AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
In a potentiometer of wire length \( l \), a cell of emf \( V \) is balanced at a length \( \frac{l}{3} \) from the positive of the wire. For another cell
of emf \( 1.5 V, \) the balancing length
becomes
A \( \cdot \frac{l}{6} \)
B. \( \frac{l}{2} \)
c. \( \frac{l}{3} \)
D. \( \frac{2 l}{3} \)
E \( \cdot \frac{4 l}{3} \)
Subject: Chemistry
The Russian chemist Dmitri Mendeleev
is generally credited with organizing the chemical elements into a
comprehensive periodic table in large part due to the fact that he was able to
use his table to predict the existence of elements, like gallium, that were not known at the time \( (1872), \) but were discovered later.

Which is the best explanation for why Mendeleev was unable to predict the existence of the noble gases (group 18
)?
A. Noble gases are not found on Earth
B. Noble gases are stable and very unreactive, and therefore, have few observable properties
c. Noble gases are synthetic elements and do not occu
D. Noble gases are very reactive and do not exist as stable elements
Subject: Chemistry
Assertion
Statement- \( 1: C u F e S_{2} \) is concentrated
by froath floatation method.
Reason
Statement-II: \( C u F e S_{2} \) is main ore of
copper.
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
An ideal gas having molar specific heat capacity at constant volume is \( \frac{3}{2} R, \) the molar specific heat capacities at constant pressure is :
A \( \cdot \frac{1}{2} R \)
в. \( \frac{5}{2} \) R
c. \( \frac{7}{2} \) R
D. \( \frac{9}{2} \) R
Subject: Maths
\( \operatorname{Let} \boldsymbol{A}=\left(\begin{array}{cc}\mathbf{3} & \mathbf{2} \\ \mathbf{5} & \mathbf{1}\end{array}\right) \) and \( \boldsymbol{B}=\left(\begin{array}{cc}\mathbf{8} & -\mathbf{1} \\ \mathbf{4} & \mathbf{3}\end{array}\right) \)
Find the matrix \( C, \) if \( C=2 A+B \)
Subject: Physics
(a) Explain giving reasons, the basic difference in converting a galvanometer into
(i) a voltmeter and (ii) an ammeter
(b) Two long straight parallel
conductors carrying steady currents \( I_{1} \)
and \( I_{2} \) are separated by a distance \( ^{\prime} d^{\prime} \) Explain briefly, with the help of a suitable diagram, how the magnetic field due to one conductor acts on the
other. Hence deduce the expression for
the force acting between the two conductors. Mention the nature of this
force.
Subject: Physics
An aeroplane with wing span \( 50 m \) is flying horizontally with a speed of \( 360 k m / h r \) over a place where the
vertical component of the earth's magnetic field is \( 2 \times 10^{-4} W b / m^{2} . \) The
potential difference between the tips of the wings would be
A . \( 0.1 V \)
в. \( 1.0 V \)
\( c .0 .2 V \)
D. \( 0.01 V \)
Subject: Chemistry
In a constant-volume calorimeter, \( 3.5 g \)
of gas with molecular weight 28 was
burnt in excess oxygen at \( 298.0 K . \) The
temperature of the calorimeter was
found to increase from \( 298.0 K \) to
\( 298.45 K \) due to the combustion
process. Given that the heat capacity of
the calorimeter is \( 2.5 k J K^{-1}, \) the
numerical value for the enthalpy of
combustion of the gas in \( k J m o l^{-1} \) is
\( \mathbf{A} \cdot 9 k J / \) mole
B. \( 75 k J / \) mole
\( \mathbf{c} .-8 k J / \)mole
D. \( -14 k J / \) mole
Subject: Maths
If \( A=\{1,2\} \) and \( B=\{3,4\} \) then find
\( A \times B \)
\( \mathbf{A} \cdot A \times B=\{(1,3),(1,2),(2,3),(2,4)\} \)
B \( . A \times B=\{(1,3),(1,4),(2,3),(2,4)\} \)
\( \mathbf{c} \cdot A \times B=\{(1,3),(1,4),(2,1),(2,4)\} \)
D . \( A \times B=\{(1,3),(1,4),(2,3),(2,1)\} \)
Subject: Chemistry
The correct order of solubility in water for \( \boldsymbol{H} \boldsymbol{e}, \boldsymbol{N} \boldsymbol{e}, \boldsymbol{A} \boldsymbol{r}, \boldsymbol{K} \boldsymbol{r}, \boldsymbol{X} \boldsymbol{e} \) is:
A. \( X e>K r>A r>N e>H e \)
в. \( A r>N e>H e>K r>X e \)
c. \( H e>N e>A r>K r>X e \)
D. \( N e>A r>K r>H e>X e \)
Subject: Physics
The power of a lens is \( +2.0 D . \) Find its focal length and state the kind of the lens.
A. Convex, \( 50 \mathrm{cm} \)
B. Convex, \( 200 \mathrm{cm} \)
c. concave, \( 50 \mathrm{cm} \)
D. Concave, \( 100 \mathrm{cm} \)
Subject: Physics
A block of mass \( 2 \mathrm{kg} \) is pushed against a rough vertical wall with a force of \( 40 \mathrm{N} \) coefficient of static friction being 0.5
Another horizontal force of \( 15 \mathrm{N} \), is
applied on the block in a direction
parallel to the wall. If the block will move, then its direction would be:
B. \( 53^{\circ} \) with \( 15 N \) force
C. \( 45^{\circ} \) with \( 15 N \) force
D. 75 \( ^{\circ} \) with 15N force
Subject: Chemistry
Two systems, \( \boldsymbol{P C l}_{5(g)} \rightleftharpoons \boldsymbol{P C l}_{3(g)}+ \)
\( \boldsymbol{C l}_{2(\boldsymbol{g})} \) and \( \boldsymbol{C O C l}_{2(\boldsymbol{g})} \rightleftharpoons \boldsymbol{C O}_{(g)}+\boldsymbol{C l}_{2(\boldsymbol{g})} \)
are simultaneously in equilibrium in a vessel at constant volume. If some \( C O \)
is introduced into the vessel then at the
new equilibrium, the concentration of :
A . \( P C l_{5} \) is increased
B. \( P C l_{3} \) remains unchanged
c. \( P C l_{5} \) is decreased
D. \( C l_{2} \) is increased
Subject: Maths
The conjugate of \( z+2 \bar{z} \) is:
\( \mathbf{A} \cdot 2 \bar{z}+z \)
B. \( \bar{z}+2 z \)
c. \( \bar{z}-2 z \)
\( \mathbf{D} \cdot \bar{z}-z \)
Subject: Physics
At \( t=0, \) the displacement of a particle
in S.H.M. is half its amplitude. Its initial phase is:
A \( \cdot \frac{\pi}{6} \) rad
B \( \cdot \frac{\pi}{3} \) rad
c. \( \frac{2 \pi}{3} \) rad
D. \( \frac{\pi}{2} \) rad
Subject: Chemistry
A body of mass 10 mg is moving with a
velocity of \( 100 m s^{-1} . \) The wavelength of
the de Broglie wave associated with it would be
A \( \cdot 6.63 \times 10^{-7} \mathrm{m} \)
B. \( 6.63 \times 10^{-31} m \)
\( c \cdot 6.63 \times 10^{-4} m \)
D. \( 6.63 \times 10^{-35} m \)
Subject: Physics
The density of a gas at N.T.P. is \( 1.5 \mathrm{gm} / \) lit its density at a pressure of \( 152 \mathrm{cm} \) of \( \mathrm{Hg} \) and temperature \( 27^{0} \mathrm{C} \)
A \( \cdot \frac{273}{100} g m / l t r \)
B . \( \frac{150}{233} \mathrm{gm} / \mathrm{ltr} \)
\( \mathbf{c} \cdot \frac{1}{273} g m / l t r \)
D. \( 1.5 \mathrm{gm} / \) lit
Subject: Physics
\( 5 \mathrm{kg} \) of water at \( 10^{\circ} \mathrm{C} \) is added to \( 10 \mathrm{kg} \)
of water at \( 40^{\circ} \mathrm{C} \) Neglecting heat
capacity or vessel and other losses, the equilibrium temperature will be
A \( \cdot 30^{\circ} \mathrm{C} \)
B . \( 25^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 35^{\circ} C \)
D. \( 33^{\circ} \mathrm{C} \)
Subject: Maths
The value \( \csc \left(\cos ^{-1}(-12 / 13)\right) \) is?
\( \mathbf{A} \cdot+12 / 5 \)
в. \( -12 / 5 \)
\( \mathbf{c} \cdot+13 / 5 \)
D. \( -13 / 5 \)
Subject: Physics
Rest mass of a \( \beta \) particle is
A \( \cdot 1.6 \times 10^{-19} k g \)
В . \( 9.1 \times 10^{-31} k g \)
C. \( 2 \times 10^{2} k g \)
D. \( 1 \times 10^{5} \mathrm{kg} \)
Subject: Chemistry
In the esterification of an organic acid R-COOH by alcohol R'OH, O of acid is isotopic. \( \boldsymbol{R}-\stackrel{\mathbb{N}}{\boldsymbol{C}}-\stackrel{\mathbf{1 8}}{\boldsymbol{O} \boldsymbol{H}}+\boldsymbol{R}^{\prime}-\boldsymbol{O}-\boldsymbol{H} \rightarrow \boldsymbol{R}- \)
\( \stackrel{0}{C}-O R^{\prime}+H_{2} O \)
Which of the following statement is correct?
A. 18 p is in ester
B. 18 O is in water
\( c \cdot 18 O \) is in both
\( D \cdot 18 O \) is in none
Subject: Chemistry
Zinc is used to protect iron from
corrosion because:
\( \mathbf{A} \cdot E_{r e d} \) of \( Z n<E_{r e d} \) of iron
B. \( E_{\text {oxidation}} \) of \( Z n<E_{\text {oxidation}} \) of iron
C . \( E_{\text {oxidation}} \) of \( Z n=E_{\text {oxidation}} \) of iron
D. zinc is cheaper than iron
Subject: Biology
Choose the correctly paired sets from
the following
\( \begin{array}{lll}\text { SET I } & \text { SET II } & \text { SET III } \\ \begin{array}{l}\text { (A) Sphenoid } \\ \text { bone }\end{array} & \begin{array}{l}\text { Keystone } \\ \text { bone }\end{array} & \text { Cranium } \\ \begin{array}{l}\text { (B) Acromion } \\ \text { process }\end{array} & \text { Collar bone } & \text { Scapula } \\ \begin{array}{l}\text { (C) Xipioid } \\ \text { process }\end{array} & \text { Breastbone } & \text { Thorax } \\ \begin{array}{l}\text { (D) Odontoid } \\ \text { process }\end{array} & \text { Atlas } & \begin{array}{l}\text { Cervical } \\ \text { vertebra }\end{array}\end{array} \)
\( A \cdot A, D \)
B. B, D
\( c \cdot B, c \)
D. A.
Subject: Chemistry
Calculate the molar mass of the
following substances
(a) Ethyne \( C_{2} H_{2} \)
(b) Sulphur molecule \( \boldsymbol{S}_{8} \)
(c) Phophorous
molecule \( P_{4}(d) \) Nitric acid \( H N O_{3}(e) \) Hydrochloride acid \( \$ \boldsymbol{H} \boldsymbol{C l} \)
Subject: Maths
An oll company nas two depots \( A \) and \( B \)
with capacities of \( 7000 L \) and \( 4000 L \)
respectively. The company is to supply
oil to three petrol pumps \( D, E \) and \( F \)
whose requirements are \( 4500 L, 3000 L \)
and \( 3500 L \) respectively. The distance
(in \( \mathrm{km} \) ) between the depots and the
petrol pumps is given in the following
table:
Distance (in km)
From/To 1 \( \boldsymbol{A} \) \( B \)
7
\( D \)
3
6 4
A
Assuming that the transportation cost
of 10 litres of oil is Re.1 per \( \mathrm{km} \), how
should the delivery be scheduled in
order that the transportation cost is
minimum? What is the minimum cost?
Subject: Chemistry
Assertion
Langmuir adsorption isotherm is based on the concept of monolayer adsorption.
Reason At high pressure, the surface is fully occupied by adsorbate molecules and the further increase in pressure does not effect adsorption.
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 white solid compound \( A \)
decomposes quite rapidly on heating in
the presence of a black substance \( X \) to
form a solid compound B and a gas C. When an aqueous solution of compound B is reacted with silver nitrate solution, then a white precipitate of silver
chloride is obtained along with potassium nitrate solution. Gas C does not burn itself but helps to burn other things.
What is the general name of substances like X?
Subject: Physics
Assertion: When number of turns in a
coil is doubled, coefficient of self inductance of the coil becomes 4 times.
Reason: This is because \( \boldsymbol{L} \propto \boldsymbol{N}^{2} \)
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
Subject: Physics
A rocket of mass \( 5700 k g \) ejects mass at
a constant rate of \( 15 k g / s \) with constant
speed of \( 12 k m / s . \) The acceleration of the rocket 1 minute after the blast is
\( \boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2} \)
A \( \cdot 34.9 m / s^{2} \)
В. \( 27.5 m / s^{2} \)
c. \( 3.50 m / s^{2} \)
D. \( 13.5 m / s^{2} \)
Subject: Maths
If \( A B=0, \) then for the matrices \( A= \) \( \left[\begin{array}{cc}\cos ^{2} \theta & \cos \theta \sin \theta \\ \cos \theta \sin \theta & \sin ^{2} \theta\end{array}\right] \) and \( B= \)
\( \left[\begin{array}{cc}\cos ^{2} \phi & \cos \phi \sin \phi \\ \cos \phi \sin \phi & \sin ^{2} \phi\end{array}\right], \theta-\phi \) is
A \( \cdot \) an odd muliple of \( \frac{\pi}{2} \)
B. an odd multiple of \( \pi \)
C . an even multiple of \( \frac{\pi}{2} \)
D.
Subject: Maths
The straight lines \( \imath_{1}, \imath_{2} \) and \( \imath_{3} \) are parallel and lie in the same plane. A
total of \( \mathrm{m} \) points are taken on the line \( \imath_{1} \)
n points on \( \imath_{2}, \) and \( \mathrm{k} \) points on \( \imath_{3} . \) How many triangles are there whose vertices are at these points?
Subject: Maths
Arrange the following steps in correct order in constructing a square whose one diagonal is \( 5 \mathrm{cm} \) Step 1: Let PQ cut AC at 0.
Step 2: Draw a diagonal \( A C=5 c m \) Step 3: Join \( A b, B C, C D \) and DA. Then ABCD is the required square. Step 4: Draw PQ the perpendicular bisector of AC.
Step 5: With 0 as centre and OA radius draw a circle. Let the circle cut QP at
points B and D.
A. 2,1,4,5,3
В. 2,5,4,1,3
c. 2,4,5,1,3
D. 2,4,1,5,3
Subject: Maths
The domain of the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( \sin ^{-1}\left(\log _{2} \frac{x^{2}}{2}\right) \) is \( ? \)
A \( \cdot[-2,2]-(-1,1) \)
B . \( [-1,2]-\{0\} \)
c. [1.2]
D \cdot \( [-2,2]-\{0\} \)
Subject: Physics
A square of side \( 4 \mathrm{cm} \) and uniform
thickness is divided into four squares.
The square portion \( \boldsymbol{A}^{\prime} \boldsymbol{A} \boldsymbol{B}^{\prime} \boldsymbol{D} \) is removed
and the removed portion is placed over
the square \( \boldsymbol{B}^{\prime} \boldsymbol{B C}^{\prime} \) D. The new position
of centre of mass is
\( A \cdot(2 \mathrm{cm}, 2 \mathrm{cm} \)
B. \( (2 \mathrm{cm}, 3 \mathrm{cm}) \)
c. \( (2 \mathrm{cm}, 2.5 \mathrm{cm}) \)
\( \mathrm{D} \cdot(3 \mathrm{cm}, 3 \mathrm{cm}) \)
Subject: Chemistry
Consider the following reaction:
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{2} \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g})= \)
\( \boldsymbol{k}\left[\boldsymbol{H}_{2}\right]\left[\boldsymbol{I}_{2}\right] \)
Which one of the following statements is correct?
A. The reaction must occur in a single step
B. This is a second order reaction overal
c. Raising the temperature will cause the value of \( k \) to decrease
D. Raising the temperature lowers the activation energy for the reaction
Subject: Chemistry
Calculate \( \boldsymbol{K}_{c} \) for \( \boldsymbol{H} \boldsymbol{g}^{2+}+\boldsymbol{H} \boldsymbol{g} \rightleftharpoons \boldsymbol{H} \boldsymbol{g}_{2}^{2+} \)
Give that \( E_{2 H g / H g^{2+}}^{o}=-0.788 V \) and
\( \boldsymbol{E}_{\boldsymbol{H} \boldsymbol{g}_{2}^{2+} / \mathbf{2 H g}^{2+}}^{\boldsymbol{o}}=-\mathbf{0 . 9 2 0} \boldsymbol{V} \)
Write answer as nearest integer after dividing by 100
Subject: Maths
If ' \( x^{\prime} \) varies inversely as ' \( y^{\prime} \) and \( x=7 \)
when \( \boldsymbol{y}=\mathbf{9} \)
(a) Find constant of variation \( (k) \)
(b) Write equation of variation.
(c) Find ' \( y^{\prime} \) when \( x=9 \)
Subject: Chemistry
The major product of the following
reaction is:-
\( \boldsymbol{C H}_{3} \)
\( \boldsymbol{C H}_{3}-\underset{\boldsymbol{H}}{\boldsymbol{C}}-\boldsymbol{C} \boldsymbol{H} \boldsymbol{C H}_{3} \frac{\boldsymbol{C H}_{3} \boldsymbol{O H}}{\boldsymbol{B} \boldsymbol{r}} \)
A. \( \quad C H_{3}-C_{I}^{I H_{3}}-C_{\mid}^{I} H C H_{3} \)
B. \( \quad C H_{3} \)
\[
C H_{3}-C_{I}^{\perp}-C H=C H_{2}
\]
c. \( \quad C H_{3} \)
\[
C H_{3}-C_{1}^{\prime}-C H_{2} C H_{3}
\]
\[
\begin{array}{l}O C H_{3}\end{array}
\]
D.
\[
C H_{3}-C=C H C H_{3}
\]
Subject: Maths
If line \( \frac{\boldsymbol{x}-\mathbf{2}}{\mathbf{3}}=\frac{\boldsymbol{y}-\mathbf{4}}{\mathbf{4}}=\frac{\boldsymbol{z}+\mathbf{2}}{\mathbf{1}} \) is
parallel to planes \( \mu x+3 y-2 z+d= \)
0 and \( x-2 \lambda y+z=0, \) then value of \( \lambda \)
and \( \mu \) are
A \( \cdot\left(\mu=4, \lambda=-\frac{2}{3}\right. \)
B. \( \mu=-6, \lambda=-2 \)
c. \( _{\mu}=\frac{-10}{3}, \lambda=\frac{-1}{2} \)
D. \( \mu=\frac{-10}{3}, \lambda=\frac{1}{2} \)
Subject: Physics
A body falls from a height of 200 m. If gravitational attraction ceases after 2
s, further time taken by it to reach the ground is \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m s}^{-2}\right) \)
A . \( 5 s \)
B. \( 9 s \)
c. \( 13 s \)
D. 17 s
Subject: Maths
If \( \sin A=\frac{1}{2} \) and \( \cos B=\frac{\sqrt{3}}{2} \) where \( A \)
lies in second quadrant and B lies in first quadrant, find the values of (a) \( \sin (A-B)(b) \cos (A-B)(c) \tan (A+ \)
\( \boldsymbol{B}) \)
Subject: Physics
A step down transformer is used on a
1000V line to deliver \( 20 A \) at \( 120 V \) at the
secondary coil If the the efficiency of the transformer is \( 80 \% \) the current drawn
from the lines is
\( A \cdot 3 A \)
B. 30A
\( c .0 .3 \mathrm{A} \)
D. 2.4A
Subject: Chemistry
The reaction \( N_{2}+3 H_{2} \rightleftharpoons 2 N H_{3} \) is
started with initial number of moles of
1,2 and 3 for \( N_{2}, H_{2}, N H_{3} \) in a 1 L vessel
If \( x \) moles of \( N_{2} \) under go dissociation
then at equilibrium the number of moles of each substance remaining are:
A. \( 1-x, 2-3 x, 2 x \)
B. \( 1-x / 3,2-x, x / 3 \)
c. \( 1-x, 2-x, 3+x \)
D. \( 1-x, 2-3 x, 3+2 x \)
Subject: Physics
Assertion
A glass ball is dropped on concrete floor can easily get broken compared if it is dropped wooden floor.
Reason
On concrete floor glass ball will take
less time to come to rest.
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
Two circular coil 1 and 2 are made from
the same wire but the radius of the 1 st
coil is twice that of the \( 2 n d \) coil. What
potential difference in volts should be applied across them so that the magnetic field at their centres is
the same-
A . 3
B. 4
\( c \cdot 6 \)
D. 2
Subject: Chemistry
At \( 25^{\circ} C \), the standard emf of a cell
having reaction involving two electrons change is found to be \( 0.295 V \). The
equilibrium constant of the reaction is
\( \mathbf{A} \cdot 29.5 \times 10^{-2} \)
B. 10
\( c \cdot 1 \times 10^{10} \)
0
D . \( 29.5 \times 10^{10} \)
Subject: Maths
If \( \alpha \& \beta \) are the zeroes of quad polynomial \( \boldsymbol{x}^{2}-(\boldsymbol{k}+\boldsymbol{6}) \boldsymbol{x}+\boldsymbol{2}(\boldsymbol{2} \boldsymbol{k}-\boldsymbol{1}) \)
Find the value of \( k \) so that \( \alpha+\beta=\frac{1}{2} \alpha \beta \)
Subject: Chemistry
Write the balanced equations for the reaction occurring when gold is dissolved in aqua regia.
A \( \cdot 2 A u+3 H N O_{3}+11 H C l \rightarrow 2 H A u C l_{4}+3 N O C l+ \)
\( 6 H_{2} O \)
B . \( 2 A u+3 H N O_{3}+13 H C l \rightarrow 2 H A u C l_{4}+2 N O C l+ \)
\( 8 H_{2} O \)
c. \( 2 A u+5 H N O_{3}+11 H C l \rightarrow 2 H A u C l_{4}+2 N O C l+ \)
\( 8 H_{2} O \)
D. None of these
Subject: Chemistry
If the decomposition of nitrogen oxides
as \( 2 N_{2} O_{5} \rightarrow 4 N O_{2}+O_{2} \)
Calculate the rate constant for a \( 0.05 M \)
solution if the instantaneous rate is
\( \mathbf{1 . 5} \times \mathbf{1 0}^{-\mathbf{6}} \mathbf{m o l} / \mathbf{l} / \mathbf{s} \)
A \( .3 \times 10^{-5} \)
В. \( 3 \times 10^{-4} \)
c. \( 3 \times 10^{-2} \)
D. \( 2 \times 10^{-4} \)
Subject: Physics
Two spherical bodies of mass \( M \) and
\( 5 M \) and radii \( R \) and \( 2 R \) respectively are
released in free space with initial separation between their centres equal
to \( 12 R \) If they attract each other due to
gravitational force only, then the distance covered by the smaller body just before collision is
A . \( 2.5 R \)
в. \( 4.5 R \)
\( c .7 .5 R \)
D. \( 1.5 R \)
Subject: Physics
Two capacitors \( C_{1} \) and \( C_{2} \) are
connected in series, assume that \( C_{1}< \)
\( C_{2} . \) The equivalent capacitance of this
arrangement is \( C, \) where
A. \( C<C_{1} / 2 \)
B. \( C_{1} / 2<C<C_{1} \)
c. \( C_{1}<C<C_{2} \)
Subject: Physics
The plates of a parallel plate capacitor
have an area of \( 90 \mathrm{cm}^{2} \) each and are
separated by \( 2.5 m m . \) The capacitor is
charged by a 400 volt supply. How much electrostatic energy is stored by the capacitor?
A \( .2 .55 \times 10^{-6} J \)
В. \( 1.55 \times 10^{-6} J \)
c. \( 8.15 \times 10^{-6} J \)
D. \( 5.5 \times 10^{-6} J \)
Subject: Chemistry
Assertion
\( \alpha- \) rays have greater ionizing power
than \( \beta- \) rays.
Reason
\( \alpha- \) particles carry two unit positive
charge while \( \beta- \) particles carry only one unit negative charge.
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
Two identical charges, \( 5 \mu C \), each are
fixed at a distance \( 8 \mathrm{cm} \) and a charged particle of mass \( 9 \times 10^{-6} k g \) and charge
\( -10 \mu C \) is placed at a distance \( 5 \mathrm{cm} \)
from each of them and is released. Find
the speed of the particle when it is
nearest to the two charges.
Subject: Maths
If \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{4}\}, \boldsymbol{B}=\{\mathbf{2}, \mathbf{4}, \mathbf{5}\} \) and \( \boldsymbol{C}= \)
\( \{2,5\}, \) then \( (A-B) \times(B-C)= \)
A \( \cdot\{(1,2),(1,5),(2,5)\} \)
В \( \cdot\{\{1,4\}\} \)
\( \mathbf{c} \cdot(1,4) \)
D・ \{(1,2)\}
Subject: Maths
The derivative of \( \tan ^{-1}\left(\frac{\sin x-\cos x}{\sin x+\cos x}\right) \)
with respect to \( \frac{x}{2}, \) where \( \left(x \epsilon\left(0, \frac{\pi}{2}\right)\right) \) is
A \( \cdot \frac{1}{2} \)
в. \( \frac{2}{3} \)
c. 1
D.
Subject: Physics
A quarter disc of radius \( R \) and mass \( m \)
is rotating about the axis \( O O^{\prime} \)
(perpendicular to the plane of the disc)
as shown. Rotational kinetic energy of
the quarter disc is
\( A \)
в.
c. \( \frac{1}{8} m R^{2} \omega^{2} \)
\( D \)
Subject: Physics
The orbital speed \( v \) of each moon, such that they maintain the triangular configuration is:
A \( \cdot \sqrt{\frac{G M}{R^{2}}+\frac{G m}{\sqrt{3} R}} \)
B. \( \sqrt{\frac{G M}{R}+\frac{G m}{\sqrt{3} R}} \)
\( ^{\mathrm{c}} \cdot \sqrt{\frac{G M^{2}}{R}+\frac{G m}{\sqrt{3} R}} \)
D. \( \sqrt{\frac{G M}{R}+\frac{G m^{2}}{3 R}} \)
Subject: Maths
The value of the determinant
\( \left[\begin{array}{lll}x^{2} & 1 & y^{2}+z^{2} \\ y^{2} & 1 & z^{2}+x^{2} \\ z^{2} & 1 & x^{2}+y^{2}\end{array}\right] \) is:
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( x^{2}+y^{2}+z^{2} \)
c. \( x^{2}+y^{2}+z^{2}+1 \)
D. None of the above
Subject: Chemistry
Which of the following molecular formulas corresponds to that of an unsaturated fatty acid?
A. \( C_{18} \mathrm{H}_{35} \mathrm{COOH} \)
в. \( C_{16} H_{33} \) СООН
c. \( C_{19} \mathrm{H}_{39} \mathrm{COOH} \)
D. \( C_{17} H_{35} \) COOH
Subject: Physics
The electric permittivity nad magnetic
permeability of free space are \( \varepsilon_{0} \) and \( \mu_{0} \) respectively. The index of refraction of
the medium, if \( \varepsilon \) and \( \mu \) are the electric
permittivity and magnetic permeability in a medium is :
A \( \cdot \frac{\varepsilon \mu}{\varepsilon_{0} \mu_{0}} \)
\( ^{\text {В }}\left(\frac{\varepsilon \mu}{\varepsilon_{0 \mu_{0}}}\right)^{1 / 2} \)
c. \( \frac{\varepsilon_{0} \mu_{0}}{\varepsilon_{\mu}} \)
\( ^{\mathrm{D}}\left(\frac{\varepsilon_{0} \mu_{0}}{\varepsilon \mu}\right)^{1 / 2} \)
Subject: Physics
A wave is travelling in a medium with frequency \( \boldsymbol{f}=\mathbf{1 0}^{\mathbf{1 4}} \boldsymbol{H} \boldsymbol{z} \) and speed \( \boldsymbol{v}= \)
\( 100 m / s, \) Find out its wavelength?
B. \( 10^{-12} m \)
c. \( 10^{10} m \)
\( \mathbf{D} \cdot 10^{12} m \)
E \( .10^{16} m \)
Subject: Physics
A long horizontal slit is place 1 mm above a horizontal plane mirror. The interference between the light coming directly from the slit and that after reflection is seen on a screen 1 m away
from the slit. If the mirror reflects only
\( 64 \% \) of the light falling on it, the ratio of
the maximum to the minimum
intensity in the interference pattern
observed on the screen is:
\( \mathbf{A} \cdot 8: 1 \)
B . 3: 1
c. 81: 1
D. 9: 1
Subject: Maths
If \( 2 x+y=23 \) and \( 4 x-y=19, \) find
the values of \( 5 y-2 x \) and \( \frac{y}{x}-2 \)
A \( \cdot 36,-\frac{1}{3} \)
в. \( _{31,-\frac{5}{7}} \)
c. \( _{38, \frac{6}{7}} \)
D. None of these