AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
If \( \Delta G \) is greater than about +20 k \( J \) this
means:
A. the equilibrium constant is so large that virtually all the reactant has become product and the reaction goes to completion
B. the reaction is at equilibrium
C. the equilibrium constant is so small that virtually no product is formed and the reaction does not occur
D. there is no link between delta \( G \) and the equilibrium constant
E. it is impossible to tell from the information given
Subject: Chemistry
The commonest disaccharide has the
molecular formula
A. \( C_{10} H_{18} O_{19} \)
В . \( C_{10} \mathrm{H}_{20} \mathrm{O}_{10} \)
c. \( C_{11} H_{22} O_{11} \)
D. \( C_{12} H_{22} O_{11} \)
Subject: Maths
Differentiate
\( \mathbf{3} \boldsymbol{x}^{\mathbf{1} / \mathbf{3}}+\frac{\mathbf{6}}{\mathbf{7}} \boldsymbol{x}^{\mathbf{7} / \mathbf{6}}+\mathbf{3} \boldsymbol{x}^{\mathbf{2} / \mathbf{3}}+\boldsymbol{C} \)
Subject: Chemistry
Which type of Linkage is present in amylopectin?
A \( \cdot \alpha-D- \) Glucose \( , C_{1}-C_{4} \& C_{2}-C_{6} \)
B . \( \alpha-D- \) Glucose, \( C_{1}-C_{4} \) \& \( C_{1}-C_{6} \)
c. \( \beta-D- \) Glucose \( , C_{1}-C_{4} \) \& \( C_{2}-C_{6} \)
D. \( \beta-D- \)Glucose\( , C_{1}-C_{4} \& C_{1}-C_{6} \)
Subject: Maths
The degree and order of the differential equation \( \left[1+\left(\frac{d y}{d x}\right)^{3}\right]^{7 / 3}=7\left(\frac{d^{2} y}{d x^{2}}\right) \)
respectively are:
A. 3 and 7
B. 3 and 2
\( c .7 \) and 3
D. 2 and 3
Subject: Chemistry
Assertion
Oxidation number of chromium in
\( \boldsymbol{C r} \boldsymbol{O}_{5} \) is \( +\boldsymbol{6} \)
Reason
Oxidation number of each oxygen atom
in \( C r O_{5} \) is -2
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
we have taken a saturated solution of
AgBr. Ksp of AgBr is \( 12 \times 10^{-4} \) if \( 10^{-7} \)
mole of \( A g N O_{3} \) are added to 1 litre of
this solution then the conductivity of solution in terms of \( 10^{-7} S m^{-1} \) units
will be \( ? \mathrm{GIVEN} \boldsymbol{\lambda} \boldsymbol{A} \boldsymbol{g}+=\mathbf{4} \times \mathbf{1 0}^{-\mathbf{3}} ; \boldsymbol{\lambda} \)
\( \mathrm{Br}_{-}=6 \times 10^{-3} \mathrm{Sm}^{2} \boldsymbol{m} \)
Subject: Chemistry
What is the mass of one molecule of
yellow phosphorus? (Atomic mass, \( \boldsymbol{P}= \)
30)
A \( \cdot 1.993 \times 10^{-22} k g \)
B . \( 1.993 \times 10^{-19} \mathrm{mg} \)
C \( .4 .983 \times 10^{-20} \mathrm{mg} \)
D. \( 4.983 \times 10^{-23} \mathrm{kg} \)
Subject: Physics
The position function of a particle is
given by \( \boldsymbol{x}(t)=\boldsymbol{k} \boldsymbol{t}^{5 / 2}, \) where \( \boldsymbol{k} \) is a
constant.
If the particle starts at rest and is propelled through some distance \( d \) so
that the trajectory matches \( x(t), \) the
work done on the particle is
proportional to which power of \( t ? \)
\( \mathbf{A} \cdot t^{5} \)
B \( \cdot t^{3} \)
\( \mathbf{c} \cdot t^{5 / 2} \)
\( \mathbf{D} \cdot t^{3 / 2} \)
E. Not enough information
Subject: Physics
The gravitational force between two stones of mass \( 1 k g \) each, separated by
a distance of \( 1 \mathrm{m} \) in vacuum is
A . zero
B . \( 6.675 \times 10^{-5} N \)
c. \( 6.675 \times 10^{-8} N \)
D. \( 6.675 \times 10^{-11} N \)
Subject: Maths
A boy has a collection of blue and green marbles. The number of blue marbles
belong to the sets \( 2,3,4,13 . \) If two marbles are chosen simultaneously and at random from his collection, then the
probability that they have different colour is \( 1 / 2 . \) Possible number of blue marbles is:
A . 2
B. 3
\( c \cdot 6 \)
D. 10
Subject: Maths
A value of \( k \) such that the straight lines \( \boldsymbol{y}-\boldsymbol{3} \boldsymbol{x}+\boldsymbol{4}=\boldsymbol{0} \) and \( (\boldsymbol{2} \boldsymbol{k}-\mathbf{1}) \boldsymbol{x}-(\boldsymbol{8} \boldsymbol{k}- \)
1) \( y-6=0 \) are perpendicular is
A \( \cdot \frac{2}{7} \)
B. \( -\frac{2}{7} \)
c.
D.
Subject: Chemistry
The resistance of a conductivity cell
containing \( 0.001 M K C l \) solution at
\( 298 K \) is \( 1500 \Omega \). What is the cell
constant if conductivity of
\( 0.001 M K C l \) solution at \( 298 K \) is
\( 0.146 \times 10^{-3} S c m^{-1} ? \)
Subject: Chemistry
In which of the following reactions,
\( H_{2} O_{2} \) acts as a reducing reagent?
A \( \cdot P b O_{2(s)}+H_{2} O_{2(a q)} \rightarrow P b O_{(s)}+H_{2} O_{(l)}+O_{2(g)} \)
B . \( N a_{2} S O_{3(a q)}+H_{2} O_{2(a q)} \rightarrow N a_{2} S O_{4(a q)}+H_{2} O_{(l)} \)
\( \mathbf{c} \cdot 2 K I_{(a q)}+H_{2} O_{2(a q)} \rightarrow 2 K O H_{(a q)}+I_{2(s)} \)
D. None of these
Subject: Maths
If \( P(x, y, z) \) is a point on the line
segment joining \( Q(2,2,4) \) and
\( \boldsymbol{R}(\boldsymbol{3}, \boldsymbol{5}, \boldsymbol{6}) \) such that the projection of
\( O P \) on the axes are \( \frac{13}{5}, \frac{19}{5}, \frac{26}{5} \)
respectively, then \( P \) divides \( Q R \) in the ratio
A .1: 2
B. 3: 2
\( c \cdot 2: 3 \)
D. 1: 3
Subject: Physics
The gap between the plates of a parallel
plate capacitor of area \( A \) and distance
between plates \( d \), is filled with a
dielectric whose permittivity varies
linearly from \( \epsilon_{1} \) at one plate to \( \epsilon_{2} \) at the
other. The capacitance of capacitor is :
\( \mathbf{A} \cdot \epsilon_{0}\left(\epsilon_{1}+\epsilon_{2}\right) A / d \)
В \( \cdot \epsilon_{0}\left(\epsilon_{2}+\epsilon_{1}\right) A / 2 d \)
\( \mathbf{c} \cdot \epsilon_{A} / d\left[d \ln \left(\epsilon_{2} / \epsilon_{1}\right)\right] \)
D. \( \epsilon_{0}\left(\epsilon_{2}-\epsilon_{1}\right) A /\left[d l n\left(\epsilon_{2} / \epsilon_{1}\right)\right] \)
Subject: Maths
Without actually performing the long division, state whether the following rational numbers will have a
terminating decimal expansion or a non-terminating repeating decimal expansion:
(i) \( \frac{\mathbf{1 3}}{\mathbf{3 1 2 5}} \)
(ii) \( \frac{17}{8} \)
(iii) \( \frac{\mathbf{6 4}}{\mathbf{4 5 5}} \) (iv) \( \frac{\mathbf{1 5}}{\mathbf{1 6 0 0}}(\mathbf{v}) \)
\( \frac{\mathbf{2 9}}{\mathbf{3 4 3}} \)
(vi) \( \frac{\mathbf{2 3}}{\mathbf{2}^{3} \mathbf{5}^{2}} \)
(vii) \( \frac{\mathbf{1 2 9}}{\mathbf{2 ^ { 2 }} \mathbf{5}^{7} \mathbf{7}^{\mathbf{5}}} \)
(viii) \( \frac{\mathbf{6}}{\mathbf{1 5}}(\text { ix }) \frac{\mathbf{3 5}}{\mathbf{5 0}} \)
(x) \( \frac{77}{210} \)
Subject: Maths
If \( \theta \) is in the first quadrant and \( \cos \theta= \)
\( \frac{3}{5}, \) then the value of \( \frac{5 \tan \theta-4 \operatorname{cosec} \theta}{5 \sec \theta-4 \cot \theta} \) is
A \( \cdot \frac{5}{34} \)
в. \( \frac{5}{16} \)
c. \( \frac{5}{-34} \)
D. \( \frac{-5}{16} \)
Subject: Maths
In the figure at right, \( A B C D \) is a
parallelogram \( \angle B A O= \)
\( \mathbf{3 0}^{\circ}, \angle \boldsymbol{D A O}=\angle \mathbf{4 5}^{\circ} \) and \( \angle \boldsymbol{C O D}= \)
\( \mathbf{1 0 5}^{\circ} . \) Calculate
\( \angle C B D \)
A \( \cdot 60^{\circ} \)
B. 30
\( c \cdot 20 \)
D. None of these
Subject: Physics
Coulomb's law for electrostatic force
between two point charges and Newton's law for gravitational force
between two stationary point masses, both have inverse-square dependence on the distance between the
charges/masses.
(a) Compare the strength of these forces by determining the ratio of their magnitudes (i) for an electron and a proton and (ii) for two protons.
(b) Estimate the accelerations of electron and proton due to the
electrical force of their mutual
attraction when they are \( 1 A \)
\( \left.\mathbf{1 0}^{-\mathbf{1 0}} \boldsymbol{m}\right) \) apart? \( \left(\boldsymbol{m}_{\boldsymbol{p}}=\mathbf{1 . 6 7} \times\right. \)
\( \left.\mathbf{1 0}^{-\mathbf{2 7}} \mathbf{k g}, \boldsymbol{m}_{e}=\mathbf{9 . 1 1} \times \mathbf{1 0}^{-\mathbf{3 1}} \mathbf{k g}\right) \)
Subject: Chemistry
IUPAC name of the compound:
\( \boldsymbol{H}-\underset{\boldsymbol{O}}{\boldsymbol{C}}-\left(\boldsymbol{C H}_{2}\right)_{4} \boldsymbol{C O O H} \)
A. Hexanoic acid-5 - al-
B. 6-oxohexanoic acid
c. Hexanal-1-carboxylic acid
D. None of these
Subject: Physics
Consider the Earth as a short magnet with its centre coinciding with the centre of the Earth and dipole moment
is \( M . \) The angle of dip \( \delta \) is related to latitude \( \lambda \) as :
\( A \cdot \tan \delta=\tan \lambda \)
B. \( \tan \delta=2 \tan \lambda \)
\( c \cdot \tan \delta=\frac{\tan \lambda}{2} \)
D. \( \tan \delta=\cot \lambda \)
Subject: Physics
An electric dipole of moment \( p \) is lying along a uniform electric field \( \boldsymbol{E} \). The
work done in rotating the dipole by \( 90^{\circ} \) is:
A \( . p E \)
B . \( \sqrt{2} p E \)
c. \( \frac{p E}{2} \)
D. \( 2 p E \)
Subject: Physics
The angle between the axes of two polaroids so as to reduce the intensity of the incident unpolarised light to \( 1 / 3 \)
and \( 1 / 10 \) are \( \left(\operatorname{given}, \cos 35^{\circ}=0.8192\right. \)
and \( \left.\cos 63^{\circ}=0.4540\right) \)
A \( .35^{\circ}, 63^{\circ} \)
в. \( 55^{\circ}, 27^{\circ} \)
\( c \cdot 63^{\circ}, 35 \)
D. \( 27^{\circ}, 55^{\circ} \)
Subject: Physics
The area under the velocity-time graph
between any two instant \( t=t_{1} \) and \( t= \)
\( t_{2} \) gives the displacement covered in
time \( \delta t=t_{2}-t_{1} . \) This is true:
A. only if the particle moves with a uniform velocity
B. only if the particle moves with a uniform acceleration
c. only if the particle moves with an acceleration increasing at a uniform rate
D. in all cases irrespective of whether the motion is one of uniform velocity, or of uniform acceleration or of variable acceleration
Subject: Maths
If \( f(x)=\frac{2^{x}+2^{-x}}{2}, \) then \( f(x+ \)
\( y) \cdot f(x-y) \) is equal to \( ? \)
A \( \left.\cdot \frac{1}{2}[f(x+y)]+f(x-y)\right] \)
B. \( \frac{1}{2}[f(2 x)+f(2 y)] \)
c. \( \left.\frac{1}{2}[. f(x+y)]+f(x-y)\right] \)
D. None of these
Subject: Chemistry
An experiment is conducted where droplets of liquid are placed on the surface of a penny. Which of the following substances would you expect to the able to place the maximum
number of drops of on the surface of the
penny?
A . \( H F \)
в. \( H_{2} \) О
c. \( C H_{3} C H_{2} C H O \)
D. \( C C l_{4} \)
Subject: Chemistry
The structure of the \( S O_{3} \) molecule in
the gaseous phase contains:
B. \( \sigma \) -bonds and a (p\pi-p \( \pi \) ) bonds between sulphur and oxygen
c. \( \sigma \) -bonds and a (d \( \pi \) -p \( \pi \) ) bonds between sulphur and oxygen
D. \( \sigma \) -bonds, and a (p\pi-p \( \pi \) ) and a (p \( \pi \) -d \( \pi \) ) bonds between sulphur and oxygen
Subject: Chemistry
The IUPAC name of the complex
\( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2} \boldsymbol{C l}\left(\boldsymbol{N} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H}_{3}\right)\right] \boldsymbol{C l} \) is :
A. Diamminechlorido (methanamine) platinum(II)chloride
B. Bisammine (methanamine) chlorido platinum(II)chloride
c. Diamminechlorido (aminomethane) platinum(II)chloride
D. Diammine (methanamine) chlorido platinum(II)chloride
Subject: Physics
In Millikan's oil drop experiment an oil drop of radius \( r \) and charge \( Q \) is held in equilibrium between the plates of a charged parallel plate 'capacitor when
the potential difference is \( V . \) To keep a
drop of radius \( 2 r \) and with a charge \( 2 Q \)
in equilibrium between the plates, the potential difference required will be :
A . \( 8 V \)
в. \( 4 V \)
\( c .2 V \)
D. \( 1 V \)
Subject: Maths
The function \( f: R / 0 \rightarrow R \) given by \( f(x)= \) \( \frac{1}{x}-\frac{2}{e^{2 x}-1} \) can be made continuous at
\( x=0 \) by
defining \( f(0) \) as
A .
B.
\( c \cdot 2 \)
D. -
Subject: Physics
At inductance \( 1 H \) is connected in
series with an \( A C \) source of \( 220 \mathrm{V} \) and
\( \mathbf{5 0} \boldsymbol{H} z . \) The inductive resistance (in
ohm) is :
A \( .2 \pi \)
в. \( 50 \pi \)
\( c .100 \pi \)
D. \( 1000 \pi \)
Subject: Maths
In a race of 12 cars, the probability that \( \operatorname{car} A \) will win is \( \frac{1}{5} \) and of \( \operatorname{car} B \) is \( \frac{1}{6} \)
and that of car \( C \) is \( \frac{1}{3} . \) Find the probability that only one of them won the race.
Subject: Maths
Verify Lagrange's mean value theorem for the following function on the indicated interval. In each case find a
point \( ^{\prime} c^{\prime} \) in the indicated interval as
stated by the Lagrange's mean value theorem:
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}-\boldsymbol{3} \boldsymbol{x}+\boldsymbol{2} \) on [-1,2]
Subject: Physics
Match the following reactions:
\( (\boldsymbol{A})_{4} \boldsymbol{B} \boldsymbol{e}^{9}+_{2} \boldsymbol{H} \boldsymbol{e}^{4} \rightarrow_{\boldsymbol{6}} \boldsymbol{C}^{12}+\cdots \)
\( (i)_{2} H e^{4} \)
\( (B)_{6} C^{12}+\cdots \rightarrow_{5} B^{10}+_{2} H e^{4} \)
\( (i i)_{0} n^{1} \)
\( (C)_{7} N^{14}+\cdots \rightarrow_{8} O^{17}+_{1} H^{1} \)
\( (i i i i)_{1} D^{2} \)
\( (D)_{20} C a^{40}+\cdots \rightarrow_{19} K^{37}+_{2} H e^{4} \)
\( (i v)_{1} H^{1} \)
\( \mathbf{A} \cdot A-i, B-i i, C-i i i, D-i v \)
\( \mathbf{B} \cdot A-i i, B-i i i, C-i, D-i v \)
\( \mathbf{c} \cdot A-i v, B-i i, C-i i i, D-i \)
\( \mathbf{D} \cdot A-i i i, B-i i, C-i, D-i v \)
Subject: Chemistry
The thermal stability of alkaline earth
metal carbonates-
\( M g C O_{3}, C a C O_{3}, S r C O_{3} \) and \( B a C O_{3} \)
follows the order:
A. \( B a C O_{3}>S r C O_{3}>C a C O_{3}>M g C O_{3} \)
в. \( C a C O_{3}>S r C O_{3}>M g C O_{3}>B a C O_{3} \)
с. \( M g C O_{3}>C a C O_{3}>S r C O_{3}>B a C O_{3} \)
D. \( B a C O_{3}>S r C O_{3}>M g C O_{3}>C a C O_{3} \)
Subject: Chemistry
Assertion
A current of 96.5 amperes is passes
into aquesous \( A g N O_{3} \) solution for 100
seconds.

The weight of silver deposited is \( 10.8 g \) (At.wt. of \( A g=108 \) ).
Reason
The mass of a substance deposited during the electorlysis of an electrolyte is inversely propotional to the quantity of elctricity passing through the electrolyute.
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. Assertion is incorrect but Reason is correct
Subject: Physics
For a transformer, the turns ratio is 3 and its efficiency is \( 0.75 . \) The current flowing in the primary coil is \( 2 A \) and the
voltage applied to it is \( 100 \mathrm{V} \). Then the
voltage and the current flowing in the secondary coil are
respectively.
A. \( 150 V, 1.5 A \)
B . \( 300 V, 0.5 A \)
c. \( 300 V, 1.5 A \)
D. \( 150 V, 0.5 A \)
Subject: Physics
A stone is dropped from a rising balloon at a height of \( 300 \mathrm{m} \) above the ground and it reaches the ground in 10 s. The velocity of the balloon when the stone
was dropped is :
A \( \cdot 19 \mathrm{m} s^{-1} \)
B . \( 19.6 \mathrm{m} s^{-1} \)
c. \( 29 \mathrm{m} s^{-1} \)
D. o m \( s^{-1} \)
Subject: Chemistry
The limiting molar conductivity and molar conductivity of acetic acid are
\( 390.5 s . c m^{2} . m o l^{-1} \) and
\( 48.15 s . c m^{2} . m o l^{-1} \) respectively
Calculate the degree of dissociation of the weak acid?
\( \mathbf{A} \cdot 1.233 \)
B. 12.33
c. 0.1233
D. 0.01233
Subject: Maths
The expression \( (\tan \Theta+\sec \theta)^{2} \) is
equal to
A \( \cdot \frac{1+\cos \Theta}{1-\cos 0} \)
B. \( \frac{1+\sin \Theta}{1-\sin 0} \)
c. \( \frac{1-\cos \Theta}{1+\cos 0} \)
D. \( \frac{1-\sin \Theta}{1+\sin \Theta} \)
Subject: Physics
If \( \boldsymbol{A}=\mathbf{1}, \boldsymbol{B}=\mathbf{0} \) then the value of \( \overline{\boldsymbol{A}}+\boldsymbol{B} \)
in terms of Boolean algebra is
A . \( A \)
в. \( B \)
c. \( B+A \)
D. A.B
Subject: Chemistry
What is the percentage of pyridine
\( \left(C_{5} H_{5} N\right) \) that forms pyridinium ion
\( \left(C_{5} H_{5} N^{+} H\right) \) in a 0.10 M aqueous
pyridine solution \( \left(\boldsymbol{K}_{\boldsymbol{b}} \text { for } \boldsymbol{C}_{\mathbf{5}} \boldsymbol{H}_{\mathbf{5}} \boldsymbol{N}=\right. \)
\( \left.1.7 \times 10^{-9}\right) ? \)
A . 0.77\%
B . 1.6\%
c. \( 0.0060 \% \)
D. 0.013\%
Subject: Physics
If Ohm's law is presumed to be valid,
then drift velocity \( V_{d} \) and electric field \( E \)
are related as
A \( \cdot v_{d} \propto E^{2} \)
B \( \cdot v_{d} \propto \sqrt{E} \)
c. \( v_{d} \propto E \)
D. \( v_{d} \propto E_{0} \)
Subject: Maths
\( \left|\begin{array}{ccc}\boldsymbol{x}+\boldsymbol{\alpha} & \boldsymbol{\beta} & \gamma \\ \boldsymbol{\alpha} & \boldsymbol{x}+\boldsymbol{\beta} & \gamma \\ \boldsymbol{\alpha} & \boldsymbol{\beta} & \boldsymbol{x}+\boldsymbol{\gamma}\end{array}\right|=\mathbf{0}, \) then \( \boldsymbol{x} \) is
equal to
\( \mathbf{A} \cdot 0,-(\alpha+\beta+\gamma) \)
B. \( 0, \alpha+\beta+\gamma \)
c. \( 1, \alpha+\beta+\gamma \)
D. \( 0, \alpha^{2}+\beta^{2}+\gamma^{2} \)
Subject: Chemistry
mol of \( [A g] A g^{\oplus} \) sol is coagulated by
This question has multiple correct options
A. 1 mol of \( K I \)
B. \( 500 \mathrm{mL} \) of \( 1 \mathrm{M} \mathrm{K}_{2} \mathrm{SO}_{4} \)
c. \( 300 \mathrm{mL} \) of \( 1 \mathrm{M} \mathrm{Na}_{3} \mathrm{PO}_{4} \) solution
D. 1 mol of \( A g I \)
Subject: Maths
If the angles of a triangle \( A B C \) are in
\( \boldsymbol{A} \cdot \boldsymbol{P} \)
\( \boldsymbol{a}=\mathbf{2}, \boldsymbol{c}=\mathbf{4}, \) then \( \boldsymbol{b}= \)
A \( \cdot 2 \sqrt{3} \)
3
B. \( \sqrt{21} \)
c. 8
D. 14
Subject: Physics
A person standing on the escalator
takes time \( t_{1} \) to reach the top of a tower
when the escalator is moving. He takes
time \( t_{2} \) to reach the top of the tower
when the escalator is standing. How long will he take if he walks up a moving escalator?
A \( \cdot t_{2}-t_{1} \)
B . \( t_{1}+t_{2} \)
c. \( t_{1} t_{2} /\left(t_{1}-t_{2}\right) \)
D. \( t_{1} t_{2} /\left(t_{1}+t_{2}\right) \)
Subject: Physics
A mass \( M \) is split into two parts \( m \) and
\( (M-m), \) which are, then separated by
a certain distance. The ratio \( \boldsymbol{m} / \boldsymbol{M} \) which maximizes the gravitational force between the parts is
A . 1: 4
B. 1: 3
c. 1: 2
D. 1: 1
Subject: Maths
If the point \( P(a, b, c), \) with reference to Eq. \( (i) \) lies on the plane \( 2 x+y+z=1 \)
then the value of \( 7 a+b+c \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. 12
\( c \cdot 7 \)
D. 6
Subject: Physics
The figure shows a capacitor having three layers of equal thickness and same area as that of plate. the layer
first is vaccum, second is conductor
and third is dielectric of dielectric
constant \( K . \) The ratio of energy stored
in region three to total energy stored in capacitor three is :
A \( \cdot \frac{1}{K+1} \)
в. \( \frac{3}{K+1} \)
\( c \cdot \frac{4}{K+3} \)
D. \( \frac{4}{K+1} \)
Subject: Maths
If \( f(x)=\log _{e}\left\{\frac{u(x)}{v(x)}\right\}, u(1)=v(1) \)
and \( u^{\prime}(x)=v^{\prime}(x)=2, \) then \( f^{\prime}(1) \) is
equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot-1 \)
D. none of these
Subject: Chemistry
The correct representation of 4
hydroxy- 2 -methylpent-2-en-1-al is:
\( \mathbf{A} \cdot C H_{3}-C H-C H=C-C H O \)
\( O_{H} \)
\( \begin{array}{rl}\mathbf{B} \cdot C H_{3}-C H-C H= & C-C H O \\ C H_{3} & O_{H}\end{array} \)
\( c \)
\( C H \) :
3.
\( C H_{3}-C_{C H_{3}}-C H=C_{C H_{3}}-C H O \)
\( \mathbf{D} \cdot C H_{3}-C H-C H_{2}-C H-C H O \)
\( O_{H}^{\mid} C H_{3} \)
Subject: Biology
The finches that populate the
Galapagos islands are genetically much more closely related to a species of ground finch found on the mainland in
South America than they are to a species of finch found on the mainland
in North America. This observation
suggests that
A. The finches on the Galapagos islands have descended directly from the finches in South America.
B. The climatic environment on the Galapagos islands is more similar to the climatic environment in South America than North America
C. The Galapagos islands were once physically connected to the continent of South America
D. The finches on the Galapagos islands and the finches on the mainland of South America are experiencing convergent evolution
Subject: Physics
A coil of area \( 500 \mathrm{cm}^{2} \) having 1000 turns
is placed such that the plane of the coil is perpendicular to a magnetic field of magnitude \( 4 \times 10^{-5} \) weber \( / m^{2} \). If it is
rotated by 180 about an axis passing through one of its diameter in \( 0.1 \mathrm{sec} \), find the average induced emf
A. zero
B. 30 mv
c. \( 40 \mathrm{mv} \)
D. 50 mv
Subject: Physics
In a certain region of space,electric field is along the z-direction throughout The magnitude of electric field is however not constant, but increases
uniformly along the positive z-direction at the rate of \( 10^{5} N \quad C^{-1} m^{-1} . \) Torque
experienced by the system is:
\( \mathbf{A} \cdot 10^{2} N \)
В. \( 10^{-2} N \)
c. zero
D. \( 10^{3} N \)
Subject: Chemistry
How many molecules are planar among the following molecules?
\( \boldsymbol{I}_{3}^{-}, \boldsymbol{H}_{2} \boldsymbol{O}, \boldsymbol{I} \boldsymbol{C l}_{2}^{-}, \boldsymbol{C}_{2} \boldsymbol{H}_{4}, \boldsymbol{C}_{2} \boldsymbol{H}_{2}, \boldsymbol{H}_{3} \boldsymbol{O}^{+} \)
Subject: Chemistry
Assertion
Oxy hydrogen blow torch is used for
welding.
Reason
The temperature produced here is
above \( 2000^{\circ} \mathrm{C} \)
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. Assertion is incorrect but Reason is correct
Subject: Chemistry
In the following reaction, the correct
statements are:
\( M g+2 H^{+} \rightarrow M g^{2+}+H_{2} \)
1. \( M g \) is a reducing agent, \( H^{+} \) is an oxidising agent
2. \( M g \) is oxidising agent, \( H^{+} \) is a reducing agent.
A. only 1
B. only 2
c. both
D. none
Subject: Maths
Find the intersection of the line \( x- \)
\( \mathbf{2} \boldsymbol{y}+\mathbf{4} \boldsymbol{z}+\mathbf{4}=\mathbf{0}, \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}-\mathbf{8}=\mathbf{0} \)
with the plane \( \boldsymbol{x}-\boldsymbol{y}+\mathbf{2} \boldsymbol{z}+\mathbf{1}=\mathbf{0} \)
Subject: Physics
The displacement of the medium in a sound wave is given by the equation
\( \boldsymbol{y}_{1}=\boldsymbol{A} \cos (\boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{t}) \) where ,a and b are
positive constants. The wave is reflected by an obstacle situated at
\( x=0 . \) The intensity of the reflected
wave is 0.64 times that of the incident
wave. Then, the wavelength ond frequency of the incident wave are
A \( . a, b \)
в. \( 2 \pi a, 2 \pi b \)
c \( .2 \pi / a, 2 \pi / b \)
D. \( 2 \pi / a, b / 2 \pi \)
Subject: Physics
The natural frequency of a \( L-C \) circuit
is
A \( \cdot \frac{1}{2 \pi \sqrt{L C}} \)
в. \( \frac{1}{2 \pi} \sqrt{\frac{C}{L}} \)
c. \( \frac{1}{2 \pi} \sqrt{\frac{L}{C}} \)
D. \( \sqrt{L C} \)
Subject: Chemistry
The commercial production of water gas utilize the reaction under standard conditions:
\[
\begin{array}{r}
\boldsymbol{C}+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \longrightarrow \\
\boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{C O}
\end{array}
\]
The heat required for this endothermic reaction may be supplied by adding a limited amount of air and burning some
carbon to \( C O_{2} . \) How many g of carbon
must be burnt to \( C O_{2} \) to provide enough heat for the water-gas conversion of 100 g carbon?
Neglect all heat losses to the
environment.Also \( \Delta_{f} H^{\circ} \) of \( \mathrm{CO}, H_{2} O(g) \)
and \( C O_{2} \) are -110.53,241.81 and -393.51
kJ/mol respectively.
A . \( 33.4 g \)
в. \( 66.72 g \)
c. \( 15.18 g \)
D. None of these
Subject: Maths
If \( a \sin ^{3} x+b \cos ^{3} x=\sin x \cos x \) and
\( a \sin x=b \cos x \) then \( a^{2}+b^{2}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3