AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Let \( f(x) \) be defined as follows:
\[
\boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}
\boldsymbol{x}^{\boldsymbol{6}}, \boldsymbol{x}^{2}>\mathbf{1} \\
\boldsymbol{x}^{3}, \boldsymbol{x}^{2} \leq \mathbf{1}
\end{array}\right.
\]
Then \( \boldsymbol{f}(\boldsymbol{x}) \) is?
This question has multiple correct options
A. continuous everywhere
B. differentiable everywhere
c. discontinuous at \( x=-1 \)
D. not differentiable at \( x=1 \)
Subject: Physics
A solid sphere of radius \( \boldsymbol{R} \) has total charge \( 2 Q \) and volume charge density
\( \rho=k r \) where \( r \) is distance from centre.
Now charges \( Q \) and \( -Q \) are placed diametrically opposite at distance \( 2 a \) where \( a \) is distance form centre of
sphere such that net force on charge \( Q \) is zero then relation between \( a \) and \( R \) is
A \( \cdot a=R / 2 \)
В . \( a=R \)
c. \( a=2 R \)
D. \( a=3 R / 4 \)
Subject: Chemistry
The Bohr radius for the hydrogen atom
\( \boldsymbol{n}=\mathbf{1}) \) is approx \( \mathbf{0 . 5 3} \boldsymbol{A}^{o} . \) The radius for
the first excited state \( (n=2 \) orbit) is
\( \left(\operatorname{in} A^{o}\right) \)
A . 0.13
B. 1.06
c. 4.77
D. 2.12
Subject: Maths
\( \sum_{r=0}^{m} n+r C_{n}= \)
A. \( ^{n+m+1} C_{n+1} \)
В. \( ^{n+m+2} C_{n} \)
\( \mathbf{c} \cdot n+m+3 C_{n+1} \)
D. none of these
Subject: Chemistry
In a reaction, 5 g ethyl acetate is hydrolyzed per litre in the presence of
dil. HCl in 300 min.lf the reaction is of
the first order and the initial
concentration of ethyl acetate is 22 g
\( L^{-1}, \) the rate constant of the reaction is:
A. \( k=8.6 \times 10^{-4} \min ^{-1} \)
В. \( k=1.4 \times 10^{-4} \min ^{-1} \)
c. \( k=6.9 \times 10^{-4} \min ^{-1} \)
D. None of these
Subject: Physics
One gram of ice at \( 0^{\circ} \mathrm{C} \) is added to 5
yarn of water at \( 10^{\circ} \mathrm{C} \). If the latent heat
of ice be 80 cal /g, then the final temperature of the mixture is
A \( .5^{\circ} \mathrm{C} \)
B. \( 0^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot-5^{\circ} \mathrm{C} \)
D. None of the above
Subject: Physics
The resistance of \( 2 \Omega \) is connected
across one gap of a meter-bridge (length of the wire is \( 100 \mathrm{cm} \) ) and an unknown resistance greater than \( 2 \Omega \) is connected across the other gap. When the resistance are interchanged, the balance point shifts by 20cm. Neglecting any corrections, the unknown resistance is: \( (\text { in } \Omega) \)
Subject: Physics
The masses of the three wires of copper
are in the ratio \( 1: 3: 5 . \) And their
lengths are in the ratio \( 5: 3: 1 . \) The
ratio of their electrical resistance is
A. 1: 3: 5
B. 5: 3: 1
c. 1: 15: 125
D. 125: 15: 1
Subject: Physics
Assuming the sum to be spherical body of radius \( R \) at a temperature of \( \boldsymbol{T} \boldsymbol{K} \) evaluate the total radiant power,
incident on Earth, at a distance \( r \) from
the Sun.
where \( r_{0} \) is the radius of the Earth and
\( \sigma \) is Stefan's constant.
\( ^{\text {A }} \cdot \frac{R^{2} \sigma T^{4}}{r^{2}} \)
\( ^{\text {В. }} \frac{4 \pi r_{0}^{2} R^{2} \sigma T^{4}}{r^{2}} \)
\( ^{\mathrm{c} \cdot} \frac{\pi r_{0}^{2} R^{2} \sigma T^{4}}{r^{2}} \)
D. \( \frac{r_{0}^{2} R^{2} \sigma T^{4}}{r^{2}} \)
Subject: Maths
The sine of the angle between the vectors \( \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}+\boldsymbol{2} \hat{\boldsymbol{k}} \) and \( \boldsymbol{2} \hat{\boldsymbol{i}}-\boldsymbol{4} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) is
A \( \cdot \sqrt{\frac{155}{156}} \)
в. \( \sqrt{\frac{115}{116}} \)
c. \( \sqrt{\frac{115}{147}} \)
D. \( \sqrt{\frac{157}{158}} \)
Subject: Maths
The length of a rectangle is \( 3 \mathrm{cm} \) more than its width and area is \( 54 \mathrm{cm}^{2} \). Find
the perimeter of the rectangle.
\( \mathbf{A} \cdot 25 \mathrm{cm} \)
B. \( 30 \mathrm{cm} \)
c. \( 35 \mathrm{cm} \)
D. \( 40 \mathrm{cm} \)
Subject: Chemistry
The electronegativities of nitrogen and chlorine are almost same. However,
\( N H_{3} \) exists as liquid whereas \( H C l \) as
gas due to between the
molecules of \( \boldsymbol{N} \boldsymbol{H}_{3} \)
A. van der Walls force of attraction
B. ionic bonding
c. H-bonding
D. dipole-dipole interaction
Subject: Chemistry
Which of the following oxides of nitrogen is anhydride of nitric acid?
A \( \cdot \mathrm{N}_{2} \mathrm{O}_{3} \)
B. \( N_{2} O_{4} \)
\( \mathbf{c} \cdot \mathbf{N}_{2} \mathbf{O}_{\mathbf{5}} \)
\( D \cdot N_{2} O \)
Subject: Physics
A child is standing in tront ot a straight plane mirror. His father is standing
behind him, as shown in the fig. The
height of the father is double the height
of the child. What is the minimum
length of the mirror required so that the
child can completely see his own image
and his fathers image in the mirror?
Given that the height of father is \( 2 H \)
\( \mathbf{A} \cdot H / 2 \)
B. \( 5 H / 6 \)
c. \( 3 H / 2 \)
D. None of these
Subject: Chemistry
Assertion
Be \( (\text { O } H) \) a dissolves in excess NaOH
solution.
Reason
Be \( (O H) \) a is an acidic compound.
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
Based on the information in each choice
below, which of the noble gases would
have the greatest density for a \( 1.00 L \)
sample at room temperature and
pressure?
A. Krypton molar mass \( 83.8 g / \)mol , atomic radius 111 picometers
B. Argon molar mass \( 39.9 g / \)mol , atomic radius 94 picometers
c. Neon molar mass \( 20.2 g / \)mol , atomic radius 70 picometers
D. Helium molar mass \( 4.0 g / \mathrm{mol} \) atomic radius 50 picometers
Subject: Chemistry
Assertion
A positive catalyst increases the rate of a reaction.
Reason
In presence of a catalyst, the activation energy of the reaction increases.
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
Find \( \boldsymbol{A}+\boldsymbol{B} \)
\( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{3} & \mathbf{- 1} \\ \mathbf{2} & \mathbf{- 5} & \mathbf{4} \\ \mathbf{3} & \mathbf{2} & \mathbf{- 6}\end{array}\right] \) and \( \boldsymbol{B}= \)
\( \left[\begin{array}{ccc}\mathbf{2} & \mathbf{4} & \mathbf{0} \\ \mathbf{3} & \mathbf{- 4} & \mathbf{5} \\ \mathbf{2} & \mathbf{3} & \mathbf{- 5}\end{array}\right] \)
Subject: Physics
A long straight wire carries a current 10 amp. An electron travels with a velocity \( \mathbf{5 . 0} \times \mathbf{1 0}^{\mathbf{6}} \mathrm{m} / \mathrm{sec} \) parallel to the wire 0.1
\( \mathrm{m} \) away from it and in a direction
opposite to the current. What force does the magnetic field of current exert on the electron?
В. \( 0.8 \times 10^{-16} N \)
c. \( 1.6 \times 10^{-17} N \)
D. \( 1.6 \times 10^{-16} N \)
Subject: Maths
If \( \boldsymbol{a} \cdot \boldsymbol{i}=\boldsymbol{a} \cdot(\boldsymbol{j}+\boldsymbol{i})=\boldsymbol{a} \cdot(\boldsymbol{i}+\boldsymbol{j}+\boldsymbol{k}) \)
then \( a \) is equal to
\( \mathbf{A} \cdot i \)
B. \( k \)
\( c \cdot j \)
D \( \cdot(i+j+k) \)
Subject: Physics
A ladder is more apt to slip when you
are high up on its rung than when you are just begin to climb. Why?
A. When you are high up, the moment of force tending to rotate the ladder about its base increases, while in the latter case, the moment of the force is insufficient to cause slipping
B. When you are high up, the ladder is in unstable, equilibrium
C. As you climb up, your potential energy increases
D. When you are high up, the centre of gravity of the system shifts upwards so the ladder is unstable, while in the latter case the system is more stable
Subject: Chemistry
For the reaction \( \mathbf{N H}_{4}^{+}+\mathbf{S}^{-2} \rightleftharpoons \)
\( \mathbf{N H}_{3}+\mathbf{H S}^{-}, \mathbf{N H}_{3} \) and \( \mathbf{S}^{-2} \) are a group
of :-
A. Acids
B. Bases
c. Acid-base pair
D. None of these
Subject: Physics
Consider the following statements A and \( \mathrm{B} \) and identify the correct answer. Statement(A):A Zener diode is always
connected in reverse bias to use it as
voltage Statement(B):The potential barrier of a p-njunction lies between 0.1 to \( 0.3 V \)
approximately.
A. A and B are correct
B. A and B are wrong
c. A is correct but B is wrong.
D. A is wrong but B is correct.
Subject: Maths
The line \( x \cos \theta+y \sin \theta=p \) meets the
axes of co-ordinates at \( A \) and \( B \)
respectively. Through A and B lines are drawn parallel to axes so as to meet the perpendicular drawn from origin to given line in \( P \) and \( Q \) respectively; then show that \( |P Q|=\frac{4 p|\cos 2 \theta|}{\sin ^{2} 2 \theta} \)
Subject: Chemistry
Which of the following solutions will
have blue colour?
\( A \cdot A 0.01- \) molar solution of \( H N O_{3} \)
B. A 0.01-molar solution of \( C H_{3} C O O H \)
C. A 0.01-molar solution of \( C u\left(N O_{3}\right)_{2} \)
D. A 0.01-molar solution of \( N a N O_{3} \)
E. A 0.01-molar solution of \( N a O H \)
Subject: Chemistry
Formula of
diamminediaquadichloroplatinum (IV)
bromide is \( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{2} \boldsymbol{C l}_{2}\right] \boldsymbol{B} \boldsymbol{r}_{2} \)
If true enter 1 , else enter 0 .
Subject: Maths
If \( \vec{x} \) is a vector whose initial point divides the line joining \( 5 \hat{i} \), and \( 5 \hat{j} \) in the ratio \( \lambda: 1 \) and the terminal point is the
origin. Also given \( |\vec{x}| \leq \sqrt{37}, \) then \( \lambda \) belongs to
\( \mathbf{A} \cdot\left[-\frac{1}{6}, \frac{1}{6}\right] \)
B \( \cdot(-\infty,-6) \cup\left(-\frac{1}{6}, \infty\right) \)
c. \( (-\infty,-8) \)
D. \( (1, \infty) \)
Subject: Physics
If \( |\overrightarrow{\boldsymbol{a}} \cdot \overrightarrow{\boldsymbol{b}}|=\sqrt{\mathbf{3}}|\overrightarrow{\boldsymbol{a}} \times \overrightarrow{\boldsymbol{b}}|, \) then the angle
between \( \vec{a} \) and \( \vec{b} \) is :-
A \( \cdot \frac{\pi}{6} \)
B.
\( c \cdot \frac{\pi}{3} \)
D.
Subject: Physics
Two tangent galvanometers, which are identical except in their number of turns, are connected in parallel. The ratio of their resistances of the coils is
1 : 3. If the reflection in the two tangents
galvanometers are \( 30^{\circ} \) and \( 60^{\circ} \)
respectively, then the ratio of their number of turns is:
A .2: 3
в. 3: 1
c. 1: 2
D. 1: 6
Subject: Physics
A standing wave is represented by \( \boldsymbol{Y}= \) \( 5 \cos (200 t-0.05 x) \) where \( Y \) and \( A \) are
in metres, t is in seconds and \( x \) is in
metre. Velocity of wave is
A \( .10 \mathrm{m} / \mathrm{s} \)
B. \( 4 \times 10^{3} \mathrm{m} / \mathrm{s} \)
c. \( 0.00025 \mathrm{m} / \mathrm{s} \)
D. \( 4000 \mathrm{m} / \mathrm{s} \)
Subject: Physics
A rain drop of radius \( 1.5 \mathrm{mm} \)
experience a drag force \( \boldsymbol{F}=(12 \times \)
\( \left.\mathbf{1 0}^{-5} \boldsymbol{v}\right) N, \) while falling through air from
a height \( 2 \mathrm{km}, \) with a velocity v. The terminal velocity of the rain drop will be nearly \( \left(u s e g=10 m / s^{2}\right) \)
A. \( 200 \mathrm{m} / \mathrm{s} \)
B. \( 80 \mathrm{m} / \mathrm{s} \)
\( c \cdot 7 m / s \)
D. \( 3 \mathrm{m} / \mathrm{s} \)
Subject: Physics
Assertion
Parallax method is used for measuring
distances of nearby stars only.
Reason
With increase of distance of star,
parallactic angle becomes too small to be measured accurately.
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
In the circuit diagram shown, \( X_{C}= \)
\( \mathbf{1 0 0 \Omega}, \boldsymbol{X}_{L}=\mathbf{2 0 0 \Omega} \& \boldsymbol{R}=\mathbf{1 0 0 \Omega} . \) The
effective current through the source is:
\( A \cdot 2 A \)
B. \( 2 \sqrt{2} A \)
\( c \cdot 0.5 \mathrm{A} \)
D. \( \sqrt{0.4 A} \)
Subject: Chemistry
Chemical equation of the industrial
preparation of \( \boldsymbol{S} \boldsymbol{O}_{3} \) is given?
\( 2 S O_{2}+O_{2} \rightleftharpoons 2 S O_{3}+ \) Heat
What is the influence of the following factors in this system at equilibrium?
(a) Increasing the amount of \( \boldsymbol{O}_{2} \)
(b) \( S O_{2} \) is removed from the system.
(c) Decreasing the temperature.
Subject: Maths
Equation of the line through the point of intersection of the lines \( 3 x+2 y+4= \)
0 and \( 2 x+5 y-1=0 \) whose distance
from (2,-1) is \( 2, \) is
A. \( 2 x-y+5=0 \)
B. \( 4 x+3 y+5=0 \)
c. \( x+2=0 \)
D. \( 3 x+y+5=0 \)
Subject: Maths
Complete activity from the following:
First term and common difference of an
A.P. are 6 and 3 respectively. Find \( S_{27} \)
Solution:

First term \( =a=6, \) common difference
\( =\boldsymbol{d}=\mathbf{3}, \boldsymbol{S}_{27}=? \)
\( \boldsymbol{S}_{\boldsymbol{n}}=\frac{\boldsymbol{n}}{2}[\square+(\boldsymbol{n}-1) \boldsymbol{d}]- \) formula
\( \boldsymbol{S}_{\mathbf{2 7}}=\frac{\mathbf{2 7}}{\mathbf{2}}[\mathbf{1 2}+(\mathbf{2 7}-\mathbf{1}) \square] \)
\( =\frac{27}{2} \times \square \)
\( =27 \times 45 \)
\( \therefore S_{27}=\square \)
Subject: Physics
A circuit of logic gates given below, some input signal \( A, B, C \) are given with their output signal \( x, y \) and \( z \) is given in respective option, choose correct
options:

This question has multiple correct options
A. If \( A=1, B=1, C=1 \) then \( x=0, y=1, z=1 \)
B. If \( A=0, B=0 \) and \( C=1 \) then \( x=1, y=0, z=1 \)
c. If \( A=0, B=0 \) and \( C=1 \) then \( x=1, y=0, z=0 \)
D. If OR gate is replaced by NOR gate then net output signal of the circuit becomes \( z=0 \) for the input \( A= \) \( 0, B=0 \) and \( C=1 \)
Subject: Physics
Two circular loops \( P \) and \( Q \) are
concentric and coplanar as shown in
figure. The loop \( Q \) is smaller than \( P . \) If
the current \( I_{1} \) flowing in loop is decreasing with time, then the current
\( I_{2} \) in the \( \operatorname{loop} Q \)
A. flows in the same direction as that of \( P \)
B. flows in the opposite direction as that of \( Q \)
c. is zero
D. None of these
Subject: Chemistry
The hybridization and shape of \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\mathbf{5}}^{-} \)
is :
A. \( s p^{3} \), tetrahedron
B . \( s p^{3} \), trigonal pyramidal
\( \mathbf{c} \cdot s p^{3} d^{2} \), trigonal bipyramidal
D. \( s p^{3} d^{3} \), pentagonal planar
Subject: Maths
Find the value of \( (4+2 i)(4-2 i) \)
given that \( i^{2}=-1 \)
\( \mathbf{A} \cdot 12 \)
B . 20
\( c \cdot 16-4 i \)
D. \( 4+16 i \)
E . \( 12-16 i \)
Subject: Physics
Four metallic plates are arranged as
shown in the figure. If \( d \) is the distance
between each plate then capacitance of
the given system between points \( A \) and
\( B \) is :
\( (\operatorname{given} \boldsymbol{d}<<\boldsymbol{A}) \)
\( \mathbf{A} \cdot \frac{\epsilon_{0} A}{d} \)
B. \( \frac{2 \epsilon_{0} A}{d} \)
c. \( \frac{3 \epsilon_{0} A}{d} \)
D. \( \frac{4 \epsilon_{0} A}{d} \)
Subject: Chemistry
Which one of the following has highest boiling point?
A. \( H_{3} C C H_{2} C H_{2} C H_{2} C l \)
в. \( \left(H_{3} C\right)_{2} C H C H_{2} C l \)
c. \( \left(H_{3} C\right)_{3} C C l \)
D. \( H_{3} C C H_{2} C H(C l) C H_{3} \)
Subject: Physics
A wooden box is placed on a table. The normal force on the box from the table
is \( N_{1} . \) Now another identical box is kept
on first box and the normal force on
lower block due to upper block is \( N_{2} \)
and normal force on lower block by the
table is \( N_{3} . \) For this situation, mark out
the correct statement(s)
A. \( N_{1}=N_{2}=N_{3} \)
в. \( N_{1}<N_{2}=N_{3} \)
c. \( N_{1}=N_{2}<N_{3} \)
D. \( N_{1}=N_{2}>N_{3} \)
Subject: Physics
An LCR series circuit contains \( \boldsymbol{L}=\mathbf{8} \boldsymbol{H} \)
\( \mathrm{C}=0.5 \mu \mathrm{F} \) and \( \mathrm{R}=100 \Omega \).The resonant
frequency of the circuit is
\( ^{\mathrm{A}} \cdot \frac{100}{\pi} H z \)
в. \( \frac{500}{\pi} H z \)
c. \( \frac{250}{\pi} H z \)
D. \( \frac{125}{\pi} H z \)
Subject: Physics
The acceleration due to gravity g is determined by dropping an object through a distance of exactly 10 m. The time is to be measured so that the
result is to be good to \( 0.1 \% \). If the
absolute error is \( n \times 10^{-4} \mathrm{S} \), find \( n \)
(Take \( g=10 \mathrm{m} / \mathrm{s}^{2} \) in calculation)
\( A \cdot 7 \)
B. 3
c. 14
D. 6
Subject: Physics
A uniform spherical shell of mass \( M \) and radius \( R \) rotates about a vertical
axis on frictionless bearing. A massless
cord passes around the equator of the
shell, over a pulley of rotational inertia \( \boldsymbol{I} \)
and radius \( R \) and is attached to a small
object of mass \( m \) that is otherwise free to fall under the influence of gravity
There is no friction of pulley's axle; the
cord does not slip on the pulley. What is
the speed of the object after it has fallen
a distance \( h \) from rest? Use work-energy
considerations
Subject: Chemistry
Insulin is dissolved in suitable solvent
and the osmotic pressure \( (\pi) \) of solutions of various concentrations
\( \left(g / c m^{3}\right) C \) is measured at \( 27^{0} C . \) The slope is plot of \( \pi \) against \( C \) is found to
be \( 4.1 \times 10^{-3} \).the molecular mass of
insulin is?
Subject: Physics
A rod of length \( 10 \mathrm{cm} \) lies along the principal axis of a concave mirror of focal length \( 10 \mathrm{cm} \) in such away that the end closer to the pole is \( 20 \mathrm{cm} \) away
from it. Find the length of the image.
A . \( 2 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
\( c \cdot 5 \mathrm{cm} \)
D. \( 6 \mathrm{cm} \)
Subject: Maths
\( \int_{3-\alpha}^{3+\alpha} f(x) d x \) equals, where \( f(3+\beta)= \)
\( f(3-\beta), \beta \in R \)
A. \( _{3} \int_{0}^{\alpha} f(x) d x \)
в. \( 3 \int_{0}^{3} f(x) d x \)
c. \( 3 \int_{\alpha-3}^{\alpha} f(x) d x \)
D. \( 3 \int_{3}^{3+\alpha} f(x) d x \)
Subject: Maths
\( \int_{2-\ell n 3}^{3+\ell n 3} \frac{\ln (4+x)}{\ell n(4+x)+\ell n(9-x)} d x \) is
equal to:
A. cannot be evaluated
B. is equal to \( \frac{5}{2} \)
c. is equal to \( 1+2 \ell n 3 \)
D. is equal to \( \frac{1}{2}+\ell n \) 3
Subject: Maths
The general solution of \( 4 \tan ^{2} \theta= \) \( \mathbf{3} \sec ^{2} \boldsymbol{\theta} \) is \( \boldsymbol{\theta}=\boldsymbol{n} \boldsymbol{\pi} \pm \frac{\boldsymbol{\pi}}{\boldsymbol{m}} . \) Then, find the
value of \( \boldsymbol{m} \)
Subject: Chemistry
0.001 mol of \( C o\left(N H_{3}\right)_{5}\left(N O_{3}\right)\left(S O_{4}\right) \)
was passed through a cation exchanger and the acid coming out of it required
\( 20 \mathrm{ml} \) of \( 0.1 \mathrm{M} \) NaOH for neutralisation.
Hence, the complex is:
\( \mathbf{A} \cdot\left[C o\left(N H_{3}\right)_{5} S 0_{4}\right] N O_{3} \)
B. \( \left[\operatorname{Co}\left(N H_{3}\right)_{5} N O_{3}\right] S O_{4} \)
c. \( \left[\operatorname{Co}\left(N H_{3}\right)_{5}\right]\left(S O_{3}\right)\left(N O_{3}\right) \)
D. none of these
Subject: Physics
Two identical balls each of mass \( 4 \mathrm{kg} \) are moving towards each other with speeds \( 2 \mathrm{m} / \mathrm{s} \) and \( 3 \mathrm{m} / \mathrm{s} \) respectively they undergo head on perfectly elastic collision. the impulse imparted by one ball on other is:
A . \( 12 \mathrm{Ns} \)
B. 8 Ns
c. \( 20 \mathrm{Ns} \)
D. \( 40 \mathrm{Ns} \)
Subject: Chemistry
The electron configuration of \( _{11} N a^{23} \) is
A \( \cdot 1 s^{2}, 2 s^{2}, 2 p^{5}, 3 s^{2} \)
B . \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{1} \)
C \( \cdot 1 s^{2}, 2 s^{2}, 2 p^{4}, 3 s^{1}, 3 p^{2} \)
D. \( 1 s^{1}, 2 s^{1}, 2 P^{6}, 3 s^{2}, 3 p^{1} \)
Subject: Maths
Assertion
The expression \( ^{40} \boldsymbol{C}_{r} .^{60} \boldsymbol{C}_{0}+^{40} \)
\( C_{r-1} .^{60} C_{1}+\ldots \) attains maximum value
when \( r=50 \)
Reason \( ^{2 n} C_{r} \) is maximum when \( r=n \)
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
At what temperature in \( ^{\circ} \boldsymbol{C}, \) the \( \boldsymbol{U}_{r m s} \) of
\( \boldsymbol{S} \boldsymbol{O}_{2} \) is equal to the average velocity of
\( O_{2} \) at \( 27^{\circ} C ? \)
A \( \cdot 118.1^{\circ} \mathrm{C} \)
B . \( 236.3^{\circ} \mathrm{C} \)
C \( .472 .6^{\circ} \mathrm{C} \)
D. None of these
Subject: Maths
\( \frac{d y}{d x} \) for \( y=\tan ^{-1}\{\sqrt{\frac{1+\cos x}{1-\cos x}}\}, \) where
\( \mathbf{0}<\boldsymbol{x}<\boldsymbol{\pi}, \) is?
\( A \cdot \frac{-1}{2} \)
B.
\( c \cdot 1 \)
D.
Subject: Chemistry
\( M n O_{4}^{-} \) is of intense pink colour through Mn is in (+7) oxidation state, it is due to:
A. oxygen gives colour to it it
B. charge transfer when Mn(+7) gives its electron to oxygen and oxidise to Mn (+8) temporarily
c. charge transfer when oxygen gives its electron to Mn (+7) changing in Mn (+6)
D. none is correct explanation
Subject: Chemistry
The difference between \( \Delta H \) and \( \Delta E \) on
a molar basis for the combustion of \( n \)
octane at \( 25^{\circ} \mathrm{C} \) would be:
B. \( -1.14 \mathrm{kJ} \)
c. \( -11.15 \text { k }] \)
D. +11.15 k
Subject: Physics
Two particles are moving along two long straight lines, in the same plane with
same speed \( 20 \mathrm{cm} / \mathrm{s} \). The angle
between the two lines is \( 60^{\circ} \) and their
intersection point is \( O . A t \) a certain
moment, the two particles are located at distance \( 3 m \) and 4 m from \( O \), and
are moving towards \( 0 . \) Subsequently,
the shortest distance between them will
be
\( \mathbf{A} \cdot 50 \mathrm{cm} \)
B. \( 40 \sqrt{2} \mathrm{cm} \)
\( \mathbf{c} \cdot 50 \sqrt{2} \mathrm{cm} \)
D. \( 50 \sqrt{3} \mathrm{cm} \)
Subject: Maths
If the probabilities of the events \( \boldsymbol{A} \cap \)
\( B, A, B \) and \( A \cup B \) are in A.P.with
second term of A.P. is equal to common difference then \( A \) and \( B \) are
A. independent
B. equally likely
c. mutually exclusive
D. can't be determined
Subject: Chemistry
\( \boldsymbol{C}_{3} \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{C}_{2} \boldsymbol{H}_{6}(\boldsymbol{g})+ \)
\( \boldsymbol{C} \boldsymbol{H}_{4}(\boldsymbol{g}) \triangle \boldsymbol{H}^{0}=? \)
\( \begin{array}{ll}C_{2} \boldsymbol{H}_{6} & \boldsymbol{H}_{2}(\boldsymbol{g}) \\ (g)\end{array} \quad \boldsymbol{C H}_{4}(\boldsymbol{g}) \quad \) graphit
-1560.1 \( \quad \) -225.0 \( \quad-090.0 \quad \) -393.5
\( \triangle H^{0} \)combustion\( \left(K J m o l^{-1}\right. \)
Subject: Physics
(a) Why does a paramagnetic sample display greater magnetisation (for the same magnetising field) when cooled?
(b) Why is diamagnetism, in contrast, almost independent of temperature?
(c) If a toroid uses bismuth for its core,
will the field in the core be (slightly) greater or (slightly) less than when the core is empty?
(d) Is the permeability of a ferromagnetic material independent
of the magnetic field? If not, is it more for lower or higher fields?
(e) Magnetic field lines are always nearly normal to the surface of a ferromagnet at every point. (This fact is analogous to the static electric field lines being normal to the surface of a conductor at every point.) Why?
(f) Would the maximum possible magnetisation of a paramagnetic sample be of the same order of magnitude as the magnetisation of a ferromagnet?
Subject: Physics
What is the disintegration constant of a radioactive element, if the number of its
atoms diminishes by \( 18 \% \) in 24 h?
A. \( 2.1 \times 10^{-3} / s \)
в. \( 2.1 \times 10^{5} / s \)
C \( .22 \times 10^{6} / s \)
D. \( 22 \times 10^{-6} / s \)