AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Biology
Match the columns.
A \( \begin{array}{clcc} & \text { List I } & & \text { List } \\ & & & \text { II } \\ \text { A } & \text { Residual volume } & 1 & 4.6 \mathrm{L} \\ \text { B } & \text { Vital capacity } & 2 & 1.2 \mathrm{L} \\ \text { C } & \begin{array}{l}\text { Inspiratory reserve } \\ \text { volume }\end{array} & 3 & 3.5 \mathrm{L} \\ \text { D } & \text { Inspiratory capacity } & 4 & 3 \mathrm{L}\end{array} \)
A. \( A-2, B-1, C-4, D-3 \)
B. \( A-2, B-1, C-3, D-4 \)
D. \( A-1, B-2, C-3, D-4 \)
Subject: Maths
In Fig. 9.20 .0 is the centre of a circle of
radius \( 5 \mathrm{cm}, \) T is a point such that \( \mathrm{OT}= \)
\( 13 \mathrm{cm} \) and \( \mathrm{OT} \) intersects the circle at \( \mathrm{E} \). If
AB is the tangent to the circle at \( \mathrm{E} \) and
it intersects the tangents PT and QT at \( A \) and \( B, \) find the length of \( A B \)
A \( \cdot \frac{10}{3} \mathrm{cm} \)
B. \( \frac{20}{3} \mathrm{cm} \)
\( c .10 \mathrm{cm} \)
D. \( 15 \mathrm{cm} \)
Subject: Chemistry
(a) Draw the structures of the following molecules:
(i) \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2} \)
(ii) \( \boldsymbol{C l} \boldsymbol{F}_{3} \)
(b) Explain the following observations:
(i) Nitrogen is much less reactive than phosphorus.
(ii) Despite having greater polarity, hydrogen fluoride boils at a lower temperature than water
(iii) Sulphur has a greater tendency for catenation than oxygen in the same
group.
Subject: Chemistry
One \( g m \) metal \( M^{3+} \) was discharged by
the passage of \( 1.81 \times 10^{23} \) electrons.
What is the atomic mass of metal?
\( \mathbf{A} \cdot 8 g / m o l \)
в. \( 9 g / m o l \)
c. \( 10 g / \) mol
D. None of these
Subject: Maths
A particle moves along a curve so that
its coordinates at time \( t \) are \( \boldsymbol{x}=\boldsymbol{t}, \boldsymbol{y}= \) \( \frac{1}{2} t^{2}, z=\frac{1}{3} t^{3} \) acceleration at \( t=1 \) is
\( \mathbf{A} \cdot j+2 k \)
B. \( j+k \)
\( c \cdot 2 j+k \)
D. none of these
Subject: Physics
The correct value of dip angle at a place
is \( 45^{\circ} . \) If the dip circle is rotated by \( 45^{\circ} \) out of the meridian, then the tangent of the angle of apparent dip at the place is
A . 1
B. \( 1 / 2 \)
c. \( 1 / \sqrt{2} \)
D. \( \sqrt{2} \)
Subject: Biology
Identify the wrong statements from the following.
(i) Branches of limited growth in
Asparagus perform photosynthesis.
(ii) Petiole of Australian Acacia helps in
climbing.
(iii) Floral buds of Agave store food materials.
(iv) Aerial roots of taeniophyllum help in
vegetative propagation.
A. i, iv
B. i, i i
C . iii, iv
D. ii, iv
Subject: Maths
\( \mathbf{f} \boldsymbol{x}=\sum_{n=0}^{\infty} \boldsymbol{a}^{n}, \boldsymbol{y}=\sum_{n=0}^{\infty} \boldsymbol{b}^{n}, \boldsymbol{z}=\sum_{n=0}^{\infty}(\boldsymbol{a} \boldsymbol{b})^{n} \)
where \( a, b<1 \) then prove that \( x z+ \)
\( \boldsymbol{y} \boldsymbol{z}=\boldsymbol{x} \boldsymbol{y}+\boldsymbol{z} \)
Another form:
For \( \mathbf{0}<\boldsymbol{\theta}, \boldsymbol{\phi}-\frac{\boldsymbol{\pi}}{\mathbf{2}} \) if \( \boldsymbol{x}=\sum_{n=0}^{\infty} \cos ^{2 n} \boldsymbol{\theta} \)
\( \boldsymbol{y}=\sum_{n=0}^{\infty} \sin ^{2 n} \phi, z=\sum_{n=0}^{\infty} \cos ^{2 n} \theta \sin ^{2 n} \phi \)
then prove that \( \boldsymbol{x} \boldsymbol{z}+\boldsymbol{y} \boldsymbol{z}-\boldsymbol{z}=\boldsymbol{x} \boldsymbol{y} \)
Subject: Chemistry
Select the correct IUPAC name for
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]^{2+} \)
A. Hexammoniacobaltate(II) ion
B. Hexaamminecobaltate(II) ion
c. Hexammoniacobalt(II) ion
D. Hexaamminecobalt(II) ion
Subject: Maths
If
\( A B \) is a chord of a circle with centre \( O \)
and \( P \) is a point on \( A B \) such that \( B P=4 P A, O P=5 \mathrm{cm} \) and the radius
of the circle is \( 7 \mathrm{cm} \), find the value of \( (\sqrt{6} \times A B) \)
Subject: Maths
Left hand derivative and right hand
derivative of a function \( f(x) \) at a point \( x=a \) are defined as
\( f^{\prime}\left(a^{-}\right)=\lim _{h \rightarrow 0^{+}} \frac{f(a)-f(a-h)}{h}= \)
\( \lim _{h \rightarrow 0^{-}} \frac{f(a)-f(a-h)}{h}= \)
\( \lim _{x \rightarrow a^{+}} \frac{f(a)-f(x)}{a-x} \) respectively
Let \( f \) be a twice differentiable function.
We also know that derivative of an even
function is odd function and derivative
of an odd function is even function.
If \( f \) is odd, which of the following is Lefthand derivative of \( f \) at \( x=a \)
A \( \cdot \lim _{h \rightarrow 0^{-}} \frac{f(a-h)-f(a)}{-h} \)
в. \( \lim _{h \rightarrow 0^{-}} \frac{f(a-h)-f(a)}{h} \)
c. \( \lim _{h \rightarrow 0^{+}} \frac{f(a)+-f(a-h)}{-h} \)
D. \( \lim _{h \rightarrow 0^{-}} \frac{f(-a)-f(-a-h)}{-h} \)
Subject: Physics
In a vertical plane \( p_{1} \) making angle \( 30^{\circ} \) with magnetic meridian, apparent
angle of dip in vertical plane \( p_{2} \) is \( 60^{\circ} \)
which is perpendicular to plane \( p_{1} \) is:
A \( .30^{\circ} \)
B . \( 45^{\circ} \)
\( \mathbf{c} \cdot \tan ^{-1}(3) \)
D. \( \tan ^{-1}\left(\frac{2}{3}\right) \)
Subject: Maths
The two curves \( x^{3}-3 x y^{2}+2=0 \) and
\( \mathbf{3} \boldsymbol{x}^{2} \boldsymbol{y}-\boldsymbol{y}^{3}-\boldsymbol{2}=\mathbf{0} \)
A. cut at right angles
B. touch each other
c. cut at an angle \( \frac{\pi}{3} \)
D. cut at an angle \( \frac{\pi}{4} \)
Subject: Maths
\( \mathbf{A}=\left[\begin{array}{cc}\mathbf{1 1} & \mathbf{1} \\ \mathbf{0} & \mathbf{1 1}\end{array}\right], \mathbf{B}=\left[\begin{array}{cc}\mathbf{0} & -\mathbf{2} \\ -\mathbf{3} & \mathbf{4}\end{array}\right], \mathbf{I}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{0} \\ \mathbf{0} & \mathbf{1}\end{array}\right] \)
Find \( \boldsymbol{A}+\mathbf{3} \boldsymbol{B}+\boldsymbol{4} \boldsymbol{I} \)
A \( \cdot\left[\begin{array}{cc}0 & 2 \\ -3 & 0\end{array}\right] \)
B \( \cdot\left[\begin{array}{cc}15 & 2 \\ -13 & -16\end{array}\right] \)
c. \( \left[\begin{array}{cc}15 & -5 \\ -9 & 27\end{array}\right] \)
D. \( \left[\begin{array}{cc}11 & 2 \\ -4 & -5\end{array}\right] \)
Subject: Chemistry
A diatomic ideal gas initially at 273 k is given 100 cal heat due to which system did \( 209 \mathrm{J} \) work Molar heat capacity
\( \left(C_{m}\right) \) of gas for the process is :
A \( \cdot \frac{3}{2} \) R
B \( \cdot \frac{5}{2} \) R
\( c \cdot \frac{5}{4} R \)
D. 5 R
Subject: Physics
In above shown figure of refrigeration
system. Which of the following
statement explains why work is an input into this system?
A. Work is needed to move thermal energy against temperature gradient.
B. Work is needed to reduce the amount of thermal energy lost during transfer.
c. work uses energy from the cold reservoir to reduce the temperature of the system.
D. Work adds energy to the cold reservoir to increase the flow to the hot reservoir.
E. Work adds heat to the system, causing the temperature of both reservoirs to increase.
Subject: Chemistry
If series limit (in \( n m \) ) of a series of
hydrogen spectrum which contains a photon of wavelength 1278.35 nm is expressed as \( \frac{1240}{x}, \) then \( x \) is:
(Given \( : h c=1240 \mathrm{eV}-\mathrm{nm}) \)
A . \( 1.51 e V \)
в. \( 2 e V \)
c. \( 3.4 e V \)
D. \( 0.66 e V \)
Subject: Physics
Two condensers each of capacitance \( 2 \mu F \) are connected in parallel and this
combination is connected in series with
a \( 12 \mu F \) capacitor. The resultant
capacity of the system will be:
A. \( 16 \mu f \)
в. \( 13 \mu f \)
c. \( 6 \mu f \)
D. \( 3 \mu f \)
Subject: Physics
Four wires of the same diameter are
connected, in turn, between two points maintained at a constant potential difference. Their resistivity's and lengths are; \( \rho \) and \( L(\text { wire } 1), 1.2 \rho \) and 1.2L (wire 2), \( 0.9 \rho \) and 0.9L (wire 3) and
\( \rho \) and \( 1.5 \mathrm{L} \) (wire 4 ). Rank the wires
according to the rates at which energy is dissipated as heat, greatest first.
A \( .4>3>1>2 \)
в. \( 4>2>1>3 \)
c. \( 1>2>3>4 \)
D. \( 3>1>2>4 \)
Subject: Physics
The diagonals of a parallelogram are represented by \( R_{1}=3 \hat{i}+2 \hat{j}-7 \hat{k} \) and \( \boldsymbol{R}_{2}=\mathbf{5} \hat{\boldsymbol{i}}+\boldsymbol{6} \hat{\boldsymbol{j}}-\boldsymbol{3} \hat{k} . \) Find the area of the
parallelogram.
Subject: Physics
Statement 1: When a man is standing on a stationary horizontal surface, the normal force exerted by the ground on him is equal and opposite to his weight.
Statement 2: According to Newton's 3 \( ^{r d} \)
law , every action has an equal and
opposite reaction.
A. Statement 1 - is true, statement- 2 is true and statement-2 is correct explanation for statement-
B. Statement 1 - is true, statement- 2 is true and statement-2 is NOT the correct explanation for statement-
c. Statement 1 - is true, statement- 2 is false
D. Statement 1 - is false, statement- - 2 is true
Subject: Maths
The geometric mean of the numbers \( \mathbf{7}, \mathbf{7}^{2}, \mathbf{7}^{\mathbf{3}}, \dots, \mathbf{7}^{n} \mathbf{i} \mathbf{s} \)
\( A \cdot 7^{7 / 4} \)
B \( \cdot 7^{4 / 7} \)
\( c \cdot 7^{\frac{n-1}{2}-\frac{1}{2}-\frac{2}{2}-\frac{2}{2}} \)
\( D \cdot 7^{\frac{n-1}{2}} \)
Subject: Maths
\( \mathbf{f} \boldsymbol{y}=\sin \left\{\tan ^{-1} \sqrt{\left(\frac{1-x}{1+x}\right)}\right\} \) prove that
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{- x}}{\sqrt{\mathbf{1 - x}^{2}}} \)
Subject: Physics
Find out the temperature of absolute
zero kelvin.
\( \mathbf{A} \cdot 0^{\circ} C \)
в. \( 100^{\circ} \mathrm{C} \)
c. \( 273^{\circ} \mathrm{C} \)
D. \( -273^{\circ} C \)
E \( .-100^{\circ} \mathrm{C} \)
Subject: Physics
A potentiometer wire \( 10 \mathrm{m} \) long has a resistance of \( 40 \Omega . \) It is connected in
series with a resistance box and a \( 2 \mathrm{V} \)
storage cell. If the potential gradient along the wire is \( 0.1 \mathrm{mV} / \mathrm{cm}, \) the resistance in the box is
\( A \cdot 760 \Omega \)
B. 260\Omega
c. \( 1060 \Omega \)
D. \( 960 \Omega \)
Subject: Physics
\( I_{1} \) is moment of inertia of a thin circular
ring about its own axis. The ring is cut at a point then it is unfolded into a
straight rod. If \( I_{2} \) is moment of inertia of
the rod about an axis perpendicular to the length of rod and passing through
its centre, then the ratio of \( I_{1} \) to \( I_{2} \) is:
A . \( 3: \pi \)
B. \( 3: \pi^{2} \)
c. \( 4: \pi \)
D. \( 4: \pi^{2} \)
Subject: Physics
If the wavelength of light used is 6000 A. The angular resolution of telescope of objective lens having diameter \( 10 \mathrm{cm} \) is rad
A \( \cdot 7.52 \times 10^{-6} \)
в. \( 6.10 \times 10^{-6} \)
c. \( 6.55 \times 10^{-6} \)
D. \( 7.32 \times 10^{-6} \)
Subject: Chemistry
Elements \( A, B, C, O \) and \( E \) having the following electronic configuration
(i) \( 1 s^{2}, 2 s^{2}, 2 p^{1} \)
(ii) \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 3 p^{1} \)
(iii) \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 3 p^{3} \)
(iv) \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 3 p^{5} \)
\( (v) 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 3 p^{6} \)
Electronic configurations belonging to
the same group are:
A. (i) and (iii)
B. (i) and (iv)
c. (i) and (ii)
D. (i) and (v)
Subject: Maths
Find the \( 7^{t h} \) term from the end in the
expansion of \( \left(2 x^{2}-\frac{3}{2 x}\right)^{8} \)
A . \( 4033 x^{9} \)
В. \( 4023 x^{11} \)
c. \( 4032 x^{10} \)
D. None of these
Subject: Maths
I: The real number x when added to its
inverse gives the minimum positive
value of the sum at \( x=1 \)
Il: If product of the two positive numbers is 400 , then the minimum value of their
sum is 20
which of the above statements are true
A . only lis true
B. only II is true
c. both I and II are true
D. niether I nor II are true
Subject: Physics
Two particle move in a uniform gravitational field with an acceleration
\( g . \) At the initial moment the particles
were located over a tower at one point
and moved with velocities \( \boldsymbol{v}_{1}=\mathbf{3} \boldsymbol{m} / s \)
and \( v_{2}=4 m / s \) horizontally opposite
directions. Find the distance between
the particles at the moment when their velocity vectors become mutually perpendicular.
Subject: Chemistry
0.75 mole of solid \( ^{\circ} A_{4}^{\prime} \) and 2 moles of
gaseous \( \boldsymbol{O}_{2} \) are heated in a sealed
vessel, completely using up the reactants and producing only one compound. It is found that when the temperature is reduced to the initial temperature, the contents of the vessel
exhibit a pressure equal to half the original pressure. What conclusions can be drawn from these data the
product of the reaction?
A. \( A_{2} O_{5} \)
в. \( A_{3} O_{4} \)
\( c \cdot A_{2} O_{2} \)
D. none of these
Subject: Physics
Two masses as shown are suspended
from a massless pulley. Calculate the
acceleration of the 10 kg mass when
masses are left free
\( \mathbf{A} \cdot \frac{2 g}{3} \)
B. \( \frac{g}{3} \)
c. \( \frac{g}{9} \)
\( D \cdot \underline{g} \)
Subject: Maths
If \( A \) and \( B \) are symmetric matrices of the same order and \( X=A B+B A \) and
\( \boldsymbol{Y}=\boldsymbol{A} \boldsymbol{B}-\boldsymbol{B} \boldsymbol{A}, \) then \( \boldsymbol{X} \boldsymbol{Y}^{\boldsymbol{T}} \) is equal to
A . \( X Y \)
в. \( Y X \)
\( \mathrm{c} \cdot-Y X \)
D. none of these
Subject: Physics
A guitar string is \( 90 \mathrm{cm} \) long and has a fundamental frequency of \( 124 H z . \) To produce a fundamental frequency of
\( 186 H z, \) the guitar should be pressed at
\( ? \)
\( \mathbf{A} \cdot 60 \mathrm{cm} \)
в. \( 30 \mathrm{cm} \)
\( c \cdot 20 c m \)
D. \( 10 \mathrm{cm} \)
Subject: Physics
An ultrasonic wave is sent from a ship towards the bottom of the sea. It is
found that the time interval between the
sending and receiving of wave is 1.6 s. What is the depth of the sea, if the
velocity of sound in sea water is \( 1400 \mathrm{m} \)
\( s^{-1} ? \)
A. \( 1120 \mathrm{m} \)
B. 60 \( m \)
\( c .1400 \mathrm{m} \)
D. 112 m
Subject: Maths
The mode of the distribution
\begin{tabular}{lccccc} 
Marks & 4 & 5 & 6 & 7 & 8 \\
No. of students & 6 & 7 & 10 & 8 & 3 \\
\hline
\end{tabular}
A. 5
B. 6
\( c \cdot 8 \)
D. 10
Subject: Physics
An air bubble of radius \( 1.0 \mathrm{cm} \) rises
with a constant speed of 3.5 mm/s
through a liquid of density \( 1.75 \times \) \( 10^{3} k g / m^{3} . \) The coefficient of viscosity
of the liquid is: (Neglect the density of
air)
A \( \cdot 109 \mathrm{Ns} / \mathrm{m}^{2} \)
В. \( 10.9 \mathrm{Ns} / \mathrm{m}^{2} \)
c. \( 1.09 \mathrm{Ns} / \mathrm{m}^{2} \)
D. \( 0.109 \mathrm{Ns} / \mathrm{m}^{2} \)
Subject: Maths
If \( \frac{l z_{2}}{m z_{1}} \) is purely imaginary number then \( \left|\frac{\boldsymbol{\lambda} \boldsymbol{z}_{1}+\boldsymbol{\mu} \boldsymbol{z}_{2}}{\boldsymbol{\lambda} \boldsymbol{z}_{1}-\boldsymbol{\mu} \boldsymbol{z}_{2}}\right| \) is equal to
A \( \cdot \frac{l}{m} \)
B. \( \frac{\lambda}{\mu} \)
\( c \cdot \frac{-\lambda}{\mu} \)
\( D \)
Subject: Maths
\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{3} & \mathbf{2} & \mathbf{0} \\ \mathbf{1} & \mathbf{4} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} & \mathbf{5}\end{array}\right] . \) Show that \( \boldsymbol{A}^{\mathbf{2}} \)
\[
\mathbf{7 A}+\mathbf{1 0}=\mathbf{0}
\]
Subject: Physics
A point charge of \( +6 \mu C \) is placed at a distance \( 20 \mathrm{cm} \) directly above the centre of a square of side \( 40 \mathrm{cm} . \) The magnitude of the flux through the
square is
\( A \cdot \epsilon_{0} \)
в. \( \frac{1}{\epsilon_{0}} \)
c. \( \epsilon_{0} \times 10^{-6} \)
D. \( \frac{1}{\epsilon_{0}} \times 10^{-6} \)
Subject: Chemistry
A metal forms two oxides. The higher oxide contains \( 80 \% \) metal. \( 0.72 g \) of the
lower oxide gave \( 0.8 g \) of higher oxide when oxidized. Then the ratio of the weight of oxygen that combines with the fixed weight of the metal in the two oxides will be:
A .2: 3
B . 2: 1
c. 4: 5
D. 3: 2
Subject: Maths
\( A=\left[\begin{array}{lll}1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1\end{array}\right], U_{1}, U_{2} \) and \( U_{3} \) are
columns matrices satisfying \( \boldsymbol{A} \boldsymbol{U}_{1}= \) \( \left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right], A U_{2}=\left[\begin{array}{l}2 \\ 3 \\ 0\end{array}\right], A U_{3}=\left[\begin{array}{l}2 \\ 3 \\ 1\end{array}\right] \) and \( U \) is
\( 3 \times 3 \) matrix whose columns are
\( U_{1}, U_{2}, U_{3} \) then answer the following question The value of \( \left[\begin{array}{lll}\mathbf{3} & \mathbf{2} & \mathbf{0}\end{array}\right] \boldsymbol{U}\left[\begin{array}{l}\mathbf{3} \\ \mathbf{2} \\ \mathbf{0}\end{array}\right] \) is
\( A \cdot[5] \)
в. \( \left[\frac{5}{2}\right] \)
\( c \cdot[4] \)
D. \( \left[\frac{3}{2}\right. \)
Subject: Maths
Tangents are drawn from the point \( (a, a) \) to the circle \( x^{2}+y^{2}-2 x-2 y- \)
\( 6=0 . \) If the angle between the tangents lies in the range \( \left(\frac{\pi}{3}, \pi\right), \) then the exhaustive range of values of \( a \) is
B. (-5,-3)\( \cup(3,5) \)
c. \( (-\infty, 2 \sqrt{2}) \cup(2 \sqrt{2}, \infty) \)
D. (-3,-1)\( \cup(3,5) \)
Subject: Chemistry
When the concentration of \( \boldsymbol{K}^{+} \) across a
cell membrane drops from \( 0.01 M \) to
\( 0.001 M, \) the potential difference across the membrane is:
A . \( 0.0 V \)
B. \( 0.0059 V \)
c. \( 0.059 V \)
D. \( 0.59 V \)
Subject: Maths
Two parallel chords in a circle are \( 10 \mathrm{cm} 10 \mathrm{cm} \) and \( 24 \mathrm{cm} 24 \mathrm{cm} \) long. If
the radius of the circle is \( 13 \mathrm{cm} 13 \mathrm{cm} \) find the distance between the chords if
thay lie on the same side of the centre.
Subject: Physics
When will the couple acting on the coil be
(i) maximum
(ii) minimum?
A. (i) When plane of coil is normal to the magnetic field,
(ii) When plane of coil is normal to the magnetic field
B. (i) When plane of coil is parallel to the magnetic field
(ii) When plane of coil is parallel to the magnetic field.
C. (i) When plane of coil is parallel to the magnetic field,
(ii) When plane of coil is normal to the magnetic field
D. None of the above
Subject: Maths
\( \mathbf{3 . 6}+\mathbf{6 . 9}+\mathbf{9 . 1 2}+\ldots+\mathbf{3 n}(\mathbf{3 n}+\mathbf{3})= \)
A \( \frac{n(n+1)(n+2)}{3} \)
B. \( 3 n(n+1)(n+2) \)
c. \( \frac{(n+1)(n+2)(n+3)}{3} \)
\( \frac{(n+1)(n+2)(n+4)}{4} \)
Subject: Physics
Q Type your question
(density \( \rho) \) moves with a velocity \( ^{\prime} v^{\prime} \)
inside the tube and comes to rest inside
the bubble. The surface tension of the
soap solution is \( T . \) After some time the
bubble, having grown to a radius' \( r^{\prime} \)
separates from the tube. Find the value
of ' \( r^{\prime} \). Assume that \( r>>b \) so that you
can consider the air to be falling
normally on the bubble's surface.
A \( \cdot \frac{4 T}{P v^{2}} \)
в. \( \frac{4 T}{P v} \)
c. \( \frac{2 T}{P v^{2}} \)
D. \( \frac{4 T}{P_{v}^{3}} \)
Subject: Chemistry
Which of the following has 0-0 linkage:
A \( \cdot \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{6} \)
в. \( \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{8} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{3} \)
D. \( \mathrm{H}_{2} \mathrm{S}_{4} \mathrm{O}_{6} \)
Subject: Physics
A wire of length L metre carrying current ampere is bent in the form of a circle.
What is the magnitude of magnetic
dipole moment?
A \( \cdot I L^{2} / 4 \pi \)
B . \( I^{2} L^{2} / 4 \pi \)
c. \( I^{2} L / 8 \pi \)
D. \( I L^{2} / 8 \pi \)
Subject: Maths
Assertion
Consider \( \boldsymbol{f}(\boldsymbol{x})=\sin ^{-1}\left(\sec \left(\tan ^{-1} \boldsymbol{x}\right)+\right. \)
\( \cos ^{-1}\left(\operatorname{cosec}\left(\cot ^{-1} x\right)\right. \)
Statement-1: Domain of \( f(x) \) is a
singleton.
Reason
Statement-2: Range of the function \( \boldsymbol{f}(\boldsymbol{x}) \)
is a singleton.
A. Statement-1 is true, Statement-2 is true and Statement-2 is correct explanation for Statement-1.
B. Statement-1 is true, Statement-2 is true and Statement-2 is NOT the correct explanation for Statement-1.
c. Statement- lis true, Statement-2 is false.
D. Statement-1 is false, Statement-2 is true
Subject: Physics
A barometer reads \( 75 \mathrm{cm} \) of mercury.
When \( 2.0 \mathrm{cm}^{3} \) of air at atmospheric
pressure is introduced into space above the mercury level, the volume of the space becomes \( 50 \mathrm{cm}^{3} \). The length
by which the mercury column descends is
A. \( 3 \mathrm{cm} \) of \( \mathrm{Hg} \)
B. \( 6 \mathrm{cm} \) of \( \mathrm{Hg} \)
c. \( 30 \mathrm{cm} \) of \( \mathrm{Hg} \)
D. \( 10 \mathrm{cm} \) of \( \mathrm{Hg} \)
Subject: Maths
If \( \boldsymbol{x}+\frac{\mathbf{1}}{\boldsymbol{x}}=\boldsymbol{a}+\boldsymbol{b} \) and \( \boldsymbol{x}-\frac{\mathbf{1}}{\boldsymbol{x}}=\boldsymbol{a}-\boldsymbol{b} \)
then, which of the following is correct?
\( \mathbf{A} \cdot a b=1 \)
B. \( a b=2 \)
\( \mathbf{c} \cdot a+b=0 \)
\( \mathbf{D} \cdot a=b \)
Subject: Chemistry
\( \boldsymbol{C O}_{2}+\boldsymbol{N} \boldsymbol{H}_{3}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{X} \)
\( \boldsymbol{X}+\boldsymbol{N} \boldsymbol{a} \boldsymbol{C l} \rightarrow \boldsymbol{Y}+\boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{C l} \)
'Y' in the above reaction is:
\( \mathbf{A} \cdot N a_{2} C O_{3} \)
в. \( \left(N H_{4}\right)_{2} C O_{3} \)
c. \( N H_{4} H C O_{3} \)
D. \( N a H C O_{3} \)
Subject: Chemistry
Which of the following is not a correct
postulate of kinetic theory of gases?
A. The molecules of a gas are continuously moving in different directions with different velocities.
B. The average kinetic energy of the gas molecules is directly proportional to the absolute temperature of the gas.
C. The volume of the gas is due to the large number of molecules present in it.
D. The pressure of the gas is due to the collision of the molecules on the walls of the container.
Subject: Biology
Assertion
Spongy bones are specialized to form
erythrocytes.
Reason
They contain osteocytes and
osteoblasts.
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
The maximum velocity of a body
undergoing S.H.M. is \( 0.2 m / s \) and its
acceleration at \( 0.1 \mathrm{m} \) from the mean
position is \( 0.4 m / s^{-2} \) The amplitude of
the S.H.M. is:
A . \( 0.25 m \)
в. \( 0.3 m \)
\( \mathrm{c} .0 .1 \mathrm{m} \)
D. \( 1.05 m \)
Subject: Maths
If \( f \) is a real-valued differentiable
function such that \( f(x) f^{\prime}(x)<0 \) for all
real \( x, \) then
A. \( f(x) \) must be a increasing function
B. \( f(x) \) must be a decreasing function
c. \( |f(x)| \) must be a increasing function
D. \( |f(x)| \) must be a decreasing function
Subject: Chemistry
Select the correct statement from
following.
A. Between \( N H_{3} \) and \( P H_{3}, N H_{3} \) is a better electron donor
because the lone pair of electrons occupies spherical s-orbital and is less directional
B. Between \( N H_{3} \) and \( P H_{3}, P H_{3} \) is a better electron donor because the lone pair of electrons occupies spherical \( s p^{3} \) orbital and is less directional
C. Between \( N H_{3} \) and \( P H_{3}, N H_{3} \) is a better electron donor because the lone pair of electrons occupies spherical \( s p^{3} \) orbital and is less directional
D. Between \( N H_{3} \) and \( P H_{3}, P H_{3} \) is a better electron donor because the lone pair of electrons occupies spherical s-orbital and is less directional
Subject: Physics
A transverse wave is passing through a light string shown in the figure.The
equation of wave is \( y=A \sin (\cos t- \)
\( k x) \). The area of cross-section of string
is \( A \) and density is \( p \).The hanging
mass is:
A. \( A \omega \)
B. \( \frac{\omega}{k g} \)
c. \( \frac{\rho A \omega^{2}}{k^{2} g} \)
D. \( \underline{k^{2}} \)
Subject: Maths
ff \( \boldsymbol{x}=\mathbf{1}+\boldsymbol{a}+\boldsymbol{a}^{2}+\boldsymbol{a}^{3}+\ldots \) and \( \boldsymbol{y}= \)
\( 1+b+b^{2}+b^{3}+\ldots ., \) then show that \( \mathbf{1}+\boldsymbol{a} \boldsymbol{b}+\boldsymbol{a}^{2} \boldsymbol{b}^{2}+\boldsymbol{a}^{3} \boldsymbol{b}^{3}+\ldots=\frac{\boldsymbol{x} \boldsymbol{y}}{\boldsymbol{x}+\boldsymbol{y}-\mathbf{1}} \)