AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The heat capacity of a certain amount
of a particular gas at constant pressure
is greater than that at constant volume by \( 29.1 \mathrm{J} / \mathrm{K} . \) Match the items given in
Column I with the items given in Column II.
List 1
If the gas is monatomic, heat capacity at constant volume

If the gas monatomic, heat capacity at constant pressure
If the gas is rigid diatomic, heat capacity at constant pressure
If the gas is vibrating diatomic, heat capacity at constant pressure
\( \mathbf{A} \cdot A \rightarrow 2, B \rightarrow 3, C \rightarrow 4, D \rightarrow 1 \)
B. \( \mathrm{B} \rightarrow 1, \mathrm{C} \rightarrow 3, \mathrm{D} \rightarrow 4, \mathrm{A} \rightarrow 1 \)
C. \( \mathrm{C} \rightarrow 1, \mathrm{D} \rightarrow 3, \mathrm{A} \rightarrow 4, \mathrm{B} \rightarrow 1 \)
D. \( D \rightarrow 1, A \rightarrow 3, B \rightarrow 4, C \rightarrow 1 \)
Subject: Chemistry
\( \boldsymbol{C a C O}_{3}+\boldsymbol{2 H C l} \rightarrow \boldsymbol{C a C l}_{2}+\boldsymbol{H}_{2} \boldsymbol{O}+ \)
\( \boldsymbol{C O}_{2} \)
The mass of calcium chloride formed
when 2.5 g of calcium carbonate is dissolved in excess of hydrochloric acid
is:
A . 1.39 g
в. 2.78 g
c. \( 5.18 \mathrm{g} \)
D. 17.8 g
Subject: Maths
If the area of a semicircle is \( 84 \mathrm{cm}^{2} \)
then the area of the circle is
A \( \cdot 144 \mathrm{cm}^{2} \)
B. \( 42 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 168 \mathrm{cm}^{2} \)
D. \( 288 \mathrm{cm}^{2} \)
Subject: Maths
An unbiased coin is tossed. If the result
is a head, a pair of unbiased dice is rolled and the number obtained by
adding the numbers on the two faces is noted. If the result is a tail, a card from
a well shuffled pack of eleven cards numbered \( 2,3,4, \dots . .12 \) is picked and the number on the card is noted. The
probability that the noted number is
either 7 and 8 is \( 1 k 3 / 792 \),where \( k \) is
ten's place of the number \( 1 k 3 . \) F ind the
value of \( k .\{1 k 3=100+10 \times k+3\} \)
Subject: Chemistry
\( X e F_{6} \) dissolves in anhydrous HF to give a good conducting solution which contains:
A \( \cdot H^{+} \) and \( X e F_{7}^{-} \) ions
B. \( H F_{2}^{-} \) and \( X e F_{5}^{+} \) ions
C. \( H X e F_{6}^{+} \) and \( F^{-} \) ions
D. none of these
Subject: Physics
A block released from rest from the top
of a smooth inclined plane of angle \( \boldsymbol{\theta}_{\mathbf{1}} \)
reaches the bottom in time \( t_{1} \). The same
block released from rest from the top of another smooth inclined plane of angle
\( \theta_{2}, \) reaches the bottom in time \( t_{2} \). If the
two inclined planes have the same height, the relation between \( t_{1} \) and \( t_{2} \) is
\( A \)
\[
\frac{t_{2}}{t_{1}}=\left(\frac{\sin \theta_{1}}{\sin \theta_{2}}\right)^{1 / 2}
\]
B. \( \frac{t_{2}}{t_{1}}=1 \)
c. \( \frac{t_{2}}{t_{1}}=\left(\frac{\sin \theta_{1}}{\sin \theta_{2}}\right) \)
D.
\[
\frac{t_{2}}{t_{1}}=\left(\frac{\sin ^{2} \theta_{1}}{\sin ^{2} \theta_{2}}\right)
\]
Subject: Biology
The presence of \( \mathrm{CO}_{2} \) in blood will lower
pH because \( \mathrm{CO}_{2} \) combines with
with the rate of reaction increased by
\( A \cdot H_{2} O \) to form \( H^{+} \) and \( H C O_{3}^{-}, \) carbonic anhydrase
B. \( \mathrm{H}_{2} \mathrm{O} \) to form only \( \mathrm{HCO}_{3} \) - carbonic anhydrase
\( \mathrm{C} \cdot \mathrm{H}_{2} \mathrm{O} \) to form only \( \mathrm{H}^{+}, \) carbonic ions
D. \( H^{+} \) to form \( \mathrm{HCO}_{3}^{-} \), oxyhaemoglobin
Subject: Physics
A wire along \( x- \) axis carries a current
\( 3.5 A . \) Find the force on a \( 1 \mathrm{m} \) section of the wire exerted by \( \vec{B}=(0.74 \hat{j}- \) \( \mathbf{0} . \mathbf{3 6} \hat{\boldsymbol{k}}) \boldsymbol{T} .(\text { in } \mathbf{N}): \)
A. \( 2.59 \hat{k}+1.263 \)
3
в. \( 1.26 \hat{k}-2.59 \hat{\jmath} \)
c. \( -2.59 \hat{k}-1.26 \hat{j} \)
D . \( -1.26 \hat{k}+2.59 \hat{j} \)
Subject: Physics
Imagine a planet having the same density as that of the earth but radius
is three times the radius of the earth. If
acceleration due to gravity on the surface of the earth is \( g \) and that on the said planet is \( g^{\prime} \), then
A \( \cdot g^{\prime}=\frac{g}{9} \)
B . \( g^{\prime}=9 g \)
c. \( g^{\prime}=\frac{g}{27} \)
D. \( g^{\prime}=3 g \)
Subject: Physics
Equation of position (x) with time (t) is given by equation \( \boldsymbol{x}=\mathbf{3} \boldsymbol{t}^{2}+\mathbf{7} \boldsymbol{t}^{2}+\mathbf{5} \boldsymbol{t}+ \)
8 \( m \). The acceleration at time \( t=1 \) sec is :
A \( \cdot 20 m / s e c^{2} \)
B. \( 32 m / \) sec \( ^{2} \)
c. zero
D. \( 14 m / s e c^{2} \)
Subject: Chemistry
A monoprotic acid in \( 100 M \) solution is \( 0.001 \% \) ionized. The dissociation
constant of this acid is:
A \( \cdot 1.0 \times 10^{-3} \)
B. \( 1.0 \times 10^{3} \)
c. \( 1.0 \times 10^{-8} \)
D. \( 1.0 \times 10^{-10} \)
Subject: Maths
Find the shortest distance between the
following pair of lines. \( \overline{\boldsymbol{r}}=(\overline{\boldsymbol{i}}+\mathbf{2} \overline{\boldsymbol{j}}+\overline{\boldsymbol{k}})+\boldsymbol{\lambda}(\mathbf{2} \overline{\boldsymbol{i}}-\overline{\boldsymbol{j}}+\mathbf{3} \overline{\boldsymbol{k}}) \& \)
\( \overline{\boldsymbol{r}}=(\overline{\boldsymbol{i}}-\mathbf{3} \overline{\boldsymbol{j}}-\overline{\boldsymbol{k}})+\boldsymbol{\mu}(\mathbf{3} \overline{\boldsymbol{i}}+\mathbf{2} \hat{\boldsymbol{j}}-\mathbf{5} \overline{\boldsymbol{k}}) \)
Subject: Physics
\( 10^{-4} m^{2} \) and a resistance of \( 2 \Omega \) (figure)
The larger circular loop is fixed and has
a radius of \( 0.1 m . \) Both the loops are
concentric and coplanar. The smaller
loop is rotated with an angular velocity
end \( s^{-1} \) about its diameter. The
magnetic flux with the smaller loop is
A \( \cdot 2 \pi \times 10^{-6} W b \)
В \( \cdot \pi \times 10^{-9} W b \)
C \( \cdot \pi \times 10^{-9} \cos \omega t W b \)
D. zer
Subject: Biology
Read the following statements carefully
(1) In fishes the heart pumps out deoxygenated blood which is oxygenated by the gills and supplied to the body parts from where deoxygenated blood is returned to the
heart
(2) The openings of the right and the left ventricles into the pulmonary artery and the aorta respectively are provided with the mitral valves.
(3) The nodal musculature has the ability to generate action potential without any external stimuli, i.e., it is auto-excitable
(4) The T-wave of ECG represents depolarization of the ventricles Which of the given two statements are correct?
A. 1 and 3
B. \( 2 \& 4 \)
c. 1 and 2
D. 3 \& 4
Subject: Biology
Assertion: Muscle contraction force
increases with rise in strength of
stimulus

Reason: This is due to increased
contraction of individual muscle fibres
with an increase in stimulus strength.
A. Assertion and the reason are true and the reason is a correct explanation of the assertion
B. Both the assertion and reason are true but the reason is
not a correct explanation of the assertion
c. Assertion is true but the reason is false
D. If both the assertion and reason are false
E. Assertion is false but reason is true
Subject: Physics
Given \( \overline{\boldsymbol{a}}+\overline{\boldsymbol{b}}+\overrightarrow{\boldsymbol{c}}+\overline{\boldsymbol{d}}=\mathbf{0}, \) which of the
following statements is/are not a
correct statement?
A \( \cdot \vec{a}, \vec{b}, \vec{c} \) and \( \vec{d} \) must be a null vector.
B. The magnitude of ( \( \vec{a}+\vec{c} \) ) equals the magnitude of \( a(\vec{b}+\vec{d}) \)
C. The magnitude of \( \vec{a} \) can never be greater than the summ of the magnitudes of \( \vec{b}, \vec{c} \) and \( \vec{d} \)
D. \( b+\vec{c} \) must He in the plane of \( \vec{a} \) and \( \vec{d} \) if \( \vec{a} \) and \( \vec{d} \) are not collinear and in the line of \( \vec{a} \) and \( \bar{d} \), if they are collinear.
Subject: Physics
A stationary ball weighing \( 0.25 \mathrm{kg} \) acquire a speed of \( 10 \mathrm{m} / \mathrm{s} \) when hit by a hockey stick. The impulse imparted to the ball is:
A. \( 0.25 N \times s \)
B. \( 2.5 N \times s \)
\( \mathbf{c} \cdot 2 N \times s \)
D. \( 0.5 N \times s \)
Subject: Physics
A particle in uniformly accelerated motion travels \( a, b \) and \( c \) distances in
the \( x^{t h}, y^{t h} \) and \( z^{t h} \) second of it's motion, respectively. Then, value of \( a(y-z)+ \)
\( b(z-x)+c(x-y) \) will be
\( A \)
B. 0
\( c \cdot 2 \)
D. 3
Subject: Maths
The \( 5^{t h} \) and \( 8^{t h} \) terms of a GP are 1458
and \( 54, \) respectively. The common ratio
of the GP is
A \( \cdot \frac{1}{3} \)
B. 3
\( c \cdot 9 \)
D. \( \frac{1}{9} \)
E
Subject: Chemistry
Allyl cyanide contains \( \sigma \) and
\( \pi \) -bonds.
\( \mathbf{A} \cdot 5 \sigma, 7 \pi \)
B. \( 9 \sigma, 3 \pi \)
c. \( 3 \sigma, 4 \pi \)
D. \( 9 \sigma, 9 \pi \)
Subject: Chemistry
Assertion
\( P b I_{4} \) doesn't exist and converts into
\( P b I_{2} \) and \( I_{2} \) spontaneously at room
temperature but \( P b C l_{4} \) needs heating
to convert into \( P b C l_{2} \) and \( C l_{2} \)
Reason
\( P b^{2+} \) is more stable than \( P b^{4+} \) due to
inert pair effect.
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 correct but Reason is not correct.
Subject: Chemistry
When a certain amount of ethylene was
burnt, \( 622 \mathrm{kJ} \) heat was evolved. If heat of
combustion of ethylene is 1411 kJ, the
volume of \( \boldsymbol{O}_{2} \) that entered into the
reaction is:
A \( .296 .5 \mathrm{mL} \)
B . 29.62 L
c. \( 6226 \times 22.4 \) 느
D. 22.4 mL
Subject: Physics
Two electric bulbs have ratings respectively of \( 25 W, 220 V \) and \( 100 W, 220 V \). If the bulbs are connected
in series with a supply of \( 440 V, \) which bulb will fuse?
\( \mathbf{A} \cdot 25 W \) bulb
B. \( 100 W \) bulb
c. Both of these
D. None of these
Subject: Chemistry
Among \( N a, H g, S, P t, \) and graphite which can be used as electrodes
in electrolytic cell having aqueous solutions ?
A. \( N \) aand \( S \)
в. \( H g, P t \), and \( S \)
c. \( N a, H g \), and \( S \)
D. \( H g, P t \), and graphite
Subject: Maths
If \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{1}{\boldsymbol{x}}+\mathbf{3} \boldsymbol{x}^{2} \) then \( \boldsymbol{y}= \)
A. \( \ln x+\frac{x^{3}}{2}+c \)
B. \( \ln x+3 x^{3}+c \)
c. \( \ln x+\frac{x^{3}}{3}+c \)
D. \( \ln x+x^{3}+c \)
Subject: Physics
A man wishes to cross a river in a boat.
If he crosses the river in minimum time,
then he takes 10 minutes with a drift of
\( 120 m . \) If he crosses the river taking
shortest path, he takes 12.5 minutes. Velocity of boat w.r.t water is :
A. \( 40 \mathrm{m} / \mathrm{min} \)
в. \( 20 \mathrm{m} / \mathrm{min} \)
c. \( 10 m / \) min
D. \( 30 m / \) min
Subject: Maths
An aeroplane can carry a maximum of
200 passengers. A profit of Rs.1000 is made on each executive class ticket
and a profit of Rs.600 is made on each economy class ticket. The airline
reserves at least 20 seats for executive
class. However, at least 4 times as many passengers prefer to travel by economy class than by the executive class. Determine how many tickets of
each type must be sold in order to maximize the profit for the airline. What is the maximum profit?
A . 136000
в. 1360000
c. 13600
D. 1360
Subject: Chemistry
Which of the following statements is
incorrect?
\( \mathbf{A} \cdot \operatorname{In} K_{3}\left[F e(C N)_{6}\right], \) the ligand has satisfied only the secondary valency of ferric ion
B. \( \ln K_{3}\left[F e(C N)_{6}\right] \), the ligand has satisfied both primary and secondary valencies of ferric ion
C \( \cdot \ln K_{4}\left[F e(C N)_{6}\right] \) the ligand has satisfied both primary and secondary valencies of ferrous ion
D. \( \ln \left[C u\left(N H_{3}\right)_{4}\right] S O_{4} \) the ligand has satisfied only the secondary valency of copper
Subject: Chemistry
The standard enthalpy of formation \( \left(\Delta_{f} H_{298}^{o}\right) \) for methane, \( C H_{4} \) is
\( -74.9 k J m o l^{-1} . \) In order to calculate
the average energy given out in the formation of a \( C-H \) bond from this, it
is necessary to know which one of the
following?
A. The dissociation energy of the hydrogen molecule, \( H_{2} \)
B. The first four ionisation energies of carbon.
C. The dissociation energy of \( H_{2} \) and enthalpy of sublimation of carbon (graphite).
D. The first four ionisation energies of carbon and electron affinity of hydrogen
Subject: Chemistry
Assertion
Both \( S O_{2} \) and \( S O_{3} \) are reducing agents
Reason

Both \( S O_{2} \) and \( S O_{3} \) bleach the articles
by reduction
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
Two identical air filled parallel plate
capacitors are charged to the same
potential in the manner shown by closing the switch S. If now the switch is opened and the space between the plates is filled with a dielectric of
relative permittivity \( \varepsilon_{r}, \) then :
A. The potential difference as well as charge on each capacitor goes up by a factor \( \varepsilon_{r} \)
B. The potential difference as well as charge on each capacitor goes down by a factor \( \varepsilon_{r} \)
c. The potential difference across A remains constant and the charge on B remains unchanged
D. The potential difference across B remains constant while the charge on A remains unchanged
Subject: Physics
A particle of mass \( 2 \mathrm{kg} \) is on a smooth
horizontal table and moves in a circular
path of radius 0.6m. The height of the table from the ground is \( 0.8 \mathrm{m} \) If the angular speed of the particle is
12rads \( ^{-1} \), the magnitude of its angular momentum about a point on the ground right under the centre of the circle is:
A. \( 8.64 \mathrm{kg} \mathrm{m}^{2} s^{-1} \)
B. \( 11.52 \mathrm{kg} \mathrm{m}^{2} \mathrm{s}^{-1} \)
c. \( 14.4 \mathrm{kg} \mathrm{m}^{2} s^{-1} \)
D. \( 20.16 \mathrm{kg} \mathrm{m}^{2} \mathrm{s}^{-1} \)
Subject: Physics
A cylinder of mass \( M_{c} \) and sphere of
\( \operatorname{mass} M_{s} \) are placed at points \( A \) and \( B \)
of two inclines, respectively. (See

Figure). If they roll on the incline without
slipping such that their accelerations are the same, then the ratio \( \frac{\sin \theta_{c}}{\sin \theta_{s}} \) is :
\( A \cdot \sqrt{\frac{8}{7}} \)
B. \( \sqrt{\frac{15}{14}} \)
\( c \)
7
D. 15
14
Subject: Physics
Two trains are moving with velocities \( \boldsymbol{v}_{1}=\mathbf{1 0} \boldsymbol{m} \boldsymbol{s}^{-1} \) and \( \boldsymbol{v}_{2}=\mathbf{2 0} \boldsymbol{m} \boldsymbol{s}^{-1} \) on the
same track in opposite directions. After
the application of brakes if their
retarding rates are \( a_{1}=2 m s^{-2} \) and
\( a_{1}=1 m s^{-2} \) respectively, then the
minimum distance of separation between the trains to avoid collision is
\( \mathbf{A} \cdot 150 m \)
В. \( 225 \mathrm{m} \)
c. \( 450 m \)
D. \( 300 m \)
Subject: Physics
If \( \vec{a}=\hat{i}+2 \hat{j}+2 \hat{k} \) and \( \vec{b}=3 \hat{i}+6 \hat{j}+ \)
\( 2 \hat{k}, \) then a vector in the direction of \( \vec{a} \)
and having magnitude as \( |\vec{b}| \) is
A \( \cdot 7(\hat{i}+\hat{j}+\hat{k}) \)
B \( \cdot \frac{7}{3}(\hat{i}+2 \hat{j}+2 \hat{k}) \)
c. \( \frac{7}{9}(\hat{i}+2 \hat{j}+2 \hat{k}) \)
D. none of these
Subject: Maths
\( \boldsymbol{f}:\left(-\frac{\boldsymbol{\pi}}{2}, \frac{\boldsymbol{\pi}}{2}\right) \rightarrow(-\infty, \infty) \) defined by
\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{1}+\mathbf{3} \boldsymbol{x} \) is
A. one-one but not onto
B. onto but not one-one
c. neither one - one nor onto
D. bijective
Subject: Physics
A ray of light incident normally on the first face of an equilateral prism undergoes total internal reflection at the second face if refractive index \( \mu \) is
A \( \cdot \) less than \( \frac{\sqrt{3}}{2} \)
B. less than \( \frac{2}{\sqrt{3}} \)
c. more than \( \frac{\sqrt{3}}{2} \)
D. more than \( \frac{2}{\sqrt{3}} \)
Subject: Chemistry
At a particular temperature, the
equilibrium concentrations of the substances in the previous question
are as follows: \( \left[N O_{2} C l\right]=0.5 \mathrm{M},\left[C l_{2}\right]= \)
\( 0.3 \mathrm{M},\left[N O_{2}\right]=0.2 \mathrm{M} . \) What is the value
of the equilibrium constant for this reaction?
A . 2.
B. 0.48
c. 0.0357
D. 20.83
E. 208.83
Subject: Chemistry
Standard electrode potential data are
useful for understanding the suitability
of an oxidant in a redox titration. Some
half cell reaction and their standard
potential are given below:
A \( \cdot M n O_{4}^{-}(a q .)+8 H^{+}(a q)+5 e^{-} \rightarrow M n^{2}(a q .)+ \)
\( 4 H_{2} O(l) \)
\[
E^{0}=1.51 V
\]
B \( \cdot C r_{2} O_{7}^{2}(a q .)+14 H^{+}(a q .)+6 e \rightarrow 2 C r^{3}(a q .)+ \)
\( 7 H_{2} O(l) \)
\[
E^{0}=1.38 V
\]
C \( \cdot F e^{3+}(a q \cdot)+e^{-} \rightarrow \)
\( F e^{2+}(a q .) \)
\( 0.77 V \)
\( \left.\mathbf{D} \cdot C\right|_{2}(g)+2 e^{-} \rightarrow \)
\( \left.2 C\right|^{-}(a q .) \)
\( 1.40 V \)
Subject: Physics
A solenoid is \( 1.5 m \) long and its inner
diameter is \( 4.0 \mathrm{cm} . \) It has 3 layers of
winding's of 1000 turns each and
carries a current of 2.0 amperes. The magnetic flux for a cross-section of the solenoid is nearly.
A . \( 4.1 \times 10^{-5} \) weber
B. \( 5.2 \times 10^{-5} \) weber
c. \( 6.31 \times 10^{-3} \) weber
D. \( 2.5 \times 10^{-7} \) weber
Subject: Chemistry
Which of the following are failures of
Bohr's Atomic model
A. Bohr model could not explain those atoms which have more than one electron like lithium, helium. This model was applicable only for those atoms which have one electron
B. Bohr theory explained only spherical orbits. There was no explanation for elliptical orbits
c. Bohr's atomic model propose that the electron revolve round then nucleus
D. Both A and B
Subject: Chemistry
Which of the following statements(s)
is(are) correct?
This question has multiple correct options
\( \mathbf{A} \cdot \) The \( \mathrm{pH} \) of \( 1.0 \times 10^{-8} \mathrm{M} \) solution of \( \mathrm{HCl} \) is 8
B. The conjugate base of \( H_{2} P O_{4}^{\ominus} \) is \( H P O_{4}^{2-} \)
C. Autoprotolysis constant of water increases with temperature
D. When a solution of weak monoprotic acid is titrated against a strong base, at half-neutralisation, point \( p H=(1 / 2) p K_{a} \)
Subject: Maths
\( (a+b)^{3}=? \)
\( \mathbf{A} \cdot a^{3}+3 a^{2} b+3 a b^{2}+b^{3} \)
B \( \cdot a^{3}+a^{2} b+a b^{2}+b^{3} \)
c. \( a^{3}-3 a^{2} b+3 a b^{2}-b^{3} \)
D \( \cdot a^{3}+3 a^{2} b-3 a b^{2}+b^{3} \)
Subject: Maths
Let \( \boldsymbol{R}=\boldsymbol{g} \boldsymbol{S}-\mathbf{4} . \) When \( \boldsymbol{S}=\mathbf{8}, \boldsymbol{R}=\mathbf{1 6} \)
When \( S=10, R \) is equal to
A . 11
B. 14
c. 20
D. 21
E. None of these
Subject: Maths
The area in square units bounded by the
curves \( \boldsymbol{y}=\boldsymbol{x}^{3}, \boldsymbol{y}=\boldsymbol{x}^{2} \) and the
ordinates \( \boldsymbol{x}=\mathbf{1}, \boldsymbol{x}=\mathbf{2} \) is
A \( \cdot \frac{17}{12} \)
B. \( \frac{12}{13} \)
\( c \cdot \frac{2}{7} \)
\( D \cdot \frac{7}{2} \)
Subject: Maths
If \( \bar{a} \) is unit vector, then \( |\overline{\boldsymbol{a}} \times \hat{\mathbf{i}}|^{2}+\mid \overline{\boldsymbol{a}} \times \)
\( \left.\hat{\boldsymbol{j}}\right|^{2}+|\overline{\boldsymbol{a}} \times \hat{\boldsymbol{k}}|^{2}= \)
\( A \cdot 2 \)
B.
\( c \cdot 0 \)
D. 3
Subject: Maths
If \( x+y=4 \) and \( \frac{1}{x}+\frac{1}{y}=4, \) then the
value of \( x^{3}+y^{3} \) is
\( \mathbf{A} \cdot 52 \)
B. 64
\( c \cdot 4 \)
D. 25
Subject: Maths
The number of sides of two regular
polygons \( A \) and \( B \) are in the ratio 1: 3.1
each interior angle of polygon \( \mathrm{B} \) is \( 168^{\circ} \) find each interior angle of polygon \( \boldsymbol{A} \)
A \( .144^{\circ} \)
B. 124
\( c \cdot 134^{\circ} \)
D. none of the above
Subject: Physics
For the refraction of light through a
prism
A. For every angle of deviation there are two angles of incidence.
B. The light travelling inside an equilateral prism is necessarily parallel to the base when prism is set for minimum deviation.
C. There are two angles of incidence for maximum deviation.
D. Angle of minimum deviation will increase if refractive index of prism is increased keeping the outside medium unchanged if \( \mu_{p}>\mu_{s} \)
Subject: Physics
A cube is arranged such that its length, breadth, height are along \( X, Y \) and \( Z \)
directions. One of its corners is situated
at the origin. Length of each side of the
cube is \( 25 \mathrm{cm} \). The components of electric field are \( E_{x}=400 \sqrt{2} N / C, E_{y}=0 \) and
\( E_{Z}=0 \) respectively. The flux coming out
of the cube at one end, whose plane is
perpendicular to \( X \) axis, will be:
\( \mathbf{A} \cdot 25 \sqrt{2} N m^{2} / C \)
\( \mathbf{B} \cdot 5 \sqrt{2} N m^{2} / C \)
\( \mathbf{c} \cdot 250 \sqrt{2} N m^{2} / C \)
D. \( 25 \mathrm{Nm}^{2} / \mathrm{C} \)
Subject: Maths
If a chord of a circle \( x^{2}+y^{2}=32 \)
makes equal intercepts of length \( l \) on
the co-ordinate axes, then
\( \mathbf{A} \cdot \ell<8 \)
в. \( \ell<16 \)
\( \mathbf{c} \cdot \ell>8 \)
D. \( \ell>16 \)
Subject: Maths
The value of
\( \int_{0}^{\pi / 2} x(\sqrt{\tan x}+\sqrt{\cot x}) d x \) is?
\( \mathbf{A} \cdot \frac{\pi}{2 \sqrt{2}} \)
B. \( \frac{\pi^{2}}{2} \)
\( \frac{\pi^{2}}{2 \sqrt{2}} \)
D. \( \frac{\pi^{2}}{2 \sqrt{3}} \)
Subject: Maths
Find the length of a diagonal of rhombus whose area is \( 100 m^{2} \) and
length of other diagonal is \( 10 m^{2} \)
A. \( 10 \mathrm{m} \)
в. 20
\( c \cdot 2 m \)
D. \( 1 \mathrm{m} \)
Subject: Physics
A body weighs \( 8 g \) when placed in one
pan and \( 18 g \) when placed on the other pan of a false balance. If the beam is
horizontal when both the pans are
empty, the true weight of the body is:
A \( \cdot 13 g \)
в. \( 12 g \)
c. \( 15.5 g \)
D. \( 15 g \)
Subject: Physics
1 fermi is equal to
\( \mathbf{A} \cdot 10^{-15} \mathrm{m} \)
B. \( 10^{15} \mathrm{m} \)
\( \mathbf{C} \cdot 10^{-12} \mathrm{m} \)
\( D \cdot 10^{12} m \)
Subject: Maths
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{cl}\frac{\tan [x]-[x] \tan 1}{x} & ; \boldsymbol{x} \neq 0 \\ \boldsymbol{0} & ; \boldsymbol{x}=0\end{array}, \) then \right.
\( \boldsymbol{f}^{\prime}\left(\mathbf{0}^{-}\right) \) is [where \( [\boldsymbol{x}] \) denotes integer part
of \( \boldsymbol{x} \)
A . 0
B.
\( c \cdot-1 \)
D. Does not exist
Subject: Maths
If \( f(x)=\frac{x-e^{x}+\cos 2 x}{x^{2}}, x \neq 0 \) is
continuous at \( x=0, \) then
A \( \quad f(0)=\frac{-5}{2} \)
B . \( [f(0)]=-2 \)
c. \( f(0)=-0.5 \)
D. \( [f(0)] . f(0)=-1.5 \)
Subject: Maths
Consider the word \( W= \)
MISSISSIPPI Number of ways in
which the letters of the word \( W \) can be
arranged if at least one vowel is separated from rest of the vowels
A \( \frac{8 ! .16 !}{4 ! 4 ! ! 2 !} \)
в. \( \frac{8 ! .16 !}{4.4 ! .2 !} \)
c. \( \frac{8 ! .16 !}{4 ! .2 !} \)
D. \( \frac{8 !}{4 ! .2 !} \cdot \frac{165}{4 !} \)
Subject: Maths
If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) satisfies \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})= \)
\( \boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{y}) \) for all \( \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{R} \) and
\( f(1)=7, \) then \( \sum_{r=1}^{n} f(r) \)
\( A \cdot \frac{7 n}{2} \)
B. \( \frac{7(n+1)}{2} \)
\( \mathbf{c} \cdot 7 n(n+1) \)
D. \( \frac{7 n(n+1)}{2} \)
Subject: Physics
Two horizontal circular discs of
different radii are free to rotate about
their central axes. One disc is given
some angular velocity and the other is
stationary. Their rims are now brought
in contact. There is friction between the
rims. Correct statement from the
following is:
A. Force of friction between the rims will disappear when the discs rotate with same angular speed
B. Force of friction between the rims will disappear when they have equal linear velocities
C. Angular Momentum of the system is conserved
D. Rotational Kinetic Energy of the system is conserved.