AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Which of the following alkyl halide is most reactive towards substitution on
reaction by \( S_{N} 1 \) mechanism?
\( \mathbf{A} \cdot\left(C H_{3}\right)_{3} C-B r \)
B \( \cdot\left(C H_{3}\right)_{2}-C H-B r \)
c. \( C H_{3}-B r \)
D. \( C H_{3}-C H_{2}-B r \)
Subject: Chemistry
Teritary alcohol is obtained as major
product in
\( \mathbf{A} \cdot\left(C H_{3}\right)_{2} C H-C H=C H_{2}^{\text {oxymercution/demercution}} \)
\( \mathbf{B} \cdot\left(C H_{3}\right)_{3} C-C H=C H_{2} \stackrel{d i l H_{2} S O_{4}}{\longrightarrow} \)
\( \mathbf{C} \cdot\left(C H_{3}\right)_{2} C H-C H=C H_{2}^{H y d r o b o r a t i o n, O x i d a t i o n} \)
D. All of the above
Subject: Physics
If the earth has no rotational motion, the
weight of a person on the equator is \( W \)
Determine the speed with which the earth would have to rotate about its
axis so that the person at the equator will weight \( \frac{3}{4} W . \) Radius of the earth is \( 6400 k m \) and \( g=10 m / s^{2} \)
Subject: Maths
The value of \( \sin 75^{\circ}= \)
\( ^{A} \cdot \frac{2-\sqrt{3}}{\sqrt{2}} \)
в. \( \frac{\sqrt{3}+1}{2 \sqrt{2}} \)
c. \( \frac{\sqrt{3}-1}{2 \sqrt{2}} \)
D. \( \frac{\sqrt{3}+1}{\sqrt{2}} \)
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}^{2}+\mathbf{2}}{[\boldsymbol{x}]}, \mathbf{1} \leq \boldsymbol{x} \leq \mathbf{3}, \) where [
represents greatest integer function,
then
A \( . f(x) \) is increasing in [1,3]
B. Least value of \( f(x) \) is 3
c. Greatest value of \( f(x) \) is \( \frac{11}{2} \)
D. \( f(x) \) has no greatest value
Subject: Biology
Assertion
Oxyhaemoglobin dissociates near the organ tissue due to Bohr effect and
oxygen is released.
Reason
Increased \( \mathrm{CO}_{2} \) concentration reduces
the affinity of haemoglobin for oxygen.
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
\( \int 5^{m x} 7^{n x} d x, m, n \in N \) is equal to
This question has multiple correct options
\( \mathbf{A} \cdot \frac{5^{m x}+7^{n x}}{m \log 5+n \log 7}+K \)
B. \( \frac{e^{(m \log 5+n \log 7) x}}{\log 5^{m}+\log 7^{n}}+K \)
C \( \cdot \frac{(m \cdot n) 5^{m x}+7^{n x}}{m \log 5+n \log 7}+K \)
D. None of these
Subject: Physics
Identify the correct ascending order of \( \boldsymbol{\alpha}, \boldsymbol{\beta} \) and \( \gamma \) with reference to their
ionizing power:
I) \( \alpha \) -ray
II) \( \gamma \) -ray III) \( \beta \) -ray
A . "।,॥,।,
в. ।,॥।,
c. ॥,।,॥|
D. I,II,II
Subject: Chemistry
Calculate the wavelength of photon
associated with an energy of 1 electron volt.
A . \( 19.875 \times 10^{-17} \mathrm{cm} \)
в. \( 1.24 \times 10^{-5} \mathrm{cm} \)
c. \( 12.41 \times 10^{-5} \mathrm{cm} \)
D. \( 20.11 \times 10^{-5} \mathrm{cm} \)
Subject: Chemistry
An aromatic hydrocarbon has the
molecular formula \( C_{10} H_{14} . \) Upon
oxidation with boiling alkaline \( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} \)
followed by acidification, it yields benzene dicarboxylic acid. The total
isomers for \( C_{10} H_{14} \) are:
\( \mathbf{A} \cdot \mathbf{9} \)
B. 8
\( c \cdot 7 \)
D. 6
Subject: Physics
A step-up transformer works on \( 220 \mathrm{V} \) and gives 2 A to an external resistor. The
ratio of the number of turns between the
primary and secondary coils is 2: 25 Assuming \( 100 \% \) efficiency, find the secondary voltage, primary current and power delivered
A . 2750 \( \vee, \) 25 \( A, 5500 W \)
B. 2750 V, 20 A, 5000 W
c. 2570 V, 25 A, 550
D. 2750 V, 20 A, 55 W
Subject: Maths
Prove that
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\cot \boldsymbol{h}^{-1} \boldsymbol{x}\right)=\frac{-\mathbf{1}}{\left(\boldsymbol{x}^{2}-\mathbf{1}\right)} \)
Subject: Chemistry
Assertion
Al obtained only by electrolytic reduction of Alumina (pure)
Reason
Aluminium metal has a strong affinity
for oxygen and the oxide of \( \mathrm{Al} \) is \( A l_{2} O_{3} \)
which is a very stable oxide. Hence ordinary chemically reducing agents
are not sufficient to reduce \( A l_{2} O_{3} \) to \( A l \)
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
Discuss the continuity and differentiability of the function, \( \boldsymbol{f}(\boldsymbol{x})=\left[\begin{array}{cc}\frac{\boldsymbol{x}}{\mathbf{1}+|\boldsymbol{x}|} & |\boldsymbol{x}|>\mathbf{1} \\ \frac{\boldsymbol{x}}{\mathbf{1}-|\boldsymbol{x}|} & |\boldsymbol{x}| \leq \mathbf{1}\end{array}\right] \)
Subject: Chemistry
Use of the Data Booklet is relevant to
this question. The gas laws can be summarised in the ideal gas equation below. \( \boldsymbol{p} \boldsymbol{V}=\boldsymbol{n} \boldsymbol{R} \boldsymbol{T} \)
The volume of a sample of methane is
measured at a temperature of \( 60^{\circ} \mathrm{C} \) and a pressure of \( 103 k \) Pa. The volume
measured is \( 5.37 \times 10^{-3} m^{3} \)
Assume the gas behaves as an ideal
gas. What is the mass of the sample of methane, given to two significant figures?
A. \( 0.00018 g \)
в. \( 0.0032 g \)
\( c \cdot 0.18 g \)
D. 3.29
Subject: Physics
The susceptibility of a paramagnetic substance was found for different
temperatures and a graph of \( \chi \) against
\( \frac{1}{T} \) was plotted. From the graph, it was
found that what \( \chi=0.5, \frac{1}{T}=5 \times \)
\( 10^{-3} / K . \) What is the curie constant for
the substance?
A. \( 50 k \)
B. 75 K
c. \( 100 \mathrm{k} \)
D. 125 K
Subject: Physics
A double convex lens of focal length \( 30 c m \) is made of glass of R.I. \( 1.6 . \) When it is immersed in a liquid, the focal length is found to be \( 90 \mathrm{cm} \).The R.I. of the liquid is
A . 1.33
в. 1.5
c. 1.4
D. 1.42
Subject: Maths
A curve passes through the point \( (2 a, a) \) and is such that sum of subtangent and abscissa is equal to a. Its equation is
A \( \cdot(x-a) y^{2}=a^{3} \)
в. \( (x-a)^{2} y=a^{3} \)
c. \( (x-a) y=a^{2} \)
D. \( (x+a) y=a^{2} \)
Subject: Chemistry
If we take \( 44 \mathrm{g} \) of \( C O_{2} \) and \( 14 \mathrm{g} \) of \( N_{2} \)
what will be the mole fraction of \( C O_{2} \) in
the mixture?
A . \( 1 / 5 \)
в. \( 1 / 3 \)
c. \( 2 / 3 \)
D. \( 1 / 4 \)
Subject: Chemistry
Greenhouse gas \( C O_{2} \) can be converted
to \( C O(g) \) by the following reaction
\( \boldsymbol{C O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \)
termed as water gas reaction.
\( \Delta G \) for the reaction at \( 1000 \mathrm{K} \) is :
\( \left(\Delta H_{1000} K=\right. \)
\( \mathbf{3 5 0 4 0} \boldsymbol{J} \boldsymbol{m o l}^{-1} ; \boldsymbol{\Delta} \boldsymbol{S}_{1000} \boldsymbol{K}= \)
\( \left.32.11 J m o l^{-1} K^{-1}\right) \)
A. \( 2930 J \)
\( J \)
B. 2934 J
c. \( 2300 J \)
D. None of these
Subject: Maths
The number of distinct real roots of \( \left|\begin{array}{lll}\sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & \cos x & \sin x\end{array}\right|=0 \) in the
nterval \( -\frac{\pi}{4}<x \leq \frac{\pi}{4} \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. 2
c. 1
\( D \cdot>2 \)
Subject: Physics
The energy of an electron of mass \( m \) moving with velocity \( \mathrm{V} \) and de-Broglie wavelength \( \lambda \) is ('h' is
Planck's constant)
A \( \cdot \frac{h}{2 m \lambda} \)
в. \( \frac{h^{2}}{2 m \lambda^{2}} \)
c. \( \frac{h \lambda}{2 m} \)
D. \( \frac{h}{m \lambda} \)
Subject: Physics
Two identical 5 kg blocks are moving with same speed of \( 2 m / s \) towards each other along a friction-less horizontal
surface. The two blocks collide, stick
together and come to rest. Consider two
blocks as a system, the work done on
the system by the external forces will
be:
A . 20 Joule
B . -20 Joule
c. 0 Joule
D. None of these
Subject: Physics
The observation deck of tall skyscraper \( 370 m \) above the street. Determine the
time required for a penny to free fall from the deck to the street below
\( \mathbf{A} \cdot 8.69 s \)
B. \( 7.69 s \)
\( c .5 .69 \)
D. \( 8.6 s \)
Subject: Chemistry
A \( 5.25 \% \) solution of a substance is isotonic with a \( 1.5 \% \) solution of urea
(molar mass \( =60 g \) mol \( ^{-1} \) ) in the same
solvent. If the densities of both the
solutions are assumed to be equal to
\( 1.0 g c m^{-3}, \) molar mass of the substance will be:
в. \( 90.0 g \) mol\( ^{-1} \)
c. \( 115.0 g \) mol \( ^{-1} \)
D. \( 105.0 g \) mol \( ^{-1} \)
Subject: Physics
A ring shaped tube contains two ideal
gases with equal masses and molar
masses \( M_{1}=32 \) and \( M_{2}=28 . \) The
gases are separated by one fixed partition \( P \) and another movable
stopper \( S \) which can move freely
without friction inside the ring. The
angle \( \alpha \) is
\( \mathbf{A} \cdot 182^{\circ} \)
B \( .170^{\circ} \)
\( c \cdot 192^{\circ} \)
D. \( 180^{\circ} \)
Subject: Maths
In fig. ABCD is a parallelogram. What
are the values of \( p \) and \( q ? \)
If \( \angle C B E=100^{\circ} \)
\( \mathbf{A} \cdot \angle p=100^{\circ}, \angle q=80^{\circ} \)
B . \( \angle p=80^{\circ}, \angle q=100^{\circ} \)
c. \( \angle p=\angle q \)
D. None
Subject: Physics
A cricket ball of mass \( 500 \mathrm{g} \) is moving with a speed of \( 36 \mathrm{km} h^{-1} . \) It is reflected
with the same speed. What is the impulse applied on it?
A. 20 kg m \( s^{-1} \)
B. \( 5 \mathrm{kg} \mathrm{m} s^{-1} \)
C. \( 25 \mathrm{kg} \mathrm{m} s^{-1} \)
D. \( 10 \mathrm{kg} \mathrm{m} s^{-1} \)
Subject: Maths
If \( \tan \theta+\tan 2 \theta+\tan \theta \tan 2 \theta=1 \) then
general value of \( \boldsymbol{\theta} \) is
\( \mathbf{A} \cdot n \pi ; n \in I \)
в. \( n \pi \pm \frac{\pi}{3} ; n \in I \)
c. \( \frac{n \pi}{3}+\frac{\pi}{12}, n \in I \)
D. None of these
Subject: Maths
If \( a, b, c, d \) are positive real numbers such that \( a+b+c+d=2 \) then \( M= \)
\( (a+b)(c+d) \) satisfies the relation
A. \( 0<M \leq 1 \)
в. \( 1 \leq M \leq 2 \)
c. \( 2 \leq M \leq 3 \)
D. \( 3 \leq M \leq 4 \)
Subject: Physics
A particle of mass \( 0.1 \mathrm{kg} \) moving with an initial speed v collides with another
particle of same mass kept at rest. If after collision the total energy becomes \( 0.2 \mathrm{J}, \) then:
A. minimum value of v is \( 2 \mathrm{m} / \mathrm{s} \)
B. maximum value v is 4 \( \mathrm{m} / \mathrm{s} \)
c. minimum value v is 3 \( \mathrm{m} / \mathrm{s} \)
D. maximum value of v is \( 6 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
Which of the following is pseudounimolecular reaction?
A. \( 2 H_{2} O_{2} \rightarrow 2 H_{2} O+O_{2} \)
в. \( C_{6} H_{5} N_{2} C l+H O H \longrightarrow C_{6} H_{5} O H+N_{2}+H C l \)
c. \( C H_{3} C O O C_{2} H_{5}+N a O H \rightarrow C H_{3} C O O N a+ \)
\( C_{2} H_{5} O H \)
D. \( 20_{3} \rightarrow 30_{2} \)
Subject: Physics
The work function of a metal surface is 1
eV. A light of wavelength \( 3000 A^{0} \) is incident on it. The maximum velocity of the photo-electrons is nearly
\( \mathbf{A} \cdot 10^{6} m s^{-1} \)
B . \( 10^{4} m s^{-1} \)
c. \( 10^{2} m s^{-1} \)
D. \( 10 m s^{-1} \)
Subject: Chemistry
Which of the following statements
is/are correct?
This question has multiple correct options
A. Extractive metallurgy of iron involves reduction by carbon monoxide and carbon.
B. Extraction of zinc from ore sphalerite involves the roasting and carbon reduction.
C. Tin contain magnetic impurity of \( \mathrm{Fe} \mathrm{Cr} \mathrm{O}_{4} \)
D. Cuprite and argentite are oxide ores.
E. Bauxite is concentrated by leaching process.
F. Electrometallurgy is preferred method for extraction of highly reactive metals.
Subject: Maths
The airthmatic mean of \( 1+\sqrt{2} \) and \( \mathbf{7}+\mathbf{5} \sqrt{\mathbf{2}} \) is \( \sqrt{\boldsymbol{a}}+\sqrt{\boldsymbol{b}} . \) Then \( \mathbf{a}-\boldsymbol{b}= \)
\( A \cdot-1 \)
в.
\( c \cdot 2 \)
\( D \cdot-2 \)
Subject: Chemistry
Identify \( (X),(Y) \) and \( (Z) \) in the given
reaction. \( \boldsymbol{X}+\boldsymbol{Y} \stackrel{Z}{\longrightarrow} \boldsymbol{C} \boldsymbol{H}_{3}-\stackrel{\boldsymbol{C} \boldsymbol{H}}{\boldsymbol{3}-\boldsymbol{H} \boldsymbol{y} d r o x y} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}_{2}- \)
\( C H O \)
A \( \cdot X=H C H O Y=C H_{3} C H O Z=K O H \)
В . \( X=C H_{3} C H O Y=C H_{3} C H O Z=N a O H \)
c. \( X=C H_{3} C H_{2} \) OH \( Y=H C H O Z=H_{2} S O_{4} \)
D. \( X=C H_{3} C H_{2} C H O Y=H C H O Z= \)Dryether
Subject: Physics
The length of air column in a capillary glass tube closed at one end containing mercury pellet \( 10 \mathrm{cm} \) long are \( 43 \mathrm{cm} \) and \( 33 \mathrm{cm} \) respectively with the closed end up and down. The atmospheric
pressure is :
A. \( 75 \mathrm{cm} \) of \( \mathrm{Hg} \)
B. 76 \( \mathrm{cm} \) of \( \mathrm{Hg} \)
c. \( 70 \mathrm{cm} \) of \( \mathrm{Hg} \)
D. \( 100 \mathrm{cm} \) of \( \mathrm{Hg} \)
Subject: Physics
A rod of length of \( 1 \mathrm{m} \) is attached to the
string at its mid point. A 6 kg mass is attached to end of the rod and another
mass \( \mathrm{M} \) is hung at a distance of \( 30 \mathrm{cm} \)
from the center of the rod as shown in
the figure. Assume mass of rod is negligible. Find out the value of \( \mathrm{M} \).
\( A \cdot 3 \mathrm{kg} \)
B. \( 5 \mathrm{kg} \)
\( c \cdot 6 \mathrm{kg} \)
D. \( 10 \mathrm{kg} \)
E. 30 kg
Subject: Chemistry
The mass in grams of a single chlorine
atom and of a single molecule of \( \boldsymbol{O}_{2} \) is :
A \( \cdot 5.89 \times 10^{-23} g / \) atom \( , 5.31 \times 10^{-23} g / \) molecule
в. \( 8.81 \times 10^{-23} g / \) atom \( , 4.31 \times 10^{-23} g / \) molecule
C. \( 5.81 \times 10^{-25} g / \) atom, \( 5.31 \times 10^{-25} g / \) molecule
D. None of the above
Subject: Chemistry
A negatively charged particle called Negatron was discovered. In the Millikan's oil-drop experiment, the charges of the oil-drops in five experiments are reported as \( 3.2 \times \)
\( 10^{-19} \) coulomb; \( 4.8 \times 10^{-19} \) coulomb
\( 6.4 \times 10^{-19} \) coulomb
Subject: Chemistry
Predict the geometrical shapes of the following molecules and then predict which molecules you would expect to have resultant dipole moments (also refer to sec-dipole moments):
(a) \( \boldsymbol{S O}_{2} \)
(b) \( \boldsymbol{N} \boldsymbol{H}_{\mathbf{3}} \)
(c) \( \boldsymbol{H}_{2} \boldsymbol{S} \)
\( (d) C_{2} H_{4} \)
\( (e) S F_{6} \)
(f) \( C H_{2} C l_{2} \)
Subject: Chemistry
\( \begin{array}{ll}\begin{array}{l}\text { List - I } \\ \text { (Compound) }\end{array} & \begin{array}{l}\text { List - II } \\ \text { (Oxidation no of sulphur) }\end{array} \\ \text { A) } H_{2} S_{2} O_{8} & \text { 1) }+1 \\ \text { B) } H_{2} S & \text { 2) }+2 \\ \text { C) } N a_{2} S O_{3} & \text { 3) }+6 \\ \text { D) } S_{2} C l_{2} & \text { 4) }+4 \\ \text { 5) }-2\end{array} \)
\( \mathbf{A} \)
\( A-3 . B-5 . C-4 . D-2 \)
\( \mathrm{B} \cdot \mathrm{A}-3, \mathrm{B}-5, \mathrm{C}-4, \mathrm{D}-1 \)
\( \mathrm{C} \cdot \mathrm{A}-6, \mathrm{B}-5, \mathrm{C}-4, \mathrm{D}-2 \)
\( D \cdot A-6, B-4, C-5, D-1 \)
Subject: Physics
Preeti reached the metro station and
found that the escalator was not
working. She walked up the stationary
escalator in time \( t_{1} . \) On other days, if
she remains stationary on the moving
escalator, then the escalator takes her
up in time \( t_{2} . \) The time taken by her
walk up on the moving escalator will be:
\( \mathbf{A} \cdot t_{1}-t_{2} \)
B. \( \frac{t_{1}+t_{2}}{2} \)
\( \mathbf{C} \cdot \frac{t_{1} t_{2}}{t_{2}-t_{1}} \)
D. \( \frac{t_{1} t_{2}}{t_{2}+t_{1}} \)
Subject: Maths
f maximum and minimum values of \( \boldsymbol{D}=\left|\begin{array}{ccc}\mathbf{1} & -\cos \boldsymbol{\theta} & \mathbf{1} \\ \cos \boldsymbol{\theta} & \mathbf{1} & -\cos \boldsymbol{\theta} \\ \mathbf{1} & \cos \boldsymbol{\theta} & \mathbf{1}\end{array}\right| \) are \( p \) and
respectively, then the value of \( 2 p+3 q \)
is
A . 16
B. 6
\( c .14 \)
\( D \)
Subject: Maths
Let \( y \) be an element of the \( \operatorname{set} A= \)
\{1,2,3,5,6,10,15,30\} and \( x_{1}, x_{2}, x_{3} \) be
integers such that \( x_{1} x_{2} x_{3}=y, \) then the
number of positive integral solutions of
\( \boldsymbol{x}_{1} \boldsymbol{x}_{2} \boldsymbol{x}_{3}=\boldsymbol{y} \) is
\( \mathbf{A} \cdot 64 \)
B . 27
c. 81
D. None of these
Subject: Physics
A potentiometer wire of length \( L \) and
resistance \( 10 \Omega \) is connected in series
with a battery of e.m.f. \( 2.5 \% \) and a
resistance in its primary circuit. The null point corresponding to a cell of
e.m.f. \( 1 V \) is obtained at a distance \( L / 2 \)
If the resistance in the primary circuit is doubled then the position of new null
point will be
\( \mathbf{A} \cdot 0.4 L \)
B. \( 0.5 L \)
c. \( 0.6 L \)
\( \mathbf{D} \cdot 0.8 L \)
Subject: Physics
A triangular prism of glass is shown in
the figure. A ray incident normally to
one face is totally reflected. If \( \boldsymbol{\theta}=\mathbf{4 5}^{\mathbf{0}} \)
the refractive index of glass is :
\( A \cdot<1.4 \)
\( B \). \( =1.4 \)
\( \mathbf{c} .>1.41 \)
D. 1.732
Subject: Chemistry
Which of the following statement(s) is incorrect ?
A . lonisation energy \( \propto \frac{1}{\text { Screening effect }} \)
B. The first ionisation energies of Be and Mg are more than ionisation energies of B and Al respectively
c. Atomic and ionic radii of Niobium and Tantalum are almost same
D. Metallic and covalent radii of potassium are 2.03 , and 2.3 \( \dot{A} \) respectively
Subject: Chemistry
Which among the following will be
named as dibromidobis
(ethylenediamine) chromium(III) bromide?
\( \mathbf{A} \cdot\left[\operatorname{Cr}(e n)_{3}\right] B r_{3} \)
в. \( \left[\operatorname{Cr}(e n)_{2} B r_{2}\right] B r \)
c. \( \left.\operatorname{Cr}(e n) B r_{4}\right] \)
D. \( \left[C r(e n) B r_{2}\right] B r \)
Subject: Physics
A large, massive man and a small boy of small mass are held far apart on an icy surface where friction is negligible. The man and the boy hold opposite ends of a bungee cord that is stretched. When the boy and the man are released,
they are each pulled by the bungee cord so that they approach one another. When they get close to each other, how will their momenta, velocity, and kinetic energies compare?
A. Magnitude of Momenta - man's greater then boy's Magnitude of Velocity - boy's greater than man's, Kinetic Energy - man's greater than boy's
B. Magnitude of Momenta - same for both, Magnitude of Velocity - boy's greater than man's, Kinetic Energy same for both
c. Magnitude of Momenta - same for both, Magnitude of Velocity - same for both, Kinetic Energy - same for both
D. Magnitude of Momenta - boy's greater then man's Magnitude of Velocity - boy's greater than man's, Kinetic Energy - same for both
E. Magnitude of Momenta - same for both, Magnitude of Velocity - boy's greater than man's, Kinetic Energy boy's greater than man's
Subject: Chemistry
The heat required to completely
evaporate 18 grams of water at \( 98^{\circ} \mathrm{C} \)
\( \left(H_{v}=2259 J / g \text { and } c=4.18 J / g K\right) \)
A. 40,812 joules
B. 40,512 joules
c. 40,666 joules
D. 150 joules
E . \( 6.12 \times 10^{6} \) joules
Subject: Maths
\( \int e^{x}\left[\log \cos x+\sec ^{2} x\right] d x= \)
A \( \cdot e^{x}\left[\log \cos x+\sec ^{2} x\right]+c \)
B . \( e^{x}[\log \cos x+\tan x]+c \)
c. \( e^{x}(\cos x)+c \)
D \( \cdot e^{x}[\log (\tan x)]+c \)
Subject: Physics
The truth table for NOT gate is
\( A \)
\[
\left[\begin{array}{ll}
1 & 1 \\
0 & 0
\end{array}\right]
\]
B.
\[
\left[\begin{array}{ll}
1 & 0 \\
0 & 0
\end{array}\right]
\]
c.
\[
\left[\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right]
\]
D.
\[
\left[\begin{array}{ll}
0 & 1 \\
1 & 1
\end{array}\right]
\]
Subject: Maths
Solve the following Linear programming problems graphically:
Maximize \( z=3 x+4 y \) subject to the
constraints \( : \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{4}, \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \)
Subject: Chemistry
The reaction \( C_{6} \boldsymbol{H}_{6}+\boldsymbol{C H}_{3} \frac{A l C l_{3}}{\text {anhydrous}} \)
\( \boldsymbol{H} \boldsymbol{C l}+\boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{C} \boldsymbol{H}_{3} \) is:
A. Friedel-Crafts alkylation
B. addition reaction
C . Friedel-Crafts acylation
D. Friedel -Craft's benzylation
Subject: Physics
A long copper wire contains a current
of I ampere. The magnetic flux per
metre of the wire for a plane surface inside the wire as shown in figure.
\( ^{A} \cdot \frac{\mu_{0}}{2 \pi} \)
В \( \frac{\mu_{0}}{4 \pi} \)
c. \( \frac{\mu_{0}}{\pi} \)
D. \( \frac{\mu_{0}}{6 \pi} \)
Subject: Chemistry
The pair of boiling point and compound
are given as,
\( \boldsymbol{C}_{6} \boldsymbol{H}_{6}, \quad \boldsymbol{C H}_{3} \boldsymbol{O H} \quad \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{N O}_{2} \)
\( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{N} \boldsymbol{H}_{\boldsymbol{2}} \)
\( \mathbf{8 0}^{\circ} \boldsymbol{C} \quad \mathbf{6 5}^{\circ} \boldsymbol{C} \quad \mathbf{2 1 2}^{\boldsymbol{o}} \boldsymbol{C} \)
\( 184^{\circ} \mathrm{C} \)
(1)
\( (\|) \)
(III)
Which will show lowest vapour pressure
at room temperature?
A. \( C_{6} H_{6} \)
в. \( C H_{3} \) ОН
\( \mathbf{c} \cdot C_{6} H_{5} N O_{2} \)
D. \( C_{6} H_{5} N H_{2} \)
Subject: Maths
In the adjacent figure, ABC is a triangle
in which \( \angle B=50^{\circ} \) and \( \angle C=70^{\circ} \)
Sides \( A B \) and \( A C \) are produced. If ' \( z^{\prime} \) is
the measure of the angle between the
bisectors of the exterior angles of
formed, then find 'z'.
Subject: Chemistry
The standard reduction potential of the \( A g^{+} \mid A g \) electrode at \( 298 \mathrm{K} \) is \( 0.80 \mathrm{V} \)
The solubility product of \( A g l \) is \( 6.4 \times \) \( 10^{-17} \) at \( 298 \mathrm{K} .(2.303 \mathrm{RT} / \mathrm{F}=0.06) \)
The potential of \( A g^{+} \mid A g \) electrode in a saturated solution of Agl at \( 298 \mathrm{K} \) is
\( \mathbf{A} \cdot-0.314 V \)
B . \( +0.314 V \)
c. \( -0.172 V \)
D. \( +0.172 \mathrm{V} \)
Subject: Chemistry
The solubility products of \( \mathrm{MA}, \mathrm{MB}, \mathrm{MC} \) and MD are \( 1.8 \times 10^{-10}, 4 \times 10^{-3}, 4 \times \)
\( 10^{-8} \) and \( 6 \times 10^{-5} \) respectively. If a 0.01
M solution of MX is added dropwise to a mixture containing \( A^{\ominus}, B^{\ominus}, C^{\ominus}, \) and \( D^{\ominus} \) ions, then the one to be precipitated first will be:
A. MA
в. мв
c. мс
D. MD
Subject: Maths
\( \sum_{x, y, z} x^{2}\left(y^{2}-z^{2}\right)=? \)
A. \( x^{2}+y^{2}+z^{2} \)
B . \( x^{2} y^{2}+y^{2} z^{2}+z^{2} x^{2} \)
c. 0
D. \( y^{2}+z^{2} \)
Subject: Chemistry
Chromium - plated steel is a material of
popular use. During its process of manufacture, the effluent contains
chromate and cyanide ions as impurities. After these are chemically removed, carbon dioxide and salt (sodium chloride) still remain as
impurities. This salt solution is purified electrolytically by adding carbonaceous matter which acts as:
A. a microcell
B. an electrode
c. a cathode
D. a salt absorber
Subject: Maths
It is known that the decay rate of radium is directly proportional to its quantity at each given instant. Find the law of variation of a mass of radium as
a function of time if at \( t=0, \) the mass of
the radius was \( m_{0} \) and during time \( t_{0} \alpha \)
\( \% \) of the original mass of radium decay.
A \( \quad m=m_{0} e^{-k t} \) where \( k=\frac{1}{t_{0}} \ln \left(1-\frac{\alpha}{100}\right) \)
B. \( m=m_{0} e^{-k(t-1)} \) where \( k=\frac{1}{t_{0}} \ln \left(1+\frac{\alpha}{100}\right) \)
c. \( m=m_{0} e^{-k(t-1)} \) where \( k=\frac{1}{t_{0}} \ln \left(1-\frac{\alpha}{100}\right) \)
D. \( m=m_{0} e^{-k t} \) where \( k=\frac{1}{t_{0}} \ln \left(1+\frac{\alpha}{100}\right) \)
Subject: Physics
A balloon of weight \( \boldsymbol{w} \) is falling vertically downward with a constant
acceleration \( (\boldsymbol{a}<\boldsymbol{g}) . \) The magnitude of
the air resistance is:
A . \( w \)
в. \( _{w\left(1+\frac{a}{g}\right)} \)
c. \( w\left(1-\frac{a}{g}\right) \)
D. \( w \frac{a}{g} \)