AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Biology
Assertion
XX-XY type of sex determination mechanism is an example of female heterogamety and is found in
Drosophila.
Reason
Male heterogamety is seen in moths
where males produce two different
types of gamete.
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
The atomic mass of \( 7^{N^{15}} \) is 15.000108
a.m.u. and that is of \( 8^{\circ}^{16} 15.994915 \)
a.m.u. If the mass of a proton is 1.007825
a.m.u. then the minimum energy provided to remove the least tightly bound proton is
B. 12.13 Mev
c. 13.018 Mev
D. 12.13 ev
Subject: Chemistry
In which case there is change in
oxidation number:
A . Aqueous solution of \( C r O_{4}^{2-\text { - - is acidified }} \)
B. \( S O_{2} \) gas is passed into \( C r_{2} O_{7}^{2} \)
c. \( C r_{2} O_{7}^{2-} \) solution is made alkaline
D. \( C r O_{2} C l_{2} \) is dissolved in \( N N a O H \)
Subject: Chemistry
Which compound is missing in the reaction given below?
\( 2 N a O H+\left(N H_{4}\right)_{2} S O_{4} \rightarrow ?+N a_{2} S O \)
A. \( O_{2} \)
в. \( H_{2} \)
c. \( N_{2} \)
D. \( 2 N H_{3} \)
Subject: Maths
\( \boldsymbol{L}=\lim _{\boldsymbol{x} \rightarrow 2} \frac{\boldsymbol{x}^{4}-\boldsymbol{8} \boldsymbol{x}}{\sqrt{\boldsymbol{x}^{2}+\mathbf{2 1}-\mathbf{5}}} \)
Subject: Biology
Assertion
Hn \( m R N A \) is larger than \( m R N A \)
Reason
Hn \( R N A \) has no translating introns and has more exons than required for translation.
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 coils \( A \) and \( B \) have mutual
inductance \( 2 \times 10^{-2} \) henry. If the
current in the primary is \( i= \)
\( 5 \sin (10 \pi t) \) then the maximum value of
e.m.f. induced in coil \( B \) is
\( \mathbf{A} \cdot \pi \) volt
в. \( \frac{\pi}{2} \) volt
c. \( \frac{\pi}{3} \) volt
D. \( \frac{\pi}{4} \) volt
Subject: Physics
An object falling freely from rest reaches ground in \( 2 s . \) If acceleration
due to gravity is \( 9.8 m s^{-2}, \) the velocity of object on reaching the ground will be
\( \mathbf{A} \cdot 9.8 m s^{-1} \)
B. \( 4.9 \mathrm{m} \mathrm{s}^{-1} \)
c. \( 19.6 \mathrm{m} \mathrm{s}^{-1} \)
D. zero
Subject: Maths
The eccentricity of the ellipse \( x^{2}+ \)
\( 4 y^{2}+8 y-2 x+1=0 \) is
\( A \cdot \frac{\sqrt{3}}{2} \)
в. \( \frac{\sqrt{5}}{2} \)
\( c \cdot \frac{1}{2} \)
D.
Subject: Maths
Find the term independent of \( x \) in \( \left(\frac{3}{2} x^{2}-\frac{1}{3 x}\right)^{9} \)
\( A \cdot \frac{6}{15} \)
в. \( \frac{7}{18} \)
\( c \cdot \frac{7}{8} \)
D.
Subject: Maths
Find the discriminant of the equation and the nature of roots. Also find the
roots.
\( 6 x^{2}+x-2=0 \)
A \( \cdot D=49, \) Real and distinct roots: \( \frac{1}{5}, \frac{-2}{3} \)
B. \( D=39 \), Real and distinct roots: \( \frac{1}{2}, \frac{-2}{3} \)
C. \( D=49 \), Real and distinct roots: \( \frac{1}{3}, \frac{-7}{3} \)
D. \( D=49 \), Real and distinct roots: \( \frac{1}{2}, \frac{-2}{3} \)
Subject: Chemistry
n changing the state of a gas adiabatically from an equilibrium state A to another equilibrium state \( \mathrm{B} \) an amount of work equal to \( 22.3 \mathrm{J} \) is done on the system. If the gas is taken from state \( A \) to \( B \) via a process in which the net heat absorbed by the system is 9.35 cal then net work done by the system in the later case is:
(Take \( 1 \mathrm{cal}=4.2 \mathrm{J} \)
A . 15 J
в. 16
c. 17
D. 18 J
Subject: Physics
A particle has an initial velocity of \( 3 \hat{i}+ \) \( 4 \hat{i} \) and an acceleration of \( 0.4 \hat{i} \$+0.3 \hat{i} \) Find speed after \( 10 s . \) [Hint: \( \vec{\nu}=\vec{u}+\vec{a} t \)
when \( \vec{a} \) is constant
\( A \cdot 8 \sqrt{2} \)
B. \( 7 \sqrt{2} \)
c. \( 17 \sqrt{2} \)
2
D. \( 18 \sqrt{2} \)
Subject: Biology
Which of the following is correct order of the evolutionary history of man?
A. Peking man, Homo sapiens, Neanderthal man, CroMagnon man
B. Peking man, Neanderthal man, Heidelberg man, CroMagnon man
c. Peking man, Heidelberg man, Neanderthal man
Cro-Magnon man
D. Peking man, Neanderthal man, Homo sapiens, Heidelberg -man
Subject: Maths
If \( \boldsymbol{f}^{\prime}(\boldsymbol{x})=\boldsymbol{g}(\boldsymbol{x})(\boldsymbol{x}-\boldsymbol{a})^{2}, \) where \( \boldsymbol{g}(\boldsymbol{a}) \neq \)
0 and is continuous at \( x=a \), then
A. \( f \) is increasing near \( a \) if \( g(a)>0 \)
B. \( f \) is increasing near \( a \) if \( g(a)<0 \)
c. \( f \) is increasing near \( a \) if \( g(a)=0 \)
D. none of these
Subject: Maths
Equation of a plane making X-intercept
4, Y-intercept \( (-6), \mathrm{Z} \) -intercept 3 is
A. \( 3 x-4 y+6 z=12 \)
B. \( 3 x-2 y+4 z=12 \)
c. \( 4 x-6 y+3 z=1 \)
D. \( 4 x-3 y+2 z=12 \)
Subject: Chemistry
In an experiment, 10 L of air (containing
\( O_{3} \) ) at 1 atm and \( 27^{\circ} C \) was passed through an alkaline KI solution. After
neutralisation, free iodine requires 1.5
\( \mathrm{mL} \) of \( 0.01 N \mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3} \) solution. The
molar percentage of \( \boldsymbol{O}_{3} \) in air is \( \boldsymbol{y} \times \)
\( 10^{-4 \%} . \) Here \( y \) is (in nearest integer):
Subject: Maths
Let \( f(x)=x^{\frac{2}{3}}, x \geq 0 . \) Then the area of
the region enclosed by the curve \( y= \) \( f(x) \) and the three lines \( y=x, x=1 \)
and \( x=8 \)
A \( \cdot \frac{63}{2} \)
в. \( \frac{93}{5} \)
c. \( \frac{105}{7} \)
D. \( \frac{129}{10} \)
Subject: Maths
appeared in a test of 100 marks in the subject of social
studies and the data about the marks
secured is as below:
\begin{tabular}{cc} 
Marks secured & Number of Students \\
\hline \( 0-25 \) & 50 \\
\( 26-50 \) & 220 \\
\hline \( 51-75 \) & 100 \\
Above 75 & 30 \\
Total number of students & 400 \\
\hline
\end{tabular} If the result card of a student he picked
up at random, what is the probability
that the student has secured more than
50 marks.
A. 0.586
B. 0.75
c. 0.325
D. 0.1
Subject: Chemistry
At what approximate temperature, zinc
and carbon have equal affinity for
oxygen?
A \( \cdot 1000^{\circ} \mathrm{C} \)
В. \( 1500^{\circ} \mathrm{C} \)
\( c \cdot 500^{\circ} C \)
D. \( 1200^{\circ} \mathrm{C} \)
Subject: Physics
An air bubble of radius \( 0.1 \mathrm{cm} \) is in a
liquid having surface tension \( 0.06 N / m \) and density \( 10^{3} k g / m^{3} . \) The pressure inside the bubble is
\( 1100 N / m^{2} \) greater than the
atmospheric pressure. At what depth is the bubble below the surface of the
liquid? \( \left(\boldsymbol{g}=\mathbf{9 . 8} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
A \( .0 .20 m \)
B. \( 0.15 \mathrm{m} \)
c. \( 0.1 m \)
D. \( 0.25 \mathrm{m} \)
Subject: Physics
A boat crossing a river moves with a velocity v relative to still water. The river
is flowing with a velocity v/2 with
respect to the bank. The angle with respectively the slow direction with which the boat should move to
minimize the drift is
A \( .30^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 180^{\circ} \)
D. \( 120^{\circ} \)
Subject: Physics
A solid uniform ball of volume \( V \) floats
on the interface of two immiscible
liquids (see the figure). The specific
gravity of the upper liquid is \( \rho_{1} \) and that
of lower one is \( \rho_{2} \) and the specific
gravity of ball is \( \rho\left(\rho_{1}<\rho<\rho_{2}\right) \). The
fraction of the volume of the ball in the
upper liquid is
\( A \cdot \frac{\rho_{2}}{\rho_{1}} \)
в.
c. \( \frac{\rho-\rho_{1}}{\rho_{2}-\rho_{1}} \)
D. \( \frac{\rho_{1}}{\rho_{2}} \)
Subject: Maths
What is the value of \( \int_{-\pi / 4}^{\pi / 4}(\sin x-\tan x) d x \)
\( ^{\mathbf{A}} \cdot-\frac{1}{\sqrt{2}}+\ln \left(\frac{1}{\sqrt{2}}\right) \)
B. \( \frac{1}{\sqrt{2}} \)
c. 0
D. \( \sqrt{2} \)
Subject: Maths
Given that \( m^{2}=27^{2 / 3} \times 16^{-3 / 2}, \) find
the value of \( m \)
A \( \cdot \frac{9}{34} \)
в. \( \frac{3}{16} \)
\( c \cdot \frac{3}{8} \)
D. \( \frac{3}{4} \)
Subject: Physics
A square is placed with its centre at origin and having sides parallel to \( x \) and
\( y- \) axes. It has surface charge density
\( \sigma(x, y)=\sigma_{0} x y \) within its boundaries.
The charge of each side of square is \( Q \)
The total charge on the square is:
A \( \cdot 2 \sigma_{0} Q^{2} \)
в. \( 4 \sigma_{0} Q^{3} \)
c. \( \sigma_{0} Q^{2} \)
D. zero
Subject: Maths
Solve the following pair of linear equations by cross miltiplication
method
\( 0.3 x+0.4 y=2.5 \) and \( 0.5 x-0.3 y= \)
\( \mathbf{0 . 3} \)
A. \( x=-3 \) and \( y=4 \)
в. \( x=3 \) and \( y=4 \)
c. \( x=4 \) and \( y=-4 \)
D. None of these
Subject: Chemistry
From the thermochemical reactions,
\( \boldsymbol{C}_{(\text {graphite})}+\frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{O}_{2} \rightarrow \boldsymbol{C O} ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -110.5 k J \)
\( \boldsymbol{C O}+\frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{O}_{2} \rightarrow \boldsymbol{C O}_{2} ; \boldsymbol{\Delta} \boldsymbol{H}=-\mathbf{2 8 3 . 2 k} \boldsymbol{J} \)
the heat of reaction of \( C_{(g r a p h i t e)}+ \)
\( \boldsymbol{O}_{2} \rightarrow \boldsymbol{C} \boldsymbol{O}_{2} \) is:
\( \mathbf{A} \cdot+393.7 k J \)
B . \( -393.7 k J \)
\( \mathbf{c} .-172.7 k J \)
\( \mathbf{D} .+172.7 k J \)
Subject: Physics
The ratio of the drifty velocity \( v_{d} \) and
r.m.s. velocity of electrons is
\( \mathbf{A} \cdot 10^{-10} \)
B . \( 10^{-5} \)
\( \mathbf{c} \cdot 10^{-3} \)
D. \( 10^{-6} \)
Subject: Chemistry
Assertion: Receptors are crucial to body's communication process
Reason : Receptors are proteins
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct and Reason is NOT the correct explanation for Assertion
C. Both Assertion and Reason are incorrect
D. Assertion is correct but Reason is incorrect
E. Assertion is incorrect but Reason is correct
\( F . \) None of these
Subject: Chemistry
12 g of \( \boldsymbol{C H}_{3} \) COOH and 4 g of NaOH are mixed and diluted to 1 litre solution. If
\( P^{K a} \) of \( C H_{3} C O O H \) is \( 4.8, \) then the \( p^{H} \)
of the solution is:
A . 4.8
B. 5
c. 5.6990
D. 5.3010
Subject: Maths
There are ' \( m^{\prime} \) copies each of \( ^{\prime} n^{\prime} \)
different books in a university library. The number of ways in which one or more than one book can be selected is
A \( \cdot m^{n}-1 \)
B . \( (m+1)^{n}-1 \)
C \( \cdot(m+1)^{n}-m^{n} \)
D. \( (m+1)^{n}-m \)
Subject: Maths
If \( \bar{a}=\bar{i}+2 \bar{j}, \bar{b}=-2 \bar{i}+\bar{j}, \bar{c}=4 \bar{i}+3 \bar{j} \)
find \( x \) and \( y \) such that \( \bar{c}=x \bar{a}+y \bar{b} \)
Subject: Chemistry
A hydrogen electrode
\( \left(p_{H_{2}}=1 a t m ; T=298 K\right) \) is placed in
buffer solution of \( C H_{3} C O O N a \) and
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \) in the molar ratio \( \boldsymbol{x}: \boldsymbol{y} \)
and then in \( y: x \) has reduction
potential values as \( E_{1} \) and \( E_{2} \) volts
respectively. Then \( p K_{e} \) of \( C H_{3} \) COOH
will be:
A \( \cdot \frac{E_{1}+E_{2}}{0.118} \)
B. \( \frac{E_{1}+E_{2}}{0.059} \)
\( \mathbf{c} \cdot \quad-\frac{E_{1}+E_{2}}{0.118} \)
D. \( \frac{E_{2}-E_{1}}{0.118} \)
Subject: Physics
An object \( A \) is placed on the principal
axis of a convex mirror at a distance of
\( 60 \mathrm{cm} \) in front of it. A plane mirror is
inserted between the object and the
convex mirror at a distance of \( 40 \mathrm{cm} \)
from the object with the reflecting
surface of the plane mirror facing the
object. If the images formed by the two
mirrors coincide, find the focal length of
the convex mirror.
A. \( 15 \mathrm{cm} \)
B. \( 25 \mathrm{cm} \)
c. \( 20 \mathrm{cm} \)
D. \( 30 \mathrm{cm} \)
Subject: Biology
Identify the wrong pair of statements.
I) The number of stamens in 5 flowers of
Allium is equal to those in 5 flowers of Solanum.
Il) The microsporangia of Hibiscus and Asparagus are having 80 pollen grains each. Then the ratio of the number of
pollen grains produced from each stamen of these two plants is 1: 1
III) The ratio of the number of stamens
in the flowers of Pisum and Datura is 2: 1
IV) The number of carpels in a flower of Smilax is equal to the number of carpels in a cyathium inflorescence.
A. ॥I, IV
B . ।, ॥
\( c \cdot 1,1 \)
D. II, III
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{cc}\cos 2 \boldsymbol{\theta} & -\sin 2 \boldsymbol{\theta} \\ \sin 2 \boldsymbol{\theta} & \cos 2 \boldsymbol{\theta}\end{array}\right] \) and \( \boldsymbol{A}+ \)
\( A^{T}=I, \) where \( I \) is the unit of matrix of
\( 2 \times 2 \) and \( A^{T} \) is the transpose of \( A, \) then
the value of \( \theta \) is equal to
A \( \cdot \frac{\pi}{6} \)
в.
c. \( \pi \)
D. \( \frac{3 \pi}{2} \)
Subject: Maths
\( \int e^{x}\left(\frac{2+\sin 2 x}{1+\cos 2 x}\right) d x= \)
A \( \cdot e^{x} \cot x+c \)
B \( \cdot 2 e^{x} \sec ^{2} x+c \)
\( \mathbf{c} \cdot e^{x} \cos 2 x+c \)
D. \( e^{x} \tan x+c \)
Subject: Chemistry
Mention catalyst in the following reaction:
\( \boldsymbol{K} \boldsymbol{C l} \boldsymbol{O}_{3} \rightarrow \boldsymbol{K} \boldsymbol{C l}+\boldsymbol{O}_{2} \)
A. \( M n O_{2} \)
в. \( F e C l_{3} \)
c. \( P d C l_{2} \)
D. \( Z n O / C u O \)
Subject: Maths
A box contains 10 white, 6 red and 10
black balls. A ball is drawn at random
from the box. What is the probability
that the ball drawn is either white or
red?
A \( \cdot \frac{7}{13} \)
в. \( \frac{7}{12} \)
c. \( \frac{8}{13} \)
D. \( \frac{9}{15} \)
Subject: Maths
Find the inverse of the matrix
\( \$ \$ \mathrm{~ l l e f t [ l b e g i n ~ \{ a r r a y \} ~} \mid 5 \& 11 \backslash 14 \& 9 \)
\( \mathrm{~ l e n d ~ \{ a r r a y \} l r i g h t ] \$ \$ ~ b y ~ e l e m e n t a r y ~} \)
transformations.
Subject: Physics
A uniform magnetic field B is set up along the positive \( x \) -axis. A particle of charge 'q' and mass 'm' moving with a velocity v enters the field at the origin in \( X-Y \) plane such that it has velocity
components both along and perpendicular to the magnetic field B. Trace, giving reason, the trajectory followed by the particle. Find out the expression for the distance moved by the particle along the magnetic field in one rotation
Subject: Physics
Find the maximum power in the form of \( (10+x) \) which can be transmitted
by means of a steel shaft rotating about
its axis with an angular velocity \( \omega= \)
\( 120 r a d / s, \) if its length \( l=200 c m \)
radius \( r=1.50 \mathrm{cm}, \) and the
permissible torsion angle \( \varphi=2.5^{\circ} \)
Round off to the nearest integer of \( x \)
Subject: Maths
The straight lines \( 4 x-3 y-5=0, x- \)
\( 2 y-10=0,7 x+y-40=0 \) and \( x+ \)
\( 3 y+10=0 \) form the sides of a
A. plain quadrilateral
B. cyclic quadrilateral
c. rectangle
D. parallelogram
Subject: Physics
The length of hour hand of a wrist watch
is \( 1.5 \mathrm{cm} . \) Find magnitude of angular acceleration?
A. \( 0 r a d / s e c^{2} \)
B. \( 2 \pi r a d / s e c^{2} \)
C \( .2 \mathrm{rad} / \mathrm{sec}^{2} \)
D. \( 1 r a d / s e c^{2} \)
Subject: Physics
The potential at \( P \) due to induced
charge is
\( ^{\text {A }} \cdot_{K q}\left(\frac{1}{r_{1}}-\frac{1}{r_{2}}\right) \)
в. \( _{K q}\left(\frac{1}{r_{1}}+\frac{1}{r_{2}}\right) \)
\( ^{\text {c. }} K q\left(-\frac{1}{r_{1}}+\frac{1}{r_{2}}\right) \)
D. \( \frac{K q}{r_{1}} \)
Subject: Chemistry
The formula for the compound tris ethane \( -1,2-\text { diamine }) \) cobalt \( (\| I) \)
sulphate is :
\( ^{\mathbf{A}} \cdot\left[\operatorname{Co}(e n)_{3}\right] S O_{4} \)
в. \( \left[\operatorname{Co}(S O)_{4}(e n)_{3}\right] \)
\( ^{\mathbf{c}} \cdot\left[\operatorname{Co}(e n)_{3}\right]\left(S O_{4}\right)_{2} \)
D. \( \left[\operatorname{Co}(e n)_{3}\right]_{2}\left(S O_{4}\right)_{3} \)
Subject: Maths
If the points \( \boldsymbol{P}(\mathbf{2}, \mathbf{1},-\mathbf{3}), \boldsymbol{Q}(\mathbf{5}, \mathbf{4}, \mathbf{3}) \) and
\( R(1,4,7) \) are three vertices of a parallelogram \( P Q R S \) then the other
vertex is
A. (1,0,0)
В . (-2,1,1)
c. (-2,2,1)
D. (2,1,2)
Subject: Physics
Three unequal resistance are connected in parallel. Two of these resistances are
in the ratio \( 1: 2 . \) The equivalent
resistance of these three connected in
parallel is \( 1 \Omega . \) What is the highest resistance value among these three resistances if no resistance is
fractional?
A . \( 10 \Omega \)
B. \( 8 \Omega \)
\( c .15 \Omega \)
D. \( 6 \Omega \)
Subject: Maths
Of the students in a school, it is known
that \( 30 \% \) have \( 100 \% \) attendance and
70\% students are irregular. Previous year results report that \( 70 \% \) of all students who have \( 100 \% \) attendance
attain A grade and \( 10 \% \) irregular students attain A grade in their annual examination. At the end of the year, one
student is chosen at random from the
school and he was found to have an \( A \)
grade. What is the probability that the student has \( 100 \% \) attendance? Is regularity required only in school? Justify your answer.
Subject: Physics
An automobile and a truck start from
rest at the same instant, with the automobile initially at some distance behind the truck. Then truck has a
constant acceleration of \( 2.2 m / s^{2} \) and the automobile has an acceleration of
\( 3.5 m / s^{2} . \) The automobile overtakes the truck when it (truck) has moved 60 \( \mathrm{m} \).
(a) How much time does it take to automobile to overtake the truck?
(b) How far was the automobile behind the truck initially?
(c) What is the speed of each during overtaking?
Subject: Maths
The principal value of \( \cos ^{-1}\left(-\sin \frac{7 \pi}{6}\right. \)
\( A \cdot \frac{5 \pi}{3 \pi} \)
B. \( \frac{7 \pi}{6} \)
\( c \cdot \frac{\pi}{3} \)
D. none of these
Subject: Maths
\( \int \frac{\sec ^{8} x}{\cos e c x} d x= \)
A \( \cdot \frac{\cos ^{7} x}{7}+c \)
в. \( \frac{7}{\cos ^{7} x}+c \)
c. \( \frac{1}{7 \cos ^{7} x}+c \)
D. \( \frac{1}{\cos ^{7} x}+c \)
Subject: Physics
A student measure the height h of a convex mirror using spherometer. The legs of the spherometer are \( 4 \mathrm{cm} \) apart and there are 10 divisions per cm on its linear scale and circular scale has 50
divisions. The student takes 2 as linear
scale division and 40 as circular scale
division. What is the radius of curvature
of the convex mirror?
A. \( 9.06 \mathrm{cm} \)
в. \( 20.66 \mathrm{cm} \)
\( c .5 .66 \mathrm{cm} \)
D. \( 9.66 \mathrm{cm} \)
Subject: Chemistry
Compare \( x \) and \( y \) bond length in above molecules? \( \boldsymbol{y}=\mathbf{2 . 6 4 4} \dot{\boldsymbol{A}} \quad \boldsymbol{x}=\mathbf{2 . 2 1} \dot{\boldsymbol{A}} \)
\( A \cdot x>y \)
B. y > x
\( c \cdot x=y \)
D. None of these
Subject: Physics
Joseph jogs from one end \( A \) to the other
end B of the straight \( 300 \mathrm{m} \) road in 2
minutes 50 seconds and then turns
around and jogs \( 100 \mathrm{m} \) back to point \( \mathrm{C} \) in another 1 minutes. Joseph's average
speeds and velocities in jogging, between points \( A \) and \( B \)
respectively, will be
A. \( 1.76 \mathrm{ms}^{-1}, 1.76 \mathrm{ms}^{-1} \)
B . \( 0.869 \mathrm{ms}^{-1}, 0.869 \mathrm{ms}^{-1} \)
c. \( 1.76 m s^{-1}, 0.869 m s^{-1} \)
D. \( 0.869 \mathrm{ms}^{-1}, 1.76 \mathrm{ms}^{-1} \)
Subject: Physics
A solenoid of 10 henry inductance and 2 ohm resistance, is connected to a 10
volt battery. In how much the magnetic
energy will be increases to \( 1 / 4 \) th of the maximum value?
A \( .3 .5 \mathrm{sec} \)
B. 2.5 sec
\( c .5 .5 \mathrm{sec} \)
D. 7.5 sec
Subject: Chemistry
Solutions of two electrolytes \( A \) and \( B \) each having concentration of \( 0.2 \mathrm{M} \) have
conductivities \( 2 \times 10^{-2}, 4 \times 10^{-4} \mathrm{S} / \mathrm{cm} \)
respectively. Which will offer greater resistance to the file of current and
why?
Subject: Physics
In YDSE, let \( A \) and \( B \) be two slits. Films
of thicknesses \( t_{A} \) and \( t_{B} \) and refractive
indices \( \mu_{A} \) and \( \mu_{B} \) are placed in front of
\( A \) and \( B, \) respectively. If \( \mu_{A} t_{A}=\mu_{B} t_{B} \)
then the central maxima will :
A. Not shift
B. Shift toward \( A \)
c. shift toward \( B \)
D. (b) if \( t_{B}>t_{A} \) and (c) if \( t_{B}<t_{A} \)
Subject: Physics
The mass of the jupiter is \( 1.9 \times 10^{2} \mathrm{kg} \)
and that of sun is \( 1.99 \times 10^{30} \) kg. The
mean distance of jupiter from the sun is \( 7.8 \times 10^{11} \mathrm{m} . \) Speed of jupiter is
(assuming that jupiter moves in circular orbit around the sun)
Subject: Chemistry
Depression of freezing point of which of the following solutions does represent the cryoscopic constant of water?
A. \( 6 \% \) by mass of urea in aqueous solution.
B. 100 g of aqueous solution containing 18 g of glucose.
c. 59 g of aqueous solution containing 9 g of glucose.
D. 1 M \( K C l \) solution in water.
Subject: Physics
A potentiometer wire is \( 10 \mathrm{m} \) long and a potential difference of \( 6 V \) is maintained between its ends.The emf of a cell which
balances against a length of \( 180 \mathrm{cm} \) of the potentiometer wire is:
A . 1.8 \( v \)
B. 1.1 \( v \)
c. \( 1.08 \mathrm{v} \)
D. 1.2
Subject: Maths
The differential equation whose solution is \( (\boldsymbol{x}-\boldsymbol{h})^{2}+(\boldsymbol{y}-\boldsymbol{k})^{2}=\boldsymbol{a}^{2} \) is
\( (a \text { is a constant }) \)
\( ^{\mathbf{A}} \cdot\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{3}=a^{2} \frac{d^{2} y}{d x^{2}} \)
B \( \cdot\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{3}=a^{2}\left(\frac{d^{2} y}{d x^{2}}\right)^{2} \)
\( ^{\mathbf{c}} \cdot\left[1+\left(\frac{d y}{d x}\right)\right]^{3}=a^{2}\left(\frac{d^{2} y}{d x^{2}}\right)^{2} \)
D. None of these
Subject: Physics
Find the mean velocity of the particle averaged over the time that the particle takes to cover the first \( s m \) of the path.
A \( \cdot \frac{3 \alpha}{2 \sqrt{s}} \)
B. \( \frac{2 \alpha \sqrt{s}}{2} \)
c. \( \frac{\alpha \sqrt{s}}{2} \)
D. \( \frac{\alpha \sqrt{s}}{3} \)
Subject: Chemistry
The stability of the hydrides follows the
order.
A. \( N H_{3}>P H_{3}>A s H_{3}>S b H_{3} \)
B. \( N H_{3}<P H_{3}<S b H_{3}<A s H_{3} \)
c. \( P H_{3}>N H_{3}>A s H_{3}>S b H_{3} \)
D. \( A s H_{3}>N H_{3}>P H_{3}>S b H_{3} \)
Subject: Physics
A certain simple harmonic vibrator of
mass \( 0.1 k g \) has a total energy of \( 10 J \)
.Its displacement from the mean
position is \( 1 \mathrm{cm} \) when it has equal
kinetic and potential energies. The amplitude \( A \) and frequency \( n \) of
vibration of the vibrator are
\( ^{\mathbf{A}} \cdot A=\sqrt{2} c m, n=\frac{500}{\pi} H z \)
B. \( A=\sqrt{2} c m, n=\frac{1000}{\pi} H z \)
\( ^{\mathbf{C}} \cdot A=\frac{1}{\sqrt{2}} c m, n=\frac{500}{\pi} H z \)
D. \( A=\frac{1}{\sqrt{2}} c m, n=\frac{1000}{\pi} H z \)
Subject: Maths
Consider the following statements in respect of the determinant \( \left|\begin{array}{cc}\cos ^{2} \frac{\alpha}{2} & \sin ^{2} \frac{\alpha}{2} \\ \sin ^{2} \frac{\beta}{2} & \cos ^{2} \frac{\beta}{2}\end{array}\right| \) where \( \alpha, \beta \) are
complementary angles
1. The value of the determinant is \( \frac{1}{\sqrt{2}} \cos \left(\frac{\alpha-\beta}{2}\right) \)
2. The maximum value of the determinant is \( \frac{\mathbf{1}}{\sqrt{\mathbf{2}}} \)
Which of the above statements is/are
correct?
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2
Subject: Chemistry
\( \boldsymbol{P H}_{4} \boldsymbol{I}+\boldsymbol{N a O H} \) forms:
A \( . P H_{3} \)
в. \( N H_{3} \)
\( \mathrm{c} \cdot P_{4} O_{6} \)
D. \( P_{4} O_{10} \)
Subject: Maths
Solve the differential equation \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
\( \frac{\boldsymbol{x} \boldsymbol{y}+\boldsymbol{y}}{\boldsymbol{x} \boldsymbol{y}+\boldsymbol{x}} \)
Subject: Physics
If the ratio of diameters, lengths and
Young's moduli of steel and brass wires
shown in the figure are \( p, q \) and \( r \)
respectively. Then the corresponding ratio of increase in their lengths would
be:
A \( \frac{3 q}{5 n^{2} r} \)
в. \( \frac{5 q}{3 p^{2}} \)
c. \( \frac{3 q}{5 p r} \)
D. \( \frac{5 q}{p r} \)