AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Critical angle is the angle of in denser medium for which the angle of in rarer
medium is
A . incidence, incidence, \( 90^{\circ} \)
B. refraction, refraction, \( 90^{\circ} \)
c. incidence, refraction, \( 90^{\circ} \)
D. refraction, incidence, \( 90^{\circ} \)
Subject: Maths
Two roads \( O A \) and \( O B \) intersect at an
angle fo \( 60^{\circ} . \) A car driver approaches 0
from \( A, \) where \( A O=800 \) metres, at a
uniform speed of 20 metres per second.
Simultaneously a runner starts running
from \( \boldsymbol{O} \) towards \( \boldsymbol{B} \) at uniform speed of \( \mathbf{5} \)
metres per second. Find the time when the car and the runner are closest.
A \( \cdot \frac{240}{7} \) sec
B. \( \frac{260}{7} \) sec
c. \( \frac{250}{7} \mathrm{sec} \)
D. \( \frac{210}{7} \mathrm{sec} \)
Subject: Maths
\( \triangle P Q R \) is an isosceles triangle with
\( P Q=P R, Q P \) is produced to \( S \) and \( P T \)
bisects the extension angle \( 2 x^{\circ} . \) Prove
that \( \angle Q=x^{o} \) and hence prove that
\( \boldsymbol{P T} \| \boldsymbol{Q} \boldsymbol{R} \)
Subject: Maths
If \( 0 \leq x \leq \pi \) and \( 81^{\sin ^{2} x}+81^{\cos ^{2} x}=30 \)
then \( x \) is equal to
This question has multiple correct options
A \( \cdot \frac{\pi}{6} \)
в.
c. \( \frac{5 \pi}{6} \)
D. \( \frac{2 \pi}{3} \)
Subject: Physics
A ball of mass \( m \) and radius \( r \) is
released in a viscous liquid. The density of the liquid is negligible compared to that of the ball.The value of its terminal
velocity is proportional to:
A \( \cdot \frac{1}{r} \) only
в. \( \frac{m}{r} \)
c. \( \sqrt{\frac{m}{r}} \)
D. m only
Subject: Maths
If from the point \( \boldsymbol{P}(\boldsymbol{f}, \boldsymbol{g}, \boldsymbol{h}) \)
perpendiculars \( P L, P M \) be drawn to \( y z \)
and \( z x \) planes, then the equation to the
plane \( \boldsymbol{O} \boldsymbol{L} \boldsymbol{M} \) is
A \( \cdot \frac{x}{f}+\frac{y}{g}-\frac{z}{h}=0 \)
В \( \cdot \frac{x}{f}+\frac{y}{g}+\frac{z}{h}=0 \)
c. \( \frac{x}{f}-\frac{y}{g}+\frac{z}{h}=0 \)
D. \( -\frac{x}{f}+\frac{y}{g}+\frac{z}{h}=0 \)
Subject: Chemistry
The atomic weights of Be were
corrected by Mendeleev using the
formula:
\( \mathbf{A} \cdot \sqrt{v}=a(z-b) \)
B. \( m v r=\frac{n h}{2 \pi} \)
C. atomic weight = equivalent weight \( \times \) valency
D. equivalent weight = atomic weight \( \times \) valency
Subject: Physics
Consider an \( \alpha \) -particle just in contact with a \( _{92}^{238} \mathrm{U} \) nucleus. The Coulombic repulsion energy (i.e, the height of the Coulombic barrier between \( ^{238} \mathrm{U} \) and
alpha particle) assuming that the distance between them is equal to the
sum of their radii is
\( \mathbf{A} \cdot 16.35 M e V \)
в. \( 46.66 \mathrm{MeV} \)
c. 22.24 MeV
D. 26.14 \( M e V \)
Subject: Chemistry
Which of the following shows maximum number of isomers?
\( \mathbf{A} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{4} C l_{2}\right] \)
B . \( \left[N i(e n)\left(N H_{3}\right)_{4}\right]^{2+} \)
c. \( \left[N i\left(C_{2} O_{4}\right)(e n)_{2}\right]^{2} \)
D. \( \left[C r(S C N)_{2}\left(N H_{3}\right)_{4}\right]^{+} \)
Subject: Physics
A plane is in a level flight at a constant speed and each of its two wings has an
area of \( 25 m^{2} . \) If the speed of air is
\( 180 \mathrm{kmh}^{-1} \) over the lower wing and
\( 234 k m h^{-1} \) over the upper wing surface, the plane's mass is : (Take density of air \( =1 k g m^{-3} . \) )
A. \( 4.400 g m \)
в. \( 4400 g \) т
c. \( 44.0 k g \)
D. \( 4400 k g \)
Subject: Maths
In the expansion of \( (1+x)^{n} \) the
coefficients of \( p^{t h} \) and \( (p+1)^{t h} \) terms
are respectively \( p \) and \( q \) then \( p+q= \)
\( \mathbf{A} \cdot \boldsymbol{n} \)
B. \( n+1 \)
\( c \cdot n+2 \)
\( \mathbf{D} \cdot n+3 \)
Subject: Physics
Which of the following is/are correct statement(s)?
This question has multiple correct options
A. The motional EMF generated by a magnetic force on a moving wire is case of Lorentz force
B. The transformer EMF generated by an electric force due to a changing magnetic field is the result of Faraday law.
C. The motional EMF generated by a magnetic force on a moving wire is case of Faraday's law.
D. Both B and C are correct.
Subject: Physics
In a half wave rectifier, the output is
taken across a \( 90 \Omega \) load resistor. If the resistance of diode in forward biased
condition is \( 10 \Omega \), the efficiency of rectification of ac power into dc power is
A . \( 40.6 \% \)
B. \( 81.2 \% \)
c. \( 73.08 \% \)
D. \( 36.54 \% \)
Subject: Maths
If \( f: R \rightarrow R \) such that \( f(x+y)-K x y= \)
\( f(x)+2 y^{2} \) for all \( x, y \in R \) and \( f(1)= \)
\( 2, f(2)=8 \) then \( f(20)-f(10) \)
A. 600
в. 300
c. 60
D. 200
Subject: Chemistry
Arrange the following elements in order of decreasing non-metallic character \( \boldsymbol{G} \boldsymbol{e}, \boldsymbol{S} \boldsymbol{n}, \boldsymbol{P} \boldsymbol{b}, \boldsymbol{S} \boldsymbol{i} \)
A. \( P b,>S n,>G e,>S i \)
в. \( P b,>G e,>S n>S i \)
\( \mathbf{c} \cdot S i,>G e>S n>P b \)
D. Equal non-metallic character
E. None of the above
Subject: Physics
A cylinder of radius \( R \) and length \( l \) is placed in a uniform electric field \( \boldsymbol{E} \)
parallel to the axis of the cylinder. The total flux over the curved surface of the
cylinder is :
A. zero
B \( \cdot \pi R^{2} E \)
\( \mathbf{c} \cdot 2 \pi R^{2} E \)
D. \( E / \pi R^{2} \)
Subject: Physics
The escape velocity on the surface of a
planet is \( V_{e} \) what would be the escape
velocity on the planet having the same radius but mass 4 times that of it.
\( A \cdot 2 V_{e} \)
B. \( 4 V_{e} \)
c. \( V_{c} \)
\( D \cdot \frac{V_{c}}{2} \)
Subject: Chemistry
Chemical oxygen demand of a sample
of \( H_{2} O \) is the amount of oxygen:
A . liberated when excess of \( H_{2} O \) is added to a known volume of \( H_{2} O \)
B. consumed by 1 litre of the sample of \( H_{2} O \) at 1 atm \( 27^{0} C \)
c. required to chemically oxidize the organic content of polluted water by \( K_{2} C r_{2} O_{7}+50 \% H_{2} S O_{4} \) in given sample of \( H_{2} O \)
D. any of the above
Subject: Maths
\( \int \frac{d x}{x^{2}+2 x+2} \) is equal to:
\( \mathbf{A} \cdot \sin ^{-1}(x+1)+c \)
B. \( \sinh ^{-1}(x+1)+c \)
c. \( \tanh ^{-1}(x+1)+c \)
D. \( \tan ^{-1}(x+1)+c \)
Subject: Chemistry
0.75 g of an organic compound on complete combustion gave 1.6 g of carbon dioxide and 0.47 g of water. \( A \) given weight of the compound when heated with nitric acid and silver
nitrate gave an equal weight of silver chloride. 0.75 g of the compound gave \( 58.57 \mathrm{ml} \) of nitrogen at 1 atm and \( 273 \mathrm{K} \) The empirical formula of the compound
is :
A \( \cdot C_{7} H_{10} N C l \)
B . \( C_{6} H_{12} N C l \)
c. \( C_{7} H_{12} N C l \)
D. \( C_{7} H_{14} N C l \)
Subject: Physics
A river is flowing with velocity \( 5 k m / h r \)
as shown in the figure. A boat starts
from \( A \) and reaches the other bank by
covering shortest possible distance.
Velocity of boat in still water is \( 3 k m / h r \)
The distance boat covers is :
\( \mathbf{A} \cdot 500 m \)
B. \( 400 \sqrt{2} \)
c. \( 300 \sqrt{2} \)
D. \( 600 m \)
Subject: Chemistry
Sulphide ions in alkaline solution react with solid sulphur to form polyvalent
sulphide ions. The equilibrium constant for the formation of \( S_{2}^{2-} \) and \( S_{3}^{2-} \) from. \( S \)
and \( S^{2-} \) ions are 1.7 and 5.3 respectively.
Calculate equuilibrium constant for the
formation of \( S_{3}^{2-} \) from \( S_{2}^{2-} \) and \( S \)
A . 0.31
в. 3.11
c. 31.3
D. 0.0313
Subject: Physics
A 6 volt battery is connected to the terminals of the three metre long wire of uniform thickness and the resistance of
100\Omega. The difference of potential between two points on the wire
separated by a distance of \( 50 \mathrm{cm} \) will be
A . \( 1.5 v \)
B. 3V
\( c .3 .5 v \)
D. \( 1 \mathrm{v} \)
Subject: Chemistry
What is the concentration of
\( C H_{3} C O O H \) which can be added to 0.5 M HCOOH solution so that dissociation
of both is same.
[Given that \( : \boldsymbol{K}_{\boldsymbol{C H}_{3} \text { COOH}}=\mathbf{1 . 8} \times \)
\( \mathbf{1 0}^{-5}, \quad \boldsymbol{K}_{\boldsymbol{H} \mathrm{COOH}}=\mathbf{2 . 4} \times \mathbf{1 0}^{-4} \mathbf{j} \)
(as nearest integer)
Subject: Physics
An electron enters a parallel plate
capacitor with horizontal speed \( \mu \) and is
found to deflect by angle \( \theta \) on leaving the capacitor as shown. It is found that \( \tan \theta=0.4 \) and gravity is negligible. If
the initial horizontal speed is doubled,
then tan will be.
A. 0.1
B. 0.2
c. 0.8
D. 1.6
Subject: Physics
A block of mass \( m \) slides down an
inclined plane of slope angle \( \theta \) with constant velocity. Now, same block is
projected up an inclined plane with an
initial velocity \( u \). If the coefficient of
kinetic friction between the block and
the plane is \( \mu, \) the distance up to which the block will rise up the plane, before coming to rest is :-
\( ^{\mathrm{A}} \cdot \frac{u^{2} \mu}{2 g \sin \theta} \)
в. \( \frac{u^{2} \mu}{2 g \cos \theta} \)
c. \( \frac{u^{2}}{4 g \sin \theta} \)
D. \( \frac{u^{2}}{4 g \cos \theta} \)
Subject: Chemistry
Calculate simultaneous solubility of \( A g C N S \) and \( A g B r \) in a solution of
water.
\( \left[\text { Given: } \boldsymbol{K}_{s p} \text { of } \boldsymbol{A} \boldsymbol{g} \boldsymbol{C} \boldsymbol{N} \boldsymbol{S}=\mathbf{1} \times \mathbf{1 0}^{-12}\right. \)
\( \boldsymbol{K}_{s p} \) of \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{B} \boldsymbol{r}=\boldsymbol{5} \times \mathbf{1 0}^{-13} \)
Subject: Chemistry
For a gaseous reaction the rate equation is \( \boldsymbol{v}=\boldsymbol{k}[\boldsymbol{A}][\boldsymbol{B}] . \) If the volume of
the gaseous system is suddenly reduced to \( 1 / 3 \) of initial volume. The rate would become:
A. \( 1 / 9 \) times
B. 9 times
c. \( 1 / 6 \) times
D. 6 times
Subject: Physics
The frequency of vibration of the string is given by \( \boldsymbol{v}=\frac{\boldsymbol{p}}{\mathbf{2 l}}\left[\frac{\boldsymbol{F}}{\boldsymbol{m}}\right]^{1 / 2} \)
Here, p is the number of segments in the string and I is the length. The dimensional formula for m will be
\( \mathbf{A} \cdot\left[M^{0} L T^{-1}\right] \)
B \( \cdot\left[M L^{0} T^{-1}\right] \)
\( \mathbf{c} \cdot\left[M L^{-1} T^{0}\right] \)
\( \mathbf{D} \cdot\left[M^{0} L^{0} T^{0}\right] \)
Subject: Chemistry
How is the retention factor or \( \boldsymbol{R}_{\boldsymbol{f}} \) of \( \mathbf{a} \)
particular compound measured in a Thin layer of Chromatography (TLC)
experiment?
A. Distance traveled by the compound on the TLC plate divided by the total distance traveled by the mobile phase
B. Distance traveled by the compound on the TLC plate multiplied by the total distance traveled by the mobile phase
C. The total distance traveled by the mobile phase divided by distance traveled by the compound on the TLC plate
D. The total distance traveled by the mobile phase multiplied by distance traveled by the compound on the TLC plate
Subject: Maths
The perimeter of a parallelogram is 22 cm. If the longer side measures \( 6.5 \mathrm{cm} \) what is the measure of the shorter side?
A. \( 4.5 \mathrm{cm} \)
B. \( 5.5 \mathrm{cm} \)
\( c .6 .5 \mathrm{cm} \)
D. 4.2 \( \mathrm{cm} \)
Subject: Maths
Let \( P Q R \) be a right angled isosceles traingle, right angled at \( P(2,1) . \) If the
equation of the line \( Q R \) is \( 2 x+y=3 \)
then the equation represnting the pair
of lines \( P Q \) and \( P R \) is
A \( \cdot 3 x^{2}-3 y^{2}+8 x y+2 x+10 y+25=0 \)
B . \( 3 x^{2}-3 y^{2}+8 x y-20 x-10 y+25=0 \)
c. \( 3 x^{2}-3 y^{2}+8 x y+10 x+15 y+20=0 \)
D. \( 3 x^{2}-3 y^{2}-8 x y-10 x-15 y-20=0 \)
Subject: Maths
\( \int x \sin x \sec ^{3} x d x= \)
A. \( \frac{1}{2}\left[\sec ^{2} x-\tan x\right]+c \)
B. \( \frac{1}{2}\left[x \sec ^{2} x-\tan x\right]+c \)
c. \( \frac{1}{2}\left[x \sec ^{2} x+\tan x\right]+c \)
D. \( \frac{1}{2}\left[\sec ^{2} x+\tan x\right]+c \)
Subject: Physics
Two radioactive substances \( A \) and \( B \)
have decay constants \( 5 \lambda \) and \( \lambda \)
respectively.At \( t=0, \) they have the same number of nuclei. The ratio of
number of nuclei of \( A \) to those of \( B \) will
be \( \left(1 / e^{2}\right) \) after a time:
A \( .4 \lambda \)
B. 2\lambda
c. \( \frac{1}{2 \lambda} \)
D. \( \frac{1}{4 \lambda} \)
Subject: Physics
Assertion
Two particles moving in the same direction do not lose all their energy in a completely inelastic collision
Reason
Principle of conservation of momentum holds true for all kinds of collision
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
The speed of an electron having a
wavelength of \( 10^{-10} m \) is :
A \( \cdot 4.24 \times 10^{6} m / s \)
B . \( 5.25 \times 10^{6} \mathrm{m} / \mathrm{s} \)
c. \( 6.25 \times 10^{6} m / s \)
D. \( 7.25 \times 10^{6} \mathrm{m} / \mathrm{s} \)
Subject: Maths
If \( \left|\begin{array}{ccc}2 a & x_{1} & y_{1} \\ 2 b & x_{2} & y_{2} \\ 2 c & x_{3} & y_{3}\end{array}\right|=\frac{a b c}{2} \neq 0, \) then the
area of the triangle whose vertices are \( \left(\frac{x_{1}}{a}, \frac{y_{1}}{a}\right),\left(\frac{x_{2}}{b}, \frac{y_{2}}{b}\right) \) and \( \left(\frac{x_{3}}{c}, \frac{y_{3}}{c}\right) \) is
A \( \cdot \frac{1}{4} a b c \)
B. \( \frac{1}{8} a b c \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{1}{8} \)
E \( \cdot \frac{1}{12} \)
Subject: Physics
There is a planet name 'ALLEN' which has radius three times that of the earth
and density two times that of the earth. The acceleration due to gravity on 'ALLEN' will be
A \( \cdot \frac{1}{9} \) times that of earth's gravity
B. \( \frac{2}{9} \) times that of earth's gravity
c. 6 times that of earth's gravity.
D. 3 times that of earth's gravity
Subject: Physics
Sound waves travel at \( 350 m s^{-1} \)
through warm air and at \( 3500 m s^{-1} \)
through brass. The wavelength of a
\( \mathbf{7 0 0} \boldsymbol{H} z \) acoustic wave as it enters
brass from warm air:
A. decrease by a factor 10
B. increase by a factor 20
c. increase by a factor 10
D. decrease by a factor 20
Subject: Physics
An iron tyre \( 100 \mathrm{cm} \) in diameter is to be fitted on to a wooden wheel of \( 100.4 \mathrm{cm} \)
in diameter if \( \alpha \) of Iron is \( 1 \times 10^{-5} /^{\circ} C \)
the temperature increase required for this purpose is :
A \( \cdot 40^{\circ} \mathrm{C} \)
B . \( 100^{\circ} \mathrm{C} \)
c. \( 400^{\circ} \mathrm{C} \)
D. \( 1000^{\circ} \mathrm{C} \)
Subject: Physics
Four waves are expressed as
(i) \( y_{1}=a_{1} \sin \omega t \)
(ii) \( y_{2}=a_{2} \sin 2 \omega t \)
(iii) \( \boldsymbol{y}_{3}=\boldsymbol{a}_{3} \cos \boldsymbol{\omega} \boldsymbol{t} \)
(iv) \( \boldsymbol{y}_{4}=\boldsymbol{a}_{4} \sin (\boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{\phi}) \)
The interference is possible between
A \( \cdot \) (i) and (iii)
B. (i) and (ii)
c. (ii) and (iv)
D. Not possible at all
Subject: Physics
A block of mass \( m \) is pulled along a
circular are by means of a constant
horizontal force \( \boldsymbol{F} \) as shown. Work done
by this force in pulling the block from \( \boldsymbol{A} \)
to \( B \) is-
A \( \frac{F R}{2} \)
в. \( F R \)
c. \( \frac{\sqrt{3}}{2} F R \)
D. \( m g R \)
Subject: Physics
If angle of minimum deviation of a
prism is equal to refracting angle of the prism, then refractive index \( \mu \) of
material of prism satisfies
A. \( 1<\mu<\sqrt{2} \)
в. \( 2<\mu<3 \)
c. \( \sqrt{2}<\mu<2 \)
D. \( 1<\mu<\sqrt{3} \)
Subject: Maths
Let \( \boldsymbol{A}=\mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}, \boldsymbol{B}= \)
\( 1,3,5,7,9,10,17,26,30 . \) Which of the
following sets of ordered pairs are (i) relations
(ii) functions (iii) neither,
from \( A \) to \( B \)
(a) \( R_{1}=\{(1,3),(3,3),(5,17),(1,2)\} \)
(b) \( R_{2}=\{(3,7),(4,5),(5,30)\} \)
(c) \( R_{3}= \) \( (x, y): x \in A, y \in B, x+y=8 \)
(d) \( R_{4}= \)
\( (x, y): x \in A, y \in B, y=x^{2}+1 \)
(e) \( R_{5}= \)
\( (x, y): x \in A, y \in B, y=2 x-1 \)
Subject: Maths
(Diet problem) A dietician has to develop a special diet using two foods \( \boldsymbol{P} \) and \( Q . \) Each packet (containing \( 30 g \) ) of
food \( P \) contains 12 units of calcium, 4
units of iron, 6 units of cholesterol and 6
units of vitamin A. Each packet of the same quantity of food \( Q \) contains 3
units of calcium, 20 units of iron, 4
units of cholesterol and 3 units of
vitamin A. The diet requires atleast 240 units of calcium, atleast 460 units of
iron and at most 300 units of
cholesterol. How many packets of each food should be used to minimise the
amount of vitamin A in the diet? What
is the minimum amount of vitamin A?
Subject: Maths
Let \( \omega=-\frac{1}{2}+i \frac{\sqrt{3}}{2}, \) then the value of the
determinant
\( \left|\begin{array}{ccc}1 & 1 & 1 \\ 1 & -1-\omega^{2} & \omega^{2} \\ 1 & \omega^{2} & \omega^{4}\end{array}\right|, \) is
This question has multiple correct options
\( A .3 \omega \)
В. \( 3 \omega(\omega-1) \)
\( c \cdot 3 \omega^{2} \)
D. \( 3(-2 \omega-1) \)
Subject: Maths
If \( \bar{a} \) and \( \bar{b} \) are position vectors of \( A \) and
\( B \) respectively, then the position vector of a point \( C \) in \( A B \) produced such that \( \boldsymbol{A C}=\mathbf{3} \overline{\boldsymbol{A} \boldsymbol{B}} \) is
A \( .3 \bar{a}-\bar{b} \)
в. \( 3 \bar{b}-\bar{a} \)
c. \( 3 \bar{a}-2 \bar{b} \bar{b} \)
D. \( 3 \bar{b}-2 \bar{a} \bar{a} \)
Subject: Physics
Figure shows position and velocities of two particles moving under mutual gravitational attraction in space at
time \( t=0 . \) The position of centre of
mass after one second is :
\( \mathbf{A} \cdot x=4 m \)
B . \( x=6 m \)
\( \mathbf{c} \cdot x=8 m \)
D. \( x=10 m \)
Subject: Maths
The area of an equilateral triangle is
\( 49 \sqrt{3} c m^{2} . \) Taking each angular point as
centre, a circle is described with radius
equal to half the length of the side of the triangle as shown in figure. Find the
area of the triangle not included in the circle. [Take \( \sqrt{\mathbf{3}}=\mathbf{1 . 7 3}] \)
\( \mathbf{A} \cdot 5.67 \mathrm{cm}^{2} \)
B. \( 6.12 \mathrm{cm}^{2} \)
c. \( 7.77 \mathrm{cm}^{2} \)
D. \( 7.98 \mathrm{cm}^{2} \)
Subject: Physics
On the bombardment of Boron with
neutron, an \( \alpha \) - particle is emitted and
product nucleus formed is
\( \mathbf{A} \cdot_{6} C^{12} \)
В \( \cdot_{2} L^{i} \)
\( \mathrm{c} \cdot_{3} L i^{7} \)
D・ \( _{4} B e^{9} \)
Subject: Maths
If the foot of the perpendicular from
(0,0,0) to a plane is \( P(1,2,2) . \) Then, the equation of the plane is
A. \( -x+2 y+8 z-9=0 \)
B. \( x+2 y+2 z-9=0 \)
c. \( x+y+z-5=0 \)
D. \( x+2 y-3 z+3=0 \)
Subject: Physics
According to given figure which of the
following options can be true?
\( \mathbf{A} \cdot Q_{1}>Q_{2}>W \)
B. In real aspects \( Q_{2}=0 \) always
C efficiency of engine is \( =\frac{W}{Q_{1}} \)
D efficiency of engine is \( =1-\frac{Q_{1}}{Q_{2}} \)
Subject: Maths
Find the angle between the following pairs of lines:
\( \frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{-3} \) and \( \frac{x+3}{-1}= \)
\( \frac{\boldsymbol{y}-\mathbf{5}}{\mathbf{8}}=\frac{\boldsymbol{z}-\mathbf{1}}{\mathbf{4}} \)
Subject: Maths
\( 2 \tan ^{-1}\left(\frac{\sqrt{a-b}}{a+b} \tan \frac{x}{2}\right)= \)
A \( \cdot \cos ^{-1}\left(\frac{b+a \cos x}{a+b \cos x}\right) \)
B. \( \cos ^{-1}\left(\frac{b+a \cos x}{a-b \cos x}\right) \)
c. \( \cos ^{-1}\left(\frac{b-a \cos x}{a+b \cos x}\right) \)
D. \( \cos ^{-1}\left(\frac{b-a \cos x}{a-b \cos x}\right) \)
Subject: Chemistry
The energy of the electron in the second and third Bohr orbits of the hydrogen atom is \( -5.42 \times 10^{-12} \) erg and \( -2.41 \times 10 \)
-12 erg, respectively. The wavelength of the emitted radiation when the electron
drops from third to second orbit is:
A \( .4 .6 \times 10^{6} \)
B . \( 6.6 \times 10^{3} \)
c. \( 0.66 \times 10^{6} \)
D. none of these
Subject: Physics
An oscillator circuit contains an
inductor \( 0.05 H \) and a capacitor
of capacity \( 80 \mu F \).When the maximum
voltage across the capacitor is \( 200 V \) the maximum current (in amperes) in the circuit is
\( A \cdot 2 \)
B. 4
c. 8
D. 10
E. 16
Subject: Maths
Find the mean height of 30 players
using direct method:
\begin{tabular}{|l|l|l|l|l|l|l|}
\hline Height(cm) & 100 & 120 & 150 & 160 & 170 & 180 \\
\hline Number of players & 3 & 6 & 2 & 5 & 10 & 4 \\
\hline
\end{tabular}
A \( .151 \mathrm{cm} \)
B. \( 149 \mathrm{cm} \)
\( \mathbf{C} \cdot 148 \mathrm{cm} \)
D. \( 150 \mathrm{cm} \)
Subject: Chemistry
The Equations of a chemical reaction
are given in the figure:
(a) To which type this chemical reaction belongs?
(b) Which is the monomer in this
reaction?
\[
\mathrm{n}_{\mathrm{H}_{2} \mathrm{C}=}^{\mathrm{CH}} \frac{\operatorname{high} \mathrm{T} \cdot \mathrm{P}_{.}}{\mid} \frac{\mathrm{H}_{2}}{\mathrm{c}_{\mathrm{Cl}}}-\left[_{\mathrm{Cl}}^{\mathrm{H}}-\right]_{\mathrm{n}}
\]
Subject: Chemistry
Which of the following will give \( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+} \) ions in the solution?
A \( \cdot\left[F e(C N)_{6}\right]^{3-} \)
B . \( \left[F e(C N)_{6}\right]^{4-} \)
c. \( N H_{4}\left(S O_{4}\right)_{2} \cdot F e S O_{4} \cdot 6 H_{2} O \)
D. \( F e_{2}\left(S O_{4}\right)_{3} \)
Subject: Chemistry
Which one of the elements with the
following outer orbital configurations may exhibit the largest number of oxidation states?
\( \mathbf{A} \cdot 3 d^{5} 4 s^{1} \)
B . \( 3 d^{5} 4 s^{2} \)
c. \( 3 d^{2} 4 s^{2} \)
D. \( 3 d^{3} 4 s^{2} \)
Subject: Chemistry
How many grams of gas are present in a \( 2.2 L \) sample of gas if the gas has a density of \( 1.8 g / L ? \)
A. \( 1.22 g \)
в. \( 4.00 g \)
\( \mathbf{c} .3 .96 g \)
D. \( 0.02 g \)
Subject: Physics
A plane polarized light is incident normally on a tourmaline plate. Its \( \overrightarrow{\boldsymbol{E}} \)
vectors make an angle of \( 60^{\circ} \) with the
optic axis of the plate. Find the percentage difference between initial and final intensities.
A . \( 25 \% \)
B . 50\%
c. \( 75 \% \)
D. 90\%
Subject: Maths
If \( z_{1} \) and \( z_{2} \) both satisfy the relation \( z+ \) \( \bar{z}=2|z-1| \) and \( \arg \left(z_{1}-z_{2}\right)=\frac{\pi}{4} \)
then the imaginary part of \( \left(z_{1}+z_{2}\right) \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. None of these
Subject: Physics
The pressure energy per unit mass of liquid of density \( \rho \) at a pressure P is
A \( \cdot \frac{P}{\rho} \)
в. \( \rho \times P \)
\( c \cdot \frac{\rho}{P} \)
D. \( \sqrt{\frac{P}{\rho} \frac{P}{\rho} \frac{P}{\rho}} \)
Subject: Physics
A body of mass \( 1 \mathrm{kg} \) falls freely form a height of \( 100 \mathrm{m}, \) on a platform of mass 3 kg which is mounted on a spering having spering constant \( \mathrm{k}=1.25 \) \( \times 10^{6} N / m . \) The body sticks to the platform and the spring's maximum compression is found to be \( x \). Given that
\( \mathrm{g}=10 \mathrm{m} \mathrm{s}^{-2}, \) the value of \( \mathrm{x} \) will be close
to :
A. \( 4 \mathrm{cm} \)
B. \( 8 \mathrm{cm} \)
\( c \cdot 80 \mathrm{cm} \)
D. 40 cm
Subject: Chemistry
The reactant which is entirely consumed in reaction is known as
limiting reagent. In the reaction \( 2 A+ \) \( 4 B \longrightarrow 3 C+4 D, \) if 5 moles of \( A \) reacts
with 6 moles of \( \mathrm{B} \) then, which is the limiting reagent?
A. \( A \)
в. \( B \)
\( c . c \)
D. \( D \)
Subject: Chemistry
Which of the following statements is
true?
\( \mathbf{A} \cdot F-N-F \) angle in \( N F_{3} \) is greater than \( H-N-H \)
angle in \( N H_{3} \)
B. \( F-N-F \) angle in \( N F_{3} \) is smaller than \( H-N-H \)
angle in \( N H_{3} \)
\( \mathbf{c} \cdot H-O-H \) angle in \( H_{2} O \) is greater than \( H-N-H \)
angle in \( N H_{3} \)
D. \( F-O-F \) angle in \( F_{2} O \) is greater than \( H-O-H \)
angle in \( H_{2} O \)