AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Which of the following statement is
incorrect according to Thomson's model
of an atom?
A. The electrons, in a sphere of positive charge, were like currants (dry fruits) in a spherical Christmas pudding.
B. The positive charge in the atom is spread all over like the red edible part of the watermelon.
C. The electrons are studded in the positively charged sphere, like the seeds in the watermelon.
D. The protons are studded in the positively charged sphere, like the seeds in the watermelon.
Subject: Maths
Calculate \( : \lim _{x \rightarrow 0}\left(\frac{1}{x^{2}}-\frac{1}{\sin ^{2} x}\right) \)
A. \( \infty \)
B. \( \frac{1}{3} \)
\( c \cdot-\frac{1}{3} \)
D. does not exist
Subject: Chemistry
For the cell
\( \boldsymbol{T} l\left|\boldsymbol{T} \boldsymbol{l}^{+}(\boldsymbol{0} \cdot \boldsymbol{0} \boldsymbol{0} \mathbf{1} \boldsymbol{M}) \| \boldsymbol{C} \boldsymbol{u}^{2+}(\boldsymbol{0} \cdot \mathbf{1} \boldsymbol{M})\right| \boldsymbol{C} \boldsymbol{u} \)
the \( E_{\text {cell}} \) at \( 25^{\circ} \mathrm{C} \) is \( 0.83 \mathrm{V} \) which can be
increased by:
This question has multiple correct options
A . increasing \( \left[C u^{2+}\right] \)
B. increasing \( \left[T i^{+}\right] \)
c. decreasing \( \left[C u^{2+}\right] \)
D. decreasing \( \left[T l^{+}\right] \)
Subject: Physics
In a square room ABCD a small plane
mirror \( \mathrm{M} \) is rotating with \( \omega=\pi / 60 \)
rad/sec about a vertical axis through
the centre of the room. The source \( S \)
directs a thin parallel beam of ray at the
centre of the mirror. Time taken by reflected spot of light to cross the wall
DA is?
A . 10 sec
B. \( 12.5 \mathrm{sec} \)
c. \( 15 \sec \)
D. 20 sec
Subject: Maths
A spherical balloon is filled with \( 4500 \pi \)
cubic meters of helium gas. If a leak in
the balloon causes the gas to escape at the rate of \( 72 \pi \) cubic meters per
minute, then the rate (in meters per minute) at which the radius of the
balloon decreases 49 minutes after the
leakage began is:
A \( \cdot 6 / 7 \)
B. \( 4 / 9 \)
c. \( 2 / 9 \)
D. None of these
Subject: Chemistry
\( 2.32 \mathrm{gm} \) mixture of \( \mathrm{FeO} \) and \( \boldsymbol{F e}_{2} \boldsymbol{O}_{3} \)
when burnt in atmosphere of oxygen, 56
\( \mathrm{ml} \) of \( \mathrm{O}_{2} \) is required at STP for complete oxidation. Find mole percentage of
\( F e_{2} O_{3} \) in the given mixture.
A . 50\%
B. 40\%
c. \( 45 \% \)
D. 60\%
Subject: Physics
A wheel of radius \( 2 \mathrm{m} \) having 8 conducting concentric spokes is rotating about its geometrical axis with an angular velocity of 10 rad/s in a uniform magnetic field of \( 0.2 T \) perpendicular to its plane. The value of induced emf between the rim of the
wheel and centre is
A . 2
B. 6
\( c \cdot 4 \)
D. 8
Subject: Maths
If \( z_{1} \) and \( z_{2} \) two non-zero complex
number such that \( \left|z_{1}+z_{2}\right|=\left|z_{1}\right|+\left|z_{2}\right| \)
then \( \arg z_{1}-\arg z_{2} \) is equal to
\( A \cdot-p \)
В. \( p / 2 \)
c. \( -p / 2 \)
\( D \)
Subject: Physics
A healthy adult of height \( 1.7 m \) has an
average blood pressure (BP) of 100mm
of \( H g . \) The heart is typically at a height
of \( 1.3 m \) from the foot. Take the density
of blood to be \( 10^{3} \mathrm{kg} / \mathrm{m}^{3} \) and note that
100mm of \( H g \) is equivalent to 13.3 KPa (Kilo pascals). The ratio of Blood

Pressure in the foot region to that in the head regions is close to :
A. one
B. two
c. three
D. four
Subject: Maths
The function \( f: R \rightarrow R \) satisfies
\( \boldsymbol{f}\left(\boldsymbol{x}^{2}\right) \cdot \boldsymbol{f}^{\prime \prime}(\boldsymbol{x})=\boldsymbol{f}^{\prime}(\boldsymbol{x}) \cdot \boldsymbol{f}^{\prime}\left(\boldsymbol{x}^{2}\right) \) for all real \( \boldsymbol{x} \)
Given that \( f(1)=1 \) and compute the
value of \( \boldsymbol{f}^{\prime}(\mathbf{1})+\boldsymbol{f}^{\prime \prime}(\mathbf{1}) \)
Subject: Maths
An aquarium is in the form of a cuboid whose external measures are \( 80 \mathrm{cm} \times \)
\( 30 c m \times 40 c m . \) The base side faces and
back face are to be covered with a
coloured paper. Find the area of the paper needed?
A. \( 3000 \mathrm{cm}^{2} \)
B . \( 5000 \mathrm{cm}^{2} \)
c. \( 8000 \mathrm{cm}^{2} \)
D. \( 7000 \mathrm{cm}^{2} \)
Subject: Physics
\( \ln \) an \( \mathrm{AC} \) circuit, \( V \) and \( I \) are given below,
then the power dissipated in the circuit:
\( V=50 \sin (50 t) V, I=50 \sin \left(50 t+\frac{\pi}{3}\right) m A \)
A. \( 0.625 W \)
В. \( 1.25 \mathrm{W} \)
c. \( 2.50 W \)
D. \( 5.0 W \)
Subject: Physics
Out of the given statements which of the
following are true:
A) Work done in moving a charge on equipotential surface is zero.
B) Electric lines of force are always
normal to equipotential surface.
C) When two like charges are brought closer, the electrostatic potential energy of the system is decreased.
D) Electric lines of force converge at
positive charge and diverge at negative charge.
\( A \cdot A, B, C, D \) are true
B. \( A, B, C \) are true
c. \( A, B \) are true
D. A only true
Subject: Physics
Two waves \( A \) and \( B \) have wavelength
\( 0.01 A^{\circ} \) and \( 9000 A^{\circ} \) respectively. Name
the two waves.
A. A-gamma, B-infrared
B. A-gamma, B-ultraviolet
c. A-ultraviolet, B-infrared
D. A-gamma, B-X rays
Subject: Physics
The valve \( V \) in the bent tube is initially
kept closed. Two soap bubbles \( \boldsymbol{A} \)
(smaller) and \( B \) (larger) are formed at
the two open ends of the tube. \( V \) is now
opened and air can flow freely between
the bubbles.
A. There will be no change in the size of the bubbles
B. The bubbles will become of equal size
c. \( A \) will become smaller and \( B \) will become larger
D. The sizes of \( A \) and \( B \) will be interchanged
Subject: Chemistry
Q Type your question-
\( (\boldsymbol{C}) \stackrel{\bullet}{\longrightarrow}(\boldsymbol{A})+(\boldsymbol{D}) \)
conc. solution of \( (C) \frac{\operatorname{conc.H}_{2} S O_{4}}{(E)} \)
(weak acid)
\( (D)+ \) cobalt oxide \( \stackrel{\Delta}{\longrightarrow}(F) \) (coloured
bead)
\( (\boldsymbol{E})+\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{H} \stackrel{\boldsymbol{\Delta}}{\longrightarrow} \) green edged flame
\( (G) \)
\( A \) to \( G \) based on the following reactions
are:
\( \mathbf{A}: \boldsymbol{N} \boldsymbol{a} \boldsymbol{B} \boldsymbol{O}_{2} \)
\( \mathbf{B}: \boldsymbol{C O}_{\mathbf{2}} \)
\( \mathbf{C}: \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{B}_{4} \boldsymbol{O}_{7} \)
\( \mathrm{D}: B_{2} O_{3} \)
E: \( \boldsymbol{H}_{3} \boldsymbol{B} \boldsymbol{O}_{3} \)
\( \mathrm{F}: \boldsymbol{C o}\left(\boldsymbol{B O}_{2}\right)_{2} \)
\( \mathrm{G}:\left(C_{2} H_{5} O\right)_{3} B \)
If the statement is true enter 1 , else
enter 0
Subject: Physics
In Young's double-slit experiment, 12 fringes are observed to be formed in a certain segment of the screen when light of wavelength 600 nm is used. If the wavelength of light is changed to \( 400 n m, \) number of fringes observed in the same segment of the screen is given by
A . 12
B . 18
\( c \cdot 24 \)
D. 30
Subject: Physics
A light bulb is constructed from \( 2 \mathrm{cm} \) of
tungsten wire of diameter \( 50 \mu m \) and is
enclosed in an evacuated glass bulb. What temperature does the filament reach when it is operated at a power of 1 watt. (Assume the emissivity of the
tungsten surface is 0.35 Stefan's constant \( =\mathbf{5 . 6 7} \times \mathbf{1 0}^{-4} \mathbf{c m}^{-\mathbf{2}} \mathbf{K}^{-\mathbf{4}} \)
A . \( 2000 K \)
в. \( 4000 K \)
\( c .2500 K \)
D. \( 1200 K \)
Subject: Physics
In a circuit inductance \( L \) and
capacitance \( C \) are connected as shown
in figure. \( A_{1} \) and \( A_{2} \) are ammeters

When key \( K \) is pressed to complete the
circuit, then just after closing key \( (\boldsymbol{K}) \)
the readings of \( A_{1} \) and \( A_{2} \) will be
A. zero in both \( A_{1} \) and \( A_{2} \)
B. maximum in both \( A_{1} \) and \( A_{2} \)
C. zero in \( A_{1} \) and maximum in \( A_{2} \)
D. maximum in \( A_{1} \) and zero in \( A_{2} \)
Subject: Maths
If \( y=\cos ^{-1}\left(\frac{2 x}{1+x^{2}}\right), \) then \( \frac{d y}{d x} \) is equal
to
A \( \cdot-\frac{2}{1+x^{2}} \) of all \( |x|<1 \)
B. \( -\frac{2}{1+x^{2}} \) of all \( |x|>1 \)
c. \( \frac{2}{1+x^{2}} \) of all \( |x|<1 \)
D. None of the above
Subject: Physics
Two plane wavefronts of light, one
incident on a thin convex lens and
another on the refracting face of a thin prism. After refraction at them, the emerging wavefronts respectively become
A. plane wavefront and plane wavefront
B. plane wavefront and spherical wavefront
c. spherical wavefront and plane wavefront
D. spherical wavefront and spherical wavefront
E . elliptical wavefront and spherical wavefront
Subject: Physics
A ray of light enters at grazing angle of incidence into an assembly of three isosceles right-angled prisms having refractive indices \( \mu_{1}=\sqrt{2}, \mu_{2}=\sqrt{x} \)
and \( \mu_{3}=\sqrt{3} . \) If finally emergent light
ray also emerges at grazing angle then
calculate \( x \)
\( A \)
B.
\( c \)
D
Subject: Maths
In a triangle \( A B C, D \) and \( E \) are points
on \( B C \) and \( A C \) respectively, such that
\( B D=2 D C, A E=3 E C, \) Let \( P \) be the
point of intersection of \( A D \) and \( B E \) Then \( \frac{\boldsymbol{B} \boldsymbol{E}}{\boldsymbol{P} \boldsymbol{E}}= \)
A .2: 3
B. 3: 8
c. 8: 3
D. 1: 2
Subject: Physics
A ceiling fan is rotating at the rate of
\( 3.5 r p s \) and its moment of inertia is
\( 1.25 k g m^{2} . \) If the current is switched off
the fan comes to rest in \( 5.5 s . \) The torque acting on the fan due to friction is:
A . \( 2.5 \mathrm{Nm} \)
B. \( 5 \mathrm{Nm} \)
\( \mathrm{c} .7 .5 \mathrm{Nm} \)
D. 10 Nm
Subject: Chemistry
When the following is added to \( 20 \mathrm{ml} \) of
\( 0.1 \mathrm{M} C H_{3} C O O H+20 \mathrm{ml} \) of
\( \boldsymbol{C H}_{3} \boldsymbol{C O O N a} . \) The pH of the solution
does not change:
A. \( 10 \mathrm{ml} \) of \( 0.1 \mathrm{M} C \mathrm{CH}_{3} \mathrm{COOH} \).
B . 10 \( \mathrm{ml} \) of \( 0.1 \mathrm{M} C \mathrm{CH}_{3} \mathrm{COONa} \)
c. \( 10 \mathrm{ml} \) of water
D. 20 mI of 0.2 M \( C H_{3} \) COOH
Subject: Chemistry
To liberate \( 5.4 \mathrm{g} \) of silver (atomic mass 108 amu) from an aqueous solution of sliver nitrate, it is required to pass:
A. 965C of electricity
B. 4825C of electricity
c. \( 9650 \mathrm{c} \) of electricity
D. \( 48250 \mathrm{c} \) of electricity
Subject: Physics
A disk with
radius R has uniform surface cha
disk as a sereis of thin concer
potential \( V \) at a point on the di the disk.Assume that the potent
A \( \cdot \frac{\sigma}{2 \varepsilon_{0}} \)
B \( \cdot \frac{\sigma}{30} \)
\( c \cdot \frac{\sigma R}{24 c-c} \)
D. \( \frac{\sigma}{66} \)
Subject: Physics
At a place, value of acceleration due to
gravity \( g \) is reduced by \( 2 \% \) of its value
on the surface of the earth (Radius of
earth \( =6400 \mathrm{km} \). The place is:-
A. \( 64 \mathrm{km} \) below the surface of the earth
B. \( 64 \mathrm{km} \) above the surface of the earth
\( \mathrm{c} .32 \mathrm{km} \) above the surface of the earth
D. \( 32 \mathrm{km} \) below the surface of the earth
Subject: Maths
Prove the following:
\[
\left|\begin{array}{ccc}
\boldsymbol{a}+\boldsymbol{b}+\mathbf{2} \boldsymbol{c} & \boldsymbol{a} & \boldsymbol{b} \\
\boldsymbol{c} & \boldsymbol{b}+\boldsymbol{c}+\mathbf{2} \boldsymbol{a} & \boldsymbol{b} \\
\boldsymbol{c} & \boldsymbol{a} & \boldsymbol{c}+\boldsymbol{a}+\mathbf{2} \boldsymbol{b}
\end{array}\right|=
\]
\( \mathbf{2}(\boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c})^{3} \)
Subject: Physics
A film of water is formed between two
straight parallel wires of length \( 10 \mathrm{cm} \)
each, separated by \( 0.5 \mathrm{cm} . \) If their separation is to be increased by 1 m \( m \) while still maintaining their parallelism, how much work will have to
be done? \( \left[\boldsymbol{T}=\mathbf{7 . 2} \times \mathbf{1 0}^{-\mathbf{2}} \boldsymbol{N} / \boldsymbol{m}\right] \)
Subject: Chemistry
\( \ln \) a closed system \( : \boldsymbol{A}(s) \rightleftharpoons 2 \boldsymbol{B}(\boldsymbol{g})+ \)
\( 3 C(g) \) if the partial pressure \( C \) is of
doubled then partial pressure B wil be:
A. Twice the original pressure
B. Half of its original pressure
c. \( \frac{1}{2 \sqrt{2}} \) times, the original pressure
D. \( 2 \sqrt{2} \) times its original pressure
Subject: Physics
Two cells \( A \) and \( B \) of e.m.f \( 2 V \) and \( 1.5 V \)
respectively, are connected as shown in figure through an external resistance
10\Omega. The internal resistance of each cell
is 5\Omega. The potential difference \( V_{A} \) and
\( V_{B} \) across the terminals of the cells \( A \)
and B respectively are.
A \( \cdot V_{A}=2.0 V, V_{B}=1.5 \mathrm{V} \)
B . \( V_{A}=2.12 V, V_{B}=1.375 V \)
C \( . V_{A}=1.875 V, V_{B}=1.625 V \)
D. \( V_{A}=1.875 V, V_{B}=1.375 V \)
Subject: Physics
An electron and a photon have same wavelength of \( 10^{-9} \mathrm{m} . \) If \( \mathrm{E} \) is the energy
of the photon and p is the momentum of the electron, the magnitude of E/p in \( \mathrm{S} \) units is?
A. \( 1.00 \times 10^{-9} \)
B. \( 1.50 \times 10^{8} \)
c. \( 3.00 \times 10^{8} \)
D . \( 1.20 \times 10^{7} \)
Subject: Maths
If the conjugate of \( (x+i y)(1-2 i) \) is
\( (1+i), \) then
A. \( x+i y=1-i \)
в. \( x+i y=\frac{1-i}{1-2 i} \)
c. \( x-i y=\frac{1-i}{1+2 i} \)
D. \( _{x-i y}=\frac{1-i}{1+i} \)
Subject: Maths
The value of determinant
\( \left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{x}+\boldsymbol{y} & \boldsymbol{x}+\boldsymbol{2} \boldsymbol{y} \\ \boldsymbol{x}+\boldsymbol{2} \boldsymbol{y} & \boldsymbol{x} & \boldsymbol{x}+\boldsymbol{y} \\ \boldsymbol{x}+\boldsymbol{y} & \boldsymbol{x}+\boldsymbol{2} \boldsymbol{y} & \boldsymbol{x}\end{array}\right| \) is:
A \( \cdot 9 x^{2}(x+y) \)
В \( \cdot 9 y^{2}(x+y) \)
c. \( 3 y^{2}(x+y) \)
D. \( 7 x^{2}(x+y) \)
Subject: Maths
Integrate the following \( \int \frac{1}{x^{2}+8 x+20} d x \)
A \( \cdot \frac{1}{2} \sin ^{-1} \frac{x+4}{2}+C \)
B. \( \frac{1}{2} \cot ^{-1} \frac{x+4}{2}+C \)
c. \( \frac{1}{2} \tan ^{-1} \frac{x+4}{2}+C \)
D. None of these
Subject: Chemistry
Write the IUPAC name of the compound:
\[
\begin{array}{cc}
\boldsymbol{C H}_{3}-\boldsymbol{C H}-\boldsymbol{C H}_{2}-\boldsymbol{C}-\boldsymbol{C H}_{3} \\
\mid & \| \\
\boldsymbol{O H} & \boldsymbol{O}
\end{array}
\]
Subject: Maths
\( z_{1} \) and \( z_{2} \) are two non-zero complex
numbers such that \( z_{1}=2+4 i \)
\( z_{2}=5-6 i, \) then \( z_{2}-z_{1} \) equals
A. \( 3-10 i \)
B. \( 3+10 i \)
c. \( 7-2 i \)
D. \( 10-24 i \)
Subject: Physics
The mean free path of conduction
electrons in copper is about \( 4 \times \)
\( 10^{-8} \) m. Find the electric field which
can give, on an average, \( 2 e V \) energy to a conduction electron in a block of
copper.
A \( \cdot 6 \times 10^{7} V / m \)
B . \( 7 \times 10^{7} V / m \)
c. \( 5 \times 10^{7} V / m \)
D. \( 5 \times 10^{9} V / m \)
Subject: Maths
A point \( P \) is such that its perpendicular
distance from the line \( \boldsymbol{y}-\mathbf{2 x + 1}=\mathbf{0} \)
is equal to its distance from the
origin,then the locus of the point \( \boldsymbol{P} \)
A \( \cdot x^{2}+4 y^{2}+4 x y+4 x-2 y-1=0 \)
B. \( x^{2}+y^{2}+4 x y+x-y-1=0 \)
c. \( x^{2}+4 y^{2}-1=0 \)
D. None of these
Subject: Physics
Calculate the approximate speed of sound in oxygen from the following data The mass of 22.4 liter of oxygen at
\( \boldsymbol{S} \boldsymbol{T} \boldsymbol{P}(\boldsymbol{T}=\mathbf{2 7 3} \boldsymbol{K} \boldsymbol{a n d \boldsymbol { p }}=\mathbf{1 . 0} \times \)
\( \left.10^{5} N m^{2}\right) \) is \( 32 g \) the molar heat
capacity of oxygen at constant volume
is \( C_{V}=2.5 R \) and that at constant
pressure is \( \boldsymbol{C}_{\boldsymbol{P}}=\mathbf{3 . 5} \boldsymbol{R} \)
Subject: Physics
A body starting from rest with uniform acceleration travels distance \( s_{1} \) in the
first \( t \) second and travels a distance \( s_{2} \)
with uniform velocity in the next \( 2 t \) second. Then:
A \( \cdot s_{2}=4 s_{1} \)
В. \( s_{2}=2 s_{1} \)
\( \mathbf{c} \cdot s_{1}=4 s_{1} \)
D. \( s_{1}=2 s_{2} \)
Subject: Maths
The vertices of a triangle \( A B C \) are \( A(2,3, \)
1), \( B(-2,2,0) \) and \( C(0,1,-1) \).Find the
magnitude of the line joining mid points of the sides \( A C \) and \( B C \).
A \( \cdot \frac{1}{\sqrt{2}} \) unit
B. 1 unit
c. \( \frac{3}{\sqrt{2}} \) unit
D. 2 unit
Subject: Maths
Matrices \( A \) and \( B \) satisfy \( A B=B^{-1} \) where \( \boldsymbol{B}=\left[\begin{array}{cc}2 & -1 \\ 2 & 0\end{array}\right], \) then
find without finding \( B^{-1}, \) the value of \( K \)
for which \( \boldsymbol{K} \boldsymbol{A}-\mathbf{2} \boldsymbol{B}^{-\mathbf{1}}+\boldsymbol{I}=\boldsymbol{O} \)
Subject: Maths
If \( g \) is inverse function of \( f \) where
\( f(x)=\int_{0}^{\pi} \frac{1}{\sqrt{1+t^{2}}} d t \quad \) and
\( \int g\left(g^{\prime}(x)\right)^{2} d x=\frac{\left[1+(g(x))^{\alpha}\right]^{\beta}}{\gamma}+c \)
Then the value of \( \alpha \beta \gamma \) is equal to [where \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma} \in \boldsymbol{R}] \)
A . 9
B. 6
\( c .3 \)
D.
Subject: Chemistry
Bond energies of H - H and Cl - Cl are \( 430 k J m o l^{-1} \) and \( 242 k J m o l^{-1} \)
respectively. \( \Delta \boldsymbol{H}_{f} \) for HCl is
\( 91 k J m o l^{-1} . \) What will be the bond
energy of H - Cl bond (per mole value)?
A . 672 kJ
B. 182 kJ
c. 245 kJ
D. 88 kJ
Subject: Chemistry
\( X \times 100 \mathrm{mL} \) water must be added to
\( 300 \mathrm{mL} \) of \( 0.2 M \) solution of
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \) for the degree of
dissociation of the acid to double?
The value of \( X \) is
\( \left[\boldsymbol{K}_{a} \text { for acetic acid }=\mathbf{1 . 8} \times \mathbf{1 0}^{-\mathbf{5}}\right] \)
Subject: Maths
If \( \int \frac{\sec x-\tan x}{\sqrt{\sin ^{2} x-\sin x}} d x=k \ln \mid f(x)+ \)
\( \sqrt{2} \sqrt{\tan x(\tan x-\sec x)} \mid+c, \) where \( c \)
is arbitrary constant and \( k \) is a fixed
constant, then
This question has multiple correct options
A. \( k=\sqrt{2} \)
в. \( k=\frac{1}{\sqrt{2}} \)
c. \( f(x)=\tan x-\sec x \)
D. \( f(x)=\sqrt{\tan x+\sec x} \)
Subject: Physics
A conductor \( A B \) of length \( L \) carrying a
current \( I^{\prime} \) as shown in figure. The force
on \( A B \) has magnitude
\( ^{\text {A }} \cdot \frac{\mu_{0} I^{\prime} I}{2 \pi} \log 2 \)
В. \( \frac{\mu_{0} I^{\prime} I}{2 \pi} \log 3 \)
\( ^{\text {c. }} \frac{3 \mu_{0} I^{\prime} I}{2 \pi} \log \frac{3}{2} \)
D. \( \frac{2 \mu_{0} I^{\prime} I}{3 \pi} \)
Subject: Physics
If the range of a gun which fires a shell with muzzle speed \( v \), is \( R \), then the angle of elevation of the gun is
\( ^{\mathbf{A}} \cdot \cos ^{-1} \frac{v^{2}}{R g} \)
B. \( \cos ^{-1} \frac{R g}{v^{2}} \)
c. \( \frac{1}{2} \sin ^{-1} \frac{v^{2}}{R g} \)
D. \( \frac{1}{2} \sin ^{-1} \frac{R g}{v^{2}} \)
Subject: Chemistry
The vapour pressure of ethanol and methanol are \( 44.5 \mathrm{mm} \) and \( 88.7 \mathrm{mm} \mathrm{Hg} \) respectively. An ideal solution is
prepared at the same temperature by mixing 60 g of ethanol with 40 gof methanol. The total vapour pressure of the solution is:
A. \( 67.13 \mathrm{mm} \) Hg
B. 66.13 \( \mathrm{mm} \) Нв
c. \( 76.13 \mathrm{mm} \) нв
D. None of the above
Subject: Maths
\( P, Q \) and \( R \) are three sets and \( \xi P \cup Q \cup \)
\( R . \) Given that \( n(\xi)=60, n(P \cap Q)=5 \)
\( n(Q \cap R)=10, n(p)=20 \) and \( n(Q)=23 \)
find \( n\left(P^{\prime} \cup Q\right) \)
A. 37
3. 38
\( c \cdot 45 \)
D. 52
Subject: Chemistry
A brown coloured mixture of two gases
is obtained by the reduction of 6N nitric acid with metallic copper. This mixture on cooling condenses to a blue liquid which on freezing \( \left(-30^{\circ} \mathrm{C}\right) \) gives a blue solid. The correct choice for blue liquid
or solid is :
A. it is referred to as the anhydride of nitrous acid
B. it is an acidic oxide and hence dissolves in alkalies producing nitrites.
C . it can also be prepared by the action of 50\% \( \mathrm{H} \mathrm{NO}_{3} \) on arsenious oxide and then cooling to \( 250 \mathrm{K} \)
D. all of the above
Subject: Maths
Inverse of \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{3} \\ \mathbf{2} & -\mathbf{2}\end{array}\right] \) is equal to? \( \mathbf{A} \)
\( \mathbf{A} \cdot-\frac{1}{8}\left[\begin{array}{cc}3 & 1 \\ -2 & 2\end{array}\right] \)
В. \( -\frac{1}{8}\left[\begin{array}{rr}-2 & -3 \\ -2 & 1\end{array}\right] \)
\( ^{\mathbf{c}} \cdot \frac{1}{8}\left[\begin{array}{cc}-1 & -3 \\ -2 & 2\end{array}\right] \)
D. None of these
Subject: Physics
A parallel beam of fast moving electrons is incident normally on a narrow slit. A fluorescent screen is placed at a large distance from the slit. If the speed of the electrons is increased, which of the
following statement is correct?
A. Diffraction pattern is not observed on the screen in the case of electrons
B. The angular width of the central maximum of the diffraction pattern will increase
c. The angular width of the central maximum will decreases
D. The angular width of the central maximum will remain unaffected
Subject: Chemistry
toppr )
Q Type your question_
watches, etc.
(ii) It consists of zinc-mercury
amalgam as anode and a paste of HgO
and carbon as the cathode.
(iii) The electrolyte is a paste of
\( Z n(O H)_{2} \) and \( K O_{2} \)
(iv) The electrode reactions for the cell
are
At anode: \( Z n(H g)+H_{2} O \rightarrow Z n O_{(s)}+ \)
\( 2 O H^{-}+2 e^{-} \)
At cathode: \( \boldsymbol{H} \boldsymbol{g} \boldsymbol{O}+\boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \)
\( \boldsymbol{H} \boldsymbol{g}_{(l)}+2 \boldsymbol{O} \boldsymbol{H} \)
A. (ii) and (iii) only
B. (i) ad (ii) only
C. (i), (iii) and (iv) only
D. (iii) and (iv) only
Subject: Maths
An urn contains 5 red and 2 black balls.
Two balls are randomly drawn. Let \( \boldsymbol{X} \) represent the number of black balls. What are the possible values of \( X ? \) Is
\( X \) a random variable ?
\( \mathbf{A} \cdot 0,1,2 \)
в. 3,5,7
c. 7,7,8
D. 1,5,7
Subject: Maths
Evaluate the integral \( \int_{0}^{\pi / 2} \sin 2 x \log (\tan x) d x \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( -1 / 2 \)
c. \( 1 / 3 \)
D. \( 1 / 4 \)
Subject: Physics
When magnetic field at \( \mathrm{P} \) and \( \mathrm{Q} \) is same then OP/OQ is:
A \( \cdot \frac{1}{3} \)
B. \( \frac{1}{\frac{1}{3}} \)
\( c \cdot 2 \sqrt{2} \)
D. \( \frac{3}{2} \)
Subject: Maths
If \( S_{1}, S_{2} \) and \( S_{3} \) are the sum of first
\( \boldsymbol{n}, \mathbf{2 n} \) and \( \mathbf{3 n} \) terms of a geometric series respectively, then prove that \( \boldsymbol{S}_{1}\left(\boldsymbol{S}_{3}-\boldsymbol{S}_{2}\right)=\left(\boldsymbol{S}_{2}-\boldsymbol{S}_{1}\right)^{2} \)
Subject: Physics
Two coils \( X \) and \( Y \) are linked such that
emf \( E \) is induced in \( Y \) when the current
in \( X \) is changing at the rate \( I^{\prime}(=d I / d t) \)
If a current \( I_{0} \) is now made to flow through \( Y \), the flux linked with \( X \) will be
A \( . E I_{0} I^{\prime} \)
в. \( \frac{I_{0} I^{\prime}}{E} \)
\( ^{\mathbf{c}} \cdot\left(\frac{E}{I_{0}}\right) I^{\prime} \)
D. \( \left(\frac{E}{I^{\prime}}\right) I_{0} \)
Subject: Physics
\( 1 m^{3} \) water is brought inside the lake
upto \( 200 m \) depth from the surface of
the lake. What will be change in the volume when the bulk modulus of
elasticity of water is 22000 at \( m ? \) (density of water is \( 1 \times 10^{3} k g / m^{3} \)
atmosphere pressure \( =10^{5} N / m^{2} \) and
\( \boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2} \)
В. \( 7.8 \times 10^{-3} m^{3} \)
\( \mathbf{c} \cdot 9.1 \times 10^{-4} m^{3} \)
D. \( 8.7 \times 10^{-4} m^{3} \)