AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
The real part of \( (1-\cos \theta+2 i \sin \theta)^{-1} \)
is?
A \( \cdot \frac{1}{3+5 \cos \theta} \)
в. \( \frac{1}{5-3 \cos \theta} \)
c. \( \frac{1}{3-5 \cos \theta} \)
D. \( \frac{1}{5+3 \cos \theta} \)
Subject: Chemistry
\( (A g+P b) \) alloy \( \frac{M e l t a n d}{Z i n c i s a d d e d}(A g+P b+ \)
\( Z n) m e l t \stackrel{C o o l}{\longrightarrow} \frac{\text {Layer} X}{\text {Layer} Y} \)
Select the correct statement based on
the above scheme:
A. Layer X contains Zn and Ag
B. Layer Y contains Pb and Ag but amount of silver in this layer is smaller than in layer \( x \)
c. \( x \) and \( Y \) are immiscilbe layer
D. All the correct statements
Subject: Maths
\( \lim _{x \rightarrow 0} \frac{1}{x} \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right) \) is equal to
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \cdot 2 \)
D. \( 1 / 2 \)
Subject: Physics
In the figure, pulleys are smooth and
strings are massless \( m_{1}=1 k g \) and
\( m_{2}=\frac{1}{3} k g . \) To keep \( m_{3} \) at rest, \( m_{3} \)
should be
A. \( 1 k g \)
в. \( \frac{1}{2} k g \)
c. \( \frac{4}{3} k g \)
D. \( 2 k \)
Subject: Maths
If \( \boldsymbol{y}=|\cos \boldsymbol{x}|+|\sin \boldsymbol{x}|, \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) at \( \boldsymbol{x}= \)
\( \frac{2 \pi}{3} \) is
A \( \cdot \frac{1-\sqrt{3}}{2} \)
B. 0
c. \( \frac{1}{2}(\sqrt{3}-1) \)
D. None of these
Subject: Maths
Suppose \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) is differentiable
function satisfying \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x})+ \)
\( \boldsymbol{f}(\boldsymbol{y})+\boldsymbol{x} \boldsymbol{y}(\boldsymbol{x}+\boldsymbol{y}) \) for every \( \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{R} \) if
\( f^{\prime}(0)=0, \) then which of the following hold(s) good?
This question has multiple correct options
\( A . f \) is an odd function
B. \( f \) is a bijective mapping
c. \( f \) has a minima but no maxima
D. \( f \) has an inflection point
Subject: Physics
Particle A and B moving in co-planar circular paths centered at O.They are
rotating in the same sense.Time periods of rotation of \( A \) and \( B \) around 0
\( \operatorname{are} \boldsymbol{T}_{A} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{T}_{B}, \) respectively, with \( \boldsymbol{T}_{B}> \)
\( T_{A} . \) Time required for \( B \) to make one
rotation around 0 relative to a is :
A \( \cdot T_{B}-T_{A} \)
в. \( T_{B}+T_{A} \)
c. \( \frac{T_{A} T_{B}}{T_{A}-T_{B}} \)
D. \( \frac{T_{B} T_{A}}{T_{B}-T_{A}} \)
Subject: Biology
The diagram given alongside represents the human heart in one phase of its activity. Study the same and then
answer the questions that follow:
(a)Name the phase.
(b)Which part of the heart is
contracting in this phase? Give a reason
to support your answer
(c)Name the parts numbered 1 to 6.
(d)What type of blood flows through the parts marked 1 and 2 respectively?
(e)How many valves are closed in this
phase?
Subject: Biology
Whcih of the following characteristics are related to group to which plant Marsilea belongs?(i) Plant body is not
differentiated into roots, stem and leaves.(ii) They have specialised tissue for the conduction of water and other
substances.(iii) They are predominanty aquatic in nature.(iv) They have naked embryos called spores.(v) They are called amphibians of plant kingdom.
A. (ii) and (iv) only
B. (iii), (iv) and (v)
\( c . \) (ii), (iii) and (iv)
D. (i), (iv) and (v)
Subject: Chemistry
\( \boldsymbol{B} \boldsymbol{r}_{2}+\boldsymbol{O} \boldsymbol{H}^{-}(\boldsymbol{H} \boldsymbol{o} \boldsymbol{t}) \rightarrow(\boldsymbol{P})+ \)
\( (Q) ;(P)+(Q)+H^{+} \rightarrow B r_{2} \)
\( (P) \) gives yellow precipitate with
\( A g N O_{3},(P) \) and \( (Q) \) are:
A. \( B r^{-}, B r O^{-} \)
B. \( B r^{-}, B r O_{3} \)
c. \( B r O^{-}, B r O_{3}^{-} \)
D. \( B r O^{-}, B r O 4 \)
Subject: Physics
The diameter of the moon is about 3500
km. What will be the diameter of the
image formed by a concave mirror of radius 3 m? Assume that the distance
of the moon is about \( 3 \cdot 5 \times 105 k m \)
\( A \cdot 5 \mathrm{mm} \)
B. 10 \( \mathrm{mm} \)
\( c \cdot 15 \mathrm{mm} \)
D. 20 mm
Subject: Physics
A bag of wheat weighs 100 kg. To what height should it be raised, so that its potential energy may be \( 9800 \mathrm{J}(\mathrm{g}=9.8 \)
\( \left.m s^{-2}\right\rangle \)
A .2
B. 100
\( c .50 \)
\( D \cdot 0 \)
Subject: Biology
How many of the given below features are associated with members of
chrysophyta?
(a) chief 'producers' in the oceans
(b) Shows photoautrophic nutrition
(c) Zygote develops into an auxospore
(d) From gritty soil
(e) Diatoms may be pennate type or centric type depending upon the
symmetry
A. Three
B. Five
c. Four
D. Two
Subject: Chemistry
\( \mathbf{5 0 m} \boldsymbol{L} \) of \( \mathbf{0 . 1 0} \boldsymbol{M} \boldsymbol{N} \boldsymbol{a}_{3} \boldsymbol{P} \boldsymbol{O}_{4}+\mathbf{5 0 m} \boldsymbol{L} \) of
\( \mathbf{0 . 1 0} \boldsymbol{M} \boldsymbol{N a H}_{2} \boldsymbol{O}_{4} \)
Subject: Physics
A gaseous mixture enclosed in a vessel
consists of one \( g \) mole of a gas \( A \) with \( \gamma=\left(\frac{5}{3}\right) \) and some amount of gas \( \mathrm{B} \) with \( \gamma=\frac{7}{5} \) at a temperature The
gasses \( A \) and \( B \) do not react with each
other and are assumed to be ideal Find
the number of \( g \) moles of the gas \( B \) if \( \gamma \) for the gaseous mixture is \( \left(\frac{19}{13}\right) \)
\( A \cdot 2 \)
\( B .5 \)
\( c \cdot 4 \)
D. 3
Subject: Physics
Let \( v_{1} \) be the frequency of the series
limited of the Lyman series, \( v_{2} \) be the frequency of the first line of the Lyman
series, and \( v_{3} \) be the frequency of the
series limited of the Balmer series.
Then:
A. \( v_{1}-v_{2}=v_{3} \)
В. \( v_{2}-v_{1}=v_{3} \)
C \( \cdot v_{3}=\frac{1}{2}\left(v_{1}+v_{3}\right) \)
D. \( v_{1}+v_{2}=v_{3} \)
Subject: Maths
The triangle \( A B C \) is defined by the vertices \( \boldsymbol{A}=(\mathbf{0}, \mathbf{7}, \mathbf{1 0}), \boldsymbol{B}=(-\mathbf{1}, \mathbf{6}, \mathbf{6}) \)
and \( C=(-4,9,6) . \) Let \( D \) be the foot of the attitude from \( B \) to the side \( A C \) then
\( B D \) is
A \( . \bar{i}+2 \bar{j}+2 \bar{k} \)
B. \( -\bar{i}+2 \bar{j}+2 \bar{k} \)
c. \( \bar{i}+2 \bar{j}-2 \bar{k} \)
D. \( \bar{i}-2 \bar{j}+2 \bar{k} \)
Subject: Maths
Let \( a=2 \hat{i}+\widehat{j}-2 \widehat{k} \) and \( b=\hat{i}+\widehat{j} . \) If \( c \) is
a vector such that \( \boldsymbol{a} . \boldsymbol{c}=|\boldsymbol{c}|,|\boldsymbol{c}-\boldsymbol{a}|= \)
\( 2 \sqrt{2} \) and the angle between \( a \times b \) and \( c \)
is \( 30^{\circ} . \) Then, \( [(a \times b) \times c] \) is equal to
A \( \cdot \frac{2}{3} \)
B. \( \frac{3}{2} \)
\( c \cdot 2 \)
D. 3
Subject: Chemistry
If a mixture of \( O_{2} \) and \( O_{3} \) is having
\( V_{r m s}=12.92 m / s \) at \( 300 K . \) Calculate
mole percentage of \( O_{2} \) in the mixture.
A. 35 \%
B. 20\%
c. \( 66.67 \% \) \%
D. none of these
Subject: Chemistry
If the bond energies of \( \boldsymbol{H}-\boldsymbol{H}, \boldsymbol{B} \boldsymbol{r}- \)
Br and \( H-B r \) are 433,192 and 364
kJ mol \( ^{-1} \) respectively. Then \( \Delta H^{o} \) for the
reaction \( \boldsymbol{H}_{\mathbf{2}(\boldsymbol{g})}+\boldsymbol{B} \boldsymbol{r}_{2(\boldsymbol{g})} \rightarrow \boldsymbol{2} \boldsymbol{H} \boldsymbol{B} \boldsymbol{r}_{(\boldsymbol{g})} \) is :
B. +103 k
\( c .+261 k \)
D. -103kJ
Subject: Maths
Prove that \( \frac{C_{1}}{C_{0}}+\frac{2 C_{2}}{C_{1}}+\frac{3 C_{3}}{C_{2}}+\ldots+\frac{n \cdot C_{n}}{C_{n-1}}= \)
\( \frac{n(n+1)}{2} \)
Subject: Physics
A solenoid with 600 turns per metre and
a radius of \( 2 \mathrm{cm}, \) carries a time varying
current \( i(t)=\left(6+4 t^{2}\right) \) A. The electric
field at a distance \( 4 \mathrm{cm} \) from the axis of
the solenoid at \( t=2 s \) will be \( (\operatorname{in} \mu \vee \mathrm{m} \)
-1 to the nearest integer
4.48
3.60
\( c .68 \)
38
Subject: Maths
If \( a, b \) are nonzero vectors and \( a \) is
perpendicular to \( b \), then \( a \) has nonzero
vector \( r \) satisfying \( r \cdot a=\alpha, \) for some
scalar \( \boldsymbol{\alpha}, \boldsymbol{a} \times \boldsymbol{r}=\boldsymbol{b} \) is
A \( \cdot \frac{\alpha a+(a+b)}{|a|^{2}} \)
в. \( \frac{\alpha a+a \times b}{|b|^{2}} \)
c. \( \frac{\alpha a-(a \times b)}{|a|^{2}} \)
D. \( \frac{\alpha a-(a \times b)}{|b|^{2}} \)
Subject: Maths
f \( \left|z_{1}\right|=2,\left|z_{2}\right|=3,\left|z_{3}\right|=4 \) and
\( \left|2 z_{1}+3 z_{2}+4 z_{3}\right|=4 \) then the absolute
value of \( 8 z_{3} z_{2}+27 z_{3} z_{1}+64 z_{1} z_{2} \)
equals
A .24
B . 48
\( c \cdot 72 \)
D. 96
Subject: Maths
The value of \( \int e^{x} \frac{1+n x^{n-1}-x^{2 n}}{\left(1-x^{n}\right) \sqrt{1-x^{2 n}}} d x \)
is equal to
A \( \cdot e^{x}(\sqrt{1-x^{2}})+c \)
B. \( e^{x} \frac{\sqrt{1+x^{2 n}}}{1+x^{2 n}}+c \)
C \( \frac{e^{x} \sqrt{1-x^{n}}}{1-x^{2 n}}+c \)
D. \( \frac{e^{x} \sqrt{1-x^{2 n}}}{1-x^{n}}+c \)
Subject: Chemistry
The uncertainty in the momentum of an
electron is \( 1.0 \times 10^{-5} \mathrm{kg} \mathrm{m} \mathrm{s}^{-1} . \) The
uncertainty of its position will be:
\( \left[h=6.626 \times 10^{-34} \mathrm{kg} \mathrm{m}^{2} \mathrm{s}^{-1}\right] \)
A \( \cdot 1.05 \times 10^{-28} \mathrm{m} \)
B . \( 1.05 \times 10^{-26} \mathrm{m} \)
c. \( 5.27 \times 10^{-30} \mathrm{m} \)
D. \( 5.25 \times 10^{-28} \mathrm{m} \)
Subject: Physics
\( A, B \) and \( C \) are the three coils of
conductor having different number of
turns, wound around a soft iron ring as
shown in the figure. Ends of coils \( B \) and
\( C \) are connected to the galvanometers.
The observation that can be made when
ends of coil \( A \) are connected to an A.C.
source is
A. Same electric current is induced in \( B \) and \( C \)
B. No electric current is induced in \( B \) and \( C \)
c. Induced electric current is more in \( B \) than in \( C \)
D. Induced electric current is less in \( B \) than in \( C \)
Subject: Chemistry
Catalyst used in dimerisation of
acetylene to prepare chloroprene is:
A. \( H g S O_{4}+H_{2} S O_{4} \)
в. \( C u_{2} C l_{2} \)
c. \( C u_{2} C l_{2}+N H_{4} C l \)
D. \( C u_{2} C l_{2}+N H_{4} O H \)
Subject: Maths
Solve: \( 4 x+\frac{6}{y}=15 \) and \( 6 x-\frac{8}{y}=14 \)
Hence find the value of \( k, \) if \( y=k x-2 \)
A \( \cdot x=4, y=1 \) and \( k=\frac{2}{3} \)
в. \( x=5, y=3 \) and \( k=\frac{3}{5} \)
c. \( _{x}=3, y=2 \) and \( k=\frac{4}{3} \)
D. \( x=1, y=2 \) and \( k=\frac{9}{2} \)
Subject: Maths
Given below are some points, with thei
\( \boldsymbol{P}(\mathbf{4}, \mathbf{3}), \boldsymbol{Q}(-\mathbf{3}, \mathbf{2}), \boldsymbol{R}(\mathbf{5}, \mathbf{1}), \boldsymbol{S}(\mathbf{0},-\mathbf{4}) \)
What is the \( x- \) coordinate of point \( P \)
\( ? \)
Subject: Chemistry
On heating with concentrated \( N a O H \)
solution in an inert atmosphere of \( \boldsymbol{C O}_{2} \)
white phosphorous gives a gas.Which of the following statement is incorrect
about the gas?
A . It is less basic than \( N H_{3} \)
B. It is more basic than \( N H_{3} \)
c. It is highly poisonous and has smell like rotten fish
D. It's solution in water decomposes in the presence of light
Subject: Chemistry
Depending on Lewis structure,
\( O F_{2}, O_{2} F_{2} \) and \( S_{2} F_{2} \) which of the
following statement is incorrect?
\( \mathbf{A} \cdot S_{2} F_{2} \) has two possible isomeric structures, whereas
\( O_{2} F_{2} \) has only one
B. The bond angle in \( O F_{2} \) is greater than in \( O C l_{2} \)
C. The O-O bond length in \( O_{2} F_{2} \) is smaller than in \( H_{2} O_{2} \)
D. The O-F bond length in \( O_{2} F_{2} \) is larger than in \( O F_{2} \)
Subject: Chemistry
Assertion
When PhCHO is made to react in
\( O D^{\ominus} / D_{2} O \) no \( D \) is incorporated into
the \( C H_{2} \) of \( P h C H_{2} O H, P h C O O^{-} \)
mixture during cannizaro's reaction
Reason
Intermolecular \( \boldsymbol{H}^{\ominus} \) transfer takes place
in the rate determining step, with out getting free in solution
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 incorrect but Reason is correct
D. Both Assertion and Reason are correct
Subject: Physics
A clear transparent glass sphere \( (\mu= \)
1.5) of radius \( R \) is immersed in a liquid of refractive index \( 1.25 . \) A parallel beam of light incident on it will converge to a point. The distance of this point from the center will be
A. \( -3 R \)
в. \( +3 R \)
c. \( -R \)
\( \mathrm{D} \cdot+R \)
Subject: Chemistry
Select the one which describe the best
among all the given options. To determine whether a water solution of
\( N a_{2} S_{2} O_{3} \) at room temperature is
supersaturated, one can:
A. heat the solution to its boiling point
B. add water to the solution
c. add a crystal of \( N a_{2} S_{2} O_{3} \) to the solution
D. acidify the solution
E. cool the solution to its freezing point
Subject: Chemistry
The compound \( ^{\prime} C^{\prime} \) in the following
reaction is :
\( \boldsymbol{C}_{7} \boldsymbol{H}_{8} \frac{3 C l_{2} / \text {Delta}}{\longrightarrow} \boldsymbol{A} \frac{\boldsymbol{B r}_{2} / \boldsymbol{F e}}{\boldsymbol{\beta}} \boldsymbol{B} \frac{\boldsymbol{Z n} / \boldsymbol{H C l}}{\boldsymbol{1}} \)
\( C \)
A. o-bromotoluene
B. m-bromotoluene
c. p-bromotoluene
D. 3-bromo-2, 4, 6-trichlorotoluene
Subject: Maths
Urn \( A \) contains 6 red and 4 black balls
and urn \( B \) contains 4 red and 6 black
balls. One ball is drawn at random from
urn \( A \) and placed in urn \( B \). Then one bal
is drawn at random from urn \( B \) and
placed in urn \( A \). If one ball is now drawn at random from urn \( A \), the probability
that it is found to be red is \( 4 k / 55 . \) Find
the value of \( k \)
Subject: Physics
A parallel plate capacitor of plate area \( A \) and plate separation \( d \) is charged to
potential difference \( V \) and then the battery is disconnected. A slab of
dielectric constant \( k \) is then inserted
between the plates of the capacitor so as to fill the space between the plates. If
\( Q, E \) and \( W \) denote respectively, the magnitude of charge on each plate, the electric field between the plates (after
the slab is inserted) and the work done
on the system, in question, in the process of inserting the slab, then:
This question has multiple correct options
A \( \cdot Q=\frac{\epsilon_{0} A V}{d} \)
в. \( Q=\frac{\epsilon_{0} k A V}{d} \)
c. \( \quad E=\frac{V}{k d} \)
D. \( W=-\frac{\epsilon_{0} A V^{2}}{2 d}\left(1-\frac{1}{k}\right) \)
Subject: Physics
Light with an energy flux of \( 18 W / c m^{2} \) falls on a non-reflecting surface at normal incidence. The pressure exerted on the surface is:
A. \( 2 N / m^{2} \)
B . \( 2 \times 10^{-4} N / m^{2} \)
c. \( 6 N / m^{2} \)
D. \( 6 \times 10^{-4} N / m^{2} \)
Subject: Biology
Several scientist gave different definition of species. One of those
definitions, a population or group of populations whose members have the potential in nature to interbreed and produce fertile offspring. Which of the statement is related to this definition?
A. Species that reproduce sexually
B. Species that reproduce asexually only
c. specie that form sterile hybrids upon mating
D. Extinct forms of life, based on fossil evidence
E. Species living on separate continents
Subject: Chemistry
The doubly ionized lithium atom is
hydrogen-like with the atomic number \( z=3 . \) Find the wavelength of the
radiation required to excite the electron
in \( L i^{2+} \) from the first to the third Bohr
orbit is:
\( \left[\text { Given: } \frac{1}{\boldsymbol{R}_{\boldsymbol{H}}}=\mathbf{9 1 2} \boldsymbol{A}\right] \)
\( \mathbf{A} \cdot 114 \stackrel{\circ}{A} \)
B \( \cdot 156^{\circ} \)
\( \mathbf{c} \cdot_{180 \stackrel{\circ}}{\mathbf{h}} \)
D \( \cdot 201 \stackrel{\circ}{A} \)
Subject: Physics
The condition of no-slip in rotation of a
pulley attached to a mass using a
string refers to
\( \mathbf{A} \cdot v=R \omega ; v \) is the linear velocity, \( \omega \) is the angular
velocity and \( \mathrm{R} \) is the radius
B. \( a=R \alpha ; a \) is the linear acceleration, \( \alpha \) is the angular acceleration and \( \mathrm{R} \) is the radius
C \( . v=R \omega \) and \( a=R \alpha ; v \) is the linear velocity, \( \omega \) is the
angular velocity, \( \alpha \) is the angular acceleration and \( \mathrm{R} \) is
the radius
\( ^{\mathrm{D}} T=M \frac{v^{2}}{R} ; T \) is the tension in the string, \( v \) is the linear
velocity, and \( R \) is the radius
Subject: Physics
The distance \( x \) covered in time \( t \) by a
body having initial velocity \( v_{0} \) and
having constant acceleration \( a \) is given
by \( \boldsymbol{x}=\boldsymbol{v}_{0} \boldsymbol{t}+\mathbf{1} / \mathbf{2} \boldsymbol{a} \boldsymbol{t}^{2} . \) This result follows
from :
A. newton's Ist law
B. newton's IInd law
c. newton's IIIrd law
D. none of the above
Subject: Maths
If \( \overrightarrow{e_{1}}=(1,1,1) \) and \( \overrightarrow{e_{2}}=(1,1,-1) \) and
\( \vec{a} \) and \( \vec{b} \) are two vectors such that \( \overrightarrow{e_{1}}=2 \vec{a}+\vec{b} \) and \( \overrightarrow{e_{2}}=\vec{a}+2 \vec{b}, \) then
the angle between \( \vec{a} \) and \( \vec{b} \) is
A \( \cdot \cos ^{-1}\left(\frac{7}{9}\right) \)
B. \( \cos ^{-1}\left(\frac{7}{11}\right) \)
\( ^{\mathrm{c}} \cdot \cos ^{-1}\left(-\frac{7}{11}\right) \)
D. \( \cos ^{-1}\left(\frac{6 \sqrt{2}}{11}\right) \)
Subject: Physics
If two vectors are \( \vec{A}=2 \hat{i}+\hat{j}-\hat{k} \) and \( \vec{B}=\hat{j}-4 \hat{k} \cdot \vec{A} \times \vec{B} \) is perpendicular to
This question has multiple correct options
A . \( \vec{A} \)
в. \( \vec{B} \)
c. \( \vec{A}+\vec{B} \)
D . \( \vec{A}-\vec{B} \)
Subject: Maths
In the Venn diagram, the universal set, \( \boldsymbol{\xi}=\boldsymbol{P} \cup \boldsymbol{Q} \cup \boldsymbol{R} \)
Which of the four regions labelled \( A, B, C \)
and D represents the sets \( \boldsymbol{P} \cap \boldsymbol{Q} \cap \boldsymbol{R} \) ?
\( A \)
B
\( c . c \)
\( D \)
Subject: Physics
In figure the voltmeter and ammeter
shown are ideal. Then voltmeter and
ammeter readings, respectively, are:
A . \( 32.978 \vee, 3 \mathrm{A} \)
B. 3 V, 0.236 A
c. \( 120 \vee, 4.198 \) A
D. \( 120 \vee, 3 \mathrm{A} \)
Subject: Physics
The force of attraction between the
plates of a charged condenser is :
A \( \cdot q^{2}\left(2 \varepsilon_{0} A\right) \)
B \( \cdot q^{2}\left(2 \varepsilon_{0} A^{2}\right) \)
\( \mathbf{c} \cdot q^{2} /\left(2 \varepsilon_{0} A\right) \)
D. none of these
Subject: Maths
Factorise the expressions and divide them as directed.
\( 12 x y\left(9 x^{2}-16 y^{2}\right) \div 4 x y(3 x+4 y) \)
A. \( 3(3 x-4 y) \)
B. \( 3(3 x+4 y) \)
c. \( 4(3 x-4 y) \)
D. \( 3(4 x-3 y) \)
Subject: Physics
A constant power is supplied to a rotating disc. The relationship between the angular velocity \( (\omega) \) of the disc and
number of rotations \( n \) made by the disc
is governed by:
A. \( \quad_{\omega} \propto n^{\frac{1}{3}} \)
в. \( \quad_{\omega} \propto n^{\frac{2}{3}} \)
c. \( \quad_{\omega} \propto n^{\frac{3}{2}} \)
D. \( \omega \propto n^{2} \)
Subject: Physics
A parallel plate condenser of capacity \( 10 \mu F \) is connected to an A.C. supply
voltage \( e=4 \sin (100 \pi t) . \) The
maximum displacement current:
A. \( 4 \pi \mu A \)
в. \( 4 \pi m A \)
c. \( 2.8 \pi \mu A \)
D. \( 2 \pi \mu A \)
Subject: Physics
A \( 10 \mathrm{kw} \) drilling machine is used to dril a bore in a small aluminium block of
mass \( 8.0 \mathrm{kg} . \) How much is the rise in temperature of the block in 2.5 minutes,
assuming \( 50 \% \) of power is used up in heating the machine itself or lost to the
surroundings. Specific heat of
aluminium \( =\mathbf{0 . 9 1} \boldsymbol{J} \boldsymbol{g}^{-1} \boldsymbol{K}^{-1} \)
Subject: Physics
Charges \( Q \) each are placed at each of two opposite corners of a square. Charges \( q \) each are placed at each of
the other two corners. Find the relation
between \( q \) and \( Q, \) when the net force on
Q is zero.
A \( \cdot_{q}=-\frac{3 Q}{2 \sqrt{2}} \)
в. \( _{q}=+\frac{Q}{2 \sqrt{2}} \)
c. \( _{q=-\frac{Q}{\sqrt{2}}} \)
D. \( _{q}=-\frac{Q}{2 \sqrt{2}} \)
Subject: Chemistry
What is the concentration of nitrate
ions if equal volumes of \( 0.1 M A g N O_{3} \)
and \( 0.1 M \) NaCl are mixed together?
\( \mathbf{A} \cdot 0.1 \mathrm{M} \)
B. 0.2 М
c. 0.05 M
D. 0.25 м
Subject: Physics
\( \frac{\boldsymbol{\alpha}}{\boldsymbol{t}^{2}}=\boldsymbol{F} \boldsymbol{v}+\frac{\boldsymbol{\beta}}{\boldsymbol{x}^{2}} \)
Find the dimensional formula for \( [\boldsymbol{\alpha}] \)
and \( [\beta] \) using the given equation
(here \( t= \) time, \( F= \) force, \( v= \) velocity, \( x= \) distance)
Subject: Maths
A rectangle DEFG is plotted in \( X Y \) plane. The co-ordinates of D , E , F and G \( \operatorname{are}(2,2),(9,2),(9,10) \) and (2,10)
Find the new co-ordinates of D when
DEFG is rotated \( 270^{\circ} \) around origin.
A \( \cdot(-2,-2) \)
в. (2,-2)
c. (2,4)
(年. \( (2,4)) \)
D. (-2,4)
Subject: Chemistry
\( 0.124 g m \) of an organic compound containing phosphorus gave \( 0.222 g m \)
of \( M g_{2} P_{2} O_{7} \) the usual analysis.
Calculate the percentage of phosphorous in the compound. \( (M g= \)
\( \mathbf{2 4}, \boldsymbol{P}=\mathbf{3 1}) \)
A .25
в. 15
\( c .62 \)
D. 50
Subject: Physics
Which of the following information is
incorrect regarding the above graph
A. The body travels \( 15 \mathrm{m} \) in the first 3 seconds.
B. The speed of the body after 5 seconds is zero
C. The initial speed of the body is \( 10 \mathrm{m} / \mathrm{s} \).
D. The body travels \( 25 \mathrm{m} \) in the first 6 seconds.
Subject: Maths
The derivative of \( f(\tan x) \) with respect
\( \operatorname{tog}(\sec x) \) at \( \quad x=\frac{\pi}{4}, \) where \( f^{\prime}(1)= \)
\( \mathbf{2} ; \quad \boldsymbol{g}^{\prime}(\sqrt{\mathbf{2}})=\mathbf{4} \) is
A \( \cdot \frac{1}{\sqrt{2}} \)
B. \( \sqrt{2} \)
c. 1
D.
Subject: Physics
A piece of cork is floating on water in a
small tank. The cork oscillates up and
down vertically when small ripples pass
over the surface of water. The velocity of
the ripples being \( 0.21 m s^{-1}, \) wave
length \( 15 \mathrm{mm} \) and amplitude \( 5 \mathrm{mm} \), the
maximum velocity of the piece of cork is \( \left(\boldsymbol{\pi}=\frac{\mathbf{2 2}}{\mathbf{7}}\right) \)
A. \( 0.44 \mathrm{ms}^{-1} \)
B. \( 0.24 \mathrm{ms}^{-1} \)
c. \( 2.4 \mathrm{ms}^{-1} \)
D. \( 4.4 \mathrm{ms}^{-1} \)
Subject: Chemistry
The main oxides formed on combustion
of \( L i, N a \) and \( K \) in excess of air are
respectively:
A. \( L i O_{2}, N a_{2} O_{2} \) and \( K_{2} O \)
в. \( L i_{2} O_{2}, N a_{2} O_{2} \) and \( K O_{2} \)
c. \( L i_{2} O, N a_{2} O_{2} \) and \( K O_{2} \)
D. \( L i_{2} O, N a_{2} O \) and \( K O_{2} \)
Subject: Physics
In Fraunhoffer diffraction experiment, is the distance between screen and the obstacle, b is the size of obstacle and \( \lambda \)
is wavelength of incident light. The general condition for the applicability of Fraunhoffer diffraction is:
\( ^{\mathbf{A} \cdot} \cdot \frac{b^{2}}{l \lambda}>>1 \)
B. \( \frac{b^{2}}{l \lambda}=1 \)
c. \( \frac{b^{2}}{l \lambda}<<1 \)
D. \( \frac{b^{2}}{l \lambda} \neq 1 \)
Subject: Maths
Let \( R \) be the set of real numbers and the
functions \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) and \( \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be
defined by \( f(x)=x^{2}+2 x-3 \) and
\( g(x)=x+1 . \) Then the value of \( x \) for
which \( f(g(x))=g(f(x)) \) is
A . -1
B.
c. 1
\( D \)
Subject: Physics
The coefficient of friction between a
car's wheels and a roadway is \( 0.5 . \) The least distance in which the car can
accelerate from rest to a speed of 72
\( \boldsymbol{k m p h} \) is \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m s}^{-2}\right) \)
A . \( 10 m \)
в. \( 20 m \)
\( c .30 m \)
D. \( 40 m \)