AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Assertion
In the reaction, \( C_{12} H_{22} O_{11}(a q)+ \) \( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \stackrel{d i \boldsymbol{l} \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}}{\longrightarrow} \boldsymbol{C}_{6} \boldsymbol{H}_{12} \boldsymbol{O}_{6}(\boldsymbol{a} \boldsymbol{q})+ \)
\( C_{6} H_{12} O_{6}(a q), H_{2} S O_{4} \) is called as a
homogeneous catalyst.
Reason
\( H_{2} S O_{4} \) is in the same phase as the reactants and products.
A. If both Assertion and Reason are correct and Reason the correct explanation of Assertion
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
c. If Assertion is correct, but Reason is incorrect
D. If Assertion is incorrect, but Reason is correct
Subject: Physics
A conveyor belt is moving horizontally with a uniform velocity of \( 2 \mathrm{m} / \mathrm{sec} \) Material is dropped at one end at the rate of \( 5 \mathrm{kg} \)./sec. and discharge at the other end. Neglecting the friction, the force required to move the belt is (N).
A . 10
B . 15
c. 20
D. 40
Subject: Physics
The work done in splitting a drop of water of 1 mm radius into \( 10^{6} \) droplets
is (surface tension of water \( 72 \times \)
\( \left.\mathbf{1 0}^{-\mathbf{3}} \mathbf{N} / \boldsymbol{M}\right) \)
A . \( 5.98 \times 10^{-5} \mathrm{J} \)
В. \( 10.98 \times 10^{-5} J \)
c. \( 16.95 \times 10^{-5} J \)
D. \( 8.95 \times 10^{-5} J \)
Subject: Chemistry
\( 100 \mathrm{ml} \) of \( 10 \mathrm{V} \mathrm{H}_{2} \mathrm{O}_{2} \) solution is heated.
The evolved gas is completely reacted with Ca to form CaO. The aqueous solution of Cao is neutralised by \( 50 \mathrm{m} \)
of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) solution. The molarity of
\( \boldsymbol{H}_{2} \boldsymbol{S O} \mathbf{4} \) is:
A. 2.43 M
B. 1.78 M
c. \( 1.55 \mathrm{M} \)
D. 2.78 м
Subject: Physics
A velocity-time graph for a moving object is shown below. What would be
the total displacement during time \( t= \)
\( \mathbf{0} \) to \( \boldsymbol{t}=\mathbf{6} \boldsymbol{s} ? \)
A. \( 10 \mathrm{m} \)
B. 20 m
\( c .15 \mathrm{m} \)
D. \( 0.0 \mathrm{m} \)
Subject: Chemistry
Buna-N synthetic rubber is a copolymer
of:
\( \mathbf{A} \cdot \mathrm{H}_{2} \mathrm{C}=\mathrm{CH}-\mathrm{C}=C H_{2} \) and \( \mathrm{H}_{2} \mathrm{C}=\mathrm{CH}-C H=\mathrm{CH}_{2} \)
B. \( \mathrm{H}_{2} \mathrm{C}=\mathrm{CH}-C H=\mathrm{CH}_{2} \) and \( \mathrm{H}_{5} \mathrm{C}_{6}-C H=\mathrm{CH}_{2} \)
\( \mathbf{C} \cdot \mathrm{H}_{2} \mathrm{C}=\mathrm{CH}-C N \) and \( \mathrm{H}_{2} \mathrm{C}=\mathrm{CH}-C H=\mathrm{CH}_{2} \)
\( \mathbf{D} \cdot \mathrm{H}_{2} \mathrm{C}=\mathrm{CH}-C N \) and \( \mathrm{H}_{2} \mathrm{C}=\mathrm{CH}-\mathrm{C}\left(\mathrm{CH}_{3}\right)=C H_{2} \)
Subject: Chemistry
Assertion
Fluorine always exhibits an oxidation
state of -1 in its compounds.
Reason
Fluorine has maximum
electronegativity and it contain seven electrons in its valence shell.
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
Above an infinitely large plane carrying
charge density \( \sigma, \) the electric field points up and is equal to \( \frac{\sigma}{2 \epsilon_{0}} . \) What is the magnitude and direction of the
electric field below the plane?
\( A \cdot \sigma / 2 \epsilon_{0}, \) down
В \( \cdot \sigma / 2 \epsilon_{0}, \) up
\( \mathrm{c} \cdot \sigma / \epsilon_{0}, \) down
D. \( \sigma / \epsilon_{0}, \) up
Subject: Chemistry
\( \boldsymbol{C o}^{2+}(\boldsymbol{a q} \cdot)+\boldsymbol{S C N}^{-}(\boldsymbol{a q} \cdot) \rightarrow \)
Complex \( (\boldsymbol{X}) \)
\( N i^{2+}(a q .)+ \)
dimethylglyoxime \( \frac{N H_{4} O H}{\longrightarrow} \)
Complex \( (\boldsymbol{Y}) \)
The coordination number of cobalt and
nickel in both the complexes \( (X) \) and \( (Y) \) is four. The geometry of complexes \( (x) \) and (Y) are respectively:
A. tetrahedral and square planar
B. both tetrahedral
c. square planar and tetrahedral
D. both square planar
Subject: Maths
Area of a sector of central angle \( 200^{0} \) of
a circle is \( 770 \mathrm{cm}^{2} \). The length of the corresponding arc of this sector is
A \( \cdot 73 \frac{1}{3} c m \)
B \( \cdot 156 \frac{1}{3} c m \)
\( \mathbf{c} \cdot 7 \frac{1}{3} c m \)
D. \( 22 \frac{1}{3} \) cm
Subject: Chemistry
One mole of stachyose on hydrolysis
yields:
A. 1 mole of glucose +1 mole of fructose +2 mole of galactose
B. 2 mole of glucose +1 mole of fructose +1 mole of galactose
C. 1 mole of glucose +2 mole of fructose +1 mole of galactose
D. 2 mole of glucose +2 mole of fructose
Subject: Maths
The value of which of the following
determinants can be non-zero?
\( \mathbf{A} \cdot\left|\begin{array}{lll}a_{1}+a_{2} & a_{2} & a_{1} \\ a_{4}+a_{5} & a_{5} & a_{4} \\ a_{7}+a_{8} & a_{8} & a_{7}\end{array}\right| \)
\( \mathbf{B} \cdot\left|\begin{array}{lll}a_{1}+2 a_{2} & a_{2} & a_{3} \\ a_{4}+2 a_{5} & a_{5} & a_{6} \\ a_{7}+2 a_{8} & a_{8} & a_{9}\end{array}\right| \)
\( \mathbf{C} \cdot\left|\begin{array}{lll}k a_{4} & k a_{5} & k a_{6} \\ a_{4} & a_{5} & a_{6} \\ a_{7} & a_{8} & a_{9}\end{array}\right| \)
D. None of these
Subject: Maths
If \( \int \log (\sqrt{1-x}+\sqrt{1+x}) d x= \)
\( \boldsymbol{x} \boldsymbol{f}(\boldsymbol{x})+\boldsymbol{A} \boldsymbol{x}+\boldsymbol{B} \sin ^{-1} \boldsymbol{x}+\boldsymbol{c}, \) then
A \( . f(x)=\log (\sqrt{1-x}+\sqrt{1+x}) \)
B. \( _{A}=-\frac{1}{3} \)
\( c \cdot_{B}=\frac{2}{3} \)
D. \( _{B}=-\frac{1}{2} \)
Subject: Chemistry
How many moles of glucose \( \left(C_{6} H_{12} O_{6}\right) \) should be dissolved into a solution with
a total volume of \( 0.500 L \) to produce a
1 \( M \) glucose solution?
\( \mathbf{A} \cdot 1 \mathrm{mol} \)
B. 24mol
\( c .0 .5 \mathrm{mol} \)
D. 0.25 mol
Subject: Chemistry
\( M e-\stackrel{\|}{C}-O-C H_{2}-C H_{2}- \)
\( \stackrel{\ominus}{\boldsymbol{N}} \boldsymbol{H}_{3} \stackrel{N a O \boldsymbol{H}}{\longrightarrow} \boldsymbol{Q} \) is
A \( \ldots_{M e-C-O-C H_{2}-C H_{2}-N H_{2}} \)
в. \( \quad_{M e-C-N H-C H_{2}-C H_{2}-O H}^{\circ} \)
\( c \)
D. \( M e C O O N a+H O C H_{2} C H_{2} N H_{2} \)
Subject: Maths
In a trapezium pqrs with \( \boldsymbol{P Q} \| \boldsymbol{S} \boldsymbol{R} \) the
diagonals \( P R \) and \( Q S \) intersect at \( x \) if \( P Q=\frac{2}{3} R S . \) Find the ratio of areas of
triangles \( P R Q \) and \( R X S \)
Subject: Physics
A thin rod of length \( \frac{f}{3} \) lies along the axis of a concave mirror of focal length \( \boldsymbol{f} \)
One end of its image touches at end of the rod. The length of the image is :
\( A \cdot f \)
в. \( \frac{f}{2} \)
c. \( 2 f \)
D. \( \frac{f}{4} \)
Subject: Chemistry
Assertion
Work done during free expansion of an ideal gas whether reversible or irreversible is positive.
Reason
During free expansion, external pressure is always less than the pressure of the system.
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
Two particles start moving from the
same point along the same stright line.
The first moves with constant velocity \( \mathbf{v} \) and the second with constant
acceleration a. During the time that
elapses before the second catches the first, the greater distance between the
particles is
A \( \cdot \frac{v^{2}}{a} \)
B. \( \frac{v^{2}}{2 a} \)
c. \( \frac{2 v^{2}}{a} \)
D. \( \frac{v^{2}}{3 a} \)
Subject: Chemistry
\( C \)
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}-\boldsymbol{C H}_{3} \)
IUPAC name of the compound is:
A. Isopropylchloride
B. 2-Chloropropane
c. 1 -chloro-1-methylethane
D. None of the above
Subject: Chemistry
For the set of reactions, \( \boldsymbol{k}_{1} \)
(i) \( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{C}, \quad(\mathrm{ii}) \boldsymbol{C}+\boldsymbol{B} \quad \stackrel{k_{3}}{\rightarrow} \boldsymbol{D} \)
\( \boldsymbol{k}_{2} \)
\( \boldsymbol{k}_{1}[\boldsymbol{A}][\boldsymbol{B}]-\boldsymbol{k}_{2}[\boldsymbol{C}]-\boldsymbol{k}_{3}[\boldsymbol{C}][\boldsymbol{B}] \) is equal
to:
\( ^{\mathbf{A}} \cdot \frac{-d[A]}{d t} \)
в. \( \frac{-d[B]}{d t} \)
c. \( \frac{d[C]}{d t} \)
D. \( \frac{d[D]}{d t} \)
Subject: Physics
Three identical positive charges each of value \( Q \) are arranged at the vertices of an equilateral triangle of side length a.
The intensity of the electric field at the
vertex of a regular tetrahedron of which the triangle is the base is:
A \( \cdot \frac{\sqrt{6} k Q}{a^{2}} \)
B. \( \frac{\sqrt{2} \text { КQ }}{\frac{a^{2}}{2}} \)
c. \( \frac{\sqrt{3} \kappa Q}{a^{2}} \)
D. None
Subject: Maths
f \( a, b, c \) are positive real numbers such
that \( a b^{2} c^{3}=64 \) then minimum value of \( \left(\frac{1}{a}+\frac{2}{b}+\frac{3}{c}\right) \) is equal to
\( A \cdot 6 \)
B. 3
\( c \cdot 2 \)
D. None of these
Subject: Physics
Alternating voltage \( V=400 \sin (500 \Omega t) \)
is applied across the resistance
\( (0.2 K \Omega) . \) The r.m.s value of current in
ampere is
\( A \cdot 1.414 \mathrm{A} \)
B. 14.14 A
\( c \cdot 0.1414 \mathrm{A} \)
\( D \cdot 2 A \)
Subject: Chemistry
Pick up the correct statement from the
following:
A. Glucose exists in two different crystalline forms, \( \alpha- \) \( D- \) glucose and \( \beta-D- \) glucose.
B. Cyclic structure of \( \alpha-D- \) glucose and \( \beta-D- \)
glucose is called pyranose structure.
C \( . \alpha-D- \) -glucose and \( \beta-D- \) glucose are
enantiomers.
D. Cellulose is a straight chain polysaccharide made up of only \( \beta \) - glucose units.
Subject: Physics
The Young's modulus of a wire of length and radius \( r \) is \( Y N / m^{2} . \) If the length
is reduced to \( L / 2 \& \) radius to \( r / 2 \), then its Young's modouls will be-
A \( \cdot \frac{Y}{2} \)
B. Y
c. 2 y
D. 4Y
Subject: Maths
If \( \lim _{x \rightarrow 1} \frac{x^{4}-1}{x-1}=\lim _{x \rightarrow k} \frac{x^{3}-k^{3}}{x^{2}-k^{2}} \) then \( k=? \)
A \( \cdot \frac{2}{3} \)
B. \( \frac{4}{3} \)
\( c \cdot \frac{8}{3} \)
D. none
Subject: Physics
The mass of the liquid flowing per second per unit area of cross-section of the tube is proportional to (pressure
difference across the ends) \( ^{n} \) and
(average velocity of the liquid ) \( ^{m} \). Which
of the following relations between \( \boldsymbol{m} \)
and \( n \) is correct?
A \( . m=n \)
B. \( m=-n \)
c. \( m^{2}=n \)
D. \( m=-n^{2} \)
Subject: Physics
Four resistances of each 20 ohm are
connected to form a square \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C}, \boldsymbol{D} \)
The resultant resistance between the
corners \( A C \) and the resistance between
\( A B \) are:
A \( .40 \Omega, 15 \Omega \)
B. \( 15 \Omega, 40 \Omega \)
c. \( 15 \Omega, 20 \Omega \)
D. \( 20 \Omega, 15 \Omega \)
Subject: Maths
Two sides of a triangle are of lengths 5 \( \mathrm{cm} \) and \( 1.5 \mathrm{cm}, \) then the length of the third side of the triangle cannot be
\( \mathbf{A} \cdot 3.6 \mathrm{cm} \)
B. \( 4.1 \mathrm{cm} \)
c. \( 3.8 \mathrm{cm} \)
D. \( 3.4 \mathrm{cm} \)
Subject: Chemistry
An inorganic compound contains \( 5.88 \% \) of hydrogen and \( 94.11 \% \) oxygen. Find out the empirical formula of the compound and predict the molecular formula.
\( A \cdot H_{2} O \)
в. \( H O \)
\( \mathrm{c} \cdot \mathrm{H}_{3} \mathrm{O}_{2} \)
D. \( H_{5} O_{2} \)
Subject: Physics
An aeroplane drops a parachutist. After covering a distance of \( 40 \mathrm{m} \), he opens
the parachute and retards at \( 2 m s^{-1} . \) If he reaches the ground with a speed of
\( 2 m s^{-1}, \) he remains in the air for about
A . \( 16 s \)
B. 3
c. \( 13 s \)
D. 10 \( s \)
Subject: Physics
Two concentric shells have radii R and
2R charges \( \boldsymbol{q}_{A} \) and \( \boldsymbol{q}_{B} \) and potentials \( 2 \mathbf{V} \) and (3/2) V respectively. Now shell B is earthed and let charges on
them become \( \boldsymbol{q}_{A}^{\prime} \) and \( \boldsymbol{q}_{B} \) '. Then :
This question has multiple correct options
A \( \cdot q A / q B=1 / 2 \)
B \( \cdot q A^{\prime} / q B^{\prime}=1 \)
c. potential of A after earthing becomes (3/2)
D. potential difference between A and B after earthing becomes V/2
Subject: Physics
Two magnetic monopoles are kept apart by a distance 'd. The magnetic force acting on each pole is ' \( \boldsymbol{F} \) ". How much percentage must the distance between the magnetic poles be changed so that the magnetic force acting on each pole
be \( 4 F \)
A. Decreases by \( 50 \% \)
B. Decreases by 20\%
c. Increased by \( 50 \% \)
D. Increased by \( 20 \% \)
Subject: Physics
Electrical conductivity of a semiconductor increases when em
radiation of \( \lambda<2480 n m \) is incident on
it. The band gap in (ev) for the semiconductor is
\( \mathbf{A} \cdot 1.1 e V \)
B . \( 2.5 e V \)
c. \( 0.7 e V \)
\( \mathbf{D} \cdot 0.5 e V \)
Subject: Maths
Equation \( 6 \sin ^{2} \theta-5 \sin \theta+1=0 \) is
satisfied by
A \( \cdot \theta=\frac{\pi}{2} \)
B. \( \theta=\frac{\pi}{3} \)
\( \mathbf{c} \cdot \theta=\frac{\pi}{4} \)
D・ \( \theta=\frac{\pi}{6} \)
Subject: Chemistry
Assertion
\( P b C l_{2} \) is more stable than \( P b C l_{4} \)
Reason
Pb \( C l_{4} \) is a powerful oxidising agent
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
Three charges \( +4 q, Q \) and \( +q \) are
placed in a straight line with \( Q \) midway
in between the other two charges. If net
force on \( +\boldsymbol{q} \) is zero, the charge \( \boldsymbol{Q} \) must
be:
A. \( -q \)
в. \( -2 q \)
c. \( \frac{-q}{2} \)
D.
Subject: Chemistry
Assertion
\( N H_{4} N O_{3} \) undergoes a redox reaction
to give \( N_{2} O \) and \( H_{2} O \)
Reason
It is a disproportionation reaction.
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: Chemistry
These questions consist of two
statements each, printed as assertion
and reason. While answering these questions you are required to choose anyone of the following five responses.
Assertion: Molecular nitrogen is less
reactive than molecular oxygen.
Reason: The bond length of \( N_{2}, \) is
shorter than that of oxygen.
A. If both assertion and reason are true and the reason is a correct explanation of the assertion
B. If both assertion and reason are true but reason is not correct explanation of the assertion
c. If the assertion is true but reason is false
D. If both the assertion and reason are false
E. If the assertion is false but the reason is true
Subject: Physics
A body dropped freely from a height h onto a horizontal plane, bounces up and down and finally comes to rest. The coefficient of restitution is e, the ratio
of distance travelled in two consecutive
rebounds
A \( .1: e \)
B . \( e: 1 \)
\( \mathbf{c} \cdot 1: e^{2} \)
D. \( e^{2}: 1 \)
Subject: Chemistry
Which of the following are isomeric
amines of the formula \( C_{3} H_{9} N ? \)
A \( \cdot C H_{3} C H_{2} C H_{2} N H_{2} \)
B. \( \left(C H_{3}\right)_{3} N \)
c. \( C H_{3} C H_{2} N H C H_{3} \)
D. All of the above
Subject: Maths
If \( A \) and \( B \) are two events such that
\( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})=\mathbf{0 . 6 5} \) and \( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})= \)
\( \mathbf{0 . 1 5}, \operatorname{then} \boldsymbol{P}(\overline{\boldsymbol{A}})+\boldsymbol{P}(\overline{\boldsymbol{B}})= \)
A . 0.6
B. 0.8
c. 1.2
D. 1.
Subject: Physics
Find the velocities of the point \( \boldsymbol{B} \)
A. \( 7.1 \mathrm{cm} / \mathrm{s} \)
B. \( 10 \mathrm{cm} / \mathrm{s} \)
\( c \cdot 5 c m / s \)
D. \( 0 \mathrm{cm} / \mathrm{s} \)
Subject: Physics
Blue,green,yellow and yellow is the color band on the resistor,find its resistance?
\( \mathbf{A} \cdot\left(75 \times 10^{4}\right) \Omega \pm 5 \% \)
B . \( \left(65 \times 10^{4}\right) \Omega \pm 5 \% \)
C \( \cdot\left(52 \times 10^{4}\right) \Omega \pm 5 \% \)
D. \( \left(65 \times 10^{4}\right) \Omega \pm 10 \% \)
Subject: Maths
If \( 3 x^{2}+4 x y-7 y^{2}=0 \) Find \( (a) \frac{d y}{d x} \) and
(b) \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}} \)
Subject: Chemistry
Assertion
For rubber and water, \( V(I)<V(s) \)
Reason
The density of both rubber and water is
more in liquid state.
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: Chemistry
The correct order regarding the
electronegativity of hybrid orbitals of
carbon is :
\( \mathbf{A} \cdot s p<s p^{2}>s p^{3} \)
В. \( s p<s p^{2}<s p^{3} \)
c. \( s p>s p^{2}<s p^{3} \)
D. \( s p>s p^{2}>s p^{3} \)
Subject: Physics
A particle of mass \( 1 g m \) and charge \( 1 \mu C \)
is held at rest on a frictional horizontal
surface at distance \( 1 \mathrm{m} \) from a fixed
charge \( 2 m C . \) If the particle is released, it will be repelled. The speed of the particle when it is at a distance of \( 10 m \)
from the fixed charge will be:
A \( \cdot 60 m s^{-1} \)
B. \( 100 \mathrm{ms}^{-1} \)
\( \mathrm{c} .90 \mathrm{ms}^{-1} \)
D. \( 180 m s^{-1} \)
Subject: Chemistry
For the formation of \( C r_{2} O_{3} \) and \( A l_{2} O_{3} \)
values of \( \Delta_{f} G^{o} \) are \( 540 \mathrm{kJ} \mathrm{mol}^{-1} \) and
\( -827 \mathrm{kJ} \mathrm{mol}^{-1} \) respectively. What will be
the possibility for reaction of \( C r_{2} O_{3} \) by
Al?
A. Reduction of \( C r_{2} O_{3} \) by Al will take place
B. Oxidation of \( C r_{2} O_{3} \) by Al will take place
c. Neither oxidation nor reduction will take place
D. Reaction is not feasible
Subject: Physics
Three point particles of masses \( 1.0 k g \)
\( 1.5 k g \) and \( 2.5 k g \) are placed at three corners of a right angle triangle of sides
4.0 \( c m, 3.0 c m \) and \( 5.0 c m \) as shown in
the figure. The centre of mass of the
system is at a point :
A. \( 1.5 \mathrm{cm} \) right and \( 1.2 \mathrm{cm} \) above \( 1 \mathrm{kg} \) mass
B. \( 2.0 \mathrm{cm} \) right and \( 0.9 \mathrm{cm} \) above \( 1 \mathrm{kg} \) mass
c. \( 0.6 \mathrm{cm} \) right and \( 2.0 \mathrm{cm} \) above \( 1 \mathrm{kg} \) mass
D. \( 0.9 \mathrm{cm} \) right and \( 2.0 \mathrm{cm} \) above \( 1 \mathrm{kg} \) mass
Subject: Maths
Find whether the following function is
differentiable at \( x=1,2: \) \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{cc}\boldsymbol{x}, & \boldsymbol{x} \leq \mathbf{1} \\ \boldsymbol{2}-\boldsymbol{x}, & \boldsymbol{1} \leq \boldsymbol{x} \leq \mathbf{2} \\ -\boldsymbol{2}+\boldsymbol{3} \boldsymbol{x}-\boldsymbol{x}^{2}, & \boldsymbol{x}>\boldsymbol{2}\end{array}\right. \)
Subject: Maths
Find the distance between the points whose position vectors are given as follows \( -2 \hat{i}+3 \hat{j}+5 \hat{k}, 7 \hat{i}-\hat{k} \)
A. \( 3 \sqrt{14} \)
(i) 144
B. \( \sqrt{54} \)
c. \( 3 \sqrt{19} \)
D. \( \sqrt{57} \)
Subject: Physics
The work done by the frictional force at the instant of pure rolling is
\( ^{\text {A }} \cdot \frac{\mu m g a t^{2}}{2} \)
B. \( \mu \) mgat \( ^{2} \)
\( \mathrm{c},_{\mu m g} \frac{a t^{2}}{\alpha} \)
D. zero
Subject: Maths
Calculate the mean of the following data with the help of shortcut method.
\begin{tabular}{|l|l|l|l|l|l|l|}
\hline Classinterval & \( 0-5 \) & \( 5-10 \) & \( 10-15 \) & \( 15-20 \) & \( 20-25 \) & \( 25-30 \) \\
\hline Frequency & 4 & 6 & 5 & 8 & 3 & 7 \\
\hline
\end{tabular}
A . 7.58
в. 5.78
c. 6.87
D. 8.67
Subject: Physics
Assertion
The kinetic energy, with any reference,
must be positive.
Reason
In the expression for kinetic energy, the
velocity appears with power 2
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
\( n \) resistors each of resistance \( R \) first
combine to give maximum effective resistance and then combine to given
minimum effective resistance. The ratio
of the maximum to minimum
resistance is:
A . \( n \)
B \( \cdot n^{2} \)
c. \( n^{2}-1 \)
\( \mathbf{D} \cdot n^{3} \)
Subject: Physics
An insulated box containing monatomic ideal gas of molar mass \( \mathrm{M} \)
is moving with a uniform speed v. The box suddenly stops and consequently the gas acquires a new temperature. Calculate the change in the
temperature of the gas. Neglect heat absorbed by the box.
A \( \cdot \Delta T=2 \frac{M v^{2}}{3 R} \)
в. \( \Delta T=\frac{M v^{2}}{3 R} \)
\( ^{\mathbf{C}} \Delta T=3 \frac{M v^{2}}{3 R} \)
D. \( \quad \Delta T=4 \frac{M v^{2}}{3 R} \)
Subject: Physics
A car moving on a straight road
accelerates from a speed of \( 4.1 \mathrm{m} / \mathrm{s} \) to
a speed of \( 6.9 m / s \) in \( 5 s . \) Its average
acceleration is
A. \( 0.5 \mathrm{m} / \mathrm{s}^{2} \)
B . \( 0.6 \mathrm{m} / \mathrm{s}^{2} \)
c. \( 0.56 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 0.65 \mathrm{m} / \mathrm{s}^{2} \)
Subject: Physics
A ray of light is incident normally on one
of the faces of a prism of apex angle \( 30^{\circ} \) and refractive index \( \sqrt{2} . \) The angle of
deviation of the ray is
A \( .30^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 15^{\circ} \)
D. \( 90^{\circ} \)
Subject: Chemistry
Graph between \( \log \left(\frac{x}{m}\right) \) and \( \log p \) is a
straight line at an angle \( 45^{\circ} \) with
intercept on y-axis \( 0,3010 . \) Calculate the amount of gas adsorbed in gram per gram of the adsorbent when pressure is
0.2 atm.
A . 0.4
B. 0.6
c. 0.8
D. 0.2
Subject: Maths
The surface area of the wooden door is
\( 416 m^{2} . \) The length and width of the
door is \( 12 \mathrm{m} \) and \( 10 \mathrm{m} \) respectively. Find its height.
A \( .2 m \)
в. \( 4 m \)
\( c .6 m \)
D. \( 8 m \)
Subject: Physics
You are to examine these two
statements carefully and select the answers to these items using the code
given below:

Statement I: The acceleration due to
gravity decreases with increase in height from the surface of the Earth. Statement II : The acceleration due to gravity is inversely proportional to the square of the distance from the centre
of the Earth.
A. Both the statements are individually true and Statement II is the correct explanation of Statement
B. Both the statements are individually true but Statement II is not the correct explanation of Statement
c. statement lis true but Statement II is false
D. Statement lis false but Statement II is true
Subject: Chemistry
A definite amount of solid \( N H_{4} H S \) is placed in a flask already containing gas at a certain temperature and 0.50 atm
pressure. \( N H_{4} H S \) decomposes to give
\( N H_{3} \) and \( H_{2} S \) and at equilibrium total
pressure in flask is 0.84 atm. The
equilibrium constant for the reaction is:
A . 0.30
B. 0.18
c. 0.17
D. 0.11
Subject: Physics
A copper wire of negligible mass, \( 1 \mathrm{m} \)
length and cross-sectional area
\( 10^{-6} m^{2} \) is kept on a smooth horizontal
table with one end fixed. A ball of mass
\( 1 \mathrm{kg} \) is attached to the other end. The
wire and the ball are rotating with an angular velocity of 20 rad/s. If the
elongation in the wire is \( 10^{-3} \mathrm{m} \)
b. If for the same wire as stated above, the angular velocity is increased to 100 rad/s and the wire breaks down, find the
breaking stress (in terms of \( \left.\times 10^{10} N / m^{2}\right) \)