AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Two identical \( 5 \mathrm{kg} \) blocks are moving
with same speed of \( 2 m s^{-1} \) towards
each other along a frictionless
horizontal surface. The two blocks
collide, stick together, and come to rest. Consider the two blocks as a system
The work done by external and internal forces are respectively,
\( A \cdot 0,0 \)
B. 0, 20J
c. 0,-20
D. 20J, -20J
Subject: Chemistry
The Keto form of phenol contains:
A. \( 3 \pi, 13 \sigma, 4 \) non-bonding electrons
B. \( 4 \pi, 15 \sigma, 3 \) non-bonding electrons
C. \( 3 \pi, 14 \sigma, 4 \) non-bonding electrons
D. \( 2 \pi, 15 \sigma, 6 \) non-bonding electrons
Subject: Maths
Out of the rational numbers
\( \frac{5}{-11}, \frac{5}{-12}, \frac{5}{-17}, \) which is the greatest?
A \( \cdot \frac{-5}{11} \)
в. \( \frac{5}{-12} \)
\( c \cdot \frac{-5}{17} \)
D. Cannot be compared
Subject: Maths
Discuss the continuity of the following function at the indicated point(s):
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}\frac{\boldsymbol{2}|\boldsymbol{x}|+\boldsymbol{x}^{2}}{\boldsymbol{x}}, & \boldsymbol{x} \neq \mathbf{0} \\ \boldsymbol{0}, & \boldsymbol{x}=\mathbf{0}\end{array}, \text { at } \boldsymbol{x}=\mathbf{0}\right. \)
Subject: Physics
The top of the atmosphere is about 400
kV with respect to the surface of the earth, corresponding to an electric field
that decreases with altitude. Near the
surface of the earth, the field is about
\( 100 V m^{-1} \)
Still, we do not get an electric shock as we step out of our house into the open house, because (assume the house to
be a steel cage so that there is no field inside)
A. There is a potential difference between our body and the ground
B . \( 100 \mathrm{Vm}^{-1} \) is not a high electric field so that we do not feel the shock
c. our body and the ground forms an equipotential surface
D. The dry atmosphere is not a conductor
Subject: Chemistry
\( \boldsymbol{C a} \boldsymbol{C O}_{3}(\boldsymbol{s}) \longrightarrow \boldsymbol{C a O}(\boldsymbol{s})+\boldsymbol{C O}_{2}(\boldsymbol{g}) \)
For this reaction relate \( \Delta H \) and \( \Delta U \)
A. \( \Delta H=\Delta U \)
в. \( \Delta H>\Delta U \)
c. \( \Delta H<\Delta U \)
D. None of these
Subject: Physics
The resultant of \( \vec{P} \) and \( \vec{Q} \) is \( \vec{R} \). If \( \vec{Q} \) isdoubled, \( \vec{R} \) is doubled; when \( \vec{Q} \) is reversed, \( \overrightarrow{\boldsymbol{R}} \) is again doubled. Find \( \boldsymbol{P} \) :
\( \boldsymbol{Q}: \boldsymbol{R} \)
Subject: Chemistry
One litre of a buffer solution containig
\( 0.01 M N H_{4} C l \) and \( 0.1 M N H_{4} O H \)
having \( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{b}} \) of \( \boldsymbol{5} \) has pH of:
A . 10
B. 9
\( c \cdot 4 \)
D. 6
Subject: Maths
The following data gives the information on the observed lifetimes (in hours) of
225 electrical components:
Lifetimes
\( 0- \)
\( \begin{array}{lll}\text { 20- } & \text { 40- } & \text { 60- }\end{array} \)
\[
\text { in } \quad 20 \quad 40 \quad 60
\]
hours)
Frequency 10
\[
35
\]
52
Determine the modal lifetimes of the
components.
A. 69.268 hours
B. 65.625 hours
c. 62.126 hours
D. 58.267 hours
Subject: Maths
In an isosceles triangle \( A B C, \) with
\( A B=A C, \) the bisectors of \( \angle B \) and \( \angle C \)
intersect each other \( O . \) Join \( A \) to \( O \)
Show that:
\( \boldsymbol{O} \boldsymbol{B}=\boldsymbol{O} \boldsymbol{C} \)
Subject: Maths
\( \sum_{r=0}^{n} r^{2} .^{n} C_{r} p^{r} q^{n-r}, \) where \( p+q=1 \)
is simplified to:
A \( \cdot n p q+n^{2} p^{2} \)
B . \( n^{2} p^{2} q^{2}+n p \)
c. \( n p(p+q) \)
D. \( \frac{p(q+1)}{2} \)
Subject: Chemistry
\( \boldsymbol{C H}_{3} \boldsymbol{B r}+\boldsymbol{M} \boldsymbol{g} \stackrel{\text {Ether}}{\longrightarrow} \boldsymbol{A} \stackrel{\boldsymbol{H C H O}}{\longrightarrow} \)
\( \boldsymbol{B} \stackrel{\boldsymbol{H O H}}{\longrightarrow} \boldsymbol{C} \)
Compound \( \boldsymbol{C} \) is:
A. acetic acid
B. acetaldehyde
c. ethyl alcohol
D. formic acid
Subject: Physics
A thunder cloud and the earth's surface
may be regarded as a pair of charged
parallel plates separated by a distance
\( h \) and the capacitance of the system is
C. When a flash of mean current ' \( i \) '
occurs for a time duration 't', the
electric field strength between the cloud and earth is:
\( \mathbf{A} \cdot \frac{i t}{C} \)
B. Cit
c. \( \frac{i t}{C h} \)
D. \( \frac{\text { Cit }}{h} \)
Subject: Physics
An electric charge \( 10^{-3} \mu C \) is placed at the origin (0,0) of \( (x, y) \) co-ordinate
system. Two points \( A \) and \( B \) are situated at \( (\sqrt{2}, \sqrt{2}) \) and (2,0) respectively. The potential difference between the points \( A \) and \( B \) will be:
A \( .4 .5 V \)
B. \( 9 V \)
c. zero
D. \( 2 V \)
Subject: Chemistry
Assertion
We apply paint on iron articles.
Reason
Iron is a metal, metals rust when they
come in contact of direct air so to
prevent rusting.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
A shopkeeper sold sarees at Rs 266 each after giving \( 5 \% \) discount on labelled price. Had he not given the discount, he would have earned a profit of \( 12 \% \) on the cost price. what was the cost price of each saree ?
This question has multiple correct options
A. Rs 240
B. Rs 260
c. Rs 280
D. Date indepequate
E. None of these
Subject: Physics
A thief is running away on a straight road with a speed of \( 9 m s^{-1} . \) A police man chases him on a jeep moving at a speed of \( 10 \mathrm{ms}^{-1} \) If the instantaneous
separation of the jeep from the motorcycle is \( 100 \mathrm{m}, \) how long will it take. for the police man to catch the thief?
A . 1 s
B. \( 19 s \)
\( c \cdot 90 s \)
D. 100 s
Subject: Maths
When the price of TV set was increased by \( 30 \% \), then number of TV sets sold
decreased by \( 20 \% . \) What was the effect
on the sales?
A. \( 5 \% \) decrease
B. \( 7 \% \) increase
c. \( 6 \% \) decrease
D. \( 4 \% \) increase
Subject: Physics
A bullet of mass \( m \) is fired with a
velocity \( v \) into a fixed log of wood and penetrates a distance s before coming to rest. Assuming that the path of the bullet in the log of wood is horizontal, the average resistance offered by the log of wood is
A \( \cdot \frac{m v}{2 s^{2}} \)
в. \( \frac{m v^{2}}{2 s} \)
c. \( \frac{2 s}{m v^{2}} \)
D. \( \frac{m s^{2}}{2 v} \)
Subject: Chemistry
Choose the group showing position isomerism:
(b)
\( (c) C H_{2}=C H-C H_{2} O H \)
(d)
\( (\mathbf{e}) \)
\( A \cdot b \) and \( e \)
B. b and c
\( \mathbf{C} \cdot \) a and \( d \)
D. \( a, b, c \) and \( e \)
Subject: Physics
The wavelength of radiation is \( \lambda_{0} \) When
an electron jumps from third to second orbit of hydrogen atom. For the electron to jump from the fourth to the second orbit of the hydrogen atom, the wavelength of radiation emitted will be
A \( \cdot \frac{16}{25} \lambda_{0} \)
в. \( \frac{20}{27} \lambda_{0} \)
c. \( \frac{27}{20} \lambda_{0} \)
D. \( \frac{25}{16} \lambda_{0} \)
Subject: Chemistry
(i) With reference to structural
variability and chemical reactivity, write the difference between
lanthanoids and actinoids.
(ii) Name a member of the lanthanoid series which is well known to exhibit +4 oxidation state
(iii) Complete the following equation:
\[
M n O_{4}^{-}+8 H^{+}+5 e^{-} \rightarrow
\]
(iv) Out of \( M n^{3+} \) and \( C r^{3+}, \) which is
more paramagnetic and why? (atomic number : \( M n=25, C r=24) \)
Subject: Maths
Draw quadrilateral ABCD with the following measurements. Also find its
area.
\( A B=6 \mathrm{cm}, \mathrm{BC}=6 \mathrm{cm}, \angle \mathrm{BAC}=50^{\circ}, \angle \)
\( A C D=30^{\circ} \) and \( \angle C A D=100^{\circ} \)
Subject: Maths
\( \frac{3 x-1}{\left(1-x+x^{2}\right)(2+x)}= \)
A \( \cdot \frac{x}{x^{2}-x+1}-\frac{1}{x+2} \)
в. \( \frac{x}{x^{2}-x+1}+\frac{1}{x+2} \)
c. \( \frac{x}{x^{2}+x+1}+\frac{2}{x+2} \)
D. \( \frac{x}{-x+1}-\frac{2}{x+2} \)
Subject: Physics
Choose the correct answer from the
alternatives given. A radio can tune to any station in 7.5 MHz to 12 MHz band. The corresponding wavelength band is
A. \( 40 \mathrm{m} \) to \( 25 \mathrm{m} \)
B. 30 m to 25 \( \mathrm{m} \)
\( c .25 \mathrm{m} \) to \( 10 \mathrm{m} \)
D. \( 10 \mathrm{m} \) to \( 5 \mathrm{m} \)
Subject: Maths
Let \( A \) and \( B \) be two sets such that \( A \times \)
\( \boldsymbol{B}= \)
\( \{(a, 1),(b, 3),(a, 3),(b, 1),(a, 2),(b, 2) \)
then
A \( \cdot A=\{1,2,3\} \) and \( B=\{a, b\} \)
B . \( A=\{a, b\} \) and \( B=\{1,2,3\} \)
\( \mathbf{c} \cdot A=\{1,2,3\} \) and \( B \subset\{a, b\} \)
D. \( A \subset\{a, b\} \) and \( B \subset\{1,2,3\} \)
Subject: Physics
In Young's double-slit experiment, the
separation between the slits is \( \boldsymbol{d} \) distance between the slit and screen is
\( D(D>>d) . \) In the interference pattern,
there is a maxima exactly in front of
each slit. Then the possible wavelength(s) used in the experiment
are
A \( \cdot d^{2} / D, d^{2} / 2 D, d^{2} / 3 D \)
B . \( d^{2} / D, d^{2} / 3 D, d^{2} / 5 D \)
C . \( d^{2} / 2 D, d^{2} / 4 D, d^{2} / 6 D \)
D. none of these
Subject: Chemistry
Which among the following compounds will not give effervescence with sodium bicarbonate?
A. \( C_{6} H_{5} C O_{2} H \)
в. \( C_{6} H_{5} S O_{3} H \)
\( \mathbf{c} \cdot C_{6} H_{5} O H \)
D. \( C_{6} H_{3} N_{3} O_{7} \)
Subject: Physics
Latent heat of vaporization of water is 538 cal/g. During the conversion of 1 g of water to steam, if the external work
done is \( 168 \mathrm{J} \), the increase in internal
energy is:
A . 638 call \( l \)
B. 538 саг \( l \)
c. 498 call \( l \)
D. 80 cal
Subject: Chemistry
Match column I with column II and
mark the appropriate choice.
Column I
(A) Pentise sugar in DNA
(i) Ascorbic acid
(B) Nucleic acid
(ii) Uracil
(C) RNA
(iii) Genetic material
(D) Vitamin
(iv) Furanose structure
\( \mathbf{A} \cdot(A) \rightarrow(i v) ;(B) \rightarrow(i i i) ;(C) \rightarrow(i i) ;(D) \rightarrow(i) \)
B. (A) \( \rightarrow \) (iii); (B) \( \rightarrow \) (ii); \( (C) \rightarrow(\text { iv ); }(D) \rightarrow \) (i)
C. \( (A) \rightarrow(\text { ii) } ;(B) \rightarrow(\text { iii) } ;(C) \rightarrow(i v) ;(D) \rightarrow(i) \)
\( D \cdot(A) \rightarrow(i) ;(B) \rightarrow(i i) ;(C) \rightarrow(i i i) ;(D) \rightarrow(i v) \)
Subject: Physics
Potential gradient along AB is
\( \mathbf{A} \cdot 1 / 5 \mathrm{Vm}^{-1} \)
B. 2/5 Vm \( ^{-1} \)
c. \( 3 / 5 \mathrm{Vm}^{-1} \)
D. \( 4 / 5 \mathrm{Vm}^{-1} \)
Subject: Chemistry
IUPAC name of \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H}- \)
\( \mathcal{H}_{2} O H \)
\( \boldsymbol{C H}_{2} \boldsymbol{C H}_{3} \) is:
A. 3-propylbutan-1-ol
B. 2-Ethylpentan-1- 이
c. 3- methyl hydroxyhexane
D. 2- ethyl-2 - propyl ethanol
Subject: Physics
Vectors \( \bar{A} \) and \( \bar{B} \) are equal in
magnitude. The magnitude of \( \bar{A}+\bar{B} \) is larger than the magnitude of \( \overline{\boldsymbol{A}}-\overline{\boldsymbol{B}} \) by
a factor of \( n, \) then the angle between them is
A \( \cdot 2 \tan ^{-1}(1 / n) \)
B. \( \tan ^{-1}(1 / n) \)
c. \( \tan ^{-1}(1 / 2 n) \)
D. \( 2 \tan ^{-1}(1 / 2 n) \)
Subject: Chemistry
The oxoacid of sulphur that does not contain bond between sulphur atoms is:
A \( \cdot H_{2} S_{4} O_{6} \)
в. \( H_{2} S_{2} O_{7} \)
c. \( H_{2} S_{2} O_{3} \)
D. \( H_{2} S_{2} O_{4} \)
Subject: Chemistry
Which of the following statement is
correct?
A. Sigma bond is weaker than pie-bond
B. \( H F \) is less polar than \( H I \)
\( \mathrm{C} \cdot \ln N H_{4}^{+} \) ions 4 coordinate bond is present
D. \( \ln S F_{6} \) all \( S-F \) bond length are same
Subject: Maths
If \( \boldsymbol{A}=\int_{1}^{\sin \theta} \frac{\boldsymbol{t}}{1+\boldsymbol{t}^{2}} \boldsymbol{d} \boldsymbol{t} \) and
\( B=\int_{1}^{\operatorname{cosec} \theta} \frac{1}{t\left(1+t^{2}\right)} d t, \) then the value
of determinant \( \left|\begin{array}{ccc}\boldsymbol{A} & \boldsymbol{A}^{2} & \boldsymbol{B} \\ \boldsymbol{e}^{\boldsymbol{A}+\boldsymbol{B}} & \boldsymbol{B}^{2} & -\mathbf{1} \\ \mathbf{1} & \boldsymbol{A}^{2}+\boldsymbol{B}^{2} & -\mathbf{1}\end{array}\right| \)
is
\( A \cdot \sin \theta \)
B. \( \operatorname{cosec} \theta \)
\( c \)
D.
Subject: Maths
Arrange the following limits in the ascending order:
(1) \( \lim _{x \rightarrow \infty}\left(\frac{1+x}{2+x}\right)^{x+2} \)
(2) \( \lim _{x \rightarrow 0}(1+2 x)^{3 / x} \)
(3) \( \lim _{\boldsymbol{\theta} \rightarrow \mathbf{0}} \frac{\sin \boldsymbol{\theta}}{\mathbf{2} \boldsymbol{\theta}} \)
(4) \( \lim _{x \rightarrow 0} \frac{\log _{e}(1+x)}{x} \)
A. 1,2,3,4
B. 1,3,4,2
c. 1,4,3,2
D. 3,4,1,2
Subject: Maths
\( f f(x)=\left|\begin{array}{ccc}x & \cos x & e^{|x|} \\ \sin x & x^{2} & \sec x \\ \tan x & 1 & 2\end{array}\right| \) then the
value of \( \int_{-\pi / 2}^{\pi / 2} f(x) d x \) is equal to
Subject: Chemistry
The product(s) formed when \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) reacts with disodium hydrogen phosphate is:
A \( \cdot P_{2} O_{5}, N a_{3} P O_{4} \)
в. \( N a_{2} H P O_{4} \cdot H_{2} O_{2} \)
c. \( N a H_{2} P O_{4} \cdot H_{2} O \)
D. \( N a_{2} H P O_{4} \cdot H_{2} O \)
Subject: Physics
If the energy, \( E=G^{p} h^{q} c^{r}, \) where \( G \) is the
universal gravitational constant, h is the Planck's constant and c is the
velocity of light, then the values of \( p, q \) and \( r \) are, respectively
A \( \cdot-1 / 2,1 / 2 \) and \( 5 / 2 \)
B. \( 1 / 2,-1 / 2 \) and \( -5 / 2 \)
c. \( -1 / 2,1 / 2 \) and \( 3 / 2 \)
D. \( 1 / 2,-1 / 2 \) and \( -3 / 2 \)
Subject: Maths
Let \( [t] \) denote the greatest integer \( \leq t \) and \( \lim _{x \rightarrow 0} x\left[\frac{4}{x}\right]=A . \) Then the function,
\( f(x)=\left[x^{2}\right] \sin (\pi x) \) is discontinuous,
when \( x \) is equal to:
\( A \cdot \sqrt{A} \)
B. \( \sqrt{A+1} \)
c. \( \sqrt{A+5} \)
D. \( \sqrt{A+21} \)
Subject: Physics
The figure shows a potentiometer
arrangement. D is the driving cell. C is
the cell whose emf is to be determined.
AB is the potentiometer wire and \( G \) is a
galvanometer.J is a sliding contact
which can touch any point on AB. Which
of the following are essential conditions
for obtaining balance?
This question has multiple correct options
A. The emf of D must be greater than the emf of \( C \).
B. Either the positive terminals of both D and C or the negative terminals of both \( D \) and \( C \) must be joined to
\( A \)
C. The positive terminals of D and C must be joined to A.
D. The resistance of G must be less than the resistance of
\( A B \)
Subject: Physics
A vessel of volume \( V \) contains \( n_{1} \) moles
of oxygen and \( n_{2} \) moles of carbon dioxide
at absolute temperature T. The pressure of the mixture is
A. \( \frac{\left(n_{1}+n_{2}\right) R T}{V} \)
В. \( \frac{\left(n_{1}-n_{2}\right) R T}{V} \)
c. \( \frac{n_{1} n_{2} R T}{V} \)
D. \( \frac{n_{1} R T}{n_{2} V} \)
Subject: Chemistry
The vapour pressures of two liquids \( A \)
and B in their pure states are in the ratio of \( 1: 2 . \) A binary solution of \( A \) and \( B \)
contains \( A \) and \( B \) in the mole proportion of \( 1: 2 . \) The mole fraction of \( A \) in the
vapour phase of the solution will be:
A . 0.33
B. 0.2
c. 0.25
D. 0.52
Subject: Chemistry
What should be the density of an aqueous solution of urea
\( (\text {molarmass}=\mathbf{6 0} \boldsymbol{g} / \text { mol}) \) such that
the molarity and molarity of the solution become equal?
A. \( 16.0 g / m l \)
в. \( 1.6 g / m l \)
c. \( 1.06 g / m l \)
D. \( 1.16 g / m l \)
Subject: Chemistry
HA is a weak electrolyte. At \( 25^{0} C \), the degree of dissociation of 0.5 mol \( L^{-1} \) HA is 0.1. What is its molar conductivity ( in \( \left.\boldsymbol{S} \boldsymbol{c m}^{2} \boldsymbol{m o l}^{-1}\right) ? \)
(The limiting molar conductivity of HA is \( 390 S c m^{2} m o l^{-1} \) )
A . 39
в. 195
\( c \cdot 3.9 \)
D. 390
Subject: Maths
When proving that a triangle is a right triangle using coordinate geometry
methods you must
A. show that the slopes of two of the sides are negative reciprocals creating perpendicular lines and right angles
B. show that the lengths of the sides satisfy the Pythagorean Theorem thus creating a right angle
C. both choices 1 and 2 may be used
D. neither choice 1 nor 2 may be used
E. none of these
Subject: Maths
The value of \( 2 \tan ^{-1}(-2) \) is equal to
This question has multiple correct options
\( ^{\mathbf{A}} \cdot \sin ^{-1}\left(-\frac{4}{5}\right) \)
B. \( -\sin ^{-1}\left(\frac{4}{5}\right) \)
\( \mathbf{C} \cdot \sin ^{-1}\left(\frac{4}{5}\right)-\pi \)
D \( -\cos ^{-1}\left(\frac{4}{5}\right)-\frac{\pi}{2} \)
Subject: Chemistry
Which of the following oxoacids of nitrogen has most acidic character?
I. \( N_{2} O_{3} \)
\( \boldsymbol{I} \boldsymbol{I} \cdot \boldsymbol{N} \boldsymbol{O}_{2} \)
III. \( N_{2} O_{5} \)
\( I V . N O \)
\( \mathbf{A} \cdot I I \)
в. \( I I I \)
\( c . I V \)
\( D \)
Subject: Physics
A photon of frequency n causes photoelectric emission from a surface
with threshold frequency \( v_{o} \). the de
Broglie wavelength \( \lambda \) of the photoelectron emitted is given as:
A \( \cdot \Delta n=\frac{h}{2 m \lambda} \)
B. \( \Delta n=\frac{h}{\lambda} \)
\( ^{\mathrm{C}}\left[\frac{1}{v_{o}}-\frac{1}{v}\right]=\frac{m c^{2}}{h} \)
D. \( \lambda=\sqrt{\frac{h}{2 m \Delta n}} \)
Subject: Physics
The twisting couple per unit twist for a
solid cylinder of radius \( 4.9 \mathrm{cm} \) is \( 0.1 N / m . \) The twisting couple per unit twist for a hollow cylinder of same material with outer and inner radii of
\( 5 \mathrm{cm} \) and \( 4 \mathrm{cm} \) respectively, will be
A. \( 0.64 N / m \)
В. \( 0.64 \times 10^{-1} N / m \)
c. \( 0.64 \times 10^{-2} N / m \)
D. \( 0.64 \times 10^{-3} N / m \)
Subject: Physics
Find the maximum velocity with which
a train can be moved on a circular track
of radius \( 200 m . \) The banking of the
track is \( 5.71^{\circ}\left(\text { given, } \tan 5.71^{\circ}=0.1\right) \)
A \( .1 .4 m / s \)
в. \( 14 \mathrm{m} / \mathrm{s} \)
c. \( 140 m / s \)
D. \( 0.14 m / s \)
Subject: Physics
Let \( A_{n} \) be the area enclosed by the \( n^{t h} \) orbit in a hydrogen atom. The graph of
\( \ln \left(A_{n} / A_{l}\right) \) against \( \ln (n) \)
This question has multiple correct options
A. Will pass through origin
B. Will be a straight line with slope 4
c. will be monotonically increasing nonlinear curve
D. will be circle
Subject: Physics
Sea water of density \( 1300 k g m^{-3} \) exerts a pressure of \( 104 \times 10^{5} P a \) on the floor.
Calculate the depth of the sea at that place \( \left(\boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-2}\right) \)
Subject: Chemistry
Given that:
\( \mathbf{2} C(s)+\mathbf{2} O_{2}(\boldsymbol{g}) \longrightarrow \mathbf{2} \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -787 k J \ldots(i) \)
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{H}_{2} \boldsymbol{O}(l) ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -286 k J \ldots(i i) \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{5}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{2} \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( \mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \ldots . \)
\( \Delta H=-1301 k J \)
Heat formation of acetylene is:
B . \( +1802 k J \)
c \( .-800 k J \)
\( \mathbf{D} \cdot+228 k J \)
Subject: Physics
(a) In Young's double slit experiment, derive the condition for
(i) constructive interference and
(ii) destructive interference at a point
on the screen.
(b) \( A \) bream of light consisting of two
wavelengths, \( 800 n m \) and \( 600 n m \) is
used to obtain the interference fringes in a Young's double slit experiment on a screen placed \( 1.4 m \) away. If the two
slits are separated by \( 0.28 n m \) calculate the least distance from the
central bright maximum where the bright fringes of the two wavelengths coincide.
Subject: Physics
A steam of water flowing horizontally
with a speed of \( 25 m s^{-1} \) gushes out of a
tube of cross-sectional area \( 10^{-3} m^{2} \)
and hits at a vertical wall nearby. What is the force exerted on the wall by the impact of water?
A . \( 125 N \)
в. 625 N
c. \( -650 N \)
D. \( -1125 N \)
Subject: Chemistry
A reaction takes place in three steps with an individual rate constant and
activation energy, as given below.
Rate constant Activation
energy
Step 1 \( \quad \boldsymbol{k}_{\mathbf{1}} \quad \boldsymbol{E}_{\boldsymbol{a}_{1}}= \)
\( 180 k J / m o l \)
Step 2 \( \quad \boldsymbol{k}_{2} \quad \boldsymbol{E}_{\boldsymbol{a}_{2}}= \)
\( \mathbf{8 0 k J} / \) mol
Step 3 \( \quad k_{3} \quad \quad E_{a_{3}}= \)
\( \mathbf{5 0 k J / m o l} \)
And overall rate constant, \( k= \) \( \left(\frac{k_{1} k_{2}}{k_{3}}\right)^{2 / 3} \)
The overall activation energy of the reaction will be:
A. \( 140 k J / \) mol
в. \( 150 k J / m o l \)
c. \( 130 k J / m o l \)
D. \( 120 k J / m o l \)
Subject: Chemistry
The major product formed when \( 2- \)
butene is reacted with \( O_{3} \) followed by
treatment with \( Z n / H_{2} O \) is
A. \( C H_{3} \) СООН
в. \( C H_{3} C H O \)
c. \( C H_{3} C H_{2} O H \)
D. \( C H_{2}=C H_{2} \)
Subject: Chemistry
Assertion
\( \boldsymbol{H}_{2} \boldsymbol{O} \) is the only hydride of group -16 which is liquid at ordinary temperature.
Reason

In ice, each oxygen atom is surrounded by two convalent bonds and two
hydrogen bonding.
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 electric field in the region \( b>r>a \)
is \( \boldsymbol{E}=\frac{\boldsymbol{Y}}{\boldsymbol{4} \boldsymbol{\pi} \varepsilon_{0}} \frac{\boldsymbol{Q}}{\boldsymbol{r}^{2}} . \) Find \( \boldsymbol{Y} ? \)
Subject: Physics
A thin lens has focal length \( f \), and its
aperture has diameter \( d \). If the central
part of the aperture, of diameter \( \boldsymbol{d} / \mathbf{2} \) is blocked by an opaque paper, the focal length of the lens and the intensity of image will become:
A \( \cdot \frac{f}{2}, \frac{1}{2} \)
в. \( _{f}, \frac{I}{4} \)
c. \( \frac{3 f}{4}, \frac{I}{2} \)
D. \( _{f, \frac{3 I}{4}} \)
Subject: Maths
The statement form \( (\boldsymbol{p} \Leftrightarrow \boldsymbol{r}) \Rightarrow(\boldsymbol{q} \Leftrightarrow \boldsymbol{r}) \)
is equivalent to
\( \mathbf{A} \cdot[(\sim p \vee r) \wedge(p \vee \sim r)] \vee \sim[(\sim q \vee r) \wedge(q \vee \sim r)] \)
\( \mathbf{B} \cdot \sim[(\sim p \vee r) \wedge(p \vee \sim r)] \wedge[(\sim q \vee r) \vee(q \vee \sim r)] \)
\( \mathbf{c} \cdot[(\sim p \vee r) \wedge(\sim p \vee \sim r)] \wedge[(\sim q \vee r) \wedge(q \vee \sim r)] \)
\( \mathbf{D} \cdot \sim[(\sim p \vee r) \wedge(p \vee \sim r)] \wedge[(\sim q \vee r) \wedge(q \vee \sim r)] \)
Subject: Maths
\( \boldsymbol{f}: \boldsymbol{Q} \rightarrow \boldsymbol{Q} \) is defined by \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{1 5} \boldsymbol{x}+\mathbf{7} \)
is
A . injective only
B. surjective only
c. bijective
D. neither injective nor surjective
Subject: Physics
A body of mass \( 5 k g \) starts motion form the origin with an initial velocity \( \vec{u}= \) \( (30 \hat{i}+40 \hat{j}) m s^{-1} \) If a constant force \( \vec{F}=-(-\hat{6} i-5 \hat{j}) N \) acts on the body than the time in which the Y-component of the velocity becomes zero is
\( \mathbf{A} \cdot 5 s \)
в. \( 20 s \)
\( c .40 s \)
D. 80
Subject: Chemistry
\( 380 \mathrm{mL} \) of a gas at \( 27^{0} \mathrm{C}, 800 \mathrm{mm} \) of \( \mathrm{Hg} \)
weight
\( 0.455 \mathrm{g} . \) the mol.wt.of gas is:
A .27
B . 28
c. 29
D. 30
Subject: Physics
A train of length \( 200 \mathrm{m} \) traveling at a speed of \( 30 m s^{-1} \) overtakes another
train of length \( 300 \mathrm{m} \) traveling at a speed of \( 20 m s^{-1} \) in the same direction.
The time taken by the first train to pass the second train is:
A. 50 s
B. 10 s
c. \( 20 \mathrm{s} \)
D. 40