AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Which of the following is not a correct
statement about enthalpy of solution?
A. For most ionic compounds, \( \Delta H_{s o l}^{0} \) is positive and the dissociation process is endothermic.
B. Solubility of most salts increases with increase in temperature
C. If the lattice enthalpy is very high, the dissolution of compound becomes very easy.
D. Enthalpy of solution is determined by the selective values of the lattice enthalpy and hydration enthalpy.
Subject: Maths
\( \text { If }\boldsymbol{f}(\boldsymbol{x})=\boldsymbol{a} \sec \boldsymbol{x}-\boldsymbol{b} \tan \boldsymbol{x}, \boldsymbol{a}\rangle \boldsymbol{b}\rangle \boldsymbol{0}, \) then
the minimum value of \( f(x) \) is
A \( \cdot \sqrt{a^{2}+b^{2}} \)
B. \( 2 \sqrt{a^{2}-b^{2}} \)
c. \( \sqrt{a^{2}-b^{2}} \)
D. \( a-b \)
Subject: Physics
A vessel contains 1 mole of \( \mathrm{O}_{2} \) (molar
\( \operatorname{mass} 32 g m) \) at a temperature \( T . \) The
pressure is \( P . \) An identical vessel
containing 1 mole of He (molar mass
\( 4 g m \) ) at a temperature \( 2 T \) has a
pressure :
A.
в. \( \frac{P}{8} \)
c. \( 2 P \)
D. 8P
Subject: Physics
Find the minimum load resistance
which can be used for the zener diode
as shown in figure. Given, \( \boldsymbol{V}_{\boldsymbol{Z}}= \)
\( \mathbf{1 0} \boldsymbol{V}, \boldsymbol{R}_{Z}=\mathbf{0} \mathbf{\Omega}, \boldsymbol{R}=\mathbf{4 5 0 \Omega}, \boldsymbol{I}_{Z}(\boldsymbol{m} \boldsymbol{i n})= \)
\( 2 m A \) and \( I_{Z}(\max )=60 m A \)
A . \( 0 \Omega \)
B. \( 333.3 \Omega \)
c. \( 31.95 \Omega \)
D. \( 319.5 \Omega \)
Subject: Physics
An object of \( 10 \mathrm{cm} \) is placed in front of a plane mirror. The height of image will be
A. \( 5 \mathrm{cm} \)
B. \( 15 \mathrm{cm} \)
c. \( 20 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)
Subject: Maths
If the function \( f \) defined on \( \left(\frac{\pi}{6}, \frac{\pi}{3}\right) \) b \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{cl}\frac{\sqrt{\mathbf{2}} \cos \boldsymbol{x}-\mathbf{1}}{\cot \boldsymbol{x}-\mathbf{1}}, & \boldsymbol{x} \neq \frac{\boldsymbol{\pi}}{\boldsymbol{4}} \\ \boldsymbol{k}, & \boldsymbol{x}=\frac{\boldsymbol{\pi}}{\boldsymbol{4}}\end{array}\right. \)
continuous, then \( k \) is equal to?
\( A \cdot \frac{1}{2} \)
B.
\( c \cdot \frac{1}{\sqrt{2}} \)
\( D \)
Subject: Maths
A bird flies in a circle on a horizontal
plane. An observer stands at a point on the ground. Suppose \( 60^{\circ} \) and \( 30^{\circ} \) are the maximum and the minimum angles
of elevation of the bird and that they
occur when the bird is at the points \( \mathrm{P} \) and \( Q \) respectively on its path. Let \( \theta \) be the angle of elevation of the bird when it is a point on the are of the circle exactly midway between \( P \) and \( Q \). Find the numerical value of \( \tan ^{2} \theta \) (Assume that
the observer is not inside the vertical
projection of the path of the bird).
Subject: Physics
n Fig, \( P Q \) and \( P R \) are the two light rays
emerging from an object \( \boldsymbol{P} \). The ray \( \boldsymbol{P Q} \)
is refracted as \( Q S \). Name the
phenomenon that occurs if the angle of
incidence \( \angle P Q N \) is increased :
A. Refraction
B. Total internal reflection
c. Minimum deviation
D. None of these
Subject: Chemistry
If \( W_{1}, W_{2}, W_{3} \) and \( W_{4} \) for an ideal gas are magnitude of work done in isothermal, adiabatic, isobaric and isochoric reversible expansion processes, the correct order will be :
A \( . w_{1}>w_{2}>w_{3}>w_{4} \)
в. \( w_{3}>w_{2}>w_{1}>w_{4} \)
c. \( w_{3}>w_{2}>w_{4}>w_{1} \)
D. \( w_{3}>w_{1}>w_{2}>w_{4} \)
Subject: Chemistry
Assertion
He and Ne do not form clatharates.
Reason

They are difficult to polarise due to
smaller size.

Read the above assertion and reason
and choose the correct option regarding
¡t.
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 true but Reason is false
D. Assertion is false but Reason is true
Subject: Maths
Find out whether the sequence
\( 1^{2}, 3^{2}, 5^{2}, 7^{2}, \dots \) is an AP. If it is, find out
the common difference.
\( A \cdot \) No
B. Yes, \( d=8 \)
\( \mathbf{c} . \) Yes, \( d=-8 \)
D. Yes, \( d=9 \)
Subject: Maths
What is the angle between the straight
\( \operatorname{lines}\left(m^{2}-m n\right) y=\left(m n+n^{2}\right) x+n^{3} \)
and \( \left(\boldsymbol{m} \boldsymbol{n}+\boldsymbol{m}^{2}\right) \boldsymbol{y}=\left(\boldsymbol{m} \boldsymbol{n}-\boldsymbol{n}^{2}\right) \boldsymbol{x}+\boldsymbol{m}^{3} \)
where \( \boldsymbol{m}>\boldsymbol{n} ? \)
\( ^{\mathbf{A}} \cdot \tan ^{-1}\left(\frac{2 m n}{m^{2}+n^{2}}\right) \)
B. \( \tan ^{-1}\left(\frac{4 m^{2} n^{2}}{m^{4}-n^{4}}\right) \)
\( ^{\mathbf{C}} \cdot \tan ^{-1}\left(\frac{4 m^{2} n^{2}}{m^{4}+n^{4}}\right) \)
D. \( 45^{\circ} \)
Subject: Physics
A panda with a mass of \( 90.0 k g \) lies
without moving on a ramp that is
inclined at \( 25.0^{\circ} \)
What is the coefficient of
static frictional force between the ramp
and the panda?
A . 0.25
B. 0.423
\( c \cdot 0.466 \)
D. 372
E. The coefficient of static friction cannot be determined with the information giver
Subject: Physics
Two charges \( 5 \times 10^{-8} C \) and \( -3 x \)
\( 10^{-8} C \) are located \( 16 \mathrm{cm} \) apart. At what
point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
A. \( 20 \mathrm{cm} \) away from the positive charge on the side of negative charge
B. \( 40 \mathrm{cm} \) away from the negative charge on the side of positive charge
c. \( 40 \mathrm{cm} \) away from the positive charge on the side of negative charge
D. \( 20 \mathrm{cm} \) away from the negative charge on the side of positive charge
Subject: Chemistry
The different zones of a candle flame
are marked by the letters, \( A, B \) and
C. Which of the following is correct?
A. \( B \) is the hottest part of the flame
B. \( C \) is moderately hot.
\( \mathrm{C} \). A is the hottest part of the flame
A is moderately hot whereas \( C \) is the coldest partt
Subject: Physics
In given Figure, a charge \( Q \) is fixed.
Another charge \( q \) is moved along a circular arc MN of radius r around it,
from the point \( \mathrm{M} \) to the point \( \mathrm{N} \) such
that the length of the arc \( M N=l . \) The
work done in this process is :
A. Zero
В. \( \frac{1}{4 \pi \epsilon_{0}} \cdot \frac{Q q}{r^{2}} l \)
c. \( \frac{Q q}{2 \epsilon_{0} r^{2}} l \)
D. \( \frac{Q q}{2 \pi \epsilon_{0} r^{2}} \)
Subject: Maths
What is the nature of the intersection of
the set of planes \( \boldsymbol{x}+\boldsymbol{a} \boldsymbol{y}+(\boldsymbol{b}+\boldsymbol{c}) \boldsymbol{z}+ \)
\( \boldsymbol{d}=\mathbf{0}, \boldsymbol{x}+\boldsymbol{b} \boldsymbol{y}+(\boldsymbol{c}+\boldsymbol{a}) \boldsymbol{z}+\boldsymbol{d}=\mathbf{0} \) and
\( \boldsymbol{x}+\boldsymbol{c} \boldsymbol{y}+(\boldsymbol{a}+\boldsymbol{b}) \boldsymbol{z}+\boldsymbol{d}=\mathbf{0} ? \)
A. They meet at a point.
B. They form a triangular prism.
c. They pass through a line.
D. They are at equal distance from the origin
Subject: Physics
Which of the following statements are
true?
a. The spectrum of sunlight has 7 colors
b. Spectrum is seen due to bending of lights of different colors at different
angles with respect to the incident ray through a prism
c. Red light bends the least whereas violet light bends the maximum
d. Rainbow is an example of dispersion of light
A. a, band c
B. c and d
c. a, c and d
D. All of these
Subject: Maths
Assertion
If \( \lim _{\boldsymbol{x} \rightarrow \mathbf{0}} \boldsymbol{f}(\boldsymbol{x}) \) and \( \lim _{\boldsymbol{x} \rightarrow \mathbf{0}} \boldsymbol{g}(\boldsymbol{x}) \) exists finitely
\( \operatorname{then} \lim _{x \rightarrow 0} f(x) \cdot g(x) \) exists finitely
Reason
If \( \lim _{x \rightarrow 0} f(x) \cdot g(x) \) exists finitely then
\( \lim _{x \rightarrow 0} f(x) \cdot g(x)=\lim _{x \rightarrow 0} f(x) \cdot \lim _{x \rightarrow 0} g(x) \)
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 and Reason is correct
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{0} & \mathbf{1} \\ -\mathbf{1} & \mathbf{0}\end{array}\right] \) then determinant of \( [\boldsymbol{A}] \)
is
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
c. 0
D.
Subject: Physics
Force of attraction between two point charges \( Q \) and \( -Q \) separated by \( d \)
meter is \( F_{e} . \) When these charges are
placed two identical sphere of radius \( R=0.3 d \) whose centries are \( d \) meter
apart the force of attraction between
them is
A. Greater than \( F_{e} \)
B. Equal to \( F_{e} \)
c. Less than \( F_{e} \)
D. None of these
Subject: Chemistry
How many of the following substances
are soluble in concentrated \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) ?
\( \boldsymbol{B} \boldsymbol{a} \boldsymbol{S} \boldsymbol{O}_{4}, \boldsymbol{C} \boldsymbol{u} \boldsymbol{S}, \boldsymbol{P b} \boldsymbol{S}, \boldsymbol{H} \boldsymbol{g} \boldsymbol{S} \)
\( A \)
B. 2
\( c \cdot 3 \)
D. 4
Subject: Maths
What should be added in vector \( 3 i+ \)
\( 4 j-2 k \) to get its resultant a unit vector
\( i \)
A . \( -2 i-4 j+2 k \)
B. \( 2 i+4 j+2 k \)
\( c .-2 i+4 j+2 k \)
D. None of these
Subject: Maths
\( \cos \frac{2 \pi}{15} \cos \frac{4 \pi}{15} \cos \frac{8 \pi}{15} \cos \frac{14 \pi}{15} \)
A . \( 1 / 4 \)
в. \( 1 / 8 \)
c. \( 1 / 16 \)
D. \( 1 / 32 \)
Subject: Chemistry
A storage battery contains a solution of
\( H_{2} S O_{4}, 38 \% \) by mass. At this
concentration, van't Hoff factor is 2.50
The temperature at which battery contents freeze will be:
\( \left(\boldsymbol{K}_{f}=\mathbf{1 . 8 6} \boldsymbol{K} \boldsymbol{m o l}^{-1} \boldsymbol{k g}\right) \)
A \( .-29.08^{\circ} \mathrm{C} \)
B . \( -25.18^{\circ} \mathrm{C} \)
c. \( -17.25^{\circ} \mathrm{C} \)
D. none of these
Subject: Maths
In a potato race 20 potatoes are placed in a line at intervals of 4 metres with
the first potato 24 metres from the
starting point. A contestant is required to bring the potatoes back to the starting place one at a time. How far would he run in bringing back all the potatoes?
A . \( 2340 \mathrm{m} \)
B. 2480 m
\( c .2540 \mathrm{m} \)
D. 2230 m
Subject: Physics
A \( 100 \Omega \) resistor is connected to a
\( 220 V, 50 H z A C \) supply. Find \( r m s \) value
of current in the circuit :
A . \( 1.10 A \)
в. \( 2.20 A \)
c. \( 3.30 A \)
D. \( 4.40 A \)
Subject: Physics
A false balance has equal arms. An
object weights \( \boldsymbol{w}_{1} \) when placed in one
pan and \( w_{2} \) when placed in the other
pan. Then weight \( \boldsymbol{w} \) of the object is :
A \( \cdot \sqrt{w_{1} w_{2}} \)
в. \( \frac{w_{1}+w_{2}}{2} \)
c. \( \left(\frac{w_{1}^{2}+w_{2}^{2}}{2}\right)-1 \)
D. \( \sqrt{w_{1}^{2}+w_{2}^{2}} \)
Subject: Chemistry
How much will the potential of
\( Z n / Z n^{2+} \) change if the solution of
\( Z n^{2+} \) is diluted 10 times?
A. increase by \( 0.03 \mathrm{V} \)
B. decreases by \( 0.03 \mathrm{V} \)
c. increases by \( 0.059 \mathrm{V} \)
D. decreases by \( 0.059 \mathrm{V} \)
Subject: Chemistry
Assertion
Molten potassium chloride is a good electrical conductor.
Reason
the melting process frees the ions in potassium chloride from their fixed positions in the crystal lattice.
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 cell balances against a length of
\( 200 \mathrm{cm} \) on a potentiometer wire, when it
is shunted by a resistance of 8\Omega. The balancing length reduces by \( 40 \mathrm{cm} \)
when it is shunted by a resistance of \( 4 \Omega \) Calculate the balancing length when the cell is in open circuit. Also calculate
the internal resistance of the cell.
Subject: Maths
The vector \( \vec{a}=\alpha \hat{i}+2 \widehat{j}+\beta \widehat{k} \) lies in the
plane of the vectors \( \overrightarrow{\boldsymbol{b}}=\widehat{\boldsymbol{i}}+\widehat{\boldsymbol{j}} \) and \( \overrightarrow{\boldsymbol{c}}= \)
\( \widehat{j}+\widehat{k} \) and bisects the angle between \( \overrightarrow{\boldsymbol{b}} \) and \( \vec{c} . \) Then, which one of the following
gives possible values of \( \alpha \) and \( \beta ? \)
A \( \cdot \alpha=2, \beta=2 \)
в. \( \alpha=1, \beta=2 \)
c. \( \alpha=2, \beta=1 \)
D. \( \alpha=1, \beta=1 \)
Subject: Chemistry
0.1 molal-equeous solution of an electrolyte \( \mathrm{FeCl}_{2} \) is \( 80 \% \) ionised. The
boiling point of the solution at 1 atm is:
\( \left[\mathbf{K}_{\mathbf{6}}\left(\mathbf{H}_{2} \mathbf{O}\right)=\mathbf{0 . 5 2} \mathbf{K} \mathbf{k g} \mathbf{m o l}^{-\mathbf{1}}\right] \)
A. \( 273.17 K \)
B . \( 273.19^{\circ} \mathrm{C} \)
c. \( 373.19^{\circ} \mathrm{C} \)
D. \( 100.17^{\circ} \mathrm{C} \)
Subject: Chemistry
Calculate the difference in the number
of carbon atoms in 1.0 g of \( C-14 \) isotope and \( 1.0 \mathrm{g} \) of \( C-12 \) isotope.
A \( .7 .2 \times 10^{21} \)
B. \( 6.2 \times 10^{20} \)
C \( \cdot 6.2 \times 10^{22} \)
D. \( 7.2 \times 10^{20} \)
Subject: Physics
In the primary circuit of potentiometer
the rheostat can be varied from 0 to
10\Omega. Initially it is at minimum
resistance (zero).The rheostat is put at
maximum resistance \( (10 \Omega) \) and the
switch \( S \) is closed. New balancing
length is found to be 8 m. Find the
internal resistance \( r(\text { in ohms }) \) of the
\( 4.5 V \) cell.
Subject: Physics
Two small balls having equal positive charge \( Q \) (coulomb) on each are
suspended by two insulating strings of equal length \( L \), from a hook
fixed to a stand. If the whole set up is
taken in a satellite
then the angle \( \theta \) between the two strings is : (in equillibrium)
A \( \cdot O^{\circ} \)
В. \( 90^{\circ} \)
\( c \cdot 180^{\circ} \)
Subject: Maths
Two complex numbers are represented
by ordered pairs \( z_{1}:(3,4) \& z_{2}:(4,5) \)
which of the following is true for \( z_{1}+z_{2} \)
\( ? \)
This question has multiple correct options
\( \mathbf{A} \cdot z_{1}+z_{2}=(7,9) \)
B . \( z_{1}+z_{2}=(7+9 i) \)
\( \mathbf{c} \cdot z_{1}+z_{2}=(1,9) \)
D. None of these
Subject: Chemistry
The structure and hybridization of
\( \boldsymbol{S} \boldsymbol{i}\left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{4} \) respectively, is:
A. bent and \( s p \)
B. trigonal and \( s p^{2} \)
c. octahedral and \( s p^{3} d \)
D. tetrahedral and \( s p^{3} \)
Subject: Maths
Let \( \boldsymbol{f}\left(\boldsymbol{x}, \boldsymbol{y}, \boldsymbol{c}_{1}\right)=\mathbf{0} \) and \( \boldsymbol{f}\left(\boldsymbol{x}, \boldsymbol{y}, \boldsymbol{c}_{2}\right)=\mathbf{0} \)
define two integral curves of a homogeneous first order differential
equation. If \( P_{1} \) and \( P_{2} \) are respectively the points of intersection of these
curves with an arbitrary line, \( \boldsymbol{y}=\boldsymbol{m} \boldsymbol{x} \)
then prove that the slopes of these two
curves at \( P_{1} \) and \( P_{2} \) are equal
Subject: Physics
A particle is thrown vertically upwards. Its velocity at half of the height is 10 \( \boldsymbol{m} / \boldsymbol{s} . \) The maximum height attained by
the particle is \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
\( A \cdot 8 m \)
B. 20m
\( c .10 m \)
D. \( 16 m \)
Subject: Maths
Find the value of \( x \) for which the matrix
product
\[
\left[\begin{array}{ccc}
2 & 0 & 7 \\
0 & 1 & 0 \\
1 & -2 & 1
\end{array}\right]\left[\begin{array}{ccc}
-x & 14 x & 7 x \\
0 & 1 & 0 \\
x & -4 x & -2 x
\end{array}\right] \text { equa }
\]
to an identity matrix.
Subject: Physics
A ball is dropped on to a horizontal plate from a height \( h=9 \) m above it. If the coefficient of restitution is \( e=1 / 2, \) the
total distance travelled before the ball
comes to rest is:
A. \( 10 \mathrm{m} \)
B. 15
\( c \cdot 20 m \)
D. 25 m
Subject: Physics
The terminals of a \( 18 V \) battery with an
internal resistance of \( 1.5 \Omega \) are
connected to a circular wire of
resistance \( 24 \Omega \) at two points distant at
one quarter of the circumference of a
circular wire. The current through the bigger arc of the circle will be
\( \mathbf{A} \cdot 0.75 A \)
в. \( 1.5 A \)
c. \( 2.25 A \)
D. \( 3 A \)
Subject: Physics
Assertion
Newton's law of universal gravitation
states that a particle attracts every other particle in the universe using a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Reason
Law of gravitation is analogous to magnetic force between the moving
charges.
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: Chemistry
We define p value of a term (say \( x \) ) as
\( \boldsymbol{p}_{\boldsymbol{x}}=-\log \boldsymbol{x} \)
Calculate \( \boldsymbol{p}_{\left(C l^{-}\right)} \) value as \( \boldsymbol{x} \times \mathbf{1 0}^{-1} \) in a
solution that is \( 2.00 \times 10^{-3} \mathrm{Min} \) NaCl
and \( 5.4 \times 10^{-4} \) M \( H C l \)
Subject: Physics
The electric current in a circuit is given by \( i=\frac{i_{0} t}{\tau} \) for some time. The rms
current for the period \( t=0 \) to \( t=\tau \) will
be
\( \mathbf{A} \cdot i_{0} \sqrt{\frac{T}{3}} \)
B. \( \frac{i_{0}}{\sqrt{3}} \)
\( c \cdot \frac{i_{0}}{2} \)
D. \( \frac{i_{0}}{3} \)
Subject: Physics
The masses of sun and earth are \( M_{s} \)
and \( M_{e}, \) respectively and the distance
between them is \( R_{e s} \) then, the distance
of a body of mass \( \mathrm{m} \), from the earth
along the line towards the sun, where the sun's gravitational pull balances that of the earth is
A \( \cdot \frac{R_{e s}}{\sqrt{M_{s} / M_{e}}+1} \)
В. \( \frac{R_{e s}}{\sqrt{M_{e} / M_{s}}+1} \)
c. \( \frac{R_{e s}}{\sqrt{M_{s} / M_{e}}-1} \)
D. \( \frac{R_{e s}}{1-\sqrt{M_{e} / M_{s}}} \)
Subject: Physics
The electric potential at a certain
distance from a point charge \( Q \) is \( 810 V \) and electric field is \( 300 N / C \). The minimum speed with which a particle of charge \( -Q \) and mass \( m=6 x \)
\( 10^{-16} k g \) should be projected from that
point so that it moves into the field free region is:
A \( \cdot 9 \times 10^{6} m / s \)
в. \( 81 \times 10^{6} \mathrm{m} / \mathrm{s} \)
c. \( 81 \times 10^{4} m / s \)
D. \( 9 \times 10^{4} m / s \)
Subject: Physics
The young's duble slit experiment is performed with blue and green light of wavelength \( 4360 \AA \) and \( 5460 \dot{A} \)
respectively. if \( x \) is the distance of \( 4 t h \) maxima from central one, then
A. \( x(b l u e)=x(g \text { reen }) \)
в. \( x(b l u e)>x(\text { green }) \)
c. \( x(b l u e)<x(\text { gree } n) \)
D. \( \frac{x(b l u e)}{x(g r e e n)}=\frac{5460}{4360} \)
Subject: Maths
The set of all points of differentiability of the function \( \mathbf{f}(\mathbf{x})=\frac{\sqrt{\mathbf{x}+\mathbf{1}}-\mathbf{x}}{\sqrt{\mathbf{x}}} \) for \( \mathbf{x} \)
\( \neq 0 \) and \( \mathrm{f}(0)=0 \) is
\( \mathbf{A} \cdot(-\infty, \infty) \)
B. \( [0, \infty) \)
\( c \cdot(0, \infty) \)
D. \( (-\infty, \infty) \sim\{0\} \)
Subject: Maths
From a pack of 52 cards, face cards and tens are removed and kept aside, then a card is drawn at random from the
remaining cards. If A: The events that the card is drawn is an ace. H: The
events that the card is drawn is a
heart.S: the events that the card is
drawn is a spade. Then, which of the following holds?
\( \mathbf{A} \cdot 9 P(A)=4 P(H) \)
B. \( P(S)=4 P(A \cap H) \)
c. \( 3 P(H)=P(A \cap S) \)
D. None of these
Subject: Biology
Read the following statements about
the given diagram carefully and state which of them are correct?
(i) A carries urine and sperms.
(ii) \( \mathrm{B} \) secretes a fluid that helps in the lubrication of penis.
(iii) D produces testosterone but not
sperms
(iv) \( \mathrm{C} \) stores sperms.
\( A \cdot \) (i) and (ii)
B. (ii) and (iii)
c. (ii) and (iv)
D. (i) and (iv)
Subject: Physics
The primary winding of a transformer
has 100 turns and its secondary winding has 200 turns. The primary is
connected to an ac supply of \( 120 \mathrm{V} \) and the current flowing in it is 10 A. The voltage and the current in the secondary
are
A. \( 240 \vee, 5 A \)
B. 340 V, 7 A
c. \( 290 \vee, 8 A \)
D. 300 V, 9 A
Subject: Maths
\( \mathbf{2} \boldsymbol{x}+\mathbf{3} \boldsymbol{y}=\left[\begin{array}{ll}\mathbf{2} & \mathbf{3} \\ \mathbf{4} & \mathbf{0}\end{array}\right] \) and \( \mathbf{3} \boldsymbol{x}+\mathbf{2} \boldsymbol{y}= \)
\( \left[\begin{array}{cc}2 & -2 \\ -1 & 5\end{array}\right] . \) Find the value of \( x \& y \)
Subject: Physics
A bob of mass \( m \), suspended by a string
of length \( l_{1} \) is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it
collides elastically with another bob of mass \( m \) suspended by a string of length
\( l_{1}, \) which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical
plane, the ratio \( l_{1} / l_{2} \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 3
\( c .5 \)
D. \( 1 / 5 \)
Subject: Chemistry
Substances \( X \) and \( Y \) are colorless
gases obtained by combination of sulphur and oxygen. Substance \( \boldsymbol{X} \) results from combination of \( 6.00 g \) of
sulphur with \( 6.00 g \) of oxygen and substance \( Y \) results from combination
of \( 8.60 g \) of sulphur with \( 12.9 g \) of oxygen If the number of moles of oxygen in \( x \)
were \( 10, \) what would be the number of
moles of oxygen in Y?
Subject: Chemistry
Which of the following has been arranged in order of increasing oxidation number of nitrogen?
A. \( N H_{3}<N_{2} O_{5}<N O<N_{2} \)
B . \( N O_{2}^{+}<N O_{3}^{-}<N O_{2}^{-}<N_{3}^{-} \)
C . \( N H_{4}^{+}<N_{2} H_{4}<N H_{2} O H<N_{2} O \)
D. \( N O_{2}<N a N_{3}<N H_{4}^{+}<N_{2} O \)
Subject: Physics
An unpolarized light beam is incident
on a surface at an angle of incidence
equal to Brewsters angle. Then,
A. the reflected and the refracted beam are both partially polarized
B. the reflected beam is partially polarized and the refracted beam is completely polarized and are at right angles to each other
C. the reflected beam is completely polarized and the refracted beam is partially polarized and are at right angles to each other
D. both the reflected and the refracted beams are completely polarized and are at right angles to each other.
Subject: Physics
The earth's magnetic field at some place on magnetic equator of the earth is \( 0.5 \times 10^{-4} \) T. Consider the radius of
the earth at that place as \( 6400 k m \)
Then, magnetic dipole moment of the
earth is \( \boldsymbol{A} \boldsymbol{m}^{2} \)
\( \left(\mu_{0}=4 \pi \times 10^{-7} T m A^{-1}\right) \)
A \( \cdot 1.31 \times 10^{23} \)
B. \( 1.05 \times 10^{23} \)
C. \( 1.15 \times 10^{23} \)
D. \( 1.62 \times 10^{23} \)
Subject: Chemistry
The correct statements with respect to Ellingham's diagram among the following are
(I) Magnesium reduces aluminium oxide below \( 1700 \mathrm{K} \)
(II) Aluminium reduces magnesium
oxide above \( 1700 \mathrm{K} \)
(III) Aluminium reduces magnesium oxide below \( 1700 \mathrm{K} \)
(IV) Magnesium reduces aluminium oxide above \( 1700 \mathrm{K} \)
\( A \cdot|\&| \mid \)
B. ॥ \& ॥ I
c. III \& IV
D. II, III \& IV