AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
\( f\left(\mu_{s}, \mu_{k}, \mu_{r} \) are coefficients of static \right.
friction, sliding friction and rolling friction then
A \( \cdot \mu_{s}<\mu_{k}<\mu_{r} \)
B . \( \mu_{k}<\mu_{r}<\mu_{s} \)
c. \( \mu_{r}<\mu_{k}<\mu_{s} \)
D. \( \mu_{r}=\mu_{k}=\mu_{s} \)
Subject: Physics
If the time period of a planet is decreased by \( 10 \% \), and the initial radius of orbit is R. What is the change
in radius of its orbit after the change in
the time period?
A \( 3 \sqrt{32} R \)
n \( \sqrt{32} \sqrt{32} \)
в. \( \sqrt{34} R \)
\( \mathbf{c} \cdot 3 \sqrt{9} R \)
D. \( 3 \sqrt{81} R \)
Subject: Maths
In \( \triangle A B C, \angle C=90^{\circ} . \) If \( B C=a, A C= \)
\( b \) and \( A B=c, \) find \( c \) when \( a=8 c m \)
and \( b=6 \mathrm{cm} \)
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
в. \( 14 \mathrm{cm} \)
c. \( 15 \mathrm{cm} \)
D. \( 20 \mathrm{cm} \)
Subject: Physics
Three closed vessels \( A, B \) and \( C \) are at the
same temperature T and contain gases which obey Maxwell distribution law of
velocities. Vessel A contains \( O_{2}, \) B only \( N_{2} \)
and \( \mathrm{C} \) mixture of equal quantities of \( \mathrm{O}_{2} \)
and \( N_{2} \). If the average speed of \( O_{2} \)
molecules in vessel \( \mathrm{A} \) is \( V_{1} \) and that of \( N_{1} \)
molecules in vessel B is \( V_{2} \), then the
average speed of the \( O_{2} \) molecules in
vessel C is
A \( \cdot \frac{\left(v_{1}+v_{2}\right)}{2} \)
B. \( V_{1} \)
c. \( \sqrt{v_{1} v_{2}} \)
D. None of these
Subject: Chemistry
Which of the following does not contain
covalent bond?
A. \( C o C l_{2} \)
в. \( M n O_{4}^{-} \)
\( \mathrm{c} \cdot \mathrm{Cr} \mathrm{O}_{4}^{2} \)
D. \( C r_{2} O_{7}^{2-} \)
Subject: Chemistry
Assertion
The endothermic reactions are favoured
at lower temperature and the exothermic reactions are favoured at
higher temperature.
Reason
When a system in equilibrium is disturbed by changing the temperature, it will tend to adjust itself so as to
overcome the effect of the change.
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
Find the electric field both inside the
shell at a distance \( r \) from the centre.
\( ^{A} \cdot \frac{Q}{4 \pi \epsilon_{0} a^{2}} \)
в. \( \frac{Q r}{4 \pi \epsilon_{0} a^{2}} \)
c. \( \frac{Q}{4 \pi \epsilon_{0} a^{3}} \)
D. \( \frac{Q r}{4 \pi \epsilon_{0} a^{3}} \)
Subject: Physics
Arrange the following steps in the proper order to explain how a sea breeze occurs, near coastal regions.
(a) The temperature of land rises rapidly as compared to sea, because the specific heat capacity of land is five times less than that of water.
(b) Due to the low pressure over the land mass, the cool air over the sea starts
blowing towards the land.
(c) The sun shines equally on the land mass and sea, giving equal amount of heat energy to both.
(d) The air above the land becomes hot
and light, rises up and hence creates
the low pressure over the land.
\( A \cdot a d c b \)
B. \( \operatorname{cd} a b \)
\( c \cdot c a b d \)
D. \( c \) a d b
Subject: Maths
\( N \) is the set of positive integers. The
relation \( R \) is defined on \( \mathrm{N} \times \mathrm{N} \) as follows:
\( (a, b) R(c, d) \Longleftrightarrow a d=b c \) Prove that
This question has multiple correct options
A. \( R \) is an equivalence relation
B. \( R \) is symmetric relation
c. \( R \) is transitive relation
D. \( R \) is not an equivalence relation.
Subject: Chemistry
The two functional groups present in a typical carbohydrate are:
A. \( -O H \) and \( -C O O H \)
B. \( -C H O \) and \( -C O O H \)
\( \mathrm{c} .>C=O \) and \( -O H \)
D. \( -O H \) and \( -C H O \)
Subject: Physics
The \( t_{1 / 2} \) of a radioactive substance is
100sec. Its decay constant is:
A \( \cdot 6.93 \times 10^{-3} \mathrm{sec}^{-1} \)
B. \( 6.93 \times 10^{-2} \) sec \( ^{-1} \)
D. \( 6.93 \times 10^{-4} s e c^{-1} \)
Subject: Maths
Solve the differential equation \( \left(x^{2}-\right. \)
\( \left.\boldsymbol{y}^{2}\right) \boldsymbol{d} \boldsymbol{x}+2 \boldsymbol{x} \boldsymbol{y} \boldsymbol{d} \boldsymbol{y}=0 ; \) given that \( \boldsymbol{y}=\mathbf{1} \)
when \( \boldsymbol{x}=\mathbf{1} \)
Subject: Physics
Two spheres of radii \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2} \) have
densities \( \rho_{1} \) and \( \rho_{2} \) and specific heat \( C_{1} \)
and \( C_{2} . \) If they are heated to the same
temperature, the ratio of their rates of cooling will be
A \( \cdot \frac{R_{2} \rho_{2} C_{2}}{R_{1} \rho_{C} C_{1}} \)
В. \( \frac{R_{1} \rho_{2} C_{2}}{R_{2} \rho_{1} C_{1}} \)
c. \( \frac{R_{2} \rho_{1} C_{2}}{R_{1} \rho_{2} C_{1}} \)
D. \( \frac{R_{2} \rho_{2} C_{1}}{R_{1} \rho_{1} C_{2}} \)
Subject: Physics
A rigid massless rod of length \( \boldsymbol{L}=\mathbf{1} \boldsymbol{m} \)
joins two particles each of mass \( m= \)
1 kg. The rod lies on a frictionless table,
and is struck by a particle of equal
mass \( m=1 k g \) and velocity \( v_{0}=7 \sqrt{2} \)
moving as shown in the figure. After the collision the partcle moves straight back. Calculate the angular velocity of mass after collision, assuming that collision is perfectly elastic.
Subject: Maths
The dot products of a vector with the vectors \( (\hat{i}+\hat{j}-3 \hat{k}),(\hat{i}+3 \hat{j}-2 \hat{k}) \) and
\( (2 \hat{i}+\hat{j}+4 \hat{k}) \) are 0,5,8 respectively
Find the vector.
Subject: Chemistry
For the reduction of \( F e O \) with \( C \) at the
temperature corresponding to \( (D) \)
which of the following statements is
correct?
A. Carbon reduces \( F e O \) below the temperature at point
(D)
B. \( \triangle G^{0} \) value for overall reduction with \( C O \) is zer
\( \mathrm{c} . \triangle G^{0} \) value for the reaction at point
(D) is positive
D. Below point
(D), for the metal exists in molten state
Subject: Chemistry
Rate constant for a particular reaction is \( 3 \times 10^{-6} \) mole \( \left.^{-2}\right|^{2} s^{-1} . \) The rate of
reaction for only single reactant is found to be \( 2.4 \times 10^{2} \) mole \( I^{-1} s^{-1} . \) The
equilibrium concentration of the
reactant could be:
A \( \cdot 0.8 \times 10^{4} \)
B . \( 2 \times 10^{2} \)
c. \( 0.8 \times 10^{2} \)
D. \( 2 \times 10^{\text { }} \)
Subject: Maths
The value of houses in a particular area
are shown in the table.
Value
\[
\begin{array}{llll}
\text { per } & \mathbf{1 0}- & \mathbf{2 0}- & \mathbf{3 0}- \\
\text { house } & \mathbf{2 0} & \mathbf{3 0} & \mathbf{4 0}
\end{array}
\]
in
lakhs)
Number
of
\[
2
\]
houses
Given the mean value of the houses is
30.14 lakhs. and assumed mean is 35
\( A \cdot 7 \)
B. 8
\( c .9 \)
D. 10
Subject: Physics
The temperature of the sun, if pressure
is \( 1.4 \times 10^{9} \) atm, density is \( 1.4 g c m^{-3} \)
and average molecular weight is \( 2, \) will
be
\( \left[\text {Given } \boldsymbol{R}=\mathbf{8 . 4} \boldsymbol{J} \boldsymbol{m o l}^{-1} \boldsymbol{K}^{-1}\right] \)
A . \( 1.2 \times 10^{7} K \)
В. \( 2.4 \times 10^{7} K \)
c. \( 0.4 \times 10^{7} K \)
D. \( 0.2 \times 10^{7} K \)
Subject: Physics
If \( \vec{r}=2 \hat{i}+\hat{j} \mathrm{m} \) and \( \vec{F}=\hat{i}+2 \hat{j} N . \) Then
the magnitude and direction of torque \( \tau \)
is :
A \( \cdot 4 N m \) along \( 45^{\circ} \) with \( x \) -axis or \( y \) -axis
B. 3Nm along 45 \( ^{\circ} \) with \( x \) -axis or \( y \) -axis.
c. \( 4 N m \) along \( z \) -axis
D. \( 3 N m \) along \( z \) -axis
Subject: Physics
At pressure \( P \) and absolute temperature T a mass \( \mathrm{M} \) of an ideal gas fills a closed container of volume \( V \). An additional
mass \( 2 \mathrm{M} \) of the same gas is added into the container and the volume is then reduced to \( \frac{v}{3} \) and the temperature to \( \frac{T}{3} \)
The pressure of the gas will now be:
A \( \cdot \frac{P}{3} \)
в. \( P \)
\( c .3 P \)
D. \( 9 P \)
Subject: Maths
Solve \( : 2 \tan ^{-1}(-3)= \)
This question has multiple correct options
\( \mathbf{A} \cdot-\cos ^{-1}(-4 / 5) \)
\( \mathbf{B} \cdot-\pi+\cos ^{-1}(4 / 5) \)
C \( \cdot-\frac{\pi}{2}+\tan ^{-1}(-4 / 3) \)
D. \( \cot ^{-1}(4 / 3) \)
Subject: Maths
\( f(a, b, c \text { are in } A . P ., \) prove that the following are also in A.P. \( \boldsymbol{a}^{2}(\boldsymbol{b}+\boldsymbol{c}), \boldsymbol{b}^{2}(\boldsymbol{c}+\boldsymbol{a}), \boldsymbol{c}^{2}(\boldsymbol{a}+\boldsymbol{b}) \) provided
\( \sum a b \neq 0 \)
Subject: Physics
Two soap bubbles of radii r and 2r are
connected by a capillary tube-valve
arrangement as shown in the diagram.
The valve is now opened. Then which one
of the following will be the result:
A. The radii of the bubbles will remain unchanged
B. The bubbles will have equal radii
c. The radius of the smaller bubble will increase and that
bigger bubble will decrease
D. Ine radius of the smaller bubble will decrease and that of the bigger bubble will increase
Subject: Chemistry
A vessel of \( 5.0 l \) capacity contains \( 1.4 g \)
nitrogen at \( 1800 \mathrm{K} \). Assuming that at this temperature, \( 40 \% \) of molecules are
dissociated into atoms and the gas is ideal, what is the gas pressure?
A .2 .07 atm
B. 1.476 atm
c. 1.05 atm
D. 2.67 atm
Subject: Physics
A person was weighing \( 102.1 \mathrm{kg} \) last
week and gained \( 0.28 k g \) this week. His
weight as of now is correctly expressed
as:
A. \( 102.38 \mathrm{kg} \)
в. \( 102.3 \mathrm{kg} \)
c. \( 102.4 \mathrm{kg} \)
D. \( 102 \mathrm{kg} \)
Subject: Maths
Identify the series.
\( \mathbf{A} \cdot\{1,2,3,4,5\} \)
B . \( 1+2+3+4+5 \)
c. \( 1 \times 2 \times 3 \times 4 \)
D. \( 2-4 \times 3+1-23 \)
Subject: Chemistry
2 moles of \( P C l_{5} \) were heated in a closed
vessel of 2 liter capacity. At
equilibrium, \( 40 \% \) of \( P C l_{5} \) dissociated
into \( P C l_{3} \) and \( C l_{2} \)

The value of equilibrium constant is:
\( \mathbf{A} \cdot 0.267 \)
в. 0.53
\( c .2 .63 \)
D. 5.3
Subject: Biology
In autogenic succession
A. Early and continued dominance of autotrophic organism takes place like green plants.
B. Replacement of existing communities cause largely by any other extremal condition.
C. Early dominance of heterotrophs takes place such as bacteria, fungi and other animals
D. Community itself modifies its own environment thus, causing its own replacement by new communities.
E. Starts with previously built up substrata with already existing matter.
Subject: Maths
A tangent is drawn to each of the
circles
\( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}=\boldsymbol{a}^{2}, \boldsymbol{x}^{2}+\boldsymbol{y}^{2}=\boldsymbol{b}^{2} \)
Show that if the two tangents are
mutually perpendicular, the locus of their point of intersection is a circle concentric with the given circles.
Subject: Maths
The probabilities of three events \( A, B \& \) \( C \operatorname{are} P(A)=0.6, P(B)=0.4 \) and \( P(C)=0.5 \)
If \( P(A \cup B)=0.8, P(A \cap C)=0.3, P(A \cap \)
\( B \cap C)=0.2 \& P(A \cup B \cup C) \geq 0.85 \)
Find the range of \( \mathrm{P}(B \cap C) \)
B . [0.25,0.35]
c. [0.2,0.3]
D. [0.2,0.4]
Subject: Maths
If \( \boldsymbol{u}=\mathbf{3}-\mathbf{5} \boldsymbol{i} \) and \( \boldsymbol{v}=-\boldsymbol{6}+\boldsymbol{i}, \) then the
value of \( (u+v)^{2} \) is
A. \( -7+24 i \)
B. \( 9+8 i \)
\( \mathrm{c} \cdot 9+16 i \)
D. \( 25-24 i \)
Subject: Chemistry
Which is the correct order of formation
of \( M g C l_{2} \) by Born-Haber cycle?
1. Sublimation of \( M g ; \quad \) 2. Bond
dissociation of \( C l_{2} \)
3. lonisation of \( M g \quad ; \quad \) 4. Electron
gained by \( C l \)
A .1,3,2,4
в. 1.3,4,2
c. 1,2,3,4
D. None of these.
Subject: Physics
A vector \( \bar{P}_{1} \) is along the positive \( x \) - axis.
If its cross product with another vector
\( \bar{P}_{2} \) is zero, then \( \bar{P}_{2} \) could be:
\( A \cdot 4 \hat{j} \)
в. \( -4 \hat{i} \)
c. \( (\hat{i}+\hat{k}) \)
D. \( -(\hat{i}+\hat{j}) \)
Subject: Chemistry
Structural isomerism and
stereoisomerism should be considered
when answering this question. The molecular formula of compound \( x \)
is \( C_{5} H_{12} O \)
Compound \( X: \)
reacts with alkaline aqueous iodine
can be dehydrated to form two alkenes only. What could be the identify of compound
X?
A. \( C H_{3} C H_{2} C H\left(C H_{3}\right) C H_{2} O H \)
B. \( C H_{3} C H_{2} C H(O H) C H_{2} C H_{3} \)
\( \mathbf{c} \cdot\left(C H_{3}\right)_{2} C H C H(O H) C H_{3} \)
D. \( C H_{3} C H_{2} C H_{2} C H(O H) C H_{3} \)
Subject: Physics
In Millikan's experiment, the slope of \( v \)
versus \( V_{o} \) graph was found to be
\( 4.125 \times 10^{-15} V s . \) Given \( e=1.6 \times \)
\( 10^{-19} C, \) the value of Planck's constant
is
B. \( 6.4 \times 10^{-34} J s \)
C \( .4 .125 \times 10^{-34} \mathrm{Js} \)
D. \( 6.6 \times 10^{-34} J s \)
Subject: Chemistry
Assertion
The mass number of an atom is the
sum of number of protons and neutrons it contains.
Reason
The mass number of an atom can never
be smaller than the atomic number.
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 \( f(x)=x^{2}+\frac{1}{x^{2}}, \) then find the value of
\( \boldsymbol{f}(\mathbf{5}) \)
A \( \cdot \frac{424}{25} \)
в. \( \frac{626}{25} \)
c. \( \frac{536}{25} \)
D. \( \frac{428}{25} \)
Subject: Chemistry
The heat of combustion of ethane,
ethylene and hydrogen are \( 372.79 k c a l \)
\( 337.0 k c a l \) and \( 68.4 k c a l \) respectively
What is the heat evolved in the
reaction?
\( \boldsymbol{C}_{2} \boldsymbol{H}_{4}+\boldsymbol{H}_{2} \longrightarrow \boldsymbol{C}_{2} \boldsymbol{H}_{6} ? \)
A. \( -32.61 k c a l \)
B. \( +32 k c a l \)
c. \( 68.4 k c a l \)
D. None of these
Subject: Chemistry
\[
\begin{array}{c}
4 F e S+7 O_{2} \longrightarrow 2 F e_{2} O_{3}+4 S O_{2} \\
C r_{2} O_{7}^{2-}+2 H^{+}+3 S O_{2} \longrightarrow \\
2 C r^{3+}+3 S O_{4}^{2-}+H_{2} O
\end{array}
\]
1 \( g \) sample of \( F e S \) was roasted with oxygen gas \( S O_{2} \) thus formed required
\( 10 m L \) of \( 0.05 M K_{2} C r_{2} O_{7} \) solution in acidic medium. Calculate percentage of \( F e S \) in the sample. \( (F e=56, S=32) \)
A . \( 1.2 \% \)
B. \( 1.32 \% \)
c. \( 1.5 \% \)
D. None of these
Subject: Chemistry
In which of the following process, the bond order increases and magnetic behaviour changes?
\( \mathbf{A} \cdot N_{2} \longrightarrow N_{2}^{+} \)
B . \( C_{2} \longrightarrow C_{2}^{+} \)
c. \( N O \rightarrow N O^{+} \)
D. \( O_{2} \rightarrow O_{2}^{+} \)
Subject: Physics
Two spheres of radii \( 3 \mathrm{cm} \) and \( 5 \mathrm{cm} \) are charged to potentials 3000 V and 4500 V respectively. They are then connected by
a thin metallic wires. The loss of electric
energy in this process is?
\( \mathbf{A} \cdot 2 \times 10^{-8} \mathbf{J} \)
B \( \cdot 4 \times 10^{-8} \mathrm{J} \)
D . \( 2.36 \times 10^{-7} \) J
Subject: Physics
The mass of a metallic beam of uniform
thickness and of length \( 6 m \) is \( 60 k g \) The beam lies horizontally and symmetrically on two vertical pillars
which are separated by a distance \( 3 m \)
A person of mass \( 75 \mathrm{kg} \) is walking on
this beam. The closest distance to
which the person can approach one end of the beam so that the beam does not
tilt down is (neglect thickness of pillars):
\( \mathbf{A} \cdot 30 \mathrm{cm} \)
B. 20 \( c m \)
c. \( 15 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)
Subject: Chemistry
Consider the above figure as Periodic
Table. Then the element with a possible
oxidation number of -2 is
\begin{tabular}{|c|c|c|c|c|c|}
\hline \( \mathbf{z}_{\mathbf{L i}} \) & & & & & \( \mathbf{( D )} \) & \( \mathbf{1 0} \) \\
\hline & \( \mathbf{( A )} \) & & & & \( \mathbf{( C )} \) & & \\
\hline \( \mathbf{( B )} \) & \( \mathbf{2 0} \) & & & & & \\
\hline
\end{tabular}
\( \mathbf{A} \)
\( B \)
a
\( D \)
Subject: Chemistry
For the reaction \( \boldsymbol{A}+\mathbf{2} \boldsymbol{B} \rightleftharpoons \mathbf{2} \boldsymbol{C} \) at
equilibrium \( [\boldsymbol{C}]=\mathbf{1 . 4} \boldsymbol{M} \cdot[\boldsymbol{A}]_{o}= \)
\( \mathbf{1} \boldsymbol{M},[\boldsymbol{B}]_{o}=\mathbf{2} \boldsymbol{M},[\boldsymbol{C}]_{o}=\mathbf{3} M . \) The value
of \( K_{c} \) is:
(Given: volume =1 litre, [ ] \( _{o} \) is initial concentration)
A .0 .084
B. 8.4
\( c \cdot 48 \)
D. None of these.
Subject: Chemistry
Following two equilibrium is simultaneously established in a
container: \( \boldsymbol{P C l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P C l}_{3}(\boldsymbol{g})+ \)
\( \boldsymbol{C l}_{2}(\boldsymbol{g}) \) and \( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \rightleftharpoons \)
\( \boldsymbol{C O C l}_{2}(\boldsymbol{g}) \)
If some \( \mathrm{Ni}(\mathrm{s}) \) is introduced in the
container forming \( N i(C O)_{4}(g), \) then at new equilibrium:
A. \( P C l_{2} \) concentration will increase
B. \( P C l_{3} \) concentration will decrease
c. \( C l_{2} \) concentration will remain same
D. \( C O \) concentration will remain same
Subject: Physics
The volume of thin brass and the
volume of a solid cube made of same
material is both equal to \( 1 m^{3} \) at \( 0^{0} C \).
What will be the ratio of change in volumes of vessel and the cube on being heated to \( 25^{0} \) C? Given \( \alpha \) for brass \( = \) \( \mathbf{1} . \mathbf{9} \times \mathbf{1 0}^{-\mathbf{5}} /^{0} \mathbf{C} \)
Subject: Chemistry
The type of hybrid orbitals used by chlorine atom in \( C l O^{-}, C l O_{2}^{-}, C l O_{3}^{-} \)
and \( C l O_{4}^{-} \) is/are:
A \( \cdot s p, s p^{2}, s p^{3} \) and \( s p^{3} d \)
B. \( s p \) and \( s p \)
C . only \( s p^{3} \)
D. only sp
Subject: Physics
The current in a coil changes from \( 1 m A \) to \( 5 m A \) in 4 milli second. If the
coefficient of self-induction of the coil is
\( 10 m H \) the magnitude of the "self-
induced" emf is:
A . \( 10 \mathrm{mV} \)
B. \( 5 \mathrm{mV} \)
c. \( 2.5 \mathrm{mV} \)
D. \( 1 \mathrm{mV} \)
Subject: Physics
If the velocity of a particle is \( \left(10+2 r^{2}\right) \)
\( \mathrm{m} / \mathrm{s} \) then the average acceleration of the particle between 2 s and 5 s is
A \( \cdot 2 m / s^{2} \)
B . \( 4 m / s^{2} \)
c. \( 12 m / s^{2} \)
D. \( 14 m / s^{2} \)
Subject: Maths
Find a unit vector perpendicular to the plane \( A B C, \) where the coordinates of
\( A, B \) and \( C \) is
\( \boldsymbol{A}(\mathbf{3},-\mathbf{1}, \mathbf{2}), \boldsymbol{B}(\mathbf{1},-\mathbf{1},-\mathbf{3}) \) and
\( \boldsymbol{C}(\mathbf{4},-\mathbf{3}, \mathbf{1}) \)
Subject: Maths
Consider the function
\( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}a x-2 & \text { for }-2<x<-1 \\ -1 & \text { for }-1 \leq x \leq 1 \\ a+2(x-1)^{2} & \text { for } \quad 1<x<2\end{array}\right. \)
What is the value of a for which \( f(x) \) is
continuous at \( x=-1 \) and \( x=1 ? \)
\( A \cdot-1 \)
B.
\( c \cdot 0 \)
\( D \)
Subject: Physics
A body of mass \( m_{1}=4 k g \) moves at
\( \mathbf{5 i} \boldsymbol{m} / \boldsymbol{s} \) and another body of mass
\( \boldsymbol{m}_{2}=2 k g \) moves at \( 10 i m / s . \) The
kinetic energy of centre of mass is
A \( \cdot \frac{200}{3} J \)
в. \( \frac{500}{3} J \)
c. \( \frac{400}{3} J \)
D. \( \frac{800}{3} J \)
Subject: Physics
mass \( m \) is hanging in front of a large non-conducting sheet having surface charge density \( \sigma \). If suddenly a charge \( +q \) is given to the bob \( \& \) it is released
from the position shown in figure. The maximum angle through which the string is deflected from vertical is \( x \tan ^{-1}\left(\frac{\sigma q_{0}}{2 \varepsilon_{0} m g}\right) . \) Find \( x \)
Subject: Physics
A Ge specimen is doped with Al. The
concentration of acceptor atom is \( \sim \)
\( 10^{21} \) atoms \( / m^{3} . \) Given that the intrinsic
concentration of electron hole pairs is \( \sim 10^{19} / m^{3} . \) The concentration of
electrons in the specimen is??
\( \mathbf{A} \cdot 10^{17} / m^{3} \)
B . \( 10^{15} / m^{3} \)
c. \( 10^{4} / m^{3} \)
D. \( 10^{2} / m^{3} \)
Subject: Maths
Find the volume of a sphere of radius
given below:
\( \mathbf{A} \cdot 1,706.25 f t^{3} \)
B. \( 1,766.15 f t^{3} \)
\( c \cdot 1,866.25 f t^{3} \)
D. \( 1,766.25 \mathrm{ft}^{3} \)
Subject: Maths
In the triangle, find the measures of the
angles.
A \( \cdot 40^{\circ}, 60^{\circ}, 80^{\circ} \)
B \( \cdot 45^{\circ}, 60^{\circ}, 75^{\circ} \)
c. \( 45^{\circ}, 45^{\circ}, 90^{\circ} \)
D. \( 50^{\circ}, 60^{\circ}, 70^{\circ} \)
Subject: Physics
The width of forbidden gap in silicon crystal is \( 1.1 e V . \) When the crystal is
converted into an n-type
semiconductor, the distance of fermi level from conduction band is
A. greater than 0.55 eV
B. equal to 0.55 eV
c. lesser than 0.55 eV
D. equal to \( 1.1 \mathrm{eV} \)
Subject: Physics
Assertion
In series \( L C R \) circuit if a ferromagnetic
rod is inserted inside an inductor,
current in the circuit may be increase
or decrease
Reason
By doing so \( X_{L} \) will increase.
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
Given the marks scored by Rita's out of \( 100, \) in five subjects in a particular
test.
\( \begin{array}{ll}\text { Subject } & \text { Marks } \\ \text { English } & \text { 78 } \\ \text { Hindi } & \text { 72 } \\ \text { Maths } & \text { 96 } \\ \text { Science } & \text { 88 } \\ \text { s.st } & \text { 80 }\end{array} \) Can we draw the bar graph for above
data?
If yes enter 1 else 0
Subject: Physics
The earth's satellite is moving round the earth in a circular orbit. Which of the
following are true regarding the satellite?
1. Its speed is constant
2. Its velocity is constant
3. Its angular momentum is constant
4. Its gravitational pull is balanced by the centrifugal force
A. 1,3 and 4
B. 2,3 and 4
c. 1,2 and 3
D. 1,2 and 4
Subject: Physics
A hypothetical magnetic field existing in a region is given by \( \vec{B}=B_{0} \vec{e}_{r}, \) where
\( \vec{e}_{r} \) denotes the unit vector along the
radial direction. A circular loop of radius \( \alpha, \) carrying a current \( i, \) is placed
with its plane parallel to \( X-Y \) plane
and the centre at \( (0,0, d) . \) Find the magnitude of the magnetic force acting on the loop.
A \( \cdot \frac{i 2 \pi b_{o} a^{3}}{\sqrt{a^{2}+d^{4}}} \)
B. \( \frac{i 2 d_{o} a^{2}}{\sqrt{a^{2}+b^{2}}} \)
c. \( \frac{\pi b_{o} a^{2}}{\sqrt{a+d^{2}}} \)
D. \( \frac{i 2 \pi b_{a} a^{2}}{\sqrt{a^{2}+d^{2}}} \)
Subject: Biology
Respiratory quotient is expressed as which of the following equations?
A. \( O_{2} / C O_{2} \)
в. \( C O_{2} / O_{2} \)
\( \mathrm{c} \cdot O_{2} / \mathrm{H}_{2} \mathrm{O} \)
D. \( C O_{2}-O_{2} \)
Subject: Maths
Three numbers are chosen at random
without replacement from \( \{1,2,3, \ldots, 8\} \) The probability that their minimum is
3, given that their maximum is \( 6, \) is:
A \( \cdot \frac{3}{8} \)
B. \( \frac{1}{5} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{2}{5} \)
Subject: Maths
Find the area of a quadrilateral piece of ground, one of whose diagonals is 60 metres long and the perpendiculars from
the other two vertices are 38 and 22
metres, respectively.
A \( \cdot 1800 m^{2} \)
В. \( 3600 m^{2} \)
c. \( 900 m^{2} \)
D. None of the above
Subject: Chemistry
Assertion
Equilibrium constant for the reverse
reaction is the inverse of the
equilibrium constant for the reaction in
the forward direction.
Reason
Equilibrium constant depends upon the way in which the reaction is written.
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