AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Two particles having masses \( 1 k g \) and
7 kg respectively attract each other. Initially they are at rest and infinite separation.The velocity of approach of the particles are at a separation of \( 1 \boldsymbol{m} \) is (G=universal gravitational constant)
\( \begin{array}{lll}\text { A } \cdot \sqrt{2} G & \text { m/s }\end{array} \)
B . \( 4 \sqrt{G} \) m/s
c. \( \sqrt{\frac{G}{2} m / s} \)
D. \( \frac{G}{4} m / s \)
Subject: Physics
A particle executes SHM with an amplitude of \( 20 \mathrm{cm} \) and time period of 12 sec. The minimum time required for it to move between two points \( 10 \mathrm{cm} \) on either side of the mean position
A . 1 s
B. 2
\( c \cdot 3 s \)
D. 4 s
Subject: Chemistry
Assertion
Medicines in the colloidal state are
more effective.
Reason
In the colloidal state, the medicines are
easily assimilated by the body.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is incorrect but Reason is correct
D. Both Assertion and Reason are correct
Subject: Physics
In a meter bridge, the balance point is obtained at \( 40 \mathrm{cm} . \) If a resistance equal
to that in the left gap is shunted across
itself, the new balance point is:
\( \mathbf{A} \cdot 40 \mathrm{cm} \)
B. \( 15 \mathrm{cm} \)
c. \( 25 \mathrm{cm} \)
D. \( 32 \mathrm{cm} \)
Subject: Chemistry
\( \left(N H_{4}\right)_{2} C r_{2} O_{7} \) on heating liberates gas The same gas will be obtained by :
A. heating \( N H_{4} N O_{2} \)
B. heating \( N H_{4} N O_{3} \)
C. treating \( M g_{3} N_{2} \) with \( H_{2} O \)
D. heating \( H_{2} O_{2} \) on \( N a N 0_{2} \)
Subject: Chemistry
\( P C l_{3} \) on hydrolysis gives fumes of:
A. \( H_{3} P O_{3}+H C l \)
в. \( H_{3} P O_{4}+H C l \)
c. \( H_{3} P O_{2} \) and \( H_{3} P O_{3} \)
D. \( H_{3} P O_{2}+H C l \)
Subject: Chemistry
Concentrated strong acid is added to a
solid mixture of 0.015 mole samples of
\( F e(O H)_{2} \) and \( C a(O H)_{2} \) placed in one litre of water. At what value of \( \mathrm{pH} \) will the dissolution of each hydroxide be
complete? (Assume negligible volume change) \( \boldsymbol{K}_{s p}\left[\boldsymbol{F e}(\boldsymbol{O H})_{2}\right]=\mathbf{7 . 9} \times \mathbf{1 0}^{-15} \) and
\( \boldsymbol{K}_{s p}\left[\boldsymbol{C u}(\boldsymbol{O} \boldsymbol{H})_{2}\right]=\mathbf{1 . 6} \times \mathbf{1 0}^{-19} \)
A . 6.67
в. 7.86
\( c .8 .86 \)
D. 7.26
Subject: Biology
Assertion
Plants utilizing first RuBP in \( C O_{2} \)
fixations are called \( C_{3} \) plants
Reason
Plants utilizing first PEP in \( C O_{2} \)
fixations are called \( C_{4} \) plants
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
The following is probabilty distribution
of r.v X.
\[
\begin{array}{lllllll}
\mathbf{x} & 1 & 2 & 3 & 4 & 5 & 6 \\
p(x) & \frac{k}{6} & \frac{k}{6} & \frac{k}{6} & \frac{k}{6} & \frac{k}{6} & \frac{k}{6}
\end{array}
\]
then value of k is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3
Subject: Chemistry
A compound contains \( N=25.94 \% \) and 0
\( =74.06 \% . \) If its vapour density is 54.2 calculate its molecular formula.
A . \( N O \)
в. \( N O_{2} \)
\( \mathrm{c} \cdot N_{2} \mathrm{O} \)
D. \( N_{2} O_{5} \)
Subject: Physics
The two surfaces \( A \) and \( B \) are at the same
potential and separated by a distance \( r \) The work done in carrying a charged particle \( (q) \) from \( A \) to \( B \) will be:
A \( \cdot \frac{K q}{r^{2}} \)
в. \( \frac{K q}{r} \)
c. \( -\frac{K q}{r} \)
D. zero
Subject: Maths
The plane \( a x+b y+c z+(-3)=0 \)
meet the co-ordinate axes in \( A, B, C . \) Then
centroid
of the triangle is
A. \( (3 a, 3 b, 3 c) \)
в. \( \left(\frac{3}{a} \frac{3}{b}, \frac{3}{c}\right) \)
\( ^{\mathbf{C}} \cdot\left(\frac{a}{3}, \frac{b}{3}, \frac{c}{3}\right) \)
D. \( \left(\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\right) \)
Subject: Physics
A ball is dropped onto a floor from a height of \( 10 \mathrm{m} \). If \( 20 \% \) of its initial energy is lost, then the height of bounce is-
\( A \cdot 2 m \)
B. \( 4 \mathrm{m} \)
\( c \cdot 8 m \)
D. \( 6.4 \mathrm{m} \)
Subject: Physics
Assertion
A body can have acceleration even if its velocity is zero at a given instant of time.
Reason
A body is numerically at rest when it reverses its direction.
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
If the two vectors \( \vec{A}=2 \hat{i}+3 \hat{j}+4 \hat{k} \) and \( \vec{B}=\hat{i}+2 \hat{j}-n \hat{k} \) are perpendicular
then the value of \( n \) is:
A . 1
B . 2
\( c \cdot 3 \)
D. 4
Subject: Chemistry
Some properties of sulphuric acid are listed below. Choose the role played by
sulphuric acid as \( A, B, C \) or \( D \) which is
responsible for the reaction
(i) to (v).
Some role/s may be repeated:
\( \boldsymbol{S}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}(\text {conc.}) \rightarrow \boldsymbol{3} \boldsymbol{S} \boldsymbol{O}_{2}+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O} \)
A . Dilute acid
B. Dehydrating agent
c. Non-volatile acid
D. oxidising agent
Subject: Maths
The range of the function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}-[\boldsymbol{x}] \)
where \( [x] \) represents the greatest
integer less than or equal to \( x \) is
\( A \cdot\{0\} \)
в. [0,1]
c. (0,1)
()
D. [0,1]
Subject: Chemistry
\( \boldsymbol{F} \boldsymbol{e} \boldsymbol{C l}_{3} \cdot \boldsymbol{6} \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{C}\left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{2}\left(\boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{O}\right)_{2} \rightarrow \)
Products.
Reaction products are:
A. \( F e C l_{3}, C H_{3} O H \) and \( C H_{3} C O C H_{3} \)
B. \( \left.C H_{3} O\right)_{3} \) Fe, HCl and \( H_{2} \) O
c. \( F e C l_{2}, H C l \) and \( C H_{3} C O C H_{3} \)
D. \( F e(O H)_{3}, F e C l_{3} \) and \( C H_{3} C O C H_{3} \)
Subject: Physics
An electric pole of dipole moment \( \underset{\boldsymbol{p}}{\rightarrow} \) is lying along uniform electric field \( \overrightarrow{\boldsymbol{E}} . \) The work done in rotating the dipole by \( 90^{\circ} \) is:-
A \( \cdot \sqrt{2} \) pE
B. \( \frac{p}{2} \)
c. 2 p
D. pE
Subject: Physics
A vertical metal cylinder of radius \( 2 \mathrm{cm} \)
and length \( 2 m \) is fixed at the lower end and a load of \( 100 k g \) is put on it. Find \( (a) \)
the stress
(b) the strain and
(c) the
compression of the cylinder. Young modulus of the metal \( =2 \times 10^{11} N m^{-2} \)
Subject: Physics
A convex lens is placed between object and a screen. The size of object is \( 3 c m \)
and an image of height \( 9 \mathrm{cm} \) is obtained on the screen. When the lens is
displaced to a new position, what will be the size of image on the screen?
\( A \cdot 2 c m \)
в. 6 ст
\( c .4 c m \)
D. \( 1 c m \)
Subject: Maths
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{y}+\boldsymbol{x} \tan \left(\frac{\boldsymbol{y}}{\boldsymbol{x}}\right)}{\boldsymbol{x}} \Rightarrow \sin \frac{\boldsymbol{y}}{\boldsymbol{x}}= \)
\( \mathbf{A} \cdot c x^{2} \)
в. \( c x \)
\( c \cdot c x^{3} \)
\( D \cdot c x^{4} \)
Subject: Chemistry
Assertion: Chloroform gives chloropicrin
with \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) vapour
Reason: Chloropicrin is used as an
insecticide
A. Both Assertion and Reason are true and Reason is the correct explanation to Assertion
B. Both Assertion and Reason are true and Reason is not the correct explanation to Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
Subject: Physics
In the circuit shown the cells \( A \) and \( B \)
have negligible resistances.For \( \boldsymbol{V}_{\boldsymbol{A}}= \)
\( 12 V, R_{1}=500 \Omega \) and \( R=100 \Omega \) the
galvanometer \( (G) \) shows no deflection.
The value of \( V_{B} \) is :-
A . \( 12 V \)
B. \( 6 V \)
\( c .4 V \)
D. \( 2 V \)
Subject: Physics
A long horizontal rigidly supported wire
carries a current \( i_{a}=96 A . \) Directly
above it and parallel to it at a distance,
another wire of \( 0.144 N \) weight per
metre is carrying a current \( i_{b}=24 A, \) in
a direction same as the lower wire. If the
weight of the second wire is balanced
by the force due to magnetic repulsion, then its distance (in mm) from the
lower wire is:
A . 9.6
B. 4.8
c. 3.2
D. 1.6
Subject: Chemistry
Assertion
Use of aspartame is limited to cold foods and soft drinks
Reason
Aspartame is roughly 100 times as
sweet as cane sugar.
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
If \( \mathrm{M} \) and \( \mathrm{N} \) are any two events, the
probability that not exactly one of them occurs is for an event set \( A \), the
complement is \( \boldsymbol{A}^{o} \)
A. \( P(M)+P(N)-2 P(M \cap N) \)
В. \( P(M)+P(N)-P(M \cap N) \)
C \( \cdot P\left(M^{o}\right)+P\left(N^{o}\right)-2 P\left(M^{o} \cup N^{o}\right) \)
D. \( P\left(M \cap N^{o}\right)+P\left(M^{o} \cup N\right) \)
Subject: Chemistry
Balance the following equation.
\( \boldsymbol{I} \boldsymbol{O}_{4}^{-}+\boldsymbol{I}^{-}+\boldsymbol{H}^{+} \rightarrow \boldsymbol{I}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \)
A \( \cdot 2 I O_{4}^{-}+14 I^{-}+16 H^{+} \rightarrow 8 I_{2}+8 H_{2} O \)
B . \( 2 I O_{4}^{-}+14 I^{-}+4 H^{+} \rightarrow 3 I_{2}+8 H_{2} O \)
c. \( I O_{4}^{-}+7 I^{-}+8 H^{+} \rightarrow 4 I_{2}+4 H_{2} O \)
D. None of these
Subject: Physics
A positively charged particle of \( 2.0 C \) moves upward into an area where both a magnetic field of the magnitude
\( 4.0 \times 10^{-4} T \) and an electric field of
the magnitude \( 0.1 N / C \) are acting. Find out the velocity at which particle must move if it is not deflected when it enters
this area?
A \( \cdot 4.0 \times 10^{-3} \mathrm{m} / \mathrm{s} \)
B. \( 125 \mathrm{m} / \mathrm{s} \)
c. \( 250 m / s \)
D. \( 500 m / s \)
E. The particle will be deflected to the left regardless of ts velocity
Subject: Physics
A rectangular coil \( 3 \times 3 \mathrm{cm} \) consisting of
100 turns caries 0.1 A. If it produces a
deflection \( 10^{0}, \) in a field of induction
\( 0.1 T, \) the couple per unit twist is
A \( \cdot 9 \times 10^{-2} \mathrm{Nm} / \) Degree
B. \( 9 \times 10^{-5} \mathrm{Nm} / \) Degree
C. \( 9 \times 10^{-2} \mathrm{Nm} / \mathrm{rad} \)
D. \( 0.9 \mathrm{Nm} / \) Degree
Subject: Biology
A mRNA coding for a secretory protein, when translated using free ribosome under in vitro conditions, resulted in a
\( 40 k D a \) protein. The same mRNA when translated using the rough endoplasmic reticulum resulted in a
\( 36 k D a \) protein. The difference in the
molecular weight of the two
polypeptides is due to the loss of a
A \( .2 k D a \) peptide from \( N \) -terminus and a \( 2 k D a \) peptide from the C-terminus
B. \( 1 k D a \) peptide from \( N \) -terminus and a \( 3 k D a \) peptide from the C-terminus
C. \( 4 k D a \) peptide from the N-terminus
D. \( 4 k D a \) peptide from the C-terminus
Subject: Chemistry
Find number of protons and neutrons
for \( (a),(b) \) and \( (c) \) respectively.
(a) \( _{17}^{35} C l(b)_{6}^{12} C(c)_{35}^{81} B r \)
\( A \cdot n_{p}=17,6,35 \)
\( n_{n}=18,6,46 \)
B . \( n_{p}=16,6,35 \)
\( n_{n}=18,6,46 \)
\( c \cdot n_{p}=17,6,35 \)
\( n_{n}=18,6,45 \)
D \( . n_{p}=16,6,35 \)
\( n_{n}=18,6,45 \)
Subject: Chemistry
For \( 2 A+B+C \rightarrow 2 D \), determine the
rate law for the reaction based on the
following data.
\( \begin{array}{lllll}\operatorname{Exp} & {[\boldsymbol{A}]} & {[\boldsymbol{B}]} & {[\boldsymbol{C}]} & \begin{array}{l}\text { Rate of } \\ \text { disappearance } \\ (\mathrm{M} / \mathrm{s})\end{array} \\ & & & & \\ 1 & 0.1 & 0.1 & 0.1 & X \\ 2 & 0.2 & 0.2 & 0.1 & 8 X \\ & & & & \\ 3 & 0.2 & 0.1 & 0.1 & 4 X \\ & & & & \\ 4 & 0.2 & 0.1 & 0.2 & 32 X\end{array} \)
A \( . \) Rate \( =k[A]^{2}[B][C] \)
B . Rate\( =k[A]^{2}[B][C]^{3} \)
c. Rate\( =k[A]^{2}[B]^{3}[C] \)
D. \( \operatorname{Rate}=k[A]^{2}[B]^{2}[C]^{3} \)
Subject: Maths
Evaluate \( \int \frac{(x-1)^{2}}{x^{4}+2 x^{2}+1} d x \)
A \( \cdot \frac{x^{3}}{3}+x+\frac{x}{x^{2}+1}+c \)
\( ^{\text {В } \cdot \frac{x^{5}+x^{3}+x+3}{3\left(x^{2}+1\right)}+c} \)
c. \( \frac{x^{5}+4 x^{3}+3 x+3}{3\left(x^{2}+1\right)}+c \)
D. None of these
Subject: Chemistry
The wave motion of electron in a Bohr's
orbit of hydrogen is as shown in
diagram. The potential energy of
electron in the given orbit of hydrogen
atom is:
A \( .-3.4 \mathrm{eV} \)
B. +3.4 ev
\( \mathbf{c} .-3.02 \mathrm{eV} \)
D. -1.51 ev
Subject: Chemistry
Assertion
When 1 mole of hypophosphorous acid is treated with excess of iodine in acidic
solution, 1 mole of iodine is reduced; on making the solution alkaline, another mole of iodine is consumed.
Reason
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2}+\boldsymbol{I}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3}+ \)
\( 2 I^{-}+2 H^{+} \)
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3}+\boldsymbol{I}_{2}+\mathbf{2} \boldsymbol{O} \boldsymbol{H}^{-} \longrightarrow \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}+ \)
\( 2 I^{-}+H_{2} O \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.
Subject: Physics
Assertion
Coaxial cables make use of a dielectric
between the two conducting lines.
Reason
dielectrics are good insulators.
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
What is the range of wavelength of the spectrum of white light in \( \boldsymbol{A}^{o} \) ?
A \( .4000 A^{\circ} \) to \( 5000 A^{\circ} \)
B. \( 5000 A^{\circ} \) to \( 6000 A^{\circ} \)
c. \( 6000 A^{\circ} \) to \( 8000 A^{\circ} \)
D. All the above
Subject: Physics
Two moles of an ideal monoatomic gas,
initially at pressure \( P_{1} \) and volume \( V_{1} \) undergo an adiabatic compression
until its volume is \( V_{2} . \) Then the gas is
given heat \( Q \) at constant volume \( V_{2} \) Find the total work done by the gas, the total change in its internal energy and the final temperature of the gas.[Give
your answers in terms of \( \boldsymbol{P}_{1}, \boldsymbol{V}_{1}, \boldsymbol{V}_{2} \mathrm{Q} \)
and \( \mathrm{R}] \)
A. \( \frac{P_{1} V_{1}^{5 / 3} V_{2}^{-2 / 3}}{2 R}+\frac{Q}{3 R} \)
в.
(ii) \( \frac{P_{1} V_{1}^{5 / 3} V_{2}^{-2 / 3}}{2 R}+\frac{Q}{4 R} \)
\( ^{\mathrm{C}} \cdot \frac{P_{1} V_{1}^{5 / 3} V_{2}^{-2 / 3}}{2 R}+\frac{Q}{5 R} \)
D. \( \frac{P_{1} V_{1}^{5 / 3} v_{2}^{-2 / 3}}{5 R}+\frac{Q}{3 R} \)
Subject: Physics
If \( \mu_{O} \) and \( \mu_{e} \) are the refractive indices
of a double
refracting crystal, then
1) \( \mu_{O}<\mu_{e} \) for quartz crystal
2) \( \mu_{O}>\mu_{e} \) for calacite crystal
A. both 1 and 2 are true
B. 1 is true 2 is false
c. 1 false 2 is true
D. both 1 and 2 are false
Subject: Physics
The \( u_{r m s} \) of gas at \( 327^{\circ} C \) is :
A \( \cdot 611.66 \frac{m}{s e c} \)
В . \( 19342.44 \frac{\mathrm{m}}{\mathrm{sec}} \)
с. \( 1223.22 \frac{m}{s e c} \)
D. \( 96.71 \frac{m}{s e c} \)
Subject: Physics
In nuclear fusion, \( 1 g m \) hydrogen is
converted into \( 0.993 g m \) Helium in one hour. If the efficiency of the generator is
\( 5 \%, \) the energy obtained in \( K W h \) is:
\( \mathbf{A} \cdot 8.75 \times 10^{3} \)
B . \( 4.75 \times 10^{3} \)
c. \( 5.75 \times 10^{3} \)
D. \( 3.73 \times 10^{3} \)
Subject: Maths
\( A \) and \( B \) are events with \( P(A)= \) \( \mathbf{0 . 6}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 7} \) then compute \( \boldsymbol{P}(\boldsymbol{A} \cap \)
\( B) \)
Subject: Chemistry
In which of the following pairs do the two species resemble each other closely in chemical properties?
A \( \cdot \frac{1}{1} H \) and \( _{1}^{2} H \)
B. \( _{8}^{16} O \) and \( _{8}^{16} O^{2-} \)
C \( \cdot \frac{24}{12} M g \) and \( _{12}^{24} M g^{2+} \)
D. \( \frac{14}{7} N \) and \( \frac{14}{7} N^{3}- \)
Subject: Physics
At a time \( t=t_{0}, \) the string is suddenly
broken and the balls are released to
move. Mark the incorrect statement.
Consider the momentum and angular momentum after and before string
breaks.
A. Total angular momentum of system is conserved in table reference frame as well as center of mass reference frame
B. In the centre of mass frame, angular momentum of each of the mass is separately conserved
c. Total linear momentum of system is conserved in table reference frame
D. In the table frame momentum of individual balls is ss conserved
E. Answer required
Subject: Maths
\( \left(\frac{-9}{13} \times \frac{5}{6}\right)-\left(\frac{-9}{13} \times \frac{4}{6}\right)=\frac{-9}{13} \times \)
\( \left(\frac{5}{6}-\frac{4}{6}\right) \)
If true then enter 1 and if false then
enter 0
Subject: Maths
Find the degree measure of the angle
subtended at the centre of a circle
of radius \( 100 \mathrm{cm} \) by an arc of length 22
\( \mathrm{cm} .\left(\boldsymbol{U s e} \boldsymbol{\pi}=\frac{\mathbf{2 2}}{\mathbf{7}}\right) \)
Subject: Maths
\( \mathbf{f} \boldsymbol{A}=\left|\begin{array}{cc}\mathbf{2} & \mathbf{0} \\ \mathbf{5} & -\mathbf{3}\end{array}\right| \boldsymbol{B}=\left|\begin{array}{cc}\mathbf{- 2} & \mathbf{1} \\ \mathbf{3} & \mathbf{-} \mathbf{1}\end{array}\right|, \) then
the find the trace of \( \left(A B^{T}\right)^{T} \)
A . 10
B. 12
\( c \cdot 14 \)
D. 16
Subject: Chemistry
List-I \( \quad \) List-II
A)Rayon 1) \( C H_{2} O+C_{6} H_{5} O H \)
B)Silicone polymers
2) \( \boldsymbol{F}_{2} \boldsymbol{C}=\boldsymbol{C} \boldsymbol{F}_{2} \)
\( \mathbf{R} \)
C) Bakelite
3) HO-Si-OH
1
\( \mathbf{R} \)
D) Teflon
4) Cellulose
A. \( A-4 B-3 C-1 D-2 \)
B. A-1 B-3 C-2 D-4
c. \( A-4 B-2 C-3 D-1 \)
D. A-2 B-4 C-3 D-1
Subject: Physics
The differential equation representing the SHM of a particuleis \( \frac{\mathbf{9 d}^{2} \boldsymbol{y}}{\boldsymbol{d t}^{2}}+\mathbf{4} \boldsymbol{y}=\mathbf{0} \)
The time period of the particle is given by
A \( \cdot \frac{\pi}{3} \sec \)
в. \( \pi \) sec
\( ^{\mathrm{c}} \cdot \frac{2}{\pi} 3 s e c \)
D. \( 3 \pi s e c \)
Subject: Physics
Match the following and choose the
correct answer.
\( \begin{array}{lllll}A & \text { String vibration } & 1 & \text { Tabla } \\ B & \begin{array}{l}\text { Membrane } \\ \text { vibration }\end{array} & 2 & \begin{array}{l}\text { Bicycle } \\ \text { bell }\end{array} \\ \text { C } & \text { Vibration of air } & 3 & \text { Sitar } \\ \text { D } & \text { Vibration of plate } & 4 & \text { Flute }\end{array} \)
A . A-1, B-2, C-3, D-4
B. A-2, B-1, C-4, D-3
c. A-3, B-1, C-4, D-2
D. A-4, B-3, C-2, D-1 -
Subject: Maths
Simplify
\( \left(a^{3}-2 a^{2}+4 a-5\right)- \)
\( \left(-a^{3}-8 a+2 a^{2}+5\right) \)
A \( \cdot 2 a^{3}+7 a^{2}+6 a-10 \)
В. \( 2 a^{3}+7 a^{2}+12 a-10 \)
c. \( 2 a^{3}-4 a^{2}+12 a-10 \)
D . \( 2 a^{3}+4 a^{2}+6 a-10 \)
Subject: Chemistry
Work done in the cyclic process shown
in figure is :
\( A \cdot 4 P_{0} V_{0} \)
\( \mathbf{B} \cdot-4 P_{0} V_{0} \)
\( ^{\mathbf{C}}-\frac{22}{7} P_{0} V_{0} \)
\( \mathbf{D} \cdot-13 P_{0} V_{0} \)
Subject: Chemistry
One litre of a sample of hard water
contain \( 4.44 m g C a C l_{2} \) and \( 1.9 m g \) of
\( M g C l_{2}, \) what is the total hardness in
terms of ppm of \( \boldsymbol{C} \boldsymbol{a} \boldsymbol{C O}_{3} \)
\( A \cdot 2 \) ppm
B. 3 ppm
c. 4 ppm
D. 6 ppm
Subject: Chemistry
Molality of a solution in aqueous medium is \( 0.8 . \) Calculate its mole
fraction and the percentage by mass of solute if molar mass of solute is 60 .
A. \( 0.014,4.8 \% \)
В. \( 0.014,5 \% \)
c. \( 0.1,4.8 \% \)
D. \( 0.4,8 \% \)
Subject: Physics
Two persons \( P \) and \( Q \) of the same height are carrying a uniform beam of length \( 3 m . \) If \( Q \) is at one end, then the
distance of \( P \) from the other end such
that \( P, Q \) receive loads in the ratio 5: 3
is:
\( \mathbf{A} \cdot 0.5 m \)
B. \( 0.6 m \)
c. \( 0.75 m \)
D. \( 1 m \)
Subject: Chemistry
If the second I.P of calcium is 275.12
kcals \( m o l^{-1}, \) then, the equation that
represents this ionization can
be written as:
A \( \cdot C a_{(S)}^{+} \rightarrow C a_{(S)}^{3+}+2 e^{-}-275.12 \) kcals
B. \( C a_{(S)}^{+} \rightarrow C a_{(S)}^{3+}+2 e^{-}+275.12 \) kcals
c. \( C a_{(S)}^{+} \rightarrow C a_{(S)}^{2++}+e^{-}+275.12 \) kcals
D. \( C a_{(S)}^{+} \rightarrow C a_{(S)}^{2+1}+e^{-}-275.12 \) kcals
Subject: Maths
Let \( \mathbf{A} \) be a square matrix. Consider
\( \left.\left.\text { 1) }\left.\mathbf{A}+\mathbf{A}^{\mathbf{T}} \text { 2 }\right) \mathbf{A} \mathbf{A}^{\mathbf{T}} \mathbf{3}\right) \mathbf{A}^{\mathbf{T}} \mathbf{A} \mathbf{4}\right) \mathbf{A}^{\mathbf{T}}+\mathbf{A} \)
5) \( \left.\mathbf{A}-\mathbf{A}^{\mathbf{T}} \mathbf{6}\right) \mathbf{A}^{\mathbf{T}}-\mathbf{A}, \) Then
A. all are symmetric matrices
B. (2),(4), (6) are symmetric matrices
c. (1),(2),(3),(4) are symmetric matrices \&
(5),(6) are skew symmetric matrices
D. 5,6 are symmetric
Subject: Physics
A \( 40 k g \) boy whose leg bones are \( 4 c m^{2} \) in
area and \( 50 \mathrm{cm} \) long falls through a
height of \( 50 c m \) without breaking his leg bones. If the bones can stand a stress of
\( 0.9 \times 10^{8} N / m^{2} . \) Calculate Young's
Modulus for the material of the bone
Subject: Chemistry
In a molecule of phosphorus (V) oxide,
there are:
A. \( 4 P-P, 10 P-O \) and \( 4 P=O \) bonds
B. \( 12 P-O \) and \( 4 P=O \) bonds
c. \( 2 P-O \) and \( 4 P=P \) bonds
D. \( 6 P-P, 12 P-O \) and \( 4 P=P \) bonds
Subject: Physics
toppr
\( Q \) тур
the photosphere) of the star emits radiations of all wavelengths, producing continuous spectrum. When these radiations pass through the outer, relatively cooler, layer of the star, the radiations of certain wavelengths are selectively absorbed by this layer. This explains the dark lines in the spectrum of a star. The dark lines are
characteristic of the substances
present in the outer layer of the star. The surface temperature T of a star can be estimated by measuring the
wavelengths \( \lambda_{m} \) at which the intensity of the emitted radiation is maximum and then using Wien's displacement
law which states that \( \lambda_{m} \times \mathrm{T}=\mathrm{b} \) where
b is a constant called Wien's constant
and the above relation is called Wien's
Displacement Law which states that as the temperature increases, the maximum intensity of emission shifts (or is displaced) towards the shorter wavelengths. The value of constant has been found experimentally to be
\( 2.89 \times 10^{-3} \mathrm{mK} \)
Which one of the curves shown in Fig represents the spectral distribution of
energy \( E_{\lambda} \) of black body radiations
where \( \lambda \) is the wavelength?
4
B.
\( c \)
D.
Subject: Physics
Two resistors are connected in series
\( \operatorname{across} \) a \( 5 ~ V \) rms source of alternating potential. The potential difference \( \operatorname{across} 6 \Omega \) resistor is \( 3 V . \) If \( R \) is
replaced by a pure inductor \( L \) of such
magnitude that current remains same, then the same potential difference \( \operatorname{across} L \) is:
\( \mathbf{A} \cdot 1 V \)
B. \( 2 V \)
c. \( 3 V \)
D. \( 4 V \)
Subject: Maths
If \( \boldsymbol{A}=\left(\begin{array}{ccc}\mathbf{8} & \mathbf{5} & \mathbf{2} \\ \mathbf{1} & \mathbf{- 3} & \mathbf{4}\end{array}\right), \) then find \( \boldsymbol{A}^{\boldsymbol{T}} \) and
\( \left(A^{T}\right)^{T} \)