AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
What will be the emf of a cell of two
hydrogen electrodes, if a negative
electrode is in contact with \( 10^{-8} M H^{+} \)
ion positive electrode is in contact with
\( \mathbf{0 . 0 2 5 M} \boldsymbol{H}^{+} \mathbf{?} \)
A. \( -0.18 V \)
в. \( -0.28 V \)
c. \( -0.38 V \)
D. - \( 0.48 V \)
Subject: Maths
The value of
\( \mathbf{1 0 1} \lim _{n \rightarrow \infty}\left(\frac{\mathbf{1}+\mathbf{2}^{100}+\ldots+\boldsymbol{n}^{100}}{\mathbf{n}^{101}}\right) \)
\( A \cdot 2 \)
B.
\( c \cdot 6 \)
\( D \)
Subject: Maths
f \( \boldsymbol{A}=\operatorname{diag}(\mathbf{2}-\mathbf{5} \mathbf{9}), \boldsymbol{B}=\operatorname{diag}(\mathbf{1} \mathbf{1}- \)
4) and \( C=\operatorname{diag}(-634), \) then find \( B+ \)
\( C-2 A \)
Subject: Physics
Capacitance of a capacitor made by a
thin metal foil is \( 2 \mu F \). If the foil is folded with paper of thickness \( 0.15 \mathrm{mm} \) dielectric constant of paper is 2.5 and width of paper is \( 400 \mathrm{mm} \), the length of foil will be
A. \( 0.34 \mathrm{m} \)
B. 1.33 \( m \)
c. \( 13.4 \mathrm{m} \)
D. 33.9 m
Subject: Physics
A student is standing at a distance of 50 metre from the bus. As soon as the
bus begins its motion with an acceleration of \( 1 m s^{-2}, \) the student starts running towards the bus with a uniform velocity \( u \). Assuming the motion to be along a straight road, the minimum value of \( u \), so that the
student is able to catch the bus is
\( \mathbf{A} \cdot 8 m s^{-1} \)
B. \( 5 m s^{-1} \)
\( \mathrm{c} \cdot 12 m s^{-} \)
D. \( 10 m s^{-1} \)
Subject: Maths
If \( A \) is square matrix such that \( \boldsymbol{A}(\boldsymbol{A} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A})=\left(\begin{array}{ccc}\mathbf{4} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{4} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} & \mathbf{4}\end{array}\right) \) then det \( (\mathbf{A} \mathrm{d} \)
\( A)= \)
\( A \cdot 4 \)
B. 16
\( c \cdot 64 \)
D. 256
Subject: Chemistry
In the equation:
\( \boldsymbol{C u}+\boldsymbol{X} \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \rightarrow \boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2}+ \)
\( \boldsymbol{Y} \boldsymbol{N} \boldsymbol{O}_{2}+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O} \)
the value of \( X \) and \( Y \) are?
A. 3 and
B. 8 and 6
c. 4 and 2
D. 7 and
Subject: Physics
The \( V-t \) graph is shown in the figure for
particle the \( (V m / s) \) acceleration of
particle is
A \( \cdot 22.5 m / s^{2} \)
B. \( 5 m / s^{2} \)
\( \mathbf{C} \cdot-5 m / s^{2} \)
\( \mathbf{D} \cdot-3 m / s^{2} \)
Subject: Physics
A large spherical planet of radius \( \mathrm{R} \) made of a material of density d, has a spherical cavity of radius R/2,with centre of cavity a distance R/2 from the
centre other planet. Find the gravitational force one small mass \( \mathrm{m} \) at
the centre of the cavity.
A. 2 RGmd/3
B. RGmd/3
c. 2RGmd
D. 4 RGmd/3
Subject: Chemistry
Balance reaction when dil. HCl is added
to lead nitrate solution.
A \( \cdot \operatorname{Pb}\left(N O_{2}\right)_{2}+2 H C l \rightarrow P b C l_{2}+2 H N O_{3} \)
В \( \cdot_{2 P b}\left(N O_{3}\right)_{2}+2 H C l \rightarrow 2 P b C l_{2}+H N O_{3} \)
c. \( \operatorname{Pb}\left(N O_{3}\right)_{2}+2 H C l \rightarrow P b C l_{2}+2 H N O_{3} \)
D. \( \operatorname{Pb}\left(N O_{3}\right)_{2}+H C l \rightarrow P b C l_{2}+H N O_{3} \)
Subject: Chemistry
Assertion (A) : Zeroth law of thermodynamics gives us the concept
of energy Reason
(R) : Internal energy is
dependent on temperature
A. 1) Both Assertion and Reason are true and reason is correct explanation of Assertion
B. 2) Both Assertion and Reason are true but reason is not correct explanation of Assertion
C. 3 ) Assertion is true but reason is false
D. 4 ) Assertion is false but reason is true
Subject: Maths
Find the circumference of the
semicircle whose diameter is 4 cm.
A. \( 3.46 \mathrm{cm} \)
B . \( 5.89 \mathrm{cm} \)
\( \mathbf{c} \cdot 6.28 \mathrm{cm} \)
D. \( 10.28 \mathrm{cm} \)
Subject: Physics
The displacement of a particle in SHM
is indicted by equation \( \boldsymbol{y}= \) \( 10 \sin \left(20 t+\frac{\pi}{3}\right) \) where \( y \) is in metres.
The value of the maximum velocity of the particle will be?
A. \( 100 \mathrm{m} / \mathrm{s} \)
в. \( 150 \mathrm{m} / \mathrm{s} \)
c. \( 200 m / s \)
D. \( 400 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
A quantity of \( 1 g \) of metallic carbonate
\( X C O_{3} \) is completely converted into a
chloride. \( \boldsymbol{X} \boldsymbol{C l}_{2} \) weighing \( 1.11 g \). The
atomic mass of the element ' \( \boldsymbol{X}^{\prime} \) is
A . 10
B. 20
c. 30
D. 40
Subject: Physics
The vector perpendicular to \( \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}} \) is
\( \mathbf{A} \cdot \hat{i}-\hat{j}+\hat{k} \)
B. \( \hat{i}-\hat{j}-\hat{k} \)
c. \( -\hat{i}-\hat{j}-\hat{k} \)
D. \( 3 \hat{i}+2 \hat{j}-5 \hat{k} \)
Subject: Chemistry
What is the correct structure of \( 3- \)
Bromoprop-1-ene?
\( \mathbf{A} \cdot C H_{3}-C B r=C H_{2} \)
B \( . B r-C H=C=C H_{2} \)
\( \mathbf{c} \cdot B r-C H_{2}=C H-C H_{2} \)
\( \mathbf{D} \cdot B r-C H_{2}-C H=C H_{2} \)
Subject: Physics
An electron revolving in an orbit of radius \( 0.5 \dot{A} \) in a hydrogen atom executes \( 10^{16} \) revolutions per second.
The magnetic moment of electron due to its orbital motion will be
A. \( 1.256 \times 10^{-23} \mathrm{Am}^{2} \)
B. \( 653 \times 10^{-26} \mathrm{Am}^{2} \)
c. \( 10^{-3} \) Am \( ^{2} \)
D. \( 256 \times 10^{-26} \mathrm{Am}^{2} \)
Subject: Chemistry
Dvide the following redox equations into oxidation half equation and reduction half equation.
\( \boldsymbol{a}) \boldsymbol{P}_{(s)}+\boldsymbol{P} \boldsymbol{O}_{4(a q)}^{3} \boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{3(a q)}^{2} \)
\( \boldsymbol{b}) \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{2(a q)} \longrightarrow \boldsymbol{N} \boldsymbol{O}_{3(a q)}^{-}+\boldsymbol{N} \boldsymbol{O}_{(g)} \)
\( \boldsymbol{c}) \boldsymbol{I} \boldsymbol{O}_{\boldsymbol{3}(\boldsymbol{a q})}^{-}+\boldsymbol{R e}_{(s)} \longrightarrow \boldsymbol{R e} \boldsymbol{O}_{4(\boldsymbol{a q})}+\boldsymbol{I}_{(a q)} \)
Subject: Maths
For a biased die the probabilities for the different faces to turn up are given
below:
The die is tossed and you are told that either face one or face two turned up.
Then the probability that it is face one
is.
Faces:
Probabilities: \( \quad \) 0.1 \( \quad \) 0.32 \( \quad \) 0.21
A. \( 1 / 6 \)
в. \( 1 / 10 \)
c. \( 5 / 49 \)
D. \( 5 / 21 \)
Subject: Maths
The number of ways of arranging the letters \( A A A A A, B B B, D, E E \& F \) in a row
if the letter \( C \) are separated from one another is
\( \mathbf{A} \cdot_{13} s_{3} \cdot \frac{12 !}{5 ! 3 ! 2 !} \)
в. \( \frac{13 !}{5 ! 3 ! 2 !} \)
c. \( \frac{14 !}{3 ! 32 !} \)
D. none
Subject: Physics
Three concentric conducting spherical shells of radii \( \boldsymbol{R}, 2 \boldsymbol{R} \) and \( \boldsymbol{3} \boldsymbol{R} \) carry
charges \( Q,-2 Q \) and \( 3 Q, \) respectively. Compute the potential at \( r=\frac{5}{2} R: \)
\( A \)
В. \( \frac{-3 Q}{25 \pi \varepsilon_{0} R} \)
\( c \)
D.
Subject: Maths
\( A B=D C=8 c m, A D=4 c m \) what
should be the length of side \( B C \), if
\( A B C D \) is parallelogram
A. \( 4 c m \)
B. 8 cm
\( \mathbf{c} \cdot 16 c m \)
D. None of the above
Subject: Physics
Two cars are moving in the same direction with the same speed
\( 30 k m / h r . \) They are separated by a
distance of \( 5 k m \) the speed of a car
moving in the opposite direction if it
meets these two cars at interval of 4
minutes, will be:
A. \( 40 k m / h r \)
в. \( 45 k m / h r \)
c. \( 30 k m / h r \)
D. \( 15 k m / h r \)
Subject: Maths
\( \mathbf{2} \times \mathbf{2} \times \mathbf{2} \times \mathbf{3} \times \mathbf{3} \times \mathbf{1 3}=\mathbf{2}^{\mathbf{3}} \times \mathbf{3}^{\mathbf{2}} \times \mathbf{1 3} \)
is equal to
A. 1004
в. 828
c. 724
D. 936
Subject: Chemistry
0.002 molar solution of NaCl having
degree of dissociation of \( 90 \% \) at \( 27^{\circ} C \)
has osmotic pressure equal to
A. 0.94 bar
B. 9.4 bar
c. 0.0934 bar
D. \( 9.4 \times 10^{-4} \) bar
Subject: Chemistry
A certain amount of a reducing agent
reduces x mole of \( K M n O_{4} \) and y mole
of \( K_{2} C r_{2} O_{7} \) in different experiments in acidic medium. If the change in oxidation state in reducing agent is same in both experiments, \( \boldsymbol{x}: \boldsymbol{y} \)
A . 5: 3
B. 3: 5
\( c .5: 6 \)
D. 6: 5
Subject: Maths
\( \left|\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{a}^{2}-\boldsymbol{b} \boldsymbol{c} & \boldsymbol{b}^{2}-\boldsymbol{c} \boldsymbol{a} & \boldsymbol{c}^{2}-\boldsymbol{a} \boldsymbol{b}\end{array}\right|= \)
\( A . \)
\( B \)
\( c . a b c \)
D. \( (a-b),(b-c),(c-a) \)
Subject: Maths
The tangent to the curve \( y=x^{2}+6 \) at \( a \)
point (1,7) touches the circle \( x^{2}+ \) \( y^{2}+16 x+12 y+c=0 \) at a point \( Q \)
then the coordinate of \( Q \) then the
coordinate of \( Q \) are.
A. (-6,-11)
B. (-9,-13)
\begin{tabular}{l} 
c. (-10,-15) \\
\hline
\end{tabular}
D. (-6,-7)
Subject: Physics
A particle of mass \( 12 \mathrm{kg} \) is acted upon
by a force \( \boldsymbol{f}=\left(\mathbf{1 0 0}-\mathbf{2 x}^{\mathbf{2}}\right) \) when \( \boldsymbol{f} \) is in
newton and \( x \) is in metre. Calculate the
wrok done by this force in moving the particle \( \boldsymbol{x}=\mathbf{0} \) to \( \boldsymbol{x}=-\mathbf{1 0 m} . \) What will
be the speed at \( x=10 m \) if it starts
from rest.
Subject: Biology
In a DNA molecule, the phosphate group is attached to \( _{--} \) carbon of the sugar
residue of its own nucleotide
and \( _{-1-1} \) carbon of the sugar
residue of the next nucleotide
by bonds.
A. 5 ', 3 ', phosphodiester
B. 5', 3', glycosidic
c. 3 ', 5', phosphodiester
D. 3', 5', glycosidic
Subject: Physics
In the following circuit the resultant
e.m.f between AB is
\( \mathbf{A} \cdot E_{1}+E_{2}+E_{3}+E_{4} \)
B \( \cdot E_{1}+E_{2}+2 E_{3}+E_{4} \)
\( \mathrm{c} \cdot_{E_{1}}+E_{2}+\frac{E_{3}}{2}+E_{4} \)
D \( \quad E_{1}+E_{2}+\frac{E_{3}}{4}+E_{4} \)
Subject: Physics
Two speakers A and B are placed 1 \( \mathrm{m} \)
apart, each produces sound waves of frequency \( 1800 \mathrm{Hz} \) in phase. \( \mathbf{A} \)
detector moving parallel to the line joining the speakers at a distance of 2.4
\( m \) away detects a maximum intensity
at 0 and then at \( P . \) Speed of the sound
wave is:
\( A \cdot 330 \mathrm{ms}^{-1} \)
B. 360 \( \mathrm{ms}^{-1} \)
c. \( 350 \mathrm{ms}^{-1} \)
D. \( 340 \mathrm{ms}^{-1} \)
Subject: Chemistry
Determine the true formula of the
compound whose molecular mass is 90.0 grams and contains \( 40.0 \% \) carbon \( 6.67 \% \) hydrogen, and \( 53.33 \% \) oxygen
A \( \cdot C_{2} H_{2} O_{4} \)
в. \( C H_{2} O_{4} \)
\( \mathbf{c} \cdot C_{3} H_{6} \)
D. \( C_{3} H O_{3} \)
E \( \cdot C_{3} H_{6} O_{3} \)
Subject: Physics
What is the difference in the
construction of an astronomical
telescope and a compound microscope
? The focal lengths of the objective and eyepiece of a compound microscope are \( 1.25 \mathrm{cm} \) and \( 5.0 \mathrm{cm}, \) respectively. Find the position of the object relative to the objective in order to obtain an angular magnification of 30 when the final image is formed at the near point.
Subject: Physics
A rod \( 100 \mathrm{cm} \) long and of \( 2 \mathrm{cm} \times 2 \mathrm{cm} \)
cross-section is subjected to a pull of 1000kg force. Modulus of elasticity of
the material is \( 2.0 \times 10^{6} k g / c m^{2} . \) If the
elongation of the rod is \( x \mathrm{mm} \), find the
value of \( 40 x \)
Subject: Physics
A river is flowing from west to east at a speed of \( 5 \mathrm{m} / \mathrm{min}^{-1} \). A man on the south
bank of the river, capable of swimming at \( 10 m / m i n^{-1} \) in still waters wants to swim
the river in the shortest time. In which
direction should swim in a direction
A \( .30^{\circ} \) west of north
B. \( 60^{\circ} \) east of north
\( \mathbf{c} \cdot 30^{\circ} \) east of north
D. due north
Subject: Physics
An object starts \( 5 \mathrm{m} \) from origin and
moves with an initial velocity of \( 5 m s^{-1} \)
and has an acceleration of \( 2 m s^{-2} \). After
10 sec, the object is how far from the origin?
A. \( 150 \mathrm{m} \)
B. 145 \( \mathrm{m} \)
c. \( 155 \mathrm{m} \)
\( D \cdot 55 \mathrm{m} \)
Subject: Biology
Study the following lists. List-
List-II
(A) Corynebacterium glutamicum
(I) Flexibility in shape
(B) Halobacterium
(II) Mineralisation
(C) Cristispira
(III) Lysine
(D) Bacillus mycoides
(IV) Gas vacuoles
(V) Parasite on bacteria
The correct match is
\( A \cdot(A)-(V),(B)-(11),(C)-(111),(D)-(1 V) \)
B. (A)-(III), (B)- (IV), (C)-(I), (D)- (II)
\( c \cdot(A)-(11),(B)-(V),(C)-(1 V),(D)-(1) \)
Subject: Biology
Match the following components of
Column 'A' with the components of
Column'B'.
Column Column 'B' 'A'
(1)
(A) A trap which looks and smells like Venus fly \( \quad \) a flower to catch the insects trap
(2)
(B) Flower opens in the morning Balsam
(3)
(C) Fruit bursts open to Drosera
(4)
(D) Tentacles on leaves which can trap Lotus \( \quad \) insects
\( A \cdot(1)-(A),(2)-(C),(3)-(D),(4)-(B) \)
B. \( (1)-(A),(2)-(C),(3)-(B),(4)-(D) \)
C \( \cdot(1)-(D),(2)-(C),(3)-(A),(4)-(B) \)
D. \( (1)-(D),(2)-(B),(3)-(A),(4)-(C) \)
Subject: Physics
The volume \( V \) of a liquid crossing through a tube is related to the area of cross-section \( A \), velocity \( v \) and time \( t \) as
\( \boldsymbol{V} \propto \boldsymbol{A}^{\boldsymbol{a}} \boldsymbol{v}^{b} \boldsymbol{t}^{c} . \) Which of the following is
correct given that \( a \neq 1 ? \)
A. \( a \neq b \) and \( b \neq c \)
B. \( a=b \) and \( b=c \)
c. \( a \neq b \) and \( b=c \)
D. \( a=b \) and \( b \neq c \)
Subject: Biology
How much oxygen is delivered by 100 \( \mathrm{ml} \) of oxygenated blood to the tissues under normal physiological conditions?
\( \mathbf{A} \cdot 15 \mathrm{m} \)
B. \( 10 \mathrm{ml} \)
\( c .5 \mathrm{m} \)
D. 2.5 m
Subject: Chemistry
If the bond dissociation energies of
\( X Y_{1} X_{2} \) and \( Y_{2} \) (all diatomic molecules)
are in the ratio of 1: 1: 0.5 and \( \delta_{1} H \) for
the formation of \( X Y \) is \( -200 k J m o l^{-1} \)
The bond dissociation energy of \( \boldsymbol{X}_{2} \) will
be:
A. \( 200 k J ; / m o l \)
в. \( 100 k J / m o l \)
c. \( 800 k J / \) mol
D. 300kJ/mol
Subject: Chemistry
\( \boldsymbol{A l C l}_{3}(\boldsymbol{a q})+\boldsymbol{N H}_{3}(\boldsymbol{a q})+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \)
Which of the following is one of the products obtained from the reaction above?
A . \( A l N \)
в. \( A l H_{3} \)
c. \( A l \)
D. \( A l\left(N O_{3}\right)_{3} \)
E \( \cdot A l(O H)_{3} \)
Subject: Maths
\( \int \frac{1}{e^{x}+e^{-x}} d x \)
\( A \cdot \tan ^{-1} x \)
B. \( \tan ^{-1} e^{x} \)
\( \mathbf{c} \cdot \cot ^{-1} e^{x} \)
D. \( \frac{1}{2} \cot ^{-1} e^{x} \)
Subject: Biology
(a) If a sperm with 'X' chromosome
fertilizes with an ovum with 'X'
chromosome, what will be the gender of
the baby?
(b) Who determines the sex/gender of
the baby, mother or father?
(c) Is it correct to blame the mother for
giving birth to a baby girl?
(d) Are all our characters resembles our
parents?
Mother's Sex Father's Chromosomes Chromosomes
Subject: Physics
If the radius of moon is \( 1.7 \times 10^{6} m \) and
its mass is \( 7.34 \times 10^{22} \) kg. Then its
escape velocity is
A \( \cdot 2.4 \times 10^{3} \mathrm{ms}^{-1} \)
В. \( 2.4 \times 10^{2} \mathrm{ms}^{-1} \)
c. \( 3.4 \times 10^{3} \mathrm{ms}^{-1} \)
D. \( 3.4 \times 10^{2} \mathrm{ms}^{-1} \)
Subject: Maths
In the given figure, if area of \( \triangle A D E \) is
\( 60 \mathrm{cm}^{2} ; \) state, giving reason, the area
of \( \square A B C F \)
\( A \cdot 120 \mathrm{cm}^{2} \)
В. \( 110 \mathrm{cm}^{2} \)
\( c \cdot 100 \mathrm{cm}^{2} \)
D. \( 150 \mathrm{cm}^{2} \)
Subject: Chemistry
Oxidation number of \( C l \) in \( C a O C l_{2} \)
(bleaching powder) is:
A . zero, since it contains \( C l_{2} \)
B. -1 , since it contains \( C l^{-} \)
c. \( -1, \) since it contains \( C l O^{-} \)
D. +1 and -1 since it contains \( C l O^{-} \) and \( C l^{-} \)
Subject: Physics
A metal is irradiated with light of
wavelength \( 600 n m . \) Given that the work
function of the metal is \( 1.0 e V \), the de
Broglie wavelength of the ejected electron is close to:
A \( \cdot 6.6 \times 10^{-7} \mathrm{m} \)
в. \( 8.9 \times 10^{-11} \) \( _{m} \)
c. \( 1.3 \times 10^{-9} m \)
D. \( 6.6 \times 10^{-13} \) и
Subject: Chemistry
Assertion
Temporary hardness in water is due to
presence of chlorides of Magnesium.
Reason

Temporary hardness is removed by
Clark's method.
Choose the correct option.
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
Degree of \( \left(\frac{d y}{d x}\right)^{2}+3 \frac{d^{2} y}{d x^{2}}=\sqrt{1+\left(\frac{d y}{d x}\right)^{2}} \)
is:
\( A \)
B. 2
\( c \cdot 3 \)
\( D \)
Subject: Physics
If the work done by stretching a wire by
1 \( m m \) is \( 2 J, \) the work necessary for stretching another wire of the same
material but with half the radius of
cross section and half the length by
1 mm is
\( ^{A} \cdot \frac{1}{4} J \)
в. 4.5
c. \( 8 J \)
D. 16.5
Subject: Physics
Six lead-acid type of secondary cells each of emf \( 2.0 \mathrm{V} \) and internal
resistance of 0.015 are joined in series to provide a supply to a resistance of
\( 8.5 . \) What are the current drawn from the supply and it's terminal voltage?
A. 11.8749
B. 12.8749
c. 13.1749
D. 10.5749
Subject: Chemistry
In the following reaction \( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{C}_{2} \boldsymbol{H}_{5}+\boldsymbol{4} \boldsymbol{H} \stackrel{\boldsymbol{R e d} \boldsymbol{P}+\boldsymbol{H I}}{\longrightarrow} \boldsymbol{2} \boldsymbol{X}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O}, \boldsymbol{X} \) is:
A. ethane
B. ethylene
c. butane
D. propane
Subject: Physics
The mass of a metal scale of uniform
thickness is \( 1.6 k g \) and its length is \( 2 m \) This scale is placed on the horizontal surface of the table such that \( \frac{1}{4}^{t h} \) of its length is beyond the edge of the table. The maximum mass that can be
suspended to this scale at a distance of 10cm from the free end of the scale so
that scale does not turn down is:
A . \( 1 k g \)
в. \( 2 k g \)
\( c \cdot 2 \cdot 4 k g \)
D. 3.2 2 k
Subject: Maths
If both the distinct roots of the equation
\( |\sin x|^{2}+|\sin x|+b=0 \) in \( [0, \pi] \) are
real, then the value of \( b \) is
\( \mathbf{A} \cdot[-2,0] \)
B . (-2,0)
\( c \cdot[-2,0) \)
D. None of these
Subject: Maths
The value of \( \int_{-\pi}^{\pi}\left(1-x^{2}\right) \sin x \cos ^{2} x d x \)
is
A. 0
в. \( _{\pi}-\frac{\pi^{3}}{3} \)
c. \( 2 \pi-\pi^{3} \)
D. \( \frac{7}{2}-2 \pi^{3} \)
Subject: Chemistry
Which of the following is the buffer solution of strong acidic nature?
A. \( H C O O H+H C O O^{-} \)
в. \( C H_{3} C O O H+C H_{3} C O O \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}+\mathrm{C}_{2} \mathrm{O}_{4}^{2} \)
D. \( H_{3} B O_{3}+B O_{3}^{3-} \)
Subject: Maths
The value of \( c, \) for which the line \( y= \)
\( 2 x+c \) is a tangent to the circle \( x^{2}+ \)
\( \boldsymbol{y}^{2}=\mathbf{1 6}, \) is
A . \( -16 \sqrt{5} \)
B. 20
c. \( 4 \sqrt{5} \)
D. \( 16 \sqrt{5} \)
Subject: Physics
In young's double slit experiment \( \beta \) is
the fringe width and \( I_{o} \) is the intensity of the central bright fringe. What will be the intensity at a distance \( x \) from the central bright fringe?
\( \mathbf{A} \cdot_{\mathrm{l}_{o}} \cos \left(\frac{x}{\beta}\right) \)
B \( \cdot \cos ^{2}\left(\frac{x}{\beta}\right) \)
\( ^{\mathrm{c}} \cdot_{1_{0} \cos ^{2}}\left(\frac{\pi x}{\beta}\right) \)
D. \( \left(\frac{I_{o}}{4}\right) \cos ^{2} \frac{\pi x}{\beta} \)
Subject: Maths
The Venn diagram shows sets \( P, Q \) and \( R \)
with regions labelled, I, II, III and IV.
State the region which represents set
\( \left[\boldsymbol{P} \cap(\boldsymbol{Q} \cup \boldsymbol{R})^{\prime}\right] \)
\( A \)
B.
\( c . \| \)
D. IV
Subject: Chemistry
On oxidation with acidified \( \boldsymbol{K}_{\mathbf{2}} \boldsymbol{C r}_{\mathbf{2}} \boldsymbol{O}_{\mathbf{7}}, \) an
compound gives a ketone which contains same number of carbon atoms
as in initial compound. The compound
is:
A. aldehyde
B . \( 1^{0} \) alcohol
C \( \cdot 2^{0} \) alcohol
D. both \( 1^{0} \) and \( 2^{0} \) alcohols
Subject: Physics
A coil is placed in transverse magnet
field of 0.02 T. If this coil starts
shrinking at a rate of \( 1 \mathrm{mm} / \mathrm{sec}, \) while
its radius remains \( 4 \mathrm{cm}, \) then what is
the value of induced emf?
\( A \cdot 2 \mu V \)
B . \( 2.5 \mu V \)
\( c .5 \mu V \)
D. \( 8 \mu V \)
Subject: Maths
If \( (\sin \alpha) x^{2}-2 x+b \geq 2, \) for all rea
values of \( \boldsymbol{x} \leq \mathbf{1} \) and \( \boldsymbol{\alpha \epsilon}\left(\mathbf{0}, \frac{\boldsymbol{\pi}}{\mathbf{2}}\right) \cup\left(\frac{\boldsymbol{\pi}}{\mathbf{2}}, \boldsymbol{\pi}\right) \)
then possible real values of \( b \) is /are
This question has multiple correct options
A .2
B. 3
\( c \cdot 4 \)
D. 5
Subject: Maths
A shopkeeper sells a badminton marked at Rs. 30 at \( 15 \% \) discount and
gives a shuttle cock costing Rs. 1.50 free with each badminton. He then
makes a profit of \( 20 \% . \) His cost price per badminton is
A . Rs. 35
B. Rs. 30
c. Rs. 25
D. Rs. 20
Subject: Physics
The electric field of certain radiation is
given by the equation \( \boldsymbol{E}= \)
\( 200\left[\sin \left(4 \pi \times 10^{10}\right) t+\sin (4 \pi x\right. \)
\( \left.\left.\mathbf{1 0}^{\mathbf{1 5}}\right) \boldsymbol{t}\right] \) falls in a metal surface having
work function \( 2.0 e V . \) The maximum
kinetic energy ( in eV) of the photoelectrons is [use Planck's
constant \( (h)=6.63 \times 10^{-34} J-s \) and
electron charge \( \left(\boldsymbol{E}=\mathbf{1 . 6} \times \mathbf{1 0}^{-\mathbf{1 9}} \boldsymbol{C}\right) \)
A. 3.3
B. 4.3
c. 5.3
D. 6.3
E. 7.3
Subject: Physics
A certain mass of an ideal gas
undergoes a reversible isothermal compression. Its molecules, compared
with the initial state, will then have the
same
(i) root mean square velocity
(ii) mean momentum
(iii) mean kinetic energy
\( A \cdot(i),(\text { ii) },( \text { iii) } \)
B. (i), (ii)
c. (ii), (iii)
D. (i)
Subject: Physics
A shell is fired from a cannon with a
speed of \( 100 \mathrm{m} / \mathrm{s} \) at an angle \( 30^{\circ} \) with the horizontal (positive \( y- \) direction). At the highest point of its trajectory, the
shell explodes into two equal fragments
of masses in the ratio \( 1: 2 . \) The lighter
fragment moves vertically upwards with an initial speed of \( 200 \mathrm{m} / \mathrm{s} \). What is the
speed of the other fragment at the time of explosion?
Subject: Physics
If the extension of the spring is \( x_{0} \) at time \( t, \) then the displacement of the second block at this instant is :
\( ^{\mathrm{A}} \cdot \frac{F t^{2}}{2 m}-x_{0} \)
\( ^{\text {В }} \cdot \frac{1}{2}\left(\frac{F t^{2}}{2 m}+x_{0}\right) \)
c. \( \frac{1}{2}\left(\frac{2 F t^{2}}{m}-x_{0}\right) \)
\( \frac{1}{2}\left(\frac{F t^{2}}{2 m}-x_{0}\right) \)
Subject: Maths
Solve \( \boldsymbol{x}^{2}-\mathbf{4} \boldsymbol{x}-\mathbf{5}=\mathbf{0} \)
\( A \cdot\{-1,5\} \)
B . \{1,5\}
\( \mathbf{c} \cdot\{-1,-5\} \)
D. None of these
Subject: Physics
Eight dipoles of charges of magnitude \( e \)
are placed inside a cube. The total
electric flux coming out of the cube will
be
\( A \cdot \frac{8 e}{\varepsilon_{0}} \)
В. \( \frac{16 e}{\varepsilon_{0}} \)
\( c \cdot \frac{e}{\varepsilon_{0}} \)
D. zero
Subject: Chemistry
When conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) is heated, it
decomposes to give-
A. \( O_{2} \) and \( N_{2} \)
B. NO
c. \( N_{2} O_{5} \)
D. \( N O_{2} \) and \( O_{2} \)
Subject: Chemistry
Each side of a cube is measured to be
7.203 \( \mathrm{m} \). What is the volume of the cube
to appropriate significant figure?
A \( \cdot 373.7 m^{3} \)
в. \( 311.3 m^{3} \)
\( \mathrm{c} \cdot 211.3 m^{3} \)
D. \( 3737 m^{3} \)