf{1}} \boldsymbol{n} \)
4. \( \frac{10}{5} \boldsymbol{B}+_{2}^{4} \boldsymbol{H} e \longrightarrow \frac{13}{7} \boldsymbol{N}+_{0}^{1} \boldsymbol{n} \)
Examples of induced radioactivity would include the reactions:
A. 3 and 4
B. 1 and 2
c. 1,3 and 4
D. 1,2,3 and 4
Subject: Maths
A school has five houses \( A, B, C, D \) and \( E \)
A class has 23 students, 4 from house
A, 8. from house B, 5 from house C, 2
from house 0 and rest from house \( \mathrm{E} \)
A single student is selected at random ,to be the class monitor. The probability that the selected student is not from \( A \),
Band C is?
\( \mathbf{A} \cdot \frac{4}{23} \)
B. \( \frac{6}{23} \)
\( c \cdot \frac{8}{23} \)
D. \( \frac{17}{23} \)
Subject: Chemistry
The resistance of \( 0.01 \mathrm{N} \) solution of an
electrolyte \( A B \) at \( 328 \mathrm{K} \) is 100 ohm. The specific conductance of solution is :
\( \left[\text { cell constant }=1 \mathrm{cm}^{-1}\right] \)
A. 100 ohm
B. \( 10^{-2} \) ohm \( ^{-1} \)
\( \mathbf{c} \cdot 10^{-2} \operatorname{ohm}^{-1} c m^{-1} \)
D. \( 10^{2} \) ohm \( -c m \)
Subject: Physics
An object kept on the principal axis and infront of a spherical mirror, is moved along the axis itself. Its lateral magnification \( \mathrm{m} \) is measured, and plotted versus object distance |ul for a
range of \( u \), as shown in fig. The magnification of the object when it is placed at a distance \( 20 \mathrm{cm} \) in front of
the mirror is:
\( A \cdot- \)
B.
\( c \)
D. 2
Subject: Maths
Represent the following mixed infinite decimal periodic fractions as common
fractions:
\( \left(\frac{\boldsymbol{P}^{3 / 2}+\boldsymbol{q}^{3 / 2}}{\boldsymbol{p}-\boldsymbol{q}}-\frac{\boldsymbol{p}-\boldsymbol{q}}{\boldsymbol{P}^{1 / 2}+\boldsymbol{q}^{1 / 2}}\right)\left(\sqrt{\boldsymbol{p} \boldsymbol{q}} \frac{\sqrt{\boldsymbol{p}}}{\boldsymbol{p}}\right. \)
Subject: Physics
Assertion
Graph between potential energy of a spring versus the extension or compression of the spring is a straight
line
Reason
Potential energy of a stretched or
compressed spring is proportional to
square of extension or compression
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: Maths
\( \triangle \boldsymbol{A B C}, \boldsymbol{X} \boldsymbol{Y} \| \boldsymbol{B C}, \frac{\boldsymbol{A} \boldsymbol{Y}}{\boldsymbol{C Y}}=\frac{1}{2} \) and
\( A X=4 . \) Find \( B X \)
Subject: Chemistry
\( \boldsymbol{P t}\left|\boldsymbol{O}_{2}(\boldsymbol{g}, \boldsymbol{1} \boldsymbol{a} \boldsymbol{t m})\right| \boldsymbol{O} \boldsymbol{H}^{-}(\boldsymbol{1} \boldsymbol{M}) \| \boldsymbol{C l}^{-}(\boldsymbol{1} \boldsymbol{M}) \mid \)
For the given cell, the cell reaction is:
Subject: Maths
In an experiment with 15 observations
on \( x, \) then following results were
available:
\( \sum x^{2}=2830, \sum x=170 \)
One observation that was 20 was found
to be wrong and was replaced by the
correct value \( 30 . \) Then the corrected
variance is:
A . 78
B . 188.6666
c. 177.3333
D. 8.3333
Subject: Physics
A metal sphere of radius \( r \) and specific heat \( \mathrm{S} \) is rotated about an axis passing through its centre at a speed of \( n \) rotations per second. It is suddenly stopped and \( 50 \% \) of its energy is used in increasing its temperature. Then the rise in temperature of the sphere is?
A \( \cdot \frac{2}{5} \frac{\pi^{2} n^{2} r^{2}}{S} \)
C \( \cdot \frac{7}{8} \pi r^{2} n^{2} S \)
D・ \( 5\left[\frac{r n x}{[145]}\right]^{2} \)
Subject: Physics
A charge \( +q \) is placed at the origin 0 of \( x-y \) axes as shown in the figure. The work done in taking a charge \( Q \) from \( A \) to B along the straight line \( A B \) is:
A \( \cdot \frac{q Q}{4 \pi \varepsilon_{0}}\left(\frac{a-b}{a b}\right) \)
в. \( \frac{q Q}{4 \pi \varepsilon_{0}}\left(\frac{b-a}{a b}\right) \)
c. \( \frac{q Q}{4 \pi \varepsilon_{0}}\left(\frac{b}{a^{2}}-\frac{1}{b}\right) \)
D. \( \frac{q Q}{4 \pi \varepsilon_{0}}\left(\frac{a}{b^{2}}-\frac{1}{b}\right) \)
Subject: Physics
From a solid sphere of mass \( M \) and
radius \( R \) a spherical portion of radius \( \boldsymbol{R} \)
\( \frac{1}{2} \) is removed, as shown in the figure. Taking gravitational potential \( V=0 \) at
\( r=\infty, \) the potential at the centre of the
cavity thus formed is : \( (G= \) gravitational constant)
\( ^{A} \cdot \frac{-2 G M}{3 R} \)
в. \( \frac{-2 G M}{R} \)
\( c \cdot \frac{-G M}{2 R} \)
D. \( \frac{-G M}{R} \)
Subject: Physics
The maximum energy in the thermal radiation from a heat source occurs at a
wavelength of \( 12 \times 10^{-5} \mathrm{cm} . \) According
to Wien's displacement law, the temperature of this source will be 'n'
times the temperature of another source for which the wavelength at maximum energy is \( 6 \times 10^{-5} \mathrm{cm} . \) Then
the value of \( n \) is
A . \( 1 / 2 \)
B. 1
\( c \cdot 2 \)
D. 4
Subject: Maths
A regular hexagon \& a regular dodecagon are inscribed in the same circle. If the side of the dodecagon is \( (\sqrt{3}-1), \) then the side of the hexagon
is
A \( \cdot \sqrt{2}+1 \)
B. \( \frac{\sqrt{3}+1}{2} \)
c. 2
D. \( \sqrt{2} \)
Subject: Maths
The mean deviation about the mean of
the set of first \( n \) natural numbers when
\( n \) is an odd number.
A \( \cdot \frac{n^{2}-1}{4 n} \)
B. \( \frac{n}{4} \)
c. \( \frac{n^{2}+1}{4 n} \)
D. \( \frac{n^{2}-1}{12} \)
Subject: Chemistry
The critical volume of a gas is 0.036 lit.mol \( ^{-1} \). The radius of the molecule
will be (in \( \mathrm{cm} \) ):
(Avogadro Number \( =\mathbf{6} \times \mathbf{1 0}^{\mathbf{2 3}} \mathbf{)} \)
\( \left(\frac{9}{4 \pi} \times 10^{-23}\right)^{\frac{1}{3}} \)
\( ^{\mathrm{B}}\left(\frac{8 \pi}{3} \times 10^{-23}\right)^{\frac{1}{3}} \)
\( \left(\frac{3}{8 \pi} \times 10^{-23}\right)^{\frac{1}{3}} \)
D. none of these
Subject: Maths
If \( S=\tan ^{-1}\left(\frac{1}{n^{2}+n+1}\right)+ \)
\( \tan ^{-1}\left(\frac{1}{n^{2}+3 n+3}\right)+\ldots+ \)
\( \tan ^{-1}\left(\frac{1}{1+(n+19)(n+20)}\right) \) then \( \tan S \) is
equal to
\( \mathbf{A} \cdot \frac{20}{401+20 n} \)
B. \( \frac{n}{n^{2}+20 n+1} \)
\( \mathbf{C} \cdot \frac{20}{n^{2}+20 n+1} \)
\( D \cdot \frac{n}{401+20 n} \)
Subject: Chemistry
A mixture of all isomers of pentane is allowed to react with chlorine radicals
(produced by photochemical cleavage
of \( C l_{2} \) ). How many different isomeric alkyl radicals can form by hydrogen abstraction in the following reaction?
Pentane (all isomers) \( +C l^{*} \rightarrow \) Penty
radicals (all isomers) \( +\boldsymbol{H} \boldsymbol{C l} \)
A . 5
B. 6
\( c \cdot 7 \)
\( D \)
Subject: Chemistry
There are two samples \( A \) and \( B . A \) is
Methanol and \( B \) is Ethanol. Both are
heated both at the same rate in closed
container separately. Which one is correct about the above test?
A \( \cdot \) At \( 60^{\circ} \mathrm{C} \), container \( A \) and \( B \) both have liquids in them
B. At \( 80^{\circ} \) C, container \( A \) and \( B \) both have vapours in them
C. At \( 70^{0} \mathrm{C} \), container \( B \) has liquid and \( A \) has vapours
D. All the above
Subject: Physics
A capacitor of \( 10 \mu F \) capacitance is charged by a \( 12 V \) battery. Now the space
between the plates of capacitors is filled with a dielectric of dielectric constant
\( K=3 \) and again it is charged. The
magnitude of the charge is :
A. \( 120 \mu C \)
в. \( 240 \mu C \)
c. \( 360 \mu C \)
D. \( 480 \mu C \)
Subject: Maths
Let \( \boldsymbol{A}=\{\mathbf{3}, \mathbf{6}, \mathbf{1 2}, \mathbf{1 5}, \mathbf{1 8}, \mathbf{2 1}\}, \boldsymbol{B}= \)
\( \{\mathbf{4}, \mathbf{8}, \mathbf{1 2}, \mathbf{1 6}, \mathbf{2 0}\}, \boldsymbol{C}= \)
\( \{\mathbf{2}, \mathbf{4}, \mathbf{6}, \mathbf{8}, \mathbf{1 0}, \mathbf{1 2}, \mathbf{1 4}, \mathbf{1 6}\} \) and \( \boldsymbol{D}= \)
\( \{\mathbf{5}, \mathbf{1 0}, \mathbf{1 5}, \mathbf{2 0}\} . \) Find \( \boldsymbol{A}-\boldsymbol{C} \)
Subject: Chemistry
The solution with the highest boiling point temperature is:
в. \( 0.1 \mathrm{M} \) НС \( \mathrm{CO}_{4} \)
c. \( 0.1 \mathrm{M} \mathrm{NH}_{4} \mathrm{OH} \)
D. 0.1 М КОН
E. \( 0.1 \mathrm{M} \) LiNO \( _{3} \)
Subject: Physics
The mobility of free electrons (charge =e, mass = m and-relaxation
time \( \tau \) ) in a metal is proportional to:
A \( \cdot \frac{e}{m} \tau \)
в. \( \frac{m}{e} \tau \)
\( c \cdot \frac{e}{m \tau} \)
D. \( \frac{m}{e \tau} \)
Subject: Physics
A bullet of mass \( 5 g \) travels with a speed
of \( 500 m s^{-1} . \) if it penetrates a fixed target which offers a constant resistive
force of \( 1000 \mathrm{N} \) to the motion of the
bullet, find :
(a) the initial kinetic energy of the bullet,
(b) the distance through which the bullet has penetrated.
\( \mathbf{A} \cdot s=0.625 m \)
B. \( s=0.725 \mathrm{m} \)
\( \mathbf{c} \cdot s=0.225 m \)
D. \( s=0.65 m \)
Subject: Chemistry
Compare thermal stability of \( Z n O \)
\( C d O \) and \( H g O \)
A. \( Z n O>C d O>H g O \)
в. \( C d O>Z n O>H g O \)
c. \( Z n O>H g O>C d O \)
D. \( H g O>Z n O>C d O \)
Subject: Chemistry
(a) Draw the molecular structures of the
following compounds:
(i) \( N_{2} O_{5} \)
(ii) \( \boldsymbol{X}_{e} \boldsymbol{O} \boldsymbol{F}_{4} \)
(b) Explain the following observations
(i) Sulphur has a greater tendency for catenation than oxygen.
(ii) \( I-C l \) is more reactive than \( I_{2} \)
(iii) Despite lower value of its electron gain enthalpy with negative sign,
fluorine \( \left(F_{2}\right) \) is a stronger oxidizing
agent than \( C l_{2} \)
Subject: Maths
f \( x \) is a proper fraction, show that \( \frac{\boldsymbol{x}}{\mathbf{1}-\boldsymbol{x}^{2}}-\frac{\boldsymbol{x}^{\mathbf{3}}}{\mathbf{1 - x}^{\mathbf{6}}}+\frac{\boldsymbol{x}^{\mathbf{5}}}{\mathbf{1 - x}^{\mathbf{1 0}}}-\dots \dots \)
\( \frac{\boldsymbol{x}}{\mathbf{1}+\boldsymbol{x}^{2}}+\frac{\boldsymbol{x}^{\mathbf{3}}}{\mathbf{1}+\boldsymbol{x}^{\mathbf{6}}}+\frac{\boldsymbol{x}^{\mathbf{5}}}{\mathbf{1}+\boldsymbol{x}^{\mathbf{1 0}}}+\dots \)
Subject: Physics
(a) Deduce the expression, \( N= \)
\( N 0 e^{-\lambda} t, \) for the law of radioactive
decay.
(b)(i) Write symbolically the process expressing the \( \beta+ \) decay of \( _{11}^{22} \) Na. Also write the basic nuclear process underlying this decay.
(ii) Is the nucleus formed in the decay of the nucleus \( _{11}^{22} N a, \) an isotope or isobar?
Subject: Maths
A variable plane at a distance of 1 unit from the origin cuts the co-ordinate axes at \( A, B \) and \( C . \) If the centroid \( D(x, y, z) \) of triangle \( A B C \) satisfies the relation \( \frac{1}{x^{2}}+ \) \( \frac{1}{y^{2}}+\frac{1}{z^{2}}=k, \) then the value of \( k \) is
A . 3
B. 1
c. \( 1 / 3 \)
D.
Subject: Physics
The maximum electric field intensity
inside the ball is:
A \( \cdot \frac{\rho_{0} R}{9 \epsilon} \)
B. \( \frac{\rho o}{9 R} \)
\( \mathbf{c} \cdot \frac{\rho_{0} R}{3 \epsilon} \)
D. \( \frac{\rho_{0} R}{6 \epsilon} \)
Subject: Maths
If s.d,of \( X \) is \( \sigma \), then s.d.of the variable \( U=\frac{a X+b}{c} \) where \( a, b, c \) are constants
is
A \( \cdot\left|\frac{c}{a}\right| \sigma \)
B \( \cdot\left|\frac{a}{c}\right| \sigma \)
\( c \cdot\left|\frac{b}{c}\right| \)
D. \( \frac{c^{2}}{a^{2}} \sigma \)
Subject: Physics
Assertion
A nucleus having enrgy \( E_{1} \) decays by \( \beta \) emission to daughter nucleus having
energy \( E_{2} \) but the \( \beta \) -rays are emitted with a continuous energy spectrum
having end point energy \( \boldsymbol{E}_{\mathbf{1}}-\boldsymbol{E}_{\mathbf{2}} \)
Reason
To conserve energy and moment in \( \boldsymbol{\beta} \)
decays at least three particles must
take part in the transformation.
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
The average \( K E \) of molecules in a gas at temperature \( T \) is \( \frac{3}{2} k T . \) Find the temperature at which the average KE of molecules equal to binding energy of its
atoms.
A . \( 1.05 \times 10^{5} K \)
В. \( 1.05 \times 10^{4} K \)
c. \( 1.05 \times 10^{3} K \)
D. none of these
Subject: Maths
ff \( y=y(x) \) satisfies the differential
equation
\[
\begin{array}{c}
\mathbf{8} \sqrt{\boldsymbol{x}}(\sqrt{\mathbf{9}+\sqrt{\boldsymbol{x}}}) \boldsymbol{d} \boldsymbol{y}= \\
(\sqrt{4+\sqrt{\mathbf{9}+\sqrt{\boldsymbol{x}}}})^{-1} \boldsymbol{d} \boldsymbol{x}, \boldsymbol{x}>\mathbf{0} \text { and } \\
\boldsymbol{y}(\mathbf{0})=\sqrt{\mathbf{7}}, \text { then } \boldsymbol{y}(\mathbf{2 5 6})_{---}
\end{array}
\]
A . 16
B. 80
\( c .3 \)
\( D \)
Subject: Physics
Equal charges \( Q \) are placed at the four corners \( A, B, C \) and \( D \) of a square of
length \( a \). The magnitude of the force on
the charge at \( B \) will be
\( ^{\mathrm{A}} \cdot \frac{3 Q^{2}}{4 \pi \varepsilon_{0} a^{2}} \)
В. \( \frac{4 Q^{2}}{4 \pi \varepsilon_{0} a^{2}} \)
c. \( \frac{k Q^{2}}{a^{2}}\left(\frac{2 \sqrt{2}+1}{2}\right) \)
D \( \cdot\left(2+\frac{1}{\sqrt{2}}\right) \frac{3 Q^{2}}{4 \pi \varepsilon_{0} a^{2}} \)
Subject: Maths
If the matrix \( \left[\begin{array}{ccc}\mathbf{0} & \mathbf{2} \boldsymbol{\beta} & \mathbf{\Upsilon} \\ \boldsymbol{\alpha} & \boldsymbol{\beta} & -\mathbf{\Upsilon} \\ \boldsymbol{\alpha} & -\boldsymbol{\beta} & \mathbf{\Upsilon}\end{array}\right] \) is
orthogonal, then
A \( \cdot \alpha=\pm \frac{1}{\sqrt{2}} \)
в. \( \beta=\pm \frac{1}{\sqrt{6}} \)
c. \( _{\gamma}=\pm \frac{1}{\sqrt{3}} \)
D. all of these
Subject: Chemistry
A pair of compounds which is an illustration of law of multiple
proportions is:
A. \( H_{2} O \) and \( D_{2} O \)
в. \( N a O H \) and \( K O H \)
c. \( N a C l \) and \( N a B r \)
D. \( C O \) and \( C O_{2} \)
Subject: Maths
Calculate the surface area of a sphere
with radius \( 3.2 \mathrm{cm} \)
A \( \cdot 110.6 \mathrm{cm}^{2} \)
B . \( 128.6 \mathrm{cm}^{2} \)
c. \( 131.5 \mathrm{cm}^{2} \)
D. None of these
Subject: Physics
A heavy block kept on a frictionless
surface and being pulled by two ropes of
equal mass \( m \) as shown in the figure. At
\( t=0, \) the force on the left rope is
withdraw but the force on the right end
continues to act, Let \( F_{1} \) and \( F_{2} \) be the
magnitudes of the force by the right
rope and the left rope on the block respectively.
\( \mathbf{A} \cdot F_{1}=F_{2}=F \quad \) for \( t<0 \)
B . \( F_{1}=F_{2}=F+m g \quad \) for \( t<0 \)
C \( \cdot F_{1}=F_{1} \quad F_{2}=F \) for \( t>0 \)
D. \( F_{1}<F_{1} \quad F_{2}=F \) for \( t>0 \)
Subject: Chemistry
Which one is wrong if electrolysis of \( C H_{3} C O O N a(a q) \) is made using \( P t \)
electrodes?
A. \( p H \) of solution increases
B. Molar ratio of gases at anode and cathode is 3: 1
\( \mathrm{c} \cdot\left[C H_{3} C O O^{\ominus}\right] \) in solution decreases
D. The molar ration of gases at anode and cathode is 2 :
1
Subject: Physics
The heat energy required to vaporize 5
kg of water at \( 373 \mathrm{K} \) is nearly (Latent
heat of vaporization \( \left.\boldsymbol{L}_{\boldsymbol{v}}=\mathbf{2 2 7 0} \boldsymbol{J}\right) \)
A . 2700 K.cal
B. 1000 K.cal
c. 27 к.са
D. 270 K.cal
Subject: Maths
In triangle \( A B C, D \) and \( E \) are mid-
points of sides \( A B \) and \( B C \)
respectively. Also, \( \boldsymbol{F} \) is a point in side
\( A C \) so that \( D F \) is parallel to \( B C \)
Find the perimeter of parallelogram
\( D B E F, \) if \( A B=10 \mathrm{cm}, B C=8 \cdot 4 \mathrm{cm} \)
and \( A C=12 \mathrm{cm} \)
A \( .28 .7 \mathrm{cm} \)
в. \( 22.5 \mathrm{cm} \)
c. \( 18.4 \mathrm{cm} \)
D. \( 18.5 \mathrm{cm} \)
Subject: Maths
A body is propelled straight up with an initial velocity of \( 500 \mathrm{ft} / \mathrm{sec} \) in a vacuum with no air resistance. How
long will it take the body to return to the ground (in seconds)?
\( \mathbf{A} \cdot 21.25 \)
B. 31.25
c . 35.25
D. 25.25
Subject: Physics
Block A has a weight of 300N and block
B has a weight of 50 N. If the coefficient
of kinetic friction between the incline
and block \( A \) is \( \mu_{k}=0.2 . \) Determine the speed of block A after it moves \( 1 \mathrm{m} \) down
the plane, starting from rest. Neglect the mass of the cord and pulleys.
Subject: Maths
A rectangle polygon of \( n \) sides is
constructed. No. of ways 3 vertices be
selected so that no two vertices are
consecutive is
\( \mathbf{A} \cdot^{n} C_{3}-n(n-4) \)
B . \( ^{n} C_{3}-n-n(n-4) \)
C. \( ^{n} C_{3}+n-n(n-4) \)
D. \( ^{n} C_{3}+n(n-4) \)
Subject: Physics
The acceleration of a particle is increasing linearly with time \( t \) as \( b t \). The particle starts from the origin with an
initial velocity \( v_{0} . \) The distance
travelled by the particle in time \( t \) will be:
A \( \cdot v_{0} t+\frac{1}{6} b t^{3} \)
B. \( v_{0} t+\frac{1}{3} b t^{3} \)
c. \( v_{0} t+\frac{1}{3} b t^{2} \)
D. \( v_{0} t+\frac{1}{2} b t^{2} \)
Subject: Chemistry
If \( K_{a} \) is more (or) \( p k_{a} \) is less then more
stronger is the acid.
lonic order: \( \boldsymbol{H} \boldsymbol{C O O H}>\boldsymbol{C}_{\mathbf{6}} \boldsymbol{H}_{\mathbf{5}} \boldsymbol{C O O H} \)
Subject: Maths
If \( \left(p^{2}+q^{2}\right)^{3}=\left(p^{3}+q^{3}\right)^{2} \) and \( p q \neq 0 \)
then the value of \( \frac{\boldsymbol{p}}{\boldsymbol{q}}+\frac{\boldsymbol{q}}{\boldsymbol{p}} \) is
Subject: Physics
A compound microscope consists of an objective of focal length \( 2 \mathrm{cm} \) and an eye-piece of focal length \( 5 \mathrm{cm} \). When an object is kept \( 2.4 \mathrm{cm} \) from the objective, final image formed is virtual and is at \( 25 \mathrm{cm} \) from the eye-piece. Determine magnifying power of this compound microscope in this set up, i.e., in normal
use.
Subject: Physics
Charge \( +q \) placed at point \( A \) is a distance \( 2 L \) apart from \( B \) and \( C \) is the
midpoint between A and B. The work
done in moving charge \( +\mathrm{Q} \) along the
semicircle CRD is
\( \mathbf{A} \cdot \frac{\mathrm{q} Q}{2 \pi \varepsilon_{\mathrm{U}}} \)
B. \( \frac{9 Q}{6 \pi \varepsilon_{0}} \)
\( \mathbf{c} \cdot-\frac{q Q}{6 \pi \varepsilon L} \)
D. \( \frac{q Q}{4 \frac{q Q}{4 \varepsilon_{0} L}} \)
Subject: Physics
The diameter of a solid disc is \( 0.5 m \) and
its mass is \( 16 k g \)
At what rate is the work done by the torque at the end of eighth second?
\( \mathbf{A} \cdot \pi W \)
в. \( \pi^{2} W \)
\( \mathbf{c} \cdot \pi^{3} W \)
D. \( \pi^{4} W \)
Subject: Physics
A stone is dropped from a height of 20
m. How long will it take to reach the ground? \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
\( A \cdot 2 s \)
B. 0.5
\( c \cdot 4 s \)
\( D \cdot 1 \mathrm{s} \)
Subject: Physics
A radio isotope \( X \) has a half life of \( 10 s \) Find the number of active nuclei in the
sample (if initally there are 1000 isotopes which are falling from rest from a height of \( 3000 m \) ) when it is at a height of \( 1000 m \) from the reference
plane:
\( \mathbf{A} .50 \)
в. 250
c. 29
D. 100
Subject: Physics
Two identical plano convex lenses are arranged in three different
combinations as:
I) the plane surfaces touching each
other
II) the curved surfaces touching each
other
III) the plane surface of one lens touching the curved surface of the
other.
Then the focal lengths of the combinations are in the ratio:
A \( \cdot 1: 2: 3 \)
B. 1: 1: 1
c. 3: 2: 1
D. 2: 2: 1
Subject: Maths
Let \( \boldsymbol{A}=\mathbf{2} \hat{\mathbf{i}}+\mathbf{4} \hat{\mathbf{j}}-\hat{\boldsymbol{k}}, \boldsymbol{B}=\mathbf{4} \hat{\mathbf{i}}+\mathbf{5} \hat{\mathbf{j}}+\hat{\boldsymbol{k}} . \) If
the centroid \( G \) of the triangle \( A B C \) is \( \mathbf{3} \hat{\mathbf{i}}+\mathbf{5} \hat{\mathbf{j}}-\hat{\boldsymbol{k}}, \) then the position vector of
\( C \) is
\( \mathbf{A} \cdot 3 \hat{i}-6 \hat{j}+3 \hat{k} \)
B . \( 3 \hat{i}-6 \hat{j}-3 \hat{k} \)
c. \( 3 \hat{i}-6 \hat{j}+2 \hat{k} \)
D. \( 3 \hat{i}+6 \hat{j}-3 \hat{k} \)
Subject: Maths
Solve the following inequation and represent the solution set on the
number line:
\( \mathbf{4} \boldsymbol{x}-\mathbf{1 9}<\frac{\mathbf{3} \boldsymbol{x}}{\mathbf{5}}-\mathbf{2} \leq-\frac{\mathbf{2}}{\mathbf{5}}+\boldsymbol{x}, \quad \boldsymbol{x} \in \boldsymbol{R} \)
Subject: Physics
A drop of water of radius \( r \) is falling
through the air of coefficient of viscosity \( \eta \) with a constant velocity of \( v \)
The resultant force on the drop is:
A \( \cdot \frac{1}{6 \pi \eta r v} \)
в. \( 6 \pi \eta r v \)
c. \( \sqrt{6 \pi \eta r v} \)
D. zero
Subject: Chemistry
Assertion
The atomic radii of the elements of
oxygen family are smaller than the atomic radii of corresponding elements of the nitrogen family.
Reason
The members of oxygen family are all more electronegative and thus have
lower value of nuclear charge than
those of the nitrogen family.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Physics
A bullet of mass \( 8 g \) strikes a vertical
wooden plank \( 5 c m \) thick with a velocity of \( 200 m / s \) in a horizontal direction and emerges out of at \( 150 \mathrm{m} / \mathrm{s} \) in same direction find retarding force bullet experience in wood for what additional thickness bullet will just emerge on
other side
Subject: Physics
A square loop of side \( b \) is rotated in a
constant magnetic field \( B \) at angular
frequency \( \omega \) as shown in figure. What is
the emf induced in it?
\( \mathbf{A} \cdot b^{2} B \omega \sin \omega t \)
\( \mathbf{B} \cdot b B \omega \sin ^{2} \omega t \)
\( \mathbf{C} \cdot b B^{2} \omega \cos \omega t \)
D. \( b^{2} B \omega \)
Subject: Physics
A balloon is rising vertically with a velocity of \( 9.8 m / s . \) A packet is dropped
from it when it is at a height of \( 39.2 \mathrm{m} \) Time taken by the packet to reach the ground is (Given \( \boldsymbol{g}=\mathbf{9 . 8 m} / \boldsymbol{s}^{2} \) )
A . \( 1 s \)
B . \( 2 s \)
\( c \cdot 3 s \)
D. \( 4 s \)
Subject: Chemistry
Assertion: Alkyl halides are polar in
nature, but they are almost insoluble in
water

Reason: They can neither form Hydrogen bond nor they can break hydrogen bond between water molecules.
A. Both Assertion and Reason are true and Reason is the correct explanation to Assertion
B. Both Assertion and Reason are true and Reason is not the correct explanation to Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
Subject: Chemistry
Two glass bulbs \( A \) and \( B \) are connected by a very small tube having a stop cock.
Bulb A has a volume of \( 100 \mathrm{cm}^{3} \) and
contained the gas, while bulb B was empty. On opening the stop cock, the pressure fell down 40\%. The volume of
the bulb B must be ?
A \( .75 \mathrm{cm}^{3} \)
В. \( 125 \mathrm{cm}^{3} \)
\( c \cdot_{150} c m^{3} \)
D. \( 250 \mathrm{cm}^{3} \)