AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A ladder \( ^{\prime} A B^{\prime} \) of weight \( 300 N \) and length \( 5 m \) is lying on a horizontal surface. Its centre of gravity is at a distance of \( 2 m \) from end \( A . \) A weight of
\( 80 N \) is attached at end \( B \). The work
done in raising the ladder to the vertical
position with end \( ^{\prime} \boldsymbol{A}^{\prime} \) in contact with the ground is.
A. \( 500 J \)
в. \( 1000 J \)
c. \( 1150 J \)
D. \( 1900 J \)
Subject: Maths
A man is known to speak the truth 3 out of 4 times. He throws a die and reports
that it is a six. The probability that it is actually a six is
A \( \cdot \frac{3}{8} \)
B. \( \frac{1}{5} \)
\( c \cdot \frac{3}{4} \)
D. None of these
Subject: Biology
Which of the following pollutant is released in larger quantity from the exhaust emission of a petrol/diesel automobile?
A . \( c o \)
B. \( \mathrm{cO}_{2} \)
c. \( \mathrm{NO}_{2}, \mathrm{SO}_{2} \) and \( \mathrm{Pb} \)
D. Hydrocarbons
Subject: Physics
An un-publicized beam of intensity \( 2 a^{2} \)
passes through a thin Polaroid. Assuming zero absorption in the Polaroid the intensity of emergent planes polarized light is
\( \mathbf{A} \cdot 2 a^{2} \)
в. \( a^{2} \)
c. \( \sqrt{2} a^{2} \)
D. \( \frac{a^{2}}{2} \)
Subject: Maths
If \( x=\cos ^{2}\left(\tan ^{-1}\left(\sin \left(\cot ^{-1} 3\right)\right)\right), \) then
\( 1331 x^{3}-3630 x^{2}+3300 x+7369= \)
\( m \) then find the sum of the second and
third digits of \( \boldsymbol{m} \)
Subject: Chemistry
\( 0.1 m^{3} \) of water at \( 80^{\circ} \) is mixed with
\( 0.3 m^{3} \) of water at \( 60^{\circ} . \) The final
temperature of mixture is :
A \( \cdot 80^{\circ} \mathrm{C} \)
B . \( 70^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 60^{\circ} \mathrm{C} \)
D. \( 75^{\circ} \mathrm{C} \)
Subject: Chemistry
What is the ethanol ethanoic acid ratio
if the breathalyzer records 1.33 V and other species are at 1 M?
A \( \cdot 10^{4} \)
B . \( 10^{-4} \)
\( c \cdot 10^{12} \)
\( \mathbf{D} \cdot 10^{-12} \)
Subject: Physics
Assertion: In Joules bulb apparatus, as
reservoir is moved up, the mercury level
raises into the bulb.

Reason: The pressure on the enclosed gas increases.
A. Both assertion (A) and reason (R) are correct and R gives the correct explanation
B. Both assertion (A) and reason (R) are correct but R doesnt give the correct explanation
C. A is true but R is false
D. A is false but R is true
Subject: Physics
In a uniform magnetic field of induction
\( B \) a wire in the form of a semicircle of
radius \( r \) rotates about the diameter of
the circle with angular frequency \( \omega . \) the
axis of rotation is perpendicular to the
field. If the total resistance of the circuit
is \( R \) the mean power generated per period of rotation is
A \( \cdot \frac{B \pi r^{2} \omega}{2 R} \)
B. \( \frac{\left(B \pi r^{2} \omega\right)^{2}}{8 R} \)
c. \( \frac{(B \pi r \omega)^{2}}{2 R} \)
D. \( \frac{\left(B \pi r \omega^{2}\right)^{2}}{8 R} \)
Subject: Chemistry
\( K_{c} \) for \( \frac{3}{2} H_{2}+\frac{1}{2} N_{2} \rightleftharpoons N H_{3} \) are 0.0266
and 0.0129 at \( m^{-1} \) respectively at \( 350^{\circ} C \)
and \( 400^{\circ} \mathrm{C} . \) Calculate heat of formation
of \( \boldsymbol{N} \boldsymbol{H}_{3} \)
A . 12.140 Kcal
B. 1.214 Kcal
c. \( -12.140 \mathrm{Kcal} \)
D. -1.214 Kcal
Subject: Physics
An element \( X \) decays into element \( Z \) by
two-step process.
\[
\begin{array}{l}
\boldsymbol{X} \longrightarrow \boldsymbol{Y}+_{2}^{4} \boldsymbol{H} \boldsymbol{e} \\
\boldsymbol{Y} \longrightarrow Z+2 \bar{e} \text { then }
\end{array}
\]
\( A \cdot X \) and \( Z \) are isobars
B. \( X \) and \( Y \) are isotopes
c. \( X \) and \( Z \) are isotones
D. \( X \) and \( Z \) are isotopes
Subject: Physics
A charge \( \boldsymbol{q}(>\mathbf{0}) \) moves towards the
centre of a circular loop of radius \( \boldsymbol{R} \)
along its axis. The magnitude of B along
the periphery of the loop is
A . zero
B. \( \frac{\mu_{0}}{4 \pi} \frac{q v R}{\sqrt{\left(R^{2}+x^{2}\right)^{3}}} \)
c. \( \frac{q v R}{\sqrt{R^{2}+x^{2}}} \)
D. \( \frac{\mu_{0}}{4 \pi} \frac{q v R}{\sqrt{R^{2}+x^{2}}} \)
Subject: Physics
A force acting on a particle varies with
the displacement \( x \) as \( F=a x-b x^{2} \)
Where \( a=1 N / m \) and \( b=1 N / m^{2} \)
The work done by this force for the first
one meter \( (F \text { is in newtons, } x \) is in
meters is:
A \( \cdot \frac{1}{6} J \)
в. \( \frac{2}{6} J \)
c. \( \frac{3}{6} J \)
D. None of these
Subject: Physics
The current in the rod is \( \left(\boldsymbol{I}_{o}=\frac{V_{o}}{R_{o}}\right) \)
A \( \cdot I_{o} e^{x / L} \)
В . \( \frac{I_{0}}{L}(L-X) \)
c. \( I_{o} e^{-x / L} / L \)
D \( \cdot \frac{I_{0}}{L}(L+X) \)
Subject: Physics
A proton enters a magnetic field of flux density \( 1.5 \mathrm{T} \) velocity of \( 20 \times 10^{2} \mathrm{ms}^{-1} \) at
an angle of \( 30^{\circ} \) with the field. The force on the position is \( \left[e_{p}=1.6 \times 10^{-19} C\right] \)
B . \( 2.403 \times 10^{-12} N \)
c. \( 3 \times 10^{-5} N \)
D. \( 3 \times 10^{-4} N \)
Subject: Chemistry
In the formation of \( N_{2}^{+} \) from \( N_{2} \), the electron is lost from:
\( \mathbf{A} \cdot \) a \( \sigma \) -orbital
B . a \( \pi \) -orbital
c. a \( \sigma^{*} \) -orbital
D. a \( \pi^{*} \) -orbital
Subject: Biology
For the formation of urea, which one of
the following is required along with ammonia?
A. Arginase, \( C O_{2} \) and \( O_{2} \)
B. Arginase, \( C O_{2} \) and water
C. Asparate, \( C O_{2} \) and water
D. Asparate, \( C O_{2} \) and \( O_{2} \)
Subject: Physics
A short linear object of length \( b \) lies along the axis of a concave mirror of
focal length \( f \) at a distance \( u \) from the pole of the mirror. The size of the image is approximately equal to:
\( A \)
\[
b\left(\frac{u-f}{f}\right)^{\frac{1}{2}}
\]
в.
\[
b\left(\frac{u-f}{f}\right)
\]
\( c \)
\[
b\left(\frac{f}{u-f}\right)^{\frac{1}{2}}
\]
D.
\[
b\left(\frac{f}{u-f}\right)^{2}
\]
Subject: Maths
To know the opinion of the student about the subject statistic, a survey of
200 students was conducted.
The data is recorded in the following table
opinion 1 Like Dislike
No. of Students 65 135
Find the probability that a student chosen at random
\( (i) \) likes statistics,
\( (i i) \) does not like it.
A.
\[
\begin{array}{l}
(i) \frac{13}{40} \\
(i i) \frac{19}{40}
\end{array}
\]
в.
\[
(i) \frac{27}{40}
\]
\( (i i) \frac{13}{40} \)
c.
\[
(i) \frac{17}{40}
\]
\( (i i) \frac{29}{40} \)
D. None of these
Subject: Physics
A particle with charge \( q \) is projected successively along the \( x \) and \( y \) axes with same speed v. The force on the particle in these situations are \( \boldsymbol{q} \boldsymbol{v} \boldsymbol{B}(-\boldsymbol{3} \hat{\boldsymbol{j}}+\boldsymbol{4} \hat{\boldsymbol{k}}) \)
and \( q v B(3 \hat{i}) \) respectively. Find the unit vector in direction of \( \vec{B} \)
Subject: Physics
Two bodies of masses \( 0.1 k g \) and \( 0.4 k g \) move towards each other with velocities
\( 1 m / s \) and \( 0.1 m / s \) respectively. After
collision they stick together. In \( 10 s \) the combined mass travels
\( \mathbf{A} \cdot 120 m \)
B. \( 0.12 m \)
\( c .12 m \)
D. \( 1.2 m \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{4}\end{array}\right], \) then number of
elements in \( A \) are
A .4
B. 3
\( c \cdot 2 \)
D. None of these
Subject: Physics
Two unknown resistances are
connected in two gaps of a meter-
bridge. The null point is obtained at \( 40 \mathrm{cm} \) from left end. A \( 30 \Omega \) resistance is
connected in series with the smaller of the two resistances, the null point shifts
by \( 20 \mathrm{cm} \) to the right end. The value of
smaller resistance in \( \Omega \) is
A . 12
B . 24
\( c .36 \)
D. 48
Subject: Maths
Calculate the rate of flow of glycerin of
density \( 1.25 \times 10^{3} k g / m^{3} \) through the
conical section of a pipe, if the radii of its ends are \( 0.1 m \) and 0.04 m and the
pressure drop across its length is
\( \mathbf{1 0} N / \boldsymbol{m}^{2} \)
A \( \cdot 6.43 \times 10^{-4} m^{3} / s \)
B. \( 5.43 \times 10^{-4} \mathrm{m}^{3} / \mathrm{s} \)
c. \( 5.44 \times 10^{-3} \mathrm{m}^{3} / \mathrm{s} \)
D. \( 6.43 \times 10^{-3} \mathrm{m}^{3} / \mathrm{s} \)
Subject: Physics
For a transistor amplifier in common emitter configuration for load
impedance of \( 1 \mathrm{k} \Omega\left(\mathrm{h}_{f e}=50 \text { and } \mathrm{h}_{\mathrm{o} e}=\right. \)
\( 25 \mu A / V \), the current gain is:
A. -5.2
B . -15.7
c. -24.8
D. -48.78
Subject: Physics
Assertion
An electron cannot exist in the nucleus.
Reason

The de Broglie wavelength of an electron is much smaller than the diameter of
the nucleus.

Read the above assertion and reason
and choose the correct option regarding
¡t.
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: Chemistry
A compound \( X \) on heating gives a colourless gas. The residue is dissolved
in water to obtain \( Y . \) Excess \( C O_{2} \) is
passed through aqueous solution of \( \boldsymbol{Y} \)
when \( Z \) is formed. \( Z \) on gentle heating
gives back \( X . \) The compound \( X \) is:
A \( \cdot \operatorname{Ca}\left(\mathrm{HCO}_{3}\right)_{2} \)
в. \( C a C O_{3} \)
с. \( _{\text {NaH } \mathrm{CO}_{3}} \)
D. \( N a_{2} C O_{3} \)
Subject: Chemistry
The following results have been obtained during the kinetic studies of
the reaction:
\( \mathbf{2} \boldsymbol{A}+\boldsymbol{B} \rightarrow \boldsymbol{C}+\boldsymbol{D} \)
Experiment \( \quad[A] / m o l L^{-1} \quad[B] / m o l L^{-1} \) \begin{tabular}{lll}
1 & 0.1 & 0.1 \\
\hline 11 & 0.3 & 0.2 \\
\hline \( \mathrm{III} \) & 0.3 & 0.4 \\
& & \\
& & \\
& & \\
\( \mathrm{V} \) & 0.4 & 0.1 \\
& &
\end{tabular}
Determine the rate law and the rate
constant for the reaction.
Subject: Maths
A has library has 6 copies of one book, 4 copies of each of three books and single
copies of 8 books. Then number of
arrangements of all the
A \( \cdot \frac{(26) !}{(4 !)^{3} 6 !} \)
В \( \cdot \frac{(26) !}{6 !(4 !)^{4}(6 !)^{3}} \)
c. \( \frac{(26) !}{6 !(4 !)^{2}(6 !)^{3}} \)
D. \( \frac{(26) !}{6 ! ! 4 ! 6 !} \)
Subject: Physics
If a block moving up at \( \boldsymbol{\theta}=\mathbf{3 0}^{\mathbf{0}} \) with a
velocity \( 5 \mathrm{m} / \mathrm{s}, \) stops after \( 0.5 \mathrm{sec}, \) then
\( \mu \) is:
A. 0.48
B. 1.25
\( c \cdot 0.58 \)
D. none of the above
Subject: Physics
Assertion
A given transformer can be used to
step-up or step-down the voltage
Reason
The output voltage depends upon the
ratio of the number of turns of the two
coils of the transformer
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 ionisation energy of 10 times ionized sodium atom is
\( \mathbf{A} \cdot \frac{13.6}{11} e V \)
B. \( \frac{13.6}{112} e V \)
C \( .13 .6 \times(11)^{2} e V \)
D. \( 13.6 e V \)
Subject: Physics
On a two lane road, car A is travelling with a speed of \( 36 \mathrm{km} h^{-1} \). two cars \( \mathrm{B} \) and \( C \) approach car \( A \) in opposite directions with a speed of \( 54 \mathrm{km} h^{-1} \) each. At a certain instant, when the distance \( A B \) is equal to \( A C, \) both being 1 \( \mathrm{km}, \mathrm{B} \) decides to overtake \( \mathrm{A} \) before \( \mathrm{C} \)
does. What minimum acceleration of
car B is required to avoid an accident?
\( A \cdot 9.8 \mathrm{m} s^{-2} \)
B \( \cdot 10 \mathrm{m} \mathrm{s}^{-2} \)
\( \mathrm{c} \cdot 1 \mathrm{m} s^{-2} \)
D. 2.0 \( \mathrm{m} s^{-2} \)
Subject: Maths
If the vectors \( \overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}}+\overrightarrow{\mathbf{c}}, \overrightarrow{\mathbf{a}}+\boldsymbol{\lambda} \overrightarrow{\mathbf{b}}+ \)
\( \mathbf{2} \overrightarrow{\mathbf{c}},-\overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}}+\overrightarrow{\mathbf{c}} \) are linearly dependent
\( \operatorname{then} \lambda= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 3 \)
D. 4
Subject: Chemistry
Assertion
SnO is more reactive towards acid than
\( \boldsymbol{S} \boldsymbol{n} \boldsymbol{O}_{2} \)
Reason
Both SnO and \( S n O_{2} \) are amphoteric
oxides
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
What is the shape of \( F e(C O)_{5} \) molecule
and which of the following d-orbitals involved in hybridization?
A . Tetrahedral \( d_{x^{2}-y^{2}} \)
B. Trigonal bipyramidal, \( d_{x^{2}-y^{2}} \)
C. Trigonal bipyramidal, \( d_{z} \)
D. Square pyramidal
Subject: Physics
A sphere of mass \( m_{1}=2 k g \) collides
with a sphere of mass \( m_{2}=3 k g \) which
is at rest. Mass \( m_{1} \) will move at right angles to the line,joining centres at the time of collision, if the coefficient of
restitution is :
\( A \cdot 4 / 9 \)
в. \( 1 / 2 \)
\( c \cdot \frac{2}{3} \)
D. \( \sqrt{2 / 3} \)
Subject: Physics
In a series LCR circuit, resonance
occurring at \( 105 \mathrm{Hz} \). At that time, the potential difference across the 100 resistance is \( 40 \mathrm{V} \) while the potential difference across the pure inductor is 30v. The inductance L of the inductor is
equal to
A \( \cdot 2.0 \times 10^{-4} \)
B . \( 3.0 \times 10^{-4} \)
c. \( 1.2 \times 10^{-4} \)
D. \( 2.4 \times 10^{-4} \)
Subject: Physics
A uniform metal rod of \( 2 m m^{2} \) cross
section is heated from \( 0^{\circ} \mathrm{C} \) to \( 20^{\circ} \mathrm{C} \). The
coefficient of linear expansion of the rod is \( 12 \times 10^{-6 / 0} \mathrm{C} \). Its Young's modulus of
elasticity is \( 10^{11} \mathrm{N} / \mathrm{m}^{2} \). The
energy stored per unit volume of the rod
is :
\( \mathbf{A} \cdot 2880 J / m^{3} \)
B . \( 1500 J / m^{3} \)
c. \( 5760 J / m^{3} \)
D. \( 1440 J / m^{3} \)
Subject: Maths
If \( \boldsymbol{A} \times \boldsymbol{B}= \)
\( (2,4),(2, a),(2,5),(1,4),(1, a),(1,5) \)
find \( B \)
A \( \cdot\{4,2,5\} \)
в. \( \{4, a, 5\} \)
c. \{4,1,5\}
D. \( \{2, a, 5\} \)
Subject: Chemistry
The reaction: \( \boldsymbol{P} \boldsymbol{C l}_{3}+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{C}_{2} \boldsymbol{O}_{4} \rightarrow \)
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3}+\boldsymbol{3} \boldsymbol{C} \boldsymbol{O}+\boldsymbol{3} \boldsymbol{C} \boldsymbol{O}_{2}+\boldsymbol{3} \boldsymbol{H} \boldsymbol{C l} \) is a
disproportionation reaction
If true enter 1 , else enter 0 .
\( A \)
Subject: Physics
If \( 2 g \) of hydrogen is converted into 1.986gm Helium in a thermonuclear
reaction, the energy released is
\( A \cdot 63 \times 10^{7} J \)
B. \( 63 \times 10^{10} J \)
c. \( 126 \times 10^{10} J \)
D. \( 6.3 \times 10^{20} J \)
Subject: Physics
Planet moves in an elliptical orbit around one of the foci. The ratio of
maximum velocity \( V_{\max } \) and minimum
velocity \( V_{\min } \) ansd eccentricity e of the
ellipse is given by
A \( \cdot \frac{1-e}{1+e e} \)
В \( \cdot \frac{e-e}{e+e e} \)
c. \( \frac{1+e}{1-e-e} \)
D. \( \frac{e}{e-e} \)
Subject: Physics
Three convex lenses are available
having focal lengths of \( 4 \mathrm{cm}, 40 \mathrm{cm} \) and
\( 4 m \) respectively. Which one could be used as magnifying glass?
A. \( 4 c m \)
в. \( 40 \mathrm{cm} \)
\( c .4 m \)
D. All
Subject: Maths
\( \mathrm{f} \mathrm{A}=\left[\begin{array}{lll}\mathbf{1} & \mathbf{2} & \mathbf{3} \\ \mathbf{4} & \mathbf{5} & \mathbf{6}\end{array}\right], \mathbf{B}=\left[\begin{array}{l}\mathbf{1} \\ \mathbf{0} \\ \mathbf{5}\end{array}\right] \) then \( \mathbf{A B}= \)
\( \mathbf{A} \cdot\left[\begin{array}{lll}1 & 0 & 15\end{array}\right] \)
В. \( \left[\begin{array}{lll}4 & 0 & 30\end{array}\right] \)
\( c \cdot \mid 1 \)
[34]
\( \mathbf{D} \cdot\left[\begin{array}{ll}16 & 34\end{array}\right] \)
Subject: Chemistry
Formic acid is considered as resonance
hybrid of the four resonating
structures
\[
\begin{array}{cc}
\mathbf{0} & \mathbf{O}^{\mathbf{\theta}} \\
\mathbf{H}-\mathbf{C}-\mathbf{O} \mathbf{H} & \longrightarrow \mathbf{H}-\mathbf{C}-\stackrel{\oplus}{\mathbf{O} \mathbf{H}} \\
\mathbf{I} & \mathbf{O}^{\oplus} \\
\mathbf{H}-\mathbf{C}-\mathbf{O}-\mathbf{H} & \mathbf{O}^{\mathbf{\theta}} \\
\mathbf{I V} & \mathbf{I}
\end{array}
\]
Subject: Maths
Find the median of the following data.
\( 22 \quad 25 \) \( \mathbf{3 0} \) \( \boldsymbol{x} \quad \mathbf{1 4} \quad \mathbf{1 8} \)
\( \begin{array}{llll}f & 7 & ! 0 & 12\end{array} \) 16 5
A . 20
B. 19
c. 21
D. 22
Subject: Chemistry
Two liquids \( X \) and \( Y \) are perfectly
immiscible. If \( X \) and \( Y \) have molecular
masses in ration \( 1: 2, \) the total vapour pressure of a mixture of \( \boldsymbol{X} \) and \( \boldsymbol{Y} \)
prepared in weight ratio 2: 3 should be:
\( \left(\boldsymbol{P}_{X}^{0}=\mathbf{4 0 0} \text { torr }, \boldsymbol{P}_{\boldsymbol{Y}}^{0}=\mathbf{2 0 0} \text { torr }\right) \)
A. 314 torr
B. 466.7 torr
c. 600 torr
D. 700 torr
Subject: Maths
Which one of the following statement is
true for the given circle?
A \( \cdot \overline{C D} \cong \overline{A B} \)
B. \( \overline{C D} \neq \overline{A B} \)
c. \( \widehat{C D} \cong \overline{A B} \)
\( \mathbf{D} \cdot \overline{C D} \cong \overline{A B} \)
Subject: Chemistry
When 3 -methylbutan-2-ol is treated with HBr, the following reaction takes
place. What are the correct steps for formation of the above product?
\[
\begin{array}{c}
\mathbf{C H}_{3}-\underset{\mathbf{C}}{\mathbf{C}} \mathbf{H}-\mathbf{C H}-\mathbf{C H}_{3} \frac{\mathbf{H B r}}{\mathbf{I}} \\
\mathbf{U}_{3} \mathbf{O H} \\
\mathbf{B H}_{3}-\mathbf{C}-\mathbf{C H}_{2}-\mathbf{C H}_{3} \\
\mathbf{C H}_{3}
\end{array}
\]
A. Formation of carbocation \( \rightarrow \) Nucleophilic attack by \( B r^{c} \)
B. Formation of carbocation \( \rightarrow 1,2 \) hydride shift Nucleophilic attack by \( B r^{\circ} \)
c. Formation of carbocation \( \rightarrow 1,2 \) methyl shift Nucleophilic attack by \( B r^{\ominus} \)
D. None of these
Subject: Maths
Evaluate the following \( \lim _{n \rightarrow \infty}\left\{\left(1+\frac{1}{n^{2}}\right)\left(1+\frac{2^{2}}{n^{2}}\right) \dots(1+\right. \)
\( \left.\left.\frac{n^{2}}{n^{2}}\right)\right\}^{1 / n} \)
B \( \cdot 2 e^{(\pi-4) / 2} \)
\( ^{c} \cdot \frac{e^{(\pi-4) / 2}}{2} \)
\( \mathbf{D} \cdot e^{(\pi-4)} \)
Subject: Physics
A ray of light from denser medium strikes a rarer medium at angle of incidence \( i . \) The reflected and refracted
rays make an angle of \( 90^{\circ} \) with each
other. The angle of reflection and
refraction are \( r \) and \( r^{\prime} . \) The critical
angle is
A \( \cdot \sin ^{-1}(\tan r) \)
B. \( \sin ^{-1}(\tan i) \)
c. \( \sin ^{-1}\left(\tan r^{\prime}\right) \)
D. \( \sin ^{-1}(\tan (i+r)) \)
Subject: Physics
A body of mass \( m \) is hauled from the
Earth's surface by applying a force \( \overrightarrow{\boldsymbol{F}} \) varying with the height of ascent \( y \) as \( \vec{F}=2(a y-1) m g, \) where \( a \) is a positive
constant. Find the work performed by
this force \( W \) and the increment in the
body's potential energy \( \Delta U \) in the gravitational field of the Earth over the
first half of the ascent.
A. \( W=\frac{3 m g}{4 a}, \Delta U=\frac{m g}{2 a} \)
в. \( W=\frac{3 m g}{a}, \Delta U=\frac{m g}{2 a} \)
c. \( _{W}=\frac{3 m g}{4 a}, \Delta U=\frac{m g}{a} \)
D. \( W=\frac{3 m g}{4 a}, \Delta U=\frac{m g}{3 a} \)
Subject: Chemistry
The energy required to break one mole
of \( C l-C l \) bonds in \( C l_{2} \) is \( 242 k J \)
mol \( ^{-1} \). The longest wavelength of light capable of breaking single \( C l-C l \)
bond is:
\( \left(c=3 \times 10^{8} m s e c^{-1}, N_{A}=6.023 \times 10^{2}\right. \)
A. 700 nm
в. 494 пт
c. 594 ит
D. 640 nm
Subject: Maths
Assertion (A): The points \( \boldsymbol{A}(\mathbf{2}, \mathbf{9}, \mathbf{1 2}), \boldsymbol{B}(\mathbf{1}, \mathbf{8}, \mathbf{8}), \boldsymbol{C}(\mathbf{2}, \mathbf{1 1}, \mathbf{8}) \boldsymbol{D}(\mathbf{1}, \mathbf{1 2} \)
are the vertices of a rhombus
Reason \( (\mathrm{R}): A B=B C=C D=D A \)
and \( \boldsymbol{A C}=\boldsymbol{B D} \)
A. Both A and R are individually true and R is the correct explanation of
B. Both A and R individually true but R is not the correct explanation of A
c. \( A \) is true but \( R \) is false
D. Both A and R false
Subject: Physics
Assertion
In case of electric bell if AC power supply is used then its amplitude of the supply must be sufficiently high.
Reason
Due to AC supply there will be continuous magnetization and demagnetization of the magnet
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
Which of the following is correct IUPAC
name of any complex compound?
A. Tris(acetylacetonato)iron(III)chloride
B. Hexachloroplatinum(IV)tetraammine dicyano platinate(IV)
C. Ammine bromochloro methylamine platinum(II)
D. cis-dichloro (ethylenediamine) platinum (II)
Subject: Chemistry
Which of the following complex is most stable among the folowing?
\( \mathbf{A} \cdot N a_{3}\left[F e\left(C_{2} O_{4}\right)_{3}\right. \)
B \( \cdot\left[C O\left(N H_{3}\right)_{6}\right]^{+3} \)
\( \mathbf{c} \cdot\left[C r\left(N H_{3}\right)_{6}\right] C l_{3} \)
D. \( N a_{3}\left[\text {CoF}_{6}\right] \)
Subject: Maths
If \( y=\left(\tan ^{-1} x\right)^{2} \) and \( \left(x^{2}+1\right)^{2} \frac{d^{2} y}{d x^{2}}+ \)
\( 2 x\left(x^{2}+1\right) \frac{d y}{d x}=k, \) then the value of \( k \)
is
A . 3
B. 2
c. 1
D.
Subject: Physics
Assertion
The positive charge particle is placed in
front of a spherical uncharged conductor. The number of lines of forces
terminating on the sphere will be more than those emerging from it.
Reason
The surface charge density at a point on the sphere nearest to the point charge will be negative and maximum in magnitude compared to other points on the sphere
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: Chemistry
Three cations \( A, B, C \) are allowed to
react with ammonium hydroxide solution. \( A \) and \( B \) produce a dirty green
precipitate and a reddish brown precipitate respectively, both of which do not dissolve on further addition of
\( N H_{4} O H . C \) gives pale blue colour precipitate with less amount of ammonium hydroxide and on further
addition of \( N H_{4} O H, \) precipitate becomes soluble and deep blue colour
solution is formed:
A \( \cdot F e^{+2}, F e^{+3}, C u^{+2} \)
B. \( F e^{+3}, F e^{+2}, C u^{+2} \)
c. \( C u^{+2}, F e^{+2}, F e^{+3} \)
D. \( C u^{+2}, F e^{+3}, F e^{+2} \)
Subject: Maths
Solution of the linear equation \( 3 x+ \)
\( 0 y+7=0 \) in two variables is of the
form
A \( \cdot\left(\frac{-7}{3}, m\right) \)
в. \( \left(n, \frac{-7}{3}\right) \)
c. \( \left(0, \frac{-7}{3}\right) \)
D. (-7,0)
Subject: Chemistry
Which equation is the most appropriate to calculate the energy of activation, if the rate of reaction is doubled by
increasing temperature from \( \boldsymbol{T}_{1} \boldsymbol{K} \) to \( T_{2} K ? \)
\( ^{\mathbf{A}} \cdot \log _{10}\left(\frac{k_{1}}{k_{2}}\right)=\frac{E_{a}}{2.303 R}\left[\frac{1}{T_{1}}-\frac{1}{T_{2}}\right] \)
B. \( \log _{10}\left(\frac{k_{2}}{k_{1}}\right)=\frac{E_{a}}{2.303 R}\left[\frac{1}{T_{2}}-\frac{1}{T_{1}}\right] \)
\( ^{\mathbf{C}} \cdot \log _{10} \frac{1}{2}=\frac{E_{a}}{2.303}\left[\frac{1}{T_{2}}-\frac{1}{T_{1}}\right] \)
D \( \cdot \log _{10} 2=\frac{E_{a}}{2.303 R}\left[\frac{1}{T_{1}}-\frac{1}{T_{2}}\right] \)