AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
The largest sphere is carved out of a cube whose edge is of length \( l \) units. Find the volume of the sphere.
A \( \cdot \frac{5 \pi l^{3}}{6} \)
в. \( \frac{3 \pi l^{3}}{5} \)
с. \( \frac{\pi l^{3}}{6} \)
D. \( \frac{2 \pi l^{3}}{7} \)
Subject: Physics
A radioactive sample at any instant has its disintegration rate 5000 disintegration per minute. After 5 minutes, the rate is 1250 disintegrations per minute. Then, the decay constant, per minute, is
A . \( 0.4 \ln 2 \)
B. \( 0.2 \ln 2 \)
c. \( 0.1 \ln 2 \)
D. \( 0.8 \ln 2 \)
Subject: Maths
If \( \frac{(1+i)^{2}}{2-i}=x+i y, \) find \( x+y \)
A \( \cdot \frac{-2}{5} \)
B. \( \frac{2}{7} \)
\( c \cdot \frac{2}{5} \)
D. \( \frac{-2}{7} \)
Subject: Physics
An electromagnetic wave is propagating along \( x \) -axis. At \( x=1 \mathrm{m} \) and
\( t=10 s, \) its electric vector \( |\bar{E}|=6 V / m \) then the magnitude of its magnetic
vector is:
A \( \cdot 2 \times 10^{-8} T \)
В. \( 3 \times 10^{-7} T \)
c. \( 6 \times 10^{-8} T \)
D. \( 5 \times 10^{-7} T \)
Subject: Physics
The linear density of a thin rod of length 1.0m varies as \( \boldsymbol{\lambda}=2 \mathrm{kg} / \mathrm{m}+\left(\frac{2 \mathrm{kg}}{\boldsymbol{m}^{2}}\right) \boldsymbol{x} \)
where \( x \) is the distance from its one end
The distance of its centre of mass from
its end is?
A \( \cdot \frac{2}{3} \mathrm{m} \)
в. \( \frac{5}{9} \mathrm{m} \)
c. \( \frac{4}{3} \mathrm{m} \)
D. \( \frac{1}{2} \) n
Subject: Physics
The position of a particle at time \( t \) is given by the relation \( \boldsymbol{x}=\frac{\boldsymbol{v}_{0}}{\boldsymbol{\alpha}}\left(\mathbf{1}-\boldsymbol{e}^{-\boldsymbol{\alpha} t}\right) \)
The dimensional formula for \( \boldsymbol{\alpha}^{2} \boldsymbol{v}_{0}^{3} \) will
be :
Subject: Chemistry
A species of an element \( A \) has a net charge of -1 and it has 18 electrons and
20 neutrons. Identify the correct
statements.

This question has multiple correct options
A . Its symbol will be \( _{17}^{3 \mathrm{A}} \)
B. Its atomic number is 18
c. The number of protons are 17
D. Its mass number is 38
Subject: Maths
If \( \left(\begin{array}{c}3 x+7 \\ y+1 & 2-3 x\end{array}\right)=\left(\begin{array}{cc}1 & y-2 \\ 8 & 8\end{array}\right) \) then the values
of \( x \) and \( y \) respectively are
A. -2,7
B. \( -\frac{1}{3}, 7 \)
\( c \cdot-\frac{1}{3},-\frac{2}{3} \)
D. 2,-7
Subject: Physics
Match List-I with List-II:
\( \begin{array}{ll}\text { List-I } & \text { List-II } \\ \text { a) } \overrightarrow{\mathrm{i}} \cdot(\overrightarrow{\mathrm{j}} \times \overrightarrow{\mathrm{k}})+\overrightarrow{\mathrm{j}} \cdot(\overrightarrow{\mathrm{k}} \times \overrightarrow{\mathrm{i}})+\overrightarrow{\mathrm{k}} \cdot(\overrightarrow{\mathrm{i}} \times \overrightarrow{\mathrm{j}}) & \text { e) } 0 \\ \text { b) }(\overrightarrow{\mathrm{i} . \overrightarrow{\mathrm{i}}})+(\overrightarrow{\mathrm{i}} \times \overrightarrow{\mathrm{i}}) & \text { f) } 1 \\ \text { c) }(\overrightarrow{\mathrm{A} \cdot \vec{B}})(\overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}})+(\overrightarrow{\mathrm{B}} \cdot \overrightarrow{\mathrm{A}})(\overrightarrow{\mathrm{B}} \times \overrightarrow{\mathrm{A}}) & \text { g) } 3 \\ \text { d) }(\overrightarrow{\mathrm{i}}+\overrightarrow{\mathrm{j}}) \cdot(2 \overrightarrow{\mathrm{i}}+2 \overrightarrow{\mathrm{k}}) & \text { h) } 2\end{array} \)
\( \mathbf{A} \cdot \mathbf{a} \rightarrow \mathbf{e} ; \mathbf{b} \rightarrow \mathbf{f} ; \mathbf{c} \rightarrow \mathbf{g} ; \mathbf{d} \rightarrow \mathbf{h} \)
\( \mathbf{B} \cdot \mathbf{a} \rightarrow \mathbf{g} ; \mathbf{b} \rightarrow \mathbf{h} ; \mathbf{c} \rightarrow \mathbf{f} ; \mathrm{d} \rightarrow \mathbf{e} \)
\( \mathbf{c} \cdot \mathbf{a} \rightarrow \mathbf{g} ; \mathbf{b} \rightarrow \mathbf{f} ; \mathbf{c} \rightarrow \mathbf{e} ; \mathrm{d} \rightarrow \mathbf{h} \)
\( \mathrm{D} \cdot \mathrm{a} \rightarrow \mathrm{f} ; \mathrm{b} \rightarrow \mathrm{g} ; \mathrm{c} \rightarrow \mathrm{h} ; \mathrm{d} \rightarrow \mathrm{e} \)
Subject: Maths
If \( \int f(x) d x=\frac{3}{55} \sqrt[3]{\tan ^{5} x}\left(5 \tan ^{2} x+\right. \)
11) \( +C \) then \( f(x) \) is equal to
This question has multiple correct options
A \( \cdot \sqrt[3]{\sin ^{2} x \cos ^{-14} x} \)
B. \( \sqrt[3]{\tan ^{2} x\left(1+\tan ^{2} x\right)^{6}} \)
c. \( \sqrt[3]{\cos ^{2} x \sin ^{-14} x} \)
D. \( \frac{7}{3} \sqrt[3]{\sin ^{2} x \cos ^{-14} x} \)
Subject: Physics
A \( 100 m \) train is moving North at a
speed of \( 16 m s^{-1} . \) A bird flying at 4
\( m s^{-1} \) towards South crosses the train
in
A . \( 5 s \)
в. \( 10 s \)
\( c \cdot 12 s \)
D. 20
Subject: Maths
The radius of the locus by the point represented by \( z, \) when \( \arg \frac{z-1}{z+1}=\frac{\pi}{4} \)
is
A \( \cdot \sqrt{2} \)
B. \( \sqrt{2} \pi \)
c. \( \frac{\pi}{\sqrt{2}} \)
D. none of these
Subject: Physics
An air bubble is inside water. The
refractive index of water is \( 4 / 3 . \) At what distance from the air bubble should a
point object be placed so as to form a
real image at the same distance from the bubble?
A \( .2 . R \)
в. \( 3 R \)
\( c .4 R \)
D. The air bubble cannot image
Subject: Physics
The fractional change in intensity of the
central maximum as function of time is
A \( \cdot \frac{A \sin \omega t}{L} \)
B. \( \frac{2 A \sin \omega t}{L} \)
c. \( \frac{3 A \sin \omega t}{L} \)
D. \( \frac{4 A \sin \omega t}{L} \)
Subject: Maths
The set of all values of a for which the
function \( \boldsymbol{f}(\boldsymbol{x})=\left(\boldsymbol{a}^{2}=-\boldsymbol{3} \boldsymbol{a}+\right. \)
2) \( \left(\cos ^{2} x / 4-\sin ^{2} x / 4\right)+(a-1) x+ \)
\( \sin 1 \) does not process critical points is
A. \( [1, \infty) \)
(n)
в. (0,1)\( \cup(1,4) \)
c. (-2,4)
D. (1,3)\( \cup(3,5) \)
Subject: Chemistry
The two electrons have the following set of quantum numbers:
\( \boldsymbol{P}=\mathbf{3}, \mathbf{2},-\mathbf{2},+\frac{\mathbf{1}}{\mathbf{2}} \)
\( \boldsymbol{Q}=\mathbf{3}, \mathbf{0}, \mathbf{0},+\frac{\mathbf{1}}{\mathbf{2}} \)
Which of the following statement is
true?
A. \( P \) and \( Q \) have same energy
B. \( P \) has greater energy than \( Q \)
c. \( P \) has lesser energy than \( Q \)
D. \( P \) and \( Q \) represent same electron
Subject: Chemistry
The simplest formula of a compound containing \( 50 \% \) of an element \( X \)
(Atomic weight 10 ) and \( 50 \% \) of element
\( Y \) (Atomic weight 20 ) is :
A . \( X Y \)
в. \( X_{2} Y \)
c. \( x Y_{2} \)
D. \( X_{2} Y_{3} \)
Subject: Physics
The energy of the reaction \( L i^{7}+p \longrightarrow \) \( 2 H e^{4} \) is (the binding energy per
nucleon in \( L i^{7} \) and \( H e^{4} \) nuclei are 5.60
and \( 7.06 \mathrm{MeV} \) respectively.
A. 17.3 Mev'
B. 1.73 MeV
c. 1.46 Mev
D. Depends on binding energy of proton
Subject: Chemistry
Which of the following statements is true regarding the typical element belonging to \( 1^{s t} \) group of \( p \) - block elements?

This question has multiple correct options
A. The element forms amphoteric oxide
B. The element forms a sulphate of formula \( M_{2}\left(S O_{4}\right)_{3} \)
c. The element shows variable valency
D. The element is a metalloid
Subject: Physics
A small metal ball of mass 'm' is
dropped in a liquid contained in a vessel, attains a terminal velocity 'v'. If a metal ball of same metarial but of mass
\( 8 \mathrm{m}^{\prime} \) is dropped in same liquid, then the terminal velocity will be:
A. \( V \)
B. \( 2 V \)
\( c .4 V \)
D. \( 8 V \)
Subject: Chemistry
on the P-T phase diagram of carbon
dioxide:
(a) At what temperature and pressure can the solid, liquid and vapour phases
of \( C O_{2} \) co-exits in equilibrium?
(b) What is the effect of decrease of
pressure on the fusion and boiling point
of \( \boldsymbol{C} \boldsymbol{O}_{2} ? \)
(c) What are the critical temperature
and pressure for \( C O_{2} \) ? what is their
significance ?
(d) Is \( C O_{2} \) solid, liquid or gas at \( (a) \)
\( -70^{\circ} \mathrm{C} \) under 1 atm, \( (\mathrm{b})-60^{\circ} \mathrm{C} \) under 10
\( \operatorname{atm},(c) 15^{\circ} C \) under 56 atm \( ? \)
Subject: Maths
\( \int_{0}^{1} \frac{\log (1+x)}{1+x^{2}} d x= \)
\( A \cdot \pi \log 2 \)
в. \( \frac{\pi}{8} \log 2 \)
c. \( \frac{\pi}{4} \log 2 \)
D. \( -\pi \log 2 \)
Subject: Chemistry
The precipitate of \( \boldsymbol{C a} \boldsymbol{F}_{2}\left(\boldsymbol{K}_{\boldsymbol{s} \boldsymbol{p}}=\mathbf{1 . 7} \times\right. \)
\( \left.10^{-10}\right) \) is obtained when equal volumes
of the following are mixed:
A \( \cdot 10^{-4} M C a^{2+}+10^{-4} M F^{-} \)
B . \( 10^{-2} M C a^{2}+10^{-3} M F^{-} \)
\( \mathbf{c} \cdot 10^{-5} M C a^{2}+10^{-3} M F^{-} \)
D. \( 10^{-3} M C a^{2}+10^{-5} M F^{-} \)
Subject: Physics
Statement 1: A charge is outside the
Gaussian sphere of radius \( R \). Then
electric field on the surface of sphere is
zero

Statement 2: As \( \oint \vec{E} . \overrightarrow{d s}=\frac{q_{i n}}{\varepsilon_{0}}, \) for the
sphere \( \boldsymbol{q}_{\boldsymbol{i n}} \) is zero, so \( \oint \overrightarrow{\boldsymbol{E}} \cdot \overrightarrow{\boldsymbol{d} s}=\mathbf{0} \)
A. Statement 1 is true, statement 2 is true and statement 2 is correct explanation for statement
B. Statement 1 is true, statement 2 is true and statement 2 is NOT the correct explanation for statement
c. Statement 1 is true, statement 2 is false
D. Statement 1 is false, statement 2 is true
Subject: Physics
Statement-1: Superposition principle is applicable only for small disturbances
Statement-2: Superposition principle is applicable only for non-linear waves.
A. If both the statements are true and statement- 2 is the correct explanation of statement-
B. If both the statements are true but statement-2 is not the correct explanation of statement-
c. If statement-1 is true and statement- 2 is false
D. If statement-1 is false and statement-2 is true
Subject: Physics
AB is a potentiometer wire of length 100
\( \mathrm{cm} \) and resistance 10 ohms. It is
connected in series with a resistance
\( \mathrm{R}=40 \) ohms and a battery of e.m.f. \( 2 \mathrm{V} \)
and negligible internal resistance. If a
source of unknown e.m.f. E is balanced
by \( 40 \mathrm{cm} \) length of the potentiometer
wire, the value of E is :-
A. \( 0.8 \mathrm{V} \)
B. \( 1.6 v \)
c. \( 0.08 \mathrm{v} \)
D. 0.16 v
Subject: Physics
The path difference between the two waves \( y_{1}=a_{1} \sin \left(\omega t-\frac{2 \pi x}{\lambda}\right) \) and
\( \boldsymbol{y}_{2}=\boldsymbol{a}_{2} \cos \left(\boldsymbol{\omega} \boldsymbol{t}-\frac{\boldsymbol{2} \boldsymbol{\pi} \boldsymbol{x}}{\boldsymbol{\lambda}}+\boldsymbol{\phi}\right) \)
\( ^{A} \cdot \frac{\lambda}{2 \pi} \)
в. \( \frac{\lambda}{2 \pi}\left(\phi+\frac{\pi}{2}\right) \)
c. \( \frac{\lambda}{2 \pi}\left(\phi-\frac{\pi}{2}\right) \)
\( D \cdot \frac{2 \pi}{\lambda} d \)
Subject: Maths
The domain of \( \boldsymbol{f}(\boldsymbol{x})=\frac{\mathbf{1}}{\sqrt{\boldsymbol{x}^{2}-\boldsymbol{4}}} \) is
\( \mathbf{A} \cdot(-\infty, 4) \)
в. (-2,3)
\( c \cdot(4, \infty) \)
D. \( (-\infty,-2) \cup(2, \infty) \)
Subject: Physics
A particle of mass \( \mathrm{m} \) is executing oscillations about the origin on the \( x \) axis. Its potential energy is \( V(x)= \)
\( k|x|^{3} \) where \( k \) is a positive constant. If
the amplitude of oscillation is a, them its time period T is?
A. proportional to \( \frac{1}{\sqrt{a}} \)
B. Independent of a
c. Proportional to \( \sqrt{a} \)
D. Proportional to \( a^{3 / 2} / 2 \)
Subject: Physics
The force experienced on an electric charge of \( 10 \mathrm{C} \) placed at a point in the electric field is 50 N. The strength of the electric field at the point is
A \( \cdot 25 \mathrm{N} \mathrm{C}^{-1} \)
B. 5 N \( c^{-1} \)
c. \( 10 \mathrm{N} \mathrm{c}^{-1} \)
D. 30 N C \( ^{-1} \)
Subject: Physics
OABC is a current carrying square loop
an electron is projected from the centre
of loop along its diagonal \( A C \) as shown.
Unit vector in the direction of initial
acceleration will be
\( A \cdot \hat{k} \)
B. \( -\left(\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right) \)
\( c .-\hat{k} \)
\( \frac{\hat{i}+\hat{j}}{\sqrt{2}} \)
Subject: Physics
The bulk modulus of a spherical objects is ' \( B \) '. If it is subjected to uniform
pressure 'P', the fractional decrease in
radius is:
A \( \cdot \frac{P}{3 B} \)
в. \( \frac{P}{B} \)
c. \( \frac{B}{3 P} \)
D. \( \frac{3 P}{B} \)
Subject: Physics
Find the electric field in the region
labelled 2.
\( \mathbf{A} \cdot k_{e} \frac{q}{r^{2}} \)
\( \mathbf{B} \cdot 2 k_{e} \frac{q}{r^{2}} \)
\( c \cdot 3 k_{e} \frac{q}{r^{2}} \)
D. \( 4 k_{e} \frac{q}{r^{2}} \)
Subject: Maths
\( e\left(\lim _{x \rightarrow \beta}(\tan x \cot \beta-1)\right) \)
is equal to
A \( \cdot \frac{1}{\sin \beta \cos \beta} \)
\( \mathbf{B} \cdot \sin \beta \cos \beta \)
c. \( \frac{-1}{\sin \beta \cos \beta} \)
D \( \cdot e^{\sec ^{2} \beta \cot \beta} \)
Subject: Physics
Find the magnitude and direction of the force vector applied to the loop if the
vector \( \vec{p}_{m} \) coincides in direction with
the magnetic field produced by the current \( I \) at the point where the loop is located
A \( \cdot \vec{F}=-\frac{\mu_{0} I p_{m}}{\pi r^{2}} \vec{e}_{r} ; \vec{F} \uparrow \downarrow \vec{r} \)
B・ \( \vec{F}=-\frac{\mu_{0} I p_{m}}{2 \pi r^{2}} \overrightarrow{e_{r}} ; \vec{F} \uparrow \downarrow \vec{r} \)
C・ \( \vec{F}=-\frac{\mu_{0} I p_{m}}{3 \pi r^{2}} \overrightarrow{e_{r}} ; \vec{F} \uparrow \downarrow \vec{r} \)
D・ \( \vec{F}=-\frac{\mu_{0} I p_{m}}{4 \pi r^{2}} \overrightarrow{e_{r}} ; \vec{F} \uparrow \downarrow \vec{r} \)
Subject: Physics
When we press the bulb of a
dropper,with its nozzle kept under water
,air in the dropper is seen to escape in the form of bubbles.lf we then,release
the pressure on the bulb,water gets
filled in the dropper.The rise in water in the dropper is due to
A. Liquid pressure
B. Weight of the bulb
c. Gravity of the earth
D. Atmospheric pressure
Subject: Chemistry
A \( 5 \% \) by mass of an aqueous solution of \( A \) of molar mass \( 342 \mathrm{g} \mathrm{mol}^{-1} \) is isotonic with \( 0.878 \% \) by mass of an aqueous solution of another substance
B. The molar mass of \( B \) in \( g \) mol \( ^{-1} \) is:
A . 120
B. 180
\( c \cdot 60 \)
D. 90
Subject: Maths
If \( \frac{1}{2} \sin ^{-1}\left[\frac{3 \sin 2 \theta}{5+4 \cos 2 \theta}\right]=\tan ^{-1} x \)
then \( \boldsymbol{x}= \)
\( \mathbf{A} \cdot \tan 3 \theta \)
B. \( 3 \tan \theta \)
c. \( (1 / 3) \tan \theta \)
D. \( 3 \cot \theta \)
Subject: Maths
If \( \mathrm{S} \) is the sample space for the event \( \mathrm{A} \)
then find the correct alternative from
the following:
A \( .0 \geq P(A) \geq 1 \)
B. \( 0 \leq P(A)<1 \)
c. \( 0<P(A) \leq 1 \)
D. \( 0 \leq P(A) \leq 1 \)
Subject: Chemistry
The general electronic configuration of f-block elements is:
A \( \cdot(n-2) f^{1-14}(n-1) d^{0-1} n s^{2} \)
B . \( (n-2) f^{1-14}(n-1) d^{0-10} n s^{1} \)
C. \( (n-2) f^{1-10}(n-1) d^{0-1} n s^{2} \)
D \( \cdot(n-2) f^{1-14}(n-1) d^{0-1} n s^{1} \)
Subject: Chemistry
\( \begin{array}{rc} & \boldsymbol{C H}_{\mathbf{3}} \\ \text { The IUPAC name of } \boldsymbol{C} \boldsymbol{H}_{3}- & \boldsymbol{C} \\ & \boldsymbol{C H}_{3}\end{array} \)
\( \boldsymbol{C H}_{2}-\boldsymbol{C l} \) is:
A. 1-chloro-2,2-dimethylpropane
B. 3-Chloro-2,2-dimethylpropane
c. 1 -chloro-1,2-dimethylpropane
D. 2-chloro-2,2-dimethylpropane
Subject: Maths
If \( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right] \) and \( \boldsymbol{a}_{i j}=\boldsymbol{i}(\boldsymbol{i}+\boldsymbol{j}) \) then
trace of \( \boldsymbol{A}= \)
A \( \cdot \frac{n(n+1)(2 n+1)}{6} \)
B. \( \frac{n(n+1)(2 n+1)}{3} \)
c. \( \frac{n(n+1)}{2} \)
D. \( \frac{n^{2}(n+1)^{2}}{4} \)
Subject: Maths
The value of \( \frac{1}{\operatorname{cosec}^{2} \theta}+\frac{1}{\sec ^{2} \theta} \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \cdot \sin ^{2} \theta \)
\( \mathbf{D} \cdot \cos ^{2} \theta \)
Subject: Physics
A Bohr hydrogen atom undergoes a transition \( n=5 \) to \( n=4 \) and emits a
photon of frequency \( f \). Frequency of
circular motion of electron in \( \boldsymbol{n}=\boldsymbol{4} \)
orbit is \( f_{4} . \) The ratio \( f / f_{4} \) is found to be 18/5m. State the value of \( m \)
Subject: Maths
Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}: \boldsymbol{y}=\cos ^{-1}\left(\frac{\boldsymbol{2} \boldsymbol{x}}{\boldsymbol{1}+\boldsymbol{x}^{2}}\right),-\boldsymbol{1}< \)
\( \boldsymbol{x}<\mathbf{1} \)
Subject: Physics
A particle moves with an initial velocity
\( \boldsymbol{v}_{0} \) and retardation \( \boldsymbol{\alpha} \boldsymbol{v}, \) where \( \boldsymbol{v} \) is its initial velocity at any time \( t \) and \( \alpha \) is a
constant
This question has multiple correct options
A \cdot The particle will cover a total distance \( \frac{v_{0}}{\alpha} \)
B. The particle will come to rest after a time \( \frac{1}{\alpha} \)
c. The particle will continue to move for a very long time.
D. The velocity of the particle will become \( \frac{v_{0}}{2} \) after a time \( \frac{1}{\alpha} \)
Subject: Physics
In a wind tunnel experiment, the
pressures on the upper and lower
surfaces of the wings are \( 0.90 \times 10^{5} \) Pa
and \( 0.91 \times 10^{5} \) Pa respectively. If the area
of the wing is \( 40 \mathrm{m}^{2} \) the net lifting force
on the wing is
A \( \cdot 2 \times 10^{4} \mathrm{N} \)
B. \( 4 \times 10^{4} \mathrm{N} \)
c. \( 6 \times 10^{4} \mathrm{N} \)
D. \( 8 \times 10^{4} \mathrm{N} \)
Subject: Maths
Find the solution of \( \frac{d y}{d x}+\frac{y}{x}= \)
\( \frac{1}{(1+\log x+\log y)^{2}} \)
A \( \cdot x y\left[1-(\log x y)^{2}\right]=-\frac{x^{2}}{2}+C \)
B. \( x y\left[1+(\log x y)^{2}\right]=\frac{x^{2}}{2}+C \)
c. \( x y\left[1+(\log x y)^{2}\right]=-\frac{x^{2}}{2}+C \)
D. \( x y\left[1-(\log x y)^{2}\right]=\frac{x^{2}}{2}+C \)
Subject: Maths
Construct a quadrilateral ABCD, when \( A B=4 \mathrm{cm}, B C=5 \mathrm{cm}, C D=6.5 \mathrm{cm} \)
\( \angle A B C=105^{\circ} \) and \( \angle D C B=80^{\circ} . \) The
length of AD is
\( \mathbf{A} \cdot 2 \cdot 9 \mathrm{cm} \)
B. \( 3.5 \mathrm{cm} \)
c. \( 5.5 \mathrm{cm} \)
D. \( 4.5 \mathrm{cm} \)
Subject: Maths
Area bounded by the region \( \boldsymbol{R} \equiv \)
\( \left\{(x, y): y^{2} \leq x \leq|y|\right\} \) is
A \( \cdot \frac{4}{3} \)
B. \( \frac{3}{4} \)
c. \( \frac{1}{3} \)
D.
Subject: Physics
The potential energy of a body of mass \( \boldsymbol{m} \) is \( \boldsymbol{U}=\boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{y} \)
where \( x \) and \( y \) are position co-ordinates of the particle. The acceleration of the particle is
A \( \cdot \frac{\left(a^{2}+b^{2}\right)^{1 / 2}}{m} \)
B. \( \frac{a^{2}+b^{2}}{m} \)
c. \( \frac{(a+b)^{1 / 2}}{m} \)
D. \( \frac{a+b}{m} \)
Subject: Chemistry
The IUPAC name of
\( \left[\boldsymbol{P t C l}\left(\boldsymbol{N H}_{2} \boldsymbol{C H}_{3}\right)\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}\right] \boldsymbol{C l} \) is :
A. diamminechloro(methylamine)platinum(II)chloride
B. (dimethylamine)chlorodiamminoplatinum(II)chloride
C. bis(ammine)chloro(methylamine)platinate(II)chloride
D. diaminechloro(mehylamine)platinum(II)chloride
Subject: Physics
topp
Q Type your question
spherical shell with inner radius \( c \) and
outer radius \( d \) (as shown in Fig). The
inner shell has total charge \( +2 q \) and the
outer shell has charge \( +4 q \). Calculate
the electric field in terms of \( q \) and the
distance \( r \) from the common centre of
the two shells for:
\( a<r<b \)
A. zero
в. \( \frac{1}{4 \pi \varepsilon_{8}} \frac{2 q}{r^{2}} \)
C. \( -\frac{1}{4 \pi \varepsilon_{0}} \frac{6 q}{r^{2}} \)
D. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{q}{r^{2}} \)
Subject: Maths
Express in radians \( 47^{\circ} 25^{\prime} 36^{\prime \prime} \)
A \( \cdot \frac{3472}{38921} \pi^{c} \)
B \( \cdot \frac{3247}{13562} \pi^{c} \)
c. \( \frac{3557}{13500} \pi^{c} \)
D. \( \frac{6582}{25700} \pi^{c} \)
Subject: Chemistry
If the standard internal energy change for the reaction \( O F_{2}(g)+H_{2} O(g) \longrightarrow \)
\( O_{2}(g)+2 H F(g), \) at \( 298 \mathrm{K} \) is \( x k J \)
[Given standard enthalpies of formation
in \( k J m o l^{-1} \) are \( O F_{2}(g)= \)
\( +20 ; H_{2} O(g)=-250 \) and \( H F(g)= \)
\( -270 . \)
Then \( -100 x \) is
Subject: Maths
f \( a, b, c \) are real numbers such that \( \left|\begin{array}{ccc}\boldsymbol{b}+\boldsymbol{c} & \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b} \\ \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{b}+\boldsymbol{c} \\ \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{b}+\boldsymbol{c} & \boldsymbol{c}+\boldsymbol{a}\end{array}\right|=0, \) then show
that either \( \boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c}=\boldsymbol{0} \) or, \( \boldsymbol{a}=\boldsymbol{b}=\boldsymbol{c} \)
Subject: Chemistry
A flash light cell reaction is :
\( \mathbf{2} M n O_{2}+Z n^{2+}+2 e^{-} \longrightarrow Z n+ \)
\( M n_{2} O_{4} . \) The current rating of the
flashlight is \( 4.6 \mathrm{mA} \). The time for which we can use this light, if we start
with 3.5 g of \( M n O_{2} \) is:
A \( .8 .44 \times 10^{5} s \)
B. \( 8.76 \times 10^{5} s \)
c. \( 8.96 \times 10^{5} s \)
D. None of these
Subject: Physics
A body of mass \( 5 k g \) is moving with a constant velocity of \( 18 \mathrm{m} / \mathrm{s} \) on a friction less horizontal surface. The force
required to keep this body moving with the same velocity is
\( A \cdot 5 N \)
B. \( 45 N \)
\( c .90 N \)
D. \( 0 N \)
Subject: Physics
What torque will increase angular velocity of a solid disc of mass \( 16 k g \)
and diameter \( 1 \mathrm{m} \) from zero to \( 2 \mathrm{rpm} \) in
\( \mathbf{8 s} ? \)
A \( \cdot \frac{\pi}{4} N-m \)
в. \( \frac{\pi}{2} N-m \)
\( ^{\mathbf{c}} \cdot \frac{\pi}{3} N-m \)
D. \( \pi N-m \)
Subject: Physics
A proton is fired from very far away towards a nucleus with charge \( Q=120 \mathrm{e} \) where e is the electronic charge. It makes a closest approach of \( 10 \mathrm{fm} \) to the nucleus. The de Broglie wavelength (in units of \( \mathrm{fm} \) ) of the proton at its start is :
(take the proton mass, \( \boldsymbol{m}_{\boldsymbol{p}}=(\mathbf{5} / \mathbf{3}) \times \)
\( 10^{-27} k g \) and
\( \boldsymbol{h} / \boldsymbol{e}=\mathbf{4 . 2} \times \mathbf{1 0}^{-15} \boldsymbol{J} . \boldsymbol{s} / \boldsymbol{C} ; \frac{1}{4 \pi \epsilon_{0}}=\mathbf{9} \times \)
\( \left.\mathbf{1 0}^{9} \boldsymbol{m} / \boldsymbol{F} ; \mathbf{1} \boldsymbol{f} \boldsymbol{m}=\mathbf{1 0}^{-\mathbf{1 5}} \boldsymbol{m}\right) \)
\( A \cdot 7 f m \)
B. 8 fm
\( c .9 f m \)
D. \( 10 \mathrm{fm} \)
Subject: Maths
From the following exact of the sine
table, the value of \( \sin 37^{0} 27^{\prime} \) is equal to
\( 12^{\prime} 18^{\prime} 24^{\prime} 30^{\prime} 36^{\prime} 42^{\prime} 48^{\prime} 54^{\prime} 1^{\prime} 2 \)
A . 0.6075
B. 0.6081
c. 0.6088
D. 0.6115
Subject: Maths
Calculate the scalar product of the following vectors. Find the vector c being given that it is perpendicular to the vectors \( \boldsymbol{a}= \)
\( \{2,3,-1\}, b=\{1,-2,3\} \) and
satisfies the condition
\( \boldsymbol{c} \cdot\{\boldsymbol{2} \boldsymbol{i}-\boldsymbol{j}+\boldsymbol{k}\}=-\boldsymbol{6} \)
Subject: Maths
The domain of the function \( y= \)
\( -2 x^{2}+6 x+5 \) is
\( \mathbf{A} \cdot x \in R \)
в. \( x \in(-2,0] \)
c. \( x \in[1,3) \)
D. \( x \in(1,3] \)
Subject: Chemistry
Which of the following shows the correct order of decreasing basicity in aqueous medium:
\( \mathbf{A} \cdot\left(C H_{3}\right)_{3} N>\left(C H_{3}\right)_{2} N H>C H_{3} N H_{2}>N H_{3} \)
в. \( \left(C H_{3}\right)_{2} N H>\left(C H_{3}\right)_{3} N>C H_{3} N H_{2}>N H_{3} \)
C \( \cdot\left(C H_{3}\right)_{2} N H>C H_{3} N H_{2}>\left(C H_{3}\right)_{3} N>N H_{3} \)
D. \( \left(C H_{3}\right)_{2} N H>C H_{3} N H_{2}>N H_{3}>\left(C H_{3}\right)_{3} N \)
Subject: Maths
If \( \boldsymbol{P}(\boldsymbol{A})=\frac{4}{5} \) and \( \boldsymbol{P}(\boldsymbol{B} / \boldsymbol{A})=\frac{2}{5}, \) find
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \)