AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A gas bubble of \( 2 \mathrm{cm} \) diameter rises
through a liquid of density \( 1.75 \mathrm{gm} \mathrm{cm}^{-3} \) with a fixed speed of \( 0.35 \mathrm{cm} s^{-1} \)
Neglect the density of the gas. The coefficient of viscosity of the liquid is:
A. 870 poise
B. 1120 poise
c. 982 poise
D. 1089 poise
Subject: Chemistry
Uncertainty in the position of an electron \( \left(\text {mass}=\mathbf{9 . 1} \times \mathbf{1 0}^{-\mathbf{3 1}} \mathbf{k g}\right) \)
moving with a velocity \( 300 m s^{-1} \)
accurate upon \( 0.001 \% \) will be:
\( \left[\boldsymbol{h}=\mathbf{6 . 6 3} \times \mathbf{1 0}^{-\mathbf{3 4}} \boldsymbol{J}-\boldsymbol{s}\right] \)
A \( \cdot 19.2 \times 10^{-2} \mathrm{m} \)
в. \( 5.76 \times 10^{-2} \) т
c. \( 1.92 \times 10^{-2} \mathrm{m} \)
D. \( 3.84 \times 10^{-2} \mathrm{m} \)
Subject: Physics
A plane polarized light is incident normally on the tourmaline plate. Its \( \overrightarrow{\boldsymbol{E}} \)
vectors, make an angle of \( 60^{\circ} \) with the
optic axis of the plate. Find the \( \% \) difference between initial and final maximum values of \( \overrightarrow{\boldsymbol{E}} \) vectors.
Subject: Physics
Consider the following statements A and B identify the correct statement from the following.
A) The width of the depletion layer in a
p-njjunction diode increases in forward bias.
B) In an intrinsic semiconductor, the
Fermi energy level is exactly in the middle of the forbidden gap.
A. A is true and B is false.
B. Both A and B are false
c. A is false and B is true
D. Both A and B are true
Subject: Physics
Force vs Elongation graph of a wire is shown in the figure for two different
temperatures \( \boldsymbol{T}_{1} \& \boldsymbol{T}_{2}, \) then
A \( \cdot T_{1}=T_{2} \)
В \( \cdot T_{1}<T_{2} \)
\( c \cdot T_{1}>T_{2} \)
D. cannot be predicted
Subject: Physics
Write the following steps of an experiment in a sequential order to show that a current carrying conductor sets up a magnetic field around it.
(a) Pass the insulted copper wire through the small hole at the centre of the carboard and perpendicular to it.
(b) Paste a white paper on a rectangular cardboard and make a small hole at its
centre.
(c) Connect this wire to a battery, a
switch and a variable resistor in series.
(d) Clamp this cardboard to a stand in a horizontal position and sprinkle some iron filings over it.
(e) Now, when the circuit is closed, the iron filings on the carboard form concentric circles around the wire.
A. bdace
B. baced
c. adbec
\( \mathbf{D} \cdot e d a b c \)
Subject: Maths
f \( A=1,3,5, \dots \dots \dots 17 \) and \( B= \)
\( 2,4,6, \dots \dots 18 \) and \( N( \) the set of natural
numbers) is the universal set, then
show that \( \boldsymbol{A}^{\prime} \cup\left((\boldsymbol{A} \cup \boldsymbol{B}) \cap \boldsymbol{B}^{\prime}\right)=\boldsymbol{N} \)
Subject: Chemistry
The oxide of element \( X \) forms a solution
with \( p H 4 \)

The oxide of element \( Y \) forms a solution
that turns Universal Indicator blue.
Which row correctly classifies elements
\( X \) and \( Y ? \)
A. Element \( X \) - metal, Element \( Y \) - meta
B. Element \( X \) - metal, Element \( Y \) - non-metal
c. Element \( X \) - non-metal, Element \( Y \) - metal
D. Element \( X \) - non-metal, Element \( Y \) - non-metal
Subject: Chemistry
Which method of purification is represented by the following equation? \( \boldsymbol{T} \boldsymbol{i}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{I}_{2}(\boldsymbol{g}) \stackrel{\boldsymbol{5} \mathbf{2} 3 \boldsymbol{k}}{\longrightarrow} \boldsymbol{T} \boldsymbol{i} \boldsymbol{l}_{4}(\boldsymbol{g}) \frac{\mathbf{1 7 0 0} \boldsymbol{k}}{\boldsymbol{\}} \)
\( \boldsymbol{T} \boldsymbol{i}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{I}_{2}(\boldsymbol{g}) \)
A. zone refining
B. Cupellation
c. Poling
D. Van Arkel
Subject: Chemistry
What is the \( K_{b} \) of a weak base
that produces an \( O H^{-} \) per molecule if a 0.05 M solution is \( 2.5 \% \) ionized?
\( \mathbf{A} \cdot 7.8 \times 10^{-8} \)
B . \( 1.6 \times 10^{-6} \)
c. \( 3.125 \times 10^{-5} \)
D. \( 1.2 \times 10^{-3} \)
Subject: Physics
Water rises in a capillary upto a height
h. If now this capillary is tilted by an
angle of \( 45^{\circ}, \) then the length of the
water column in the capillary becomes
\( A \cdot 2 h \)
в. \( \frac{h}{2} \)
c. \( \frac{h}{\sqrt{2}} \)
D. \( h \sqrt{2} \)
Subject: Maths
The equation of the plane passing through the straight line \( \frac{x-1}{2}= \) \( \frac{\boldsymbol{y}+\mathbf{1}}{\mathbf{- 1}}=\frac{\boldsymbol{z}-\mathbf{3}}{\mathbf{4}} \) and perpendicular to
plane \( \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\boldsymbol{z}=\mathbf{1 2} \) is:
A. \( 9 x+2 y-5 z+8=0 \)
в. \( 9 x+2 y-5 z+10=0 \)
c. \( 9 x-2 y+5 z+6=0 \)
D. \( 9 x-2 y-5 z+4=0 \)
Subject: Maths
There is \( 25 \% \) chance that it rains on any
particular day. What is the probability that there is at least one rainy day within a period of 7 days?
\( ^{A} \cdot_{1-}\left(\frac{1}{4}\right)^{7} \)
B. \( \left(\frac{1}{4}\right)^{7} \)
\( ^{c}\left(\frac{3}{4}\right)^{7} \)
D. \( _{1-}\left(\frac{3}{4}\right)^{7} \)
Subject: Maths
In the following figure, \( A E \perp B C, D \) is the
mid point of BC, then \( x \) is equal to
A \( \cdot \frac{1}{a}\left[b^{2}-d^{2}-\frac{a^{2}}{4}\right] \)
B. \( \frac{h+d}{3} \)
c. \( \frac{c+d-h}{2} \)
\( \frac{a^{2}+b^{2}+d^{2}-c^{2}}{4} \)
Subject: Chemistry
Which of the following sequence of
explanation is appropriate for explaining the reason for the periodicity of reducing property in a period or
group?
(a) Tendency to undergo oxidation decreases in a period and increases in a
group.
(b) In a period ionization energy increases and in a group it decreases.
(c) In a period the atomic size
decreases and in a group it increases.
(d) The elements present in the left side of the periodic table have strong reducing property.
\( A \cdot \cos a \)
B. c d b a
\( c \cdot d c a b \)
D. \( d \) b a c
Subject: Chemistry
An unknown alkyl halide [X] reacts with alcoholic KOH and produces a
hydrocarbon \( \left(C_{4} H_{8}\right) \) as the major product. Ozonolysis of this hydrocarbon affords one mole of propanaldehyde and one mole of formaldehyde. Suggest
which organic compound among the following has the correct structure of the above alkyl halide \( [\mathbf{X}] ? \)
A \( \cdot C H_{3} C H_{2} C H_{2} C H_{2} B r \)
в. \( C H_{3} C H(B r) C H_{2} C H_{3} \)
c. \( C H_{3} C H(B r) C H(B r) C H_{3} \)
D. \( B r\left(C H_{2}\right)_{4} B r \)
Subject: Chemistry
A violet colour compound is formed in
detection of \( S \) in a compound:
A \( \cdot \operatorname{Na}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{5} \mathrm{NOS}\right] \)
В \( \cdot \operatorname{Na}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{5} \mathrm{NOS}\right] \)
c. \( \operatorname{Na}_{2}\left[\mathrm{Fe}(\mathrm{CN})_{5} \mathrm{NOS}\right] \)
D. \( \operatorname{Na}\left[\text {Fe}(\text {CN})_{5} \) NOS\right.
Subject: Physics
Two skaters have weight in the ratio 4:
5 and are \( 9 \mathrm{m} \) apart, on a smooth
frictionless surface,They pull on a rope stretched between them. The ratio of the
distance covered by them when they meet each other will be
A .5: 4
в. 4: 5
c. 25: 16
D. 16: 25
Subject: Chemistry
During conductometric titration of \( 0.1 \mathrm{M} \)
HCl with \( 1.0 \mathrm{M} \mathrm{KOH} \), which of the following
will be observed?
A. Resistance of the solution decreases upto equivalence point and then increases
B. Resistance of the solution increases upto equivalence point and then decreases
C. Conductance increases upto equivalence point and then decreases
D. Conductance decreases upto equivalence point and then becomes almost constant
Subject: Chemistry
Arrange the following compounds in increasing order of boiling points:
\( \mathrm{I}: C H_{3} C l \quad \|: C H_{2} C l_{2} \)
\( \left\|: \boldsymbol{C} \boldsymbol{H} \boldsymbol{C l}_{3} \quad \quad\right\| \boldsymbol{V}: \boldsymbol{C} \boldsymbol{l}_{4} \)
A. \( I<I I<I I I<I V \)
в. \( I V<I I I<I I<I \)
c. \( I I<I V<I<I I I \)
D. \( I V<I I<I<I I I \)
Subject: Physics
A conductor (shown in the figure) carrying constant current I is kept in
the \( x \) -y plane in a uniform magnetic field \( \vec{B} \). If \( F \) is the magnitude of the total
magnetic force acting on the conductor, then the correct statement(s) is (are)
This question has multiple correct options
\( \mathbf{A} \cdot \) if \( \vec{B} \) is along \( \hat{z}, F \propto(L+R) \)
B. if \( \vec{B} \) is along \( \widehat{x}, F=0 \)
C. if \( \vec{B} \) is along \( \hat{y}, F \propto(L+R) \)
D. if \( \vec{B} \) is along \( \hat{z}, F=0 \)
Subject: Chemistry
Which of the following pairs of ions are
isoelectronic and isostructural?
A \( \cdot C l O_{3}^{-}, S O_{3}^{2} \)
в. \( \mathrm{ClO}_{3}-, \mathrm{CO}_{3}^{2} \)
c. \( C O_{3}^{2-}, N O_{3} \)
D. \( S O_{3}^{2-}, N O_{3} \)
Subject: Physics
A charge is projected with a velocity of \( 10^{5} m / s . \) In a perpendicular magnetic field. Find the magnetic of a transverse electric field if if moves undeflected
\( \left(B=4 * 10^{-5} T\right) \)
A . \( 4 \mathrm{N} / \mathrm{C} \)
в. \( 4 \times 10^{-2} \mathrm{N} / \mathrm{C} \)
c. \( 24 \times 10^{-2} N / C \)
D. not possible
Subject: Maths
\( \lim _{x \rightarrow 1} \frac{\sqrt[3]{x^{2}}-2 \sqrt[3]{x}+1}{(x-1)^{2}} \) is equal to
A \( \cdot \frac{1}{9} \)
B.
\( c \cdot \frac{1}{3} \)
D. none of these
Subject: Maths
Taking \( O^{\prime} \) as origin and the position vectors of \( \boldsymbol{A}, \boldsymbol{B} \) are \( \overrightarrow{\boldsymbol{i}}+\boldsymbol{3} \overrightarrow{\boldsymbol{j}}-\boldsymbol{2} \overrightarrow{\boldsymbol{k}}, \boldsymbol{3} \overrightarrow{\boldsymbol{i}}+ \)
\( \vec{j}-2 \vec{k} . \) The vector \( \overrightarrow{O C} \) is bisecting the
angle \( A O B \) and if \( C \) is a point on line \( A B \) then \( C \) is
A \( \cdot 4(\vec{i}+\vec{j}-\vec{k}) \)
В . \( 2(\vec{i}+\vec{j}-\vec{k}) \)
c. \( (\vec{i}+\vec{j}-\vec{k}) \)
D. \( 6(\vec{i}+\vec{j}-\vec{k}) \)
Subject: Physics
Two waves of sound \( \boldsymbol{y}_{1}= \)
\( \mathbf{1 0} \sin (\mathbf{4 0 4} \boldsymbol{\pi} \boldsymbol{t}-\mathbf{0 . 2 x}) \) and \( \boldsymbol{y}_{\mathbf{2}}= \)
\( 8 \sin (400 \pi t-0.2 x) \) superpose. As a
result
A. at several places maximum intensity and at other places minimum intensity will be heard
B. 4 beats will be heard in a second
c. 2 beats will be heard in a second
D. there will be no change in intensity of the sound rather two separate waves would be heard
Subject: Maths
Express in radians \( 345^{\circ} 25^{\prime} 36^{\prime \prime} \)
A . \( 1.726268 \pi^{c} \)
B . \( 1.3465338 \pi^{c} \)
\( \mathbf{c} \cdot 1.91903 \pi^{c} \)
D. \( 1.1978258 \pi^{c} \)
Subject: Physics
The self inductance of a choke coil is
mH. when it is connected with a 10 VDC
source then the loss of power is 20 watt.
When it connected with 10 volt \( A C \)
source loss of power is 10 watt. The frequency of AC source will bw-
\( A \cdot 50 \mathrm{Hz} \)
B. 60 Н
c. 80 н
D. 100 нz
Subject: Maths
Given, \( \boldsymbol{A}=\{\text { Triangles }\}, \boldsymbol{B}=\{ \)
Isosceles triangles \( \} \) \( C=\{\text { Equilateral triangles }\} . \) State
whether the following statement are correct or incorrect. Give reasons.
\( \boldsymbol{C} \subset \boldsymbol{A} \)
Subject: Chemistry
Which of the following species has a molecular shape similar to that of
ammonia, \( N H_{3} ? \)
\( A \cdot B H_{3} \)
в. \( H_{2} O \)
\( \mathrm{c} \cdot \mathrm{H}_{3} \mathrm{O}^{+} \)
D. \( C H_{4} \)
E \( . N H_{4}^{+} \)
Subject: Physics
The system shown is in equilibrium in
vertical plane. All the rods and the supports \( A \& B \) are light and friction
coefficient between supports and
horizontal rod is \( \mu . \) If maximum value of
angle \( \alpha \) is \( 37^{0} \) then find the value of \( 4 \mu \)
Assume light rod exerts force only along
the rod.
\( A \cdot 2 \)
B. 3
\( c .5 \)
\( D \)
Subject: Maths
If \( \vec{a}=\hat{i}-2 \hat{j}+3 \hat{k}, \vec{b}=2 \hat{i}+3 \hat{j}-\hat{k} \) and
\( \overrightarrow{\boldsymbol{c}}=\boldsymbol{r} \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+(\boldsymbol{2} \boldsymbol{r}-\boldsymbol{1}) \hat{\boldsymbol{k}} \) are three
vectors such that \( \vec{c} \) is parallel to the plane of \( \vec{a} \) and \( \vec{b}, \) then \( r \) is equal to?
\( \mathbf{A} \cdot \mathbf{0} \)
B . 2
c. -1
\( D \)
Subject: Chemistry
Assertion: K-shell electron capture is detected by analyzing the wavelength of X-ray emitted. Reason: The wavelength of the X-ray is characteristic of the daughter element and not the parent element.
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
E. Both Assertion and Reason are false
Subject: Chemistry
The oxidation of iodide ion by
perdisulphate ion is described as follows :
\( \boldsymbol{I}^{\Theta}+\boldsymbol{S}_{2} \boldsymbol{O}_{8}^{2-} \rightarrow \boldsymbol{I}_{3}^{\Theta}+\boldsymbol{S} \boldsymbol{O}_{4}^{2-} \)
If the rate disappearance of \( S_{2} O_{8}^{2-} \) ions is \( 1.5 \times 10^{-3} M s^{-1}, \) the rate of
formation of \( \boldsymbol{S O}_{4}^{2-} \) ions is:
\( \mathbf{A} \cdot 3.0 \times 10^{-3} M s^{-1} \)
B . \( 2.5 \times 10^{-3} M s^{-1} \)
C \( .2 .75 \times 10^{-3} \mathrm{M} \mathrm{s}^{-1} \)
D. None of these
Subject: Chemistry
Two oxides of a metal contain \( 50 \% \) and
\( 40 \% \) of the metal respectively. The formula of the first oxide is \( M O \). The
formula of the second oxide is :
A. \( M O_{2} \)
B. \( M_{2} O_{3} \)
c. \( M_{2} O \)
D. \( M_{2} O_{5} \)
Subject: Maths
Find the length of a chord which is at a distance of \( 3 \mathrm{cm} \) from the centre of a
circle of radius \( 5 \mathrm{cm} \)
A . \( 2 \mathrm{cm} \)
B. \( 6 \mathrm{cm} \)
\( c \cdot 8 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)
Subject: Maths
If \( a_{1}, a_{2}, a_{3}, \dots \) are in AP then \( a_{p}, a_{q}, a_{r} \)
\( \operatorname{are} \operatorname{in} A P \) if \( p, q, r \) are in
\( A \cdot A P \)
в. GP
c. нр
D. none of these
Subject: Physics
A small child tries to move a large
rubber toy placed on the ground. The toy
does not move but gets deformed under her pushing force \( (\overrightarrow{\boldsymbol{F}}) \) which is obliquely upward as shown. Then
A \( \cdot \) The resultant of the pushing force \( (\vec{F}), \) weight of the toy, normal force by the ground on the toy and the frictional force is zero
B. The normal force by the ground is equal and opposite to the weight of the toy
C . The pushing force \( (\vec{F}) \) of the child is balanced by the equal and opposite frictional force
D. The pushing force \( (\vec{F}) \) of the child is balanced by the total internal force in the toy generated due to deformation
Subject: Maths
Evaluate the determinant :
\( \left|\begin{array}{ccc}\mathbf{1}+\boldsymbol{a} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{1}+\boldsymbol{a} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} & \mathbf{1}+\boldsymbol{a}\end{array}\right| \)
Subject: Chemistry
Assuming the additivity of covalent radii in the \( C-I \) bond, what would be
the iodine-iodine distance in each of the
diiodobenzene? Assume that the ring is
regular hexagon and that each \( C-I \)
bond lies on a line through the centre of the hexagon. (Take \( C-C \) bond-length \( =1.40 A \) radius of iodine atom \( =1.33 \dot{A} \) radius of carbon atom \( =0.77 \dot{A} \) )
\( \ln o-, m- \) and \( p- \) isomers, bond
angles are respectively \( 60^{\circ}, 120^{\circ} \) and
\( 180^{\circ} . \) Hence, the distance between two-
atoms is:
A . \( 3.5 \hat{A} \)
в. \( 4.0 \hat{A} \)
\( c .7 .0 \hat{A} \)
D. \( 8.0 \hat{A} \)
Subject: Physics
A satellite of mass m revolves around
the earth of radius \( R \) at a height \( x \) from its surface. If \( g \) is the acceleration due
to gravity on the surface of the earth, the orbital speed of the satellite is
\( \mathbf{A} \cdot g x \)
B. \( \sqrt{\frac{g R^{2}}{R+x}} \)
c. \( \frac{g R^{2}}{R+x} \)
D. \( \frac{g R}{R-x} \)
Subject: Physics
An inclined plane making an angle \( 30^{\circ} \)
with the horizontal is placed in a uniform horizontal electric field of
\( 100 V m^{-1} . \) A particle of mass \( 1 k g \) and
charge \( 0.01 C \) is allowed to slide down
from rest from the top of the inclined plane. If the coefficient of friction is 0.2
the particle reaches the bottom of the
inclined plane in 1 second. Then the length of the inclined plane is (Acceleration due to gravity \( =10 m s^{-2} \) )
A \( .1 .150 m \)
в. \( 1.323 m \)
c. \( 1.151 m \)
D. \( 1.172 m \)
Subject: Chemistry
Assertion: \( P_{2} O_{3} \) is more basic than
\( N_{2} O_{3} \)
Reason: Metallic nature of the oxides
increases down the group.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true and Reason is not the correct explanation of Assertion
c. Assertion is true and Reason is false
D. Assertion is false but Reason is true
Subject: Physics
A string fixed at both ends, oscillate in
\( 4^{t h} \) harmonic. The displacement of a particle of string is given as:
\( \boldsymbol{Y}=\boldsymbol{2} \boldsymbol{A} \sin (\boldsymbol{5} \boldsymbol{\pi} \boldsymbol{x}) \cos (\boldsymbol{1} \boldsymbol{0} \boldsymbol{0} \boldsymbol{\pi} \boldsymbol{t}) . \) Then find
the length of the string?
\( \mathbf{A} \cdot 80 \mathrm{cm} \)
B. 100 ст
\( \mathbf{c} .60 \mathrm{cm} \)
D. \( 120 \mathrm{cm} \)
Subject: Physics
The formula for the velocity of electromagnetic waves in vacuum is given by
A. \( c=\sqrt{\mu_{0} \varepsilon} \)
B. \( c=\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}} \)
c. \( _{c}=\sqrt{\frac{\mu_{0}}{\varepsilon_{0}}} \)
D. \( c=\sqrt{\frac{\varepsilon_{0}}{\mu_{0}}} \)
Subject: Maths
If \( \mathbf{a} \in[-\mathbf{1 0}, \mathbf{0}] \) then the probability that
the graph of the function \( \mathbf{y}=\mathbf{x}^{2}+ \)
\( 2(a+3) x-(2 a+3) \) is strictly above \( x \)
axis is
A \( \cdot \frac{3}{5} \)
B. \( \frac{2}{5} \)
\( c \cdot \frac{1}{5} \)
D. \( \frac{4}{5} \)
Subject: Chemistry
The correct set of four quantum numbers for the outermost electrons of
rubidium \( (z=37) \) is:
A. \( _{5,0,0,+\frac{1}{2}} \)
в. \( _{5,1,0,+\frac{1}{2}} \)
c. \( _{5,1,1,+\frac{1}{2}} \)
D. \( _{6,0,0,+\frac{1}{2}} \)
Subject: Physics
If the speed of light in a medium at a given temperature is \( 348 \mathrm{m} / \mathrm{s} \) at a
pressure of 2 atm. Now the pressure is increased to 5 atm, temperature remaining constant. Now the speed of sound in the same medium will be:
A. Less than \( 348 \mathrm{m} / \mathrm{s} \)
B. Greater than \( 348 \mathrm{m} / \mathrm{s} \)
c. Equal to \( 348 \mathrm{m} / \mathrm{s} \)
D. None of these
Subject: Physics
The diagram above represents the energy states for a particular atom.Photons having which of the
following energies could be absorbed by
atoms of this kind in the ground state?
Assume that the absorbed electrons do
not ionize the atom.
\( \mathbf{A} \cdot 7 e V \)
B. 6 eV
\( \mathbf{c} .5 \mathrm{eV} \)
D. \( 4 e V \)
\( \mathrm{E} \cdot 3 \mathrm{eV} \)
Subject: Physics
Assertion
Molar mass of \( C a \) is not always 40 gm.
Reason

Average molar mass of \( C a \) is 40 gm and is calculated by abundance percentage of all isoptopes of \( \boldsymbol{C} \boldsymbol{a} \)
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
Explain the principle of a device that can build up high voltage of the order of few million volts

Draw a schematic diagram and explain the working of this device Is there any restriction on the upper
limit of high voltage set up in this machine? Explain.
OR
(a) Define electric flux. Write its S.
units
(b) Using Gauss's law, prove that the electric field at a point due to a uniformly charge infinite plane sheet is independent of the distance from it
(c) How is the field directed if (i) the
sheet is positively charged,(ii) negatively charged?
Subject: Maths
\( \operatorname{Let} \overrightarrow{\boldsymbol{A}}=\mathbf{2} \hat{\mathbf{i}}+\mathbf{7} \hat{\boldsymbol{j}}, \overrightarrow{\boldsymbol{B}}=\hat{\boldsymbol{i}}+\mathbf{2} \hat{\boldsymbol{j}}+ \)
\( \mathbf{4} \hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{C}}=\frac{\mathbf{9} \hat{\mathbf{i}}+\mathbf{3 0} \hat{\mathbf{j}}+\mathbf{4} \hat{\boldsymbol{k}}}{\mathbf{5}} \)
The ratio in which \( \vec{C} \) divides \( \overrightarrow{A B} \)
internally is?
A . 1: 4
B . 2: 3
c. 3: 2
D. 5: 1
Subject: Physics
A bob of mass \( m \) hangs from the ceiling
of a smooth trolley car which is moving
with a constant acceleration \( a \). If the
Young's modulus, radius and length of
the string are \( Y, r \) and \( l \) respectively
f the stress in the string is \( \frac{2 m \sqrt{g^{2}+d^{2}}}{x \pi r^{2}} . \) Find \( x \)
Subject: Physics
A current of i ampere is flowing in an equilateral triangle of side a. The magnetic induction at the centroid will
be?
A \( \cdot \frac{\mu_{i}}{3 \sqrt{3} \pi a} \)
в. \( \frac{3 \mu_{i}}{2 \pi a} \)
\( ^{\mathrm{c}} \cdot \frac{5 \sqrt{2} \mu_{i}}{3 \pi a} \)
D. \( \frac{9 \mu_{i}}{2 \pi a_{i}} \)
Subject: Physics
A body of mass \( 3 k g \) falls from the multi-
storeyed building \( 100 m \) high and
buries itself \( 2 m \) deep in the sand. The
time of penetration is
A. \( 9 s e c \)
B. 0.9 sec
\( c .0 .09 s e c \)
D. 10 sec
Subject: Maths
solve:
\( 4 x+\frac{x-y}{8}=17 \)
\( \mathbf{2} \boldsymbol{y}+\boldsymbol{x}-\frac{\mathbf{5} \boldsymbol{y}+\mathbf{2}}{\mathbf{3}}=\mathbf{2} \)
Subject: Maths
If \( \frac{1-x+6 x^{2}}{x-x^{3}}=\frac{A}{x}+\frac{B}{1-x}+\frac{C}{1+x} \)
then \( \mathbf{A}= \)
\( A \)
B . 2
\( c .3 \)
D. 4
Subject: Chemistry
A square planar complex is formed by hybridization of which atomic orbitals?
A \( \cdot s, p_{x}, p_{y}, d_{y z} \)
B. \( s, p_{x} . p_{y}, d_{x^{2}-y^{2}} \)
C \( \cdot s, p_{x} \cdot p_{y}, d_{z} \)
D. \( s, p_{x}, p_{y}, d_{x y} \)
Subject: Maths
The surface area of a sphere is \( 616 \mathrm{cm}^{2} \) What is its volume? \( \left[\boldsymbol{\pi}=\frac{\mathbf{2 2}}{\mathbf{7}}\right] \)
A. \( 1277.33 \mathrm{cm}^{3} \)
В. \( 1437.33 \mathrm{cm}^{3} \)
c. \( 1627.33 \mathrm{cm}^{3} \)
D. \( 1337.33 \mathrm{cm}^{3} \)
Subject: Biology
Statements \( (A, B, C, D) \) in column I have
to be matched with statements \( (p, q, r, s) \)
in column II.
\( \mathbf{A} \)
\( A-q, B-t, C-p, D-r \)
B. A-r, B- t, C- p, D- q
C. \( A-t, B-p, C-r, D-q \)
D. \( A-r, B-t, C-q, D- \)
Subject: Physics
A stone dropped from the top of a tower travels \( 15 \mathrm{m} \) in the last second of its
motion. If \( g=10 m s^{-2} \) then the time of
fall is
\( \mathbf{A} \cdot 2 s \)
в. \( 2.5 s \)
c. \( 5 s \)
D. \( 3 s \)
Subject: Maths
The slope and y-intercept of the following line are respectively
\( \mathbf{7} \boldsymbol{x}-\boldsymbol{y}+\mathbf{3}=\mathbf{0} \)
A. slope \( =m=7 / 3 \) and \( y- \) intercept \( =1 \)
B. slope \( =m=-7 \) and \( y- \) intercept \( =3 \)
c. slope \( =m=-7 / 3 \) and \( y- \) intercept \( =1 \)
D. slope \( =m=7 \) and \( y- \) intercept \( =3 \)
Subject: Maths
Tangents are drawn from (4,4) to the \( \operatorname{circle} x^{2}+y^{2}-2 x-2 y-7=0 \)
meet the circle at \( A \) and \( B \). The length
of the chord \( A B \) is
A \( \cdot 2 \sqrt{3} \)
3
B. \( 3 \sqrt{2} \)
c. \( 2 \sqrt{6} \)
D. \( 6 \sqrt{2} \)
Subject: Chemistry
When copper is treated with a certain
concentration of nitric acid, nitric oxide
and nitrogen dioxide are liberated in equal volumes according to the equation:
\( \boldsymbol{x} \boldsymbol{C u}+\boldsymbol{y} \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \longrightarrow \boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2}+ \)
\( N O+N O_{2}+H_{2} O \)
The coefficients of \( x \) and \( y \) are
respectively:
\( A \cdot 2 \) and 3
B. 2 and 6
c. 1 and 3
D. 3 and 8