AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A denser medium of refractive index 1.5
has a concave surface of radius of
curvature \( 12 \mathrm{cm} . \) An object is situated in the denser medium at a distance of 9
\( \mathrm{cm} \) from the pole. Locate the image due
to refraction in air
A. A real image at \( 8 \mathrm{cm} \)
B. A virtual image at \( 8 \mathrm{cm} \)
c. A real image at \( 4.8 \mathrm{cm} \)
D. A virtual image at \( 4.8 \mathrm{cm} \)
Subject: Chemistry
Which out of following hydrocarbons undergo addition reactions?
\( C_{2} H_{6}, C_{3} H_{8}, C_{3} H_{6}, C_{2} H_{2} \) and \( C H_{4} \)
A. \( C_{2} H_{6} \) and \( C_{3} H_{8} \)
B. \( C_{3} H_{6} \) and \( C_{2} H_{2} \)
c. \( C H_{4} \) and \( C_{2} H_{6} \)
D. \( C_{3} H_{8} \) and \( C_{2} H_{2} \)
Subject: Physics
A spring balance whose maximum extension of its spring is \( 20 \mathrm{cm} \) can
sustain a maximum load of \( 20 k g_{w t} \)
within its elastic limit on the surface of
the earth. Now the same balance
is taken to the moon. Given that
gearth \( =6 g_{\text {moon }}, \) what is the maximum
mass of the load that can be attached to
the balance to have half its maximum
extension?
A . 76
B. 65
c. 60
D. 55
Subject: Maths
\( \int \frac{1}{\sqrt{e^{5 x}, \sqrt[4]{\left(e^{2 x}+e^{-2 x}\right)^{3}}}} d x \)
\( \mathbf{A} \cdot-t^{1 / 4}, \) where \( 1+e^{-4 x}=t \)
B. \( t^{1 / 4}, \) where \( 1+e^{-4 x}=t \)
\( \mathbf{c} \cdot-t^{3 / 4}, \) where \( 1+e^{-4 x}=t \)
\( \mathbf{D} \cdot-t^{1 / 2}, \) where \( 1+e^{-4 x}=t \)
Subject: Maths
If \( \boldsymbol{p}=\boldsymbol{q} \) then \( \boldsymbol{p} \boldsymbol{x}= \)
\( \mathbf{A} \cdot \mathbf{q} \)
B. \( q x \)
\( \mathbf{c} \cdot q+x \)
D.
Subject: Physics
What is the approximate range of audible sound frequencies for a human
with good hearing?
A. From \( 20 H z \) to \( 2000 H z \)
B. From \( 20 H z \) to \( 20000 H z \)
c. From \( 200 H z \) to \( 20000 H z \)
D. From \( 200 H z \) to \( 200000 H z \)
Subject: Physics
A man sets his watch by the noon
whistle of a factory at a distance of
1.5 \( k m \). Then the number of seconds his
watch slower than the clock of the
factory (velocity of sound \( =\mathbf{3 3 2 m} / \mathrm{s} \)
is
A. 4.52 sec
B. 5.35 sec
c. 2.18 sec
D. 3.76 sec
Subject: Chemistry
An organic compound was used with sodium metal and extracted with
distilled water. On adding freshly
prepared \( F e S O_{4} \) solution followed by
the addition of \( F e C l_{3} \) and dil. \( H C l \)
produced greenish blue solution. \( 0.30 \mathrm{g} \) of the organic compound after kjeldahlisation evolved a gas (X) which
was passed on \( 100 \mathrm{ml} \) of \( 0.1 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4} \)
The excess of acid required \( 20 \mathrm{ml} \) of 0.5
M \( N a O H \) for neutralisation.
Dil. \( H C l \) is added to the solution in the
above test to:
A. make the solution acidic
B. to dissolve \( F e S O_{4} \)
c. to dissolve \( F e(O H) \) )
D. to change \( F e S O_{4} \) to \( F e C l_{2} \)
Subject: Biology
Pyruvic acid \( +C o A+N A D^{+} \frac{M g^{2+}}{X} \rightarrow \)
\( \boldsymbol{Y}+\boldsymbol{C O}_{2}+\boldsymbol{N} \boldsymbol{A} \boldsymbol{D} \boldsymbol{H}+\boldsymbol{H}^{+} \)
In the following reaction, identify \( X \) and Y respectively:
A. Water, Acetyl CoA
B. Acetyl CoA, Pyruvate dehydrogenase
c. Pyruvate dehydrogenase, Acetyl CoA
D. Pyruvate dehydrogenase, Oxalo-acetic acid
Subject: Maths
\( A: \) The angle between \( 2 \hat{i}-m \hat{j}+3 m \hat{k} \)
and \( (1+m) \hat{i}-2 m \hat{j}+\hat{k} \) is acute angle
for \( \boldsymbol{m} \notin\left[-\mathbf{2},-\frac{\mathbf{1}}{\mathbf{2}}\right] \)
\( \boldsymbol{R}: \) If \( (\boldsymbol{a}, \boldsymbol{b}) \) is acute, then \( \boldsymbol{a} \cdot \boldsymbol{b}>0 \)
A. Both \( A \) and \( R \) are true and \( R \) is the correct explanation of \( A \)
B. Both \( A \) and \( R \) are true and \( R \) is not correct explanation of \( A \)
c. \( A \) is true but \( R \) is false
D. \( A \) is false but \( R \) is true
Subject: Maths
Suppose \( a, b, c \epsilon R \) and \( a b c=1 . \) If \( A= \) \( \left[\begin{array}{ccc}2 a & b & c \\ b & 2 c & a \\ c & a & 2 b\end{array}\right] \) is such that \( |A|\left|A^{\prime}\right|=64 \)
and \( |A|>0, \) then find the value of
\( \left(a^{3}+b^{3}+c^{3}\right)^{4} \)
\( \left(A^{\prime} \text { denotes transpose of a matrix } A .\right) \)
A . 1
B. 2
\( c .3 \)
\( D \)
Subject: Maths
The length of latus rectum of the hyperbola \( 4 x^{2}-9 y^{2}-16 x-54 y- \)
\( \mathbf{1 0 1}=\mathbf{0} \) is
\( A \cdot \frac{8}{5} \)
B. \( \frac{8}{7} \)
\( c \cdot \frac{8}{9} \)
D. \( \frac{8}{3} \)
Subject: Physics
The maximum vertical distance
through which a fully dressed astronaut canjump on the earth is \( 0.5 m . \) If mean
density of the Moon is two-third that of the earth and radius is one quarter that of the earth, the maximum vertical
distance which he can jump on the
Moon and the ratio of the time of
duration of the jump on the Moon to hold on the earth are
в. \( 6 m, 3: \) ?
\( c .3 m, 1: 6 \)
D. \( 6 m, 1: 6 \)
Subject: Chemistry
Solubility product of a salt \( A B \) is \( 1 \times \) \( 10^{-8} \) in a solution in which
concentration of \( A \) is \( 10^{-3} \) M. The salt
will precipitate when the concentration of B becomes more than:
A \( \cdot 10^{-4} \)
B. \( 10^{-7} \)
\( \mathrm{c} \cdot 10^{-6} \)
D. \( 10^{-5} \)
Subject: Physics
Consider the situation shown in the
figure. The capacitor A has a charge q on it whereas \( \mathrm{B} \) is uncharged. Find the
charge appearing on the capacitor \( \mathrm{B} \) a long time after the switch is closed
A. zero
B. \( q / 2 \)
\( c \cdot q \)
D. \( 2 q \)
Subject: Maths
For any two events \( A \) and \( B \), the
conditional probability \( \boldsymbol{P}(\boldsymbol{B} / \boldsymbol{A})= \)
\( \frac{P(B \cap A)}{P(A)} \) and ifAand \( B \) are independent
\( \boldsymbol{P}(\boldsymbol{B} \cap \boldsymbol{A})=\boldsymbol{P}(\boldsymbol{B}) \cdot \boldsymbol{P}(\boldsymbol{A}) \) So,
\( \boldsymbol{P}(\boldsymbol{B} / \boldsymbol{A})=\boldsymbol{P}(\boldsymbol{B}) \)
A lot contains 50 defective and 50 non-
defective bulbs. Two bulbs are drawn at
random one at a time with replacement. The events \( A, B, C \) are defined as:
\( \mathbf{A}: \) 1st bulb is defective
\( \mathrm{B}: \) 2nd bulb is non-defective
\( \mathrm{C}: \) both are defective or both are non-
defective
then,
A. A, B, C are pair-wise independent as well as mutually independent
B. A, B, C are pair-wise independent but mutually not
c. \( A, B, C \) are mutually independent but pair-wise not
D - of these
Subject: Physics
It takes ten minutes to increase the
temperature of a body from \( 70^{\circ} \mathrm{C} \) to \( 80^{\circ} \)
c. Time required to increase the
temperature of the body from \( 60^{\circ} \) to \( 70^{\circ} \)
would be.
A. More than 10 minutes
B. Less than 10 minutes
c. 10 minutes
D. Data is inadequate so can't be determined
Subject: Physics
In Young's double slit experiment the two slits are illuminated by light of
wavelength \( 5890^{\circ} \mathrm{A} \) and the distance between the fringes obtained on
the screen is \( 0.2^{\circ} . \) If the whole
apparatus is immersed in water then
the angular fringe width will be (refractive index of water is \( 4 / 3 \) ):
A .0 .30
then 0.0 .030
в. \( 0.15^{\circ} \)
\( c \cdot 15 \)
D. \( 30^{\circ} \)
Subject: Physics
A block \( A \), whose weight is \( 200 N \), is
pulled up a slope of length \( 5 m \) by
means of a constant force \( \boldsymbol{F}(=\mathbf{1 5 0} \boldsymbol{N}) \)
as illuminated in figure. By how much has the potential energy of the block \( \boldsymbol{A} \)
increased?
\( A \cdot 0 J \)
В. \( 750 J \)
\( c .600 J \)
D. \( 450 J \)
Subject: Physics
Unpolarised light of intensity \( 32 \mathrm{W} \mathrm{m}^{-2} \)
passes through three polarizes is crossed with that of the first. The
intensity of final emerging light is 3 \( \mathrm{W} \mathrm{m}^{-2} . \) The intensity of light transmitted by first polarizer will be
\( A \cdot 32 W m^{-2} \)
B. \( 16 \mathrm{W} \mathrm{m}^{-2} \)
\( c \cdot 8 w m^{-2} \)
D. \( 4 \mathrm{Wm}^{-2} \)
Subject: Maths
\( \triangle R H P \sim \triangle N E D \) in \( \triangle N E D, N E= \)
\( 7 \mathrm{cm}, \angle E=30^{\circ}, \angle N=20^{\circ} \) and \( \frac{H P}{E D}=\frac{4}{5} \)
Construct \( \triangle R H P \)
Subject: Maths
For what value of \( \boldsymbol{K} \) will the following
pair of linear equations have infinitely many solutions?
\( \boldsymbol{K} \boldsymbol{x}+\boldsymbol{3} \boldsymbol{y}-(\boldsymbol{K}-\boldsymbol{3})=\mathbf{0} \)
\( \mathbf{1 2} \boldsymbol{x}+\boldsymbol{K} \boldsymbol{y}-\boldsymbol{K}=\mathbf{0} \)
Subject: Physics
Calculate the escape velocity of a body from the surface of the earth. [Average
density of earth \( =5.5 \times \)
\( \mathbf{1 0}^{\mathbf{3}} \mathbf{k g} / \boldsymbol{m}^{\mathbf{3}}, \boldsymbol{G}=\mathbf{6 . 6 7} \times \)
\( 10^{-11} N m^{2} / k g^{2}, \) radius of earth \( R= \)
\( \left.\mathbf{6 . 4} \times \mathbf{1 0}^{\mathbf{6}} \mathbf{m}\right] \)
Subject: Chemistry
\( N_{2} \) and \( H_{2} \) are taken in 1: 3 molar ratio
in a closed vessel to attained the
following equilibrium \( N_{2(g)}+ \)
\( \mathbf{3} \boldsymbol{H}_{\mathbf{2}(\boldsymbol{g})} \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{\boldsymbol{3}(\boldsymbol{g})} \) Find \( \boldsymbol{K}_{\boldsymbol{p}} \) for reaction
if total pressure at equilibrium is 2 P
and \( P_{N_{2}} \) is P/3.
A \( \cdot \frac{1}{3 P^{2}} \)
в. \( \frac{4}{3 P^{2}} \)
c. \( \frac{4 P^{2}}{3} \)
D. none
Subject: Physics
The flux of the electric field due to
charges distributed in a sphere of
radius \( 5 \mathrm{cm} \) is \( 10 \mathrm{Vm} \). What will be the
electric flux, through a concentric
sphere of radius \( 10 \mathrm{cm} ? \)
\( \mathbf{A} \cdot 20 \mathrm{Vm} \)
B. \( 30 \mathrm{Vm} \)
\( \mathbf{c} .5 \mathrm{Vm} \)
D. \( 10 \mathrm{Vm} \)
Subject: Chemistry
In the equilibrium \( N H_{4} H S(s) \Leftrightarrow \) \( N H_{3}(g)+H_{2} S(g) \) If the equilibrium
pressure is 2 atm at \( 80^{\circ} \mathrm{C} \mathrm{K}_{p} \) for the reaction is;
A. 0.5
B. 2
\( c \)
D. 1.5
Subject: Physics
Bulk modulus of water is \( 2 \times 10^{9} \) Pa. Air
is \( _{--}- \) - times more compressible than
water
A . 200
B . \( 2 \times 10^{3} \)
c. \( 2 \times 10^{5} \)
D . \( 2 \times 10^{4} \)
Subject: Chemistry
In a certain electronic transition in the
hydrogen atom from an initial state (1) to a final state (2), the difference in the
orbital radius \( \left(r_{1}-r_{2}\right) \) is 24 times the
first Bohr radius. Identify the transition:
\( \mathbf{A} \cdot 5 \rightarrow 1 \)
B . \( 25 \rightarrow 1 \)
c. \( 8 \rightarrow 3 \)
D. \( 1 \rightarrow 5 \)
Subject: Physics
an object \( A B E D \) is placed in front of a
concave mirror beyond the center of
curvature \( C \) as shown in figure. State the shape of the image
\( A \cdot\left|m_{A B}\right|<1 \) and \( \left|m_{E D}\right|<1 \)
B \cdot \( \left|m_{A B}\right|>1 \) and \( \left|m_{E D}\right|<1 \)
c. \( \left|m_{A B}\right|<1 \) and \( \left|m_{E D}\right|>1 \)
D. \( \left|m_{A B}\right|>1 \) and \( \left|m_{E D}\right|>1 \)
Subject: Physics
The force per unit length between two long straight conductors carrying currents 3 A each in the same direction
and separated by a distance of \( 2.0 \mathrm{cm} \) is
A \( \cdot 9 \times 10^{-7} N / m \)
В. \( 9 \times 10^{-6} N / m \)
c. \( 9 \times 10^{-5} N / m \)
D. \( 9 \times 10^{-4} N / m \)
Subject: Physics
The work done in carrying 20 coulomb charge through a distance of \( 5 \mathrm{m} \) is \( 2 J \)
The potential difference between these
two points will be:
\( \mathbf{A} \cdot 2 \times 10^{-1} V \)
B. \( 1 \times 10^{-2} V \)
c. \( 2 \times 10^{-2} V \)
D. \( 1 \times 10^{-1} V \)
Subject: Physics
Two long conductors, separated by a
distance \( d \) carry current \( I_{1} \) and \( I_{2} \) in the
same direction. They exert a force \( \boldsymbol{F} \) on
each other. Now the current in one of
them increased to two times and its
direction reversed. The distance is also
increased to \( 3 d \). The new value of the
force between them is
A . \( -2 F \)
в. \( F / 3 \)
\( \mathrm{c} \cdot-2 F / 3 \)
D. \( -F / 3 \)
Subject: Chemistry
\( N H_{2} C N_{(s)}+\frac{3}{2} O_{2(g)} \rightarrow N_{2(g)}+ \)
\( \boldsymbol{C O}_{2(g)}+\boldsymbol{H}_{2} \boldsymbol{O}_{(l)} \)
This reaction is carried out in a bomb
calorie-meter. The heat released was
\( 743 K J \) mol \( ^{-1} \). The value of \( \Delta H_{300} \) for
this reaction would be:
A. \( -740 \mathrm{KJ} \mathrm{mol}^{-1} \)
В. -741.75 КJ mol\( ^{-1} \)
c. \( -743.0 K J \) mol\( ^{-1} \)
D. \( -744.25 \mathrm{KJ} \mathrm{mol}^{-1} \)
Subject: Physics
The electric field in a certain region is acting radially outward and is given by \( E=A r . A \) charge contained in a sphere
of radius 'a' centered at the origin of the
field, will be given by :
A \( \cdot 4 \pi \epsilon_{0} A a^{3} \)
В \( \cdot \epsilon_{0} A a^{3} \)
\( \mathbf{c} \cdot 4 \pi \epsilon_{0} A a^{2} \)
D. \( A \epsilon_{0} a^{2} \)
Subject: Physics
In a certain double slit experimental arrangement interference fringes of width 1.0 mm each are observed when
light of wavelength \( 5000 \dot{A} \) is used. Keeping the set up unaltered, if the source is replaced by another source of wavelength \( 6000 A \), the fringe width will
be
A. \( 0.5 \mathrm{mm} \)
в. \( 1.0 \mathrm{mm} \)
\( \mathrm{c} .1 .2 \mathrm{mm} \)
D. \( 1.5 \mathrm{mm} \)
Subject: Chemistry
Match column I with column II and
select the correct answer using the codes given below:
Column I \( \quad \) Column
(A) \( \frac{14}{6} C \) and \( _{6}^{13} C \)
(p) Different
number of neutrons
(B) 40
20 \( \mathrm{Ca} \) and \( _{18}^{40} \boldsymbol{A r} \)
(q) Different
number of protons and neutrons
(C) \( \boldsymbol{K}(\mathbf{1} \mathbf{9}) \)
(r) Non-metal
(D) Chlorine (17)
(s) Metal
\( A \cdot A-(p) ; B-(q) ; C-(r) ; D-(s) \)
B. \( A-(q) ; B-(p) ; C-(s) ; D-(r) \)
c. \( A-(p) ; B-(q) ; C-(s) ; D-(r) \)
\( D \cdot A-(p) ; B-(s) ; C-(q) ; D-(r) \)
Subject: Maths
What is the value of \( p \) for which the
polynomial \( \boldsymbol{x}^{\mathbf{3}}+\mathbf{4} \boldsymbol{x}^{\mathbf{2}}-\boldsymbol{p} \boldsymbol{x}-\boldsymbol{6} \) is
completely divisible by \( (x-1) \)
Subject: Biology
Assertion
One is every six person in the world in
an Indian.
Reason
In India, there are more females than
males.
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 uniform conducting wire \( A B C \) lying in \( X Y \) plane has a mass of \( 10 g . A \)
current of \( 2 A \) flows through it. The wire
is kept in a uniform magnetic field \( B=2 T \) which acceleration of the wire
is
A. Zero
B \( \cdot 12 m / s^{2} \) and along postive \( Y \) -axis
C. \( 12 \times 10^{-3} \mathrm{m} / \mathrm{s}^{2} \) along postive \( Y \) -axis
D. \( 12 m / s^{2} \) and along postive \( X \) -axis
Subject: Physics
A particle of mass \( m \) strikes a wall with
a velocity \( v \) making an angle \( \theta \) with the
wall and rebounds.The change in
momentum of the particle will be :
\( \mathbf{A} \cdot-2 m \bar{v} \cos \theta \)
B. 0
\( \mathrm{c} \cdot 2 m \bar{v} \)
D. \( -2 m \bar{v} \sin \theta \)
Subject: Physics
A plano-convex lens has thickness \( 4 \mathrm{cm} \) When placed on a horizontal table with the curved surface in contact with it,
the apparent depth of the bottom-most point of the lens is found to be \( 3 \mathrm{cm} \). If the lens is inverted such that the plane face is in contact with the table, the
apparent depth of the centre of the
plane face of the lens is found to be \( 25 / 8 \mathrm{cm} . \) Find the focal length of the lens
Subject: Maths
Find the order of the following matrices.
(i) \( \left.\begin{array}{ccc}1 & -1 & 5 \\ -2 & 3 & 4\end{array}\right) \)
(ii)
(iii) \( \begin{array}{rl}3 & -26 \\ 6 & -11 \\ 2 & 4\end{array} \)
(iv) (345)
\( (v)\left[\begin{array}{cc}1 & 2 \\ -2 & 3 \\ 9 & 7 \\ 6 & 4\end{array}\right] \)
Subject: Chemistry
toppr
Q Type
solutıon (C). Lıthıum Is reacted with (B)
yielding a solid product (D) which effervescence with water to give a
strongly basic solution (E). When \( C O_{2} \) gas is bubbled through the solution (C), a white ppt (F) is formed but this redissolved forming solution (G) when
more \( C O_{2} \) is passed. The precipitate (F) effervesced when moistened with conc.
\( H C l \) and give deep red coloration to the Bunsen burner flame. (F) on heating
with an excess of carbon at \( 2000^{\circ} C \)
give (H).

Solution (G) contains a salt which:
(i) causes permanent hardness of water
(ii) can not be obtained in solid-state
(iii) causes temporary hardness of
water
(iv) can be obtained in solid-state
Identify the salt with correct options.
A. (i) and (ii)
B. (i) and (iv)
c. (ii) and (iii)
D. (ii) and (iv)
Subject: Chemistry
The number of \( 1^{0}, 2^{0} \) and \( 3^{0} \) alcoholic
groups in Mannitol or Sorbitol are:
\( A \cdot 2,4 \) and 0
B. 1,4 and 0
c. 2,2 and 0
D. 2, 1 and 1
Subject: Physics
left of a thin convex lens of focal length
\( 30 \mathrm{cm} . \) A convex spherical mirror of
radius of curvature \( 100 \mathrm{cm} \) is placed to
the right of the lens at a distance of
\( 50 \mathrm{cm} . \) The mirror is titled such that the
axis of the mirror is at a angle \( \boldsymbol{\theta}=\mathbf{3 0}^{\circ} \)
to the axis of the lens, as shown in the
figure.

If the origin of the coordinate system is
taken to be at the centre of the lens, the
coordinates \( (\text { in } c m) \) of the point \( (x, y) \)
at which the image is formed are:
\( \mathbf{A} \cdot(125 / 3,25 / \sqrt{3}) \)
B \( \cdot(50-25 \sqrt{3}, 25) \)
c. (0,0)
D. \( (25,25 \sqrt{3}) \)
Subject: Physics
Two coaxial coils are very close to each
other and their mutual inductance is
\( 5 m H . \) If a current 50 sin500t is passed
in one of the coils then the peak value of induced emf in the secondary coil will
be
A . \( 5000 V \)
B. \( 500 V \)
\( \mathbf{c} \cdot 150 V \)
D. \( 125 V \)
Subject: Physics
A solid metal sphere of radius \( \boldsymbol{R} \) has a
charge \( +2 Q . \) A hollow spherical shell of
radius \( 3 R \) placed concentric with the
first sphere has net charge - \( \boldsymbol{Q} \)
A. The electric field between the spheres at a distance \( r \) from the centre of the inner sphere at \( R<r<2 R \) is
\( \frac{Q}{2 \pi \epsilon_{0} r^{2}} \)
3. The potential difference between the spheres is \( \frac{Q}{3 \pi \epsilon_{0} R} \)
c. The final distribution of charges if the spheres are joined by a conducting wire is zero on both inner and outer surfaces of the outer sphere
\( D \)
If the inner sphere is earthed, the charge on it is
Subject: Maths
If \( X \) is normally distributed with mean 6 and standard deviation \( 5, \) find:
(i) \( \boldsymbol{P}[\mathbf{0} \leq \boldsymbol{X} \leq \mathbf{8}] \)
(ii) \( \boldsymbol{P}(|\boldsymbol{X}-\mathbf{6}|<\mathbf{1 0}) \)
Here \( \boldsymbol{P}(\mathbf{0}<\boldsymbol{Z}<\mathbf{1} . \mathbf{2})=\mathbf{0 . 3 8 4 9} \)
\( \boldsymbol{P}(\mathbf{0}<Z<\mathbf{0 . 4})=\mathbf{0 . 1 5 5 4} \)
\( \boldsymbol{P}(\mathbf{0}<\boldsymbol{Z}<\mathbf{2})=\mathbf{0 . 4 7 7 2} \)
Subject: Maths
In Hostel, one day reading hours of 20 students was observed, whose result is mentioned in the table below. Form the
table, find the Mode.
\[
\begin{array}{llllll}
\text { No. of } & 1- & 3- & 5- & 7- & 9- \\
\text { reading } & 3 & 5 & 7 & 9 & 11
\end{array}
\]
Student's strength in the nostel
Subject: Maths
Which of the following is a rational number?
\( \mathbf{A} \cdot 3^{29 / 27} .3^{27 / 29} \)
B \( \cdot \sqrt[6]{\left(3^{50 / 51} .3^{52 / 51}\right)^{3}} \)
\( \mathbf{c} \cdot 3^{15 / 6}-3^{7 / 8} \)
D. \( \sqrt[15]{\left(3^{3}\right)^{1 / 5}} \)
Subject: Maths
A particle is moving in a straight line such that its distance at any time t is given by \( \mathbf{S}=\frac{\boldsymbol{t}^{4}}{\mathbf{4}}-\mathbf{2} \boldsymbol{t}^{\mathbf{3}}+\mathbf{4} \boldsymbol{t}^{2}+\mathbf{7} \) then
its acceleration is minimum at \( t= \)
\( A \)
B. 2
\( c \cdot 1 / 2 \)
D. 3/2
Subject: Chemistry
Find the number of photons of radiation of frequency \( 5 \times 10^{13} s^{-1} \) that must be
absorbed in order to melt one gm ice when the latent heat of fusion of ice is
\( 331.5 j / g \)
A \( \cdot 10^{2} \)
2
B. \( 10^{25} \)
\( c \cdot 10^{28} \)
D. \( 10^{35} \)
Subject: Physics
In the figure shown \( X \) and \( Y \) components of acceleration of center of mass are [All
surfaces are smooth]
A \( \cdot\left(a_{C M}\right)_{X}=\frac{m_{1} m_{2} g}{m_{1}+m_{2}} \)
В. \( \left(a_{C M}\right)_{X}=\frac{m_{1} m_{2} g}{\left(m_{1}+m_{2}\right)^{2}} \)
\( ^{\mathrm{c}}\left(a_{C M}\right)_{Y}=\left(\frac{m_{2}}{m_{1}+m_{2}}\right)^{2} g \)
D. Both (B) and (C) are correct
Subject: Physics
A sample of \( 2 \mathrm{kg} \) of monoatomic Helium(assume ideal) is taken through
the process \( A B C \) and another sample of
\( 2 \mathrm{kg} \) of the same gas is taken through the process ADC. Given, relative molecular mass of Helium \( =4 \)
What is the temperature of Helium in
each of the states \( A, B, C \) and \( D ? \)
A \( \cdot T_{A}=220.33 K ; T_{B}=T_{D}=2 T_{A} ; T_{C}=5 T_{A} \)
B. \( T_{A}=320.33 K ; T_{B}=T_{D}=3 T_{A} ; T_{C}=4 T_{A} \)
\( \mathbf{c} \cdot T_{A}=120.33 K ; T_{B}=T_{D}=2 T_{A} ; T_{C}=4 T_{A} \)
D. \( T_{A}=520.33 K ; T_{B}=T_{D}=2 T_{A} ; T_{C}=4 T_{A} \)
Subject: Chemistry
Select the correct statements:
This question has multiple correct options
A. ferric bromide is obtained when chlorine gas is bubbled through a solution of ferrous bromide.
B. sodium sulphate is obtained when \( S O_{2}(g), H_{2} O(g) \) and air are passed over heated sodium chloride.
\( \mathrm{C} \cdot \mathrm{H}_{2} \mathrm{S} \) gas is liberated when aluminium sulphide becomes damp.
D. nitrogen dioxide gas is liberated by the reaction of ammonia with neutral \( K M n O_{4} \)
Subject: Maths
\( \int \frac{1}{1+\sin x} d x= \)
A \( \cdot \tan x+\sec x+c \)
B. \( \tan x-\sec x+c \)
c. \( \cot x-\operatorname{cosec} x+c \)
D. - \( \cot x+\sec x+c \)
Subject: Maths
A farmer bought a cow and a calf together for Rs. \( 14000 . \) After some time, he sold the cow at a profit of \( 20 \% \) and the calf at a profit of \( 13 \% \). On the whole he got a profit of \( 17 \% \). Find the cost price of the cow and the calf.
A. Rs. 8000, Rs. 6000
B. Rs. 6000, Rs. 6000
c. Rs. 8000, Rs. 8000
D. Rs. 9000, Rs. 5000
Subject: Physics
A source \( S_{1} \) is producing, \( 10^{15} \) photons
per second of wavelength \( 5000 A^{0} \)
Another source \( S_{2} \) is producing \( 1.02 \times \)
\( 10^{15} \) photon per second of wave length
\( 5100 A^{\circ}, \) then ratio of power of Source
\( \boldsymbol{S}_{2} \) and power of Source \( \boldsymbol{S}_{1} \)
A . 1.00
B. 1.02
\( c \cdot 1.04 \)
D. 2.00
Subject: Physics
The energy emitted per second by sun is approximately
A . \( 3.8 \times 10^{26} \) Joule
B. \( 3.8 \times 10^{14} \) Joule
c. \( 3.8 \times 10^{12} \) Joule
D. \( 3.8 \times 10^{-26} \) Joule
Subject: Physics
Assertion
The given equation \( \boldsymbol{x}=\boldsymbol{x}_{0}+\boldsymbol{u}_{0} \boldsymbol{t}+ \)
\( \frac{1}{2} a t^{2} \) is dimensionally correct, where
is the distance travelled by a particle in
time \( t, \) initial position \( x_{0}, \) initial velocity
\( u_{0} \) and uniform acceleration a is along the direction of motion
Reason
Dimensional analysis can be used for checking the dimensional consistency or homogeneity of the equation.
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
If \( \boldsymbol{A}-\boldsymbol{B}=\boldsymbol{\phi}, \) then relation between \( \mathbf{A} \)
and B is
This question has multiple correct options
\( \mathbf{A} \cdot A \neq B \)
в. \( B \subset A \)
c. \( A \subset B \)
D. \( A=B \)
Subject: Maths
Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} ; \) if \( \boldsymbol{y}=\tan ^{-1}\left(\frac{\sin \boldsymbol{x}}{\mathbf{1}+\cos \boldsymbol{x}}\right) \)