AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A moving coil galvanometer has a coil of area \( A \) and number of turns \( N . A \)
magnetic field B is applied on it. The
torque acting on it is given by \( \boldsymbol{\tau}=\boldsymbol{k} \boldsymbol{i} \)
where i is current through the coil. If moment of inertia of the coil is I about
the axis of rotation.
If the value of k in terms of
galvanometer parameters \( (\mathrm{N}, \mathrm{B}, \mathrm{A}) \) is given by \( k=x \times N B A \). Find \( x \)
Subject: Maths
The standard deviation of some
temperature data in \( ^{\circ} \boldsymbol{C} \) is \( 5 . \) If the data
were converted into \( ^{\circ} \boldsymbol{F} \), the variance
would be
\( A \cdot 81 \)
B. 57
\( c . \) 36
D. 25
Subject: Chemistry
The enthalpy of neutralisation of a strong acid by a strong base is \( -57.32 k J \) mol \( ^{-1} . \) The enthalpy of
formation of water is
\( -285.84 k J \) mol\( ^{-1} . \) The enthalpy of
formation of hydroxy ion is:
A \( .+228.52 k J \) mol \( ^{-1} \)
B. \( -114.26 k J \) mol\( ^{-} \)
c. \( -228.52 k J \) mol \( ^{-1} \)
D. \( +114.2 \mathrm{kJ} \mathrm{mol}^{-1} \)
Subject: Maths
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}(\boldsymbol{x}-1) \) in the interval \( [\mathbf{1}, \mathbf{2}] \) if
\( \boldsymbol{f}^{\prime}(\boldsymbol{c})=\boldsymbol{f}(1) . \) Find \( c \)
Subject: Physics
A converging lens (focal length \( ^{\prime} f^{\prime} \) ) is broken in two equal pieces and placed at \( 60 \mathrm{cm} \) as shown along with the
object. It is found that real images are formed at the same place and ratio of
image heights is \( 9: 1, \) if the value of \( ^{\prime} f^{\prime} \) is \( \left(22+\frac{1}{x}\right) \mathrm{cm} \) then value of \( ^{\prime} x^{\prime} \) is :
Subject: Chemistry
For an ideal binary liquid solution with \( \boldsymbol{p}_{\boldsymbol{x}}^{0}>\boldsymbol{p}_{\boldsymbol{y}}^{0} \) in which relation between \( \boldsymbol{X}_{\boldsymbol{x}} \)
(mole fraction of \( x \) in liquid phase) and
\( Y_{x} \) (mole of fraction of \( x \) in vapour
phase) is correct where \( \boldsymbol{X}_{\boldsymbol{y}} \) and \( \boldsymbol{Y}_{\boldsymbol{y}} \) are mole fraction of \( y \) in liquid and vapour phase respectively.
A \( \cdot X_{x}>Y_{x} \)
в. \( X_{x}=Y_{x} \)
с. \( \frac{X_{x}}{X_{y}}<\frac{Y_{x}}{Y_{y}} \)
D. \( X_{x}, Y_{x}, X_{y} \) and \( Y_{y} \) cannot be correlated
Subject: Chemistry
un tne basıs or Ivlenaeleevs rerıoaıc
Table given below, answer the question
that follow the table:
Ref. image
Besides gallium, which two other
elements have since been discovered
for which Mendeleev had left gaps in his
Periodic Table? Using atomic masses of
Li,NaLi,Na, find the average atomic
mass of and compare it with the atomic
mass of. State the conclusion drawn
from this activity.
Subject: Physics
Assertion
The electrical conductivity of a gas
increases when \( X \) -rays or \( \gamma \) -rays pass through it
Reason
lonization in the gas is produced by \( x \)
rays or \( \gamma- \) rays
A. Assertion is True and Reason is True; Reason is a correct explanation of Assertion
B. Assertion is True and Reason is True but Reason is not a correct explanation of Assertion
c. Assertion is True and Reason is False
D. Assertion is False and Reason is True
Subject: Physics
The Vander waal's equation for ideal gas is given by \( \left(p+\frac{a}{V^{2}}\right)(V-b)=R T \)
where \( P \) is pressure, \( V \) is volume \( a \) and
\( b \) are constants, \( R \) is universal gas
constant and \( \boldsymbol{T} \) is
absolute temperature. Then the dimensions of \( \frac{a}{b} \) are same as that of:
A. Force
B. Momentum
c. Energy
D. Power
Subject: Physics
Find how the volume density of the elastic deformation energy is distributed in a steel rod depending on
the distance \( r \) from its axis. The length
of the rod is equal to \( l \), the torsion angle
to \( \varphi \)
A. \( u=\frac{1}{2} \frac{G \varphi^{2} r^{2}}{l^{2}} \)
B. \( u=\frac{3}{2} \frac{G \varphi^{2} r^{2}}{l^{2}} \)
c. \( _{u=\frac{5}{2} \frac{G \varphi^{4} r^{2}}{l^{2}}} \)
D. None of these
Subject: Maths
Solve the following pair of equations
graphically; \( 2 x-3 y=1, \& 4 x-3 y+ \)
\( \mathbf{1}=\mathbf{0} \)
A. \( x=1 y=-1 \)
В. \( x=-1 y=-1 \)
c. \( x=-1 y=1 \)
D. \( x=1 y=1 \)
Subject: Maths
Let \( S \) be the set of all values of \( x \) such
\( \operatorname{that} \log _{2 x}\left(x^{2}+5 x+6\right)<1 \) then the
sum of all integral value of \( x \) in the set
S, is
\( A \cdot O \)
B. 8
\( c \cdot s \)
D. 10
Subject: Physics
Two deuterium nuclei each of mass ' \( \boldsymbol{m}^{\prime} \)
fuse together to form a Helium nucleus,
releasing an energy \( \boldsymbol{E} \). If \( ^{\prime} \boldsymbol{c}^{\prime} \) is the
velocity of light, the mass of Helium nucleus formed will be:
A \( \cdot 2 m+\frac{E}{c^{2}} \)
в. \( \frac{E}{m c^{2}} \)
c. \( _{m+\frac{E}{c^{2}}} \)
D. \( 2 m-\frac{E}{c^{2}} \)
Subject: Maths
Area bounded by the lines \( y=x, x= \)
\( -1, x=2 \) and \( x \) -axis is
A \( \cdot \frac{5}{2} \) sq. units
B. \( \frac{3}{2} \) squnits
c. \( \frac{1}{2} s q \) units
D. None of these
Subject: Chemistry
The standard potential of the following
cell is \( 0.23 V \) at \( 15^{\circ} C \) and \( 0.21 V \) at
\( 25^{\circ} C \)
\( \boldsymbol{P t H}_{2}(\boldsymbol{g})|\boldsymbol{H} \boldsymbol{C l}(\boldsymbol{a q} .) \| \boldsymbol{A} \boldsymbol{g} C l(s)| \boldsymbol{A} \boldsymbol{g}(s) \)
(i) Write cell reaction.
(ii) Calculate \( \triangle H^{\circ} \) and \( \triangle S^{\circ} \) for the cell
reaction by assuming that these quantities remain unchanged in the range \( 15^{\circ} \mathrm{C} \) to \( 35^{\circ} \mathrm{C} \)
(iii) Calculate the solubility of \( A g C l \) in
water at \( 25^{\circ} C . \) Given the standard
reduction potential of the \( \boldsymbol{A} \boldsymbol{g}^{+} / \boldsymbol{A} \boldsymbol{g} \)
couple is 0.80 volt at \( 25^{\circ} \mathrm{C} \)
Subject: Physics
Assume that a neutron breaks into a
proton and an electron. The energy released during this process is (Mass of neutron \( =1.6725 \times 10^{-27} k g \)
Mass of proton \( =1.6725 \times 10^{-27} k g \)
Mass of electron \( \left.=\mathbf{9} \times \mathbf{1 0}^{-\mathbf{3 1}} \mathbf{k g}\right) \)
B. \( 7.10 \mathrm{MeV} \)
c. \( 6.30 \mathrm{MeV} \)
D. \( 5.40 \mathrm{MeV} \)
Subject: Maths
If \( \boldsymbol{A}=(\mathbf{6}, \mathbf{7}, \mathbf{8}, \mathbf{9}), \boldsymbol{B}=(\mathbf{4}, \mathbf{6}, \mathbf{8}, \mathbf{1 0}) \) and
\( C=\{x: x \in N: 2<x \leq 7\} ; \) find :
\( B-C \)
A \( \cdot\{4,6\} \)
в. \{4,6,8\}
c. \{6,8,10\}
D. \{8,10\}
Subject: Physics
Which of the following is included in laws of refraction?
This question has multiple correct options
A \( \cdot \frac{\sin i}{\sin r}=\mu \)
B. The incident ray, the refracted ray and normal at the point of incidence all lie in the same plane
c. \( \angle i=\angle r, \) where \( r \) is angle of refraction
D. \( \angle i<\angle r \), where \( r \) is angle of refraction
Subject: Maths
Consider three planes \( 2 x+p y+6 z= \)
\( \mathbf{8}, \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\boldsymbol{q} \boldsymbol{z}=\mathbf{5} \) and \( \boldsymbol{x}+\boldsymbol{y}+\mathbf{3} \boldsymbol{z}=\mathbf{4} \)
These planes do not have any common point of intersection if-
A. \( p=2, q \neq 3 \)
B . \( p \neq 2, q \neq 3 \)
c. \( p \neq 2, q=3 \)
D. \( p=2, q=3 \)
Subject: Chemistry
The olefin which on ozonolysis gives
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H O} \) and \( \boldsymbol{C H}_{3} \boldsymbol{C H O} \) is :
A. 1 -butene
B. 2-butene
c. 1-pentene
D. Pent-2-ene
Subject: Maths
If an edge of a cube measure \( 2 \mathrm{m} \) with a
possible error of \( 0.5 \mathrm{cm} . \) Find the corresponding error in the calculated volume of the cube.
\( \mathbf{A} \cdot 0.6 m^{3} \)
В. \( 0.06 m^{3} \)
c. \( 0.006 m^{3} \)
D. \( 0.0006 \mathrm{m}^{3} \)
Subject: Maths
\( \operatorname{Let}\left(a_{1}, a_{2}, a_{3}, \dots, a_{2011}\right) \) be a
permutation (that is a rearrangement) of the numbers \( 1,2,3, \ldots, 2011 . \) Show
that there exist two numbers \( j, k \) such that \( 1 \leq j<k \leq 2011 \) and \( \left|a_{j}-j\right|= \)
\( \left|\boldsymbol{a}_{\boldsymbol{k}}-\boldsymbol{k}\right| \)
A. 20101005
B. 2011 1006
c. 20111005
D. 2011 1010
Subject: Physics
Q Type your question
user. Given below are some of the
applications of science. Formulate your views on whether the particular application is good, bad or something that cannot be so clearly categorised:
(a) Mass vaccination against small pox
to curb and finally eradicate this disease from the population. (This has already been successfully done in
India).
(b) Television for eradication of
illiteracy and for mass communication of news and ideas.
(c) Prenatal sex determination
(d) Computers for increase in work efficiency
(e) Putting artificial satellites into
orbits around the Earth
(f) Development of nuclear weapons
(g) Development of new and powerful techniques of chemical and biological
warfare).
(h) Purification of water for drinking
(i) Plastic surgery
(j) Cloning
Subject: Physics
A body is tied at the end of a string of length " and rotated in a vertical
circle, The suring is just taut when the body is at highest point. Velocity of the body when the string is in horizontal position is
A. \( 3 \sqrt{g r} \)
B . \( \sqrt{g r} \)
c. \( \sqrt{5 g r} \)
D. \( \sqrt{3 g r} \)
Subject: Physics
A flat plate is moving normal to its plane through a gas under the action of a constant force \( \boldsymbol{F} \). The gas is kept at a
very low pressure. The speed of the plate
\( v \) is much less than the average speed
\( u \) of the gas molecules. Which of the
following options is/are true? This question has multiple correct options
A. The resistive force experienced by the plate is proportional to \( v \)
B. At a later time the external force \( F \) balances the resistive force
C. The plate will continue to move with constant non-zero acceleration, at all times
D. The pressure difference between the leading and trailing faces of the plate is proportional to \( u v \)
Subject: Physics
toppr
Q Type your question
the block \( A \) is placed is taken to be
smooth. A horizontal force \( F, \) increasing linearly with time, begins to act on B.
The accelerations \( a_{A} \) and \( a_{B} \) of
blocks A and B respectively are plotted
against t. The correctly plotted graph is:
4
B.
\( c \)
D. none of the above
Subject: Maths
State the following statement is True or False
If \( k^{2} x^{2}-2(k-1) x+4=0 \) has
equal roots, then \( \boldsymbol{k}=-\mathbf{1} \) or \( \boldsymbol{k}=\frac{\mathbf{1}}{\mathbf{3}} \)
A. True
B. False
Subject: Maths
The solution of the differential equation
\( \boldsymbol{x}^{2} \boldsymbol{d} \boldsymbol{y}+\boldsymbol{y}(\boldsymbol{x}+\boldsymbol{y}) \boldsymbol{d} \boldsymbol{x}=\mathbf{0} \) is:
A \( \cdot x^{2} y=c^{2}(2 x+y) \)
B . \( x y^{2}=c^{2}(2 x+y) \)
C. \( x^{2} y=c^{2}(x+2 y) \)
D. \( x y^{2}=c^{2}(x+2 y) \)
Subject: Maths
If \( \boldsymbol{u}=\boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{h} \boldsymbol{x} \boldsymbol{y}+\boldsymbol{b} \boldsymbol{y}^{2} \)
\( \operatorname{then} x \frac{\partial^{2} u}{\partial x \partial y}+y \frac{\partial^{2} u}{\partial y^{2}}=? \)
\( \mathbf{A} \cdot 2(h x+b y) \)
B. \( 2(h x-b y) \)
c. \( 2(b x+h y) \)
D. \( 2(b x-h y) \)
Subject: Physics
If \( l=50 \mathrm{kg}-m^{2}, \) then how much torque
will be applied to stop it in 10 sec. Its initial angular speed is 20 rad sec.
A . \( 100 \mathrm{N}-\mathrm{m} \)
B . \( 150 \mathrm{N}-\mathrm{m} \)
c. \( 200 \mathrm{N}-\mathrm{m} \)
D. \( 250 \mathrm{N}-\mathrm{m} \)
Subject: Physics
When an \( \alpha \) -particle of mass ' \( m^{\prime} \) moving
with velocity \( ^{\prime} v^{\prime} \) bombards on a heavy
nucleus of charge \( ^{\prime} Z e^{\prime}, \) its distance of
closest approach from the nucleus
depends on \( m \) as:
A \( \cdot \frac{1}{m} \)
в. \( \frac{1}{\sqrt{m}} \)
c. \( \frac{1}{m^{2}} \)
D. \( m \)
Subject: Maths
\( \int \frac{d x}{\sin x-\cos x+\sqrt{2}} \) is equal to.
A \( \cdot-\frac{1}{\sqrt{2}} \tan \left(\frac{x}{2}+\frac{\pi}{8}\right)+C \)
B. \( \frac{1}{\sqrt{2}} \tan \left(\frac{x}{2}+\frac{\pi}{8}\right)+C \)
c. \( \frac{1}{\sqrt{2}} \cot \left(\frac{x}{2}+\frac{\pi}{8}\right)+C \)
D. \( -\frac{1}{\sqrt{2}} \cot \left(\frac{x}{2}+\frac{\pi}{8}\right)+C \)
Subject: Physics
Find the unit vectors perpendicular to
each of the following pairs of vectors:
\( \vec{i}+\vec{j}+\vec{k} \) and \( \vec{i}+\overrightarrow{2} j-\vec{k} \)
\( \mathbf{A} \cdot a_{1} \vec{i}+a_{2} \vec{j}+a_{3} \vec{k}, \) where \( a_{1}=\mp 3 / \sqrt{14}, a_{2}= \)
\( \pm 2 / \sqrt{14}, a_{3}=\pm 1 / \sqrt{14} \)
B \( \cdot a_{1} \vec{i}+a_{2} \vec{j}+a_{3} \vec{k}, \) where \( a_{1}=\mp 3 / \sqrt{14}, a_{2}= \)
\( \pm 2 / \sqrt{14}, a_{3}=\pm 2 / \sqrt{14} \)
C \( \cdot a_{1} \vec{i}+a_{2} \vec{j}+a_{3} \vec{k}, \) where \( a_{1}=\mp 2 / \sqrt{14}, a_{2}= \)
\( \pm 2 / \sqrt{14}, a_{3}=\pm 1 / \sqrt{14} \)
\( \mathbf{D} \cdot a_{1} \vec{i}+a_{2} \vec{j}+a_{3} \vec{k}, \) where \( a_{1}=\mp 3 / \sqrt{14}, a_{2}= \)
\( \pm 2 / \sqrt{14}, a_{3}=\pm 3 / \sqrt{14} \)
Subject: Physics
The stress-strain graphs are shown in
the figure for two materials \( A \) and \( B \) are
shown in figure. Young's modulus of \( \boldsymbol{A} \)
is greater than that of \( B \).
Reason
The Young's modules for small strain is, \( Y=\frac{\text {stress}}{\text {strain}}= \) slope of linear portion of
graph; and slope of \( A \) is more than that
of \( B \)
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-1
C. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True
Subject: Maths
\( \boldsymbol{x}(\boldsymbol{x}-1) \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}-(\boldsymbol{x}-\boldsymbol{2}) \boldsymbol{y}=\boldsymbol{x}^{3}(\boldsymbol{2} \boldsymbol{x}- \)
1). The solution to the above given differential equation is \( \boldsymbol{y}(\boldsymbol{x}+\boldsymbol{k})= \)
\( \boldsymbol{x}^{m}\left(\boldsymbol{x}^{n}-\boldsymbol{x}+\boldsymbol{c}\right) . \) Find \( \boldsymbol{k}+\boldsymbol{m}+\boldsymbol{n} ? \)
Subject: Physics
The top in figure has a moment of
inertia of \( 4.00 \times 10^{-4} k g-m^{2} \) and is
initially at rest. It is free to rotate about
the stationary axis \( \boldsymbol{A} \boldsymbol{A}^{\prime} \) A string
wrapped around a peg along the axis of the top, is pulled in such a manner as to
maintain a constant tension of \( 2.5 M . \) If
the string does not slip while it is unwound from the peg, what is the
angular speed of the top after \( 80.0 \mathrm{cm} \)
string has been pulled off the peg?
A \( .75 \mathrm{rad} / \mathrm{s} \)
B. 50 rad \( / s \)
c. \( 125 r a d / s \)
D. 100 rad \( / s \)
Subject: Physics
In an experiment, 1.35 mol of oxygen (O2) are heated at constant pressure starting at \( 11.0^{\circ} \mathrm{C} \). How much heat must be added
to the gas to double its volume?
A \( \cdot 1.12 \times 10^{4} J \)
В. \( 1.40 \times 10^{4} \)
c. \( \$ \$ 2.12 \) ltimes \( 10^{\wedge} 4 \$ \$ \) J
D. \$\$3.12x10^4 J\$\$
Subject: Chemistry
Assertion
The solubility of a substance changes
with temperature.
Reason
Heat is required to break the bonds
holding molecules together so solubility is dependent on temperature.in dissolution, energy, in the form of heat, is required to break the bonds joining
the molecules in the solid together.
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: Biology
Select the false statement.
A. Scientists who study and contribute to the classification of organisms are known as systematists.
B. Carolus Linnaeus developed the first scientific system of naming species.
C. A five kingdom arrangement of organisms was introduced by R. H. Whittaker.
D. Genus is a group of species which are related and have less characters in common as compared to species.
E. Phycomycetes are called club fungi because of a club shaped end of mycelium known as basidium.
Subject: Chemistry
Identify the correct order of lattice energies.
A. \( C s C l<R b C l<K C l<N a C l \)
в. \( K C l>C a C l_{2}>A l C l_{3} \)
c. \( N a C l<L i C l<M g C l_{2}<A l C l_{3} \)
D. \( L i C l>N a C l<M g C l_{2}<A l C l_{3} \)
Subject: Physics
Three particles, each having a charge of \( 10 \mu C \) are placed at the corners of an
equilateral triangle of side \( 10 \mathrm{cm} \). The electronic potential energy of the system is: \( \left(\text { Given } \frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} N-\right. \)
\( \left.m^{2} / C^{2}\right) \)
A. Zero
B. Infinite
c. 27
D. \( 100 J \)
Subject: Chemistry
Which of the following statements are
correct?
This question has multiple correct options
A. In gas phase, the basic character of amine is \( 3>2>1 \)
Due to the +1effect of (R-), the availability of \( L P e^{-^{\prime}} s \) on N increases.
B. In aqueous medium, the basic character of amines is \( M e_{2} N H>M e_{3} N>M e N H_{2}>N H_{3} \)
C. In aqueous medium, the addition of protons increases crowding and thus strains setup, which being the highest in 3 amine decreases its basic character.
D. In aqueous medium, the ammonium ions in solution are stabilised not only by alkyl groups but also by \( \mathrm{H}- \) bond donation to the solvent.
Subject: Physics
Pictured above is a red point charge and
a blue point charge. The blue point charge is moved from loication 1 to location 2. The force
between the point charges is \( 5.00 \mathrm{N} \)
when blue charge is at location 1
How much force exist between the point charges when the blue charges is at
location 2?
A . 25.0
B. 30.0 N
c. \( 125 \mathrm{N} \)
D. \( 180 \mathrm{N} \)
E . \( 1.0 \mathrm{N} \)
Subject: Physics
A particle is projected vertically
upwards with velocity \( 80 \mathrm{m} / \mathrm{s} \). Then the
(Take \( \left.\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
A. Displacement and distance travelled by the particle in \( 2 \sec \) in \( 160 \mathrm{m} \)
B. Displacement and distance travelled by the particle in \( 4 \sec \) in \( 240 \mathrm{m} \)
C. Displacement and distance travelled by the particle in \( 6 \sec \) in \( 300 \mathrm{m} \) and \( 100 \mathrm{m} \)
D. Displacement and distance travelled by the particle in \( 8 \sec \) is \( 320 \mathrm{m} \) and \( 10 \mathrm{m} \)
Subject: Chemistry
Determine the empirical formula of an oxide of iron which has \( 69.9 \% \) iron and
\( 30.1 \% \) oxygen. \( (F e=55.85 a m u ; O= \)
16.00 \( a m u \)
\( \mathbf{A} \cdot F e_{2} O_{3} \)
в. \( F e_{4} O_{6} \)
\( \mathrm{c} \cdot F e_{8} O_{12} \)
D. 'None of the above
Subject: Maths
If the H.C.F. of \( A \) and \( B \) is 24 and that of
\( C \) and \( D \) is \( 56, \) then the H.C.F. of \( A, B, C \)
and \( D \) is
A .4
B. 12
\( c \cdot 8 \)
D. 3
Subject: Physics
A round uniform body of radius \( R \), mass \( M \) and moment of inertia \( I, \) rolls down
(without slipping) an inclined plane making an angle with the horizontal. Then its acceleration is :
A. \( \frac{g \sin \theta}{1+I / M R^{2}} \)
B. \( \frac{g \sin \theta}{1+M R^{2} / I} \)
c. \( \frac{g \sin \theta}{1-I / M R^{2}} \)
D. \( \frac{g \sin \theta}{1-M R^{2} / I} \)
Subject: Chemistry
For a gaseous phase reaction, \( \boldsymbol{A}+ \) \( \mathbf{2} \boldsymbol{B} \rightleftharpoons \boldsymbol{A} \boldsymbol{B}_{2} \boldsymbol{K}_{C}=\mathbf{0 . 3 4 7 5} \) litre \( ^{2} \boldsymbol{m o l}^{-2} \)
at \( 200^{\circ} \mathrm{C} \). When 2 mole of \( B \) are mixed
with one mole of \( A \). What total pressure
is required to convert \( 60 \% \) of \( A \) in \( A B_{2} \) ?
Subject: Maths
The diagonals \( A C \) and \( B D \) of a
parallelogram \( A B C D \) intersect each
other at the point \( O \)
If \( \angle D A C=32^{\circ} \) and \( \angle A O B=70^{\circ}, \) then
\( \angle D B C \) is equal to?
A \( \cdot 24^{\circ} \)
B. \( 86^{\circ} \)
\( c \cdot 38^{\circ} \)
\( D \cdot 32^{\circ} \)
Subject: Physics
Energy liberated in the de-excitation of hydrogen atom from the third level to the first level falls on a photo-cathode. Later when the same photo-cathode is exposed to a spectrum of some unknown hydrogen-like gas, excited to the second energy level, it is found that the de Broglie wavelength of the fastest photoelectrons now ejected has
decreased by factor of \( 3 . \) For this new gas, difference of energies of the second Lyman line and the first Balmer line is
found to be 3 times the ionization
potential of the hydrogen atom. Select
the correct answers.
This question has multiple correct options
A. The gas is lithium
B. The gas is helium
c. The work function of photo-cathode is 8.5 eV
D. The work function of photo-cathode is 5.5 eV
Subject: Maths
\( \boldsymbol{A}=(\mathbf{0}, \mathbf{1}, \mathbf{2}), \boldsymbol{B}=(\mathbf{3}, \mathbf{0}, \mathbf{1}), \boldsymbol{C}= \)
\( (4,3,6), D=(2,3,2) \) are the
rectangular cartesian co-ordinates. Find the area of the triangle \( A B C \).
A. \( \sqrt{90} \)
B. \( \sqrt{\frac{45}{2}} \)
c. 45
D. 18
Subject: Chemistry
Non-ionogenic surfactants are:
\( \mathbf{A} \)
\( \mathbf{B} \cdot C_{17} H_{35} C O O N a \)
\( \mathbf{c} \cdot C_{n} H_{2 n+1}\left(O C H_{2} C H_{2}\right)_{x} \)
D. all the above
Subject: Physics
A load of \( 4.0 \mathrm{kg} \) is suspended from a ceiling through a steel wire of length \( 20 m \) and radius \( 2.0 m m . \) It is found
that the length of the wire increases by
\( 0.031 m m \) as equilibrium is achieved. If
\( \boldsymbol{g}=\mathbf{3 . 1} \boldsymbol{x} \boldsymbol{\pi} \boldsymbol{m} \boldsymbol{s}^{-2}, \) the value of young's
modulus in \( N m^{-2} \) is
\( \mathbf{A} \cdot 2.0 \times 10^{12} \)
B . \( 4.0 \times 10^{11} \)
\( \mathbf{c} \cdot 2.0 \times 10^{11} \)
D. \( 0.02 \times 10^{9} \)
Subject: Maths
The following graph represents:
\( \mathbf{A} \cdot \cot ^{-1}(x+1) \)
\( B \cdot \sin ^{-1}\left(x^{4}+1\right) \)
\( \mathbf{c} \cdot \tan ^{-1}\left(x^{3}+1\right) \)
\( D \cdot \cos ^{-1}\left(x^{2}+1\right) \)
Subject: Chemistry
Assertion
Sulphur dioxide is a more powerful
reducing agent in alkaline medium
than in acidic medium.
Reason
Sulphur dioxide reacts with hydrogen
sulphide in presence of moisture and
sulphur is precipitated.
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: Maths
Negation of \( \boldsymbol{q} \vee \sim(\boldsymbol{p} \wedge \boldsymbol{r}) \) is
A \( \cdot \sim q \wedge \sim(p \wedge r) \)
В . \( q \wedge(p \wedge r) \)
\( \mathbf{c} \cdot \sim q \vee(p \wedge r) \)
D. None of these
Subject: Chemistry
Calculate the change in enthalpy for the
following process at 1 atm \( \boldsymbol{H}_{2} \boldsymbol{O}\left(\boldsymbol{l}, \mathbf{5} \boldsymbol{0}^{o} \boldsymbol{C}\right) \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}\left(\boldsymbol{g}, \mathbf{1 5 0}^{\boldsymbol{o}} \boldsymbol{C}\right) \)
given that \( \Delta H_{v} \) at \( 100^{\circ} \mathrm{C} \) is
\( 40.7 k J m o l^{-1} \)
\( C_{P}\left(H_{2} O, l\right)=75.0 J m o l^{-1} K^{-1} \)
\( \boldsymbol{C}_{\boldsymbol{P}}\left(\boldsymbol{H}_{2} \boldsymbol{O}, \boldsymbol{g}\right)=\mathbf{3 3} . \boldsymbol{3} \boldsymbol{J} \boldsymbol{m o l}^{-1} \boldsymbol{K}^{-1} \)
A \( .64 .8 K J \)
в. \( 52.5 K J \)
c. \( 48.6 K J \)
D. \( 46.1 K J \)
Subject: Chemistry
From among the elements, choose the
following:
\( \mathrm{Cl}, \mathrm{Br}, \mathrm{F}, \mathrm{O}, \mathrm{Al}, \mathrm{C}, \mathrm{Li}, \mathrm{Cs} \) and \( \mathrm{Xe} \)
The element which shows diagonal relationship with Mg.