AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
\( A 30 g \) of ice that is at a temperature
\( 0^{\circ} \mathrm{C} \) falls 6 meters from the eaves of a
house to the ground below. If \( 5 \% \) of the kinetic energy that the ice possesses when it strikes the ground converts into heat, Identify the correct statement?
(Note: \( \left.\boldsymbol{H}_{f} \boldsymbol{w} \boldsymbol{a} \boldsymbol{t} \boldsymbol{e} \boldsymbol{r} \boldsymbol{0} . \boldsymbol{3} \boldsymbol{3} \boldsymbol{5} \boldsymbol{J} / \boldsymbol{g}\right) \)
A. The ice would become colder during the fall; therefore, no ice would melt
B. This would not happen because it would break the law of conservation of mass
c. Less than \( .3 g \) of the ice would melt
D. The frictional work done to stop the icicle's fall would use up all the energy and leave none for anything else
E. The icicle would shatter and the energy would convert into momentum
Subject: Chemistry
\( \boldsymbol{S} \boldsymbol{O}_{2} \boldsymbol{C l}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g}) \)
The given reaction is a first order gas reaction with \( k=2.2 \times 10^{-5} s e c^{-1} \) at
\( 320^{\circ} \mathrm{C} . \) What \( \% \) of \( S O_{2} C l_{2} \) is
decomposed on heating this gas for 90
\( \min ? \)
\( \mathbf{A} \cdot 11.2 \% \)
B . 12.3\%
c. \( 13.4 \% \)
D. 14.5\%
Subject: Biology
Assertion
Neurospora is commonly called water-
mould.
Reason
It belongs to basidomycetes fungi.
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
Draw the graph for the equation given below; hence find the co-ordinates of
the points where the graph drawn meets the co-ordinate axes:
\( \frac{2 x+15}{3}=y-1 \)
\( \mathbf{A} \cdot(4,0) \) and (0,9)
B \( \cdot(-1,0) \) and (0,6)
\( \mathbf{c} \cdot(-9,0) \) and (0,6)
D. (5,0) and (0,-9)
Subject: Physics
In a series \( \mathrm{L}, \mathrm{R}, \mathrm{C}, \) circuit which is
connected to a.c. source. When resonance is obtained then net
impedance Z will be
A. \( z=R \)
B. \( z=L-1 / C \)
\( c \cdot z=L \)
D. z = 1/C
Subject: Maths
\( \int_{0}^{\pi / 2} \sin ^{5} x \cos ^{6} x d x= \)
A \( \cdot \frac{8}{693} \)
в. \( \frac{32}{693} \)
c. \( \frac{8}{99} \)
D. \( \frac{16}{63} \)
Subject: Physics
For a common emitter amplifier, the current gain is \( 70 . \) If the emitter current
is \( 8.8 \mathrm{mA} \), then the collector current is:
\( \mathbf{A} \cdot 0.124 m A \)
в. \( 4.34 m A \)
\( c .8 .68 m A \)
D. \( 1.72 m A \)
Subject: Physics
Equations of motion in the same
direction is given by \( \boldsymbol{y}_{1}=\boldsymbol{A} \sin (\boldsymbol{\omega} \boldsymbol{t}-\boldsymbol{k} \boldsymbol{x}), \boldsymbol{y}_{2}=\boldsymbol{A} \sin (\boldsymbol{\omega} \boldsymbol{t}- \)
\( k x-\theta) . \) The amplitude of the medium
particle will be
A. \( \sqrt{2} A \cos \theta \)
B. \( 2 A \cos \theta \)
c. \( \sqrt{2} A \cos \frac{\theta}{2} \)
D. \( 2 A \cos \frac{\theta}{2} \)
Subject: Chemistry
The correct order regarding the
solubility of alkaline earth metal halides in water is :
A \( \cdot B e C l_{2}<M g C l_{2}<C a C l_{2}<S r C l_{2}<B a C l_{2} \)
в. \( M g C l_{2}<C a C l_{2}>B e C l_{2}>B a C l_{2}>S r C l_{2} \)
C. \( B a C l_{2}>M g C l_{2}>C a C l_{2}>B e C l_{2}>S r C l_{2} \)
D. \( B e C l_{2}>M g C l_{2}>C a C l_{2}>S r C l_{2}>B a C l_{2} \)
Subject: Maths
The straight lines \( \frac{\boldsymbol{x}-\mathbf{1}}{\mathbf{1}}=\frac{\boldsymbol{y}-\mathbf{2}}{\mathbf{2}}= \)
\( \frac{z-3}{3} \) and \( \frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{3} \) are
A. Parallel lines
B. Intersecting at \( 60^{\circ} \)
c. skew lines
D. Intersecting at right angle
Subject: Biology
Match the column I with column II and
select the correct option from the gives
codes
\( \begin{array}{llll} & \text { Column } & & \text { Column II } \\ & \text { I } & & \\ \text { A. } & \text { Pedicel } & \text { (i) } & \text { Reduces leaf } \\ \text { B. } & \text { peduncle } & \text { (ii) } & \begin{array}{l}\text { Stalk of the } \\ \text { flower }\end{array} \\ \text { C. } & \text { Bract } & \text { (iii) } & \text { Stalk of the leaf } \\ \text { D. } & \text { Petiole } & \text { (iv) } & \begin{array}{l}\text { Inflorescence } \\ \text { axis }\end{array}\end{array} \)
\( \mathbf{A} \)
B. \( A-(\text { iii) }, B-(i v), C-(i), D-(i i) \)
C. A-(iii), B-(ii), C-(i), D-(iv)
D. A-(ii), B-(iii), C-(i), D-(iv)
Subject: Physics
\( \boldsymbol{x}_{1}=\boldsymbol{A} \sin (\omega \boldsymbol{t}-\mathbf{0 . 1} \boldsymbol{x}) \) and \( \boldsymbol{x}_{2}= \)
\( A \sin \left(\omega t-0.1 x-\frac{\phi}{2}\right) . \) The resultant
amplitude of combined wave is:-
A \( \cdot 2 A \cos \frac{\phi}{4} \)
B. \( A \sqrt{2 \cos \frac{\phi}{2}} \)
\( \mathrm{c} \cdot_{2 A \cos \frac{\phi}{2}} \)
D. \( A \sqrt{2\left(1+\cos \frac{\phi}{4}\right)} \)
Subject: Maths
Prove that \( \left|\begin{array}{ccc}\boldsymbol{y} \boldsymbol{z}-\boldsymbol{x}^{2} & \boldsymbol{z} \boldsymbol{x}-\boldsymbol{y}^{2} & \boldsymbol{x} \boldsymbol{y}-\boldsymbol{z}^{2} \\ \boldsymbol{z} \boldsymbol{x}-\boldsymbol{y}^{2} & \boldsymbol{x} \boldsymbol{y}-\boldsymbol{z}^{2} & \boldsymbol{y} \boldsymbol{z}-\boldsymbol{x}^{2} \\ \boldsymbol{x} \boldsymbol{y}-\boldsymbol{z}^{2} & \boldsymbol{y} \boldsymbol{z}-\boldsymbol{x}^{2} & \boldsymbol{z} \boldsymbol{x}-\boldsymbol{y}^{2}\end{array}\right| \) is
divisible by \( (x+y+z), \) and hence find
the quotient
OR
Using elementary transformations, find the inverse of the matrix \( \boldsymbol{A}= \) \( \left(\begin{array}{lll}8 & 4 & 3 \\ 2 & 1 & 1 \\ 1 & 2 & 2\end{array}\right) \) and use it to solve the
following system of linear equations:
\( 8 x+4 y+3 z=19 \)
\( 2 x+y+z=5 \)
\( x+2 y+2 z=7 \)
Subject: Chemistry
\( X_{2} \) represents halogen molecule. Bond
energy of different halogen molecules will lie in following sequences:
A \( \cdot F_{2}>C l_{2}>B r_{2}>I_{2} \)
В. \( C l_{2}>B r_{2}>F_{2}>I_{2} \)
c. \( I_{2}>C l_{2}>B r_{2}>F_{2} \)
D. \( B r_{2}>F_{2}>I_{2}>C l_{2} \)
Subject: Physics
An electron moving with a constant velocity \( v \) along \( X \) -axis enters a uniform electric field applied along Y-axis. Then,
the electron moves
A. with uniform acceleration along Y-axis
B. without any acceleration along Y-axis
C \( . \) in a trajectory represented as \( y=a x^{2} \)
D. in a trajectory represented as \( y=a x \)
E. with uniform deceleration along \( \mathrm{x} \) -axis
Subject: Maths
ff \( \boldsymbol{x}=\boldsymbol{a} \sin \boldsymbol{\theta}+\boldsymbol{b} \cos \boldsymbol{\theta}, \boldsymbol{y}=\boldsymbol{a} \cos \boldsymbol{\theta} \)
\( -b \sin \theta \)
then show that \( (a x+a y)^{2}+(b x-a y)^{2} \)
\( =\left(a^{2}+b^{2}\right)^{2} \)
Subject: Physics
A piece of copper weighing 500 g is heated to \( 100^{\circ} \mathrm{C} \) and dropped into \( 200 \mathrm{g} \)
of water at \( 25^{\circ} \mathrm{C} \). Find the temperature of the mixture. The specific heat of Cu is \( 0.42 J g^{-1} o C^{-1} \)
A \( \cdot 30^{\circ} \mathrm{C} \)
B . \( 40^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 50^{\circ} C \)
D. \( 60^{\circ} \mathrm{C} \)
Subject: Maths
The Cartesian product \( \boldsymbol{P} \times \boldsymbol{P} \) has 16
elements among which two elements \( \operatorname{are}(a, b) \) and \( (c, d) . \) Find the set \( P \) and
the remaining elements of \( \boldsymbol{P} \times \boldsymbol{P} \)
Subject: Chemistry
Copper matte is a molten mixture of :
A \( \cdot C u_{2} S+F e S(\text { little }) \)
в. \( C u_{2} S+ \) Fe \( O \) (little)
\( \mathrm{c} \cdot \mathrm{Cu}_{2} \mathrm{O}+\mathrm{FeO} \) (little)
D. \( C u_{2} O+F e S(\text { little }) \)
Subject: Physics
A block \( A, \) whose weight is \( 200 N \), is
pulled up a slope of length \( 5 m \) by
means of a constant force \( \boldsymbol{F}(=\mathbf{1 5 0} \boldsymbol{N}) \)
as illustrated in Figure.
What is the work done by the force \( \boldsymbol{F} \) in
moving the block \( A, 5 m \) along the
slope?
A \( .450 J \)
B. \( 600 J \)
\( c .0 J \)
D. \( 750 J \)
Subject: Physics
A gravitational field is present in a
region. A point mass is shifted from \( \boldsymbol{A} \)
to \( B, \) along different paths shown in the
figure. If \( W_{1}, W_{2} \) and \( W_{3} \) represent the
work done by gravitational force for
respective paths, then
\( \mathbf{A} \cdot W_{1}=W_{2}=W_{3} \)
В. \( W_{1}>W_{2}>W_{3} \)
c. \( W_{1}>W_{3}>W_{2} \)
D. none of these
Subject: Biology
What is the length of human DNA
containing \( 6.6 \times 10^{9} \) bp nitrogen
bases?
\( \mathbf{A} \cdot 22 n m \)
B. \( 0.22 \mathrm{mm} \)
\( \mathbf{c} .2 .2 \mathrm{m} \)
D. 22m
Subject: Physics
When a source moves away from stationary observer with velocity v then
apparent change in frequency is \( \Delta n_{1} \)
When an observer approaches the stationary source with same velocity
then change in frequency is \( \Delta n_{2} \) then :
A \( \cdot \Delta n_{1}=\Delta n_{2} \)
в. \( \Delta n_{1}>\Delta n_{2} \)
c. \( \Delta n_{1}<\Delta n_{2} \)
D. \( \Delta n_{1}=2 \Delta n_{2} \)
Subject: Physics
Two trains \( A \) and \( B \) of length 400 m each are moving on two parallel tracks with uniform speed of
\( 20 \mathrm{m} / \mathrm{s} \) in the same direction. with \( \mathrm{A} \)
ahead of \( \mathrm{B} \), driver of \( \mathrm{B} \) accelerates at
\( 1 m / s^{2} \) in order to overtrake. if after 50 sec, the guard of B just brushes past driver of \( A, \) what was original distance between drivers of the trains?
A. \( 450 m \)
В. \( 1250 m \)
\( \mathbf{c} .850 m \)
D. 1650m
Subject: Physics
A body starts with an initial velocity of
\( 10 m s^{-1} \) and acceleration \( 5 m s^{-2} \). Find
the distance covered by it in 5 s.
\( \mathbf{A} \cdot 62.5 m \)
в. 32.5 т
c. \( 112.5 m \)
D. \( 50 m \)
Subject: Maths
If \( a, b, c, d \) and \( p \) are distinct real
number such that \( \left(a^{2}+b^{2}+c^{2}\right) p^{2}- \)
\( \mathbf{2}(\boldsymbol{a} \boldsymbol{b}+\boldsymbol{b} \boldsymbol{c}+\boldsymbol{d} \boldsymbol{c}) \boldsymbol{p}+\left(\boldsymbol{b}^{2}+\boldsymbol{c}^{2}+\boldsymbol{d}^{2}\right) \geq \mathbf{0} \)
then \( a, b, c, d: \)
\( A \cdot \operatorname{arein} A \cdot P \)
B. are in G.P.
c. are in \( H . P \)
D. satisfy \( a b=c d \)
Subject: Physics
Assertion
A solid sphere and a hollow sphere when allowed to roll down on an inclined
plane, the solid sphere reaches the bottom first.
Reason
Moment of inertia of solid sphere is greater than that of hollow sphere.
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 Torque \( \vec{\tau} \) on a body about a given point is found to be equal to \( \overrightarrow{\boldsymbol{A}} \times \overrightarrow{\boldsymbol{L}} \)
where \( \vec{A} \) is the constant vector and \( \overrightarrow{\boldsymbol{L}} \) is
the force on the body about that point. From this it follows that:
This question has multiple correct options
A \( \cdot \frac{d \vec{L}}{d t} \) is perpendicular to \( \vec{L} \) at all instants of time
B. the component of \( \vec{L} \) in the direction of \( \vec{A} \) does not change with time
c. the magnitude of \( \bar{L} \) does not change with time
D. \( \vec{L} \) does not change with time
Subject: Physics
A circular coil has 500 turns of wire and
its radius is \( 5 \mathrm{cm} \). The self inductance of
the coil is:-
A \( \cdot 25 \times 10^{-3} m H \)
в. \( 25 m H \)
c. \( 50 \times 10^{-3} H \)
D. \( 50 \times 10^{-3} \mathrm{mH} \)
Subject: Chemistry
Select the correct statement(s) about
the following This question has multiple correct options
A \( \cdot O_{3} \) is used as germicide for purification of air
B. \( \ln O_{3} \), 0 -o bond length is identical with that of molecular oxygen
\( \mathrm{c} \cdot O_{3} \) molecule is angular in shape
D. \( O_{3} \) is an oxidizing agent
Subject: Physics
Two different ideal diatomic gases \( A \)
and B are initially in the same state. A and \( \mathrm{B} \) are then expanded to the same
final volume through adiabatic and isothermal processes respectively. If
\( P_{A}, P_{B} \) and \( T_{A}, T_{B} \) represents the final
pressure and temperature of \( A \) and \( B \) respectively then
A \( \cdot P_{A}<P_{B} \) and \( T_{A}<T_{B} \)
В \( \cdot P_{A}>P_{B} \) and \( T_{A}>T_{B} \)
\( \mathbf{c} \cdot P_{A}>P_{B} \) and \( T_{A}<T_{B} \)
D. \( P_{A}<P_{B} \) and \( T_{A}>T_{B} \)
Subject: Maths
If \( \boldsymbol{a}>\mathbf{0} \) and \( \int_{0}^{a}[\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(-\boldsymbol{x})] \boldsymbol{d} \boldsymbol{x}= \)
\( \int_{-a}^{a} \phi(x) d x \) then one of the possible
values of \( \phi(x) \) can be
A \( \cdot f(-x) \)
B . \( -f(x) \)
c. \( \frac{1}{2} f(x) \)
D. none of these
Subject: Maths
Area of the region bounded by the curve
\( \boldsymbol{y}=\mathbf{2 5}^{\boldsymbol{x}}+\mathbf{1 6} \) and curve \( \boldsymbol{y}=\boldsymbol{b} . \mathbf{5}^{\boldsymbol{x}}+\mathbf{4} \)
whose tangent at the point \( \boldsymbol{x}=\mathbf{1} \)
makes an angle \( \tan ^{-1}(40 \log 5) \) with
the \( x- \) axis is:
\( ^{\mathbf{A}} \cdot_{2 \log _{5}}\left(\frac{e^{4}}{27}\right) \)
\( ^{\mathbf{B}} \cdot_{4 \log _{5}}\left(\frac{e^{4}}{27}\right) \)
\( \mathbf{c} \cdot_{3 \log _{5}}\left(\frac{e^{4}}{27}\right) \)
D. None of these
Subject: Maths
Evaluate the given integral. \( \int \frac{x^{9}}{\left(4 x^{2}+1\right)^{6}} d x \)
\( ^{\mathrm{A}} \frac{1}{5 x}\left(4+\frac{1}{x^{2}}\right)^{-5}+C \)
в. \( \frac{1}{5}\left(4+\frac{1}{x^{2}}\right)^{-5}+C \)
\( ^{\mathrm{c}} \frac{1}{10 x}\left(\frac{1}{x^{2}}+4\right)^{-5}+C \)
\( ^{\mathrm{D}} \frac{1}{10}\left(\frac{1}{x^{2}}+4\right)^{-5}+C \)
Subject: Chemistry
What is the enthalpy of vaporisation of
liquid water in \( k J \) mol \( ^{-1} \) if:
\( (\mathrm{i}) \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{H}_{2} \boldsymbol{O}(l)+ \)
\( 285.77 k J m o l^{-1} \)
\( (\text { ii }) \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{v})+ \)
\( 241.84 k J \) mol \( ^{-1} \)
\( \mathbf{A} \cdot+43.93 \)
B . -43.93
c. +527.61
D. -527.61
Subject: Physics
\( q_{1}, q_{2}, q_{3}, \) and \( q_{4} \) are point charges located at points as shown in the figure and \( \mathrm{S} \) is a spherical Gaussian surface
of radius R. Which of the following is
true according to the Gauss's law?
A \( \cdot \oint_{5}\left(\vec{E}_{1}+\vec{E}_{2}+\vec{E}_{3}\right) \cdot d \vec{A}=\frac{q_{1}+q_{2}+q_{3}}{2 \varepsilon_{0}} \)
B.
c. \( \oint_{5}\left(\vec{E}_{1}+\vec{E}_{2}+\vec{E}_{3}\right) \cdot d \vec{A}=\frac{\left(q_{1}+q_{2}+q_{3}+q_{4}\right)}{\varepsilon_{0}} \)
D. None of the above
Subject: Physics
Statement 1: If dot product and cross product of \( \vec{A} \) and \( \vec{B} \) are zero, it implies that one of the vector \( \vec{A} \) and \( \vec{B} \) must be
a null vector.

Statement 2: Null vector is a vector with
zero magnitude.
A \( . \) a) statement- -1 is false, statement- 2 is true
B. b) Statement-1 is true, Statement-2 is true, Statement
2 is a correct explanation for statement-
c. c) Statement- - is true, Statement-2 is true; Statement
2 is not a correct explanation for statement-
D. d) Statement-1 is true, Statement-2 is false
Subject: Physics
in the horizontal plane of the circle as shown in the figure. The path
consists of eight arcs with alternating
radii \( r \) and \( 2 r . \) Each segment of arc
subtends equal angle at the common
centre \( P . \) The magnetic field produced
by current path at point \( \boldsymbol{P} \) is
A \( \cdot \frac{3}{8} \frac{\mu_{0} I}{r} ; \) perpendicular to the plane of the paper and directed inward.
B. \( \frac{3}{8} \frac{\mu_{0} \mathrm{I}}{\mathrm{r}} ; \) perpendicular to the plane of the paper and directed outward.
C \( \cdot \frac{1}{8} \frac{\mu_{0} I}{r} ; \) perpendicular to the plane of the paper and directed inward.
D. \( \frac{1}{8} \frac{\mu_{0} \mathrm{I}}{\mathrm{r}} ; \) perpendicular to the plane of the paper and directed outward
Subject: Maths
If \( \tan \alpha=2 \sqrt{2}, \) then the value of
\( \frac{\tan \alpha}{\frac{\sin ^{3} \alpha}{\cos \alpha}+\sin \alpha \cdot \cos \alpha} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. 2
c. \( 2 \sqrt{2} \)
\( D \)
Subject: Physics
Two point charges \( Q \) and \( -Q / 4 \) are
separated by a distance \( x . \) Then:
This question has multiple correct options
A. potential is zero at a point on the axis which is \( x / 3 \) on the right side of the charge \( -Q / 4 \)
B. potential is zero at a point on the axis which is \( x / 5 \) on the left side of the charge \( -Q / 4 \)
C. electric field is zero at a point on the axis which is at a distance \( x \) on the right side of the charge \( -Q / 4 \)
D. there exist two points on the axis where electric field is zero
Subject: Chemistry
If four moles of electrons are transferred
from anode to cathode in a experiment
on electrolysis of water, then total volume of the two gases produced at
STP will be:
\( \mathbf{A} \cdot 224 L \)
B. \( 72.6 L \)
c. \( 67.2 L \)
D. \( 89.4 L \)
Subject: Physics
In a silicon diode, the reverse current increases from \( 10 \mu A \) to \( 20 \mu A \). when the
reverse voltage change from \( 2 V \) to \( 4 V \)
The reverse ac resistance of the diode is
A \( \cdot 1 \times 10^{5} \Omega \)
В. \( 3 \times 10^{5} \Omega \)
c. \( 2 \times 10^{5} \Omega \)
D. \( 4 \times 10^{5} \Omega \)
Subject: Physics
A coil is needed to operate an arc lamp of \( 150 \mathrm{V}, 50 \mathrm{Hz} \). The lamp of resistance of 5 ohms when running at 10 A. Find inductance of the choke coil, if the
same arc lamp is to be operated on 160 V, DC. What is the additional resistance
required?
A . \( 5 \Omega \)
B. \( 4.5 \Omega \)
c. \( 5.5 \Omega \)
D. 2.5\Omega
Subject: Chemistry
Which of the following is used to
prepare \( C l_{2} \) gas at room temperature
from concentrated \( \boldsymbol{H} \boldsymbol{C l} \) ?
A. \( M n O_{2} \)
в. \( H_{2} \).
c. \( K M n O_{4} \)
D. \( C r_{2} O_{3} \)
Subject: Maths
If \( \mathbf{A} \) and \( \mathbf{B} \) are two events such that \( P(\mathbf{A} \cup B) \geq \frac{3}{4} \) and \( \frac{1}{8} \leq P(A \cap B) \leq \frac{3}{8} \)
then
This question has multiple correct options
A \( \cdot \mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B}) \leq \frac{11}{8} \)
в.
c. \( \mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B}) \geq \frac{7}{8} \)
D. \( \mathrm{P}(\mathrm{A}) \cdot \mathrm{P}(\mathrm{B}) \geq \frac{1}{8} \)
Subject: Maths
Evaluate \( \int \frac{x^{2}}{(x \sin x+\cos x)^{2}} d x \)
A. \( \frac{\sin x-x \cos x}{x \sin x+\cos x}+c \)
в. \( \frac{\cos x-x \sin x}{x \sin x+\cos x}+c \)
c. \( \frac{\cos x-x \sin x}{x \sin x-\cos x}+c \)
D. \( \frac{\sin x+x \cos x}{x \sin x+\cos x}+c \)
Subject: Physics
Q Type your question
illustrated in Fig.
Ball \( X \) has an initial velocity of
\( 3.0 m s^{-1} \) in a direction along line \( A B \)
Ball \( Y \) has a mass of \( 2.5 k g \) and an
initial velocity of \( 9.6 m s^{-1} \) in a
direction at an angle of \( 60^{\circ} \) to line \( A B \)
The two balls collide at point \( B \). The
balls stick together and then trave along the horizontal surface in a
direction at right-angles to the line \( \boldsymbol{A B} \)
as shown in Fig.

Calculate the common speed \( V \) of the
two balls after the collision
Subject: Physics
The periodic time of a body executing SHM is \( 4 s \). After how much interval from
time \( t=0, \) its displacement will be half
of its amplitude?
A . \( 1 / 2 s \)
B. \( 1 / 3 s \)
c. \( 1 / 4 s \)
D. \( 1 / 6 s \)
Subject: Physics
A particle moving along a circular path
of radius \( 6 m \) uniform speed of \( 8 m s^{-1} \)
The average acceleration when the particle completes one half of the revolution is -
A \( \cdot \frac{16}{3 \pi} m / s^{2} \)
B. \( \frac{32}{3 \pi} m / s^{2} \)
c. \( \frac{64}{3 \pi} m / s^{2} \)
D. None of these
Subject: Maths
Assertion
The greatest value of the moduli of
complex numbers \( z \) satisfying the equation \( \left|z-\frac{4}{z}\right|=2 \) is \( \sqrt{5}+1 \)
Reason
For any two complex number \( z_{1} \) and \( z_{2} \)
\( \left|z_{1}-z_{2}\right| \geq\left|z_{1}\right|-\left|z_{2}\right| \)
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
A point charge \( +q \) is placed at the centre of a cube of side \( L \). The electric
flux emerging from the cube is
A \( \cdot \frac{q}{\varepsilon_{0}} \)
B. Zero
c. \( \frac{6 q L^{2}}{\varepsilon_{0}} \)
D. \( \frac{q}{6 L^{2} \varepsilon_{0}} \)
Subject: Physics
The height above the surface of earth at which acceleration due to gravity is half the acceleration due to gravity at
surface of earth is \( \left(R=6.4 \times 10^{6} m\right) \)
A \( \cdot 6.4 \times 10^{6} m \)
В. \( 2.6 \times 10^{6} \mathrm{m} \)
c. \( 12.8 \times 10^{6} m \)
D. \( 19.2 \times 10^{6} \mathrm{m} \)
Subject: Chemistry
Which of the following are the best
methods for the preparation of n-propy
benzene \( (\boldsymbol{A}) ? \)
This question has multiple correct options
\( \mathbf{A} \)
\[
\bigcirc+\mathrm{Me}^{\mathrm{Cl}}+\mathrm{AlCl}_{3} \longrightarrow(\mathrm{A})
\]
\( B \)
\[
\square+\mathrm{Me} \overbrace{\mathrm{BF}_{3}}^{\mathrm{OH}} \rightarrow(\mathrm{A})
\]
\( c \)
\[
\bigcirc+\mathrm{Me} \overbrace{\|}_{\mathrm{O}}^{\mathrm{Cl}}+\mathrm{AlCl}_{3} \longrightarrow
\]
D.
\[
\bigcirc+\mathrm{Me} \overbrace{\|}_{\mathrm{O}}^{\mathrm{Br}}+\mathrm{AlBr}_{3} \longrightarrow
\]
\[
\mathrm{NH}_{2} \mathrm{NH}_{2}+\stackrel{\oplus}{\mathrm{OH}}
\]
Subject: Maths
\( \operatorname{Matrix} \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{3} & \mathbf{3} \\ \mathbf{2} & \mathbf{4} & \mathbf{1 0} \\ \mathbf{3} & \mathbf{8} & \mathbf{4}\end{array}\right] \) is similar to
\( A \)
\[
\left[\begin{array}{lll}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array}\right]
\]
в.
\[
\left[\begin{array}{ccc}
1 & 0 & 9 \\
0 & 1 & -2 \\
0 & 0 & -7
\end{array}\right]
\]
\( c \)
\[
\left[\begin{array}{lll}
1 & 0 & 5 \\
0 & 1 & 2 \\
0 & 4 & 1
\end{array}\right]
\]
D. Both A and B
Subject: Physics
A straight horizontal conducting rod of length \( 0.45 \mathrm{m} \) and mass \( 60 \mathrm{g} \) is suspended by two vertical wires at its ends. A current of \( 5.0 \mathrm{A} \) is set up in the rod through the wires.
(a) What magnetic field should be set up normal to the conductor in order that
the tension in the wires is zero?
(b) What will be the total tension in the wires if the direction of current is
reversed keeping the magnetic field same as before?(Ignore the mass of the wires.) \( g=9.8 m s^{-2} \)
Subject: Physics
Two boys enter a running escalator on the ground floor in a shopping mall and they do some fun on it. The first boy
repeatedly follows \( p_{1}=1 \) step up and
then \( q_{1}=2 \) steps down whereas the
second boy repeatedly follows \( p_{2}=2 \)
steps up and then \( q_{2}=1 \) step down.
Both of them move relative to escalator
with speed \( v_{r}=50 c m s^{-1} . \) If the first
boy takes \( t_{1}=250 s \) and the second boy
\( \operatorname{takes} t_{2}=50 s \) to reach the first floor
how fast is the escalator running?
Subject: Physics
Two point charges \( +\boldsymbol{q} \) and \( -\boldsymbol{q} \) are held fixed at \( (-d, 0) \) and \( (d, 0) \) respectively of a \( (x, y) \) coordinate system, then
A. the electric field \( \vec{E} \) at all points on the \( x \) -axis has the same direction
B. \( \vec{E} \) at all points on the \( y \) -axis is along \( \hat{i} \)
C. positive work is done in bringing a test charge from infinity to the origin
D. all of the above