AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
The order and degree of the differentia
equation \( \left[1+\left(\frac{d y}{d x}\right)^{2}+\sin \left(\frac{d y}{d x}\right)\right]^{3 / 4}=\frac{d^{2} y}{d x^{2}} \)
are:
A. order \( =2 ; \) degree \( =3 \)
B. order= \( 2 ; \) degree \( =4 \)
\( ^{\mathrm{c}} \cdot_{\mathrm{order}=} 2 ; \) degree \( =\frac{3}{4} \)
D. order= \( 2 ; \) degree \( = \) not defined
Subject: Physics
Three charges \( +\boldsymbol{q},+\boldsymbol{q} \) and \( -\boldsymbol{q} \) are situated in \( x \) -y plane at the point \( (0, a),(0,0),(0,-a) . \) Then, the electric potential at a point in first quadrant
whose position vector makes an angle \( \theta \) with the \( y \) -axis and at a distance \( r(r> \) \( >a) \) from the origin is :
A \( \cdot \frac{q a \cos \theta}{2 \pi \varepsilon_{0} r^{2}} \)
в. \( \frac{q}{4 \pi \varepsilon_{0} r}\left(1+\frac{2 a \cos \theta}{r}\right) \)
c. \( \frac{q}{4 \pi \varepsilon_{0} r} \)
D. \( \frac{q}{4 \pi \varepsilon_{0} r}\left(1-\frac{2 a \cos \theta}{r}\right) \)
Subject: Physics
Two thermally insulated vessels 1 and 2
are filled with air at temperature
\( \left(\mathbf{T}_{1}, \mathbf{T}_{2}\right), \) volume \( \left(\mathbf{V}_{1}, \mathbf{V}_{2}\right) \) and pressure
\( \left(\mathbf{P}_{1}, \mathbf{P}_{2}\right) \) respectively. If the valve joining the two vessels is opened, the
temperature inside the vessel at equilibrium will be:
\( \mathbf{A} \cdot \mathbf{T}_{1}+\mathbf{T}_{2} \)
B. \( \left(\mathrm{T}_{1}+\mathrm{T}_{2}\right) / 2 \)
\( \mathrm{c} \cdot \mathrm{T}_{1} \mathrm{T}_{2}\left(\mathrm{P}_{1} \mathrm{V}_{1}+\mathrm{P}_{2} \mathrm{V}_{2}\right) \)
\( \mathrm{P}_{1} \mathrm{V}_{1} \mathrm{T}_{2}+\mathrm{P}_{2} \mathrm{V}_{2} \mathrm{T}_{1} \)
D. \( \frac{\mathrm{T}_{1} \mathrm{T}_{2}\left(\mathrm{P}_{1} \mathrm{V}_{1}+\mathrm{P}_{2} \mathrm{V}_{2}\right)}{\mathrm{P}_{1} \mathrm{V}_{1} \mathrm{T}_{1}+\mathrm{P}_{2} \mathrm{V}_{2} \mathrm{T}_{2}} \)
Subject: Maths
A manufacturer of a certain item can
sell all he can produced at the selling price of Rs 60 each. It cost him Rs 40 in materials and labour to produce each item and he has overhead expenses of Rs 3000 per week in order to operate that plant. The number of units he should produce and sell in order to make a profit of at least Rs 1000 per weeks is
A . 250
в. 300
\( c .400 \)
D. 200
Subject: Physics
An experiment is carried on a fixed
amount of gas at different temperature and at high pressure such that it
deviates from the ideal gas behaviour.
The variation of \( \frac{\boldsymbol{p} \boldsymbol{V}}{\boldsymbol{R T}} \) with \( \boldsymbol{p} \) is shown in
the diagram. The correct variation will
correspond to :
A. curve \( A \)
B. curve \( B \)
c. curve \( C \)
D. curve \( D \)
Subject: Physics
Find the electric field at a distance " \( z " \)
from the plane. This question has multiple correct options
A \( \cdot \vec{E}=\frac{\sigma}{2 \epsilon_{0}} \hat{k} \) for \( z>0 \)
B・ \( \vec{E}=-\frac{\sigma}{2 \epsilon_{0}} \hat{k} \) for \( z>0 \)
c. \( \vec{E}=\frac{\sigma}{2 \epsilon_{0}} \hat{k} \) for \( z<0 \)
D・ \( \vec{E}=-\frac{\sigma}{2 \epsilon_{0}} \hat{k} \) for \( z<0 \)
Subject: Chemistry
Which of the following is not correctly matched?
A. Neoprene
\[
\left[-C H_{2}-C_{C l}=C H-C H_{2}-\right]_{n}
\]
в. \( \left[-N H-\left(C H_{2}\right)_{6}-N H-C O-\left(C H_{2}\right)_{4}-C-O-\right] \)
Nylon-6,6
c. Terylene
\( \mathrm{D} \cdot+\mathrm{CF}_{2}-\mathrm{CF}_{2}+ \)
Teflon
Subject: Physics
A bead of mass \( 1 / 2 \) kg starts from rest
from A to move in a vertical plane along
a smooth fixed quarter ring of radius
\( 5 m, \) under the action of a constant
horizontal force \( F=5 \mathrm{N} \) as shown in Fig.
\( 8.263 . \) The speed of bead as it reaches
point B is
A . \( 14.14 m s^{-1} \)
B. \( 7.07 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 5 \mathrm{ms}^{-1} \)
D. \( 25 \mathrm{ms}^{-1} \)
Subject: Maths
If \( \sin ^{-1} x+\sin ^{-1} y=\frac{2 \pi}{3}, \) then
\( \cos ^{-1} x+\cos ^{-1} y= \)
A \( \cdot \frac{\pi}{6} \)
в.
\( c \cdot \frac{\pi}{3} \)
D.
Subject: Maths
Prove that points \( A, B, C \) having positions vectors \( \vec{a}, \vec{b}, \vec{c} \) are collinear, if \( [\overrightarrow{\boldsymbol{b}} \times \overrightarrow{\boldsymbol{c}}+\overrightarrow{\boldsymbol{c}} \times \overrightarrow{\boldsymbol{a}}+\overrightarrow{\boldsymbol{a}} \times \overrightarrow{\boldsymbol{b}}]=\overrightarrow{\mathbf{0}} \)
Subject: Maths
If the normal to the curve \( y=f(x) \) at
(3,4) makes angle \( \frac{3 \pi}{4} \) with \( O \bar{X} \) then
\( \boldsymbol{f}^{1}(\mathbf{3})= \)
A . -1
B.
c. \( (-3 / 4) \)
D. \( (4 / 3) \)
Subject: Physics
A planet in solar system has a mass double that of earth and density equal to that of earth. An object weigh Won the earth, will weigh on the other
planet as \( W^{1} . \) Then:
\( \mathbf{A} \cdot W^{1}=W \)
В. \( W^{1}=2 W \)
c. \( w^{1}=\frac{W}{2} \)
D.
\[
W^{1}=2^{\frac{1}{3}} W
\]
Subject: Physics
A electron experiences a force \( (4.0 \hat{i}+ \) \( \mathbf{3} . \mathbf{0} \hat{\boldsymbol{j}}) \times \mathbf{1 0}^{-\mathbf{1 3}} \boldsymbol{N} \) in a uniform magnetic
field when its velocity is \( 2.5 \hat{k} \times \) \( 10^{7} m s^{-1} . \) The magnetic field vector \( \vec{B} \)
is
\( \mathbf{A} \cdot-0.075 \hat{i}+0.1 \hat{j} \)
B. \( 0.1 \hat{i}+0.075 \hat{j} \)
c. \( -0.075 \hat{i}-0.1 \hat{j}+\hat{k} \)
D. \( -0.075 \hat{i}-0.1 \)
Subject: Biology
Match the following.
\( \begin{array}{ll}\text { 1. Incisors } & \text { a. Grinding teeth } \\ \text { 2. Canines } & \text { b. Cracking teeth } \\ \text { 3. Premolars } & \text { c. Cutting teeth } \\ \text { 4. Molars } & \text { d. Tearing teeth }\end{array} \)
\( A \cdot 1-b, 2-d, 3-a, 4-c \)
B. \( 1-b, 2-a, 3-d, 4-c \)
\( c \cdot 1-c, 2-b, 3-d, 4-a \)
D. \( 1-c, 2-d, 3-b, 4-a \)
Subject: Chemistry
In reaction \( \boldsymbol{C O}(\boldsymbol{g})+\mathbf{2} \boldsymbol{H}_{2}(\boldsymbol{g}) \rightleftarrows \)
\( \boldsymbol{C H}_{3} \boldsymbol{O H}(\boldsymbol{g}) ; \boldsymbol{\Delta}_{f} \boldsymbol{H}^{o}=-\mathbf{9 2 . 0} \boldsymbol{k J} / \boldsymbol{m o l} \)
What will happen if:
A. volume of the rection vessel in which reactants is reduced to half
B. some amount of \( C H_{3} O H \) is removed
c. the partial pressure of hydrogen is suddenly doubled
D. an inert gas is added to the system under constant volume conditions
Subject: Chemistry
Find the oxidation number of elements
in each case.
\( S \) in \( N a_{2} S_{2} O_{3}, S_{4}, S_{8} \) and \( N a_{2} S_{2} O_{7} \)
\( \mathbf{A} \cdot+2,0,0,+6 \)
B. +1,1,0,+5
c. 0,0,1,+4
D. None of these
Subject: Maths
Assertion
STATEMENT \( 1: \sim(p \leftrightarrow \sim q) \) is equivalent
to \( (\boldsymbol{p} \vee \sim \boldsymbol{q}) \wedge(\sim \boldsymbol{p} \vee \boldsymbol{q}) \)
Reason
STATEMENT \( 2: \sim(p \leftrightarrow q) \) is equivalent
to \( (\boldsymbol{p} \wedge \sim \boldsymbol{q}) \vee(\sim \boldsymbol{p} \wedge \boldsymbol{q}) \)
A. Statement 1 is True, Statement 2 is True; Statement 2 i a correct explanation for Statement 1
B. Statement 1 is True, Statement 2 is True ; Statement 2 is NOT a correct explanation for Statement 1
c. statement 1 is True, Statement 2 is False
D. Statement 1 is False, Statement 2 is True
Subject: Physics
What conclusion can you draw from the following observations on a resistor
made of alloy manganin?
\( \begin{array}{llll}\begin{array}{l}\text { Current } \\ \text { A }\end{array} & \begin{array}{l}\text { Voltage } \\ \text { V }\end{array} & \begin{array}{l}\text { Current } \\ \text { A }\end{array} & \begin{array}{l}\text { Voltage } \\ \text { v }\end{array} \\ \begin{array}{l}\text { 0.2 } \\ \text { 0.4 }\end{array} & \begin{array}{l}\text { 3.94 } \\ \text { 7.87 }\end{array} & \begin{array}{l}\text { 3.0 } \\ \text { 4.0 }\end{array} & \begin{array}{l}\text { 59.2 } \\ \text { 78.8 }\end{array} \\ \begin{array}{l}\text { 0.6 } \\ \text { 0.8 }\end{array} & \begin{array}{l}\text { 11.8 } \\ \text { 15.7 }\end{array} & \begin{array}{l}\text { 5.0 } \\ \text { 1.0 }\end{array} & \begin{array}{l}\text { 6.0 } \\ \text { 19.7 }\end{array} & \begin{array}{l}\text { 98.6 } \\ \text { 7.0 }\end{array} & \begin{array}{l}\text { 118.5 } \\ \text { 138.2 }\end{array} \\ \begin{array}{ll}\text { 2.0 } & \text { 39.4 } & \text { 8.0 } & \text { 158.0 }\end{array}\end{array} \)
Subject: Chemistry
\( X Y_{2} \) dissociates as: \( X Y_{2}(g) \rightleftharpoons \)
\( \boldsymbol{X} \boldsymbol{Y}(\boldsymbol{g})+\boldsymbol{Y}(\boldsymbol{g}) \)
Initial pressure of \( \boldsymbol{X} \boldsymbol{Y}_{2} \) is \( \boldsymbol{6} \boldsymbol{0} \boldsymbol{0} \boldsymbol{m} \boldsymbol{m} \boldsymbol{H} \boldsymbol{g} \)
The total pressure at equilibrium is \( 800 m m H g . \) Assuming volume of system to remain constant, the value of
\( \boldsymbol{K}_{p} \) is:
A . 50
в. 100
c. 200
D. 400
Subject: Physics
A moving coil galvanometer A has 100
turns and resistance \( 10 \Omega \). Another
galvanometer B has 50 turns and 5 \( \Omega \)
The other quantities are same in both the cases. Then the voltage sensitivity of :
A. A is greater than that of
B. B is greater than that of
c. \( A \) and \( B \) is same
D. Cannot be compared
Subject: Chemistry
Assertion:
In the periodic table, the atomic radius increases from left to right.
Reason:
The number of protons is increasing
from left to right.
\( A \)
Both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
B. Both Assertion and Reason are true, but Reason is not the correct explanation of the Assertion.
c. Assertion is true, but the Reason is false.
D. Assertion is false, but the Reason is true
E. Both assertion and reason is incorrect
Subject: Chemistry
The values of heat of combustion of
graphite and \( H_{2} \) are -395 and -269 kJ/mol respectively. If heat of formation of glucose is \( -1169 \mathrm{kJ} / \mathrm{mol} \), then the heat of combustion of glucose is:
A . -2815 kJ/mol
B. -1169 kJ/mol
c. 1169 kJ/mol
D. 2815 kJ/mol
Subject: Chemistry
Assertion
The configuration of \( B \) -atom cannot be
\( 1 s^{2} 2 s^{2} \)
Reason
Hund's rule demands that the
configuration should display maximum multiplicity.
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 resistor has resistance R. When the
potential difference across the resistor
is \( V \), the current in
the resistor is I. The power dissipated in
the resistor is P. Work W is done when
charge \( Q \) flows through the resistor. What is not a valid relationship between
these variables?
\( \mathbf{A} \cdot I=\frac{P}{V} \)
В \( \cdot Q=\frac{W}{V} \)
C \( \cdot R=\frac{P}{I^{2}} \)
D \( \cdot R=\frac{V}{P} \)
Subject: Physics
Two coils 'P' and 'Q' are separated by
some distance. When a current of 3 A
flows through coil 'P', a magnetic flux of
\( 10^{-3} \) Wh passes through 'Q'. No current is passed through 'Q'. When no current
passes through 'P' and a current of 2 A passes through 'Q', the flux through 'P' is?
A \( \cdot 6.67 \times 10^{-3} \mathrm{Wb} \)
В. \( 6.67 \times 10^{-4} \mathrm{wb} \)
c. \( 3.67 \times 10^{-4} \mathrm{wb} \)
D. \( 3.67 \times 10^{-3} \mathrm{Wb} \)
Subject: Maths
From the table, find the median class
for the following data.
\begin{tabular}{|c|c|c|c|}
\hline\( x \) & \( f \) & Class Boundaries & c.f \\
\hline \( 8-10 \) & 2 & \( 7.5-10.5 \) & 2 \\
\( 11-13 \) & 4 & \( 10.5-13.5 \) & 6 \\
\( 14-16 \) & 6 & \( 13.5-16.5 \) & 12 \\
\( 17-19 \) & 4 & \( 16.5-19.5 \) & 16 \\
\( 20-22 \) & 3 & \( 19.5-22.5 \) & 19 \\
\( 23-25 \) & 1 & \( 22.5-25.5 \) & 20 \\
\hline & 20 & & \\
\hline
\end{tabular}
A . \( 13.5-16.5 \)
B . \( 12.5-13.5 \)
c. \( 10.5-14.5 \)
D. \( 12.5-10.5 \)
Subject: Physics
Identify the logic gate whose truth table is given below and draw its symbol:
\( \begin{array}{ccc}\boldsymbol{A} & \boldsymbol{B} & \boldsymbol{Y} \\ 0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0\end{array} \)
Subject: Maths
The acceleration of a particle starting from rest moving in a straight line with uniform acceleration is \( 8 m / s^{2} . \) The
time taken by the particle to move the second metre is
A \( \cdot \frac{\sqrt{2}-1}{2} s \)
B. \( \frac{\sqrt{2}+1}{2} s \)
\( \mathbf{c} \cdot(1+\sqrt{2}) s \)
D. \( (\sqrt{2}-1) s \)
Subject: Maths
The probability of the simultaneous occurrence of two events \( A \) and \( B \) is \( p \). If
the probability that exactly one of \( A, B \)
occurs is \( \boldsymbol{q} \), then This question has multiple correct options
A \( \cdot P\left(A^{\prime}\right)+P\left(B^{\prime}\right)=2+2 q-p \)
B . \( P\left(A^{\prime}\right)+P\left(B^{\prime}\right)=2-2 p-q \)
c. \( P(A \cap B \mid A \cup B)=\frac{p}{p+q} \)
D . \( P\left(A^{\prime} \cap B^{\prime}\right)=1-p-q \)
Subject: Maths
Which of the following is correct?
A \( \cdot \vec{a} \cdot(\vec{b}+\vec{c}) \) is equal to \( \vec{a} \cdot \vec{b}+\vec{d} \cdot \vec{c} \)
В . \( \vec{a} .(\vec{b}+\vec{c}) \) is equal to \( \vec{a} \cdot \vec{b}-\vec{d} . \vec{c} \).
c. \( \vec{a} \times(\vec{b}+\vec{c}) \) is equal to \( \vec{a} \cdot \vec{b}+\vec{a} \cdot \vec{c} \)
D. All of the above
Subject: Physics
Two point mass \( m_{1} \) and \( m_{2} \) are placed
at point \( A \) and \( B \) respectively as shown in figure.Point A is the centre of hollow sphere of uniformly distributed total
mass \( m_{3} . \) Consider only gravitational
interaction between all masses and
neglect other gravitational forces.
Select the incorrect alternative.
A . Hollow sphere and point mass \( m_{1} \) moves with same acceleration
B. \( m_{1} \) and \( m_{2} \) moves with same acceleration
C. Net force on \( m_{1} \) is non-zero
D. Net force on hollow sphere and point mass \( m_{1} \) as a system is equal to force experienced by point mass \( m_{2} \) in magnitude
Subject: Chemistry
Fill in the blanks by choosing the appropriate word/words from those given in the brackets:
(square pyramidal, electrical, 74, 26, \( s p^{3} d^{2}, s p^{3} d, \) chemical, 68,32
tetrahedral, yellow, white, iodoform, Lucas)
The shape of \( X e O F_{4} \) molecule is
and the
hybridisation of xenon atom in the
molecule is
Subject: Chemistry
\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}+\boldsymbol{C} \longrightarrow-----+ \)
\( \mathbf{A} \cdot C O_{2}, N O_{2}, H_{2} O \)
B. \( C O, N O, H_{2} O \)
\( \mathbf{c} \cdot C O_{2}, N H_{2}, H_{2} O \)
\( \mathbf{D} \cdot C O_{2}, N O, H_{2} O \)
Subject: Physics
Two particles \( A \) and \( B \) are moving as
shown in the figure. At this moment
of time the angular speed of \( A \) with
respect to \( B \) is
A \( \cdot \frac{1}{r\left(v_{a}+v_{b}\right)} \)
B. \( \frac{v_{a} \sin \theta_{a}+v_{b} \sin \theta_{b}}{r} \) in the anticlockwise direction
c. \( \frac{v_{a} \sin \theta_{a}-v_{b} \sin \theta_{b}}{r} \) in the clockwise direction
D \( \frac{1}{r\left(v_{a}-v_{b}\right)} \)
Subject: Chemistry
a) An ion with mass number 37
possesses one unit of negative charge.
If the ion contains \( 11.1 \% \) more neutrons
than the electrons. Find the symbol of the ion.
b) An electron is in 3d orbitals. Give the
possible values of \( n, \) land \( m_{1} \)
c) What is the maximum number of
emission lines, When the excited
electron of a \( \boldsymbol{H} \) atom in \( \boldsymbol{n}=\boldsymbol{6} \) drops to the ground state?
Subject: Chemistry
Match the entries of column-I with
appropriate entries of column-II
Column(Metal to be \( \quad \) (Method used for extracted) \( \quad \) reduction of oxide
(i) Reduction with
(A) Iron or Zinc \( \quad \) aluminium
(B) Manganese or
(ii) Reduction with Carbon Chromium
(C) Mercury
(iii) Electrolytic reduction
(D) Aluminium
(iv) Reduction of heating alone
A \( .(A) \longrightarrow(i v) ;(B) \longrightarrow(i) ;(C) \longrightarrow(i i) ;(D) \longrightarrow(i i i) \)
B. \( (A) \longrightarrow(i i i) ;(B) \longrightarrow(i) ;(C) \longrightarrow(i v) ;(D) \longrightarrow(i i) \)
c. \( (A) \longrightarrow(i i) ;(B) \longrightarrow(i) ;(C) \longrightarrow(i v) ;(D) \longrightarrow(i i i) \)
D. \( (A) \longrightarrow(i) ;(B) \longrightarrow(i i) ;(C) \longrightarrow(i i i) ;(D) \longrightarrow(i v) \)
Subject: Chemistry
Assertion
The law of conversation of mass apply to
the burning a candle.
Reason
During the burning of candle, the wax is converted into smoke, gas, soot and
melted wax.The mass of these products
is same as the melted wax.
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 \( \vec{a}=\hat{i}+2 \hat{j}+\hat{k}, \vec{b}=2 \hat{i}+\hat{j} \) and \( \vec{c}= \)
\( \mathbf{3} \hat{\mathbf{i}}-\mathbf{4} \hat{\mathbf{j}}-\mathbf{5} \hat{k}, \) then find a unit vector
perpendicular to both of the vectors \( (\vec{a}-\vec{b}) \) and \( (\vec{c}-\vec{b}) \)
Subject: Physics
If charges \( \boldsymbol{q} / 2 \) and \( 2 q \) are placed at the centre of face and at the corner of a
cube, then the total flux through the
cube will be:
A \( \cdot \frac{q}{2 \varepsilon_{0}} \)
в. \( \frac{q}{\varepsilon_{0}} \)
c. \( \frac{q}{6 \varepsilon_{0}} \)
D. \( \frac{q}{8 \varepsilon_{0}} \)
Subject: Maths
\( \int\left(\cot ^{n+2} x+\cot ^{n} x\right) d x= \)
A. \( \quad \frac{-\cot ^{n+1} x}{n+1}+c \)
B \( \cdot \frac{-\cot ^{n-1} x}{n-1}+C \)
c. \( \frac{-\cot ^{n+3} x}{n+3}+c \)
D. \( \frac{-\cot ^{2 n} x}{2 n}+C \)
Subject: Physics
A satellite is orbiting the earth at 17,500 MPH, a rock is released from the satellite. Identify what would happen to
the rock.
A. The rock would orbit the earth at a velocity of 17,500 MPH next to the satellite
B. As the rock cannot generate its own force, it will slow down
c. Gravity will pull the rock towards earth
D. As the rock is smaller than the satellite, it will accelerate and orbit at a greater velocity
E. As the rock is smaller than the satellite, its inertia will pull it further away from earth
Subject: Physics
In Thomsons experiment for determining e/m, the potential difference between the cathode and
the anode is same as that between the
deflecting plates ( in the region of crossed fields). If the
potential difference is doubled. Then the factor by which the magnetic field be increased to ensure that the electron
beam remains undeflected is:
A \( \cdot \sqrt{2} \)
B. 2
\( c \cdot 2 \sqrt{2} \)
\( D \cdot 4 \)
Subject: Chemistry
If \( E^{o} \) denotes reduction potential, then
which is true?
\( \mathbf{A} \cdot E_{c e l l}^{0}=E_{r i g h t}^{o}-E_{l e f t}^{o} \)
B \( \cdot E_{\text {cell }}^{0}=E_{\text {left }}^{o}+E_{\text {right }}^{o} \)
\( \mathbf{c} \cdot E_{c e l l}^{0}=E_{l e f t}^{o}-E_{r i g h t}^{o} \)
D. \( E_{c e l l}^{0}=-\left(E_{l e f t}^{o}+E_{r i g h t}^{o}\right) \)
Subject: Physics
A thin circular ring of mass \( M \) and
radius \( r \) is rotating about its axis with constant angular velocity \( \omega . \) Two objects each of mass \( \mathrm{m} \) are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with angular velocity given by
A \( \cdot \frac{(M+2 m) \omega}{2 m} \)
в. \( \frac{2 M \omega}{M+2 m} \)
c. \( \frac{(M+2 m) \omega}{M} \)
D. \( \frac{M \omega}{M+2 m} \)
Subject: Maths
Perpendiculars \( A P, A Q \) and \( A R \) are drawn to the \( x-, y- \) and \( z- \) axes, respectively
from the point \( \boldsymbol{A}(\mathbf{1},-\mathbf{1}, \mathbf{2}) . \) The A.M. of
\( A P^{2}, A Q^{2} \) and \( A R^{2} \) is
A .4
B. 5
\( c .3 \)
D.
Subject: Chemistry
Balance the given below reaction
\( \boldsymbol{x} \boldsymbol{A} \boldsymbol{s}_{2} \boldsymbol{S}_{3}+\boldsymbol{y} \boldsymbol{N} \boldsymbol{a} \boldsymbol{O} \boldsymbol{H}+\boldsymbol{z} \boldsymbol{N} \boldsymbol{a} \boldsymbol{C l} \boldsymbol{O}_{3} \rightarrow \)
\( \boldsymbol{a} \boldsymbol{N} \boldsymbol{a}_{3} \boldsymbol{A} \boldsymbol{s} \boldsymbol{O}_{4}+\boldsymbol{b} \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{c} \boldsymbol{N} \boldsymbol{a} \boldsymbol{C l O}+ \)
\( d H_{2} O \) Calculate the value of \( (x-y+z+a) \)
b+c), when the molar coefficient are in simplest whole number ratio.
Subject: Maths
The values of \( \lambda \) such than \( (x, y, z) \neq \) (0,0,0)
and \( (i \hat{+} \hat{j}+3 \hat{k}) x+(3 \hat{i}-3 \hat{j}+\hat{k}) y+ \)
\( (-4 \hat{i}+5 \hat{j}) z=\lambda(x \hat{i}+y \hat{j}+z \hat{k}) \) are
Subject: Physics
When two bodies at different
temperatures are placed in thermal
contact with each other, heat flows from
the body at a higher temperature until they both acquire the same temperature. Assuming that there is no loss of heat to the surroundings, then:
A. The heat gained by the hotter body will be equal to the heat lost by the colder body
B. The heat gained by the hotter body will be less than the heat lost by the colder body
c. The heat gained by the hotter body will be greater than the heat lost by the colder body
D. The heat lost by the hotter body will be equal to the heat gained by the colder body
Subject: Chemistry
Assertion
Malonic acid \( \left(\boldsymbol{H} \boldsymbol{O} \boldsymbol{O} \boldsymbol{C}-\boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C O O H}\right) \)
does not form cyclic anhydride on heating.
Reason
It is like \( \beta \) -keto acid, on heating it prefer to decarboxylate.
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
The basic character of the transition
metal monoxides follows the order:
(Atomic number \( \mathrm{Ti}=22, \mathrm{V}=23, \mathrm{Cr}=24 \)
\( F e=26) \)
A. TiO > Fe0 > VO > cro
в. тio > vo > cro > Feo
c. тio \( > \) Cro \( > \) vo \( > \) Feo
D. crosvo \( > \) Fe0 > Tio
Subject: Physics
\( \mathbf{A} \)
1 kg body slides from the point \( A \) (see figure), along a horizontal track with an initial speed of \( 6 m s^{-1}, \) towards a weightless horizontal spring of length
\( 2 m \) and force constant \( 4 N m^{-1} \). The
part \( A B \) of the track is frictionless and
the part \( B C \) has the coefficients of
static and dynamic friction as 0.22 and
\( 0.2, \) respectively. Find the total distance
through which the block moves, before
it comes to rest completely \( .(g= \)
\( 10 m s^{-2} \) ), if \( A B=4 m \) and \( B D= \)
\( \mathbf{4 . 2 8 m} \)
Subject: Physics
A ball of radius a is made to oscillate in
a bowl of radius b then time period of vibration of ball is \( (\boldsymbol{b}>\boldsymbol{a}) \)
A \( \cdot 2 \pi \sqrt{\frac{a}{g}} \)
В \( \cdot 2 \pi \sqrt{\frac{b-a}{g}} \)
\( ^{\mathrm{c}} \cdot 2 \pi \sqrt{\frac{b}{g}} \)
D. \( 2 \pi \sqrt{\frac{b+a}{q}} \)
Subject: Physics
A gas is enclosed in a vessel of volume
\( 1000 \mathrm{cc} \) at a pressure of \( 72.6 \mathrm{cm} \) of Hg. It is being evacuated with the help of a piston pump, which expels \( 10 \% \) gas in each stroke. The pressure after the second stroke will be nearest to
\( A \cdot 60 \mathrm{cm} \)
B. 55 \( \mathrm{cm} \)
\( c \cdot 66 \mathrm{cm} \)
D. 50 cm
Subject: Maths
\( A, B, C \) are three sets such that \( \boldsymbol{n}(\boldsymbol{A})=\boldsymbol{2}, \boldsymbol{n}(\boldsymbol{B})=\boldsymbol{3}, \boldsymbol{n}(\boldsymbol{C})=\boldsymbol{4}, \) If \( \boldsymbol{P}(\boldsymbol{x}) \)
denotes power set of \( \boldsymbol{X}, \boldsymbol{k}= \) \( \frac{\boldsymbol{n}(\boldsymbol{P}(\boldsymbol{P}(\boldsymbol{C})))}{\boldsymbol{n}(\boldsymbol{P}(\boldsymbol{P}(\boldsymbol{A}))) \times \boldsymbol{n}(\boldsymbol{P}(\boldsymbol{P}(\boldsymbol{B})))} \).then find
the Sum of digits of \( k \)