AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Biology
Select the correct option for contractile proteins from the given diagram labelled as (a) and
\( A \cdot a=G-a c \operatorname{tin} ; b=F-\operatorname{actin} \)
B. a = Meromyosin; b = Myosin
c. a = Tropomyosin; b = Troponin
D. a = Troponin; b = Tropomyonin
Subject: Physics
In a region of space the electronic field is given by \( \vec{E}=(8 \hat{i}+4 \hat{j}) N / C . \) The electric
flux through a surface of area \( 10 \mathrm{m}^{2} \) in the
x-y plane is
A. 80 units
B. 40 units
c. 120 units
D. zero
Subject: Physics
A positive charge \( +Q \) is fixed at a point
A. Another positively charged particle of mass \( \mathrm{m} \) and charge \( +\mathrm{q} \) is projected from a point B with velocity u as shown in the figure. The point B is at a large distance from \( A \) and at a large distance d from the line AC. The initial velocity is parallel to the line AC. The point \( C \) is at very large distance from A. Find the minimum distance (in meter) of \( +q \)
from \( +Q \) during the motion. \( [\text { take } Q q= \)
\( \left.4 \pi \epsilon_{0} m u^{2} d\right] \)
A. \( d(1+\sqrt{2}) \)
B . \( d(\sqrt{2}-1) \)
c. \( \frac{d}{(1+\sqrt{2})} \)
D. \( \frac{d}{(\sqrt{2}-1)} \)
Subject: Physics
A mass \( \mathrm{M} \) is broken in two parts: \( \mathrm{m} \) and \( (M-m) . \) Relation between \( m \) and \( M s o \)
that the force of gravitation between the two parts is maximum is.
\( A \cdot m M=2 \)
в. \( m=\frac{M}{2} \)
c. \( M=m^{2} \)
D. None of these
Subject: Maths
Let \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{3}, \mathbf{5}, \mathbf{7}\} \) and \( \boldsymbol{B}=\{\mathbf{2}, \mathbf{4}, \mathbf{6}, \mathbf{8}\} \)
be two sets \( R \) be a relation from \( A \) to \( B \)
defined by the phrase \( "(x, y) \in R \Rightarrow \)
\( \boldsymbol{x}>\boldsymbol{y}^{\prime \prime} . \) Find relation \( \boldsymbol{R} \) and its domain
and range
Subject: Chemistry
Calculate the minimum and maximum
number of electrons which may have
magnetic quantum number, \( \boldsymbol{m}=+\mathbf{1} \) and spin quantum number, \( s=-\frac{1}{2} \) in Chromium \( (\mathrm{Cr}) \)
A . 0,1
в. 1,2
c. 4,6
D. 2,
Subject: Chemistry
Q Type your question
Clapeyron equation describes this
relationship. The Clausius-Clapeyron equation is :
\( \ln \left(P_{v a p o u r}\right)=-\frac{\Delta H_{v a p o u r}}{R}\left[\frac{1}{T}\right]+C \)
According to the graph, at high temperatures, which substance has
the greatest vapour pressure?
\( A \cdot w \)
B. \( x \)
\( c \)
\( D \)
Subject: Chemistry
Statement \( (\mathrm{A}): C I_{2}+2 N a O H \rightarrow \)
\( N a C I+N a O C I+H_{2} O \) is a
disproportion reaction Statement \( (\mathrm{B}): \boldsymbol{A} \boldsymbol{g}_{(a q)}^{2+}+\boldsymbol{A} \boldsymbol{g}_{(g)} \rightarrow \)
\( \mathbf{2} \boldsymbol{A} \boldsymbol{g}_{(a q)}^{+} \) is comproportionation reaction Statement \( (\mathrm{C}): 2 \mathrm{Ca} \mathrm{CO}_{3} \stackrel{\Delta}{\longrightarrow} 2 \mathrm{CaO}+ \)
\( 2 C_{2} \) is a combination reaction.
A. All the statement are correct
B. All the statement are incorrect
C. \( A, B \) are correct and \( C \) is incorrect
D. \( A, B \) are incorrect and \( C \) is correct
Subject: Maths
Smith invested \( \$ 5000 \) for two years. For
the first year, the rate of interest was \( 7 \% \) and the second year it was \( 8.5 \% \)
How much interest did he earn at the
end of the two year period?
A . \( \$ 804.75 \)
в. \( \$ 604.54 \)
\( c . \$ 304.54 \)
D. None of these
Subject: Chemistry
In the reaction series:
\( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{C l} \frac{\boldsymbol{N H}_{\boldsymbol{3}}}{\boldsymbol{C u _ { 2 } \boldsymbol { O } , \mathbf { 2 0 0 } ^ { \boldsymbol { o } } \boldsymbol { C }}} \boldsymbol{X} ; \boldsymbol{X} \frac{\boldsymbol{H} \boldsymbol{N O}_{2}}{\boldsymbol{0}-\boldsymbol{5}^{0} \boldsymbol{C}} \)
\( Z ; X+Z \rightarrow A, \) the number of \( \sigma \) and \( \pi \)
bonds in \( A \) are:
\( \mathbf{A} \cdot 25 \sigma \) and \( 6 \pi \)
B . 25 \( \sigma \) and \( 7 \pi \)
c. \( 27 \sigma \) and \( 7 \pi \)
D. \( 27 \sigma \) and \( 6 \pi \)
Subject: Chemistry
\( 10 \mathrm{L} \) of hard water required \( 0.56 \mathrm{g} \) of lime \( (C a O) \) for removing hardness.
Hence, temporary hardness in ppm of \( \boldsymbol{C a C O}_{3} \) is :
A . 100
в. 200
c. 10
D. 20
Subject: Physics
A ray of light denser medium strikes a
rarer medium at an angle of incidence \( i \)
shown in the figure. The reflected and
refracted rays make angle \( 90^{\circ} \) with
each other. The angles of reflection and
refraction are \( r \) and \( r^{\prime} . \) The critical angle
is :
A \( \cdot \sin ^{-1}(\cot r) \)
B \( \cdot \sin ^{-1}(\tan i) \)
c. \( \sin ^{-1}\left(\tan r^{\prime}\right) \)
D \( \cdot \tan ^{-1}(\sin i) \)
Subject: Chemistry
Assertion
Both Be and Al can form complexes
\( \operatorname{such} \operatorname{as} B e F_{4}^{-2} \) and \( A I F_{6}^{3-} \)
respectively, \( B e F_{6}^{-3} \) is not formed.
Reason
In the case of Be, no vacant d-orbitals
are present in its outermost shell.
These questions consist of two statements each, printed as assertion
and reason. While answering these questions you are required to choose any one of the following four responses.
A. If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion, then mark
B. If both Assertion and Reason are true but the Reason is not the correct explanation of the Assertion, then mark
C. If Assertion is true statement but Reason is false, then mark
D. If both Assertion and Reason are false statements, then mark
Subject: Chemistry
The total number of isomers shown by
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)_{2}\right]\left(\boldsymbol{N} \boldsymbol{O}_{3}\right) \) complex is:
A . 10
B. 6
\( c \cdot 4 \)
D. 12
Subject: Chemistry
For the given cell \( \boldsymbol{P t}_{D_{2} \mid D^{+}} \| \boldsymbol{H}^{+}|\boldsymbol{P t}| \boldsymbol{H}_{2} \)
if \( \boldsymbol{E}_{D_{2} \mid D^{\oplus}=0.003 V}^{\ominus}, \) what will be the ratio of \( D^{\oplus} \) and \( H^{\oplus} \) at \( 25^{\circ} C \) when he
reaction: \( D_{2}+2 H^{\oplus} \rightarrow 2 D^{\oplus}+H_{2} \)
attains equilibrium:
A .1 .34
B . 1.24
c. 1.124
D. 1.45
Subject: Chemistry
Equivalent conductance and molar
conductance of \( \boldsymbol{F e}_{2}\left(\boldsymbol{S} \boldsymbol{O}_{4}\right)_{3} \) are related
by relation:
\( \mathbf{A} \cdot \wedge_{e}=\Lambda_{m} \)
B \( \cdot \wedge_{e q}=\frac{\Lambda_{m}}{3} \)
\( \mathbf{C} \cdot \wedge_{e q}=3 \wedge_{m} \)
D \( \cdot \wedge_{e q}=\frac{\Lambda_{m}}{6} \)
Subject: Physics
A pulley has a light rope running over it, with a \( 10 N \) weight on one side and a
\( 20 N \) weight on the other. Ropes always
pull with equal force on each end; this is called tension. If the masses are
allowed to fall, what is the tension, \( \boldsymbol{T} \) in
the rope?
A . \( 0 N \)
В. \( 1 N<T<10 N \)
\( c \cdot 10 N \)
D. None of these
Subject: Physics
A rocket with a lift-off mass \( 3.5 \times 10^{4} \)
kg is blasted upwards with an initia
acceleration of \( 10 m / s^{2} . \) Then the initial
thrust of the blast is:
A \( \cdot 3.5 \times 10^{5} N \)
в. \( 7.0 \times 10^{5} N \)
c. \( 14.0 \times 10^{5} N \)
D. \( 1.75 \times 10^{5} N \)
Subject: Physics
Three \( 10 \Omega, 2 W \) resistors are as in
figure. The maximum possible voltage
between points \( A \) and \( B \) without exceeding the power limits of any of the
resistors is
\( \mathbf{A} \cdot 5 \sqrt{3} V \)
B. \( 3 \sqrt{5} V \)
\( \mathbf{c} .15 V \)
\( D \cdot \frac{5}{2} V \)
Subject: Physics
The resistance of a wire at temperature
\( 30^{\circ} \mathrm{C} \) is found to be \( 10 \Omega . \) Now to
increase the resistance by \( 10 \%, \) the temperature of the wire must be ( The temperature coefficient of resistance of the material of the wire is \( 0.002^{\circ} \mathrm{C}^{-1} \)
and reference temperature is \( 0^{\circ} C \) ).
A \( \cdot 35^{\circ} \mathrm{C} \)
B . \( 36^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 33^{\circ} C \)
D. \( 83^{\circ} \mathrm{C} \)
Subject: Maths
If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) is defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{2} \boldsymbol{x} \)
\( \mathbf{3} \forall \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{R}, \) which of the following is / are
correct?
\( \mathbf{A} \cdot f \) is a function
B. \( f \) is an injection
c. \( f \) is surjection
D. \( f \) is not onto
Subject: Physics
A boy is sitting on a horizontal platform in the shape of a disc at a distance of
\( 5 m \) from its center. The boy begins to
slip when the speed of wheel exceeds 10rpm. The coefficient of friction
between the boy and platform is \( (g= \)
\( \left.10 m s^{-2}\right) \)
A \( \cdot \pi^{2} / 6 \)
в. \( \pi^{2} / 18 \)
c. \( \pi / 6 \)
D. \( \pi / 2 \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{cc}2 & 0 \\ 5 & -3\end{array}\right] \) and \( B=\left[\begin{array}{cc}-2 & 1 \\ 3 & -1\end{array}\right] \)
then find the trace of \( \left(A B^{T}\right)^{T} \)
Subject: Physics
4 charges are placed each at a distance
a' from origin. The dipole moment of
configuration is :
A \( \cdot 2 q a \hat{j} \)
в. \( 3 q a \hat{j} \)
\( \mathbf{c} \cdot 2 a q[\hat{i}+\hat{j}] \)
\( 0 . \) none
Subject: Physics
A uniform ladder of length \( 5 m \) is placed against the wall as shown in the figure. If coefficient of friction \( \mu \) is the same for
both the walls. what is the minimum
value of \( \mu \) for it not to slip?
A \( \cdot \mu=1 / 2 \)
B. \( \mu=1 / 4 \)
c. \( \mu=1 / 3 \)
D. \( \mu=1 / 5 \)
Subject: Maths
The number of rational numbers \( \frac{\boldsymbol{p}}{\boldsymbol{q}} \)
where \( \boldsymbol{p}, \boldsymbol{q} \in \mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}, \mathbf{6} \) is
A . 23
B. 32
\( c \cdot 36 \)
D. 63
Subject: Physics
A particle with a specific charge \( \mathrm{S} \) is fired with a speed \( V \) towards a wall at a
distance d, perpendicular to the wall. The minimum magnetic field that must exist in this region for the particle to not hit the wall is :
A \( \cdot \frac{V}{s d} \)
в. \( \frac{2 V}{s d} \)
c. \( \frac{V}{2 s d} \)
D. \( \frac{V}{4 s d} \)
Subject: Chemistry
The density of water is not same at all temperatures because of its anomalous expansion. The density is maximum at:
\( \mathbf{A} \cdot 0^{\circ} C \)
B. \( 4^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 40^{\circ} C \)
D. \( 100^{\circ} \mathrm{C} \)
Subject: Physics
A polnt sources \( \boldsymbol{s} \) emicting IIght of
wavelength 600 nm is placed at a very
small height \( h \) above a flat reflecting
surface \( \boldsymbol{A B} \) (see figure). The intensity
of the reflected light is \( 36 \% \) of the
incident intensity. Interference fringes
are observed on a screen placed parallel
to the reflecting surface at a very large
distance \( D \) from it.What is the shape of
the interference fringes on the screen?
A. Circular
B. helical
C . eliptical
D. spiral
Subject: Chemistry
Which statement is incorrect?
A. Catalytic decomposition of \( K C l O_{3} \) by \( M n O_{2} \) is an example of homogeneous catalysis.
B. Only the surface atoms in an adsorbent play an active role in adsorption.
C. The rate of adsorption is very rapid in the beginning but decreases gradually until equilibrium is attained.
D. Absorption proceeds at a steady rate.
Subject: Physics
Two particles of mass \( 1 \mathrm{kg} \) and \( 2 \mathrm{kg} \) are located at \( x=0 \) and \( x=3 \) m. Find the position of their center of mass.
\( A \cdot 4 m \)
B. 2 \( m \)
\( c \cdot 6 m \)
D. 8 m
Subject: Maths
Jabu is building a new flower bed and is using a bucket to carry soil from another part of the garden to the new bed. He knows his bucket has a
capacity of 10 litres. If he has 300 litres of soil, and for each trip he fills the bucket to the top, how many trips will Jabu have to make with bucket?
A . 10
B . 20
c. 30
D. 40
Subject: Maths
The perpendicular bisector of the line segment joining \( \boldsymbol{P}(1,4) \) and \( \boldsymbol{Q}(\boldsymbol{k}, \boldsymbol{3}) \)
has \( \boldsymbol{y}- \) intercept \( -4 . \) Then a possible
value of \( k \) is \( ? \)
A . -2
B. -4
c.
D. 2
Subject: Chemistry
Which of the following factors is of no significance for roasting sulphide ores to the oxides and not subjecting the sulphide ores to carbon reduction directly?
A. Metal sulphides are thermodynamically more stable \( \operatorname{than} C S_{2} \)
B. \( C O_{2} \) is thermodynamically more stable than \( C S_{2} \)
c. Metal sulphides are less stable than the corresponding oxides
\( \mathrm{D} \cdot \mathrm{CO}_{2} \) is more volatile than \( \mathrm{CS}_{2} \)
Subject: Chemistry
Select whether the following combinations of reactants will react by
substitution \( \left(S_{N^{1}} \text { Or } S_{N^{2}} \) mechanism) \right.
elimination \( \left(E_{1} \text { or } E_{2} \) mechanism) \right.
A \( \cdot\left(S_{N^{1}}\right) \)
в. \( \left(S_{N^{2}}\right) \)
\( c \cdot E_{1} \)
D. \( E_{2} \)
Subject: Physics
The value of universal gravitational
constant \( G \) is-
A. \( 6.67 \times 10^{-11} \frac{N m^{2}}{k g} \)
в. \( 6.67 \times 10^{-11} \frac{N m^{2}}{k g^{2}} \)
c. \( 66.7 \times 10^{-11} \frac{N m^{2}}{k g^{2}} \)
D. \( _{66.7} \times 10^{-11} \frac{N m^{2}}{k g} \)
Subject: Chemistry
Assertion
Reaction of liquor ammonia with nitric acid is a neutralization reaction.
Reason
Ammonia in the gaseous form or in
aqueous solution as ammonium
hydroxide neutralizes the nitric acid
forming the respective ammonium
salts.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Chemistry
The cathode ray experiment is conducted in a discharge tube containing four different gases \( A, B, C \) and \( D, \) the molecular weight of \( A=B>D \) \( >\mathrm{C}, \) then \( \mathrm{e} / \mathrm{m} \) as observed will be:
\( A \cdot A>B>D>C \)
B. \( A<D<B<C \)
\( \mathrm{c} \cdot \mathrm{A}=\mathrm{B}>\mathrm{D}>\mathrm{C} \)
D. \( A=B=C=D \)
Subject: Maths
\( \int e^{x} 2^{3 \log _{2} x} d x=e^{x} f(x)+c, \) then
\( \boldsymbol{f}(\boldsymbol{x})= \)
A. \( x^{3}-3 x^{2}+6 x-6 \)
B. \( x^{3}-3 x^{2}-6 x-3 \)
c. \( x^{3}-3 x^{2}+6 x+6 \)
D. \( x^{3}+3 x^{2}+6 x+6 \)
Subject: Physics
In the pictured circuit, If the reading of
voltmeter 1 is \( 3.0 V \) the reading of
ammeter 2 is \( 20 A \) and the reading of
voltmeter 3 is \( 5.0 ~ V, \) what is the
terminal voltage of the battery?
\( \mathbf{A} \cdot 8.0 V \)
B. \( 3.0 V \)
c. \( 5.0 V \)
D. \( 10.0 V \)
E. Not enough is given to answer this
questio
Subject: Physics
The phase difference between two
waves represented by
\( \boldsymbol{y}_{1}=\mathbf{1 0}^{-6} \sin \left[\mathbf{1 0 0 t}+\frac{x}{50}+\mathbf{0 . 5}\right] \boldsymbol{m} \)
\( \boldsymbol{y}_{2}=\mathbf{1 0}^{-6} \cos \left[\mathbf{1 0 0} \boldsymbol{t}+\frac{\boldsymbol{x}}{50}\right] \boldsymbol{m} \)
where \( x \) is expressed in metres and t is expressed in seconds is approximately
A . 1.07 rad
B. 2.07 rad
c. 0.5 rad
D. 1.5 rad
Subject: Chemistry
Indicate the incorrect statement:
A. Number of hybrid orbitals formed is equal to no. of atomic involved
B. \( 2 p_{x} \) and \( 2 p_{y} \) - orbitals of carbon can be hybridized to yield two new more stable orbitals
C. Effective hybridisation is not possible with orbitals of widely different energies
D. The concept of hybridisation has a greater significance in the VB theory of localised orbitals than \( M O \) theory.
Subject: Maths
Evaluate the following limits. If \( \lim _{x \rightarrow a} \frac{x^{5}-a^{5}}{x-a}=405, \) find all possible
values of a.
A \( \cdot a=3,-3 \)
B. \( a=2,-2 \)
\( \mathbf{c} \cdot a=5,-5 \)
D. None of these
Subject: Chemistry
The mass of \( N a_{2} C O_{3} \) required to
prepare \( 500 \mathrm{ml} \) of \( 0.1 \mathrm{M} \) solution is:
A . 10.6 g
B. \( 5.3 \mathrm{g} \)
c. \( 2.65 \mathrm{g} \)
D. 7.95
Subject: Biology
Beads on string of A are seen in B which
condense to form chromosomes in \( C \)
stage of cell division.
A. A- Chromonema B- Chromatin C- Metaphase
B. A-Chromatin B- Metaphase C- Metaphase
c. A- chromonema
B-Chromosome C- Anaphase
D. A- chromonema B- Chromatid C- Anaphase
Subject: Maths
Prove that the general equation \( a x^{2}+ \)
\( 2 h x y+b y^{2}+2 g x+2 f y+c=0 \) will
represent two parallel straight lines if
\( h^{2}=a b \) and \( b g^{2}=a f^{2} . \) Also prove that
the distance between them is \( 2 \sqrt{\left\{\frac{g^{2}-a c}{a(a+b)}\right\}} \)
Also prove that \( \frac{a}{h}=\frac{h}{b}=\frac{g}{f} \)
Subject: Maths
The differential equation of all parabolas having their axis of symmetry with the axis of \( x \) is?
A \( \cdot \quad y \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}=0 \)
B. \( \quad y \frac{d^{2} x}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}=0 \)
\( \mathbf{c} \cdot y=2 x \frac{d y}{d x} \)
D. \( y \frac{d^{2} y}{d x^{2}}-\left(\frac{d y}{d x}\right)=0 \)
Subject: Physics
The focal length of a lens is \( 0.12 \mathrm{m} \) and the Refractive Index (R.I.) is \( 1.5 . \) The focal
length of the same lens for blue colour is \( 0.1 \mathrm{m} \). The R.I. of the lens for blue
colour is
A . 1.5
B. 1.25
c. 1.45
D. 1.6
Subject: Physics
A street car moves rectilinear from
station \( \boldsymbol{A} \) to the next station \( \boldsymbol{B}( \) from rest to rest \( ) \) with an acceleration
varying according to the law \( \boldsymbol{f}=\boldsymbol{a}- \)
\( b x ; \) where \( a \) and \( b \) are constants and \( x \) is
the distance from station \( \boldsymbol{A} \). The
distance between the two stations and
the maximum velocity are
A \( \cdot x=\frac{2 a}{b}, v_{m a x}=\frac{a}{\sqrt{b}} \)
B. \( x=\frac{b}{2 a}, v_{m a x}=\frac{a}{\sqrt{b}} \)
c. \( _{x}=\frac{a}{2 b}, v_{\max }=\frac{b}{\sqrt{a}} \)
D. \( x=\frac{a}{b}, v_{\max }=\frac{\sqrt{a}}{b} \)
Subject: Physics
How many electron will constitute \( 32 \mathrm{C} \)
of charge?
A \( .2 \times 10^{19} \)
B . \( 2 \times 10^{18} \)
\( \mathrm{c} \cdot 2 \times 10^{17} \)
D. \( 2 \times 10^{20} \)
Subject: Physics
A metallic rod of length \( l^{\prime} \) is tied to a
string of length \( 2 l \) and made to rotate
with angular speed \( \omega \) on a horizontal table with one end of the string fixed. If
there is a vertical magnetic field \( B^{\prime} \) in the region, the e.m.f. induced across the
ends of the rod is:
A \( \cdot \frac{3 B \omega l^{2}}{2} \)
в. \( \frac{4 B \omega l^{2}}{2} \)
c. \( \frac{5 B \omega l^{2}}{2} \)
D. \( \frac{2 B \omega l^{2}}{2} \)
Subject: Maths
\( A \) and \( B \) are two candidates seeking
admission in I.I.T. The probability that \( \boldsymbol{A} \)
is selected is 0.5 and the probability that both \( A \) and \( B \) are selected is
atmost \( 0.3 . \) Is it possible that the probability of \( \boldsymbol{B} \) getting selected is \( \mathbf{0 . 9} \) ?
If it is possible then enter 1 , else enter 0
Subject: Physics
A charged particle is moving with velocity \( \vec{v} \) in a uniform magnetic field \( \vec{B} \) The magnetic force acting on it will be maximum when
A \( \cdot \vec{v} \& \vec{B} \) are in same direction
B . \( \vec{v} \& \vec{B} \) are in opposite direction
c. \( \vec{v} \& \vec{B} \) are mutually perpendicular
D. \( \vec{v} \& \vec{B} \) make an angle of \( 45^{\circ} \) with each other
Subject: Physics
The applied potential difference in the
circuit shown is \( V=10 \sin 100 t \) where
\( V \) is in volt and \( t \) is in second. If the
power factor of the circuit is \( \frac{1}{\sqrt{2}}, \) then
the value of capacitance \( C \) of the
circuit, nearly is:
A. \( 111 \mu F \)
в. \( 333 \mu F \)
c. \( 222 \mu F \)
D. \( 444 \mu F \)
Subject: Chemistry
10 g mixture of \( N a H C O_{3} \) and
\( N a_{2} C O_{3} \) has 1.68 g \( N a H C O_{3} . \) It is
heated at 400 K. Weight of the residue will be :
A. \( 9.38 \mathrm{g} \)
B. 8.32 g
c. \( 10.0 \mathrm{g} \)
D. 1.68 g
Subject: Maths
The following table of grouped data
represents the weight (in kg) of 100 gas
cylinders. Calculate the mode weight of
a cylinder.
Weight \( \begin{array}{cccc}\mathbf{3}- & \mathbf{5}- & \mathbf{7}- & \mathbf{9}- \\ \mathbf{5} & \mathbf{7} & \mathbf{9} & \mathbf{1 1}\end{array} \)
\( (\%) \)
Number of gas
16
13
15
cylinders
A. 12.96
B. 15.96
\( \mathbf{c} .9 .96 \)
D. 10.96
Subject: Maths
If the vertices of a triangle are \( (1,2),(4,-6), \) and \( (3,5), \) then its area is
\( ^{\mathbf{A}} \cdot \frac{23}{2} s q u n i t \)
B \( \cdot \frac{25}{2} \) squnit
c. 12 sq unit
D. none of these
Subject: Physics
If a nuclues \( z^{A} \) emits \( 9 \alpha \) and \( 5 \beta \) particles, then the ratio of the total protons and neutrons in the final nucles is
A \( \cdot \frac{(Z-13)}{(A-36)} \)
в. \( \frac{(Z-13)}{(A-Z-13)} \)
c. \( \frac{(Z-18)}{(A-36)} \)
D. \( \frac{(Z-13)}{(A-Z-23)} \)
Subject: Physics
A battery of \( \boldsymbol{E} \boldsymbol{M} \boldsymbol{F} \) 3 \( \boldsymbol{v} \) and internal
resistance \( r \) connected in series with
the resistor \( 55 \Omega \) through can ammeter
of resistance \( 1 \Omega \) it reads \( 50 m A \)
Calculate \( r \)
Subject: Physics
Figure below shows two infinitely long
and thin current carrying conductors \( \boldsymbol{X} \)
and \( Y \) kept in vacuum, parallel to each
other, at a distance \( ^{\prime} a \)

How much force per unit length acts on
the conductor \( Y \) due to the current
flowing through \( X ? \) Write your answer in terms of \( \left(\frac{\mu_{0}}{4 \pi}\right), I_{1}, I_{2} \) and \( a \)
(Derivation of formula is not required)
Subject: Chemistry
The decreasing order of \( A r S_{N} \) reaction
with \( C_{2} H_{5} O^{\ominus} / E t O H \) is:
A \( \cdot(I)>(I I)>(I I I)>(I V) \)
B. \( (I V)>(I I I)>(I I)>(I) \)
C. \( (I I I)>(I V)>(I I)>(I) \)
D. \( (I V)>(I I I)>(I)>(I I) \)
Subject: Chemistry
A mixture of three gases P (density
0.90)\( , Q(\text { density } 0.178) \) and \( R( \) density
0.42) is enclosed in a vessel at the
constant temperature. When the equilibrium is established:
A. the gas P will be at the top of the vessel
B. the gas Q will be at the top of the vessel
c. the gas \( R \) will be at the top of the vessel
D. the gases will mix homogeneously throughout the vessel
Subject: Maths
Find the values of other trigonometric
function \( (\sin , \cos , \tan ) \) in each of the
following problems
i) \( \sin \theta=3 / 5: \theta \) in \( I^{s t} \) quadrant
ii) \( \cos \theta=-1 / 2: \theta \) in \( I I^{s t} \) quadrant
iii) \( \sin \theta=3 / 4: \theta \) in \( I I I^{s t} \) quadrant \( \$ \$ \)
Subject: Maths
The area of the figure bounded by two branches of the curve \( (\boldsymbol{y}-\boldsymbol{x})^{2}=\boldsymbol{x}^{3} \)
and the straight line \( x=1 \) is:
A \( \cdot \frac{1}{3} \) sq.unit
B \( \cdot \frac{4}{5} \) sq.unit
c. \( \frac{5}{4} \) sq.unit
D. 3 sq.unit
Subject: Maths
For the ellipse \( 12 x^{2}+4 y^{2}+24 x- \)
\( \mathbf{1 6} \boldsymbol{y}+\mathbf{2 5}=\mathbf{0} \)
A. centre is (-1,2)
B. Length of axes are \( \sqrt{3} a n d 1 \)
\( ^{\mathrm{c}} \cdot_{\text {eceentricity is }} \sqrt{\frac{2}{3}} \)
D. All of these
Subject: Physics
Two cars \( P \) and \( Q \) start from a point at the same time in a straight line and their positions are represented by \( \boldsymbol{x}_{\boldsymbol{p}}(\boldsymbol{t})=\boldsymbol{a t}+\boldsymbol{b t}^{2} \) and \( \mathbf{x}_{\mathbf{Q}}(\mathbf{t})=\mathbf{f} \mathbf{t}-\mathbf{t}^{2} \mathbf{A} \mathbf{t} \)
what time do the cars have the same
velocity?
A \( \cdot \frac{a+f}{2(1+b)} \)
B. \( \frac{f-a}{2(1+b)} \)
\( \mathbf{c} \cdot \frac{a-f}{1+b-b} \)
D. \( \frac{a+f}{2(b+1)} \)
Subject: Physics
A steel ring of radius \( r \) and cross
sectional area \( A \) is fitted on to a wooden
disc of radius \( \boldsymbol{R}(\boldsymbol{R}>\boldsymbol{r}) . \) If Young;s
modulus be \( Y \), then the force with
which the steel ring is expanded, is
\( ^{\mathbf{A}} \cdot_{A Y} \frac{R}{r} \)
в. \( \quad A Y\left(\frac{R-r}{r}\right) \)
c. \( \frac{Y(R-r)}{A} \frac{r}{r} \)
D. \( \frac{Y r}{A R} \)