AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If the area enclosed between the curves
\( \boldsymbol{y}=\boldsymbol{k} \boldsymbol{x}^{2} \) and \( \boldsymbol{x}=\boldsymbol{k} \boldsymbol{y}^{2},(\boldsymbol{k}>\mathbf{0}), \) is \( \mathbf{1} \)
square unit. Then \( k \) is?
A \( \cdot \frac{1}{\sqrt{3}} \)
в. \( \frac{2}{\sqrt{3}} \)
c. \( \frac{\sqrt{3}}{2} \)
D. \( \sqrt{3} \)
Subject: Maths
A 20 m deep well with diameter 7 m is dug up and the earth from digging is evenly spread out to form a platform 22 \( m \times 14 m \) The height of the platform is
\( \mathbf{A} \cdot 2.5 \mathrm{m} \)
B. \( 1.5 \mathrm{m} \)
c. \( 1 \mathrm{m} \)
D. 2 m
Subject: Maths
If the eccentricity of the ellipse \( a x^{2}+ \)
\( 4 y^{2}=4 a,(a<4) \) is \( \frac{1}{\sqrt{2}}, \) then its semi minor axis is equal to
A .2
B. \( \sqrt{2} \)
c. 1
D. \( \sqrt{3} \)
E . 3
Subject: Biology
Identify the correct statements from the
following.
(I) A single male and a few female flowers are present in a flowers like inflorescence in poinsettia.
(II) Sessile or subsessile flowers formed
in the axils of leaves are crowded at the
nodes in Leonotis.
(III) In Ficus, a fruit like inflorescence is
present with all fertile flowers.
(IV) The floral axis is sympoidal in
Hamelia.
\( A \cdot(11),(1 \vee) \)
B. (1), (IV)
c. (॥), (॥I)
D. (I), (III)
Subject: Chemistry
Molecule \( A B \) has a bond length of 1.617 A and a dipole moment of 0.38 D. The fractional charge on each atom (absolute magnitude) is :
\( \left(e_{0}=4.802 \times 10^{-10} \mathrm{esu}\right) \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. 0.05
c. 0.5
D. 1.0
Subject: Maths
If the centroid of tetrahedron \( O A B C \)
where \( A, B, C \) are given by \( (a, 2,3),(1, b, 2) \) and \( (2,1, c) \)
respectively is \( (1,2,-2), \) then distance of \( \boldsymbol{P}(\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}) \) from origin is
\( \mathbf{A} \cdot \sqrt{195} \)
в. \( \sqrt{14} \)
c. \( \sqrt{\frac{107}{14}} \)
D. \( \sqrt{13} \)
Subject: Maths
\( \boldsymbol{p} \boldsymbol{t}(\boldsymbol{5},-\boldsymbol{2}) \) is the mid pt of line segment
joining the \( p t s\left(\frac{x}{2}, \frac{y+1}{2}\right) \) and \( (x+ \) \( \mathbf{1}, \boldsymbol{y}-\mathbf{3}) \) then find the value of \( \boldsymbol{x} \) \& \( \boldsymbol{y} \)
Subject: Physics
When two capacitors are connected in parallel the resulting combination has capacitance \( 10 u F . \) The same
capacitors when connected in series results in a capacitance \( 0.5 u F . \) The respective values of individual
capacitors are
A . \( 1.9 u F \) and \( 0.2 u F \)
B . \( (8+2 \sqrt{5}) u F \) and \( (2-2 \sqrt{5}) u F \)
c. \( (5+2 \sqrt{5}) u F \) and \( (5-2 \sqrt{5}) u F \)
D. \( 12 u F \) and \( 17 u F \)
E . \( 5 u F \) and \( 2 u F \)
Subject: Physics
The dimension of permittivity of
vacuum
B \( \cdot\left[M^{-1} L^{-3} T^{4} A^{3}\right] \)
\( \mathbf{c} \cdot\left[M^{-1} L^{-3} T^{4} A^{2}\right] \)
\( \mathbf{D} \cdot\left[M^{-1} L^{-5} T^{4} A^{2}\right] \)
Subject: Chemistry
Which of the following has only \( 1^{\circ} \) and
\( \mathbf{2}^{\circ} \boldsymbol{C} \) atom?
A. \( 2- \) Methylbutane
B. Butane
c. \( 2,2- \) Dimethylbutane
D. 2,2,3,3 - Tetramethylpentane
Subject: Chemistry
When \( S_{2} O_{8}^{2-} \) oxidise \( F e^{2+} \) then product formed is:
\( \mathbf{A} \cdot S_{2} O_{6}^{2} \)
B \( . S O_{4}^{2-} \)
\( \mathrm{c} \cdot S_{2} O_{3}^{2} \)
D. \( S O_{5}^{2-} \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & 3 \\ 1 & 1 & 1\end{array}\right], \) Find \( A^{-1} . \) Using
\( A^{-1} \), solve the following system or liner
equation.
\( \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\boldsymbol{z}=\mathbf{4} ;-\boldsymbol{z}+\boldsymbol{y}+\boldsymbol{z}=\mathbf{0} ; \boldsymbol{x}- \)
\( \mathbf{3} \boldsymbol{y}+\boldsymbol{z}=\mathbf{2} \)
Subject: Chemistry
Assertion
In 5 th period, an element with \( Z=57 \) is
followed by element \( Z=72 \)
Reason
The intermediate elements are not
represented in the main body of the periodic table.
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
The variance of following:
\begin{tabular}{lllll}
\multirow{2}{*} { Age } & \multirow{2}{*} { \( \mathbf{2 0}- \) \( \mathbf{2 5} \)} & \( \mathbf{2 5}- \) & \( \mathbf{3 0}- \) & \( \mathbf{3 5}_{-} \) \\
& & \( \mathbf{3 0} \) & \( \mathbf{3 5} \) & \( \mathbf{4 0} \)
\end{tabular}
\begin{tabular}{l|c|c} 
Number & \\
of & 170 \\
persons
\end{tabular} 15 80 45
\( \mathbf{A} \cdot 62.62 \)
B . 56.56
c. 7.93
D. 9.24
Subject: Physics
What is the value of \( p_{1} \) and \( m_{2} ? \)
\( \begin{array}{lll}\mathrm{m}(\mathrm{kg}) & \mathrm{v}(\mathrm{m} / \mathrm{s}) & \mathrm{p}=\mathrm{mv}(\mathrm{kgm} / \mathrm{s}) \\ 85 & 60 & p_{1} \\ m_{2} & 2.5 & 6.25\end{array} \)
\( A \cdot 5100,2.5 \)
B. 5.1 , 2.5
c. 2500,
D. 55, 2.6
Subject: Chemistry
Which of the following will not be
oxidised by \( \mathrm{O}_{3} ? \)
A . KI
в. \( \mathrm{FeSO}_{4} \)
\( c \cdot \) кмпО
D. \( \mathrm{K}_{2} \mathrm{Mn} \mathrm{O}_{4} \)
Subject: Physics
A system consists of two identical
small balls of mass 2 kg each
connected to the two ends of a 1 m long light rod. The system is rotating about a fixed axis through the centre of the rod and perpendicular to it at angular speed of 9 rad/s. An impulsive force of
average magnitude \( 10 N \) acts on one of the masses in the direction of its
velocity for \( 0.20 s . \) Calculate the new
angular velocity of the system.
Subject: Physics
The linear momentum \( P \) of a particle
varies with time as follow \( \boldsymbol{P}=\boldsymbol{a}+\boldsymbol{b} \boldsymbol{t}^{2} \)
Where \( a \) and \( b \) are constants. The net
force acting on the particle is:
A. Proportional to \( t \)
B. Proportional to \( t^{2} \)
c. zero
D. constant
Subject: Maths
In an election between two candidates,
one got \( 55 \% \) of the total valid votes,
\( 20 \% \) of the votes were invalid. If the total
number of votes was 7500 , the number of valid votes that the other candidate
got, was:
A . 3260
в. 2700
\( c .1290 \)
D. 1600
Subject: Chemistry
The incorrectly matched pair, among the following is Molecule Shape
A . \( B r F_{5} \) Trigonal bipyramidal
B. \( S F_{4} \) See saw
c. \( C l F_{3} \) T-shape
D. \( N H_{4}^{+} \) Tetrahedral
E . \( N H_{3} \) Trigonal pyramidal
Subject: Chemistry
Given that,
\( C_{(g r a p h i t e)} \rightarrow C_{(g)} ; \Delta H=+716.7 K J \)
\( C_{(\text {diamond })} \rightarrow C_{(g)} ; \Delta H=714.8 K J \)
The \( \Delta \mathrm{H} \) for the following reaction is
\( C_{(g r a p h i t e)} \rightarrow C_{(\text {diamond})} \)
\( \mathbf{A} \cdot \) 1.9 \( \mathrm{KJ} \)
B . -1.9 KJ
c. zero
D. 714.8 KJ
Subject: Physics
Assertion
A small electric dipole is moved translationally from higher potential to lower potential in uniform electric field.
Work done by electric field is positive.
Reason

When a positive charge is moved from
higher potential to lower potential, work
done by electric field is positive.
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
S.D.of the first \( (\boldsymbol{n}+\mathbf{1}) \) natural number
is
A. \( \sqrt{\frac{n^{2}-1}{12}} \)
в. \( \sqrt{\frac{n^{2}+1}{12}} \)
c. \( \sqrt{\frac{n(n+2)}{12}} \)
D. None of these
Subject: Physics
A particle of mass \( \mathrm{m} \) is moving in a
circular path of constant radius r such that centripetal acceleration is varying
with time \( t \) as \( k^{2} r t^{2}, \) where \( k \) is a
constant. The power delivered to the
particle by the force acting on it is
A \( \cdot m^{2} k^{2} r^{2} t^{2} \)
B. \( m k^{2} r^{2} t \)
\( \mathbf{c} \cdot m k^{2} r t^{2} \)
\( \mathbf{D} \cdot m k r^{2} t \)
Subject: Physics
Consider a point charge with \( \boldsymbol{q}=\mathbf{1 . 5} \times \)
\( 10^{-8} C . \) Then, the radius of an
equipotential surface having a potential of \( 30 V \) is :
A \( .0 .45 m \)
в. 4.5 т
c. infinite
D. none of the above
Subject: Physics
A square plate \( A B C D \) of mass \( m \) and
side \( l \) is suspended with the help of two
ideal strings \( P \) and \( Q \) as shown
determine the acceleration \( \left(\text { in } m / s^{2}\right) \) of
corner \( A \) of the square just at the
moment the string \( Q \) is cut \( (g= \)
\( \left.10 m / s^{2}\right) \)
Subject: Physics
Consider the three long,straight,parallel wires as shown in figure.Find the force experienced by a \( 25 \mathrm{cm} \) length of wire \( \mathrm{C} \)
A \( \cdot 2 \times 10^{-4} N \)
B. \( 3 \times 10^{-4} N \)
c. \( 5 \times 10^{-4} N \)
D. \( 6 \times 10^{-4} N \)
Subject: Chemistry
Which of the following have highest boiling point?
A. \( C H_{3} C l \)
в. \( C H_{3} C H_{2} C H_{2} C l \)
\( \mathbf{c} \cdot C H_{3} C H_{2} C H_{2} B r \)
D. \( C H_{3} C H_{2} C H_{2} I \)
Subject: Maths
If \( \vec{a}, \vec{b}, \vec{c} \) are three vectors such that \( |\vec{a}|=|\vec{c}|=1,|\vec{b}|=4,|\vec{b} \times \vec{c}|=2 \)
and \( 2 \vec{b}=\vec{c}+\lambda \vec{a} \) then \( \lambda \) is
A \( \cdot \sqrt{65-8 \sqrt{3}} \)
B. \( \sqrt{17} \)
\( c \cdot \sqrt{3} \)
D. \( \sqrt{\frac{17}{2}(2+\sqrt{3})} \)
Subject: Biology
In alveolar air, the partial pressure of
\( C O_{2} \) is
A. \( 40 \mathrm{mm} \) of \( \mathrm{Hg} \)
B. \( 42 \mathrm{mm} \) of \( \mathrm{Hg} \)
c. \( 44 \mathrm{mm} \) of \( \mathrm{Hg} \)
D. \( 46 \mathrm{mm} \) of \( \mathrm{Hg} \)
Subject: Maths
How many spherical lead shots each
\( 4.2 \mathrm{cm} \) in diameter can be obtained
from a rectangular solid (cuboid) of lead with dimensions
\( \left.66 c m, 42 c m, 21 c m . \text { (Take } \pi=\frac{22}{7}\right) \)
A. 1500
B. 1200
c. 1300
D. 1600
Subject: Chemistry
In the reaction,
\( \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g})+\mathbf{5} \boldsymbol{F}_{2} \rightarrow \boldsymbol{N}_{2} \boldsymbol{F}_{4}+\boldsymbol{6} \boldsymbol{H} \boldsymbol{F} \)
\( 3.56 g N_{2} F_{4} \) is obtained by mixing \( 2 g \)
\( N H_{3} \) and \( 8 \mathrm{g} F_{2} . \) The percentage yield of the production is:
A . 81.28\%
B . 71.2\%
c. \( 68 \% \)
D. 79\%
Subject: Chemistry
The number of redox reactions from the
following equations are:
a. \( \boldsymbol{H}_{2} \boldsymbol{S}+\boldsymbol{F} \boldsymbol{e}^{3+} \longrightarrow \boldsymbol{F} \boldsymbol{e}^{2+}+\boldsymbol{S} \downarrow+\boldsymbol{H}^{\oplus} \)
b. \( \boldsymbol{I}^{\ominus}+\boldsymbol{I} \boldsymbol{O}_{3}^{\ominus}+\boldsymbol{H}^{\oplus} \longrightarrow \boldsymbol{I}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \)
c. \( \boldsymbol{B} \boldsymbol{i}(\boldsymbol{s})+\boldsymbol{N} \boldsymbol{O}_{3}^{\ominus}+\boldsymbol{H}^{\oplus} \longrightarrow \boldsymbol{N} \boldsymbol{O}_{2}+ \)
\( B i^{3+}+H_{2} O \)
\( \mathbf{d .} \boldsymbol{I}^{\ominus}+\boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \boldsymbol{I}_{2}+\stackrel{\ominus}{\boldsymbol{O}} \boldsymbol{H} \)
e. \( \boldsymbol{C u}(\boldsymbol{s})+\boldsymbol{A} \boldsymbol{u}^{\oplus} \longrightarrow \boldsymbol{A} \boldsymbol{u}(\boldsymbol{s})+\boldsymbol{C} \boldsymbol{u}^{2+} \)
Subject: Physics
Match List I with List II and select the
correct answer using the codes given below the list
\begin{tabular}{ll} 
List I & List II \\
P. Boltzmann constant & 1. \( \left[M L^{2} T^{-1}\right] \) \\
Q. Coefficient of viscosity & 2. \( \left[M L^{-1} T^{-1}\right] \) \\
R. Planck constant & 3. \( \left[M L T^{-3} K^{-1}\right] \) \\
S. Thermal conductivity & 4. \( \left[M L^{2} T^{-2} K^{-1}\right] \) \\
\hline
\end{tabular}
\( A \cdot 3124 \)
B. 3 214
\( c \cdot 4213 \)
D. 4 1 2 3
Subject: Physics
A particle falls from a height ' \( h^{\prime} \) upon a
fixed horizontal plane and rebounds. If
\( e^{\prime} \) is the coefficient of restitution, the
total distance travelled before it comes
to rest is
\( ^{\text {A }} \). \( h\left(\frac{1+e^{2}}{1-e^{2}}\right) \)
B \( \quad h\left(\frac{1-e^{2}}{1+e^{2}}\right) \)
c. \( \frac{H}{2}\left(\frac{1-e^{2}}{1+e^{2}}\right) \)
D. \( \frac{H}{2}\left(\frac{1+e^{2}}{1-e^{2}}\right) \)
Subject: Physics
If the series limit of the Balmer series
for hydrogen is 2700 Angstrom. Calculate the atomic no. of the element
which gives X-ray wavelength of \( \boldsymbol{K}_{\boldsymbol{\alpha}} \) line
as 1.0 Angstrom.
\( A \cdot z=21 \)
B. \( z=31 \)
\( c \cdot z=61 \)
\( D \cdot z=5 \)
Subject: Maths
If the ratio of the height of tower and the length of its shadow is \( 1: \sqrt{3} \), then the
angle of elevation of the sum has
measure
A . \( 60^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 30^{\circ} \)
D. \( 75^{\circ} \)
Subject: Physics
In copper, each atom releases one electron. If a current of \( 1.1 \mathrm{A} \) is flowing in the copper wire of diameter 1mm then
the drift velocity of electrons, will a pproximately be (density of copper \( = \) \( 9 \times 10^{3} \mathrm{Kgm}^{-3} \) and its atomic weight
\( =\mathbf{6 3}) \)
A. \( 10.3 \mathrm{mm} / \mathrm{s} \)
B. \( 0.1 \mathrm{mm} / \mathrm{s} \)
c. \( 0.2 \mathrm{mm} / \mathrm{s} \)
D. \( 0.2 \mathrm{cm} / \mathrm{s} \)
Subject: Maths
If point \( C(\bar{c}) \) divides the segment joining the point \( \boldsymbol{A}(\overline{\boldsymbol{a}}) \) and \( \boldsymbol{B}(\overline{\boldsymbol{b}}) \)
internally in the ratio \( m: n \), then prove
\( \operatorname{that} \bar{c}=\frac{m \bar{b}+n \bar{a}}{m+n} \)
Subject: Chemistry
Which of the following is/are correct?
This question has multiple correct options
\( \mathbf{A} \cdot \Delta H=\Delta U+\Delta(P V) \) when \( P \) and \( V \) both changes
B. \( \Delta H=\Delta U+P \Delta V \) when pressure is constant
C \( . \Delta H=\Delta U+V \Delta P \) when volume is constant
D. \( \Delta H=\Delta U+P \Delta V+V \Delta P \) when \( P \) and \( V \) both
changes
Subject: Chemistry
In a hydrogen atom, if energy of an electron in the ground state is \( 13.6 \mathrm{eV} \) then that in the 2 nd excited state is:
A . \( 1.51 \mathrm{eV} \)
B. 3.4 ev
\( c \cdot 6.04 \mathrm{ev} \)
D. 13.6 ev
Subject: Physics
Given unit vectors \( \overline{\boldsymbol{m}}, \overline{\boldsymbol{n}} \) and \( \overline{\boldsymbol{p}} \) such that
angle between \( \bar{m} \) and \( \bar{n}= \) angle between \( \bar{p} \) and \( (\bar{m} \times \bar{n})=\pi / 6 \) then
\( [\overline{\boldsymbol{n}} \overline{\boldsymbol{p}} \overline{\boldsymbol{n}}]= \)
A. \( \sqrt{3} / 4 \)
B. 3/4
\( c \cdot 1 / 4 \)
D. none
Subject: Chemistry
A buffer solution is made up of acetic
acid \( \left[\boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}}=\mathbf{5}\right] \) having conc. \( =\mathbf{1 . 5} \boldsymbol{M} \)
and sodium acetate having conc. \( = \)
\( 0.15 M . \) What is the number of \( O H^{-} \)
ions present in 1 litre solution?
В. \( 10^{-4} M \)
\( \mathrm{c} \cdot 10^{-3} M \)
D. \( 10^{-6} M \)
Subject: Biology
There is continuous multiplication in
cell nuclei and all nuclei have same
genetic information. The cell is undergoing
A. Multiple rounds of karyokinesis, but no cytokinesis
B. Multiple rounds of the M phase, but no rounds of the phase
c. Multiple rounds of cytokinesis, but no rounds of karyokinesis
D. Multiple rounds of the cell cycle, but no rounds of mitosis
E. multiple rounds of the S phase, but no other phases of the cell cycle
Subject: Chemistry
Out of the following which does not
liberate \( N_{2} \) gas on heating?
A \( . N a N O_{2}+N H_{4} C l \)
в. \( B a\left(N_{3}\right)_{2} \)
\( c \cdot O_{3}+N O \)
D. \( \left(N H_{4}\right)_{2} C r_{2} O_{7} \)
Subject: Physics
Assertion
When a gun is fired, the bullet moves forward (action). The gun recoils backward (reaction)
Reason
Driving a nail into a wooden block without holding the block is difficult.
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
\( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{H} \boldsymbol{S}(s) \rightleftharpoons \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{G})+\boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g}) \)
The equilibrium pressure at \( 25^{\circ} C \) is
0.660 atm. What is \( K_{p} \) for the reaction?
\( \mathbf{A} \cdot 0.109 \)
B. 0.218
c. 1.89
D. 2.18
Subject: Physics
A block is suspended by an ideal spring of force constant k. If the block is pulled
down by applying a constant force \( F \) and if maximum displacement of the block from its initial position of rest is \( \delta, \) then
A \( \cdot \frac{F}{k}<\delta>\frac{2 F}{k} \)
B . \( \delta \frac{2 F}{k} \)
c. work done by force F is equal to \( F \delta \)
D. Increase in energy stored in the spring is \( \frac{1}{2} k \delta^{2} \)
Subject: Maths
The equation of the plane passing through the point (1,1,1) and perpendicular to the planes \( 2 x+y- \)
\( 2 z=5 \) and \( 3 x-6 y-2 z=7 \) is?
A. \( 14 x+2 y-15 z=1 \)
B. \( -14 x+2 y+15 z=3 \)
c. \( 14 x-2 y+15 z=27 \)
D. \( 14 x+2 y+15 z=31 \)
Subject: Physics
Three observers \( A, B \) and \( C \) measure
the speed of light coming from a source
to be \( \boldsymbol{v}_{A}, \boldsymbol{v}_{B} \) and \( \boldsymbol{v}_{C} . \) The observer \( \boldsymbol{A} \)
moves towards the source and \( C \) moves
away from the source at the same
speed. The observer \( \boldsymbol{B} \) stays stationary. The surrounding space is vacuum
everywhere.
This question has multiple correct options
\( \mathbf{A} \cdot v_{A}>v_{B}>v_{C} \)
В . \( v_{A}<v_{B}<v_{C} \)
\( \mathbf{c} \cdot v_{A}=v_{B}=v_{C} \)
D. \( v_{B}=\frac{1}{2}\left(v_{A}+v_{C}\right) \)
Subject: Maths
A salesman has a \( 70 \% \) chance to sell a
product to any customer. The behaviour of successive customers is independent. If two customers \( A \) and \( B \) enter, what is the probability that the salesman will sell the product to
customer A or B?
A . 0.98
B. 0.91
c. 0.70
D. 0.49
Subject: Physics
A block of mass \( M \) is at rest on a rough horizontal surface. The coefficient of
friction between the block and the
surface is \( \mu . \) A force \( \boldsymbol{F}=\boldsymbol{M} \boldsymbol{g} \) acting at
an angle \( \theta \) with the vertical side of the block pulls it. In which of the following cases, the block can be pulled along the surface?
\( \mathbf{A} \cdot \tan \theta \geq \mu \)
B. \( \cot \theta \geq \mu \)
\( \mathbf{c} \cdot \tan \theta / 2 \geq \mu \)
D. \( \cot \theta / 2 \geq \mu \)
Subject: Physics
Hailstone at \( 0^{\circ} \mathrm{C} \) falls from a height of
1 km on an insulating surface
converting whole of its kinetic energy into heat. What part of it will melt?
\( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
A \( \cdot \frac{1}{33} \)
B. \( \frac{1}{8} \)
c. \( \frac{1}{33} \times 10^{-4} \)
D. All of it will melt
Subject: Physics
Which differential equation correctly represents the above process?
A \( \cdot \frac{d N}{d t}+\lambda N=q_{0} t \)
в. \( \frac{d N}{d t}-\lambda N=q_{0} t \)
c. \( \frac{d N}{d t}+q_{0} t=\lambda N \)
D. \( \frac{d N}{d t}+q_{0} t=-\lambda N \)
Subject: Physics
Two identical circular loops, \( P \) and \( Q \)
each of radius \( r \) and carrying equal
currents are kept in the parallel planes having a common axis passing through
O. The direction of current in \( \boldsymbol{P} \) is
clockwise and in \( Q \) is anti-clockwise as
seen from \( O \) which is equidistant from
the loops \( P \) and \( Q . \) Find the magnitude
of the net magnetic field at \( O \)
Subject: Chemistry
The increasing order of paramagnetism of the following compound is:
(।) \( M n S O_{4} .4 H_{2} O \)
(II) \( F e S O_{4} .7 H_{2} O \)
(III) \( N i S O_{4} .6 H_{2} O \)
\( (\mathrm{IV}) \mathrm{C} u S O_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O} \)
\( A \cdot|<||<|||<\mid V \)
B. IV<III<II<I
c. \( \||<| V<\|<1 \)
Subject: Physics
A compound lens is made of two lenses
in contact having power \( +12.5 D \) and \( -2.5 D . \) An object is placed at \( 15 \mathrm{cm} \) from compound lens. Find the position of image formed
\( \mathbf{A} \cdot 60 \mathrm{cm} \)
B. \( 30 \mathrm{cm} \)
c. \( 15 \mathrm{cm} \)
D. \( 45 \mathrm{cm} \)
Subject: Maths
Let \( a, b \) be two distinct roots of a polynomial \( f(x) \). Then there exists at least one root lying between a and b of the polynomial
A \( . f(x) \)
B. \( f^{\prime}(x) \)
c. \( f^{\prime \prime}(x) \)
D. \( f^{\prime \prime \prime}(x) \)
Subject: Physics
The figure shows cross section of a
hollow glass tube of internal radius \( r \)
external radius \( \boldsymbol{R} \) and index of
refraction \( n . \) For two rays DE and \( A B C \) (in
which DE lies on ODE and DE is parallel
to BC), the separation \( r_{1} \) will be :
A \( \cdot r_{1}=(n-1) R \)
\( \mathbf{B} \cdot r_{1}=n^{2} R \)
\( \mathbf{c} \cdot r_{1}=n r \)
\( \mathbf{D} \cdot r_{1}=n^{2} r \)
Subject: Physics
The following arrangement consists of five identical metal plates. Area of each plate is \( A \) and separation between the successive plates is d. The capacitance between \( P \) and
A. \( \frac{5 \varepsilon_{0} A}{d} \)
В. \( \frac{7}{3} \varepsilon_{0} \frac{A}{d} \)
c. \( \frac{4}{3} \frac{\varepsilon_{0} A}{d} \)
D. \( \frac{5}{3} \frac{\varepsilon_{0} A}{d} \)
Subject: Maths
f the determinant \( D= \)
\[
\left|\begin{array}{ccc}
\mathbf{1} & \mathbf{1} & \mathbf{1} \\
\boldsymbol{\alpha}+\boldsymbol{\beta} & \boldsymbol{\alpha}^{2}+\boldsymbol{\beta}^{2} & \mathbf{2} \boldsymbol{\alpha} \boldsymbol{\beta} \\
\boldsymbol{\alpha}+\boldsymbol{\beta} & \mathbf{2} \boldsymbol{\alpha} \boldsymbol{\beta} & \boldsymbol{\alpha}^{2}+\boldsymbol{\beta}^{2}
\end{array}\right| \text { and }
\]
\( \boldsymbol{D}_{1}=\left|\begin{array}{ccc}\mathbf{1} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \boldsymbol{\alpha} & \boldsymbol{\beta} \\ \mathbf{0} & \boldsymbol{\beta} & \boldsymbol{\alpha}\end{array}\right|, \) then find the
determinant of \( D_{2} \) such that \( D_{2}=\frac{D}{D_{1}} \)
Subject: Physics
Assertion
It takes more fuel for a spacecraft to
travel from the earth to the Moon than
for the return trip.
Reason
The point of zero gravitational field
intensity due to the earth and the Moon
is Iying nearer to the Moon, i.e., in the
diagram shown, for \( r<r_{0} . E_{g} \) is
towards the earth's centre and for \( r> \)
\( r_{0}, E_{g} \) is towards the Moon's centre, and
\( \operatorname{at} r=r_{0}, E_{g} \) is zero.
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 and Reason is correct
Subject: Physics
A refrigerator placed in a room at \( 300 \mathrm{K} \) has inside temperature at \( 264 \mathrm{K} \). How many calories of heat shall be delivered
to the room for each 1 kcal of energy consumed by the refrigerator ideally
A . 7.2 kcal
B. 7.83 kcal
c. 8.33 kcal
D. 8.94 kcal
Subject: Physics
Mass of a body is \( 210 \mathrm{gm} \) and its density is \( 7.981 g m / c m^{3} . \) What will be its volume with regard to significant digits?
A \( \cdot 26.312 \mathrm{cm}^{3} \)
В. \( 26 \mathrm{cm}^{3} \)
\( \mathbf{c} \cdot 27 c m^{3} \)
D. \( 26.3 c m^{3} \)
Subject: Chemistry
The equation for the solubility product
constant of \( \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{C r} \boldsymbol{O}_{4} \) is:
A \( \cdot K_{s p}=\left[A g^{2+}\right] \cdot\left[C r O^{2-}\right] \)
B . \( K_{s p}=\left[A g^{+}\right]^{2} \cdot\left[C r^{6+}\right] \cdot\left[O_{4}^{8-}\right] \)
C \( \cdot K_{s p}=\left[A g^{+}\right] \cdot\left[C r^{6+}\right] \cdot\left[O_{4}^{8-}\right. \)
D. \( K_{s p}=\left[A g^{+}\right]^{2} \cdot\left[C r O_{4}^{2-}\right] \)
Subject: Chemistry
Is the following reaction is a redox
reaction?
\( \boldsymbol{B} \boldsymbol{a} \boldsymbol{O}_{2}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \rightarrow \boldsymbol{B} \boldsymbol{a} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{H}_{2} \boldsymbol{O}_{2} \)