AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If \( \boldsymbol{A}\left(\boldsymbol{a}^{2}, \boldsymbol{2} \boldsymbol{a}\right) \boldsymbol{B}=\left(\frac{\mathbf{1}}{\boldsymbol{a}^{2}}, \frac{\boldsymbol{-} \boldsymbol{2}}{\boldsymbol{a}}\right), \boldsymbol{P}=(\boldsymbol{1}, \boldsymbol{0}) \)
then \( \frac{\boldsymbol{1}}{\boldsymbol{P} \boldsymbol{A}}+\frac{\boldsymbol{1}}{\boldsymbol{P} \boldsymbol{B}}= \)
Subject: Physics
angled isosceles triangle of height
\( 10 \mathrm{cm} \) is kept such that the \( 90^{\circ} \) vertex
is very close to an infinitely long
conducting wire (see the figure). The
wire is electricity insulted from the loop
The hypotenuse of the triangle is parallel to the wire. The current in the
triangle loop is in counterclockwise
direction and increased at a constant
rate of \( 10 A s^{-1} . \) Which of the following
statement(s) is(are) true?
This question has multiple correct options
A \cdot The magnitude of induced emf in the wire is \( \left(\frac{\mu_{0}}{\pi}\right) \) volt
B. If the loop is rotated at a constant angular speed about the wire, an additional emf of \( \left(\frac{\mu_{0}}{\pi}\right) \)
C. The induced current in the wire is in opposite direction to the current along the hypotenuse
D. There is a repulsive force between the wire and the loop
Subject: Chemistry
2.5 litre of \( 1 \mathrm{M} \) NaOH solution mixed
with another 3 litre of \( 0.5 ~ M \) NaOH
solution. Then find out molarity of resultant solution.
в. \( 1.0 \mathrm{M} \)
c. 0.73 М
D. \( 0.50 M \)
Subject: Maths
If \( \int \frac{2^{x}}{\sqrt{1-4^{x}}} d x=K \sin ^{-1}\left(2^{x}\right)+C \)
then \( K \) is equal to
A \( . e n 2 \)
в. \( \frac{1}{2} \ell n 2 \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{1}{\ell n^{2}} \)
Subject: Physics
A zener diode, having breakdown
voltage equal to \( 15 V \), is used in a
voltage regulator circuit shown in figure. The current through the diode is :
\( A \cdot 5 m A \)
B. \( 10 \mathrm{mA} \)
\( \mathbf{c} \cdot 15 m A \)
D. \( 20 m A \)
Subject: Maths
State true or false:
In parallelogram \( A B C D . E \) is the mid-
point of \( A B \) and \( A P \) is parallel to \( E C \)
which meets \( D C \) at point \( O \) and \( B C \)
produced at \( \boldsymbol{P} \). Hence
\( O \) is mid-point of \( \boldsymbol{A} \boldsymbol{P} \)
A. True
B. False
Subject: Chemistry
The following reaction is at equilibrium, \( \boldsymbol{F} \boldsymbol{e}_{(a q)}^{3+}+\boldsymbol{S C} \boldsymbol{N}_{(a q)}^{-} \rightleftharpoons \)
\( \left[\boldsymbol{F e}(\boldsymbol{S C N})_{(a q)}^{2+} ; \boldsymbol{K}_{c}=\frac{[\boldsymbol{F e}(\boldsymbol{S C N})]^{2+}}{\left[\boldsymbol{F e}^{3+}\right]\left[\boldsymbol{S C N}^{-}\right]}\right. \)
In the above reaction, color intensity of
red colour can be increased by:
A. addition of KSCN
B. addition of oxalic acid which reacts with \( F e^{3+} \) ions
C. addition of \( H g^{2+} \) ions which reacts with \( S C N^{-} \) ions
D. red colour intensity cannot be changed.
Subject: Physics
The resistor of resistance \( \boldsymbol{R} \) is
connected between the terminals of a
cell of emf \( \boldsymbol{E} \) and internal resistance \( \boldsymbol{r} \)
The current \( I \) through the circuit is :
A \( \cdot \frac{E}{R r} \)
в. \( \frac{E}{R+r} \)
c. \( \frac{R+r}{E} \)
D. \( \frac{E}{R}+r \)
Subject: Chemistry
\( C l F_{3} \) is a............ in the reaction
\( \boldsymbol{C I F}_{3}+\boldsymbol{A s F}_{3} \longrightarrow\left[\boldsymbol{C l F}_{2}\right]^{+}\left[\boldsymbol{A} \boldsymbol{s} \boldsymbol{F}_{4}\right]^{-} \)
and is a \( \ldots \ldots . . . . . . . . . . \) in the reaction
\( \boldsymbol{C l F}_{3}+\boldsymbol{N O F} \ldots \rightarrow[\boldsymbol{N O}]^{+}\left[\boldsymbol{C l} \boldsymbol{F}_{4}\right]^{-} \)
A . Lewis base, Lewis base
B. Lewis acid, Lewis acid
c. Lewis acid, Lewis base
D. Lewis base, Lewis acid
Subject: Physics
Assertion
The linear portion of the stress-strain
curve is the elastic region and the slope
is the modulus of elasticity or Young's
Modulus.
Reason Young's Modulus is the ratio of the
compressive stress to the longitudinal
strain.
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: Maths
In given figure \( P \) and \( Q \) are points on
sides \( A B \) and \( A C \) respectively of \( \triangle A B C \)
If \( A P=3 \mathrm{cm}, P B=6 \mathrm{cm}, A Q=5 \mathrm{cm} \) and
\( \mathrm{QC}=10 \mathrm{cm}, \) show that \( \mathrm{BC}=3 \mathrm{PQ} \)
Subject: Physics
A body travels \( 200 \mathrm{cm} \) in the first two
seconds and \( 220 \mathrm{cm} \) in the next 4
seconds. The velocity at the end Of the
eleventh second is
A. 0
B. \( 10 \mathrm{cms}^{-1} \)
\( \mathbf{c} \cdot 82 c m s^{-1} \)
D. \( 100 \mathrm{cms}^{-1} \)
Subject: Physics
An electric charge \( q \) is placed at the centre of a cube of side \( a \) The electric
flux through one of its faces is
A \( \cdot \frac{q}{6 \epsilon_{0}} \)
B. \( \frac{q}{6 \epsilon_{0} a^{2}} \)
c. \( \frac{q}{6 \pi \epsilon_{0} a^{2}} \)
D. \( \frac{q}{\epsilon_{0}} \)
Subject: Physics
A very long uniform helix is made of thin
metal wire. The axis of helix is vertical.
A small bead begins to slide down the
fixed helix starting from rest.

Considering friction between bead and
wire of helix to be non-zero, which of the
following statements is/ are true as
long as bead moves on helix.
This question has multiple correct options
A. The speed of bead keeps on increasing.
B. The magnitude of frictional force on bead remains constant
C. The speed of bead first increases and then remains constant
D. The magnitude of frictional force increases and then remains constant.
Subject: Chemistry
A metal reacts with chlorine to form two
chlorides \( A \) and \( B . A \) has \( 77.45 \% \) while
\( B \) has \( 84.93 \% \), by mass of chlorine. This
data is in accordance with the:
A. law of conservation of mass
B. law of multiple proportions
c. law of definite proportions
D. law of reciprocal proportions
Subject: Chemistry
In the first world war, \( 1.1 \times 10^{8} \) kg of
poison gas were fired on the allied forces. If the gas is assumed to be phosgene, how many molecules of the gas correspond to the amount fired on allied forces?
A \( \cdot 1.9 \times 10^{-15} \)
B. \( 6.7 \times 10^{32} \)
c. \( 2.9 \times 10^{-15} \)
D. \( 6.7 \times 10^{29} \)
Subject: Maths
A complex number is represented by an ordered pair \( (a, b), \) which of the following is true for \( a \) and \( b ? \)
A. \( a \) and \( b \) both are imaginary numbers
B. \( a \) and \( b \) both are real numbers
c. \( a \) is real and \( b \) is an imaginary number.
D. None of these
Subject: Maths
Find the minimum value of \( |z-1| \) if
||\( z-3|-| z+||1=2 \)
A \( \cdot|z-1| \geq 0 \)
B \( \cdot|z-1| \geq 1 \)
c. \( |z-1| \geq 2 \)
D. \( |z-1| \geq 3 \)
Subject: Chemistry
The cell potential of \( \mathbf{A} \mathbf{g}|\mathbf{A} \mathbf{g} \mathbf{B} \mathbf{r}(\mathbf{s})| \mathbf{H} \mathbf{B} \mathbf{r}_{(0.02 \mathrm{M})}\left|\mathbf{H}_{\mathbf{2}(\mathbf{0 . 5} \mathrm{atm})}\right| \mathbf{P} \mathbf{t}(\mathbf{G} \mathbf{i} \)
is:
A . \( 0.26 v \)
B. -0.26V
c. \( 0.16 v \)
D . -0.16v
Subject: Physics
A loop made of straight edges has six corners at \( A(0,0,0), B(L, 0,0), c(L, L, 0) \)
\( \mathrm{D}(0, \mathrm{L}, 0), \mathrm{E}(0, \mathrm{L}, \mathrm{L}) \) And \( F(0,0, \mathrm{L}) \)
A magnetic field \( \bar{B}=B_{0}(\hat{i}+\hat{k}) T \) is
present in the region.The flux passing through the loop ABCDEFA (in the order)
is
A. \( B_{0} L^{2} W b \)
В \( \cdot 2 B_{0} L^{2} W b \)
c. \( \sqrt{2} B_{0} L^{2} W b \)
D. \( 4 B_{0} L^{2} W b \)
Subject: Physics
\( S_{1}, S_{2} \) are two coherent sources (having
initial phase difference zero) of sound
located along \( x- \) axis separated by \( 4 \lambda \)
where \( \lambda \) is wavelength of sound emitted
by them. Number of maxima located on
the elliptical boundary around it will be :
A . 16
B. 12
\( c \)
\( D .4 \)
Subject: Physics
A copper wire of diameter \( 1.6 m m \)
carries a current \( i . \) The maximum
magnetic field due to this wire is \( 5 x \)
\( 10^{-3} T . \) The value of \( i \) is
A \( .40 A \)
в. \( 5 A \)
\( c \cdot 20 A \)
D. 2A
Subject: Biology
Bryophytes resemble algae in which of the following aspects?
A. Filamentous body, presence of vascular tissues and autotrophic nutrition
B. Differentiation of plant body into root, stem and leaves and autotrophic nutrition
c. Thallus like plant body, presence of root and autotrophic nutrition
D. Thallus-like plant body, lack of vascular tissues and autotrophic nutrition
Subject: Physics
A flat coil, \( C \) of \( n \) turn, area \( A \) and
resistance \( R \), is placed in a uniform
magnetic field of magnitude \( \boldsymbol{B} \). The plane of the coil is initially perpendicular to \( B \). The coil is rotated
by an angle \( \theta \) about a diameter and
charge of amount \( Q \) flows through it. The plane of the coil is initially kept
parallel to \( B \). The coil is rotated by an
angle \( \theta \) about the diameter
perpendicular to \( B \) and charge of
amount \( Q \) flows through it.Choose the correct alternatives
This question has multiple correct options
A \( \cdot \theta=90^{\circ}, Q=(\operatorname{Ban} / R) \)
B . \( \theta=180^{\circ}, Q=(2 B a n / R) \)
C \( \cdot \theta=180^{\circ}, Q=0 \)
D . \( \theta=360^{\circ}, Q=0 \)
E. answer required
Subject: Chemistry
Assertion
The reaction in \( C a C O_{3} \) and \( H C l \) goes
to completion.
Reason
Reactions that form a precipitate go to
completion
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
Identical metal plates are located in air at equal distance \( d \) from one another.
The area of each plate is equal to \( A \). If
the capacitance of the system between \( P \) and \( Q \) if the plates are interconnected
as shown in the figure \( \boldsymbol{x} \varepsilon_{0} \frac{\boldsymbol{A}}{\boldsymbol{d}} \). Find \( \boldsymbol{x} \)
Subject: Physics
Assertion
The equivalent thermal conductivity of two plates of same thickness in contact
is less than the smaller value of thermal
conductivity
Reason
For two plates of equal thickness in contact the equivalent thermal conductivity is given by:
\( \frac{1}{K}=\frac{1}{K}_{1}+\frac{1}{K} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
Atmospheric pressure is \( N m^{-2} \) at sea level.
A \( \cdot 2.026 \times 10^{5} \)
В. \( 1.013 \times 10^{5} \)
c. \( 3.039 \times 10^{5} \)
D. \( 1.013 \times 10^{6} \)
Subject: Maths
f \( x \) is a positive integer, then \( \left|\begin{array}{ccc}\boldsymbol{x} ! & (\boldsymbol{x}+\mathbf{1}) ! & (\boldsymbol{x}+\mathbf{2}) ! \\ (\boldsymbol{x}+\mathbf{1}) ! & (\boldsymbol{x}+\mathbf{2}) ! & (\boldsymbol{x}+\mathbf{3}) ! \\ (\boldsymbol{x}+\mathbf{2}) ! & (\boldsymbol{x}+\mathbf{3}) ! & (\boldsymbol{x}+\mathbf{4}) !\end{array}\right| \) is equa
to
A \( \cdot 2 x !(x+1) ! \)
в. \( 2 x !(x+1) !(x+2) \)
c. \( 2 x !(x+3) ! \)
D. \( 2(x+1) !(x+2) !(x+3) ! \)
Subject: Chemistry
(i) What is the pH of \( 10^{-8} N H C l ? \)
(ii) Calculate pH of the basic solutions
having \( \left[\boldsymbol{O} \boldsymbol{H}^{-}\right] \) as \( - \)
(a) \( \left[\boldsymbol{O H}^{-}\right]=\mathbf{0 . 0 5} \boldsymbol{M} \)
(b) \( \left[\boldsymbol{O} \boldsymbol{H}^{-}\right]=\boldsymbol{4} \times \mathbf{1 0}^{-\boldsymbol{6}} \boldsymbol{M} \)
Subject: Maths
Prove that \( \boldsymbol{f}^{\prime}(\mathbf{1})+\boldsymbol{f}(-1)=-\boldsymbol{f}(\mathbf{0}), \) i
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{5}+\boldsymbol{x}^{3}-\boldsymbol{2} \boldsymbol{x}-\boldsymbol{3} \)
Subject: Maths
\( \operatorname{Let} \boldsymbol{S}_{\boldsymbol{n}}=\sum_{\boldsymbol{k}=1}^{n} \frac{\boldsymbol{n}}{\boldsymbol{n}^{2}+\boldsymbol{k} \boldsymbol{n}+\boldsymbol{k}^{2}}, \boldsymbol{T}_{\boldsymbol{n}}= \)
\( \sum_{k=0}^{n-1} \frac{n}{n^{2}+k n+k^{2}} \) for \( n=1,2,3 \dots \) Then
This question has multiple correct options
A \( \cdot S_{n}<\frac{\pi}{3 \sqrt{3}} \)
в. \( s_{n}>\frac{\pi}{3 \sqrt{3}} \)
c. \( T_{n}<\frac{\pi}{3 \sqrt{3}} \)
D. \( T_{n}>\frac{\pi}{3 \sqrt{3}} \)
Subject: Physics
Pressure at a certain depth in river
water is \( p_{1} \) and at the same depth in
sea water is \( p_{2} \). Then (Density of sea water is greater than that of river water):
A \( \cdot p_{1}=p_{2} \)
в. \( p_{1}>p_{2} \)
c. \( p_{1}<p_{2} \)
D. \( p_{1}-p_{2}= \) atmospheric pressure
Subject: Physics
A uniform chain has a mass \( M \) and
length \( L \). It is placed on a frictionless table with length \( l_{0} \) hanging over the edge. The chain beings to slide down. Then the speed \( V \) with which the end
slides away from the edge is given by :
A \( \cdot V=\sqrt{\frac{g}{L}\left(L+l_{o}\right)} \)
B. \( V=\sqrt{\frac{g}{L}\left(L-l_{o}\right)} \)
c. \( V=\sqrt{\frac{g}{L}\left(L^{2}-l_{o}^{2}\right)} \)
D. \( V=\sqrt{2 g\left(L-l_{o}\right)} \)
Subject: Physics
Two bars of masses \( m_{1} \) and \( m_{2} \)
connected by a weightless spring of stiffness \( \kappa \) (figure shown above) rest on a smooth horizontal plane. Bar 2 is
shifted a small distance \( x \) to the left
and then released. If the velocity of the centre of inertia of the system after bar
breaks off the wall is given as \( v_{c m}= \)
\( \frac{s x \sqrt{m_{2} k}}{\left(m_{1}+m_{2}\right)} . \) Find \( s \)
Subject: Physics
What is the focal length of a double convex lens \( (\mu=3 / 2) \) if radius of
curvature of its sides is \( 15 \mathrm{cm} \) ?
\( \mathbf{A} \cdot 30 \mathrm{cm} \)
в. \( 7.5 \mathrm{cm} \)
\( \mathbf{c} \cdot 15 c m \)
D. \( 45 \mathrm{cm} \)
Subject: Maths
Let \( a, b, c \epsilon R \) such that \( a+b+c=0 \) and
\( a+b-c=0, \) then the polynomial function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{c} ;(\boldsymbol{a}>\boldsymbol{0}) \)
attains its least value at 'x' equal to
\( A \cdot O \)
в.
\( c \cdot \frac{1}{2} \)
D. not possible
Subject: Chemistry
For a reaction following first-order kinetics, which of the following statements is/are correct?
A. The time taken for the completion of \( 50 \% \) of the reaction is \( t_{1 / 2} \)
B. A plot of the reciprocal of the concentration of the reactants against time gives a straight line.
c. The degree of dissociation is equal to \( 1-e^{-k t} \)
D. A plot of \( [A]_{0} /[A] \) versus time gives a straight line
Subject: Chemistry
In a pseudo first order acid catalysed
hydrolysis of ester in water the following
results were obtained:
\( t / s \)
0.30
60
[ester]/M 0.550 .31
0.17 \( \quad 0.085 \)
Which of the following is/are correct for
the given reaction? This question has multiple correct options
A. The average rate of reaction between time interval 30 to 60 seconds is \( 4.67 \times 10^{-3} \) mol \( L^{-1} s^{-1} \)
B. Order of reaction is 2.
c. Pseudo first order rate constant for the acid catalysed hydrolysis of ester is \( 1.92 \times 10^{-2} s^{-1} \)
D. All are correct.
Subject: Maths
What is the common ratio of the G.P.
\( \boldsymbol{a}_{\boldsymbol{n}}=-\boldsymbol{4} . \boldsymbol{3}^{\boldsymbol{n}-1} ? \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 4
Subject: Physics
Ultraviolet light of wavelength \( \lambda_{1} \) and \( \lambda_{2} \) when allowed to fall on hydrogen atoms in their ground state is found to liberate electron with kinetic energy \( 1.8 e V \) and 4.0 \( e V \) respectively. Find the value of \( \frac{\lambda_{1}}{\lambda_{2}} \)
A \( -\frac{7}{8} \)
B. \( \frac{8}{7} \)
c. \( \frac{9}{20} \)
D. \( \frac{20}{9} \)
Subject: Physics
A steel wire with cross section \( 3 \mathrm{cm}^{2} \)
has elastic limit \( 2.4 \times 10^{8} \) Pa. Find the
maximum upward acceleration that can be given to a \( 1200 k g \) elevator supported by this cable if the stress is not to exceed \( 1 / 3 r d \) of the elastic limit
\( \mathbf{A} \cdot 9 m s^{-2} \)
B. \( 10 \mathrm{ms}^{-2} \)
\( \mathrm{c} \cdot 11 \mathrm{ms}^{-2} \)
D. \( 12 \mathrm{ms}^{-2} \)
Subject: Physics
A wire is stretched and fixed at two
ends. Transverse stationary waves are formed in it. It oscillates in its third
overtone mode. The equation of stationary wave is \( Y=A \sin k x \cos \omega t \)
Choose the correct options.
This question has multiple correct options
A \( \cdot \) Amplitude of constituent waves is \( \frac{A}{2} \)
B. The wire oscillates in three loops
C ' the length of wire is \( \frac{4 \pi}{k} \)
D. speed of stationary wave is \( \frac{\omega}{k} \)
Subject: Physics
Two thin rods each of mass \( m \) and
length 1 are joined to form L shape as
shown. The moment of inertia of rods
about an axis passing through free end
(O) of a rod end and perpendicular to
both the ends is
A \( \cdot \frac{5 m l^{2}}{3} \)
B. \( \frac{m l^{2}}{6} \)
c. \( \frac{5}{7} M R^{2} \)
D. \( \frac{7}{12} M R^{2} \)
Subject: Physics
The instability of the nucleus can be due to various cause.An unstable
nucleus emits radiations if possible to transform into less unstable state.Then
the cause and the result can be
This question has multiple correct options
A. a nucleus of excess nucleons is \( \alpha \) active
B. an excited nucleus of excess protons is \( \beta^{-} \) active
C. an excited nucleus of excess protons is \( \beta^{+} \) active
D. an nucleus of excess neutrons is \( \beta^{-} \) active
Subject: Physics
Reactance of a coil is \( 157 \Omega \). On
connecting the coil across a source of frequency \( 100 H z \), the current lags
behind e.m.f. by \( 45^{\circ} . \) The inductance of
the coil is
A \( .0 .25 H \)
в. \( 0.5 H \)
\( c .4 H \)
D. \( 314 H \)
Subject: Physics
Which of the following are correct?
This question has multiple correct options
A. 0.0304 can be rounded off to 0.030 (to two significant figures)
B. The less the number of significant figures, the greater the reliability of the measurement the number represents.
C. A result can be made more significant by a mathematical operation.
D. 487.56 can be rounded off to 490 (to two significant figures)
Subject: Chemistry
\( \left(C H_{3}\right)_{3} C M g B r \) on reaction with \( D_{2} O \)
produces:
A \( \cdot\left(C H_{3}\right)_{3} C D \)
в. \( \left(C H_{3}\right)_{3} C O D \)
\( \mathbf{c} \cdot\left(C D_{3}\right)_{3} C D \)
D \( \cdot\left(C D_{3}\right)_{3} O D \)
Subject: Chemistry
Assertion
The nucleus of gold is stable even though there is a very strong coulombic
repulsion among the protons.
Reason
The inverse square coulomb force is exactly balanced by another inverse square force which is very powerful than nuclear force.
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
Equilibrium constants is given (in atm)
for the following reaction \( 0^{\circ} C \)
\( N a_{2} H P O_{4} \cdot 12 H_{2} O(s) \rightleftharpoons \)
\( N a_{2} H P O_{4} .7 H_{2} O(s)+ \)
\( \mathbf{5} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) ; \quad \boldsymbol{K}_{\boldsymbol{p}}=\mathbf{2 . 4 3} \times \mathbf{1 0}^{-\mathbf{1 3}} \)
The vapour pressure of water at \( 0^{\circ} \mathrm{C} \) is
4.56 torr
At what relative humidities will
\( N a_{2} H P O_{4} \cdot 12 H_{2} O(s) \) be efflorescent
when exposed to air at \( 0^{\circ} \mathrm{C} \) ?
Subject: Chemistry
Find the product(s) when methane,
\( C H_{4}, \) burns in excess of oxygen?
A \( \cdot C H_{4} O_{2} \)
в. \( C O+H_{2} O \)
c. \( C O+C H_{2} O H \)
D. \( C O_{2}+H_{2} O \)
E \( \cdot C O_{2}+2 H_{2} \)
Subject: Physics
Figure shows a series LCR circuit
connected to a variable frequency 230 V
source. \( L=5.0 \mathrm{H}, \mathrm{C}=80 \mu \mathrm{F}, \mathrm{R}=40 \Omega \)
(a) Determine the source frequency
which drives the circuit in resonance.
(b) Obtain the impedance of the circuit
and the amplitude of current at the
resonating frequency.
(c) Determine the rms potential drops
across the three elements of the circuit.
Show that the potential drop across the
LC combination is zero at the resonating
frequency.
Subject: Physics
Unpolarized light of intensity \( \boldsymbol{I}_{0} \) is incident on surface of a block of a glass
of Brewster's angle. In that case, which one of the following statement is true?
A. transmitted light is partially polarized with intensity \( I_{0} / 2 \)
B. transmitted light is completely polarized with intensity less than \( I_{0} / 2 \)
C . reflected light is partially polarized with intensity \( I_{0} / 2 \)
D. reflected light is completely polarized with intensity less than \( I_{0} / 2 \)
Subject: Physics
An ideal gas is found to obey an
additional law \( V P^{2}= \) constant. The gas
is initially at temperature T and volume
V. When it expands to a volume 2 V, the temperature becomes:
A \( \cdot \frac{T}{\sqrt{2}} \)
в. 27
c. \( \frac{2 T}{\sqrt{2}} \)
D. 47
Subject: Physics
Statement - 1
Two vessels \( A \) and \( B \) are connected to
each other by a stopcock. Vessel \( A \)
contains a gas at \( 0^{\circ} \mathrm{C} \) and 1 atmosphere pressure and vessel B is evacuated. The
two vessels are thermally insulated from the surroundings. If the stopcock is suddenly opened, there will be no change in the internal energy of the gas.
Statement - 2
No transfer of heat energy takes place between the system and the surroundings.
A \( \cdot 1) \) Statement - - lis true, Statement - \( \| \) is true; statement
- I is a correct explanation for statement- -
B. 2) Statement - - lis true, statement - - ll is true statement - II is NOT a correct explanation for statement - -
c. 3 statement - 1 is true, statement- - \( \| \) is false
D. 4 statement - - lis false, statement - - II is true
Subject: Physics
A particle in SHM is described by the displacement function: \( \boldsymbol{x}(\boldsymbol{t})= \) \( \boldsymbol{A} \cos (\boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{\phi}) \cdot \) If the initial \( (\mathbf{t}=\mathbf{0}) \)
position of the particle is \( 1 \mathrm{cm} \) and its initial velocity is \( \pi \mathrm{cm} / \mathrm{sec}, \) what is the amplitude?
A. \( \sqrt{2} \mathrm{cm} \)
B. \( 2 c m \)
c. \( \sqrt{7} c m \)
D. \( 12 \mathrm{cm} \)
Subject: Chemistry
Indicate the following compound as
\( 1^{\circ}, 2^{\circ} \) and \( 3^{\circ} \)
\( \boldsymbol{E} \boldsymbol{t}_{3} \boldsymbol{N} \)
\( \mathbf{A} \cdot 1^{\circ} \)
B. \( 2^{\circ} \)
\( c \cdot 3^{\circ} \)
D. Non of the above
Subject: Maths
Which of the following is a cubic polynomial?
A. \( x^{3}+3 x^{2}-4 x+3 \)
B. \( x^{2}+4 x-7 \)
\( c \cdot 3 x^{2}+4 \)
D. \( 3\left(x^{2}+x+1\right) \)
Subject: Physics
A positively charged ball hangs from a silk thread. We put a positive test
charge \( q_{0} \) at a point and measure \( F / q_{0} \) then it can be predicted that the electric field strength E.
\( A \cdot>F / q_{0} \)
в. \( =F / q \)
c. \( <F / q_{0} \)
D. Cannot be estimated
Subject: Physics
A ball is thrown at an angle of incidence
\( \boldsymbol{\theta}^{\prime} \) on a horizontal plane such that the incident direction and the reflected
direction are at right angles to each other if the coefficient of restitution is
'e' then' \( \theta \) 'is equal to
A \( \cdot \tan ^{-1}(e) \)
B \( \cdot \tan ^{-1}(2 e) \)
c. \( \tan ^{-1}(\sqrt{2} e) \)
D. \( \tan ^{-1}(\sqrt{e}) \)
Subject: Maths
In a series of 3 one-day cricket matches between teams \( A \) and \( B \) of a college, the probability of team A winning or drawing are \( 1 / 3 \) and \( 1 / 6 \) respectively. If a
win, loss or draw gives 2,0 and 1 point
respectively, then what is the
probability that team A will score 5
points in the series?
A \( \cdot \frac{17}{18} \)
B. \( \frac{11}{12} \)
\( c \cdot \frac{1}{12} \)
D. \( \frac{1}{18} \)