AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Mass of one atom of \( \boldsymbol{X} \) is \( \mathbf{6 . 6 6} \times \mathbf{1 0}^{-\mathbf{2 3}} \)
g. Hence, number of mole of atom \( X \) in
\( 40 \mathrm{kg} \) is :
\( \mathbf{A} \cdot 10^{3} \mathrm{mol} \)
B . \( 10^{-3} \) mol
c. \( \frac{40 \times 10^{3}}{6.66 \times 10^{-23}} \mathrm{mol} \)
D. \( \frac{40 \times 10^{3}}{6.022 \times 10^{23}} \mathrm{mol} \)
Subject: Maths
15 coupons are numbered \( 1,2,3, \dots, 15 \)
respectively. 7 coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is 9 is
\( ^{A} \cdot\left(\frac{9}{16}\right)^{6} \)
\( ^{\mathrm{B}}\left(\frac{8}{15}\right)^{7} \)
\( ^{c}\left(\frac{3}{5}\right)^{7} \)
D. \( \frac{9^{7}-8^{7}}{15^{7}} \)
Subject: Maths
The set values of \( x \) for which function
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x} \ln \boldsymbol{x}-\boldsymbol{x}+\mathbf{1} \)
\( A \cdot(1, \infty) \)
B. \( \left(\frac{1}{e}, \infty\right) \)
c. \( [e, \infty) \)
( \( ) \)
D \( \cdot(0,1) \cup(1, \infty) \)
Subject: Maths
If one of the diagonals of a square is along the line \( 4 x=2 y \) and one of its
vertices is \( (3,0), \) then its side through this vertex nearer to the origin is given by the equation.
A. \( y-3 x+9=0 \)
В. \( 3 y+x-3=0 \)
c. \( x-3 y-3=0 \)
D. \( 3 x+y-9=0 \)
Subject: Physics
A rectangular coil 100 turns and size \( 0.1 m \times 0.05 m \) is placed perpendicular
to a magnetic field of \( 0.1 \mathrm{T} \). If the field drops to \( 0.05 \mathrm{T} \) in 0.05 second, the magnitude of the e.m.f. induced in the coil is
\( A \cdot 2 \)
B. 3
c. 0.5
D.
Subject: Physics
A particle of mass \( 0.3 \mathrm{kg} \) is subjected to a force \( \boldsymbol{F}=-\boldsymbol{k} \boldsymbol{x} \) with \( \boldsymbol{k}=\mathbf{1 5} \boldsymbol{N} / \boldsymbol{m} \)
What will be its initial acceleration if it
is released from a point \( 20 \mathrm{cm} \) away
from the origin?
Subject: Maths
Construct \( \Delta L M N \) in which \( \angle N= \)
\( \mathbf{7 3}^{\circ}, \boldsymbol{L} \boldsymbol{N}=\mathbf{5 . 7} \mathbf{c m}, \boldsymbol{M} \mathbf{N}=\mathbf{6 . 8 c m} \)
Subject: Chemistry
When one litre of a saturated solution of
\( \boldsymbol{P b C l}_{2} \) (molecular weight \( =\mathbf{2 7 8} \) g/mol)
is evaporated, the residue is found to
weigh 2.78 g. If \( K_{s p} \) of \( P b C l_{2} \) is
represented as \( y \times 10^{-6}, \) then find the
value of \( \boldsymbol{y} \)
\( A \cdot 4 \)
B. 5
\( c \cdot 6 \)
D.
Subject: Chemistry
Which of the following complex shows
ionization isomerism :
\( ^{\mathbf{A}} \cdot\left[C r\left(N H_{3}\right)_{6}\right] C l_{3} \)
в. \( \left[C r(e n)_{2}\right] C l_{2} \)
\( c \)
\( \left[\mathrm{Cr}(e n)_{3}\right] \mathrm{Cl}_{3} \)
D. \( \left[\operatorname{CoBr}\left(N H_{3}\right)_{5}\right] S O_{4} \)
Subject: Chemistry
0.1 normal solution of \( N a C l \) is found to
be isotonic with \( 1.1 \% \) solution of Urea.
Calculate the apparent degree of
ionisation of \( N a C l \)
\( \mathbf{A} \cdot 0.083 \)
B. 8.3
c. 0.83
D. 0.42
Subject: Physics
The resistance of a wire of \( 100 \mathrm{cm} \)
length is \( 10 \Omega . \) Now, it is cut into 10 equal parts and all of them are twisted to form a single bundle. Its resistance is:
A . \( 1 \Omega \)
B. \( 0.5 \Omega \)
\( c .5 \Omega \)
D. \( 0.1 \Omega \)
Subject: Chemistry
At what partial pressure, oxygen will have a solubility of \( 0.006 g L^{-1} \) in water
at \( 293 K ? \) Henry's law constant \( \left(K_{H}\right) \) of
\( O_{2} \) in water at \( 303 K \) is \( 46.82 k \) bar.
(Assume the density of the solution to be the same as that of water).
Subject: Chemistry
The van der Waal's parameters for
\( \operatorname{gases} A, B, C \) and \( D \) are:
\begin{tabular}{lll} 
Gas & \( a \) \( \left(l i t r e^{2} a t m / m o l^{2}\right) \) & \( b(l i t r e / m o l \) ) \\
\( A \) & 4.0 & 0.027 \\
\( B \) & 8.0 & 0.030 \\
\( C \) & 6.0 & 0.032 \\
\( D \) & 12.0 & 0.027 \\
\hline
\end{tabular} Which one of these gases has the
highest critical temperature?
\( \mathbf{A} \cdot A \)
\( \mathbf{B} \cdot B \)
\( c \cdot C \)
D. \( D \)
Subject: Physics
When a sphere of radius \( 2 \mathrm{cm} \) is
suspended at the end of a wire,
elongation is 'e'. When the same wire is loaded with a sphere of radius \( 3 \mathrm{cm} \) and made of the same material,
the elongation would be :
A \( \cdot \frac{8}{27} e \)
в. \( \frac{27}{8} e \)
c. \( \frac{4}{9} e \)
D. \( \frac{9}{4} \)
Subject: Physics
A body of mass 5 kg falls from a height of \( 10 m \) to 4 m. Calculate the loss in
potential energy of the body. (Take \( g= \) \( \left.10 m s^{-2}\right) \)
A . \( 0 . J \)
в. \( 300000 J \)
c. \( 3 J \)
D. \( 300 J \)
Subject: Physics
A uniform chain has a mass \( m \) and
Iength \( l \). It is held on a frictionless table with one-sixth of its length hanging over the edge. The work done injust puling the hanging part back on the table is:
A \( \cdot m g \frac{l}{72} \)
в. \( \frac{m g l}{36} \)
c. \( \frac{m g l}{12} \)
D. \( \frac{m g l}{6} \)
Subject: Chemistry
Charge distribution in iodine
monochloride is best represented as:
\( \mathbf{A} \cdot I^{+} C l \)
B . \( I^{\delta+}-C l^{\delta-} \)
c. \( I^{-} C l^{+} \)
D. \( I^{\delta-}-C l^{\delta+} \)
Subject: Maths
A random variable ' \( X \) ' has the following probability distribution:
\[
\begin{array}{lcccc}
x=x & 0 & 1 & 2 & 3 \\
P(X=x) & 0 & k & 2 k & 2 k
\end{array}
\]
Find:
(i) \( k \)
(ii) The Mean and
(iii) \( \boldsymbol{P}(\boldsymbol{0}<\boldsymbol{X}<\mathbf{5}) \)
Subject: Maths
An ellipse having foci at (3,1) and
(1,1) passes through the point (1,3)
Its eccentricity is:
A \( \cdot \sqrt{2}-1 \)
B. \( \sqrt{3}-1 \)
c. \( \frac{1}{2}(\sqrt{2}-1) \)
D. \( \frac{1}{2}(\sqrt{3}-1) \)
Subject: Physics
The mass of planet Jupiter is \( 1.9 \times 10^{27} \)
kg and that of the Sun is \( 1.99 \times 10^{30} \mathrm{kg} \)
The mean distance of Jupiter from the
Sun is \( 7.8 \times 10^{11} \) m. Calculate the
gravitational force which Sun exerts on Jupiter. Assuming that Jupiter moves in circular orbit around the Sun, also
calculate the speed of Jupiter. \( \boldsymbol{G}= \)
\( \mathbf{6 . 6 7} \times \mathbf{1 0}^{-\mathbf{1 1}} \mathbf{N m}^{\mathbf{2}} \mathbf{k g}^{-\mathbf{2}} \)
\( \mathbf{A} \cdot=5 \times 10^{23} \mathrm{N} \)
B. \( =4.15 \times 10^{23} \mathrm{N} \)
\( \mathbf{C} .=15 \times 10^{23} \mathbf{N} \)
D. \( =1 \times 10^{23} \mathrm{N} \)
Subject: Chemistry
Assertion
Critical temperature is the temperature at which the intermolecular attraction
in gas molecules vanishes.
Reason
At critical point, the density of substance in gaseous and liquid states becomes same.
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: Physics
Two identical loops \( A \) and \( B \) lying in the
same plane carry equal currents. Four points \( P, Q, R \) and \( S \) are in the plane of
the loops. Choose the correct statement
A. The field at P must be out of the plane of the paper
B. The field at \( Q \) must be into the plane of the paper
c. the field at \( R \) must be out of the plane of the paper
D. The field at \( s \) must be out of the plane of the paper
Subject: Maths
Evaluate the integral \( \int_{0}^{\frac{\pi}{2}} \frac{\sin ^{\frac{3}{2} x} d x}{\sin ^{\frac{3}{2}} x+\cos ^{\frac{3}{2}} x} \)
A \( \cdot \frac{\pi}{2} \)
в. \( \frac{\pi}{4} \)
c. \( \pi \)
D.
Subject: Chemistry
Assertion
\( A l_{2} O_{3} \) is converted into \( A l \) by reduction
with carbon at high temp
Reason
Carbon has greater affinity for oxygen than aluminium
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 and Reason is correct
Subject: Physics
Assertion
Microwaves are better carrier of signals
than the optical waves.
Reason
Microwaves move faster than optical
waves.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Chemistry
Assertion
Aqueous solution of \( C H_{3} C O O N H_{4} \) is
exactly neutral. \( \left(\boldsymbol{K}_{\boldsymbol{a}}=\boldsymbol{K}_{\boldsymbol{b}}\right) \)
Reason
\( C H_{3} C O O N H_{4} \) is a salt of weak acid
and strong base.
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: Maths
What is the degree of polynomial \( \boldsymbol{P} \)
defined by :
\( \boldsymbol{P}(\boldsymbol{x})=-\mathbf{5}(\boldsymbol{x}-\mathbf{2})\left(\boldsymbol{x}^{3}+\mathbf{5}\right)+\boldsymbol{x}^{5} ? \)
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5
Subject: Chemistry
Consider the reaction at \( 300 K \)
\( \boldsymbol{C}_{6} \boldsymbol{H}_{6}(\ell)+\frac{\mathbf{1 5}}{\mathbf{2}} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \mathbf{6} \boldsymbol{C O}_{2}(\boldsymbol{g})+ \)
\( \mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O}(\ell) ; \boldsymbol{\Delta} \boldsymbol{H}=-\mathbf{3 2 7 1} \boldsymbol{k} \boldsymbol{J} \)
What is \( \Delta U \) for the combustion of 1.5
mole of benzene at \( 27^{\circ} \mathrm{C} \) ?
A. \( -3267.25 k J \)
\( J \)
в. \( -4900.88 k J \)
c. \( -4906.5 k J \)
D. \( -327.754 k J \)
Subject: Physics
The dipolemoment of the given system is:
A. \( \sqrt{3} q l \) along perpendicular bisector of \( q-q \) line
B. \( 2 q l \) along perpendicular bisector of \( q-q \) line
C \( \cdot q l \sqrt{2} \) along perpendicular bisector of \( q-q \) line
D. 0
Subject: Physics
The horizontal component of the flux density of earth's magnetic field is
\( 1.7 \times 10^{-5} T . \) The value of the horizontal
component of the intensity of earth's magnetic field will be:
A \( \cdot 24.5 A m^{-1} \)
B. \( 13.5 A m^{-1} \)
c. \( 1.53 A m^{-1} \)
D. \( 0.35 A m^{-1} \)
Subject: Physics
The top of an insulated cylindrical container is covered by a disc having emissivity \( 0.6, \) conductivity
\( 0.167 W K^{-1} m^{-1} \) and thickness \( 1 \mathrm{cm} \)
The temperature is maintained by circulating oil.
(a) Find the radiation loss to the
surroundings in \( J m^{-2} s^{-1} \) if
temperature of the upper surface of the
disc is \( 127^{\circ} \mathrm{C} \) and temperature of
surroundings is \( 27^{\circ} \mathrm{C} \)
(b) Also find the temperature of the circulating oil. Neglect the heat loss due
to convection.
Subject: Maths
If \( \vec{a}=2 \hat{i}+2 \hat{j} \) and \( \vec{b}=3 \hat{i}+4 \hat{j} \) then \( \vec{a}+ \)
\( \vec{b} \) is
\( \mathbf{A} \cdot \hat{i}+2 \hat{j} \)
B. \( 5 \hat{i}+6 \hat{j} \)
c. \( 5 \hat{i}+2 \hat{j} \)
D. \( \hat{i}+6 \hat{j} \)
Subject: Chemistry
Statement- 1: Alkanes participate in
substitution reactions.

Statement- 2: Alkanes are saturated
hydrocarbons.
A. Both statement- 1 and statement-2 are correct statement-2 is a correct explanation of statement-1.
B. Both statement-1 and statement-2 are correct statement-2 is not a correct explanation of statement-
1.
C. Statement-1 is correct, statement-2 is incorrect.
D. Statement-1 is incorrect, statement-2 is correct.
Subject: Physics
In a certain hypothetical radioactive decay process, species A decays into species B and species B decays into species \( C \) according to the reactions \( \boldsymbol{A} \rightarrow 2 \boldsymbol{B}+ \) particles \( + \)energy
\( \boldsymbol{B} \rightarrow \mathbf{2} \boldsymbol{C}+\boldsymbol{\text {particles}}+ \)energy
The decay constant for species A is \( \lambda_{1}=1 s^{-1} \) and that for species B is
\( \lambda_{2}=100 s^{-1} . \) Initially, \( 10^{4} \) moles of
species of A were present while there was none of \( \mathrm{B} \) and \( \mathrm{C} \). It was found that
while there was none of \( B \) and \( C \). It was
found that species B reaches its
maximum number at a time \( t_{0}= \) \( 2 \ln (10) s . \) Calculate the value of
maximum number of moles of B
Subject: Physics
A 27 mw laser beam has a cross-
sectional area of \( 10 \mathrm{mm}^{2} \). The
magnitude of the maximum electric field in this electromagnetic wave is given by?[Given permittivity of space \( €_{0} \)
\( =9 \times 10^{-12} \mathrm{Sl} \) units, Speed of light \( c= \)
\( \left.3 \times 10^{8} m / s\right] \)
A. \( 1 \mathrm{kV} / \mathrm{m} \)
B. 2 kv/m
c. \( 1.4 \mathrm{kV} / \mathrm{m} \)
D. \( 0.7 \mathrm{kV} / \mathrm{m} \)
Subject: Maths
\( f\left[\begin{array}{cc}\cos ^{2} \alpha & \cos \alpha \sin \alpha \\ \cos \alpha \sin \alpha & \sin ^{2} \alpha\end{array}\right] \) and \( B= \)
\( \left[\begin{array}{cc}\cos ^{2} \beta & \cos \beta \sin \beta \\ \cos \beta \sin \beta & \sin ^{2} \beta\end{array}\right] \) are two
matrices such that the product \( A B \) is
null matirx, then \( \alpha-\beta \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. Multiple of \( \pi \)
c. An odd number of \( \frac{\pi}{2} \)
D. None of the above
Subject: Physics
Three equal masses \( 3 k g \) are connected
by massless string of cross-sectional
area \( 0.005 c m^{2} \) and Young's modulus
\( 2 \times 10^{11} N m^{2} . \) In the absence of friction
the longitudinal strain in the wire:
\( \mathbf{A} \cdot A \) is \( 10^{-4} \)
B. \( B \) is \( 2 \times 10^{-4} \)
\( c . \) Both a and \( b \)
D. None of these
Subject: Maths
Construct a \( 2 \times 3 \) matrix \( A=\left[a_{i j}\right] \)
whose elements are given by \( \boldsymbol{a}_{\boldsymbol{i} j}= \)
\( \mathbf{2}(\boldsymbol{i}-\boldsymbol{j}) \)
В. \( \left[\begin{array}{ccc}0 & -2 & 4 \\ 2 & 0 & -2\end{array}\right] \)
\( \begin{array}{lll}\text { c. } & {\left[\begin{array}{ccc}0 & -2 & -4 \\ 2 & 0 & 2\end{array}\right]} \\ & \text { I }\end{array} \)
D. \( \left[\begin{array}{ccc}0 & -2 & 4 \\ 2 & 0 & 2\end{array}\right] \)
Subject: Maths
If \( \boldsymbol{A}=\left\{\boldsymbol{x}: \boldsymbol{x}^{2}-\boldsymbol{3} \boldsymbol{x}+\boldsymbol{2}=\boldsymbol{0}\right\} \) and \( \boldsymbol{B}= \)
\( \left\{x: x^{2}+4 x-5=0\right\} \) then the value of
\( A-B \) is
\( \mathbf{A} \cdot\{1,2\} \)
B . \{2\}
\( c \cdot\{1\} \)
D \( \cdot\{5,2\} \)
Subject: Physics
Which of the following is an \( (n . p) \) reaction?
A \( \cdot \frac{13}{5} C+\frac{1}{1} C \longrightarrow_{6}^{14} C \)
B \( \cdot \frac{4}{7} N+\frac{1}{1} H \rightarrow_{8}^{15} O \)
C・ \( 133 l+\frac{1}{0} n \rightarrow 27 M g+1 \)
\( 13 A l+0 \)
D \( \cdot \frac{235}{92} U+_{1}^{0} N \longrightarrow_{54}^{140} X e+_{38}^{94} S r+_{30}^{1} n \)
Subject: Chemistry
The energy barrier to free rotation about carbon carbon bond of ethane is about:
A. \( 30 k J \) mol \( ^{-1} \)
B. 3 kJ mol \( ^{-1} \)
c. 3 kcal mol \( ^{-1} \)
D. \( 40 \mathrm{kJ} \mathrm{mol}^{-1} \)
Subject: Maths
\( \int \frac{4 \sec ^{2} x \tan x}{\sec ^{2} x+\tan ^{2} x} d x= \)
A \( \cdot 2 \log \left(\sec ^{2} x+\tan ^{2} x\right)+c \)
B \( \cdot \log \left(2 x+\tan ^{2} x\right)+c \)
c. \( 2 \tan ^{2} x+c \)
\( \mathbf{D} \cdot \log \left(\sec ^{2} x+\tan ^{2} x\right)+c \)
Subject: Chemistry
melting points and boiling points due to
relatively weak intermolecular
attractions that hold the molecules in
their solid form.
\( t^{\circ}(C) \) Molecular Solid \( \quad \) Boiling Point
\( H_{2} T e \) 0
\( H_{2} S e \) -50
\( H_{2} S \) -75
\( H_{2} O \) 100
Which of the following reasons explain
why \( H_{2} O \) does not appear to follow this
fact?
\( \mathbf{A} \cdot H_{2} O \) is relatively small compared to the other molecules
B. \( H_{2} O \) is not a molecular solid
C. \( H_{2} O \) have hydrogen bonding
D. \( H_{2} O \) is ionicly bonded while the others are covalently bonded
Subject: Maths
The straight line \( A B \) is divided at \( C \) so that \( A C=3 C B . \) Circles are described
on \( A C \) and \( C B \) as diameters and a
common tangent meets AB produced at
D. Then \( B D \) equals.
A. the diameter of the smaller circle
B. the radius of the smaller circle
c. the radius of the larger circle
D. \( \overline{C B} \sqrt{3} \)
E. the difference of the two radi
Subject: Physics
A mass of ideal gas at pressure \( \boldsymbol{P} \) is expanded isothermally to four times the
original volume and then slowly compressed adiabatically to its original
volume. Assuming \( \gamma \) to be \( 1.5, \) the new
pressure of gas is
A \( .2 P \)
в. \( P \)
c. \( 4 P \)
D. \( \frac{P}{2} \)
Subject: Chemistry
The vapour pressure of two liquids \( \boldsymbol{P} \)
and \( Q \) are 80 torr and 60 torr
respectively. The total vapour pressure obtained by mixing 3 mole of \( \mathrm{P} \) and 2 mole of \( Q \) would be:
A. 68 torr
B. 20 torr
c. 140 tor
D. 72 torr
Subject: Physics
A force of \( 10 \mathrm{N} \) acts on a body for 3
microsecond \( (\mu \mathrm{s}) . \) If mass of the body is \( 6 \mathrm{g} \), calculate the change of velocity.
\( \mathbf{A} \cdot 26 \times 10^{-2} m s^{-1} \)
B . \( 16 \times 10^{-3} \mathrm{m} \mathrm{s}^{-1} \)
C \( .5 \times 10^{-3} \mathrm{m} \mathrm{s}^{-1} \)
D. \( 36 \times 10^{-2} \mathrm{m} \mathrm{s}^{-1} \)
Subject: Biology
Identify the correct arrangement of
tissues in an old dicot stem
A. Cork, Cork cambium, Oldest phloem, Bast, Vascular cambium, Sec. xylem
B. Secondary xylem, Vascular cambium, Bast, Oldest phloem, Cork cambium, Cork
C. Cork, Cork cambium, Oldest pholem, Bast, Vascular cambium, Heart wood
D. Heart wood, Vascular cambium, Youngest phloem, Oldest phloem, Sec.cotex, Cork cambium, Cork
Subject: Chemistry
Assertion
Alkali metals are strong reducing agents, while halogens [non-metals], are strong oxidising agents.
Reason
Metals have 1,2 or 3 valence electrons so
they always ionize by losing electrons while non metals have 4,5,6 or 7 valence electrons so they ionize by gaining electrons.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
The volume of the \( y= \) tethradron formed by the coterminous edges \( \bar{a}, \bar{b}, \bar{c} \) is 3 Then the volume of the parallelepiped
formed by the coterminous edges \( \overline{\boldsymbol{a}}+ \) \( \bar{b}, \bar{b}+\bar{c}, \bar{c}+\bar{a} \) is
\( \mathbf{A} \cdot \mathbf{6} \)
B. 18
\( c .36 \)
D.
Subject: Physics
characteristic for a semiconductor
device. Which of the following
statement is correct?
A. It is V-I characteristic for solar cell where, point represents open circuit voltage and point B short
circuit current
B. It is for a solar cell and points A and B represent open circuit voltage and current, respectively
C. It is for a photodiode and points \( A \) and \( B \) represent open circuit voltage and current respectively
D. It is for a LED and points A and B represent open circuit voltage and short circuit current, respectively
Subject: Physics
Non-relativistic protons move
reactilinearly in the region of space where there are uniform mutually perpendicular electric and magnetic fields with E and B. The trajectory of the
protons lie in the plane \( X \) -Y as shown in
fig. and forms an angle \( \phi \phi \) with \( X \) -axis. If the pitch of the helical trajectory
along which the protons will move after
the electric field is switched off is
Pitch \( =\frac{\boldsymbol{x} \boldsymbol{\pi} \boldsymbol{m} \boldsymbol{E}}{\boldsymbol{q} \boldsymbol{B}^{2}} \boldsymbol{t a n} \boldsymbol{\phi} \). Find \( \boldsymbol{x} \)
Subject: Chemistry
A recent investigation of the
complexation of \( \boldsymbol{S C N}^{-} \) with \( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+} \)
represented by constant \( \boldsymbol{K}_{1}, \boldsymbol{K}_{2} \) and \( \boldsymbol{K}_{3} \)
as 130,16 and 1.0 respectively. What is the overall formation constant of
\( \boldsymbol{F} \boldsymbol{e}(\boldsymbol{S} \boldsymbol{C} \boldsymbol{N})_{3} \) from its component ions
and what is the dissociation constant of
\( F e(S C N)_{3} \) into its simplest ions on the basis of these data?
Subject: Physics
The length of the tube of a microscope is \( 10 \mathrm{cm} . \) The lengths of the objective and eye lenses are \( 0.5 \mathrm{cm} \) and \( 1 \mathrm{cm} \)
respectively. The magnifying power of the microscope when the images at far point is about
A. 5
B. 23
\( c \cdot 166 \)
D. 500
Subject: Chemistry
Brine is electrolysed by using inert
electrodes. The reaction at anode is
\( \mathbf{A} \cdot C l_{(a q)}^{-} \rightarrow \frac{1}{2} C l_{2(g)}+e^{-} ; E_{c e l l}^{0}=1.36 V \)
B \( \cdot 2 H_{2} O_{(l)} \rightarrow O_{2(g)}+4 H^{+}+4 e^{-} ; E_{c e l l}^{0}=1.23 V \)
\( \mathbf{C} \cdot N a_{(a q)}^{+}+e^{-} \rightarrow N a_{(s)} ; E_{c e l l}^{0}=2.71 V \)
\( \mathbf{D} \cdot H_{(a q)}^{+}+e^{-} \rightarrow \frac{1}{2} H_{2(g)} ; E_{c e l l}^{0}=0.00 V \)
Subject: Physics
A regular hexagon of side \( 10 \mathrm{cm} \) has a charge \( 5 \mu C \) at each of its vertices.
Calculate the potential at the centre of the hexagon.
\( \mathbf{A} \cdot 5.8 \times 10^{6} V \)
В. \( 3.2 \times 10^{6} V \)
c. \( 9.3 \times 10^{6} V \)
D. \( 2.7 \times 10^{6} V \)
Subject: Physics
Two rail tracks are \( 1 m \) apart and insulated from each other and
insulated from ground. A milli-voltmeter is connected across the rail-tracks.
When a train travelling at \( 180 \mathrm{km} / \mathrm{h} \)
passes through what will be the reading in milli-voltmeter? Given : horizontal
component of earth's field \( \sqrt{3} \times 10^{-4} T \)
and dip at the place \( 60^{\circ} \)
A. \( 1.5 \mathrm{mV} \)
B. \( 15 \mathrm{mV} \)
c. \( \frac{15}{\sqrt{3}} m V \)
D. \( \frac{1.5}{\sqrt{3}} m V \)
Subject: Chemistry
Assertion
Decomposition of hydrogen peroxide is an example of disproportionation
reaction.
Reason
In a disproportionation reaction, an
element in one oxidation state is
simultaneously oxidised and reduced.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Chemistry
For a given reaction \( \boldsymbol{A} \rightarrow \) Products, rate
is \( 1 \times 10^{-4} M s^{-1} \) when \( [A]=0.01 \mathrm{M} \)
and rate is \( 1.41 \times 10^{-4} M s^{-1} \) when
\( [\boldsymbol{A}]=\mathbf{0 . 0 2} \) M. Hence, rate law is:
A \( \cdot-\frac{d[A]}{d t}=k[A]^{2} \)
B. \( -\frac{d[A]}{d t}=k[A] \)
\( ^{\mathrm{c}}-\frac{d[A]}{d t}=\frac{k}{4}[A] \)
D. \( -\frac{d[A]}{d t}=k[A]^{1 / 2} \)
Subject: Physics
The electron beam in a television
picture tube travels a distance lin evacuated space of the tube. If the speed of the electrons is \( v \) and the beam
current is i, then the number of
electrons in the beam at any instant will
be
A. \( \frac{i l}{e v} \)
в. \( \frac{i}{l e v} \)
c. \( \frac{v}{i l e} \)
D. \( \frac{e}{i l v} \)
Subject: Maths
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be given by \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{5} \boldsymbol{x}, \) if
\( \boldsymbol{x} \in \boldsymbol{Q} \) and \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{6} \) if \( \boldsymbol{x} \in \boldsymbol{R}-\boldsymbol{Q} \)
then
A. f is continuous at \( x=1 \) and \( x=2 \)
B. fis not continuous at \( x=1 \) and \( x=2 \)
c. \( f \) is continuous at \( x=1 \) but not at \( x=2 \)
D. fis continuous at \( x=2 \) but not at \( x=1 \)