AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Assertion
\( \boldsymbol{\operatorname { T r }}(\boldsymbol{A})=\mathbf{0} \)
Reason
\( |A|=0 \)
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
Three boys rahul, raju, and ravi stand at
three places and clap their hands
simultaneously. Calculate the time between the clap and the echo of the clap of each body. Infer how can the
time between the clap and echo of the
clap varied. Velocity of sound in air is
\( \mathbf{3 3 0} \quad \boldsymbol{m s}^{-1} \)
Subject: Maths
A student answers a multiple choice question with 5 alternatives, of which
exactly one is correct. The probability that he knows the correct answer is
\( \boldsymbol{p}, \boldsymbol{0}<\boldsymbol{p}<1 . \) If he does not know the
correct answer, he randomly ticks one answer. Given that he has answered the
question correctly, the probability that he did not tick the answer randomly, is
A. \( \frac{3 p}{4 p+3} \)
в. \( \frac{5 p}{3 p+2} \)
c. \( \frac{5 p}{4 p+1} \)
D. \( \frac{4 p}{3 p+1} \)
Subject: Chemistry
Heating of 2 -chloro-1-phenylbutane with
EtOK / EtOH gives \( X \) as the major
product. Reaction of \( \boldsymbol{X} \) with
\( \boldsymbol{H} \boldsymbol{g}(\boldsymbol{O} \boldsymbol{A} \boldsymbol{c})_{2} / \boldsymbol{H}_{2} \boldsymbol{O} \) followed by \( \boldsymbol{N} \boldsymbol{a} \boldsymbol{B} \boldsymbol{H}_{4} \)
gives \( Y \) as the major product. \( Y \) is :
\( A \)
в.
\( c \)
\( D \)
Subject: Chemistry
Zeise's salt is :
A \( \cdot \operatorname{Fe}\left(\eta^{5}-C_{5} H_{5}\right)_{2} \)
B \( \cdot \operatorname{Cr}\left(\eta^{6}-C_{6} H_{6}\right)_{2} \)
c. \( _{K}\left[P t\left(\eta^{2}-C_{2} H_{4}\right) C l_{3}\right] \)
D. \( K\left[P t\left(\eta^{2}-C_{2} H_{4}\right)_{2} C l_{2}\right] \)
Subject: Physics
The photo electric work function for a metal surface is 4.125 eV. The cut-off
wavelength for this surface
A \( \cdot 4125 ~ A^{\circ} \)
B. 2062.5 \( A^{\circ} \)
c. \( 3000 A^{\circ} \)
D. 6000A \( ^{\text {о }} \)
Subject: Physics
A capacitor of capacitance \( \boldsymbol{C}=\mathbf{1 5 p} \boldsymbol{F} \)
is charged with voltage \( V=500 V . \) The
electric field inside the capacitor with
dielectric is \( 10^{6} V / m \) and the area of the plate is \( 10^{-4} m^{2}, \) then the dielectric
constant of the medium is : \( \left(\varepsilon_{0}=\right. \)
\( 8.85 \times 10^{-12} \) in S.l.units
A. 12.47
B. 8.47
c. 10.85
D. 14.85
Subject: Chemistry
The de Broglie wavelength of a particle with mass \( 1 \mathrm{gm} \) and velocity \( 100 \mathrm{m} / \mathrm{s} \) is:
A \( \cdot 6.63 \times 10^{-33} m \)
B. \( 6.63 \times 10^{-34} m \)
D. \( 6.635 \times 10^{-35} m \)
Subject: Maths
The value of the limit \( \lim _{x \rightarrow 1} \frac{\sin \left(e^{x-1}-1\right)}{\log x} \)
is
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( e \)
\( c \cdot \frac{1}{e} \)
D.
Subject: Physics
A straight wire of 0.3 m carrying a current of \( 2 \mathrm{A} \) in the downward direction
is placed in a magnetic field of \( 0.1 \mathrm{T} \) as shown in the figure. Find out the magnitude of the force on the wire?
A . \( 0.06 N \)
B. 2.0 N
c. \( 6.7 \mathrm{N} \)
D. 0.15N
E. 0.015N
Subject: Physics
A balloon is blown up to a radius \( R \). It is
then has a positive charge \( +Q \) added to it. Air is then let out so that the radius
reduces to \( R / 2 \), however, the net charge remains the same.
How is the charge density affected by the reducing of the radius?
A. The charge density increases.
B. The charge density is unaffected.
c. The charge density decreases.
D. There is not enough information to answer the question
Subject: Physics
A particle of charge \( q \) and mass \( m \) moves in a circular orbit of radius r with
angular speed \( \omega . \) The ratio of the
magnitude of its magnetic moment to that of its angular momentum depends
on
A. \( \omega \) and \( q \)
B. \( \omega, q \) and \( m \)
c. \( q \) and \( m \)
D. \( \omega \) and \( m \)
Subject: Maths
Find the inverse of the following
functions:
\( \boldsymbol{f}(\boldsymbol{x})=\sin ^{-1}\left(\frac{\boldsymbol{x}}{\mathbf{3}}\right), \boldsymbol{x} \in[-\mathbf{3}, \mathbf{3}] \)
\( \operatorname{then} \boldsymbol{f}^{-1}(\boldsymbol{\pi} / \mathbf{2}) \)
Subject: Physics
Suppose a vertical tunnel is dug along
the diameter of the earth, assumed to
be a sphere of uniform mass density \( \rho \)
If a body of mass \( m \) is thrown in this
tunnel, its acceleration at a distance \( y \)
from the centre is given by:
A.
\[
\frac{4 \pi}{3} G \rho y m
\]
B.
\[
\frac{3}{4} \pi \rho y
\]
\( c \)
\[
\frac{4}{3} \pi \rho y
\]
\( D \)
\[
\frac{4}{3} \pi G \rho y
\]
Subject: Physics
Q Type your question.
\( n=v \) an with its centre al origin.
Current \( I=1 A \) is lead to the sphere in
one of the wires lying (on y-axis) and in the other wire (on x-axis) it is lead away
from the sphere. A uniform and
constant external magnetic field
exists in positive z-direction and has
magnitude \( B_{o}=2 T . \) Then find the
magnitude of magnetic force
(in newtons) on the solid sphere due to
external magnetic field.
\( A \)
B. 4
\( c .5 \)
\( D \)
Subject: Physics
Assertion
The frequency of a sound wave changes
as it travels from one medium to
another medium.
Reason
The velocity of the wave changes as well
as the wavelength if the medium
changes.
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
Let \( I_{A} \) and \( I_{B} \) be moments of inertia of \( a \)
body about two axes \( A \) and \( B \)
respectively. The axis \( A \) passes through
the centre of mass of the body but \( B \)
does not
A \( \cdot I_{A}<I_{B} \)
B. If \( I_{A}<I_{B} \)
C. If the axes are parallel, \( I_{A}<I_{B} \)
D. If the axes are not parallel, then \( I \geq I_{B} \)
Subject: Chemistry
Which one of the following complexes is not expected to exhibit isomerism?
\( \mathbf{A} \cdot\left[N i\left(N H_{3}\right)_{4}\left(H_{2} O\right)_{2}\right]^{2+} \)
B \( \cdot\left[P t\left(N H_{3}\right)_{2} C l_{2}\right] \)
\( \mathbf{c} \cdot\left[N i\left(N H_{3}\right)_{2} C l_{2}\right] \)
D. \( \left[N i(e n)_{3}\right]^{2+} \)
Subject: Maths
Function \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}^{2}-\mathbf{2}}{\sqrt{\mathbf{1}+\boldsymbol{x}^{2}}} \)
A. is always increasing
B. is always decreasing
C. has exactly one point of minima
D. has exactly one point of maxima
Subject: Chemistry
Which of the following pairs of ions are isoelectronic and isostructural?
\( A \cdot S O_{3}^{2-}, N O_{3}^{-} \)
B . \( \mathrm{ClO}_{3}^{-}, \mathrm{CO}_{3}^{2} \)
\( \mathrm{c} \cdot \mathrm{CO}_{3}^{2-}, \mathrm{NO}_{3} \)
D. \( C l O_{3}^{-}, S O_{3}^{2} \)
Subject: Physics
Using \( \boldsymbol{E}=\boldsymbol{m} \boldsymbol{c}^{2}, \) find out the energy
released, when \( 2 u \) of mass is destroyed
completely Take \( 1 \boldsymbol{u}=\mathbf{1 . 6 6} \times \mathbf{1 0}^{-\mathbf{2 7}} \mathbf{k g} \)
A. \( 4.65 \mathrm{MeV} \)
B. \( 3627 \mathrm{MeV} \)
c. \( 91.5 \mathrm{MeV} \)
D. \( 1865 M e V \)
Subject: Chemistry
\( \boldsymbol{P b S}+\boldsymbol{H}_{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}+\ldots \ldots \)
A \( . P b S O_{3} \)
в. \( P b S O_{4} \)
c. \( P b\left(S O_{4}\right)_{2} \)
D. \( P b\left(S O_{4}\right)_{3} \)
Subject: Physics
For the damped oscillator shown in Fig
the mass of the block is \( 200 g, k= \)
\( 80 N m^{-1} \) and the damping constant \( b \)
is \( 40 g s^{-1} \) Calculate.
(a) The period of oscillation,
(b) Time period for its amplitude of
vibrations to drop to half of its initial
value
(c) The time for the mechanical energy
to drop to half initial value.
Subject: Physics
A group of \( N \) cells whose emf varies
directly with the internal resistance as
per the equation \( \boldsymbol{E}_{\boldsymbol{N}}=\mathbf{1 . 5 r}_{\boldsymbol{N}} \) are
connected as shown in the figure above.
The current \( I \) in the circuit is:
\( \mathbf{A} \cdot 5 \cdot 1 A \)
B. \( 0.51 A \)
c. \( 1.5 A \)
D. 0.15 A
Subject: Physics
The force of repulsion between two similar magnetic poles each of strength
\( 2 A m \) at a distance \( 2 m \) from each other
in vacuum is :
A \( \cdot 10^{-5} N \)
В. \( 10^{-7} N \)
c. \( 10^{-3} N \)
D. \( 2 \times 10^{-7} N \)
Subject: Physics
A particle rotates along a circle of radius \( R=\sqrt{2} \mathrm{m} \) with an angular acceleration \( \boldsymbol{\alpha}=\frac{\boldsymbol{\pi}}{\boldsymbol{4}} \boldsymbol{r} \boldsymbol{a} \boldsymbol{d} / \boldsymbol{s}^{2} \) starting
from rest. Calculate the magnitude of average velocity of the particle over the time it rotates a quarter circle.
Subject: Physics
A \( 10 \mathrm{N} \) force applied on a body produces in it an acceleration of \( 2 m s^{-2}, \) then the mass of the body is
\( A \cdot 10 \mathrm{kg} \)
B. 2 kg
\( c .5 \mathrm{kg} \)
\( D \cdot 6 \mathrm{kg} \)
Subject: Chemistry
In order to prepare a 1 amine from an alkyl halide with simultaneous addition
of one \( C H_{2} \) group in the carbon chain, the reagent used as source of nitrogen is:
A. Sodium amide \( N a N H_{2} \)
B. Sodium azide \( N a N_{3} \)
c. Potassium cyanide \( K C N \)
D. Potassium phthalimide \( C_{6} H_{4}(C O)_{2} N^{-} K \)
Subject: Physics
If \( n \) is the orbit number of the electron
in a hydrogen atom, the correct statement among the following is
A. Electron energy increases as \( n \) increases
B. Hydrogen emits infrared rays for the electron transition from \( n=\infty \) to \( n=1 \)
C. Electron energy is zero for \( n=1 \)
D. Electron energy varies as \( n^{2} \)
Subject: Chemistry
In the reaction of \( H_{2} O_{2} \) with acidified
\( \boldsymbol{K}_{4}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right], \) the oxidation state of
iron changes to:
\( \mathbf{A} \cdot+2 \) from +1
B. +3 from 0
\( \mathbf{c} \cdot+3 \) from +2
\( \mathbf{D} \cdot+2 \) from 0
Subject: Chemistry
Adsorption of gas follows Freundlich
adsorption isotherm. In the given plot, \( x \)
is the mass of the gas absorbed on
mass \( m \) of the adsorbent at pressure \( p \)
is proportional to:
\( \mathbf{A} \cdot P^{\frac{1}{4}} \)
B. \( P^{2} \)
\( c \cdot P \)
\( D \cdot P^{\frac{1}{2}} \)
Subject: Maths
From a point 0 in the interior of a
\( \Delta A B C, \) perpendiculars \( 0 D, O E, \& \) OF
are drawn to the sides BC, CA \& AB
respectively. Prove that
[i] \( A F^{2}+B D^{2}+C E^{2}=O A^{2}+ \)
\( O B^{2}+O C^{2}-O D^{2}-O E^{2}-O F^{2} \)
[ii] \( A F^{2}+B D^{2}+C E^{2}=A E^{2}+ \)
\( C D^{2}+B F^{2} \)
Subject: Chemistry
In the hydrogen atom spectrum
\( \lambda_{3-1} \) and \( \lambda_{2-1} \) represent wavelengths emitted due to transition from second
and first excited states to the ground state respectively. The value of \( \frac{\lambda_{3-1}}{\lambda_{2-1}} \) is :
\( \mathbf{A} \cdot 27 / 32 \)
в. \( 32 / 27 \)
c. \( 4 / 9 \)
D. \( 9 / 4 \)
Subject: Physics
A transformers has an efficiency of \( 80 \% \)
.It is connected to a power output of kw and 100 V.If the secondary voltage is \( 240 \mathrm{V} \),the secondary current is
A \( .4 .6 \mathrm{A} \)
B. 40 A
\( c \cdot 4.3 \mathrm{A} \)
D. 13.3 A
Subject: Maths
\( \boldsymbol{A}(\boldsymbol{3}, \boldsymbol{2}, \boldsymbol{0}), \boldsymbol{B}(\boldsymbol{5}, \boldsymbol{3}, \boldsymbol{2}), \boldsymbol{C}(-\boldsymbol{9}, \boldsymbol{6},-\boldsymbol{3}) \) are
three points forming a triangle and \( A D \) is the bisectors of the \( \angle B A C \) meet BC
at \( D, \) then co-ordinates of \( D \) are:
\( ^{\mathbf{A}} \cdot\left(\frac{17}{16}, \frac{57}{16}, \frac{28}{16}\right) \)
в. \( \left(\frac{38}{16}, \frac{57}{16}, \frac{17}{16}\right) \)
\( ^{\mathbf{C}} \cdot\left(\frac{38}{16}, \frac{17}{16}, \frac{57}{166}\right) \)
D. \( \left(\frac{57}{16}, \frac{38}{16}, \frac{17}{16}\right) \)
Subject: Physics
A block tied between two identical
springs is in equilibrium. If upper spring is cut, then the acceleration of
the block just after the cut is \( 6 m s^{-2} \)
Now if instead of upper string lower spring is cut, then the acceleration of
the block just after the cut will be
(Take \( \left.g=10 m / s^{2}\right) \)
A \( .1 .25 \mathrm{ms}^{-2} \)
B. \( 4 m s^{-2} \)
\( \mathrm{c} \cdot 10 \mathrm{ms}^{-2} \)
D. \( 2.5 \mathrm{ms}^{-2} \)
Subject: Chemistry
\( H I \) was heated in a sealed tube at
\( 400^{\circ} \mathrm{C} \) till the equilibrium was reached.
\( H I \) was found to be \( 22 \% \) decomposed.
The equilibrium constant for dissociation is:
A . 1.99
B. 0.0199
c. 0.0796
D. 0.282
Subject: Chemistry
In the dichromate dianion, the nature of
bonds are:
A. four equivalent \( C r-O \) bonds
B. six equivalent \( C r-O \) bonds and one \( O-O \) bond
C . six equivalent \( C r-O \) bonds and one \( C r-C r \) bond
D. six non-equivalent \( C r-O \) bonds
E. six equivalent \( C r-O \) bonds and one \( C r-O-C r \)
bond
Subject: Chemistry
In which of the following salts, cation does not undergo hydrolysis but anion undergoes hydrolysis?
A. \( B a C O_{3} \)
в. \( C a C l_{2} \)
\( \mathrm{c} \cdot \mathrm{K}_{2} \mathrm{CO}_{3} \)
D. \( \operatorname{NaNO}_{3} \)
Subject: Chemistry
mole of \( \boldsymbol{P C l}_{5} \) is heated with 0.2 mole
of chlorine in a one litre vessel till
equilibrium is established.At equilibrium if 0.8 mole of chlorine is
present in the vessel, the equilibrium
constant for the dissociation of \( \boldsymbol{P C l}_{5} \) is:
A. 0.9
B. 1.8
c. 1.2
D. 0.5
Subject: Physics
A chain of length \( l \) and mass \( m \) lies on
the surface of a smooth sphere of
radius \( R>l \) with one end tied to the
top of the sphere. Suppose the chain is released and slides down the sphere.
Find the kinetic energy of the chain,
when it has slid through an angle \( \theta \)
\( ^{\mathbf{A}} \cdot \frac{m R^{2} g}{l}\left[\sin \left(\frac{l}{R}\right)+\sin \theta-\sin \left(\theta+\frac{l}{R}\right)\right] \)
\( ^{\mathbf{B}} \cdot \frac{m R^{2} g}{l}\left[\sin \left(\frac{l}{R}\right)+\sin \theta+\sin \left(\theta+\frac{l}{R}\right)\right] \)
\( ^{\mathbf{C}} \cdot \frac{m R^{2} g}{l}\left[\sin \left(\frac{l}{R}\right)+\sin \theta+\sin \left(\theta-\frac{l}{R}\right)\right] \)
\( D \)
\[
\frac{m R^{2} g}{l}\left[\sin \left(\frac{l}{R}\right)+\sin \theta-\sin \left(\theta-\frac{l}{R}\right)\right]
\]
Subject: Maths
Given \( \xi=\{x: x \text { is a natural number }\} \) \( A=\{x: x \text { is an even number } x \in N\} \) \( \mathrm{B}=\{\mathrm{x}: \mathrm{x} \text { is an odd number, } \mathrm{x} \in \mathrm{N}\} \)
Then \( (\boldsymbol{B} \cap \boldsymbol{A})-(\boldsymbol{x}-\boldsymbol{A})=\dots \)
\( A \cdot \phi \)
в.
\( c . B \)
D. \( A-B \)
Subject: Chemistry
If \( p K_{b} \) for fluoride ion at 25 is 10.83 , the
ionisation constant of hydrofluoric acid
in water at this temperature is :
A \( \cdot 1.74 \times 10^{-5} \)
В. \( 3.52 \times 10^{-3} \)
c. \( 6.75 \times 10^{-4} \)
D. \( 5.38 \times 10^{-2} \)
Subject: Chemistry
Assertion
Ca \( F_{2} \) has been given the name
fluorspar.
Reason
Solid \( C a F_{2} \) emits light when heated.
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
Consider the following \( \boldsymbol{E}^{0} \) values:
\( \boldsymbol{E}_{\boldsymbol{F} \boldsymbol{e}^{3+} / \boldsymbol{F} e^{2+}}^{\boldsymbol{0}}=\boldsymbol{0 . 7 7 V} \)
\( E_{S n^{2+} / S n}^{0}=-0.14 V \)
Under standard conditions the potential
for the reaction, is:
\( \boldsymbol{S} \boldsymbol{n}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \boldsymbol{2} \boldsymbol{F} \boldsymbol{e}^{2+}(\boldsymbol{a} \boldsymbol{q})+ \)
\( \boldsymbol{S} \boldsymbol{n}^{2+}(\boldsymbol{a} \boldsymbol{q}) \)
A . \( 0.91 \mathrm{V} \)
B. 1.40V
c. \( 1.68 v \)
D. 0.63v
Subject: Chemistry
Three gases \( A, B \) and \( C \) are at same temperature if their r.m.s speed are in the ratio \( 1: \frac{1}{\sqrt{2}}: \frac{1}{\sqrt{3}} \) then their molar
masses will be in the ratio:
A .1: 2: 3
B. 3: 2: 1
c. \( 1: \sqrt{2}: \sqrt{3} \)
D. \( \sqrt{3}: \sqrt{2}: 1 \)
Subject: Physics
In the figure, a point source \( ^{\prime} \boldsymbol{P}^{\prime} \) is
placed at a height \( h \) above the plane
mirror in a medium of refractive index
An observer \( O \), vertically above \( P \) outside the liquid, sees \( P \) and it image in the mirror. The apparent distance between these two is :
\( A \cdot 2 \mu h \)
B. \( 2 h \) \( \mu \)
c. \( \frac{2 h}{\mu-1} \)
' \( \quad h\left(1+\frac{1}{\mu}\right) \)
Subject: Maths
The following question is based on simple arithmetic principles. Find the right answer from the given
alternatives. \( \frac{26}{4}+\frac{14}{3}=? \)
A. 11.0
в. \( _{10} \frac{1}{6} \)
c. \( _{11} \frac{1}{6} \)
D. \( _{12} \frac{1}{5} \)
E \( \cdot 11 \frac{2}{3} \)
Subject: Maths
Statement-1: The variance of first n
even natural numbers is \( \frac{n^{2}-1}{4} \) Statement-2: The sum of first n natural
numbers is \( \frac{n(n+1)}{2} \) and The sum of
squares first n natural numbers is \( \frac{\boldsymbol{n}(\boldsymbol{n}+\mathbf{1})(\boldsymbol{2} \boldsymbol{n}+\mathbf{1})}{\boldsymbol{6}} \)
A. Statement-1 is true, Statement-2 is true ;Statement-2 is not a correct explanation for Statement-
B. Statement-1 is true, Statement-2 is false
c. Statement-1 is false, Statement-2 is true
D. Statement-1 is true, Statement-2 is true ;Statement-2 is a correct explanation for Statement-
Subject: Physics
The force between two parallel
conductors, each of length \( 50 m \) and
distant \( 20 \mathrm{cm} \) apart, is \( 1 \mathrm{N} \). If the
current in one conductor is double than
that in another one, then their values
will respectively be:
\( \mathbf{A} \cdot 100 A \) and \( 200 A \)
B. \( 50 A \) and \( 400 A \)
c. \( 10 A \) and \( 30 A \)
D. \( 5 A \) and \( 25 A \)
Subject: Chemistry
Which of the following is a suitable example for illustrating the law of conservation of mass? (Atomic mass of
\( \boldsymbol{O}=\mathbf{1 6} ; \boldsymbol{H}=\mathbf{1}) \)
A. \( 18 g \) of water is formed by the combination of 16 g oxygen with \( 2 g \) of hydrogen
B. \( 18 g \) of water in liquid state is obtained by heating 18 g of ice
c. \( 18 g \) of water is completely converted into vapour state n heating
D. \( 18 \mathrm{g} \) of water freezes at \( 4^{\circ} \mathrm{C} \) to give same mass of ice
Subject: Maths
In a right \( \triangle A B C, \) right angled at \( C, M \)
is the mid point of the hypotenuse of
\( A B . C \) is joined to \( M \) produced to a
point \( D \) such that \( D M=C M . \) Point \( D \)
is joined to point \( \boldsymbol{B} \). Then
rhis question has multiple correct options
A. \( \triangle A M C \cong \triangle B M D \)
B. \( \angle D B C \) is a right angle
c. \( \triangle D B C \cong \triangle A C B \)
\( ^{\mathrm{D}} \cdot C M=\frac{1}{2} A B \)
Subject: Physics
A stone of attached to a rope of length
\( =80 \mathrm{cm} \) is roated with a speed of 240 rpm. If the rope breaks, find the height to which the stone rises
A . \( 10.3 \mathrm{m} \)
B. 41.2 \( m \)
c. \( 20.6 \mathrm{m} \)
D. 24.9
Subject: Maths
Normal of the parabola \( x^{2}=8 y \) at (2,1)
is
A. \( 2 x+y+5=0 \)
в. \( 2 x+y=5 \)
\( \mathbf{c} \cdot 2 x-y+5=0 \)
D. \( 2 x-y-5=0 \)
Subject: Maths
The co-efficient of \( x^{5} \) in the expansion of
\( (1+x)^{21}+(1+x)^{22}+\dots \dots+ \)
\( (1+x)^{30} \) is:
A . \( ^{51} C_{5} \)
в. \( ^{9} C_{5} \)
c. \( ^{31} C_{6}-^{21} C_{6} \)
D. \( ^{30} C_{5}+^{20} C_{5} \)
Subject: Maths
\( \int \frac{d x}{\sqrt{(x-a)(b-x)}} \) equals
A \( \cdot \sin ^{-1} \sqrt{\left(\frac{x+a}{b-a}\right)}+c \)
B. \( \cos ^{-1} \sqrt{\left(\frac{x+a}{b-a}\right)}+c \)
\( ^{\mathrm{c}} 2 \sin ^{-1} \sqrt{\left(\frac{x+a}{b-a}\right)}+c \)
D. None of these
Subject: Chemistry
For a reaction \( 2 A+3 B \rightarrow \) Products
the rate law expression is given by rate
\( =K(A)^{1}(B)^{2} . \) The order of the reaction
with respect to \( A, B \) and overall order of
reaction are:
\( \mathbf{A} \cdot 2,1,3 \)
в. 1,2,3
c. 0,1,2
D. 2,1,0
Subject: Chemistry
\( \boldsymbol{Z} \boldsymbol{n}(\boldsymbol{s})\left|\boldsymbol{Z} \boldsymbol{n} \boldsymbol{C l}_{2}(\boldsymbol{a} \boldsymbol{q}) \| \boldsymbol{C l}^{-}(\boldsymbol{a q})\right| \boldsymbol{C l}_{2}(\boldsymbol{g}) \mid \boldsymbol{C} \)
In the electrochemical cell described by
the cell diagram above, what reaction occurs at the anode?
A. \( Z n \rightarrow Z n^{2+}+2 e^{-} \)
B. \( Z n^{2+}+2 e^{-} \rightarrow Z n \)
c. \( C l_{2}+2 e^{-} \rightarrow 2 C l \)
D. \( 2 C l^{-} \rightarrow C l_{2}+2 e^{-} \)
Subject: Physics
A man (mass \( =50 \mathrm{kg} \) ) and his son \( (\operatorname{mas} s=20 \mathrm{kg}) \) are standing on a
frictionless surface facing each other. The man pushes his son so that he
starts moving at a speed of \( 0.70 m s^{-1} \) with respect to the man. The speed of the man with respect to the surface is :
A. \( 0.20 \mathrm{ms}^{-1} \)
B . \( 0.14 m s^{-1} \)
c. \( 0.47 m s^{-1} \)
D. \( 0.28 m s^{-1} \)
Subject: Physics
At a place the angle of dip is \( 30^{\circ} \). If the horizontal component of the earth's magnetic field is \( H, \) then the total field
intensity will be given by
A \( \cdot \frac{H}{2} \)
в. \( \frac{2 H}{\sqrt{3}} \)
c. \( \frac{H}{\sqrt{2}} \)
D. \( H \sqrt{2} \)
Subject: Maths
If \( A, B \) and \( C \) are mutually exclusive and exclusive events of a random
experiment such that \( \boldsymbol{P}(\boldsymbol{B})=\frac{\boldsymbol{3}}{2} \boldsymbol{P}(\boldsymbol{A}) \)
and \( P(C)=\frac{1}{2} P(B), \) then \( P(A \cup C)= \)
A \( \cdot \frac{10}{13} \)
в. \( \frac{3}{13} \)
c. \( \frac{6}{13} \)
D. \( \frac{7}{13} \)
Subject: Chemistry
Which of the following will exhibit
highest boiling point?
A. \( C H_{3} C H_{2} O C H_{2} C H_{3} \)
в. \( C H_{3} C H_{2} C H_{2} C H_{2} C H_{2} O H \)
c. \( C H_{3} C H_{2} C H_{2} C H\left(C H_{3}\right) O H \)
D. \( C H_{3} C H_{2} C\left(C H_{3}\right)_{2} O H \)
Subject: Maths
\( \operatorname{Let}\left(\frac{2 x^{2}+x+2}{x}\right)^{n}=\sum_{r=m}^{r=t} a_{r} x^{r} \)
then answer the following:
\( f\left(a_{p}=a_{q} \text { then } p+q=\dots\right. \)
Subject: Maths
If
\( \lim _{x \rightarrow 0^{+}} x\left(\left[\frac{1}{x}\right]+\left[\frac{5}{x}\right]+\left[\frac{11}{x}\right]+\left[\frac{19}{x}\right]+\right. \)
430 (where [.] denotes the greatest
integer function), then \( n= \)
A . 8
B. 9
\( c .10 \)
D. 11
Subject: Physics
Snapshot for a rope shown, at an instant is carrying a travelling wave towards
right, created by source vibrating with the frequency "n". Then,
This question has multiple correct options
A. the speed of the wave is \( (4 \mathrm{n}) \) (distance ab)
B. the particle at point a will be in the present phase of after \( \frac{4}{3 n} \) sec.
C . the phase difference between b and e is \( \frac{3 \pi}{2} \)
D. the wave is harmonic
Subject: Maths
Inverse circular functions,Principal
values of \( \sin ^{-1} x, \cos ^{-1} x, \tan ^{-1} x \)
\[
\begin{array}{l}
\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1} \frac{x+y}{1-x y} \\
x y<1 \\
\quad \pi+\tan ^{-1} \frac{x+y}{1-x y}, \quad x y>1
\end{array}
\]
(a) Find whether \( x=2 \) satisfies the
equation
\[
\begin{array}{c}
\tan ^{-1} \frac{x+1}{x-1}+\tan ^{-1} \frac{x-1}{x}= \\
\tan ^{-1}(-7)
\end{array}
\]
If not, then how should the equation be re-written?
(b) \( \tan ^{-1} \frac{4}{3}+\tan ^{-1} \frac{5}{6}+\tan ^{-1} \frac{39}{2}- \)
\( \pi=\dots \)
(c) If \( x_{1}, x_{2}, x_{3}, x_{4} \) are roots of equation
\[
x^{4}-x^{3} \sin 2 \beta+x^{2} \cos 2 \beta-x \cos \beta-
\]
\( \sin \beta=0, \) then prove that
\[
\sum_{i=1}^{4} \tan ^{-1} x_{1}=\frac{\pi}{2}-\beta
\]