AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Consider the matrix \( A, B, C, D \) with
order \( 2 \times 3,3 \times 4,4 \times 4,4 \times 2 \)
respectively. Let \( \boldsymbol{x}=\left(\boldsymbol{\alpha} \boldsymbol{A} \boldsymbol{B} \boldsymbol{\gamma} \boldsymbol{C}^{2} \boldsymbol{D}\right)^{3} \)
where \( \alpha \) and \( \gamma \) are scalars. Let \( |x|= \)
\( k\left|A B C^{2} D\right|^{3} . \) Then the value of \( k \)
A \( \cdot \alpha^{6} \gamma^{6} \)
в. \( \alpha \gamma \)
c. \( \alpha^{3} \gamma^{3} \)
D. \( \alpha^{6} \gamma^{12} \)
Subject: Chemistry
Which reaction does not represent autoredox or disproportionation?
A \( \cdot C l_{2}+2 O H^{-} \rightarrow C l^{-}+C l O^{-}+H_{2} O \)
B. \( 2 H_{2} O_{2} \rightarrow 2 H_{2} O+O_{2} \)
\( \mathbf{c} \cdot 2 C u^{+} \rightarrow C u^{+2}+C u \)
D. \( \left(N H_{4}\right)_{2} C r_{2} O_{7} \longrightarrow N_{2}+C r_{2} O_{3}+4 H_{2} O \)
Subject: Maths
The sum of the solution of the equation \( 2 \sin ^{-1} \sqrt{x^{2}+x+1}+ \)
\( \cos ^{-1} \sqrt{x^{2}+x}=\frac{3 \pi}{2} \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. - 1
\( c \cdot 1 \)
\( D \)
Subject: Chemistry
Select Redox reaction from the
following:
A \( . Z n+C u S O_{4} \rightarrow Z n S O_{4}+C u \)
в. \( C a O+2 H C l \rightarrow C a C l_{2}+H_{2} O \)
c. \( N a O H+2 H C l \rightarrow N a C l+H_{2} O \)
D. \( C a C O_{3} \rightarrow C a O+C O_{2} \)
Subject: Physics
Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the
acceleration due to gravity on the surface of earth is \( g \) and that on the surface of the new planet is \( g^{\prime} \), then:
A \( \cdot g^{\prime}=3 g \)
B. \( g^{\prime}=\frac{g}{3} \)
c. \( g^{\prime}=9 g \)
D. \( g^{\prime}=27 g \)
Subject: Maths
xand \( \frac{8}{9} \) are the additive inverse of each other.Then the value of \( x \) is
A \( \cdot \frac{-8}{9} \)
в. \( \frac{-4}{9} \)
c. \( \frac{-5}{9} \)
D. \( \frac{-7}{9} \)
Subject: Physics
A circular current carrying coil has a radius \( R \). The distance from the centre
of the coil on the axis where the magnetic induction will be \( \frac{1}{8} \) to its value at the centre of the coil, is :
A \( \cdot \frac{R}{\sqrt{3}} \)
в. \( R \sqrt{3} \)
c. \( 2 \sqrt{3} R \)
D. \( \frac{2}{\sqrt{3}} R \)
Subject: Maths
The vectors \( \bar{a}, \bar{b}, \bar{c} \) are equal in length and taken pairwise they make equal angles. If \( \bar{a}=\bar{i}+\bar{j}, \bar{b}=\bar{j}+\bar{k} \) and \( \bar{c} \)
makes an obtuse angle with \( x \) -axis
then \( \bar{c}= \)
A. \( \bar{i}+\bar{k} \)
the
B . \( -\bar{i}+4 \bar{j}-\bar{k} \)
c. \( \frac{1}{3}(-\bar{i}+4 \bar{j}-\bar{k}) \)
D \( \frac{1}{3}(\bar{i}-4 \bar{j}+\bar{k}) \)
Subject: Physics
A compound microscope has an objective of focal length \( 4 \mathrm{mm} \) and an eyepiece of focal length \( 25 \mathrm{mm} \). The objective produces a real image at a distance of \( 180 \mathrm{mm} \). If the eye-piece is in normal adjustment, then the magnification is
A . 45
B. 90
\( c \cdot 225 \)
D. 440
Subject: Physics
A steel ball is dropped in a viscous
liquid. The distance of the steel ball
from the top of the liquid is shown
below. The terminal velocity of the ball
is closest to:
\( \mathbf{A} \cdot 0.26 m / s \)
B. \( 0.33 \mathrm{m} / \mathrm{s} \)
\( \mathrm{c} \cdot 0.45 \mathrm{m} / \mathrm{s} \)
D. \( 0.21 \mathrm{m} / \mathrm{s} \)
Subject: Physics
Two trains \( A \) and \( B \) of length \( 400 m \)
each are moving on two parallel tracks with a uniform speed of \( 72 \mathrm{km} / \mathrm{h} \) in the same direction, with \( A \) ahead of \( B \)
decides to overtake \( A \) and accelerates
by \( 1 m / s^{2} . \) If after \( 50 s \) the guard of \( B \)
just brushes past the driver of \( A \), what
was the original distance between the
guard of \( \boldsymbol{B} \& \) driver of \( \boldsymbol{A} \) ?
Subject: Physics
In Youngs double slit experiment using monochromatic light, the fringe pattern
shifts by a certain distance on the
screen when a mica sheet of \( R . l . \) and
thickness 1.964 micron is introduced in
the path of one of the interfering waves.
The mica sheet is then removed and the
distance between the slits and the
screen is doubled, it is found that the distance between successive maxima
(or minima) now is the same as the
observed fringe shift upon the introduction of the mica sheet.
Calculate the wavelength of monochromatic light used in the experiment.
Subject: Physics
The parts of two concentric circular arcs joined by two radial lines and carries current \( i . \) The arcs subtend an
angle \( \theta \) at the center of the circle. The magnetic field at the centre 0 , is
A \( \cdot \frac{\mu_{0} i(b-a) \theta}{4 \pi a b} \)
В. \( \frac{\mu_{0} i(b-a)}{\pi-\theta} \)
c. \( \frac{\mu_{0} i(b-a) \theta}{\pi a b} \)
D. \( \frac{\mu_{0} i(a-b)}{2 \pi a b} \)
Subject: Chemistry
A hydrogen like species (atomic number \( Z \) ) is present in a higher excited
state of quantum number \( n \). This excited atom can make a transition to
the first excited state by successive emission of two photons of energies \( 10.20 e V \) and \( 17.0 e V \) respectively. Alternatively, the atom from the same excited state can make a transition to
the second excited state by successive emission of two photons of energy \( 4.25 e V \) and \( 5.95 e V \) respectively.
Determine the value of \( Z \).
A . 1
B. 2
\( c \cdot 3 \)
D. 4
Subject: Physics
A nucleus \( X^{235} \) splits into two nuclei having the mass numbers in the ratio
\( 2: 1 . \) The ratio of the radii of those two
nuclei is:
A .2: 1
B. 1: 2
c. \( 2^{1 / 3}: 1 \)
D. \( 1: 2^{1 / 3} \)
Subject: Chemistry
What are the oxidation states of
phosphorus in the following:
(i) \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \)
(ii) \( \boldsymbol{P C l}_{3} \)
(iii) \( \boldsymbol{C a}_{3} \boldsymbol{P}_{2}(\text { iv }) \)
\( N a_{3} P O_{4}(v) P O F_{3} ? \)
Subject: Physics
A person has a tuning fork that sounds with a frequency of \( 250 H z . \) The person strikes the fork and plays a white key that sounds with a frequency of \( 220 H z \) Calculate the beat frequency that the piano person hears?
A. \( 0 H z \)
\( z \)
B. \( 0.8 \mathrm{Hz} \)
c. \( 1.25 H z \)
D. \( 30 H z \)
E . \( 450 \mathrm{Hz} \)
Subject: Physics
Assertion
Gauss's law show diversion when
inverse square law is not obeyed.
Reason

Gauss's law is a consequence of
conservation of charges.
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 walls of an enclosure are
maintained at a steady temperature \( T \) When two similarly calibrated thermometers are placed inside the
enclosure, they give the same reading \( \boldsymbol{T} \) after thermal equilibrium has been established. Which statement correctly describes the required conditions?
A. under all circumstances
B. only if they absorb radiation at equal rates
c. only if they have equal thermal capacities
D. only if both are perfect absorbers
Subject: Chemistry
Mixture of \( K B r \) and \( K B r O_{3} \) in acidic
medium can be used as brominating
agent
The chemical reaction is, \( 5 B r^{-}+ \)
\( \boldsymbol{x} \boldsymbol{B r} \boldsymbol{O}_{3}^{-}+\boldsymbol{6} \boldsymbol{H}^{+} \rightarrow \boldsymbol{3} \boldsymbol{B r}_{\boldsymbol{y}}+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O} \)
Then \( \boldsymbol{x}+\boldsymbol{y} \) is :
\( A \cdot 6 \)
B. 3
\( c .5 \)
D. 1
Subject: Physics
A particle starts from the point \( 0.8 \mathrm{m} \) and moves with a uniform velocity of 3 \( \mathrm{m} / \mathrm{s} . \) what is the angular momentum of the particle after 5 seconds about origin.mass of the particle is \( 1 \mathrm{kg} \)
A \( \cdot 12 k g m^{2} / \mathrm{s} \)
B. \( 24 k g m^{2} / s \)
\( \mathbf{c} \cdot 32 k g m^{2} / s \)
D. \( 44 \mathrm{kgm}^{2} / \mathrm{s} \)
Subject: Chemistry
Assertion
Following reaction is a
disproportionation reaction:
\( \boldsymbol{B} \boldsymbol{r}_{2}+\boldsymbol{2} \boldsymbol{O} \boldsymbol{H}^{-} \rightarrow \boldsymbol{B} \boldsymbol{r} \boldsymbol{O}^{-}+\boldsymbol{B} \boldsymbol{r}^{-}+ \)
\( 2 H_{2} O \)
Reason
\( B r_{2} \) is oxidized to \( B r O^{-} \) as well as
reduced to \( B r^{-} \)
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 car is initially traveling due north at \( 23 m / s . \) Find the velocity of the car after
\( 4 s \) if its acceleration is \( 2 m / s^{2} \) due south. \( (\text { in } \mathrm{m} / \mathrm{s}): \)
A. 10 due south
B. 15 due north
c. 14 due north
D. 12 due south
Subject: Maths
What is the solution of \( (1+2 x) d y- \)
\( (1-2 y) d x=0 ? \)
A. \( x-y-2 x y=c \)
в. \( y-x-2 x y=c \)
c. \( y+x-2 x y=c \)
D. \( x+y+2 x y=c \)
Subject: Chemistry
In the electroysis of \( A g N O_{3} \) solution,
\( 0.7 \mathrm{g} \) of \( \mathrm{Ag} \) is deposited after a certain period of time. Calculate the quantity of electricity required in coulomb. (Molar mass of \( A g \) is \( 107.9 g \) mol \( ^{-1} \) ).
Subject: Maths
\( |\vec{a}+\vec{b}|^{2}-|\vec{a}-\vec{b}|^{2} \) is equal to
\( \mathbf{A} \cdot 4|\vec{a}||\vec{b}| \sin (\theta) \)
B . \( 4|\vec{a}||\vec{a}| \sin (\theta) \)
\( \mathbf{c} \cdot \mathbf{4}|\vec{a}||\vec{b}| \cos (\theta) \)
\( \mathbf{D} \cdot \mathbf{4}|\vec{a}||\vec{b}| \tan (\theta) \)
Subject: Chemistry
Point out the correct statement
amongst the following.
\( \mathbf{A} \)
\( \left[C u\left(C N_{4}\right)\right]^{3-} \) has tetrahedral geometry and \( d s p^{2} \)
hybridization
B. \( \left[N i\left(C N_{6}\right)\right]^{4-} \) is octahedral and \( \mathrm{Ni} \) had \( d^{2} s p^{3} \)
hybridization
\( ^{\mathbf{C}} \cdot\left[Z n B r_{4}\right]^{2-} \) is tetrahedral and diamagnetic
D. \( \left[C r\left(N H_{3}\right)_{6}\right]^{3+} \) has octahedral geometry and \( s p^{3} d^{2} \)
hybridization
Subject: Chemistry
Write balanced net ionic equation for
the following reaction in acidic solution
\( \boldsymbol{H} \boldsymbol{S} \boldsymbol{O}_{4}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{A} \boldsymbol{s}_{4}(\boldsymbol{s})+\boldsymbol{P} \boldsymbol{b}_{3} \boldsymbol{O}_{4}(\boldsymbol{s}) \rightarrow \)
\( \boldsymbol{P b S O}_{4}(\boldsymbol{s})+\boldsymbol{H}_{2} \boldsymbol{A} \boldsymbol{s} \boldsymbol{O}_{4}^{-}(\boldsymbol{a} \boldsymbol{q}) \)
Subject: Maths
f \( a+b+c=8 \), then the value of
\( (a-4)^{3}+(b-3)^{3}+(c-1)^{3}-3(a- \)
4) \( (b-3)(c-1) \) is:
\( A \cdot 2 \)
B. 4
\( c \cdot 1 \)
\( D \)
Subject: Maths
If \( \boldsymbol{y}=\sec ^{-1}\left(\frac{\boldsymbol{x}+\mathbf{1}}{\boldsymbol{x}-\mathbf{1}}\right)+\sin ^{-1}\left(\frac{\boldsymbol{x}-\mathbf{1}}{\boldsymbol{x}+\mathbf{1}}\right) \)
then \( \frac{d y}{d x} \) is equal to
A .
B. \( x+1 \)
\( c \cdot 1 \)
D. -
Subject: Chemistry
The thermal decomposition of a compound is of first order. If \( 50 \% \) of a sample of the compound is decomposed in 120 min how long will it
take for \( 90 \% \) of the compound to decompose?
A. 412 min
B. 399 min
c. \( 450 \mathrm{min} \)
D. 499 min
Subject: Chemistry
Assertion
Transition of electron between \( \boldsymbol{p}_{\boldsymbol{x}} \) and \( \boldsymbol{p}_{\boldsymbol{y}} \)
would not lead to an spectral line.
Reason
\( p \) -orbitals are degenerate orbitals.
Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Both Assertion and Reason are correct and the Reason is the correct explanation of Assertion
B. Both Assertion and Reason are correct but the Reason is not the correct explanation of the Assertion
c. Assertion is correct but the Reason is incorrect
D. Assertion is incorrect and Reason is correrct
Subject: Biology
Statement - 1: During secondary growth in dicot stem the wood formed in winter
is called late wood.
Statement - 2: In spring season cambium becomes inactive therefore it
does not produce xylary elements. Which of the following option is true for
the above given statements?
A. Only statement 1 is correct
B. Only statement 2 is correct
c. Both the statements are correct
D. Both the statements are incorrect
Subject: Physics
A wire with an area of cross-section as
\( 10 m m^{2} \) has a resistance of \( 5 \Omega, \) when a
potential difference across its ends is
\( 25 V . \) Calculate the drift velocity of electrons. Given the number density of
electrons as \( 5 \times 10^{20} \) electrons per
cubic meter \( \left(e / m^{-3}\right) \)
Subject: Chemistry
\( Z n S \) is not precipitated by passing
\( \boldsymbol{H}_{2} \boldsymbol{S} \) in acidic medium but \( \boldsymbol{C} \boldsymbol{u} \boldsymbol{S} \)
precipitated. The reason for it is:
\( \mathbf{A} \cdot K_{s p} C u S<<K_{s p} Z n S \)
B . \( K_{s p} C u S>>K_{s p} Z n S \)
c. \( K_{s p} C u S=K_{s p} Z n S \)
D. None of these
Subject: Chemistry
Which of the reagents listed below
could be added to water to make \( 0.1 \mathrm{M} \)
solution of \( \boldsymbol{N} \boldsymbol{H}_{4} \) ions?
¡. \( \boldsymbol{N} \boldsymbol{H}_{\mathbf{3}} \)
ii. \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{C l} \)
A. \( N H_{3} \) because it is a strong electrolyte
B. \( N H_{4} C l \) because it is a strong electrolyte
C. \( N H_{3} \) because it is a weak electrolyte
D. \( N H_{4} C l \) because it is a weak electrolyte
Subject: Physics
A step down transformer has 50 turns
on secondary and 1000 turns on primary winding. If a transformer is connected
to \( 220 V, 1 A \) A.C. source, what is output
current of the transformer?
A \( \cdot \frac{1}{20} A \)
B. 20 A
\( c \cdot 100 A \)
D. 2 A
Subject: Physics
A bullet of mass \( m \) is fired into a large
block of wood of mass \( \mathrm{M} \) with velocity \( \mathrm{v} \) The final velocity of the system is?
\( ^{\mathbf{A}} \cdot\left(\frac{m}{M-m}\right)^{v} \)
в. \( \left(\frac{m+M}{M}\right) v \)
\( ^{\mathbf{c}} \cdot\left(\frac{M-m}{M}\right) v \)
D. \( \left(\frac{m}{m+M}\right) v \)
Subject: Maths
A cow is tied to a pole, fixed to the
midpoint of a side of a square field of dimensions \( 40 m \times 40 m \), by means of
\( 14 m \) long rope. Find the area that the
cow can graze.
A \( .254 m^{2} \)
в. \( 308 m^{2} \)
c. \( 245 \mathrm{m}^{2} \)
D. \( 380 m^{2} \)
Subject: Maths
A particle is moving in a straight line such that its distance at any time \( t \) is given by \( s=\frac{t^{4}}{4}-2 t^{3}+4 t^{2}-7 . \) The
acceleration of the particle is minimum
when \( t= \)
\( A \cdot 1 \)
B. 2
\( c .3 \)
\( D \)
Subject: Maths
The lengths of the sides of some triangles are given, which of them is not a right angled triangle?
\( A \cdot 5 \mathrm{cm}, 12 \mathrm{cm}, 13 \mathrm{cm} \)
B. \( 7 \mathrm{cm}, 24 \mathrm{cm}, 25 \mathrm{cm} \)
\( \mathrm{c} .5 \mathrm{cm}, 8 \mathrm{cm}, 10 \mathrm{cm} \)
D. \( 3 \mathrm{cm}, 4 \mathrm{cm}, 5 \mathrm{cm} \)
Subject: Chemistry
The correct order of increasing bond length of \( \mathrm{C}-\mathrm{H}, \mathrm{C}-\mathrm{O}, \mathrm{C}-\mathrm{C} \) and \( \mathrm{C}=\mathrm{C} \) is :
A. C-H<C-O<C-C<C=C
B. C-H<C=C<C-O<C-C
c. \( c-c<c=c<c-0<c-H \)
D. C-O<C-H<C-C<C=C
Subject: Physics
A tank is filled with water and two holes
\( A \) and \( B \) are made in it. For getting same
\( \boldsymbol{h} \)
ranges, ratio of \( \frac{\pi}{h^{\prime}} \) is
\( A \)
B. 1 \( \overline{2} \)
\( c \cdot 1 \)
3
\( D \)
Subject: Maths
In a circle of diameter \( 10 \mathrm{cm} \), the length of each of 2 equal and parallel chords is \( 8 \mathrm{cm}, \) then the distance between these
two chords is
A. \( 4 \mathrm{cm} \)
B. \( 5 \mathrm{cm} \)
\( c \cdot 6 \mathrm{cm} \)
D. \( 7 \mathrm{cm} \)
Subject: Physics
Two coherent sources separated by
distance d are radiating in phase having wavelength \( \lambda \). A detector moves
in a big circle around the two sources in
the plane of the two sources. The angular position of \( n=4 \) interference maxima is given as
A \( \cdot \sin ^{-1} \frac{n \lambda}{d} \)
B. \( \cos ^{-1} \frac{4 \lambda}{d} \)
c. \( \tan ^{-1} \frac{d}{4 \lambda} \)
D. \( \cos ^{-1} \frac{\lambda}{4 d} \)
Subject: Maths
If the points \( (a, 0),(0, b) \) and (1,1) are
collinear, which of the following is true?
A \( \cdot \frac{1}{a}+\frac{1}{b}=2 \)
B. \( \frac{1}{a}-\frac{1}{b}=1 \)
c. \( \frac{1}{a}-\frac{1}{b}=2 \)
D. \( \frac{1}{a}+\frac{1}{b}=1 \)
Subject: Physics
A ball of mass \( m \) is thrown vertically up
with an initial velocity so as to reach a
height \( h . \) The correct statement is:
A. potential energy of the ball at the ground is \( m g h \)
B. kinetic energy imparted to the ball at the ground is zero
c. kinetic energy of the ball at the highest point is \( m g h \)
D. potential energy of the ball at the highest point is \( m g h \)
Subject: Physics
\( H-\operatorname{atom} \) is of \( _{-}-_{-}----k g \)
\( \mathbf{A} \cdot 1.675 \times 10^{-27} \)
B . \( 1.673 \times 10^{-27} \)
C \( \cdot 9.109 \times 10^{-31} \)
D. \( 3.348 \times 10^{-27} \)
Subject: Physics
The dimension of magnetic field in \( M, L, T \) and \( C \) (Coulomb) is given as:
A. \( M L T^{-1} C^{-1} \)
B. \( M T^{2} C^{-2} \)
c. \( M T^{-1} C^{-1} \)
D. \( M L T^{-2} C^{-1} \)
Subject: Physics
Two particles \( A \) and \( B \) initially at rest move towards each other under a
mutual force of attraction. The speed of
center of mass at the instant when the
speed of \( A \) is \( v \) and the speed of \( B \) is \( 2 v \) is
\( A \)
B. Zero
c. \( 2 v \)
D. \( \frac{3 v}{2} \)
Subject: Maths
If a random variable \( X \) takes value 0 and
1 with respective probabilities \( \frac{2}{3} \) and \( \frac{1}{3} \) then the expected value of \( X \) is
A \( \cdot \frac{2}{3} \)
B. \( \frac{1}{3} \)
c. 0
D.
Subject: Physics
If the length of the cylinder is measured as \( 25 \mathrm{mm} \), the diameter is \( 3.09 \mathrm{cm} \) and mass of the cylinder is measured as \( 50.0 \mathrm{gm} \) find the density of the cylinder in proper significant figures.(in \( \boldsymbol{g} \boldsymbol{m} / \boldsymbol{c m}^{3} \boldsymbol{)} \)
A . 2.700 \( g m / c m^{3} \)
в. 2.7 \( g m / c m^{3} \)
c. \( 0.27 g m / c m^{3} \)
D. \( 2.70 g m / c m^{3} \)
Subject: Maths
\( \operatorname{Let} \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R}, \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{f}(\boldsymbol{x})+\mathbf{3} \boldsymbol{x}-\mathbf{1} \)
then the least value of function \( y= \)
\( \boldsymbol{g}(|\boldsymbol{x}|) \) is
A. \( -\frac{9}{4} \)
B. \( -\frac{5}{4} \)
c. -2
D. -
Subject: Maths
A train 110 metres long is running with a speed of \( 60 \mathrm{km} / \mathrm{hr} \). In what time it pass
a man who is running at 6 kmph in the direction opposite to that in which the train is going?
A . 5 sec
B. 6 sec
\( c \cdot 7 \sec \)
D. 10 sec
Subject: Chemistry
If the wavelength is equal to the distance travelled by the electron in one second, then:
\( A \cdot \lambda=\frac{h}{p} \)
B. \( \lambda=\frac{h}{m} \)
\( c \cdot \lambda=\sqrt{\frac{h}{p}} \)
D. \( \lambda=\sqrt{\frac{h}{m}} \)
Subject: Physics
Assertion
In an elastic collision of two bodies, the momentum and energy of the system are conserved.
Reason
If two bodies stick to each other, after
colliding, the collision is said to be perfectly inelastic.
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 particle of mass \( 1 \mathrm{gm} \) and charge \( 1 \mu C \) is held at rest on a frictionless horizontal surface at distance \( 1 \mathrm{m} \) from the fixed charge 2 mC. If the particle is released, it will be repelled. The speed of the particle when it is at a distance of
\( 10 \mathrm{m} \) from the fixed charge
A \( \cdot 60 m s^{-1} \)
B. \( 100 \mathrm{ms}^{-1} \)
c. \( 90 m s^{-1} \)
D. \( 180 \mathrm{ms}^{-1} \)
Subject: Maths
Let \( \vec{p} \) is the position vector of the
orthocentre \( \& \vec{g} \) is the position vector of the centroid of the triangle \( A B C \) where circumcentre is the origin. If \( \overrightarrow{\boldsymbol{p}}=\boldsymbol{K} \overrightarrow{\boldsymbol{g}} \)
then \( \boldsymbol{K}= \)
A . 3
B. 2
c. \( \frac{1}{3} \)
D. \( \frac{2}{3} \)
Subject: Physics
Assertion
When a body dropped from a height explodes in mid-air, its center of mass
keeps moving in vertically downward
direction
Reason
Explosion occur under internal forces
only. External force 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. Both Assertion and Reason are incorrect
Subject: Maths
\( \mathbf{I f A}=(\mathbf{1}, \mathbf{2}, \mathbf{3}), \mathbf{B}=(\mathbf{2}, \mathbf{3}, \mathbf{4}) \) and \( \mathbf{C} \) is a
point of trisection of AB such that \( \mathbf{C}_{\mathbf{x}}+ \) \( \mathbf{C}_{\mathbf{y}}=\frac{\mathbf{1 3}}{\mathbf{3}} \) then \( \mathbf{C}_{\mathbf{z}}= \)
A \( \cdot \frac{10}{3} \)
B. \( \frac{11}{3} \)
c. \( \frac{11}{2} \)
D. 11
Subject: Chemistry
Assertion
Dodecyl pyridinium chloride forms
positive micelles in water.
Reason
Dodecyl pyridinium chloride possesses hydrophobic and hydrophilic moities in
its cationic part.
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
An electron of charge \( e \) and mass \( m \) is
moving in a circular loop of radius \( \boldsymbol{r} \)
with a uniform angular speed \( \omega . \) Then
which of the following statements are
correct?
This question has multiple correct options
A. The equivalent current flowing in the circular path is proportional to \( r^{2} \)
B. The magnetic moment due to circular current loop is independent of \( m \)
C. The magnetic moment due to circular loop is equal to \( 2 e / m \) times the angular momentum of the electron
D. The angular momentum of the particle is proportional to the areal velocity of electron
Subject: Maths
Evaluate \( \lim _{x \rightarrow 4} \frac{3-\sqrt{5+x}}{1-\sqrt{5-x}} \)
A \( \cdot \frac{1}{3} \)
B. \( -\frac{1}{3} \)
\( c \cdot \frac{2}{3} \)
D. \( -\frac{2}{3} \)
Subject: Physics
Assertion
An electric bulb becomes dim, when the
electric heater in parallel circuit is switched on.
Reason
Dimness decreases after sometime.
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
Show that the determinant \( \boldsymbol{a}^{2}+\boldsymbol{b}^{2}+\boldsymbol{c}^{2} \quad \boldsymbol{b} \boldsymbol{c}+\boldsymbol{c} \boldsymbol{a}+\boldsymbol{a} \boldsymbol{b} \quad \boldsymbol{b} \boldsymbol{c}+\boldsymbol{c} \boldsymbol{a} \)
\( \boldsymbol{b} \boldsymbol{c}+\boldsymbol{c} \boldsymbol{a}+\boldsymbol{a} \boldsymbol{b} \quad \boldsymbol{a}^{2}+\boldsymbol{b}^{2}+\boldsymbol{c}^{2} \quad \boldsymbol{b} \boldsymbol{c}+\boldsymbol{c} \boldsymbol{a} \)
\( \boldsymbol{b} \boldsymbol{c}+\boldsymbol{c} \boldsymbol{a}+\boldsymbol{a b} \quad \boldsymbol{b c}+\boldsymbol{c a}+\boldsymbol{a b} \quad \boldsymbol{a}^{2}+\boldsymbol{b}^{2} \)
is always non-negative.
Subject: Maths
If \( z_{1}, z_{2}, \dots, z_{n} \) lie on \( |z|=r \) and \( \operatorname{Re}\left(\sum_{j=1}^{n} \sum_{k=1}^{n} \frac{z_{j}}{z_{k}}\right)=0, \) then
This question has multiple correct options
\( ^{\mathbf{A}} \cdot \sum_{j=1}^{n} z_{j}=0 \)
\( ^{\mathbf{B}} \cdot\left|\sum_{j=1}^{n} z_{j}\right|=0 \)
\( ^{\mathrm{c}} \cdot \sum_{j=1}^{n} \frac{1}{z_{j}}=0 \)
D. None of these