AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
\( K_{1} \) and \( K_{2} \) for oxalic acid are \( 6.5 \times \)
\( 10^{-2} \) and \( 6.1 \times 10^{-5} \) respectively. What
will be \( \left[\boldsymbol{H} \boldsymbol{O}^{-}\right] \) in a \( \mathbf{0 . 0 1} \boldsymbol{M} \) solution of
sodium oxalate?
A \( .9 .6 \times 10^{-6} \)
B. \( 1.4 \times 10^{-1} \)
c. \( 1.3 \times 10^{-6} \)
D. \( 1.3 \times 10^{-8} \)
Subject: Physics
sphere of radii 'a' and 'b' respectively (see figure), has volume charge density \( p=\frac{A}{r}, \) Where \( A \) is a constant and \( r \) is
the distance from the centre. At the
centre of the spheres is a point charge
Q. The value of A such that the electric
field in the region between the spheres
will be constant, is:
\( A \)
B.
\( c \cdot \frac{2 Q}{\pi a^{2} Q} \)
D. \( \frac{Q}{2 \pi a^{2}} \)
Subject: Physics
A battery of \( V \) voltage is connected
across the potentiometer wire \( \boldsymbol{A} \boldsymbol{C} \) of
total resistance \( R_{0} \) as shown. Calculate
the potential across the resistance \( \boldsymbol{R} \) if
the sliding contact point \( B \) is exactly at
the middle of the potentiometer wire.
\( A \)
в. \( \frac{4 V R_{0}}{2 R_{0}+R} \)
c. \( \frac{2 V R}{R_{0}+4 R} \)
D. \( \frac{4 V R_{0}}{R_{0}+2 R} \)
Subject: Maths
Number of ways in which 9 different
prizes be given to 5 students if one particular boy receives 4 prizes \( \& \) the rest of the students can get any
numbers of prizes, is:
A \( \cdot^{9} \mathrm{C}_{4} \cdot 2^{10} \)
B. \( ^{9} \mathrm{C}_{5} \cdot 5^{4} \)
c. \( 4.4^{5} \)
D. none
Subject: Physics
A conducting square loop of side \( L \) and
resistance \( R \) moves in it's plane with a
uniform velocity \( v \) perpendicular to one of it's sides. A magnetic induction \( B \) constant in time and space, pointing perpendicular to and into the plane of the loop exists everywhere. The current induced in the loop is
A \( \cdot \frac{B L v}{R}, \) clockwise
B. \( \frac{B L v}{2 R} \) clockwise
c. \( \frac{2 B L v}{2 R} \) anticlockwise
D. zero
Subject: Chemistry
If the compression factor of a gas is
more than unity at \( S T P \), then the value
of \( V_{m} \) is:
A . greater than \( 22.4 d m^{3} \)
B. lesser than \( 22.4 d m^{3} \)
c. equal to \( 22.4 d m^{3} \)
D. dependent on its molecular mass
Subject: Maths
\( \boldsymbol{A}=(\mathbf{2}+\mathbf{1})\left(\mathbf{2}^{2}+\mathbf{1}\right)\left(\mathbf{2}^{4}+\right. \)
1) \( \dots . .\left(2^{2016}+1\right) . \) The value of
\( (\boldsymbol{A}+\mathbf{1})^{\frac{1}{2016}} \) is
\( \mathbf{A} \cdot \mathbf{4} \)
в. 2016
c. \( 2^{403} \)
D.
Subject: Maths
The value of \( \lim _{n \rightarrow \infty} \frac{(n !) \frac{1}{n}}{n} \) is?
\( \mathbf{A} \cdot \mathbf{1} \)
в. \( \frac{1}{e^{2}} \)
c. \( \frac{1}{2 e} \)
D.
Subject: Maths
The rational number lying between the numbers \( \frac{1}{3} \) and \( \frac{3}{4} \) are
A. \( \frac{97}{300}, \frac{299}{500} \)
в. \( \frac{99}{300}, \frac{301}{400} \)
c. \( \frac{95}{300}, \frac{301}{400} \)
D. \( \frac{117}{300}, \frac{287}{400} \)
Subject: Chemistry
Assertion
Adding inert gas to dissociation
equilibrium of \( N_{2} O_{4} \) at constant
temperature and pressure increases
the dissociation of \( N_{2} O_{4} \)
Reason
Due to the addition of inert gas molar concentration of reactants and
products decreases.
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
Probability is 0.45 that a dealer will sell
at least 20 television sets during a day, and the probability is 0.74 that he will
sell less that 24 televisions. The
probability that he will sell 20,21,22 or
23 televisions during the day, is
A . 0.19
в. 0.32
c. 0.21
D. None of these
Subject: Chemistry
The Born Haber cycle below represents
the energy changes occurring at \( 298 \mathrm{K} \) when \( \mathrm{KH} \) is formed from its elements
\( \mathbf{v}: \Delta \boldsymbol{H}_{\text {atomisation}} \mathbf{K}=\mathbf{9 0} \mathbf{k J} / \mathrm{mol} \)
\( \mathbf{w}: \mathbf{\Delta} \boldsymbol{H}_{\text {ionisation}} \mathbf{K}=\mathbf{4 1 8} \mathbf{k} \mathbf{J} / \mathrm{mol} \)
\( \mathbf{x}: \boldsymbol{\Delta} \boldsymbol{H}_{\text {dissociation}} \mathrm{H}=\mathbf{4 3 6} \mathrm{kJ} / \mathrm{mol} \)
\( \mathbf{y}: \boldsymbol{\Delta} \boldsymbol{H}_{\text {electronaffinity}} \mathbf{H}=\mathbf{7 8} \mathbf{k J} / \mathrm{mol} \)
\( \mathbf{z}: \boldsymbol{\Delta} \boldsymbol{H}_{\text {lattice}} \mathrm{KH}=710 \mathrm{kJ} / \mathrm{mol} \)
In terms of the letters \( v \) to \( z \) the
expression for
\( \boldsymbol{\Delta} \boldsymbol{H}_{\text {electronaffinity}} \) of H is
\( \boldsymbol{\Delta} \boldsymbol{H}_{\text {electronaffinity}} \) is \( _{--} \)
A . \( y \)
в. \( y / 2 \)
\( c \cdot 2 y \)
D. \( y / 3 \)
Subject: Physics
A solid conducting sphere of radius a
having a charge \( q \) is surrounded by
a concentric conducting spherical shell
of inner radius \( 2 a \) and outer radius \( 3 a \)
as shown in figure. Find the amount of heat produced when switch is closed \( \left(\boldsymbol{K}=\frac{\mathbf{1}}{\mathbf{4} \boldsymbol{\pi} \varepsilon_{0}}\right) \)
\( ^{\mathrm{A}} \cdot_{K}=\frac{k q^{2}}{2 a} \)
в. \( _{K}=\frac{k q^{2}}{3 a} \)
\( ^{\mathrm{c}} \cdot_{K}=\frac{k q^{2}}{4 a} \)
D. \( _{K}=\frac{k q^{2}}{6 a} \)
Subject: Chemistry
Shanti, a domestic helper of Mrs. Anuradha, fainted while mopping the
floor. Mrs. Anuradha immediately took her to the nearby hospital where she was diagnosed to be severely 'anaemic'. The doctor prescribed an iron rich diet and multivitamins supplement to her.
Mr.s Anuradha supported her financially to get the medicines. After a month, Shanti was diagnosed to be normal.
(i) What values are displayed by Mrs. Anuradha?
(ii) Name the vitamin whose deficiency causes 'pernicious anaemia!
(iii) Give an example of a water soluble vitamin
Subject: Physics
The two cells are connected in series, in
a potentiometer experiment, in such a
way so as to support each other and to
oppose each other. The balancing lengths in two conditions are obtained as \( 150 \mathrm{cm} \) and \( 50 \mathrm{cm} \) respectively. The ratio of emf's of two cells will be
A . 1: 2
B. 2:
c. 1: 4
D. 4:
Subject: Maths
In two similar triangles \( A B C \) and \( P Q R \), if their corresponding altitudes \( A D \) and \( P s \) are in the ratio \( 4: 9, \) find the ratio of the
areas of \( \triangle A B C \) and \( \triangle P Q R \)
A . 16: 81
B. 9: 16
c. 81: 16
D. 16: 9
Subject: Maths
Determine the values of \( a, b, c \) for which
\[
\left\{\begin{array}{ll}
f(x)=\frac{\sin (a+1) x+\sin x}{x} & \text { for } x< \\
=c & \text { for } x= \\
\frac{\left(x+b x^{2}\right)^{\frac{1}{2}}-x^{\frac{1}{2}}}{1} & \text { for } x>
\end{array}\right.
\]
is continuous at \( \boldsymbol{x}=\mathbf{0} \)
Subject: Maths
The radius of the cylinder whose lateral surface area is \( 704 \mathrm{cm}^{2} \) and height
\( 8 c m, \) is
A. \( 6 \mathrm{cm} \)
в. 4 ст
\( c .8 c m \)
D. \( 14 \mathrm{cm} \)
Subject: Chemistry
Consider the following statements and
predict the wrong statement(s)
a. Half filled and fully filled orbitals have greater stability due to greater exchange energy and symmetrical
distribution
b. The energy of \( 3 s \) orbital is less than
\( 3 p \) orbital for hydrogen atom.
c. The uncertainty principle is \( \Delta \boldsymbol{E} \times \) \( \Delta t \leq \frac{h}{4 \pi} \)
\( \boldsymbol{d} \boldsymbol{E}=-\boldsymbol{2} . \boldsymbol{1} \boldsymbol{7} \boldsymbol{8} \times \boldsymbol{1} \boldsymbol{0}^{-18}\left(\frac{\boldsymbol{Z}^{2}}{\boldsymbol{n}^{2}}\right) \boldsymbol{J} \boldsymbol{a t o m}^{-1} \)
can be used to calculate the change in
energy when the electron changes orbit in H-atom
A. b and conly
B. b, c and donly
c. a and b only
D. a and donly
Subject: Maths
Two dice are thrown. The events \( A, B \)
and \( C \) are as follows:
A : getting an even number on the first die
B : getting an odd number on the first die
C : getting the sum of the numbers on the dice \( \leq 5 \)

State true or false : (give reason for your answer)
(i) \( A \) and \( B \) are mutually exclusive
(ii) \( A \) and \( B \) are mutually exclusive and exhaustive
(iii) \( \boldsymbol{A}=\boldsymbol{B}^{\prime} \)
(iv) \( A \) and \( C \) are mutually exclusive
(v) \( A \) and \( B^{\prime} \) are mutually exclusive
(vi) \( A^{\prime}, B^{\prime}, C \) are mutually exclusive and exhaustive
Subject: Physics
For the circuit shown in the figure the
current through the inductor is \( 1.6 A \)
while the current through the condenser is \( 0.4 A \), then the current \( l \) drawn from
the source is :
A \( \cdot 2 \sqrt{2} A \)
B. \( 1.65 A \)
\( c .1 .2 A \)
D. 2.0
Subject: Maths
Degree measure of \( \left(\frac{1}{4}\right)^{c} \) is
A \( \cdot 15^{\circ} 19^{\prime} 5^{\prime \prime} \)
B . \( 14^{\circ} 19^{\prime} 5^{\prime \prime} \)
\( \mathbf{c} \cdot 15^{\circ} 18^{\circ} 6 " \)
D. \( 14^{\circ} 18^{\circ} 6 " \)
Subject: Physics
Two forces simultaneously act on a
particle making an angle \( 120^{\circ} \) with
each other if one of them is reversed the
acceleration of the particle becomes \( \sqrt{3} \) times its initial value. The ratio of the
magnitude of the forces is?
A . 1: 2
B. 1: 1
\( c \cdot 2: 1 \)
D. 1: 3
Subject: Maths
Two parallel chords are drawn on the
same side of the centre of a circle of
radius 20. It is found that they subtend
\( 60^{0} \) and \( 120^{0} \) angles at the centre of the circle. Then the perpendicular distance between the chords is:
\( \mathbf{A} \cdot 5(\sqrt{3}-1) \)
B . \( 10(\sqrt{3}-1) \)
c. \( 10(\sqrt{2}-1) \)
() \( 5(\sqrt{2}-1-1) \)
D. \( 5(\sqrt{3}+1) \)
Subject: Chemistry
\( 100 \mathrm{ml} \) of \( 0.5 \mathrm{N} \) NaOH solution is added
to \( 10 \mathrm{ml} \) of \( 3 \mathrm{N} H_{2} \mathrm{SO}_{4} \) solution and 20
\( \mathrm{ml} \) of \( 1 \mathrm{N} \) HCl solution. The mixture is :
A . acidic
B. alkaline
c. neutral
D. none of these
Subject: Chemistry
At \( 25^{\circ} \mathrm{C} \) the heat of formation of \( H_{2} \mathrm{O}(l) \) is
\( -285.9 \mathrm{KJ} \) mole \( ^{-1} \) and that for \( H_{2} O(g) \) is
\( -242.8 \mathrm{KJmole}^{-1} . \) The heat of vaporization
of water at the same temperature is
A \( \cdot 43.1 \mathrm{KJ} \mathrm{mole}^{-1} \)
B. 242.8 KJ mole \( ^{-1} \)
C . -43.1 KJ mole \( ^{-1} \)
D. - 242.8 KJ mole \( ^{-1} \)
Subject: Chemistry
What does 'like dissolves like' mean?
A. That compounds that are from the same period on the periodic table will dissolve each other.
B. Polar solutes dissolve in polar solvents.
C. Nonpolar solutes dissolve in polar solvents.
D. Polar solutes dissolve in nonpolar solvents.
E. That compounds from the same family on the periodic table will dissolve each other.
Subject: Physics
Two cars \( A \) and \( B \) are travelling in the
same direction with velocities \( \boldsymbol{v}_{A} \) and
\( \boldsymbol{v}_{B}\left(\boldsymbol{v}_{A}>\boldsymbol{v}_{B}\right) . \) When the car \( \boldsymbol{A} \) is at a
distance \( d \) behind the car \( B \) the driver
of the car \( A \) applies brakes producing a
uniform retardation \( a \). There will be no
collision when
A \( \cdot \quad d<\frac{\left(v_{A}-v_{B}\right)^{2}}{2 a} \)
B. \( d<\frac{v_{A}^{2}-v_{B}^{2}}{2 a} \)
c. \( _{d}>\frac{\left(v_{A}-v_{B}\right)^{2}}{2 a} \)
D. \( d>\frac{v_{A}^{2}-v_{B}^{2}}{2 a} \)
Subject: Maths
If \( I, m, n \) are the direction cosines of \( a \) line OP then the maximum value of
I.m.n is
A \( \cdot \frac{1}{\sqrt{3}} \)
в. \( \frac{1}{3 \sqrt{3}} \)
\( c \cdot \frac{1}{3} \)
D.
Subject: Physics
The bulk modulus of water is \( 2.0 \times \)
\( 10^{9} N / m^{2} \) The pressure required to
increase the density of water by \( 0.1 \% \) is
A \( \cdot 2.0 \times 10^{3} N / m^{2} \)
B . \( 2.0 \times 10^{6} N / m^{2} \)
C \( \cdot 2.0 \times 10^{5} \mathrm{N} / \mathrm{m}^{2} \)
D. \( 2.0 \times 10^{7} N / m^{2} \)
Subject: Physics
Two identical wires \( A \) and \( B \), each of
length \( l \), carry the same current \( l \). Wire
\( A \) is bent into a circle of radius \( R \) and
wire \( B \) is bent to form a square of side \( a \)
If \( B_{A} \) and \( B_{B} \) are the values of
magnetic field at the centres of the circle and square respectively, then the ratio \( \frac{B_{A}}{B_{B}} \) is:
A \( \cdot \frac{\pi^{2}}{16 \sqrt{2}} \)
в. \( \frac{\pi^{2}}{16} \)
c. \( \frac{\pi^{2}}{8 \sqrt{2}} \)
D. \( \frac{\pi^{2}}{8} \)
Subject: Physics
Two gases \( A \) and \( B \) having same pressure
P, volume \( V \) and temperature \( T \) are mixed. if the mixture has volume and
temperature as \( \mathrm{V} \) and \( \mathrm{T} \) respectively the pressure of mixture is
\( A \cdot 2 P \)
B.
\( c \cdot P / 2 \)
D. \( 4 P \)
Subject: Chemistry
\( N H_{4} N O_{3} \) and \( N H_{4} N O_{2} \) on heating decomposes into:
A \( . N O_{2}, N_{2} \)
в. \( N O_{2}, N O_{3} \)
c. \( N_{2} O, N_{2} \)
D. \( N O_{3}, N O_{2} \)
Subject: Physics
An infinite number of charges each equal to \( Q \) are placed along the \( X \) -axis at \( X= \) \( 4, X=8 \) and so on. The potential at the
point \( X=0 \) due to set of charges is :
\( ^{A} \cdot \frac{Q}{8 \pi \epsilon_{0}} \)
в. \( \frac{Q}{3 \pi \epsilon_{0}} \)
c. \( \frac{1}{4 \pi \epsilon_{0}} \frac{2}{3} Q \)
D. \( \frac{1}{4 \pi \epsilon_{0}} \frac{Q}{3} \)
Subject: Maths
If \( a, b, c, d \) are real and no two of them
are simultaneously zero, then the equation \( \left(x^{2}+a x-3 b\right)\left(x^{2}-c x+\right. \)
b) \( \left(x^{2}-d x+2 b\right)=0 \) has
A. at least two real roots
B. at least four real roots
c. all roots real
D. at least two imaginary roots
Subject: Maths
If \( \alpha \) and \( \beta \) are the roots of \( a x^{2}+b x+ \)
\( c=0, \) then the quadratic equation
whose roots are \( \frac{1}{\alpha} \) and \( \frac{1}{\beta} \) is
A \( \cdot a x^{2}+b x+c=0 \)
B. \( b x^{2}+a x+c=0 \)
c. \( c x^{2}+b x+a=0 \)
D. \( c x^{2}+a x+c=0 \)
Subject: Maths
\( \lim _{x \rightarrow a^{+}} \frac{\{x\} \sin (x-a)}{(x-a)^{2}}= \) where \( \{x\} \)
denotes fractional part of \( x \) and \( a \epsilon N \)
A . 0
B. 1
\( c \cdot a \)
D. 5
Subject: Maths
If the cube equation \( x^{3}-p x+q \) has
three distinct real roots, where \( p>0 \)
and \( \boldsymbol{q}>\mathbf{0} \)
Then, which one of the following is
correct?
A \( \cdot \) the cubic has maxima at both \( \sqrt{\frac{p}{3}} \) and \( -\sqrt{\frac{p}{3}} \)
B. The cubic has minima at \( \sqrt{\frac{p}{3}} \) and maxima at \( -\sqrt{\frac{p}{3}} \)
c. The cubic has minima at \( -\sqrt{\frac{p}{3}} \) and maxima at \( \sqrt{\frac{p}{3}} \)
D. The cubic has minima at both \( \sqrt{\frac{p}{3}} \) and \( -\sqrt{\frac{p}{3}} \)
Subject: Chemistry
For a certain atom, there are energy
levels \( A, B, C \) of a certain atom
corresponds to increasing values of
energy, i.e., \( \boldsymbol{E}_{\boldsymbol{A}}<\boldsymbol{E}_{\boldsymbol{B}}<\boldsymbol{E}_{\boldsymbol{C}} . \) Choose the
correct option if \( \lambda_{1}, \lambda_{2} \) and \( \lambda_{3} \) are the
wavelengths of radiations
corresponding to the transitions \( C \) to
\( B, B \) to \( A \) and \( C \) to \( A \) respectively:
\( A \cdot \lambda_{3}=\lambda_{1}+\lambda_{2} \)
B. \( \lambda_{3}=\frac{\lambda_{1} \lambda_{2}}{\lambda_{1}+\lambda_{2}} \)
c. \( \lambda_{1}+\lambda_{2}+\lambda_{3}=0 \)
D. \( 3 \lambda_{2}=\lambda_{3}+2 \lambda_{2} \)
Subject: Chemistry
(II) \( \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{B} \boldsymbol{r} \)
Arrange the following compounds in increasing order of their boiling points:
\( (\mathbf{I}) \)
(III)
\( A \cdot(\mid I)<(1)<(\| 1) \)
B. (I) <(II) <(III)
\( c \cdot(\| I)<(1)<(11) \)
D. (III) <(II) < (I)
Subject: Physics
Assume that if the shear stress in stee
exceeds about \( 4.00 \times 10^{8} N / m^{2}, \) the steel reptures. Determine. the shearing force necessary to (a) shear a steel bolt \( 1.00 \mathrm{cm} \) in diameter and
(b) punch a
1.00-cm-diameter hole in a steel plate \( 0.500 \mathrm{cm} \) thick.
Subject: Physics
A \( 2 F \) capacitor is initially charged to \( 20 V \) and then shorted across a \( 5 m H \)
inductor. The angular frequency of oscillation is.
A. \( 1000 \mathrm{rad} / \mathrm{s} \)
B. 100 rad/s
c. \( 10000 \mathrm{rad} / \mathrm{s} \)
D. \( 10 \mathrm{rad} / \mathrm{s} \)
Subject: Physics
Two concentric coils of radius \( r \) are
kept mutually perpendicular to each other. If current flowing through both
the coils is \( I, \) then the resultant
magnetic moment due to the two coils will be
A . \( \sqrt{2} I \pi r^{2} \)
В. \( \sqrt{2} I r^{2} \)
c. \( \sqrt{2} I r \)
D. \( 2 \pi r^{2} \)
Subject: Physics
The electric flux through a certain area of dielectric is \( 8.76 \times 10^{3} t^{4} \). The
displacement current through the area
is \( 12.9 p A \) at \( t=26.1 m s . \) Find the
dielectric constant of the material.
A \( .2 \times 10^{-8} \)
B. \( 4 \times 10^{-8} \)
c. \( 8 \times 10^{-8} \)
D. \( 2 \times 10^{-7} \)
Subject: Maths
A wooden toy in the form of cone surmounted on a hemisphere. The
diameter of the base of the cone is \( 6 \mathrm{cm} \)
and height is \( 4 \mathrm{cm} \). find the cost of painting the toy at the rate of \( R s .5 \) per
\( 1000 \mathrm{cm}^{2} \)
Subject: Physics
A neutral water molecule is placed in electic field \( \boldsymbol{E}=\mathbf{1 . 2 5} \times \mathbf{1 0}^{\mathbf{4}} \boldsymbol{N} / \boldsymbol{C} . \) The
work done to rotate it by \( 180^{\circ} \) is \( 2.5 \times \)
\( 10^{-25} J . \) Find aproximate separation of
center of charges.
A. \( 0.625 \times 10^{-9} \mathrm{m} \)
в. \( 0.65 \times 10^{-10} \mathrm{m} \)
C \( .0 .75 \times 10^{-10} \mathrm{m} \)
D. \( 0.625 \times 10^{-10} m \)
Subject: Maths
In the figure given \( \Delta A B C \) is a right
isosceles triangle with right angle at \( C \)
CD is a parallel to \( A B \) and \( B D=B A \). The
degree measure of \( \angle D B C \) equals:
A . \( 10^{\circ} \)
B . \( 15^{\circ} \)
\( c \cdot 20^{\circ} \)
D. 25
Subject: Chemistry
Which of the following is the best example of law of conservation of
mass?
In and \( m \) are the masses of reactants
and \( p \) and \( q \) are the masses of products formed.]
A \( . n-m=p-q \)
в. \( n+m=p+q \)
c. \( n=m \)
D. \( p=q \)
Subject: Maths
\( f\left(a_{1}, a_{2}, a_{3}, \dots \) from a geometric \right.
progression and \( a_{i}>0 \) for all \( i \geq 1 \)
\[
\operatorname{then}\left|\begin{array}{ccc}
\log \boldsymbol{a}_{m} & \log \boldsymbol{a}_{m+1} & \log \boldsymbol{a}_{m+2} \\
\log \boldsymbol{a}_{m+3} & \log \boldsymbol{a}_{m+4} & \log \boldsymbol{a}_{m+5} \\
\log \boldsymbol{a}_{m+\boldsymbol{6}} & \log \boldsymbol{a}_{m+\boldsymbol{7}} & \log \boldsymbol{a}_{m+8}
\end{array}\right| \text { is }
\]
equal to
\( \mathbf{A} \cdot \log a_{m+8}-\log a_{m} \)
B. \( \log a_{m} \)
\( \mathbf{c} \cdot 2 \log a_{m+1} \)
D.
Subject: Physics
STATEMENT-1: A Solenoid tend to
contract (along its length) when a current is passed through it. STATEMENT-2: If current in two coaxial
circular rings of equal radii is in same sense( as seen by an observer on axis away from both the rings), the rings
attract each other. Further the given current carrying rings attract each other because parallel current attracts.
A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-
c. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True
Subject: Physics
A particle experiences constant acceleration for 20 s after starting from
rest. If it travels a distance of \( X_{1} \) in the
first 10 s and a distance of \( X_{2} \), in the
remaining 10 s, then which of the following is true?
A. \( X_{1}=2 X_{2} \)
В. \( X_{1}=X_{2} \)
\( \mathbf{c} \cdot X_{1}=3 X_{2} \)
D. \( 3 X_{1}=X_{2} \)
Subject: Maths
Force \( 3 \mathrm{N}, 4 \mathrm{N} \) and \( 12 \mathrm{N} \) act at a point in mutually perpendicular directions. The magnitutde of the resultant force is :-
\( A \cdot 19 N \)
B. 13 N
c. \( 11 \mathrm{N} \)
D. 5 N
Subject: Chemistry
\( N_{2} O_{2}(g) \rightarrow 2 N O \) is a first-order
reaction interms of the concentration of
\( N_{2} O_{2}(g) . \) Which of the following is
valid, \( \left[N_{2} O_{2}\right] \) being constant?
A \( \cdot[N O]=\left[N_{2} O_{2}\right]_{0} e^{-k t} \)
B . \( [N O]=\left[N_{2} O_{2}\right]_{0}\left(1-e^{k t}\right) \)
C \( \cdot[N O]=\left[N_{2} O_{2}\right]_{0}\left(e^{-k t}-1\right) \)
D \( \cdot[N O]=\left[N_{2} O_{2}\right]_{0}\left(1-e^{-k t}\right) \)
Subject: Physics
If the mass of proton \( =1.008 a . m . u \)
and mass of neutron \( =1.009 a . m . u \)
then binding energy per nucleon for \( _{4} B e^{9}(\text { mass }=9.012 a m u) \) would be:
A . 40.065 Mev
B. \( 60.44 \mathrm{MeV} \)
c. 67.2 Mev
D. 6.72 Mev
Subject: Physics
The volume of a liquid (v) flowing per second through a cylindrical tube depends upon the pressure gradient
(p/I) radius of the tube (r) coefficient of viscosity ( \( \eta \) ) of the liquid by dimensional method the correct
formula is
A \( \cdot v \alpha \frac{P r^{4}}{\eta l} \)
в. \( v \alpha \frac{P r}{\eta l^{4}} \)
\( ^{\mathrm{c}} \cdot_{V \alpha} \frac{P l^{4}}{\eta r} \)
D. None
Subject: Maths
A rectangular tank \( 28 m \) long and \( 22 m \) wide is required to receive entire water from a full cylindrical tank of internal
diameter \( 28 m \) and depth \( 4 m . \) Find the
least height of the tank that will serve
the purpose. (Take \( \boldsymbol{\pi}=\mathbf{2 2} / \mathbf{7}) \)
A. \( 4.0 \mathrm{m} \)
в. \( 4.5 \mathrm{m} \)
\( c .5 .0 m \)
D. \( 5.2 m \)
Subject: Chemistry
The change in internal energy of the
methanol is
A \( \cdot 9.6 \times 10^{5} J \)
B . \( 7.14 \times 10^{5} \mathrm{J} \)
c. \( 6.89 \times 10^{4} J \)
D. \( 6.86 \times 10^{5} J \)
Subject: Maths
Find the product of \( x^{2} y z \times x y^{2} z^{3} \)
A \( \cdot x^{3} y^{3} z^{4} \)
В. \( x^{3} y^{3} z^{3} \)
c. \( x^{3} y^{4} z^{3} \)
D. \( x^{3} y^{3} z \)
Subject: Chemistry
Arrange the following in the decreasing order of their melting points.
I. Decane
II. Nonane
III. Octane
IV. Heptane
\( A \cdot(1)>(11)>(111)>(1 v) \)
B. (IV) > (III) > (II) > (I)
\( c \cdot(1)>((11)>(11)>(11)) \)
\( D \cdot(\mid V)>(||)>(\| \mid)>(\mid) \)
Subject: Chemistry
For the reactions,
\( \boldsymbol{A} \rightleftharpoons \boldsymbol{B}, \boldsymbol{K}_{c}=\mathbf{1} ; \boldsymbol{B} \rightleftharpoons \boldsymbol{C}, \boldsymbol{K}_{c}=\mathbf{3} ; \boldsymbol{C} \rightleftharpoons \)
\( \boldsymbol{D}, \boldsymbol{K}_{c}=\mathbf{5} . \boldsymbol{K}_{c} \) for reaction \( \boldsymbol{A} \rightleftharpoons \boldsymbol{D} \) is:
A . 15
B. 5
\( c .3 \)
D.
Subject: Chemistry
At \( 380^{\circ} C, \) the half life period for the first
order decomposition of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) is \( \boldsymbol{3} \boldsymbol{6} \boldsymbol{0} \)
min. The energy of activation of the
reaction is \( 200 k J \) mol \( ^{-1} \). Calculate the
time required for \( 75 \% \) decomposition at
\( 450^{\circ} \mathrm{C} \)
Subject: Maths
A body at an unknown temperature is placed in a room which is held at a
constant temperature of \( 30^{0} F . \) If after
10 minutes the temperature of the body
is \( 0^{0} F \) and after 20 minutes the
temperature of the body is \( 15^{0} F, \) find the unknown initial temperature.
A . -50
B. -20
c. -40
D. -30
Subject: Biology
Which of the following shows correct sequence of conduction of action
potential in the heart?
A. SA node \( \rightarrow \) Bundle of His \( \rightarrow \) AV node \( \rightarrow \) Right and left branches of bundle of His \( \rightarrow \) Purkinje fibre
B. SA node \( \rightarrow \) AV node \( \rightarrow \) Purkinje fibre Bundle of His \( \rightarrow \) Right and left branches of bundle of His
C. SA node \( \rightarrow \) AV node \( \rightarrow \) Bundle of His \( \rightarrow \) Right and left branches of bundle of His \( \rightarrow \) Purkinje fibre
D. AV node \( \rightarrow \) SA node \( \rightarrow \) Bundle of His \( \rightarrow \) Right and left branches of bundle of His \( \rightarrow \) Purkinje fibre