AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
If the lens is thick what will be its focal
length in air?
A \( \cdot \frac{1}{f}=(n-1)\left[\frac{1}{R_{1}}-\frac{1}{R_{2}}+\frac{t(n-1)}{n R_{1} R_{2}}\right. \)
B. \( \frac{1}{f}=(n-1)\left[\frac{1}{R_{1}}-\frac{1}{R_{2}}-\frac{t(n-1)}{n R_{1} R_{2}}\right) \)
c. \( \frac{1}{f}=(n-1)\left[\frac{1}{R_{1}}-\frac{1}{R_{2}}+\frac{t(n+1)}{n R_{1} R_{2}}\right] \)
D. none of these
Subject: Biology
Osteoporosis, an age-related disease of
skeleton system, may occur due to
A. Decreased level of estrogen
B. Accumulation of uric acid leading to inflammation of joints
C. Immune disorder affecting neuro-muscular junction leading to fatigue
D. High concentration of \( \mathrm{Ca}^{++} \) and \( \mathrm{Na}^{+} \)
Subject: Physics
The value of the resistor, \( \boldsymbol{R}_{S}, \) needed in
the DC voltage regulator circuit shown
here, equals
A \( \cdot \frac{\left(V_{i}+V_{L}\right)}{(n+1) I_{L}} \)
B. \( \frac{\left(V_{i}-V_{L}\right)}{n I_{L}} \)
c. \( \frac{\left(V_{i}+V_{L}\right)}{n I_{L}} \)
D. \( \frac{\left(V_{i}-V_{L}\right)}{(n+1) I_{L}} \)
Subject: Chemistry
Which of the following compound exhibits Hydrogen bonding?
\( \boldsymbol{C H}_{3} \boldsymbol{N} \boldsymbol{H}_{2} \) and \( \boldsymbol{C H}_{3} \boldsymbol{S H} \)
A. \( C H_{3} N H_{2} \)
в. \( C H_{3} S H \)
c. Both
D. None
Subject: Chemistry
1) Drive the formula for the ionization
constant \( \left(K_{b}\right) \) for weak bases.
2) Drive the relation \( \boldsymbol{p} \boldsymbol{H}+\boldsymbol{p} \boldsymbol{O} \boldsymbol{H}= \)
\( \boldsymbol{p} \boldsymbol{K} \boldsymbol{w} \)
Subject: Maths
If \( \boldsymbol{P}=\mathbf{3} \boldsymbol{x}-\mathbf{4} \boldsymbol{y}-\mathbf{8} \boldsymbol{z}, \boldsymbol{Q}=-\mathbf{1 0} \boldsymbol{y}+ \)
\( 7 x+11 z \) and \( R=19 z-6 y+4 x, \) then
\( \boldsymbol{P}-\boldsymbol{Q}+\boldsymbol{R} \) is equal to
A \( .13 x-20 y+16 z \)
B. 0
c. \( x+y+z \)
D. \( 2 x-b y+3 z \)
Subject: Maths
Find the values of \( x \) for which the angle between the vectors \( \vec{a}=x \hat{i}-3 \hat{j}-1 \hat{k} \) and \( \vec{b}=2 x \hat{i}+x \hat{j}-1 \hat{k} \) is acute and
the angle between the vector b and \( y- \) axis is obtuse.
\( \mathbf{A} \cdot x<0 \)
B . \( x>0 \)
c. \( _{x}<\frac{1}{2} \)
D. \( x>\frac{1}{2} \)
Subject: Physics
A body is moving along a straight line.
Its distance \( X_{t} \) from a point on its path
at a time \( t \) after passing that point is
given by \( X_{t}=8 t^{2}-3 t^{3}, \) where \( X_{t} \) is in
meter and \( t \) is in second. The correct
statement(s) is/are:
This question has multiple correct options
A. Average speed during the interval \( t=0 \) s to \( t=4 s \) is \( 20.21 \mathrm{ms}^{-1} \)
B. Average velocity during the interval \( t=0 \) s to \( t=4 s \) is
\( -16 m s^{-1} \)
C. The body starts from rest and at \( t=\frac{16}{9} s \) it reverses its
direction of motion at \( x_{t}=8.43 \mathrm{m} \) from the start
D. It has an acceleration of \( -56 \mathrm{ms}^{-2} \) at \( t=4 \mathrm{s} \)
Subject: Maths
Find the range of the following function:
\( f(x)=\frac{|x-4|}{x-4} \)
\( \mathbf{A} \cdot[-1,1] \)
В. \( \left[-\frac{\pi}{2}, \frac{3 \pi}{2}\right] \)
c. \( (-2 \pi, 0] \)
D. \( \left[\frac{-3 \pi}{2}, \frac{\pi}{2}\right. \)
Subject: Chemistry
Which of the following are basic oxides?
\( M n_{2} O_{7}, V_{2} O_{3}, V_{2} O_{5}, C r_{2} O_{3}, C r O \)
A. \( M n_{2} O_{7} \) and \( V_{2} O_{3} \)
B. \( V_{2} O_{3} \) and \( C r O \)
c. \( C r O \) and \( C r_{2} O_{3} \)
D. \( V_{2} O_{5} \) and \( V_{2} O_{3} \)
Subject: Physics
Matching pairs in the two lists given below are
ListList-II
A) Gravitions
E) Hyperons
B) Baryons
F) Positrons
C) Pions
G) Particles with zero mass nd with a spin of unity
D) Leptons
H) Decay to -mesons
I) Massless
particles with a probable spin of two units
\( A \cdot A-E, B-H, C-G, D-1 \)
B. A-I,B-E,C-H,D-F
c. \( A-H, B-F, C-1, D-E \)
D. A-F,B-G,C-E,D-H
Subject: Chemistry
In an auto engine with no pollution
controls, about \( 5 \% \) of the fuel \( \left(C_{8} H_{18}\right) \)
is unburned. Molar ratio of \( C O \) and
\( \left(C_{8} H_{18}\right), \) emitted in the exhaust gas is:
A . 100
B. 152
\( c .50 \)
D. 5
Subject: Physics
A capacitor of capacitance \( C_{0} \) is
charged to a potential \( V_{0} \) and then
isolated. A small capacitor \( C \) is then
charged from \( C_{0}, \) discharged and charged again. This process is being
repeated \( n \) times. Due to this, the
potential of the larger capacitor is
decreased to \( V \). The value of \( C \) is :
\( ^{\mathbf{A}} \cdot_{C_{0}}\left(\frac{V_{0}}{V}\right)^{1 / n} \)
\( ^{\mathrm{B}} C_{0}\left[\left(\frac{V_{0}}{V}\right)^{1 / n}-1\right] \)
\( ^{\mathbf{c}} \cdot_{C_{0}}\left[\left(\frac{V}{V_{0}}\right)-1\right]^{n} \)
\( ^{\mathrm{D}} C_{0}\left[\left(\frac{V_{0}}{V}\right)^{n}+1\right] \)
Subject: Maths
The value of \( \sin ^{-1}\left(\cos \left(\cos ^{-1}(\cos x)+\right.\right. \)
\( \left.\sin ^{-1}(\sin x)\right), \) where \( x \epsilon\left(\frac{\pi}{2}, \pi\right), \) is
equal to
A \( \cdot \frac{\pi}{2} \)
в. \( -\pi \)
\( c \)
D. \( -\frac{\pi}{2} \)
Subject: Chemistry
\( p H \) of saturated solution of silver salt of
monobasic acid \( H A \) is found ton be 9
Find the \( K_{s p} \) of sparingly soluble salt
\( A g A(s) \)
Given \( : \boldsymbol{K}_{\boldsymbol{a}}(\boldsymbol{H} \boldsymbol{A})=\mathbf{1 0}^{\mathbf{1 0}} \)
A \( \cdot 1.1 \times 10^{-9} \)
В. \( 1.1 \times 10^{-10} \)
\( c \cdot 10^{-12} \)
D. None of these
Subject: Physics
A particle starting from a point \( A \) and
moving with a positive constant
acceleration along a straight line reaches another point \( B \) in time \( T \)
Suppose that the initial velocity of the particle is \( u>0 \) and \( P \) is the mid-point
of the line \( A B . \) If the velocity of the
particle at point \( \boldsymbol{P} \) is \( \boldsymbol{v}_{1} \) and if the velocity at time \( \frac{T}{2} \) is \( v_{2}, \) then
\( \mathbf{A} \cdot v_{1}=v_{2} \)
B \( . v_{1}>v_{2} \)
\( \mathbf{c} \cdot v_{1}<v_{2} \)
D. \( v_{1}=\frac{1}{2} v_{2} \)
Subject: Maths
A wire in the shape of an equilateral
triangle encloses an area of \( s \mathrm{cm}^{2} \). If
the same wire is bent to form a circle,
then the area of the circle will be
A \( \cdot \frac{\pi s^{2}}{\pi} \)
B. \( \frac{3 s^{2}}{\pi} \)
\( c \cdot \frac{3 s}{\pi} \)
D. \( \frac{3 s \sqrt{3}}{\pi} \)
Subject: Chemistry
toppr
Q Type your question.
radicals with almost equal ease,
whereas bromine free radicals have a
clear preference for the formation of
tertiary free radicals. So, bromine is
less reactive, and more selective
whereas chlorine is less selective and
more effective.
The relative rate of abstraction of
hydrogen by Br is
\( \begin{array}{c}\mathbf{3}^{\circ}>\mathbf{2}^{\circ}>\mathbf{1}^{\circ} \\ \mathbf{( 1 6 0 0})\end{array}>\mathbf{( 8 2 )}^{\circ} \)
The relative rate of abstraction of
hydrogen by Cl is \( \mathbf{3}^{\circ}>\mathbf{2}^{\circ}>\mathbf{1}_{\mathbf{1}}^{\circ} \)
\( (\mathbf{5}) \)
2,Bromo-2,5,5 trimethyl hexane(x\%)
What is the value of \( x(\% \) yield of
product) \( ? \)
\( \mathbf{A} \cdot 18 \% \)
B. 82 \%
c. \( 90 \% \)
D. 60 \%
Subject: Chemistry
\( 100 \mathrm{ml} \) of liquid \( \mathrm{A} \) and \( 50 \mathrm{ml} \) of liquid \( \mathrm{B} \) are mixed to form \( 138 \mathrm{ml} \) of solution. It
is :
A. Ideal solution
B. High boiling azeotrope
c. Low boiling azeotrope
D. None of these
Subject: Biology
Which one of the following correctly describes the location of some body parts in the earthworm (Pheretima)?
A. Four pairs of spermathecae in 4 - 7 segments
B. One pair of ovaries attached at inter-segmental septum of 14th and 15th segments
c. Two pairs of testes in 10 th and 11 th segments
D. Two pairs of accessory glands in 16-18th segments
Subject: Maths
If the area of a rectangle is equal to the area of a square and length of the rectangle is equal to the perimeter of
the square, then the breadth of rectangle is
A. side \( \div 2 \)
B. \( (\text {side})^{2} \div 2 \)
\( c \cdot \operatorname{side} \div 4 \)
D. side \( \div 3 \)
Subject: Chemistry
The diameters of a bubble at the
surface of a lake is \( 4 m m \) and at the
bottom of the lake is 1 mm. If
atmospheric pressure is 1 atm and the temperature of the lake-water and the atmosphere are equal. What is the depth of the lake? [The density of lake-water and \( H g \) are
1 \( g m / m l \text { and } 13.6 g m / m l \text { respectively }] \)
A. \( 120.5 \mathrm{m} \)
B. 200.4 m
\( c \cdot 184.5 \mathrm{m} \)
D. 153.03 \( \mathrm{m} \)
Subject: Physics
Two vectors \( \vec{A} \) and \( \vec{B} \) such that \( (\vec{A}+ \)
\( \vec{B}) \perp(\vec{A}-\vec{B}) . \) Then
\( \mathbf{A} \cdot \vec{A} \| \vec{B} \)
B. \( \vec{A} \perp \vec{B} \)
C \( \cdot|\vec{A}|=|\vec{B}| \)
D \( \cdot|\vec{A}| \neq|\vec{B}| \)
Subject: Physics
If collision between the block and the
incline is completely elastic, the the vertical (upward) component of the velocity of blocks at point \( \boldsymbol{B} \)
immediately after it strikes the second
incline is
A \( . \sqrt{30} \mathrm{m} / \mathrm{s} \)
B. \( \sqrt{15} \mathrm{m} / \mathrm{s} \)
\( c .0 \)
D. \( -\sqrt{15} \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
Among the following statements which is/are incorrect?
A. In the preparation of compounds of \( X e \), Bartlett had \( \operatorname{taken} O_{2} P t F_{6} \) as a base compound because both \( O_{2} \)
and \( X e \) have almost same ionisation enthalpy
B. Nitrogen does not show allotropy
C. A brown ring is formed in the ring test for \( N O_{3}^{-} \) ion. It is due to the formation of \( \left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5}(\mathrm{NO})\right]^{2+} \)
D. On heating white phosphorous with concentrated \( N a O H \) solution in an inert atmosphere of \( C O_{2}, P H_{3} \)
gas is formed
Subject: Biology
The correct sequence of occurrence of
the given stages of mitosis is
A. II, IV, VI, I, V, III
B. \( \|, \) ।V, \( \vee \), ।, VI, II
c. ॥, \( v, \) ।V, VI, ।, ॥ा
D. III, VI, V, I, IV, II
E . \( \| \) II, IV, \( \vee \), VI, I, ।
Subject: Physics
If \( \epsilon_{0} \) and \( \mu_{0} \) are the permittivity and
permeability of free space and \( \epsilon \) and \( \mu \) are the corresponding quantities for a medium, then refractive index of the
medium is:
A. \( \sqrt{\frac{\mu_{0} \epsilon_{0}}{\mu \epsilon}} \)
в. \( \sqrt{\frac{\mu \epsilon}{\mu_{0} \epsilon_{0}}} \)
c. 1
D. Insufficient information
Subject: Physics
A physical quantity of the dimensions of mass that can be formed out of \( c, G \) and \( \frac{e^{2}}{8 \pi \varepsilon_{0}} \) is \( (c \text { is velocity of light, } G \) is
universal constant of gravitation and \( e \)
is charge, \( \left.\varepsilon_{0} \text { is electrical permittivity }\right) \)
\( ^{\mathbf{A}} \cdot\left[G \frac{e^{2}}{8 \pi \varepsilon_{0}}\right]^{\frac{1}{2}} \)
\( ^{\mathbf{B}} \cdot_{c^{0}}\left[\frac{G e^{2}}{8 \pi \varepsilon_{0}}\right]^{2} \)
\( c \cdot\left[\frac{e^{2}}{G 8 \pi \varepsilon_{0}}\right]^{\frac{1}{2}} \)
\( c^{0}\left[\frac{G e^{2}}{8 \pi \varepsilon_{0}}\right]^{\frac{1}{2}} \)
Subject: Chemistry
The rate constants of a reaction at
\( 500 K \) and \( 700 K \) are \( 0.02 s^{-1} \) and
\( 0.07 s^{-1} \) respectively.

Calculate the values of \( \boldsymbol{E} \boldsymbol{a} \) and \( \boldsymbol{A} \) :
Subject: Chemistry
Equilibrium constant for following
reactions respectively \( \boldsymbol{K}_{1}, \boldsymbol{K}_{2} \) and \( \boldsymbol{K}_{3} \)
\( N_{2}+3 H_{2} \rightleftharpoons 2 N H_{3} \quad K_{1} \)
\( N_{2}+O_{2} \rightleftharpoons 2 N O \quad K_{2} \)
\( \boldsymbol{H}_{2}+\frac{1}{2} \boldsymbol{O}_{2} \rightleftharpoons \boldsymbol{H}_{2} \boldsymbol{O} \quad \boldsymbol{K}_{3} \)
\( \mathbf{2} N \boldsymbol{H}_{3}+\frac{5}{2} \boldsymbol{O}_{2} \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{O}+\mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O} \quad \boldsymbol{K}_{4} \)
Which of the following relation is
correct?
\( \mathbf{A} \cdot K_{1}=\frac{K_{2} \times\left(K_{3}\right)^{3}}{K_{4}} \)
B \( \cdot K_{4}=K_{1} \times K_{2} /\left(K_{3}\right)^{3} \)
\( \mathbf{C} \cdot K_{2}=\frac{K_{4}+K_{1}}{\left(K_{3}\right)^{3}} \)
D. None of these
Subject: Physics
A particle executing simple harmonic motion along y-axis has its motion described by the equation \( y= \) \( \boldsymbol{A} \sin (\boldsymbol{\omega} \boldsymbol{t})+\boldsymbol{B} . \) The amplitude of the
simple harmonic motion is:
\( A \cdot A \)
в. \( B \)
c. \( A+B \)
D. \( \sqrt{A+B} \)
Subject: Chemistry
The adsorption of gases on solid can be described by Freundlich's equation \( \frac{\boldsymbol{x}}{\boldsymbol{m}}=\boldsymbol{k} \boldsymbol{P}^{1 / \boldsymbol{n}} \)
(a)How are the value of K and \( n \)
determined experimentally?
(b) Explain, why should the value of \( n \) be equal to or greater than one.
Subject: Physics
The electric potential due to an infinite sheet of positive charge density \( \sigma \) at a point located at a perpendicular distance \( Z \) from the sheet is (Assume
\( V_{0} \) to be the potential at the surface of sheet):
A. \( V_{0} \)
в. \( _{V_{0}-\frac{\sigma Z}{\epsilon_{0}}} \)
\( ^{\mathbf{c}} \cdot_{V_{0}}+\frac{\sigma Z}{2 \epsilon_{0}} \)
D. \( _{V_{0}-} \frac{\sigma Z}{2 \epsilon_{0}} \)
Subject: Maths
A triangle and a parallelogram have the same base and some area. If the sides
of the triangle are \( 26 \mathrm{cm}, 28 \mathrm{cm} \) and 30 \( \mathrm{cm} \) and the parallelogram stands on the
base \( 28 \mathrm{cm} . \) Find the height of the parallelogram.
Subject: Physics
A beam of light consisting of red, green and blue is incident on a right angled prism. The refractive index of the material of the prism for the above red, green and blue wavelengths are 1.39 1.44 and 1.47 respectively. The prism will
A. separate part of the red color from the green and blue colors
B. separate part of the blue color from the red and green colors
c. Separate all the three colors from the other two colors
D. not separate even partially any color from the other two colors
Subject: Physics
A ray of light travelling in a transparent medium falls on a surface separating the medium from air at an angle of
incidence \( 45^{\circ} \) and undergoes total
internal reflection. If \( \mu \) is the refractive
index of medium the possible values of
\( \mu \) are
This question has multiple correct options
A \( . \mu=1.3 \)
в. \( \mu=1.4 \)
c. \( \mu=1.5 \)
D. \( \mu=1.6 \)
Subject: Maths
Given: \( \vec{a} \) and \( \vec{b} \) are unit vector, and \( \theta \) be
the angle between them. Then \( \frac{1-\vec{a} \cdot \vec{b}}{1+\vec{a} \cdot \vec{b}}= \)
\( A \cdot \sin ^{2} \frac{\theta}{2} \)
B. \( \cos ^{2} \frac{\theta}{2} \)
\( c \cdot \tan ^{2} \frac{\theta}{2} \)
\( D \cdot \cot ^{2} \frac{\theta}{2} \)
Subject: Physics
Assertion
Separation of isotope is possible because of the difference in electron
numbers of isotope.
Reason
Isotope of an element can be separated by using a mass spectrometer
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. Reason is correct but Assertion is incorrect
Subject: Chemistry
A piston cylinder device initially contains \( 0.2 m^{3} \) neon (assume ideal) at
\( 200 \mathrm{kPa} \) inside at \( T_{1}^{0} C . A \) value is now
opened and neon is allowed to escape until the volume reduces to half the
initial volume. At the same time heat
transfer with outside at \( T_{2}^{0} C \) ensures a constant temperature inside. Select the statement(s) for given process:
A. \( \Delta U \) must be zero
B. \( \Delta U \) may not be zero
c. \( q \) may be \( + \) ve
D. q may not be -ve
Subject: Physics
Assertion
A ray of light is incident from outside on
a glass sphere surrounded by air. This ray may suffer total internal reflection
at second interface.
Reason
If a ray of light goes from denser to rarer
medium, it bends away from the
normal.
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
Assertion
According to Lenz Law, since the same
magnetic flux passes through both the primary and secondary windings in an ideal transformer,a voltage is induced
in each winding.
Reason
Voltage induced is same in both the
windings, ideally.
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect
Subject: Physics
Two balls \( A \) and \( B \) having masses \( 1 k g \)
and \( 2 k g, \) moving with speeds \( 21 m / s \) and \( 4 m / s \) respectively in opposite direction, collide head on. After collision \( A \) moves with a speed of \( 1 m / s \) in the same direction, the correct statements
is :
This question has multiple correct options
A. The velocity of \( B \) after collision is \( 6 m / s \) opposite to the direction of motion before collision
B. The coefficient of restitution is 0.2
c. The loss of kinetic energy due to collision is 200 J
D. The impulse of the force between the two balls is \( 40 \mathrm{Ns} \)
Subject: Physics
The time taken by a particle performing
S.H.M. to pass from point \( \boldsymbol{A} \) to \( \boldsymbol{B} \) where its velocities are same is 2 seconds.
After another 2 seconds it returns to \( \mathrm{B} \)
The time period of oscillation is (in seconds):
A .2
B. 4
\( c \cdot 6 \)
\( D \)
Subject: Chemistry
Assertion
Nitroalkanes and alkyl nitrites exhibit functional isomerism.
Reason
Compounds having same molecular formula but different functional group
are called functional isomers.
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 dielectric strength of air is \( 3.0 \times \)
\( 10^{6} N C^{-1} . \) The largest charge that a
\( 0.30 \mathrm{cm} \) radius metal sphere can hold without sparking is:
A. 9 nc
B. 8.2 nc
\( c \cdot 6 n c \)
D. 3 nc
Subject: Chemistry
Assertion
Soaps and detergent are macro-
molecular colloids.
Reason
Soaps and detergent are molecules of
large size.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Physics
One mole of an ideal gas is compressed from 0.5 lit to 0.25 lit. During the
compression, \( 23.04 \times 10^{2} J \) of work is
done on the gas and heat is removed to keep the temperature of the gas constant at all times. Find the
temperature of the gas. (Take universal gas constant \( \boldsymbol{R}=\mathbf{8 . 3 1} \boldsymbol{J} \boldsymbol{m o l}^{-1} \boldsymbol{K}^{-1} \mathbf{)} \)
Subject: Physics
A liter of air at \( 20^{\circ} \mathrm{C} \) is heated until both
the pressure and the volume are tripled, what is the tempertare then.
В . \( 927^{\circ} \) К
\( \mathbf{c} \cdot 200^{\circ} K \)
D. \( 977^{\circ} K \)
Subject: Physics
A bullet of mass \( 10 \times 10^{-3} \mathrm{kg} \) moving
with a speed of \( 20 m s^{-1} \) hits an ice
block \( \left(0^{\circ} c\right) \) of \( 990 g \) kept at rest on a frictionless floor and gets embedded in
it. If ice takes \( 50 \% \) of \( K . E, \) for melting,
then the mass of the ice block that has
melted is \( (J=4.2 J / C a l) \) (Latent heat
of ice \( =\mathbf{8 0} \) cal \( / \mathbf{g} \) )
A. 6
B. 3
c. \( 6 \times 10^{-3} \)
D. \( 3 \times 10^{-3} \)
Subject: Physics
What is the torque of a force \( \boldsymbol{F}=(2 \hat{\boldsymbol{i}}- \) \( 3 \widehat{j}+4 k) N \) acting at a point \( r=(3 \hat{i}+ \) \( 2 \widehat{j}+3 \widehat{k}) \mathrm{m} \) about the origin in \( \mathrm{N}-\mathrm{m} \)
? (Given \( \boldsymbol{\tau}=\boldsymbol{r} \times \boldsymbol{F}) \)
A \( .6 \hat{i}-6 \hat{j}+12 \widehat{k} \)
B . \( 17 \hat{i}-6 \widehat{j}-13 \widehat{k} \)
\( \mathbf{c} .-6 \hat{i}+6 \widehat{j}-2 \widehat{k} \)
D. \( -17 \hat{i}+6 \hat{j}+13 \widehat{k} \)
Subject: Physics
Show that \( _{92}^{230} U \) does not decay be emitting a neutron or proton. Given:
\( M\left(_{92}^{230} U\right)=230.033927 a m u \)
\( M\left(_{92}^{230} U\right)=229.033496 a m u \)
\( M\left(_{92}^{229} P a\right)=229.032089 a m u \)
\( \boldsymbol{m}(\boldsymbol{n})=\mathbf{1 . 0 0 8 6 6 5 a m u} \)
\( \boldsymbol{m}(\boldsymbol{p})=\mathbf{1 . 0 0 7 8 2 5 a m u} \)
Subject: Maths
Four letters mailed today each have a
probability of arriving in two days or sooner equal to \( \frac{2}{3} . \) Calculate the probability that exactly two of the four letters will arrive in two days or sooner.
\( \mathbf{A} \cdot \frac{4}{81} \)
B. \( \frac{16}{81} \)
c. \( \frac{6}{27} \)
D. \( \frac{8}{27} \)
E \( \cdot \frac{4}{9} \)
Subject: Maths
The point equidistant from the points (0,0,0),(1,0,0),(0,2,0) and (0,0,3) is
A \( .(1,2,3) \)
B \( \cdot\left(\frac{1}{2}, 1, \frac{3}{2}\right) \)
\( ^{c} \cdot\left(-\frac{1}{2},-1,-\frac{3}{2}\right) \)
D. (1,-2,3)
Subject: Chemistry
What would be thw minimum
uncertainty in de-Broglie wavelenght of a moving electron accelerated by potential difference of 6 volt and whose uncertainty in position is \( \frac{7}{22} n m ? \)
A. \( 6.25 \AA \)
в. \( 6 \dot{A} \)
c. \( 0.625 \hat{A} \)
D. \( 0.3125 \dot{A} \)
Subject: Chemistry
For an organic monoprotic acid solution of concentration \( C_{o} \) mol litre\( ^{-1} \), if \( K_{a} \)
has a value comparable to \( \boldsymbol{K}_{\boldsymbol{w}}, \) show
that the hydronium ion concentration is given by:
\[
\left[\boldsymbol{H}^{+}\right]==\left[\frac{\boldsymbol{K}_{\boldsymbol{w}}}{\left[\boldsymbol{H}^{+}\right]}+\frac{\boldsymbol{K}_{\boldsymbol{a}} \cdot \boldsymbol{C} \boldsymbol{o}}{\left[\boldsymbol{K}_{\boldsymbol{a}}+\boldsymbol{H}^{+}\right]}\right]
\]
\( \mathbf{f}\left[\boldsymbol{H}^{+}\right]=\mathbf{1} \mathbf{0}^{-\mathbf{3}} \boldsymbol{M} \) and \( \boldsymbol{C}_{\boldsymbol{o}}=\mathbf{1 0}^{-\mathbf{1}} \boldsymbol{M} \) in
solution of some organic monoportic acid. According to the above equation,
the order of magnitude of \( K_{a} \) must be \( 10^{-X}, \) the value of \( X \) should be:
Subject: Maths
What normal to the curve \( y=x^{2} \) form
the shortest chord?
\( \mathbf{A} \cdot x+\sqrt{2} y=\sqrt{2} \) or \( x-\sqrt{2} y=-\sqrt{2} \)
B \( . x+\sqrt{2} y=\sqrt{2} \) or \( x-\sqrt{2} y=\sqrt{2} \)
c. \( x+\sqrt{2} y=-\sqrt{2} \) or \( x-\sqrt{2} y=-\sqrt{2} \)
D. \( x+\sqrt{2} y=-\sqrt{2} \) or \( x-\sqrt{2} y=\sqrt{2} \)
Subject: Chemistry
Consider the chemical reaction,
\( N_{2}(g)+3 H_{2}(g) \longrightarrow 2 N H_{3}(g) \)
The rate of reaction can be expressed in terms of time derivative of
concentration of \( \boldsymbol{N}_{2}(\boldsymbol{g}), \boldsymbol{H}_{2}(\boldsymbol{g}) \) or
\( N H_{3}(g) . \) Identify the correct
relationship amongst the rate expressions.
A \( \cdot \operatorname{Rate}=-\frac{d\left[N_{2}\right]}{d t}=-\frac{1}{3} \frac{d\left[H_{2}\right]}{d t}=+\frac{1}{2} \frac{d\left[N H_{3}\right]}{d t} \)
B. Rate \( =-\frac{d\left[N_{2}\right]}{d t}=-3 \frac{d\left[H_{2}\right]}{d t}=+2 \frac{d\left[N H_{3}\right]}{d t} \)
\( ^{\mathbf{c}} \cdot_{\mathrm{Rate}}=\frac{d\left[N_{2}\right]}{d t}=\frac{1}{3} \frac{d\left[H_{2}\right]}{d t}=\frac{1}{2} \frac{d\left[N H_{3}\right]}{d t} \)
D. \( \operatorname{Rate}=-\frac{d\left[N_{2}\right]}{d t}=-\frac{d\left[H_{2}\right]}{d t}=\frac{d\left[N H_{3}\right]}{d t} \)
Subject: Maths
The sum of the first \( n \) terms of the
series \( 1^{2}+2 \cdot 2^{2}+3^{3}+2 \cdot 4^{2}+5^{2}+ \)
\( 2 \cdot 6^{2}+\cdots \) is \( \frac{n(n+1)^{2}}{2} \) when \( n \) is even
when \( n \) is odd the sum is
A \( \cdot \frac{3 n(n+1)}{2} \)
B. \( \frac{n^{2}(n+1)}{2} \)
c. \( \frac{n(n+1)^{2}}{4} \)
D. \( \left[\frac{n(n+1)}{2}\right]^{2} \)