AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A boat is traveling due east at \( 12 m s^{-1} \)
A flag on the boat flaps at \( 53 N \) of \( W \) Another flag on the shore flaps due
north.
This question has multiple correct options
A. speed of wind with respect to ground is \( 16 \mathrm{ms}^{-1} \)
B. Speed of wind with respect to ground is \( 20 \mathrm{ms}^{-1} \)
c. speed of wind with respect to boat is \( 20 \mathrm{ms}^{-1} \)
D. speed of wind with respect to boat is \( 16 \mathrm{ms}^{-1} \)
Subject: Physics
A luminous object is placed at a distance of \( 30 \mathrm{cm} \) from the convex lens
of focal length \( 20 \mathrm{cm} . \) The distance from
the lens a convex mirror of radius of
curvature \( 10 \mathrm{cm} \) should be placed on the
other side of the lens such that the real
images formed on the source itself is
\( \mathbf{A} \cdot 12 c m \)
B. \( 30 \mathrm{cm} \)
\( \mathbf{c} .50 \mathrm{cm} \)
D. \( 60 \mathrm{cm} \)
Subject: Chemistry
In the following reaction:
\( 2 S O_{2}(g)+O_{2}(g) \rightleftharpoons 2 S O_{3}(g) \) the
equilibrium is not attained. The rate of forward reaction is greater than that of backward reaction. Thus, which of the following is the correct relation between
\( \boldsymbol{K}_{\boldsymbol{p}} \) and \( \boldsymbol{Q}_{\boldsymbol{p}} ? \)
\( \mathbf{A} \cdot K_{p}=Q_{p} \)
B \( \cdot Q_{p}>K_{p} \)
\( \mathbf{c} \cdot Q_{p}<K_{p} \)
D. \( K_{p}=Q_{p}=1 \)
Subject: Maths
In the figure below, \( \angle Q>\angle R \) and \( M \) is
a point on \( Q R \) such that \( P M \) is the
bisector of \( \angle Q P R \) If the perpendicular
from \( P \) on \( Q R \) meets \( Q R \) at \( N \) then prove that \( \angle M P N=\frac{1}{2}(\angle Q-\angle R) \)
Subject: Chemistry
Which of the following compound is more acidic?
\( ^{\mathbf{A}} \cdot_{C H_{2}-C}^{\circ}-O H \)
No
в. \( _{C H_{2}}-C H_{2}-\stackrel{\circ}{C}-O H \)
\( N O_{2} \)
2
c.
\[
\begin{array}{l}C H_{2}-C H_{2}-C-O H \\ \text { I }\end{array}
\]
D.
\[
C H_{3}-\begin{array}{c}c_{1} \\ _{1} \\ C \\ C l\end{array}-C_{-} O H
\]
Subject: Maths
toppr LoGin Joln Now
Q Type your question
two classes of alphabets as in the two matrices given below. The columns and
rows of Matrix I are numbered from 0 to
4 and that of Matrix II are numbered
from 5 to \( 9 . \) A letter from these matrices
can be represented first by its row and
next by its column, e.g., \( ^{\prime} \boldsymbol{R}^{\prime} \) can be
represented by 04,42 etc., and \( ^{\prime} D^{\prime} \) can
be represented by 57,76 etc. Similarly, you have to identify the set for the word \( \mathrm{ROAD}^{\prime} \) Matrix
1 \begin{tabular}{cc|c|c|c|c} 
& 0 & 1 & 2 & 3 & 4 \\
\hline 0 & \( F \) & \( O \) & \( M \) & \( S \) & \( R \) \\
1 & \( S \) & \( R \) & \( F \) & \( O \) & \( M \) \\
2 & \( O \) & \( M \) & \( S \) & \( R \) & \( F \) \\
3 & \( R \) & \( F \) & \( O \) & \( M \) & \( S \) \\
4 & \( M \) & \( S \) & \( R \) & \( F \) & \( O \)
\end{tabular}
Matrix I
\begin{tabular}{cccc|cc} 
& 5 & 6 & 7 & 8 & 9 \\
5 & \( A \) & \( T \) & \( D \) & \( I \) & \( P \) \\
6 & \( I \) & \( P \) & \( A \) & \( T \) & \( D \) \\
7 & \( T \) & \( D \) & \( I \) & \( P \) & \( A \) \\
8 & \( P \) & \( A \) & \( T \) & \( D \) & \( I \) \\
9 & \( D \) & \( I \) & \( P \) & \( A \) & \( T \)
\end{tabular}
\( A \)
42,32,49,58
B. 23,32,98,99
\( c \)
11,13,67,69 13,67,69
00
\( D \)
Subject: Maths
I a \( \triangle A B C, \angle A=90^{\circ}, C A=A B \) and \( D \) is a
point on AB produced prove that \( \boldsymbol{D} \boldsymbol{C}^{2}=\boldsymbol{B} \boldsymbol{D}^{2}=\boldsymbol{2} \boldsymbol{A} \boldsymbol{B} \times \boldsymbol{A} \boldsymbol{D} \)
Subject: Maths
The sum of \( n \) terms of the series \( 1^{2}+ \)
\( \mathbf{2} . \mathbf{2}^{\mathbf{2}}+\mathbf{3}^{\mathbf{2}}+\mathbf{2 . 4}^{\mathbf{2}}+\mathbf{5}^{\mathbf{2}}+\mathbf{2 . 6}^{\mathbf{2}}+\ldots . \) is
\( \frac{n(n+1)^{2}}{2}, \) where \( n \) is even. Find the
sum, where \( n \) is odd
Subject: Physics
Two homogenous spheres \( A \) and \( B \) of
masses \( m \) and \( 2 m \) having radii \( 2 a \) and
\( a \) respectively are placed in touch. The distance of centre of mass from first
sphere is:
\( A \)
B . \( 2 a \)
\( c .3 a \)
D. \( 3 a / 2 \)
Subject: Maths
If \( \Delta_{1}=\left|\begin{array}{ll}\mathbf{1} & \mathbf{0} \\ \boldsymbol{a} & \boldsymbol{b}\end{array}\right| \) and \( \boldsymbol{\Delta}_{2}=\left|\begin{array}{ll}\mathbf{1} & \mathbf{0} \\ \boldsymbol{c} & \boldsymbol{d}\end{array}\right| \) then
\( \Delta_{2} \Delta_{1} \) is equal to
\( \mathbf{A} \cdot a c \)
B. \( b d \)
c. \( (b-a)(d-c) \)
D. none of these
Subject: Maths
A firm has the cost function \( C=\frac{x^{3}}{3}- \)
\( 7 x^{2}+111 x+50 \) and demand function
\( \boldsymbol{x}=\mathbf{1 0 0}-\boldsymbol{p} \)
Write the total revenue function in
terms of \( \boldsymbol{x} \)
Subject: Chemistry
The densities of air at \( 25^{\circ} \mathrm{C} \) and \( 100^{\circ} \mathrm{C} \)
\( \operatorname{are} 1.2 g L^{-1} \) and \( 0.9 g L^{-1} \) respectively Assuming that the air obey's Charle's law the value of absolute zero of
temperature in degree Celsius is:
B . \( 200^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot-200^{\circ} \mathrm{C} \)
D. \( 0^{\circ} \mathrm{C} \)
Subject: Chemistry
Coagulation value of the electrolytes
\( A l C l_{3} \) and \( N a C l \) for \( A s_{2} S_{3} \) sol are
0.093 and 52 repectively. How many
times \( A l C l_{3} \) has greater coagulating
power than \( N a C l ? \)
A . 930
в. 520
\( c .560 \)
D. None of these
Subject: Physics
A pan containing a layer of uniform thickness of ice is placed on a circular turn- table with its centre coinciding with the centre of the turn-table.
The turn-table is now rotated at a
constant angular velocity about a vertical axis passing through its centre and the driving torque is withdrawn. There is no friction between the table
and the pivot. The pan rotates with the
table. As the ice melts,
This question has multiple correct options
A. the angular velocity of the system decreases
B. the angular velocity of the system increases
c. the angular velocity of the system remains unchanged
D. the moment of inertia of the system increases
Subject: Chemistry
Statement I: \( _{6}^{14} C \) and \( _{6}^{12} C \) are isomers of the element carbon.

Statement II: Isomers contain the same
number of protons but a different number of neutrons
A. Both Statement I and Statement II are correct and Statement II is the correct explanation of Statement
B. Both Statement I and Statement II are correct, but Statement II is not the correct explanation of Statement I.
c. Statement I is correct, but Statement II is incorrect
D. Both Statement I and Statement II are incorrect
Subject: Maths
Find the area of a quadrilateral one of
whose diagonals is \( 30 \mathrm{cm} \) long and the perpendiculars from the two other
vertices on this diagonal are \( 19 \mathrm{cm} \) and
\( 11 \mathrm{cm} \) respectively.
A \( \cdot 450 \mathrm{cm}^{2} \)
В. \( 540 \mathrm{cm}^{2} \)
D. \( 350 \mathrm{cm}^{2} \)
Subject: Chemistry
Conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) reacts with carbon and
forms:
This question has multiple correct options
A \( \cdot C O_{2} \)
в. \( S O_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{CO}_{3} \)
D. \( H_{2} S O_{3} \)
Subject: Chemistry
Ethylene is produced by, \( C_{4} H_{8} \stackrel{\Delta}{\longrightarrow} \)
\( 2 C_{2} H_{4} . \) The constant is \( 2.48 \times \)
\( 10^{-4} \)sec\( ^{-1} \). Time in hours (nearest
integer) in which the molar ratio of the
ethylene to cyclobutane in reaction mixture will attain the value of 100
is
Subject: Chemistry
\( \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{S}+\boldsymbol{X} \longrightarrow \boldsymbol{N} \boldsymbol{a}_{2}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{5}\right. \)
purple colc
The reason of color of \( X \) is :
A. d-d transition
B. charge transfer
c. colorless compound
D. None
Subject: Maths
\( \boldsymbol{v}=\frac{\mathbf{2} \boldsymbol{\pi} \boldsymbol{r}}{\boldsymbol{T}} \)
In Physics, Uniform Circular Motion is used to describe the motion of an object traveling at a constant speed in a circle. The speed of the object, also called tangential velocity, can be calculated using the formula above. Here, \( r \)
represents the radius of the circle, \( \boldsymbol{T} \) the
time it takes for the object to make one complete revolution, called a period. Determine which of the following formulae could be used to find the
length of one period if one knows the tangential velocity and the radius of the circle?
A \( \cdot T=\frac{v}{2 \pi r} \)
B・ \( T=\frac{2 \pi r}{v} \)
c. \( T=2 \pi r v \)
D. \( T=\frac{1}{2 \pi r v} \)
Subject: Physics
A body \( P \) moving with a velocity of 20
\( \mathrm{ms}^{-1} \) collides with another body \( Q \) of
same mass at rest. After collision \( \boldsymbol{P} \)
comes to rest. What is the velocity of the
body \( Q ? \)
A \( \cdot 10 \mathrm{ms}^{-1} \)
B. \( 20 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 30 \mathrm{ms}^{-1} \)
D. \( 5 \mathrm{ms}^{-1} \)
Subject: Maths
The following table shows the age distribution of cases of a certain disease admitted during a year in a particular hospital
\( \begin{array}{ll}\text { Age } & \text { 5 } \\ \text { (in } & \text { - } \\ \text { Years) } & \text { 14 }\end{array} \) 15
25
34 24 44
No. of 6 11
\( \begin{array}{ll}21 & 23\end{array} \)
case
Find the nearest integer to the modal
age.
Subject: Chemistry
0.01 mol of \( A g N O_{3} \) is added to 1 L of a
solution which is \( 0.1 M N a_{2} C r O_{4} \) and
\( 0.005 M \) in \( N a I O_{3} . \) Calculate
\( \left[\boldsymbol{A} \boldsymbol{g}^{\oplus}\right],\left[\boldsymbol{I} \boldsymbol{O}_{3}^{\ominus}\right] \) and \( \left[\boldsymbol{C r} \boldsymbol{O}_{4}^{2-}\right] \)
\( K_{s p} A g_{2} C r O_{4} \) and \( A g I O_{3} \) are \( 10^{-8} \) and \( 10^{-13} \) respectively
\( \mathbf{A} \cdot\left[A g^{\oplus}\right]=0.316 \times 10^{-4} M,\left[I O_{3}^{\ominus}\right]=0.31 \times \)
\( 10^{-10} M,\left[C r O_{2}^{2-}\right]=0.0975 M \)
B \( \cdot\left[A g^{\oplus}\right]=3.16 \times 10^{-4} M,\left[I O_{3}^{\ominus}\right]=3.1 \times \)
\( 10^{-10} M,\left[C r O_{2}^{2-}\right]=0.975 M \)
C \( \cdot\left[A g^{\oplus}\right]=31.6 \times 10^{-4} M,\left[I O_{3}^{\odot}\right]=31 \times \)
\( 10^{-10} M,\left[C r O_{2}^{2-}\right]=9.75 M \)
D. None of these
Subject: Physics
Three force \( \overrightarrow{\boldsymbol{p}}, \overrightarrow{\boldsymbol{Q}} \) and \( \quad \overrightarrow{\boldsymbol{R}} \) acting
with TA,IB,IC where I is the incentance of
\( \triangle A B C \) are in equim \( \vec{P}_{Q}, \quad_{R} \)
is
Subject: Chemistry
The deep red colouration is due to the
formation of:
\( \mathbf{A} \cdot \operatorname{Fe}\left(C H_{3} C O O\right) \)
в. \( F e(O H)_{2} C H_{3} C O O \)
c. \( \left[F e_{3}(O H)_{2}\left(C H_{3} C O O\right)_{6}\right]^{+} \)
D. \( \left[F e_{3}\left(C H_{3} C O O\right)_{6}\right. \)
Subject: Physics
\( P Q \) is an infinite current carrying
conductor. \( A B \) and \( C D \) are smooth
conducting rods on which a conductor
\( E F \) moves with constant velocity \( v \) as
shown. The force needed to maintain
constant speed to \( \boldsymbol{E} \boldsymbol{F} \) is
\( ^{\mathbf{A}} \cdot \frac{1}{v R}\left[\frac{\mu_{0} I v}{2 \pi} \ln \frac{(b)}{(a)}\right]^{2} \)
\( ^{\mathrm{B}} \cdot \frac{v}{R}\left[\frac{\mu_{0} I v}{2 \pi} \ln \frac{(a)}{(b)}\right]^{2} \)
\( ^{\mathrm{c}} \cdot \frac{v}{R}\left[\frac{\mu_{0} I v}{2 \pi} \ln \frac{(b)}{(a)}\right]^{2} \)
D. None of these
Subject: Maths
In the problem below, \( f(x)=x^{2} \) and
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{4} \boldsymbol{x}-\boldsymbol{2} \)

Find the following function: \( (\boldsymbol{f}+\boldsymbol{g})(\boldsymbol{x}) \)
A \( \cdot x^{2}+4 x-2 \)
B. \( x^{2}-4 x-2 \)
c. \( x^{2}-4 x+2 \)
D. \( x^{2}-2 \)
Subject: Physics
In the absence of air resistance, a ball
thrown horizontally from a tower with velocity v, will land after time T seconds.
If, however, air resistance is taken into account, which statement is correct?
A. The ball lands with a horizontal velocity less than v after more than T seconds
B. The ball lands with a horizontal velocity less than v after T seconds
c. The ball lands with a horizontal velocity v after more than \( T \) seconds
D. The ball lands with a horizontal velocity v after seconds
Subject: Maths
Let \( \boldsymbol{S}_{\boldsymbol{k}}=\frac{\mathbf{1}+\mathbf{2}+\mathbf{3}+\ldots+\boldsymbol{k}}{\boldsymbol{k}} . \) If \( \boldsymbol{S}_{1}^{2}+ \)
\( S_{2}^{2}++S_{10}^{2}=\frac{5}{12} A \) then \( A \) is equal to
A . 303
в. 283
c. 156
D. 301
Subject: Biology
In order to manage energy resources within the cell, the potential energy of an electrochemical gradient must be coupled with endergonic (less favorable) processes. If the membrane that sustains the
concentration gradient is disrupted, what happens to the cell?
A. The energetics of the cell will not be affected and will continue functioning normally.
B. The gradient will be reversed but still able to support cellular activity
C. The loss of a concentration gradient reduces the potential energy of the cell and diminishes the ability to do work
D. The endergonic nature of the reduced gradient can be coupled to endergonic reactions such as the synthesis of ATP
Subject: Maths
The area enclosed between the curve
\( \boldsymbol{y}^{2}=\boldsymbol{x} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{y}=|\boldsymbol{x}| \) is
A \( \cdot \frac{1}{6} \)
в. \( \frac{1}{3} \)
\( c \cdot \frac{2}{3} \)
D. 1
Subject: Physics
A car moving with a speed of \( 40 \mathrm{km} / \mathrm{h} \) can be stopped by applying brakes at least after \( 2 \mathrm{m} \). If the same car is moving with a speed of \( 80 \mathrm{km} / \mathrm{h} \), what is the minimum stopping distance?
\( A \cdot 8 c m \)
B. \( 6 m \)
\( c .4 m \)
D. \( 2.6 m \)
Subject: Physics
Parallel rays of light of intensity \( l= \)
\( 912 W m^{-2} \) are incident on a spherical
black body kept in surroundings of temperature 300 K. Take Stefan-
Boltzmann constant \( \sigma=5.7 \times \)
\( 10^{-5} W m^{-2} K^{-4} \) and assume that the
energy exchange with the surroundings is only through radiation. The final
steady state temperature of the black body is close to:
\( A \cdot \) 330 \( K \)
B. 660 K
c. \( 990 \mathrm{k} \)
D. \( 1550 \mathrm{K} \)
Subject: Physics
On a smooth surface there are five
identical equally spaced balls \( A, B, C, D \) and E present with initial velocities \( 10 \mathrm{m} / \mathrm{s},-5 \mathrm{m} / \mathrm{s}, 2 \mathrm{m} / \mathrm{s},-3 \mathrm{m} / \mathrm{s} \)
\( 3 \mathrm{m} / \mathrm{s} \) respectively, Collision between any two ball assumed to be elasitc.
Then after all possible collision which pair of balls will have same speed as of initial
\( A \cdot A \& D \)
B. B \&
\( c \cdot c \& D \)
\( D \cdot A \& C \)
Subject: Maths
Value of \( x \) for which \( \cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right)= \)
\( 2 \tan ^{-1} x \) satisfied is \( x \epsilon[a, \infty) \)
Find the value of \( a \)
A \( . a=-\infty \)
B . \( a=-1 \)
\( \mathbf{c} \cdot a=0 \)
D. \( a=1 \)
Subject: Chemistry
Which of the following is not a good method to make \( 2,2- \)
dimethylpropanoic acid?
A \( \cdot\left(C H_{3}\right)_{3} C C H_{2} O H^{K_{2} C r_{2} O_{7}, H_{2} S O_{4}} \)
B. \( \left(C H_{3}\right)_{3} C B r_{\text {Diethylether }(i)} \stackrel{M g}{\stackrel{(i)}{H_{2} O}, H} \)
\( ^{\mathbf{c}} \cdot\left(C H_{3}\right)_{3} C B r \stackrel{N a C N}{\longrightarrow} \frac{H_{3} \bar{\phi}}{H e a t} \)
D. \( \left(C H_{3}\right)_{3} C C=C H \stackrel{O_{3}}{\longrightarrow} \stackrel{O H_{2}}{\longrightarrow} \)
Subject: Physics
Liquid ammonia is used in ice factory
for making ice from water. If water at
\( 20^{\circ} \mathrm{C} \) is to be converted to \( 2 \mathrm{kg} \) ice at
\( 0^{\circ} \mathrm{C}, \) how many grams of ammonia are to be evaporated? (Given:The latent heat of vapourization of ammonia \( = \) \( 341 \mathrm{cal} / \mathrm{g} \)
Subject: Physics
A wire suspended from one end carries a sphere at its other end. The elongation in the wire reduces from 2mm to
1.6 \( m m \) on completely immersing the sphere in water. The density of the material of the sphere is
A. \( 3200 \mathrm{kg} / \mathrm{m}^{3} \)
в. \( 800 \mathrm{kg} / \mathrm{m}^{3} \)
c. \( 1250 \mathrm{kg} / \mathrm{m}^{3} \)
D. \( 5000 \mathrm{kg} / \mathrm{m}^{3} \)
Subject: Chemistry
An alcohol of formula \( C_{9} \boldsymbol{H}_{12} \boldsymbol{O} \) reacts
with \( N a_{2} C r_{2} O_{7} \) to from a compound
having formula \( C_{9} \boldsymbol{H}_{10} \boldsymbol{O} \). The original alcohol might be
\( \langle\square\rangle-\mathrm{cH}_{2}-\mathrm{cH}_{2}-\mathrm{cH}_{2}-\mathrm{o} \)
B.
\( c \)
D
Subject: Physics
A solid cylinder of mass 2 Kg and radius
\( 0.2 \mathrm{m} \) is rotating about its own
axis without friction with angular
velocity 3 rad/s. A particle of mass 0.5
Kg and moving with a velocity of \( 5 \mathrm{m} / \mathrm{s} \) strikes the cylinder and sticks to it as
shown in. The angular momentum of the
cylinder before collision will be
A. 0.12 Joule/s
B. 12 Joule/s
c. 1.2 Joule/s
D. 1.12 Joule/s
Subject: Chemistry
Acetyl salicylic acid (aspirin) ionises in
water as: \( \boldsymbol{H} \boldsymbol{C}_{9} \boldsymbol{H}_{7} \boldsymbol{O}_{4}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \)
\( \boldsymbol{H}_{3} \boldsymbol{O}^{+}+\boldsymbol{C}_{9} \boldsymbol{H}_{7} \boldsymbol{O}_{4}^{-} ;\left(\boldsymbol{K}_{a}=\boldsymbol{2} . \boldsymbol{7} \boldsymbol{5} \times \mathbf{1} \boldsymbol{0}^{-\boldsymbol{9}}\right) \)
If two tablets of aspirin each of 0.32 g is dissolved in water to produce \( 250 \mathrm{mL} \) solution, calculate \( [\stackrel{\ominus}{\boldsymbol{O}} \boldsymbol{H}] \)
A \( \cdot 1.61 \times 10^{-9} M \)
В. \( 1.61 \times 10^{-7} \) М
c. \( 1.61 \times 10^{-3} M \)
D. \( 1.61 \times 10^{-5} M \)
Subject: Physics
The circumference of a circular track is
\( 400 \pi / m . \) If the optimum speed with which a vehicle can be driven along it is
to be \( 20 m / s \), the angle of banking of the road must be about
A \( \cdot \tan ^{-1}(0.02) \)
B. \( \tan ^{-1}(0.4) \)
c. \( \tan ^{-1}(0.8) \)
D. \( \tan ^{-1}(0.2) \)
Subject: Physics
The dimensions of self-inductance L are
\( \mathbf{A} \cdot\left[M L^{2} T^{-2} A^{-2}\right] \)
B. \( \left[M L^{2} T^{-1} A^{-2}\right] \)
\( \mathbf{c} \cdot\left[M L^{2} T^{-1} A^{-1}\right] \)
D. \( \left[M L^{-2} T^{-2} A^{-2}\right] \)
Subject: Physics
In an \( n \) -p-n transistor circuit, the collector current is \( 10 m A \). If \( 90 \% \) of the
electrons emitted reach the collector,
then
This question has multiple correct options
A. the emitter current, the will be \( 9 m A \)
B. the base current will be \( 1 m A \)
c. the emitter current will be \( 11.11 m A \)
D. The base current will be \( 1.11 \mathrm{mA} \)
Subject: Physics
The diagram shows a venturimeter through which water is flowing. The
speed of water \( X \) is \( 2 \mathrm{cms}^{-1} . \) The speed
of water at \( Y\left(\text { taking } g=10 \mathrm{ms}^{-2}\right) \) is
A \( .23 \mathrm{cms}^{-1} \)
B. \( 32 \mathrm{cms}^{-1} \)
c. \( 101 \mathrm{cms}^{-1} \)
D. \( 1024 \mathrm{cms}^{-1} \)
Subject: Physics
A string fastened at both ends has
successive resonances with
wavelengths of \( 0.54 m \) for the \( n^{t h} \)
harmonic and \( 0.48 m \) for the \( (n+1)^{t h} \)
harmonic. The wavelength of the fundamental frequency is \( 432 \times 10^{-x} m \)
What is the value of \( x ? \)
A . 1
B. 2
\( c .3 \)
D.
Subject: Physics
Assertion
The ferromagnetic substance do not obey Curie's law.
Reason
At Curie point a ferromagnetic substance start behaving as a paramagnetic substance.
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 radioactive sample has 5000 disintegration per minute initially and 1250 disintegration per minute after 5
seconds. Then the decay constant is
A \( .0 .4 \ln 2 \)
B. \( 0.2 \ln 2 \)
c. \( 0.1 \ln 2 \)
D. \( 0.8 \ln 2 \)
Subject: Chemistry
Soil has five components. The
proportions of different components are
A. Mineral Matter- \( 40 \% \), Organic Matter- \( 10 \% \), Soil Moisture \( -25 \% \), Soil Atmosphere \( -25 \% \), Soil OrganismVariable
B. Mineral Matter- \( 40 \% \), Organic Matter- \( 10 \% \), Soil Moisture \( -25 \% \), Soil Atmosphere \( -25 \% \), Soil Organism\( 10 \% \)
C. Mineral Matter- \( 40 \% \), Organic Matter- \( 10 \% \), Soil Moisture \( -35 \% \), Soil Atmosphere \( -25 \% \), Soil Organism\( 10 \% \)
D. Mineral Matter-30\%, Organic Matter-20\%, Soil Moisture \( -25 \% \), Soil Atmosphere \( -25 \% \), Soil Organism\( 10 \% \)
Subject: Maths
\( \int\left\{\frac{(\log x-1)}{1+(\log x)^{2}}\right\}^{2} d x \) is equals to?
A. \( \frac{\log x}{(\log x)^{2}+1}+C \)
в. \( \frac{x}{x^{2}+1}+C \)
c. \( \frac{x e^{x}}{1+x^{2}}+C \)
D. \( \frac{x}{(\log x)^{2}+1}+C \)
Subject: Maths
Evaluate: \( \int_{0}^{\pi / 2} \sin ^{3} x \cdot \cos ^{3} x d x \)
A \( \cdot \frac{1}{12} \)
в. \( \frac{\pi}{24} \)
c. \( \frac{\pi}{12} \)
D. \( \frac{1}{24} \)
Subject: Physics
Arrange the following physical quantities in the decreasing order of dimension of length.
I. Density
II. Pressure
III. Power
IV. Impulse
\( \mathbf{A} \cdot \) ।, ॥, ॥ा, ।V
B. ॥II, II, I, IV
c. \( 1 \mathrm{V}, \) । ॥ \( , \) ॥)
D. III, IV, II, I
Subject: Maths
Find the mode of given data.
\( \begin{array}{llll}\text { Marks } & \begin{array}{l}0- \\ 10\end{array} & \begin{array}{l}10- \\ 20\end{array} & \begin{array}{l}20- \\ 30\end{array}\end{array} \)
Frequency \( 20 \quad 24 \) In
Subject: Chemistry
Larger number of oxidation states are
exhibited by the actinoids than those by the lanthanoids, the main reason being:
A. more reactive nature of the actinoids than the lanthanoids
B. 4f orbitals more diffused than the 5 f orbitals
c. more energy difference between 5 5 and \( 6 d \) than between 4 f and 5d orbitals
D. lesser energy difference between 5 and \( 6 d \) than between \( 4 \mathrm{f} \) and \( 5 \mathrm{d} \) orbital
Subject: Physics
When a body is projected from a level
ground, the ratio of it's speed in the
vertical and horizontal direction is 4: 3
If the velocity of projection is \( u, \) the time
after which the ratio of the velocities
in the vertical and horizontal directions
is reversed is
A. \( \frac{7 u}{20 g} \)
B. \( \frac{35 u}{10 g} \)
c. \( \frac{9 u}{g} \)
D. \( \frac{10 u}{g} \)
Subject: Chemistry
In an atom, an electron is moving with a
speed of \( 600 m / s \) with an accuracy of \( 0.005 \% . \) Certainty with which the position of the electron can be located
is:
\( \left(h=6.6 \times 10^{-34} k g m^{2} s^{-1} \) mass of \right.
elecrtron \( \left.\boldsymbol{m}_{e}=\mathbf{9 . 1} \times \mathbf{1 0}^{-\mathbf{3 1}} \mathbf{k g}\right) \)
A \( .5 .10 \times 10^{-3} \mathrm{m} \)
В. \( 1.92 \times 10^{-3} \mathrm{m} \)
c. \( 3.84 \times 10^{-3} \mathrm{m} \)
D. \( 1.52 \times 10^{-3} \mathrm{m} \)
Subject: Physics
A shell of mass \( 0.020 k g \) is fired by a
gun of mass \( 100 k g . \) If the muzzle speed
of the shell is \( 80 m s^{-1} . \) What is the
recoil speed of the gun?
\( \mathbf{A} \cdot 1.6 \mathrm{cm} s^{-1} \)
B. \( 0.5 \mathrm{cms}^{-1} \)
\( \mathrm{c} \cdot 2 \mathrm{cms}^{-1} \)
D. \( 3 c m s^{-1} \)
Subject: Chemistry
Regarding the magnetic properties of
lanthanides and actinides the correct
statement is:
A. Lanthanides are weakly paramagnetic while actinides are strongly paramagnetic
B. Quenching of orbital contribution is greater in lanthanides than in actinides
C. \( 5 f \) electrons in actinides are too diffuse and are less
effectively shielded which results in considerable quenching of orbital contribution, and hence the magnetic moments of actinides are significantly less than theoretically predicted values
D. Because of diffused f electrons there is no quenching of orbital contribution towards magnetic moment