AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
A coin is tossed 100 times and tail is
obtained 10 times. Now, if a coin is
tossed at random, what is the
probability of getting a head?
A \( \cdot \frac{11}{10} \)
в. \( \frac{9}{10} \)
c. \( \frac{90}{10} \)
D. \( \frac{100}{10} \)
Subject: Physics
f velocity of C immediately after
collision becomes \( v_{0} / 2 \) in the initial
direction of motion, the impulse due to
string on sphere \( A \) is :
A. \( \frac{m v_{0}}{8} \)
в. \( \frac{m v_{0}}{2} \)
c. \( \frac{\sqrt{m v_{0}}}{4} \)
D. none of thes
Subject: Physics
A uniform slab of dimension \( 10 \mathrm{cm} \times \)
\( 10 \mathrm{cm} \times 1 \mathrm{cm} \) is kept between two heat
reservoirs at temperatures \( 10^{0} C \) and \( 90^{0} C \)
The larger surface areas touch the reservoirs. The thermal conductivity of
the material is \( 0.80 W / m-^{0} C . \) Find the
amount of heat flowing through the slab per second.
Subject: Physics
Imagine that a reactor converts all
given mass into energy and that it
operates at a power level of \( 10^{9} W \). The
mass of the fuel consumed per hour in
the reactor will be (velocity of light, c is
\( \left.3 \times 10^{8} m / s\right) \)
\( \mathbf{A} \cdot 0.8 g m \)
в. 0.96 gm
c. \( 4 \times 10^{-2} g m \)
D. \( 6.6 \times 10^{-5} g m \)
Subject: Biology
Read the given statements and select
the correct option.

Statement 1: About 70\% of \( C O_{2} \) that
enters RBCs changes into. \( \boldsymbol{H} \boldsymbol{C O}_{3} \) for transport in plasma to the lungs where
it reconverts into \( C O_{2} \) for elimination.
Statement 2: About \( 40 \% \) of \( C O_{2} \) that
enters RBCs changes into carbaminohaemoglobin which releases
\( O_{2} \) in the lungs.
A. Both statements 1 and 2 are correct.
B. Statement 1 is correct but statement 2 is incorrect
c. Statement 1 is incorrect but statement 2 is correct
D. Both statements1 and 2 are incorrect.
Subject: Maths
Construct the following Quadrilateral of
given measures.
In Quadrilateral MORE: \( \ell(M O)= \)
\( \mathbf{5 . 8} \boldsymbol{c m}, \ell(\boldsymbol{O} \boldsymbol{R})=\mathbf{4 . 4} \boldsymbol{c m}, \boldsymbol{m} \angle \boldsymbol{M}= \)
\( \mathbf{5 8}^{\circ}, \boldsymbol{m} \angle \boldsymbol{O}=\mathbf{1 0 5}^{\circ}, \boldsymbol{m} \angle \boldsymbol{R}=\mathbf{9 0}^{\circ} \mathbf{?} \)
Subject: Physics
If in Millikan's oil drop experiment charges on drops are found to be
\( 8 \mu C, 12 \mu C, 20 \mu C, \) then quanta of quanta of charge is :-
\( A \cdot 8 \mu C \)
в. \( 4 \mu C C \)
c. \( 20 \mu C \)
D. \( 12 \mu C \)
Subject: Physics
A resistance \( \boldsymbol{R} \) and a capacitor \( \boldsymbol{C} \) are
joined to a source of \( \boldsymbol{A} \boldsymbol{C} \) of constant
e.m.f and variable frequency.
The potential difference across \( C \) is \( V \)
If the frequency of \( \boldsymbol{A} \boldsymbol{C} \) is gradually increased, \( \boldsymbol{V} \) will
A. increase
B. decrease
c. remain constant
D. first increase and then decreas
Subject: Maths
A player throws 2 ordinary die with faces numbered 1 to 6. What is the
probability of obtaining a total score of atmost \( 6 ? \)
A \( \cdot 12 / 36 \)
B. \( 16 / 36 \)
c. \( 15 / 36 \)
D. \( 10 / 36 \)
Subject: Physics
and mass \( 1 k g \) are placed (fixed) symmetrically about a movable central charges of magnitude \( 5 \times 10^{-5} C \) and
mass \( 0.5 k g \) as shown. The charge at \( P_{1} \) is removed. The acceleration of the
central charge is
\( \left[\text { Given } \boldsymbol{O} \boldsymbol{P}_{1}=\boldsymbol{O} \boldsymbol{P}_{2}=\boldsymbol{O} \boldsymbol{P}_{3}=\boldsymbol{O} \boldsymbol{P}_{4}=\right. \)
\( O P_{5}=1 m ; \frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} \) in \( S I \) units
\( A \cdot 9 m s^{-2} \) upwards
B. \( 9 m s^{-2} \) downwards
c. \( 4.5 m s^{-2} \) upwards
D. \( 4.5 m s^{-2} \) downwards
Subject: Biology
People living at sea level have around 5
million RBC per cubic millimetre of their blood whereas those living at an altitude of 5400 metres have around 8
million. This is because at high altitude
A. people eat more nutritive food, therefore more RBCs are formed
B. people get pollution-free air to breathe and more oxygen is available
C. atmospheric \( O_{2} \) level is less and hence more RBCs are needed to absorb the required amount of \( O_{2} \) to survive
D. there is more UV radiation which enhances RBC production
Subject: Chemistry
The correct order of activation of
benzene ring towards an electrophile is
\( A \cdot(\mid V)>(|I|)>(\mid I)>(\mid) \)
B. \( (\| I)>(|>>(\mid V)>(||) \)
\( \mathbf{c} \cdot(\|\|)>(|V\rangle>(\mid)>(\|) \)
\( D \cdot(\mid V)>(|| \mid)>(||)>(\mid) \)
Subject: Maths
\( \operatorname{Let} h(x)=f(x)-(f(x))^{2}+(f(x))^{3} \) for
every real number \( x, \) then
A. \( h \) is increasing whenever \( f \) is increasing and decreasing whenever \( f \) is decreasing
B. \( h \) is increasing whenever \( f \) is decreasing
c. \( h \) is decreasing whenever \( f \) is increasing
D. Nothing can be said in general
Subject: Chemistry
Which of the following contains alcoholic functional group?
\( ^{\mathbf{A}}+_{H}-O-H_{\perp}^{H}-H \)
в. \( C H_{2}=C H-C H_{2} O H \)
\( ^{\mathrm{c}} \mathrm{CH}_{3}-\underset{_{c t_{3}}^{\mathrm{C}}}{C}-O-_{H} \)
D. All of the above
Subject: Maths
The number of envelopes that can be
made out of sheet of paper \( 384 \mathrm{cm} \) by
\( 172 \mathrm{cm} \) if each envelope requires a
piece of paper of size \( 16 \mathrm{cm} \) by \( 12 \mathrm{cm} \), is
A. 340
B. 344
c. 338
D. 342
Subject: Physics
Ten small planes are flying at a speed of \( 150 \mathrm{km} h^{-1} \) in total darkness in an air
space that is \( 20 \times 20 \times 1.5 k m^{3} \) in
volume. You are in one of the planes, flying at random within this space with no way of knowing where the other planes are. On the average about how long a time will elapse between near collision with your plane. Assume for this rough computation that a safety region around the plane can be approximated by a sphere of radius 10
\( \mathrm{m} \)
A. 125 h
в. 220h
c. 432 h
D. 225h
Subject: Physics
External and internal diameters of a
hollow cylinder are measured to be \( (4.23 \pm 0.01) \mathrm{cm} \) and \( (3.89 \pm 0.01) \mathrm{cm} \)
The thickness of the wall of the cylinder is
A . \( (0.34 \pm 0.03) \mathrm{cm} \)
B. \( (0.17 \pm 0.04) \mathrm{cm} \)
c. \( (0.17 \pm 0.01) \mathrm{cm} \)
D. \( (0.34 \pm 0.02) \mathrm{cm} \)
Subject: Physics
Two strings with mass per unit length of \( 25 g / c m \) and \( 9 g / c m \) are joined together in series. The reflection coefficient for the vibration waves are
A \( \cdot \frac{9}{25} \)
в. \( \frac{3}{5} \)
c. \( \frac{1}{16} \)
D. \( \frac{9}{16} \)
Subject: Chemistry
Activation energy \( \left(\boldsymbol{E}_{\boldsymbol{a}}\right) \) and rate
constants \( \left(k_{1} \text { and } k_{2}\right) \) of a chemical reaction at two different temperature
\( T_{1} \) and \( T_{2} \) ) are related by:
\( ^{\mathbf{A}} \cdot \ln \frac{k_{2}}{k_{1}}=-\frac{E_{a}}{R}\left[\frac{1}{T_{1}}-\frac{1}{T_{2}}\right] \)
в. \( \ln \frac{k_{2}}{k_{1}}=-\frac{E_{a}}{R}\left[\frac{1}{T_{2}}-\frac{1}{T_{1}}\right] \)
\( ^{\mathrm{c}} \cdot \ln \frac{k_{2}}{k_{1}}=-\frac{E_{a}}{R}\left[\frac{1}{T_{2}}+\frac{1}{T_{1}}\right] \)
D \( \cdot \ln \frac{k_{2}}{k_{1}}=\frac{E_{a}}{R}\left[\frac{1}{T_{1}}-\frac{1}{T_{2}}\right] \)
Subject: Biology
The correct sequence of human
evolution is
A. Australopithecus \( \rightarrow \) Homo-Habilis \( \rightarrow \) Homoerectus \( \rightarrow \) Homo-Neanderthalensis \( \rightarrow \) Cro-magnon
B. Australopithecus \( \rightarrow \) Homo-Habilis \( \rightarrow \) HomoNeanderthalensis \( \rightarrow \) Homoerectus \( \rightarrow \) Cro-magnin \( \rightarrow \) Homosapiens
C. Australopithecus \( \rightarrow \) Homo-Neander thalensis \( \rightarrow \) Homo-Habilis \( \rightarrow \) Homoerectus \( \rightarrow \) Cro-magnon \( \rightarrow \) Homosapiens
D. Homo-Habilis \( \rightarrow \) Homo-Neanderthalensis \( \rightarrow \) Australopithecus \( \rightarrow \) Homoerectus \( \rightarrow \) Cro-magnon \( \rightarrow \) Homosapiens
Subject: Chemistry
In context with the industrial
preparation of hydrogen from water gas
\( \left(C O+H_{2}\right), \) which of the following is the
correct statement?
\( \mathbf{A} \cdot \mathrm{H}_{2} \) is removed through occlusion with \( \mathrm{Pd} \)
B. \( C O \) is oxidised to \( \mathrm{CO}_{2} \) with steam in the presence of a
catalyst followed by absorption of \( \mathrm{CO}_{2} \) in alkal
C \( \cdot C O \) and \( \mathrm{H}_{2} \) are fractionally separated using differences in their densities
D. \( C O \) is removed by absorption in aqueous \( \mathrm{Cu}_{2} \mathrm{C} 1_{2} \) solution
Subject: Chemistry
\( 1^{\circ} \mathrm{C} \) rise in temperature is equal to rise
of:
\( \mathbf{A} \cdot 1^{0} F \)
B . \( 9 / 5^{\circ} \mathrm{F} \)
c. \( 5 / 9^{0} F \)
D. \( 33^{0} F \)
Subject: Chemistry
Match list I with list II and select the
correct answer using the codes given below the lists:
\( \begin{array}{ll}\text { List I } & \text { List II } \\ \text { A. }\left(\frac{\delta G}{\delta P}\right)_{T} & \text { 1. } \mu_{H} \\ \text { B. }\left(\frac{\delta G}{\delta T}\right)_{P} & \text { 2. } T \\ \text { C. }\left(\frac{\delta H}{\delta S}\right)_{P} & \text { 3. }-S \\ \text { D. }\left(\frac{\delta T}{\delta P}\right)_{H} & \text { 4. } P \\ & \text { 5. } V\end{array} \)
A. \( A-5, B-1, C-2, D-4 \)
B . \( A-5, B-3, C-2, D-4 \)
\( \mathbf{c} \cdot A-3, B-5, C-2, D-1 \)
D . \( A-5, B-3, C-2, D-1 \)
Subject: Physics
In above shown figure, a ball of mass 4 kg slides over frictionless surface and
strikes the post with velocity of \( 1 \mathrm{m} / \mathrm{s} \)
and rebounds toward the north at the
same speed. The change in the magnitude of the eastward component
of the momentum of the disk is:
A. \( -4 k g-m / s \)
в. \( -1 k g-m / s \)
c. \( 0 k g-m / s \)
D. \( 1 k g-m / s \)
E . \( 4 k g-m / s \)
Subject: Maths
The value of
\( \lim _{x \rightarrow 0}\left[\tan ^{-1}\left(\frac{2 x+1}{4 x+1}\right)-\frac{x}{4}\right] \) is equal to
\( A \cdot \frac{\pi}{4} \)
B. \( -\frac{\pi}{2} \)
c. \( \frac{-\pi}{4} \)
D. \( -\frac{3 \pi}{4} \)
Subject: Maths
Graph ( \( i v \) ) is represented by which
equation?
\( (i) \)
(i)
(iii)
(iv)
A \( \cdot y=2 x \)
B. \( y+x=2 \)
\( \mathbf{c} \cdot y=2+x \)
D. \( x=y+22 \)
Subject: Physics
Consider the charges \( \boldsymbol{q}, \boldsymbol{q} \) and \( -\boldsymbol{q} \) placed at the vertices of an equilateral triangle of each side \( l \). The sum of forces
acting on each charge is
A \( \cdot \frac{q^{2}}{4 \sqrt{2} \pi \varepsilon_{0} l^{2}} \)
в. \( \frac{-q^{2}}{4 \pi \varepsilon_{0} l^{2}} \)
c. \( \frac{q^{2}}{4 \pi \varepsilon_{0} l^{2}} \)
D. zero
Subject: Physics
Two spheres of mass \( M \) and \( 7 M \) are
connected by a rod whose mass is negligible, and the distance between
the centers of each sphere is \( d \). How far
from the center of the \( 7 M \) sphere is the
Center of Mass for this object?
A \( \cdot d / 8 \)
B. \( d / 7 \)
c. \( d / 2 \)
D. \( 6 d / 7 \)
E \( .7 d / 8 \)
Subject: Maths
Circle O has diameters AB and CD
perpendicular to each other. AM is any
chord intersecting \( \mathrm{CD} \) at \( \mathrm{P.} \) Then \( A P . \overline{A M} \) is equal to:
A. \( \overline{A O} . \overline{O B} \)
в. \( \overline{A O} . \overline{A B} \)
\( c \cdot \overline{C P} \cdot \overline{C D} \)
D. \( \overline{C P} . \overline{P D} \)
ह. \( \overline{c O} . \overline{O P} \)
Subject: Physics
A ray of white light of incident on a
spherical water drop whose center is \( C \)
as shown in figure. When observed from
the opposite side, the emergent light.
A. Will be white and will emerge without deviating
B. Will be internally reflectedd
C. Will split into different colors such that the angles of deviation will be different for different colors
D. Will split into different colors such that the angles of deviation will be the same for all colors
Subject: Chemistry
Match the complex ions listed in
column-I with the characteristics listed
in column-II using the codes given
below.
ColumnColumn-II
(a)
\[
\left[N i\left(N H_{3}\right)_{6}\right]^{2+}
\]
(p) \( d^{2} s p^{3} \) and diamagnetic
\( (b) \)
\[
\left[C r\left(N H_{3}\right)_{6}\right]^{3+}
\]
(q) \( s p^{3} d^{2} \) and diamagnetic
\( (c) \)
(r) \( s p^{3} d^{2} \) and two unpaired
\[
\left[C o\left(N H_{3}\right)_{6}\right]^{3+}
\]
electrons
\( (d) \)
(s) \( d^{2} s p^{3} \) and three unpaired
\[
\left[Z n\left(N H_{3}\right)_{6}\right]^{2+}
\]
electrons
A. a-r, b-s, c-p, d-q
B. a-s, b-r, c-q, d-p
c. \( a-r, b-s, c-q, d-p \)
D. a-p, b-q, c-r, d-s
Subject: Maths
The range of \( y=\sin 3 x+\sin x \) is-
A \( \cdot\left[\frac{-8}{3 \sqrt{3}}, \frac{8}{3 \sqrt{3}},\right] \)
в. \( \left[\frac{-4}{3 \sqrt{3}}, \frac{4}{\sqrt[3]{3}}\right] \)
c. \( \left[\frac{-3}{\sqrt{2}}, \frac{3}{\sqrt{2}},\right] \)
D. \( \left[\frac{-3}{3 \sqrt{2}}, \frac{3}{2 \sqrt{2}},\right] \)
Subject: Physics
Two polarizers have their axes inclined
at \( 45^{\circ} \) to each other. If unpolarized light
of intensity \( I \) is incident on the first
poilarizer, then the intensity of transmitted light through second
polarizer is:
A \( \cdot \frac{I}{4} \)
B. \( \frac{1}{2} \)
c. \( I \)
D.
Subject: Physics
Let \( S_{1} \) and \( S_{2} \) be the two slits in Young's double-slit experiment. If central maxima is observed at \( \boldsymbol{P} \) and angle
\( \angle S_{1} P S_{2}=\theta, \) then the fringe width for
the light of wavelength \( \lambda \) will be
(assume \( \theta \) to be a small angle)
\( A \cdot \lambda / \theta \)
в. \( \lambda \theta \)
c. \( 2 \lambda / \theta \)
D. \( \lambda / 2 \theta \)
Subject: Physics
Of the following, the equation of plane progressive wave is:
A. \( y=r \sin \omega t \)
в. \( y=r \sin (\omega t-k x) \)
c. \( y=\frac{a}{\sqrt{r}} \sin (\omega t-k x) \)
D. \( y=\frac{a}{r} \sin (\omega t-k t) \)
Subject: Physics
Assertion
The flux of electric field through a spherical surface of radius 1.5 a is more
than flux of electric field through a
spherical surface of radius 0.5 a. (Both
centred at origin)
Reason
The electric field at \( x=1.5 \) a is more than
electric field at 0.5 a
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: Maths
Find area enclosed by \( |x|+|y| \leq 3 \) and
\( x y \geq 2 \)
\( \mathbf{A} .5-2 \log 4 \)
B. \( 3-2 \log 4 \)
c. \( 3-\log 4 \)
D. \( 3-2 \log 7 \)
Subject: Chemistry
The final product \( (Y) \) in the following sequence of chemical reaction is:
\( \boldsymbol{C H}_{3} \boldsymbol{O H} \frac{\boldsymbol{C u}}{\mathbf{3 0 0}^{\circ} \boldsymbol{C}} \boldsymbol{X} \stackrel{\boldsymbol{N a O H}}{\longrightarrow} \boldsymbol{Y}+ \)
\( \boldsymbol{C H}_{3} \boldsymbol{O} \boldsymbol{H} \)
\( A \). an alkene
B. a carboxylic acid
c. an aldehyde
D. sodium salt of carboxylic acid
Subject: Physics
Light enters an isosceles right
triangular prism at normal incidence
through face \( A B \) and undergoes
total internal reflection at face \( \mathrm{BC} \) as
shown below.

The minimum value of the refractive
index of the prism is close to
A \( \cdot 1.10 \)
B . 1.55
c. 1.42
D. 1.72
Subject: Physics
The largest and the shortest distance of
the earth from sun are a and b,
respectively. The distance of the earth from sun when it is at a point where perpendicular drawn from the sun on
the major axis meets the orbit is
A \( \cdot \frac{a b}{a+b} \)
в. \( \frac{a b}{2(a+b)} \)
c. \( \frac{2 a b}{a+b} \)
D. \( \frac{a+b}{2 a b} \)
Subject: Physics
A train of mass \( M \) is moving on a
circular track of radius \( R \) with a
constant speed \( v \). The length of the train is half of the perimeter of the track. The linear momentum of the train will be
A . zero
в. \( \frac{2 M v}{\pi} \)
c. \( M v R \)
D. \( M v \)
Subject: Maths
There are two balls in an urn whose
colours are not known (each ball can be
either white or black). A white ball is put
into the urn. A ball is drawn from the
urn. The probability that it is white is
A . \( 1 / 4 \)
в. \( 1 / 3 \)
\( c \cdot 2 / 3 \)
D. \( 1 / 6 \)
Subject: Chemistry
\( x \)
Liquid sodium \( \quad \) Breathing apparatus metal \( \quad \) submarine
Potassium \( \quad \) Explosive
Potassium nitrate Coolant in nuclear reaction
Potassium
superoxide Soft soap
Match the compounds/metal in(X) with
their used in (Y). hence correct order is.
A . A-l, B-III, C-II, D-IV
B. A-III, B-IV, C-II, D-I
C . A-II, B-I, C-III, D-IV
D. A-IV, B-II, C-III, D-1
Subject: Chemistry
Everyone has the right to live. Yet, is everybody getting enough water to live or even water to drink? Why is it that some people have to buy drinking water? Should it be like this? Water on
this earth is for one and all. Some
people draw out water from the ground by deep bore wells. How far is it correct? Have you ever seen this? Why do some people is pump directly in the Jal Board pipe line? What problems would other people face due to this? Do you have any such experience?
Subject: Physics
The diagram shows four charges
\( q_{1}, q_{2}, q_{3}, \) and \( q_{4} \) all lying in the plane of the page. The diagram also shows the dotted circle that represents the crosssection of a spherical Gaussian surface
Point \( P \) is a single point on that surface
Which of the charges contributes to the
electric field at point \( P ? \)
\( \mathbf{A} \cdot q_{1} \) and \( q_{3} \)
\( \mathbf{B} \cdot q_{2} \) and \( q_{4} \)
\( \mathbf{c} \cdot q_{1} \) and \( q_{2} \)
\( \mathbf{D} \cdot q_{3} \) and \( q_{4} \)
E \( . q_{1}, q_{2}, q_{3}, \) and \( q_{4} \)
Subject: Physics
The method of dimensional analysis
can be used to derive which of the
following relations?
A. \( N_{0} e^{-\lambda} \)
B. \( \operatorname{Asin}(\omega+k x) \)
c. \( \frac{1}{2} m v^{2}+\frac{1}{2} \omega^{2} \)
D. None of these
Subject: Physics
A parallel-plate air capacitor is connected to a battery. The quantities charge, voltage, electric field and energy associated with this capacitor are given
by \( Q_{0}, V_{0}, E_{0} \) and \( U_{0} \) respectively. \( A \) dielectric slab is now introduced to fill
the space between the plates with battery still in connection. The corresponding quantities now given by Q, \( V \), E and \( U \) are related with previous
ones as:
This question has multiple correct options
A. \( V>V_{0} \)
в. \( U>U_{0} \)
c. \( Q>Q_{0} \)
D. \( E>E_{0} \)
Subject: Chemistry
A magnetic moment of \( 1.73 B M \) will be
shown by one among of the following compounds:
\( \mathbf{A} \cdot\left[C u\left(N H_{3}\right)_{4}\right]^{2+} \)
B : \( \left[N i(C N)_{4}\right]^{2-} \)
\( \mathrm{c} \cdot \operatorname{Ti} \mathrm{Cl}_{4} \)
D \( \cdot\left[\mathrm{CoCl}_{6}\right]^{-3} \)
Subject: Chemistry
Which of the following is correct regarding the Langmuir's model of
adsorption of a gas on a solid surface?
A. The rate of desorption of adsorbed molecules from the surface does not depend on the surface covered
B. The adsorption at a single site on the surface may involve multiple molecules at the same time
C. The mass of gas striking a given area of surface is proportional to the pressure of the gas
D. The mass of gas striking a given area of surface is independent of the pressure of the gas
Subject: Physics
Two particles are simultaneously projected in the horizontal direction
from a point \( \boldsymbol{P} \) at a certain height. The
initial velocities of the particles are
oppositely directed to each other and
have magnitude v each. The separation between the particles at a time when their position vectors (drawn from the point \( P \) ) are mutually perpendicular, is
\( ^{\mathrm{A}} \cdot \frac{v^{2}}{2 g g} \)
В. \( \frac{v^{2}}{g} \)
c. \( \frac{4 v^{2}}{g} \)
D. \( \frac{2 v^{2}}{g} \)
Subject: Physics
Find the acceleration of the bar.
A. \( w_{0}=\frac{2 g m r^{2}}{I} \)
B. \( w_{0}=\frac{g m r^{2}}{I} \)
c. \( _{w_{0}}=\frac{g m r^{2}}{2 I} \)
D. \( w_{0}=2 \frac{g m r^{2}}{I} \)
Subject: Physics
Two particles are projected in air with
speed \( u \) at angles \( \theta_{1} \) and \( \theta_{2} \) (both acute) to the horizontal, respectively. If the height reached by the first particle is greater than that of the second, then
which one of the following is correct?
(where \( T_{1} \) and \( T_{2} \) are the time of flight.)
A. \( \theta_{1}>\theta_{2} \)
a
B \( \cdot \theta_{1}=\theta_{2} \)
c. \( T_{1}<T_{2} \)
D. \( T_{1}=T_{2} \)
Subject: Chemistry
Assertion
Ethers are regarded as a hydride of alcohols.
Reason
Ethers may be obtained by elimination of water molecule from two alcohol
molecules.
A. If both Assertion and Reason are correct and Reason is 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
One end of a horizongal thick copper wire of length \( 2 L \) and radius \( 2 R \) is welded to an end of another horizontal
thin copper wire of length \( L \) and radius
\( R \) When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is then
A . 0.25
B. 0.50
\( c .2 .00 \)
D. 4.00
Subject: Physics
Assertion
The force exerted by the fluid is due to
the collisions of molecules with their
surroundings.
Reason
The normal force exerted by the fluid
particles on the walls of the container
results pressure.
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
Figure shows a bar magnet and a long
straight wire \( \mathrm{W} \), carrying current into
the
plane of paper.Point \( P \) is the point of intersection of axis of magnet and the
line
of shortest distance between magnet
and the wire. If \( P \) is the midpoint of the
magnet, then which of the following
statements is correct?
A. magnet experiences a torque in clockwise direction
B. magnet experiences a torque in anticlockwise direction
C. magnet experiences a force, normal to the line of shortest distance
D. magnet experiences a force along the line of shortest distance
Subject: Maths
\( a^{12}-1 \) can be factorised as:
\( \mathbf{A} \cdot(a-1)(a-2)(a-3)(a-4) \)
B \( \cdot(a-1)\left(a^{2}+a+1\right)(a+1)\left(a^{2}+a+1\right) \)
C \( \cdot\left(a^{2}+a+1\right)\left(a^{2}-a+1\right) \)
D \( \cdot(a-1)\left(a^{2}+a+1\right)(a+1)\left(a^{2}-a+1\right)\left[\left(a^{2}+1\right)\left(a^{4}-\right.\right. \)
\( \left.a^{2}+1\right) \)
Subject: Physics
The position of a particle as a function
of time is described by relation \( \boldsymbol{x}= \)
\( 3 t-3 t^{2}+t^{3} \) where the quantities are
expressed in S.I. units. If mass of the particle be \( 10 \mathrm{kg} \), the work done in first
three seconds is
A . 10
B. 30 J
c. \( 300 J \)
D. 675 J
Subject: Physics
A tunnel is dug along a diameter of the Earth. The force on a particle of mass \( \boldsymbol{m} \)
placed in the tunnel at a distance \( x \)
from the centre is:
A \( \cdot \frac{G M_{e} m}{R^{3}} x \)
в. \( \frac{G M_{e} m}{R^{2}} x \)
c. \( \frac{G M_{e} m}{R^{3} x} \)
D. \( \frac{G M_{e} m R^{3}}{x} \)
Subject: Maths
Find the mean, mode and median of
marks obtained by 20 students in an examination. The marks are given below.
\( \begin{array}{lllll}\text { Marks } & 0- & 10- & 20- & 3 \\ 10 & 20 & 30 & 4\end{array} \)
No. of 1 1 4 tident