AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
The correct name for the complex
\( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]\left[\boldsymbol{C o}\left(\boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)_{3}\right] \) is:
A. hexaaminechromium(III) trioxalatocobalt (III)
B. hexaamminechromate
(III) trioxalatocobalate (III)
c. hexaamminechromium
(III) trioxalatocobaltate (III)
D. hexaamminechromate
(III) trioxalatocobalt (III)
Subject: Chemistry
When \( C l_{2} \) is passed through moist slaked lime, the compound formed is :
A. \( C a O_{2} C l_{2} \)
в. \( C a O_{2} C l \)
c. \( C a O C l \)
D. \( \operatorname{CaCl}_{2} \mathrm{O}_{4} \)
Subject: Chemistry
Assertion
Density is expressed as \( g m L^{-1} \) whereas specific gravity is dimensionless.
Reason
Specific gravity is ratio of the masses of solution and solvent.
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
A wave represented by the equation \( \boldsymbol{Y}=\boldsymbol{A} \cos (\boldsymbol{k} \boldsymbol{x}-\boldsymbol{\omega} \boldsymbol{t}) \) is superimposed
with another wave to form a stations
wave such that the point \( x=0 \) is a node. The equation of the other wave is
A \( .-A \sin (k x+\omega t) \)
B. \( -A \cos (k x+\omega t) \)
c. \( A \sin (k x+\omega t) \)
D. \( A \cos (k x+\omega t) \)
Subject: Chemistry
The minimum work which must be done
to compress \( 16 g \) of oxygen isothermally, at \( 300 K \) from pressure of \( 1.01325 \times \) \( \mathbf{1 0}^{3} \boldsymbol{N} / \boldsymbol{m}^{2} \) to \( \mathbf{1 . 0 1 3 2 5} \times \mathbf{1 0}^{\mathbf{5}} \boldsymbol{N} / \boldsymbol{m}^{\mathbf{2}} \) is
\( \mathbf{n} \mathbf{1 0 0}=\mathbf{4 . 6}, \boldsymbol{R}=\mathbf{8 . 3} \boldsymbol{J} / \boldsymbol{K}-\boldsymbol{m o l} \)
\( \mathbf{A} \cdot 5727 J \)
в. \( 11.454 k J \)
c. \( 123.255 k J \)
D. \( 1232.55 J \)
Subject: Physics
Two solids \( A \) and \( B \) float in water. It is
observed that \( A \) floats with half of its
volume immersed and B floats with \( 2 / 3 \) of its volume immersed. The ratio of
their densities is
A .4: 3
B. 3:4
\( c \cdot 2: 3 \)
D. 3:2
Subject: Physics
\( \mathbf{A} \)
300 pound fullback carrying the football towards the goal line encounters a 150 pound defensive back
near the goal line. The two are moving at the same speed when they both leave their feet and collide head-on in mid-air.
The defensive back goes flying backward, and the fullback continues
forward, scoring a touchdown. As a result of the collision. How do the
player's changes in momentum compare?
A. The amount of the defensive back's momentum changes is twice as much as the fullback's
B. The amount of the fullback's momentum changes is twice as much as the back's
c. The amount of the defensive back's momentum changes is more than twice as much as the fullback's
D. The amount of the fullback's momentum change is more than twice as much as the fullback's
E. The amount of momentum change for each player is the same
Subject: Chemistry
Match the column I with Column II and
select the correct option from the codes
given below.
(a) \begin{tabular}{l|l|l} 
column I & & Column II \\
& \\
Hottest zone of candle flame & (i) & Zone of unburunt wax vapours. \\
Yellow zone of candle flame & (ii) & Nonluminous zone \\
Black innermost zone of the candle flame & (iii) & Incomplete combustion zone/ \\
\hline
\end{tabular}
(b)
\( (c) \)
\( A \)
(a) - (i), (b) - (ii), (c) - (iii)
B. (a) - (ii), (b) - (i), (c) - (iii)
c. (a) - (i), (b) - (iii), (c) - (ii)
D. (a) - (ii), (b) - (iii), (c) - (i)
Subject: Maths
Let \( \bar{X} \) and M.D. be the mean and the
mean deviation about \( \bar{X} \) of \( n \)
observations \( x_{i}, i=1,2, \ldots . ., n . \) If each
of the observations is increased by 5
then the new mean and the mean
deviation about the new mean, respectively, are :
A. \( \bar{X}, \) М.D.
в. \( \bar{X}+5, M . D \)
c. \( \bar{X}, M . D .+5 \)
D. \( \bar{X}+5 m, M . D .+5 \)
Subject: Physics
Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a
loop and produces magnetic field \( B_{1} \) at
its centre when a current \( I \) passes
through it. The second wire is bent into
a coil with free identical loops adjacent to each other and produces magnetic
field \( B_{2} \) at the centre of loops with
current \( I / 3 \) passing through it. The
ratio \( \boldsymbol{B}_{1}: \boldsymbol{B}_{2} \)
A. 1: 1
B. 1: 3
c. 1: 9
D. 9: 1
Subject: Chemistry
The shapes and hybridisation of
\( B F_{3} \) and \( B H_{4} \) respectively are:
\( \mathbf{A} \cdot B F_{3}- \) Trigonal, \( s p^{2} \) hybridisation
\( B H_{4}^{-}- \) Square planar, \( s p^{3} \) hybridisation
B. \( B F_{3} \) - Triangular, \( s p^{3} \) d hybridisation
\( B H_{4}^{-}- \) Hexagonal, \( s p^{3} \mathrm{d} \) hybridisation
\( \mathbf{C} \cdot B F_{3}- \) Trigonal, \( s p^{2} \) hybridisation
\( B H_{4}^{-}- \) Tetrahedral, \( s p^{3} \) hybridisation
D. \( B F_{3} \) - Tetrahedral, \( s p^{3} \) hybridisation;
\( B H_{4}^{-}- \) Tetrahedral, \( s p^{3} \) hybridisation.
Subject: Biology
Assertion
Oceans and lakes tend to maintain a
relatively constant temperature.
Reason
Water has high heat capacity and it can withhold large amounts of heat.
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: Chemistry
Assertion
Metals are good conductors of heat and
electricity.
Reason
The positive nuclei are surrounded by a
"sea" of mobile electrons.
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 value of self inductance of a coil is
\( 5 H . \) The value of current changes from
\( 1 A \) to \( 2 A \) in 5 sec., then value of
magnitude of induced emf in it :-
A . \( 10 V \)
в. \( 0.1 V \)
\( c .1 .0 V \)
D. \( 100 V \)
Subject: Maths
If \( \Delta A B C \cong \Delta X Y Z, \) which of the
following statements is incorrect?
\( \mathbf{A} \cdot \angle A=\angle X \)
В. \( \angle B=\angle Z \)
c. \( A B=X Y \)
\( \mathbf{D} \cdot B C=Y Z \)
Subject: Chemistry
Arrange the following elements in terms of increasing first ionization energy:
\( \boldsymbol{G} \boldsymbol{a}, \boldsymbol{B} \boldsymbol{a}, \boldsymbol{R} \boldsymbol{u}, \boldsymbol{F}, \boldsymbol{N} \)
A. \( B a<R u<G a<N<F \)
в. \( G a<B a<R u<F<N \)
c. \( R u<B a<G a<N<F \)
D. None of the above
Subject: Maths
If \( \sum_{i=1}^{10}\left(x_{1}-15\right)=12 \) and \( \sum_{i=1}^{10}\left(x_{i}-\right. \)
15)\( ^{2}=18, \) then the S.D. of observations
\( \boldsymbol{x}_{1}, \boldsymbol{x}_{2} \ldots \ldots \ldots \ldots \boldsymbol{x}_{\mathbf{1 0}} \) is
A \( \cdot \frac{2}{5} \)
B. \( \frac{3}{5} \)
\( c \cdot \frac{4}{5} \)
D. none of these
Subject: Physics
If the binding energy of the electron in a hydrogen atom is \( 13.6 e V \), the energy
required to remove the electron from the first excited state of \( L i^{2+} \) is:
A. 30.6 eV
в. 13.6 eV
c. \( 3.4 e V \)
D. \( 122.4 \mathrm{eV} \)
Subject: Maths
If \( ^{n-1} C_{r}=\left(K^{2}-3\right)^{n} C_{r+1^{\prime}}, \) then \( k \)
belongs to
\( \mathbf{A} \cdot[-\sqrt{3}, \sqrt{3}] \)
В \( \cdot(-\infty,-2) \)
\( \mathbf{c} \cdot(2, \infty) \)
D. \( [-2,-\sqrt{3}] \cup[\sqrt{3}, 2] \)
Subject: Maths
Show that the equation of the line passing through the origin and making an angle \( \theta \) with the line \( y=m x+c \) is
\( \frac{\boldsymbol{y}}{\boldsymbol{x}}=\frac{\boldsymbol{m} \pm \tan \boldsymbol{\theta}}{1 \mp \boldsymbol{m} \tan \boldsymbol{\theta}} \)
Subject: Maths
In the diagram, \( A, B, C, D, E \) are points
on the circle. \( A B \| D C, \angle A D E=39^{\circ} \)
and \( \angle A B C=62^{\circ} . \) Then the values of
and \( y \) respectively are:
A \( \cdot 23^{\circ}, 51^{\circ} \)
B \( \cdot 79^{\circ}, 62 \)
\( c \cdot 62^{\circ}, 79^{\circ} \)
\( 0.51^{\circ}, 23 \)
Subject: Chemistry
The freezing point depression constant
for water is \( -1.86^{0} \mathrm{Cm}^{-1} . \) If \( 5.00 \mathrm{g} \)
\( N a_{2} S O_{4} \) is dissolved in 45.0 g \( H_{2} O, \) the
freezing point is changed by \( 3.82^{0} C \)
Calculate the vant Hoff factor for
\( N a_{2} S O_{4} \)
A . 2.05
B . 2.63
c. 3.11
D. 0.381
Subject: Chemistry
A terpene has molecular formula
\( A\left(C_{10} H_{16} O\right) \) and it is a major
constituent of lemongrass oil. \( \boldsymbol{A} \) on
treatment with acidified \( K M n O_{4} \)
solution produces acetone, Oxalic acid
and \( \boldsymbol{C H}_{3} \boldsymbol{C O C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C O O H} . \boldsymbol{A} \| \mathbf{s o}, \boldsymbol{A} \)
does not give silver mirror test with Tollen's reagent. The correct deduction regarding \( \boldsymbol{A} \) is/are:
A. \( A \) gives positive iodoform test
B. \( A \) has two stereoismers
c. \( A \) has one chiral carbon
D. \( A \) on treatment with \( N H_{2} O H \) gives six pair of diastereomers
Subject: Chemistry
A solution of hydrochloric acid is required for an experiment. The experimenter must first prepare the
solution for use by diluting \( 10.0 m L \) of
the hydrochloric acid to create \( 200 m L \)
of the solution.
Which of the following would be the poorest choice of glassware for measuring the solute for the dilution?
A. A graduated cylinder
B. A volumetric flask
c. A burrette
D. A volumetric pipette
Subject: Biology
During glycolysis, fructose 1,6 biphosphate is split into
A. Dihydroxyacetone phosphate and 2 phosphoglyceraldehyde
B. Dihydroxyacetone phosphate and 1 phosphoglyceraldehyde
c. Dihydroxyacetone phosphate and 4 phosphoglyceraldehyde
D. Dihydroxyacetone phosphate and 3phosphoglyceraldehyde
Subject: Maths
Simplify: \( \left(a^{2} b^{2} c^{3}-a^{2} b^{2} c^{3}+a^{2} b^{2} c^{3}\right) \div \)
\( a^{2} b^{2} c^{3} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c \)
D. None of these
Subject: Maths
Evaluate \( \int_{0}^{1} \frac{\mathbf{1}-\boldsymbol{x}}{\mathbf{1}+\boldsymbol{x}} \cdot \frac{\boldsymbol{d} \boldsymbol{x}}{\sqrt{\boldsymbol{x}+\boldsymbol{x}^{2}+\boldsymbol{x}^{3}}} \)
A \( \cdot \frac{\pi}{3} \)
в.
c. \( \frac{\pi}{12} \)
D.
Subject: Physics
An isosceles glass prism with angles
\( 40^{\circ} \) is clamped over a tray of water in a position such that the base is just dipped in water. A ray of light incident normally on the inclined face suffers
total internal reflection at the base. If
the refractive index of water is 1.33 then
the condition imposed on the refractive
index \( \mu \) of the glass is :
A \( . \quad \mu<2.07 \)
в. \( \mu>2.07 \)
c. \( \mu<1.74 \)
D. \( \mu>1.74 \)
Subject: Maths
Construct a \( \triangle A B C \) in which \( A B= \)
\( \mathbf{5} c \boldsymbol{m} \cdot \angle \boldsymbol{B}=\mathbf{6 0}^{\circ} \) altitude \( \boldsymbol{C} \boldsymbol{D}=\mathbf{3} \boldsymbol{c m} \)
Construct a \( \triangle A Q R \) similar to \( \triangle A B C \)
such that side of \( \triangle A Q R \) is 1.5 times
that of the corresponding sides of
\( \triangle \boldsymbol{A} \boldsymbol{C} \boldsymbol{B} \)
Subject: Physics
Water is filled to a height \( \boldsymbol{H} \) behind \( \boldsymbol{a} \)
dam of width \( w . \) The resultant force on
dam is:
A. \( p g w H^{2} \)
В \( \cdot \frac{1}{2} p g w H^{2} \)
c. \( 2 p g w H^{2} \)
D. \( 4 p g w H^{2} \)
Subject: Chemistry
The value of \( k_{c} \) for the reaction
\( \mathbf{2} \boldsymbol{A} \rightleftharpoons \boldsymbol{B}+\boldsymbol{C} \) is \( 2 \times 10^{-3} \)
At a given time the composition of reaction mixture is \( [A]=[B]=[C]=3 x \)
\( 10^{-4} \) M. In which direction the reaction
will proceed?
A. From left to right
B. From right to left
c. The reaction is at equilibrium
D. First to the right than left
Subject: Maths
\( \int \frac{2 \sin x}{(3+\sin 2 x)} d x \) is equal to
\( \mathbf{A} \cdot \frac{1}{2} \ln \left|\frac{2+\sin x-\cos x}{2-\sin x+\cos x}\right| \)
\( \frac{1}{\sqrt{2}} \tan ^{-1} x\left(\frac{\sin x+\cos x}{\sqrt{2}}\right)+c \)
B. \( \frac{1}{2} \ln \left|\frac{2+\sin x-\cos x}{2-\sin x+\cos x}\right| \)
\( \frac{1}{2 \sqrt{2}} \tan ^{-1} x\left(\frac{\sin x+\cos x}{\sqrt{2}}\right)+c \)
C \( \frac{1}{4} \ln \left|\frac{2+\sin x-\cos x}{2-\sin x+\cos x}\right| \)
\( \frac{1}{\sqrt{2}} \tan ^{-1} x\left(\frac{\sin x+\cos x}{\sqrt{2}}\right)+c \)
D. none of these
Subject: Chemistry
\( \mathbf{5 0} \boldsymbol{m} \boldsymbol{L} \) of \( \mathbf{0 . 0 5} \boldsymbol{M} \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{C O}_{3} \) is titrated
against \( 0.1 M H C l . \) On adding \( 40 m L \) of \( H C l, p H \) of the solution will be
[Given for \( \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{O}_{3}, \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}_{1}}= \)
\( \mathbf{6 . 3 5} ; \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}_{2}}=\mathbf{1 0 . 3 3} ; \log \mathbf{3}= \)
\( \mathbf{0 . 4 7 7}, \log \mathbf{2}=\mathbf{0 . 3 0}] \)
A . 6.35
B. 6.526
c. 8.34
D. 6.173
Subject: Physics
A ball of mass \( M \) falls from a height \( h \) on a floor which the coefficient of
restitution is \( e . \) The height attained by the ball after two rebounds is:
\( \mathbf{A} \cdot e^{2} h \)
B \( \cdot e h^{2} \)
\( \mathbf{c} \cdot e^{4} h \)
D. \( \frac{h}{e^{4}} \)
Subject: Maths
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\{\log (\boldsymbol{x}+\sqrt{\boldsymbol{a}^{2}+\boldsymbol{x}^{2}})\}= \)
A. \( \frac{1}{(x+\sqrt{a^{2}+x^{2}})} \)
в. \( \frac{x}{\sqrt{a^{2}+x^{2}}} \)
c. \( \frac{1}{x(x+\sqrt{a^{2}+x^{2}})} \)
D. \( \frac{1}{\sqrt{a^{2}+x^{2}}} \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}+\frac{1}{\boldsymbol{x}} \)
prove that \( [\boldsymbol{f}(\boldsymbol{x})]^{3}=\boldsymbol{f}\left(\boldsymbol{x}^{3}\right)+\boldsymbol{3} \boldsymbol{f}\left(\frac{1}{x}\right) \)
Subject: Physics
Kepler's third law of planetary motion states that : (Symbols have their usual
meaning)
A. \( V_{0}=\sqrt{R g} \)
B . \( \overrightarrow{F_{12}}=-\overrightarrow{F_{21}} \)
\( \mathbf{c} \cdot r^{2} \propto T^{3} \)
\( \mathbf{D} \cdot r^{3} \propto T^{2} \)
Subject: Physics
A block is gently placed at the top of a inclined plane \( 6.4 \mathrm{m} \) long. Find the time taken by the block of slide down to the
bottom of plane. The plane makes an
angle 30 with the horizontal. coefficient
of friction between the block and the
plane is \( 0.2 .\left[\mathrm{g}=10 \mathrm{m} / \mathrm{sec}^{2}\right] \)
Subject: Physics
A ball of mass \( 50 g \) moving at a speed of \( 2.0 m / s \) strikes a plane surface at an
angle of incidence \( 45^{\circ} \) The ball is
reflected by the plane at equal angle of reflection with the same speed.
Calculate
(a) the magnitude of the change in momentum of the ball (b) the change in the magnitude of the
momentum of the ball
Subject: Physics
\( \ln \) an \( A C \) circuit \( , \) the current is given by \( 1=4 \sin (100 \pi+300) \) ampere. The
current becomes maximum first time
(after \( t=0 \) ) at \( t \) equal to
A \( \cdot(1 / 200) \) sec
B. 300sec
c. \( (1 / 50) \) sec
D. \( (1 / 300) \) sec
Subject: Physics
In the given circuit initially the charge
on capacitor is \( Q_{0} \) At \( t=0 \) the switch \( S \)
is closed Which of the following statement(s) is/are correct?
This question has multiple correct options
A . Maximum current through the inductor is \( \frac{Q_{0}}{\sqrt{L C}} \)
B. charge on the capacitor is zero at \( t=\frac{\pi}{2} \sqrt{L C} \)
C. Current through the inductor is maximum at \( t= \)
\( \frac{\pi}{2} \sqrt{L C} \)
D. Maximum magnetic energy can be stored in the inductor is \( \frac{Q_{0}^{2}}{2 C C} \)
Subject: Chemistry
If \( E_{f} \) and \( E_{b} \) are in the ration \( 20: 31 E_{f} \)
and \( E_{b} \) at \( 30 \mathrm{K} \) respectively are:
A. 60 kJ and 93 kJ
B. -44 kJ and 93 kJ
c. 13 ks and -63 k
D. none of these
Subject: Physics
A man in a car at location \( Q \) on a
straight highway is moving with speed
\( \boldsymbol{v} . \) He decides to reach a point \( \boldsymbol{P} \) in a
field at a distance \( \boldsymbol{d} \) from highway
(point \( M) \) as shown in the figure. Speed
of the car in the field is half to that on
the highway. What should be the
distance \( R M, \) so that the time taken to
reach P is minimum?
A \( \cdot \frac{d}{\sqrt{3}} \)
B. \( d \) \( \overline{2} \)
c. \( \frac{d}{\sqrt{2}} \)
D.
Subject: Maths
The \( \boldsymbol{f}(\boldsymbol{x})=(3-\boldsymbol{x}) e^{2 x}-4 \boldsymbol{x} e^{x}-\boldsymbol{x} \) has
\( \mathbf{A} \cdot \) a maximum at \( x=0 \)
B. a minimum at \( x=0 \)
C. neither of two at \( x=0 \)
D. \( f(x) \) is not differentiable at \( x=0 \)
Subject: Maths
If square matrices \( A \) and \( B \) are such
that \( \boldsymbol{A} \boldsymbol{A}^{\prime}=\boldsymbol{A}^{\prime} \boldsymbol{A}, \boldsymbol{B} \boldsymbol{B}^{\prime}=\boldsymbol{B}^{\prime} \boldsymbol{B}, \boldsymbol{A} \boldsymbol{B}^{\prime}= \)
\( \boldsymbol{B}^{\prime} \boldsymbol{A} \)
then is the statement \( A B(A B)^{\prime}= \)
\( (A B)^{\prime} A B \) is
where \( A^{\prime} \) is transpose of \( A \)
If true enter 1 else enter 0
Subject: Maths
\( M \) and \( N \) are the midpoints of the diagonals \( A C \) and \( B D \) respectively of quadrilateral \( \boldsymbol{A B C D} \), then \( \overline{\boldsymbol{A B}}+ \) \( A D+\overline{C B}+\overline{C D}= \)
\( \mathbf{A} \cdot 2 \overline{M N} \)
в. \( 2 \overline{N M} \)
\( c .4 \overline{M N} \)
D. \( 4 \overline{N M} \)
Subject: Physics
current induced in the loop when arm
PQ is moved with velocity \( 20 \mathrm{m} / \mathrm{s} \)
\begin{tabular}{c|ccccc|cc}
\( \times \mathrm{N} \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \mathrm{P} \times \) & \( \times \) & \\
\hline\( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) \\
\( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) \\
\( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & 0 \\
\( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \\
\( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \\
\( \times \mathrm{M} \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \mathrm{Q} \times \) & \( \times \) &
\end{tabular}
Subject: Physics
The purpose of soft iron cylinder
between the pole pieces of the horse-
shoe magnet in a moving
coil galvanometer is
A. to increase the magnetic induction in the polar
\( \operatorname{gap} \)
B. to evenly distribute the magnetic lines of force
C. to provide a radial magnetic field
D. to reduce the magnetic flux leakage in the polar
\( \operatorname{gap} \)
Subject: Physics
Let \( V_{s} \) be the speed of the source
emitting sound waves, \( n \) the actual
frequency of the source of sound, \( V \) the speed of the sound in the medium and
\( n_{1} \) the frequency of sound waves as
perceived by a stationary observer to whom the source of sound is
approaching. The formula for
calculating \( n_{1} \) is :
\( \mathbf{A} \cdot \mathbf{n}_{1}=\mathbf{n}\left(1-\mathbf{V}_{\mathbf{s}} / \mathbf{V}\right) \)
B. \( n_{1}=n\left(\frac{V}{V-V_{s}}\right) \)
\( \mathbf{c} \cdot \mathbf{n}_{1}=\mathbf{n} /\left(1+\mathbf{V}_{\mathbf{s}} / \mathbf{V}\right) \)
\( \mathbf{D} \cdot \mathbf{n}_{1}=\mathbf{n} \)
Subject: Chemistry
\( \mathbf{4} \boldsymbol{H}^{+}+\boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}^{-}+\boldsymbol{C}_{2} \boldsymbol{O}_{4}^{2-} \rightarrow \boldsymbol{M} \boldsymbol{n}^{2+}+ \)
\( 2 C O_{2}+4 O H^{-} \)
For the preceding reaction, which of the following statements is not always true based on the knowledge that oxalate reacts slowly at room temperature causing a fade in the purple colour due to the manganate ion?
A. Using an acid-base catalyst will increase the overal rate of the reaction
B. There are multiple steps in the reaction mechanism.
c. The reaction is carried out at elevated temperatures to make the procedure practical in terms of time
D. Use of a spectrophotometer and a Beer's Law plot will help determine the rate for the overall reaction mechanism.
Subject: Physics
Neglecting the density of air, the terminal velocity obtained by a raindrop of radius 0.3 mm falling through air of viscosity \( 1.8 \times 10^{-5} N s m^{-2} \) will be:
\( \mathbf{A} \cdot 10.9 \mathrm{ms}^{-1} \)
B. \( 7.48 \mathrm{ms}^{-1} \)
c. \( 3.7 \mathrm{ms}^{-1} \)
D. \( 12.8 \mathrm{ms}^{-1} \)
Subject: Chemistry
A constant pressure calorimeter consists of an insulated beaker of mass
\( 82 g \) made up of glass with heat capacity \( 0.75 J K^{-1} g^{-1} . \) The beaker
contains \( 100 \mathrm{m} L \) of \( 1 \mathrm{M} \) HCl at
\( \mathbf{2 2 . 6}^{\circ} \boldsymbol{C} \) to which \( \mathbf{1 0 0} \boldsymbol{m} \boldsymbol{L} \) of \( \mathbf{1} \boldsymbol{M} \)
NaOH at \( 23.4^{\circ} C \) is added. The final
temperature after the reaction is complete at \( 29.3^{\circ} \mathrm{C} \). What is \( \Delta H \) per mole for this neutralisation reaction?
Assume tha the heat capacities of all solutions are equal to that of same
volumes of water
Subject: Physics
Statement \( 1: \frac{13}{6} C \) and \( _{6}^{14} C \) are isotopes of the element carbon.
Statement 2: Isotopes of an element
have the same number of protons in the nucleus but have a different number of
neutrons.
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both Statement 1 and Statement 2 are correct but Statement 2 is not the correct explanation of Statement 1.
c. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct
E. Both the Statement 1 and Statement 2 are not correct
Subject: Physics
When two progressive waves of
intensity \( \boldsymbol{I}_{1} \) and \( \boldsymbol{I}_{2} \) but slightly different
frequencies superpose, the resultant
intensity fluctuates between
\( \mathbf{A} \cdot(\sqrt{I_{1}}+\sqrt{I_{2}})^{2} \) and \( (\sqrt{I_{1}}-\sqrt{I_{2}})^{2} \)
B \( \cdot(\sqrt{I_{1}}-\sqrt{I_{2}}) \) and \( (\sqrt{I_{1}}+\sqrt{I_{2}}) \)
\( \mathbf{C} \cdot\left(I_{1}+I_{2}\right) \) and \( \left(I_{1}-I_{2}\right) \)
D. \( \left(I_{1}+I_{2}\right)^{2} \) and \( \left(I_{1}-I_{2}\right)^{2} \)
Subject: Chemistry
\( \boldsymbol{p} \boldsymbol{K}_{a} \) and \( \boldsymbol{K}_{a} \) of an acid are connected
by the relation - -
A \( \cdot p k_{a}=\log k_{a} \)
B \( \cdot p k_{a}=-p H \)
c. \( p k_{a}=-\log k_{a} \)
D・ \( p k_{a}=- \) logk \( _{b} \)
Subject: Chemistry
For the reaction, \( \left[\boldsymbol{A} \boldsymbol{g}(\boldsymbol{C} \boldsymbol{N})_{2}\right]^{-} \rightleftharpoons \)
\( A g^{+}+2 C N^{-}, \) the equilibrium
constant \( \boldsymbol{K}_{c} \) at \( \mathbf{2 5}^{\boldsymbol{o}} \boldsymbol{C} \) is \( \mathbf{4} \times \mathbf{1 0}^{-\mathbf{1 9}} \). Then
\( A g^{+} \) concentration in a solution which
has \( 0.1 M K C N \) and \( 0.03 M A g N O_{3} \)
is:
A. \( 7.5 \times 10^{18} \)
B . \( 7.5 \times 10^{-18} \)
c. \( 7.5 \times 10^{19} \)
D. \( 7.5 \times 10^{-19} \)
Subject: Physics
A tunnel is dug along a chord of the
\( \boldsymbol{R} \)
earth at a perpendicular distance
from the earth's centre. Assume wall of
the tunnel is frictionless. Find the force
exerted by the wall on mass m at a
distance \( x \) from the centre of the tunnel
\( \mathbf{A} \)
B. \( \frac{m g x}{\sqrt{R^{2} / a+x^{2}}} \)
\( c \cdot \frac{m g}{3} \)
D. \( \frac{m g x}{R} \)