AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The charge stored in a capacitor is \( 20 \mu C \) and the potential difference across the plates is \( 500 \mathrm{V} \). Its capacity is :
A. \( 0.04 \mu F \)
B . \( 10^{-2} \mu F \)
c. \( 2 \times 10^{-6} \mu F \)
D. 250 \muF
Subject: Biology
Solve the following crossword puzzle with the clues given. Across:
2. Plantation prevents it.
5. Use should be banned to avoid soil
pollution.
6. Type of soil used for making pottery.
7. Living organism in the soil
Down:
1. In desert soil erosion occurs through.
2. Clay and loam are suitable for cereals
like.
3. This type of soil can hold very little
water
4. Collective name for layers of soil.
Subject: Physics
A 6 -kg weight is fastened to the end of a steel wire of un-stretched length \( 60 \mathrm{cm} \)
It is whirled in a vertical circle and has
an angular velocity of 2 revolution per second at the bottom of the circle. The
area of cross-section of the wire is
\( 0.05 c m^{2} . \) Calculate the elongation of the
wire when the weight is at the lowest point of the path. Young's modulus of steel \( =2 \times 10^{11} \mathrm{Pa} \)
Subject: Maths
Show that \( \left|\begin{array}{lll}\boldsymbol{b} \boldsymbol{c} & \boldsymbol{b}+\boldsymbol{c} & \mathbf{1} \\ \boldsymbol{c} \boldsymbol{a} & \boldsymbol{c}+\boldsymbol{a} & \mathbf{1} \\ \boldsymbol{a} \boldsymbol{b} & \boldsymbol{a}+\boldsymbol{b} & \mathbf{1}\end{array}\right|= \)
\( (\boldsymbol{a}-\boldsymbol{b})(\boldsymbol{b}-\boldsymbol{c})(\boldsymbol{c}-\boldsymbol{a}) \)
Subject: Maths
n the figure (1) given below, AB I CR and LM | QR Prove that \( \frac{\boldsymbol{B} \boldsymbol{M}}{\boldsymbol{M} \boldsymbol{C}}=\frac{\boldsymbol{A} \boldsymbol{L}}{\boldsymbol{L} \boldsymbol{Q}} \)
Subject: Maths
The construction of a triangle \( A B C \)
given that \( B C=6 \mathrm{cm}, B=45^{\circ} \) is not
possible when difference of \( A B \) and \( A C \) is equal to:
\( A .6 .9 \mathrm{cm} \)
B. \( 5.2 \mathrm{cm} \)
c. \( 5.0 \mathrm{cm} \)
D. \( 4.0 \mathrm{cm} \)
Subject: Maths
Divide \( p(x) \) by \( g(x) \) in the following case
and verify division algorithm
\( \boldsymbol{p}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{4} \boldsymbol{x}+\boldsymbol{4} ; \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{x}+\boldsymbol{2} \)
Subject: Maths
The line \( 2 x-3 y=4 \)
A . passes through origin and \( m=-\frac{2}{3} \)
B. passes through (2,0) and \( m=\frac{2}{3} \)
c. passes through (0,2) and \( m=\frac{2}{3} \)
D. passes through (0,-2) and \( m=-\frac{2}{3} \)
Subject: Maths
If \( \frac{1+3 p}{3}, \frac{1-2 p}{2} \) are probabilities of two mutually exclusive event, then \( p \) lies in the interval
\( ^{A} \cdot\left[-\frac{1}{3}, \frac{1}{2}\right] \)
B \( \cdot\left(-\frac{1}{2}, \frac{1}{2}\right) \)
\( ^{\mathbf{C}} \cdot\left[-\frac{1}{2}, \frac{2}{3}\right] \)
D. \( \left(-\frac{1}{3}, \frac{2}{3}\right) \)
Subject: Chemistry
Consider this equilibrium, for which \( \Delta H<0 \)
\( \boldsymbol{H} \boldsymbol{g} \boldsymbol{O}(\boldsymbol{s})+\boldsymbol{4} \boldsymbol{I}^{-}(\boldsymbol{a} \boldsymbol{q} \cdot)+\boldsymbol{H}_{2} \boldsymbol{O}(l) \rightleftharpoons \)
\( \boldsymbol{H} \boldsymbol{g} \boldsymbol{I}_{4}^{2-}+\boldsymbol{2} \boldsymbol{O} \boldsymbol{H}^{-} \)
Which changes will increase the
equilibrium concentration \( \boldsymbol{H} \boldsymbol{g} \boldsymbol{I}_{4}^{2-} \) ?
I. Increasing the mass of \( \boldsymbol{H} \boldsymbol{g} \boldsymbol{O}(\boldsymbol{s}) \)
present
II. Increasing \( \left[\boldsymbol{I}^{-}\right] \)
III. Adding \( 1 M H C l \)
A. \( I \) only
B. II only
c. \( I I \) and \( I I I \) only
D. \( I, I I \) and \( I I I \)
Subject: Biology
Assertion
Suppression of growth of axillary buds is called apical dominance.
Reason

It is due to effect of downward
movement of Auxin from apical region
towards the lower side.
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
The first order rate constant for the
decomposition of ethyl iodide by the
reaction:
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{I}(\boldsymbol{g}) \rightarrow \boldsymbol{C}_{2} \boldsymbol{H}_{4}(\boldsymbol{g})+\boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \)
at \( 600 \mathrm{K} \) is \( 1.60 \times 10^{-5} s^{-1} . \) Its energy
of activation is \( 209 \mathrm{kJ} \) mol\( ^{-1} \). The rate
constant of the reaction at \( 700 \mathrm{K} \) will be:
A \( .2 .88 \times 10^{-3} s^{-1} \)
В. \( 2.96 \times 10^{-3} s^{-1} \)
c. \( 2.76 \times 10^{-3} s^{-1} \)
D. None of these
Subject: Chemistry
Assertion
Paraffin wax is a white or colourless
soft solid derivable from petroleum.
Reason
Paraffins are unsaturated hydrocarbons with straight or branched chains which contain only carbon and hydrogen.
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
Select the correct statement(s) about
the given polymer:
(i) Monomer is \( \boldsymbol{C H}_{2}=\boldsymbol{C H}-\boldsymbol{C H}= \)
\( \boldsymbol{C H}_{2} \) and \( \boldsymbol{C H}_{2}=\boldsymbol{C H}-\boldsymbol{C N} \)
(ii) It is a copolymer.
(iii) It is an addition polymer.
\[
\left[\begin{array}{cc}
\mathrm{CH}_{2}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH} \\
& \mid \\
& \mathrm{CN}
\end{array}\right]_{\mathrm{n}}
\]
\( A \cdot(i) \) and (ii) only
B. (iii) only
c. (ii) only
D. (i), (ii) and (iii)
Subject: Maths
If \( (\boldsymbol{m}+\mathbf{1})^{t h},(\boldsymbol{n}+\mathbf{1})^{t h} \) and \( (\boldsymbol{r}+\mathbf{1})^{t h} \)
terms of an A.P. are in G.P and \( \boldsymbol{m}, \boldsymbol{n}, \boldsymbol{r} \)
are in H.P., then ratio of the first term of
the A.P. to its common difference in
terms of \( n \) is
\( A \cdot \frac{n}{2} \)
B. \( -\frac{n}{2} \)
\( c \cdot \frac{n}{3} \)
D. \( -\frac{n}{3} \)
Subject: Physics
A transistor-oscillator using a resonant circuit with an inductor \( L \) (of negligible resistance) and a capacitor \( \mathrm{C} \) in series produce oscillations of frequency f. If is doubled and \( C \) is changed to \( 4 C \), the frequency will be:-
\( A \cdot \frac{f}{4} \)
B. 8f
\( c \cdot \frac{f}{2 \sqrt{2}} \)
\( D \cdot \frac{f}{2} \)
Subject: Physics
Two points of a rod move with velocities
\( 3 v \& v \) perpendicular to the rod and in the same direction, separated by a distance 'r'. The angular velocity of rod is :
A \( \cdot \frac{3 v}{r} \)
в. \( \frac{4 v}{r} \)
c. \( \frac{5 v}{r} \)
D. \( \frac{2 v}{r} \)
Subject: Chemistry
Assertion
When a cell is placed in hypertonic solution, it shrinks.
Reason
Reverse osmosis is used for
desalination of water.
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: Maths
Fill in the blanks
\begin{tabular}{lllll} 
S. no & cost price & Selling price & Profit & Loss \\
\hline (a) & Rs 1,200 & Rs Rs & Rs \\
(b) & 2,000 & & 800 & 180 \\
(c) & & Rs & Rs & \\
(d) & Rs & 5,100 & 850 & \\
& 10,800 & & Rs & 216
\end{tabular}
Subject: Chemistry
Find the two third life \( \left(t_{2 / 3}\right) \) of a first order reaction in which \( \boldsymbol{K}=\mathbf{5 . 4 8} \times \)
\( 10^{-14} s e c^{-1} \)
A \( \cdot t_{2 / 3}=5 \times 10^{13} \) sec
B . \( t_{2 / 3}=2 \times 10^{13} \) sec
C \( \cdot t_{2 / 3}=1.25 \times 10^{13} \mathrm{sec} \)
D. none of these
Subject: Maths
n the figure, \( \angle P Q S=\angle P R T \) and
\( \mathrm{QS}=\mathrm{TR} . \) then \( \Delta P Q S \cong \Delta P R T \mathrm{by} \)
congruence postulate
\( A \cdot \operatorname{sas} \)
B. sss
\( c . \) RHS
D. AAS
Subject: Chemistry
The atomic masses of \( H e \) and \( N e \) are 4
and 20 amu, respectively. The value of
the de Broglie wavelength of \( H e \) gas at
\( -73^{0} C \) is \( " M^{\prime \prime} \) times that of the de
Broglie wavelength of \( N e \) at \( 727^{0} C . M \)
is:
\( \mathbf{A} \cdot \mathbf{5} \)
B. 0.2
\( c \cdot 2 \)
D. 0.5
Subject: Physics
A solid at temperature \( T_{1} \) is kept in an evacuated chamer at temperature
\( T_{2}>T_{1} . \) The rate of increase of
temperature of the body is proportional
to
A \( \cdot T_{2}-T_{1} \)
B . \( T_{2}^{2}-T_{1}^{2} \)
\( \mathbf{c} \cdot T_{2}^{3}-T_{1}^{3} \)
D. \( T_{2}^{4}-T_{1}^{4} \)
Subject: Chemistry
\( \mathbf{2} \boldsymbol{A} \boldsymbol{l}+\boldsymbol{6} \boldsymbol{H} \boldsymbol{C l} \rightarrow \mathbf{2} \boldsymbol{A l} \boldsymbol{C l}_{3}+\mathbf{3} \boldsymbol{H}_{2}, \) in the
given reaction oxidation state of \( A l C l_{3} \)
is?
\( A \cdot+2 \)
\( B \cdot+3 \)
\( c \cdot+4 \)
D. +5
Subject: Maths
Assertion
If \( \vec{a}=5 \hat{i}-\hat{j}+2 \widehat{k}, \) then a vector having magnitude of 8 units along \( \vec{a} \) is \( \frac{8}{\sqrt{30}}(5 \hat{i}-\widehat{j}+2 \widehat{k}) \)
Reason
Vector having modulus m along a given
vector \( ^{\prime} \boldsymbol{a}^{\prime} \) is given by, \( \boldsymbol{m} \times \widehat{\boldsymbol{a}} \)
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
A convex lens is given, for which the minimum distance between an object
and its rel image is \( 40 \mathrm{cm} . \) An object is
placed at a distance of \( 15 \mathrm{cm} \) from this lens. The liner magnification of adjustment will be
A \( \cdot \frac{5}{3} \)
B. - 2
\( c \cdot 2 \)
D.
Subject: Chemistry
A half cell reaction: \( \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{S}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \)
\( \mathbf{3} A \boldsymbol{g}(s)+\boldsymbol{S}^{2-} \) is carried out in a half
\( \operatorname{cell} P t_{A g_{2}} s \mid A g, H_{2} S(0.1 M) \boldsymbol{a t}\left[\boldsymbol{H}^{\oplus}\right]= \)
\( 10^{-3}, \) The EMF of the half cell is:
\( \left[\boldsymbol{E}_{A \boldsymbol{g}^{\oplus} \mid \boldsymbol{A} \boldsymbol{g}}^{\ominus}=\mathbf{0 . 8 0} \boldsymbol{V}, \boldsymbol{K}_{a\left(\boldsymbol{H}_{2} \boldsymbol{S}\right)}=\right. \)
\( \left.\mathbf{1 0}^{-\mathbf{2 1}}, \boldsymbol{a n d} \boldsymbol{K}_{s p} \boldsymbol{o} \boldsymbol{f} \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{S}=\mathbf{1 0}^{-49}\right] \)
\( \mathbf{A} \cdot-0.1735 V \)
в. \( -0.19 V \)
c. \( +0.1735 V \)
D. \( +0.19 V \)
Subject: Maths
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{x}{\sqrt{1+x^{2}}}, \) then \( (\text { fofof }(x)) \) is
A \( \cdot \frac{x}{\sqrt{1+x^{2}}} \)
В. \( \frac{x}{\sqrt{1+3 x^{2}}} \)
c. \( x \)
D.
Subject: Physics
Figure shows three circular arcs, each
of radius \( R \) and total change as
indicated. The net electric potential at
the center of curvature is :-
\( A \)
в. \( \frac{Q}{2 \pi \epsilon_{0} R} \)
с. \( \frac{2 Q}{\pi \epsilon_{0} R} \)
D. \( \frac{Q}{\pi \epsilon_{0} R} \)
Subject: Chemistry
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H}(\boldsymbol{F})-\boldsymbol{C H}_{3} \) is a
alkyl flouride.
A. primary
B. secondary
c. tertiary
D. None of these
Subject: Maths
The diameter of the base of the cylinder
is \( 12 \mathrm{cm} \) and the height is \( 8 \mathrm{cm} . \) Find the surface area of the solid cylinder.
A \( \cdot 520 \mathrm{cm}^{2} \)
B. \( 524 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 528 \mathrm{cm}^{2} \)
D. \( 532 \mathrm{cm}^{2} \)
Subject: Physics
Two Resistor \( 2 \Omega \) and \( 4 \Omega \) are connected
in parallel. Two more Resistor \( 3 \Omega \) and
\( 6 \Omega \) are connected in parallel. These two combinations are in series with a
battery of emf \( 5 V \) and internal
Resistance \( 0.7 \Omega \). Calculate the current
through \( 6 \Omega \) Resistors.
Subject: Maths
A vector \( \vec{V} \) is given in a rectangular coordinates system as \( \boldsymbol{V}=\boldsymbol{6} \overrightarrow{\boldsymbol{i}}+\boldsymbol{8} \overrightarrow{\boldsymbol{j}} \)
where \( \vec{i} \) and \( \vec{\jmath} \) are the unit vectors along \( x \) and \( y \) axes, then the angle \( \theta \) which the vector \( \vec{V} \) makes with the \( x- \)
axis is
A. \( \tan \theta=8 / 6 \)
B. \( \tan \theta=6 / 8 \)
\( \mathbf{c} \cdot \tan \theta=6 \)
\( \mathbf{D} \cdot \tan \theta=8 \)
Subject: Chemistry
\( 100 m L \) of a saturated solution of
\( A g_{2} S O_{4} \) is added to \( 250 m L \) of a
saturated solution of \( P b C r O_{4} . \) Will any
precipitate form and if so what?
Given that \( : \boldsymbol{K}_{s p} \) for
\( A g_{2} S O_{4}, A g_{2} C r O_{4}, P b C r O_{4} \) and
\( P b S O_{4} \) are \( 1.4 \times 10^{-5}, 2.4 \times 10^{-12} \)
\( 2.8 \times 10^{-13} \) and \( 1.6 \times 10^{-8} \)
respectively.
\( \mathbf{A} \cdot A g_{2} C r O_{4} \)
B \( \cdot P b C r O_{4} \)
\( \mathbf{c} \cdot A g_{2} S O_{4} \)
\( \mathrm{D} \cdot \mathrm{PbSO}_{4} \)
Subject: Chemistry
A candle is burnt in a beaker until it
extinguishes itself. A sample of gaseous mixture in the beaker contains \( 6.08 \times 10^{20} \) molecules of \( N_{2}, 0.76 \times \)
\( 10^{20} \) molecules of \( O_{2}, \) and \( 0.50 \times 10^{20} \)
molecules of \( C O_{2} . \) The total pressure is
\( 734 \mathrm{mm} \) of Hg. The partial pressure of
\( O_{2} \) would be:
A. \( 760.0 \mathrm{mm} \) of \( \mathrm{Hg} \)
B. 76.0 mm of Hg
c. \( 7.6 \mathrm{mm} \) of \( \mathrm{Hg} \)
D. \( 0.76 \mathrm{mm} \) of \( \mathrm{Hg} \)
Subject: Physics
A beam of light composed of red and green rays is incident obliquely at a point on the face of a rectangular glass slab. When coming out on the opposite parallel face, the red and green
rays emerge from :-
A. Two points propagating in two different parallel directions
B. One point propagating in two different directions through slab
c. one point propagating in the same direction through slab
D. Two points propagating in two different non paralle directions
Subject: Chemistry
1.0 mole of ethyl alcohol and 1.0 mole
of acetic acid are mixed. At equilibrium, 0.666 mole of ester is formed. The value
of equilibrium constant is:
A . \( 1 / 4 \)
в. \( 1 / 2 \)
\( c \cdot 4 \)
\( D \)
Subject: Physics
A uniform circular disc of radius \( R \) lies
in the \( X Y \) plane with the centre coinciding with the origin. The moment of inertia about an axis
passing through a point on the \( X \) axis at a distance \( x=2 R \) and perpendicular
to the \( X Y \) plane is equal to its moment
of inertia about an axis
passing through a point on the \( Y \) axis at a distance \( y=d \) and parallel to the
\( X \) axis in the \( X \) -Y plane. The value of \( d \) is:
A \( \cdot \frac{4 R}{3} \)
В \( \cdot \sqrt{17}\left(\frac{R}{2}\right) \)
c. \( \sqrt{15}\left(\frac{R}{2}\right) \)
D \( \cdot \sqrt{13}\left(\frac{R}{2}\right) \)
Subject: Chemistry
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}=\boldsymbol{C H}_{2} \frac{\boldsymbol{B r}_{2}}{\Delta} \frac{\boldsymbol{M} \boldsymbol{g}}{\text {Dryether}} \)
\( \frac{\boldsymbol{C} \boldsymbol{H}_{3}-\stackrel{\boldsymbol{N}}{\boldsymbol{C}-\boldsymbol{C} \boldsymbol{H}_{3}}}{\boldsymbol{N H}_{4} \boldsymbol{C l}} \quad \frac{\boldsymbol{H}^{+}}{\boldsymbol{\Delta}} \quad(\boldsymbol{M} \boldsymbol{a} \boldsymbol{j} \boldsymbol{o} \boldsymbol{r}) \)
product of above reaction is:
\( \mathrm{A} \)
\( \mathrm{CH}_{2}=\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{N}-\mathrm{CH}_{3} \)
B. \( H_{2} C=C H-C H=C_{C H_{3}}-C H_{3} \)
c.
\[
H_{2} C=C H-C H_{2}-\underbrace{C}_{\mid}^{O H}-C H_{3}
\]
D. \( H_{2} C=C H-C H_{2}-C_{\} C H-C H_{2}-O H \)
Subject: Physics
The diameter of a solid disc is \( 0.5 m \) and
its mass is \( 16 k g \)

What torque is required to increase its angular velocity about an axis perpendicular to its plane from zero to 120 rotations/minute in 8 seconds?
\( ^{\mathbf{A}} \cdot \frac{\pi}{4} N / m \)
в. \( \frac{\pi}{2} N / m \)
c. \( \pi N / m \)
D. \( 2 \pi N / m \)
Subject: Chemistry
In the given, lewis structure of \( S_{2} O_{3}^{2-} \)
formal charge present on sulphur
atoms 1 and 2 respectively are:
A. \( z e r o,+1 \)
\( \mathbf{B} \cdot+1,+1 \)
\( \mathbf{c} .+2,+2 \)
D. zero, zero
Subject: Chemistry
Balance the following equations by ion electron method:
\( \boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{2+}+\boldsymbol{S O}_{2}+\boldsymbol{H}^{+} \rightarrow \boldsymbol{C r}^{3+}+ \)
\( \boldsymbol{H} \boldsymbol{S O}_{4}^{-}+\boldsymbol{H}_{2} \boldsymbol{O} \)
Subject: Physics
Electrons move at right angles to a magnetic field of \( 0.03 \mathrm{T} \) and enter with a velocity \( 9 \times 10^{7} m / s . \) The value of e \( / \mathrm{m} \)
will be: (Given radius of circular path =
\( 1.764 \mathrm{cm} \)
A \( \cdot 1.7 \times 10^{11} \mathrm{Ckg}^{-1} \)
В . \( 2 \times 10^{11} \mathrm{Ckg}^{-} \)
c. \( 2.5 \times 10^{11} \mathrm{Ckg}^{-1} \)
D. none of these
Subject: Chemistry
For the reaction: \( \boldsymbol{C O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \leftrightharpoons \)
\( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}), \mathrm{K} \) is found to be 16 at
a given temperature. Originally equal
numbers of moles of \( \boldsymbol{H}_{2} \) and \( \boldsymbol{C} \boldsymbol{O}_{2} \) were
placed in the flask. At equilibrium, the
pressure of \( \boldsymbol{H}_{2} \) is 1.20 atm. What is the
partial pressure of \( \boldsymbol{C O} \) and \( \boldsymbol{H}_{2} \boldsymbol{O} \) ?
\( A \cdot 4.80 \) atm each
B. 9.60 atm each
c. 2.40 atm each
D. 1.20 atm each
Subject: Chemistry
Assertion
Generally, covalent compounds are gases, liquids or soft solids at room temperature.
Reason
Between covalent compounds Vander
Waal's forces of attraction exists.
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
Consider a circular coil of wire carrying
constant current I, forming a magnetic dipole. The magnetic flux through an infinite plane contains the circular coil and excluding the circular coil area is
given by \( \mathbf{\Phi}_{\mathbf{i}} . \) The magnetic flux through
the area of the circular coil area is given
by \( \mathbf{\Phi}_{\mathbf{0}} \)
Which of the following options is
correct?
\( \mathbf{A} \cdot \Phi_{\mathrm{i}}<\Phi_{0} \)
\( \mathbf{B} \cdot \Phi_{\mathrm{i}}=\Phi_{0} \)
\( \mathbf{c} \cdot \Phi_{\mathrm{i}}>\Phi_{0} \)
\( \mathbf{D} \cdot \Phi_{\mathrm{i}}=-\Phi_{0} \)
Subject: Chemistry
We have taken a saturated solution of
\( A g B r . K_{s p} \) of \( A g B r \) is \( 12 \times 10^{-14} .1 f \)
\( 10^{-7} \) mole of \( A g N O_{3} \) are added to 1 litre of this solution find conductivity (specific conductance) of this solution in terms of \( 10^{-7} \mathrm{Sm}^{-1} \)
Given: \( \lambda_{A g^{+}}^{0}=6 \times 10^{-3} \mathrm{Sm}^{2} \mathrm{mol}^{-1} \)
\( \lambda_{B r^{-}}^{0}=8 \times 10^{-3} \mathrm{Sm}^{2} \mathrm{mol}^{-1} \) and
\( \lambda_{N O_{3}^{-}}^{0}=7 \times 10^{-3} \mathrm{Sm}^{2} \mathrm{mol}^{-1}[ \) If answe
is \( X \) then give answer in form of \( \frac{X}{11} \)
Subject: Physics
Given: \( \vec{a} \) and \( \vec{b} \) are unit vector, and \( \theta \) be
the angle between them. Then \( \frac{1-\vec{a} \cdot \vec{b}}{1+\vec{a} \cdot \vec{b}}= \)
A \( \cdot \sin ^{2} \frac{\theta}{2} \)
в. \( \cos ^{2} \frac{\theta}{2} \)
c. \( \tan ^{2} \frac{\theta}{2} \)
D. \( \cot ^{2} \frac{\theta}{2} \)
Subject: Biology
For the given DNA sequence, the complementary mRNA sequence is given as below
\( \mathbf{5}^{\prime} \boldsymbol{C G T A C G T A 3}^{\prime} \)
A . \( 3^{\prime} U C U A U G A A 5^{\prime} \)
B. \( 3^{\prime} \)TACATAGA \( 5^{\prime} \)
c. \( 3^{\prime} G C A U G C A U 5 \)
D. 3'UACAAGGA5'
E . \( 3^{\prime} \) ATGTCCTT5
Subject: Maths
find the equation of a line passing
through the point (1,2,-4) and
perpendicular to two lines. \( \vec{r}= \) \( (8 \hat{i}-19 \hat{j}+10 \hat{k})+ \)
\( \boldsymbol{\lambda}(\boldsymbol{3} \hat{\boldsymbol{i}}-\boldsymbol{1 6} \hat{\boldsymbol{j}}+\boldsymbol{7} \hat{\boldsymbol{k}}) \) and \( \overrightarrow{\boldsymbol{r}}= \)
\( (15 \hat{i}+29 \hat{j}+5 \hat{k})+ \)
\( \boldsymbol{\mu}(\mathbf{3} \hat{\boldsymbol{i}}+\quad \boldsymbol{8} \hat{\boldsymbol{j}}-\boldsymbol{5} \hat{\boldsymbol{k}}) \)
Subject: Chemistry
Assertion
The molecular weight of acetic acid determined by depression in freezing point method in benzene and water was found to be different.
Reason
Water is polar and benzene is non-polar.
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: Maths
A shopkeeper sells an article at its list price (Rs. 3,000) and charges sales-tax at the rate of \( 12 \% \). If the VAT paid by the
shopkeeper is Rs. \( 72, \) at what price did the shopkeeper buy the article inclusive of sales-tax?
A. Rs. 2688
B. Rs. 2966
c. Rs. 3422
D. Rs. 3966
Subject: Physics
A given object taken \( n \) times more time
to slide down a \( 45^{\circ} \) rough inclined plane
as it takes to slide down a perfectly
smooth \( 45^{\circ} \) incline. The coefficient of
kinetic friction between the object and the incline is :
A \( \cdot \sqrt{1-\frac{1}{n^{2}}} \)
в. \( _{1-\frac{1}{n^{2}}} \)
c. \( \frac{1}{2-n^{2}} \)
D. \( \sqrt{\frac{1}{1-n^{2}}} \)
Subject: Physics
A pulse of a wave train travels along a stretched string and reaches the fixed end of the string. It will be reflected
back with:
A. a phase change of \( 180^{\circ} \) with velocity reversed
B. the same phase as the incident pulse with no reversal of velocity
C. a phase change of \( 180^{\circ} \) with no reversal of velocity
D. the same phase as the incident pulse but with velocity reversed
Subject: Maths
Degree of \( \boldsymbol{y} \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}=\left[\boldsymbol{3}+\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{2}\right]^{\frac{2}{3}} \) is:
\( A \cdot 4 \)
в. 3
\( c \cdot 2 \)
\( D \)
Subject: Maths
The harmonic mean of two numbers is
4. The arithmetic mean \( A \) \& the
geometric mean G satisfy the relation
\( \mathbf{2} \boldsymbol{A}+\boldsymbol{G}^{2}=\mathbf{2} 7 . \) Find the largest of those
numbers?
\( \mathbf{A} \cdot \mathbf{6} \)
B. 4
c. 8
D. 5
Subject: Physics
A positive ion having only one electron
ejects it if a photon of \( \gamma \leq 228 A^{0} \) is
abosrbed by it. The ion is
A \( . H e^{+} \)
B. \( L i^{+} \)
\( \mathbf{c} \cdot B e^{+3} \)
D. \( B^{+4} \)
Subject: Physics
A car accelerates from rest at \( 5 m / s^{2} \) and then retards to rest at \( 3 m / s^{2} . \) The
maximum velocity of the car is \( 30 m / s \)
The distance covered by the car is
A . \( 150 \mathrm{m} \)
B. 240 m
c. \( 300 \mathrm{m} \)
D. 360 \( m \)
Subject: Physics
Dimensional analysis of the equation
\( (V e l o c i t y)^{x}= \)
\( (\text {Pressuredifference})^{\frac{3}{2}} \cdot(\text { density })^{\frac{-3}{2}} \)
gives the value of \( x \) as:
\( A \)
B. 2
\( c \cdot 3 \)
\( D \cdot-3 \)
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}^{2}+\boldsymbol{c} \boldsymbol{x}+\boldsymbol{d} \) and
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{x}-\boldsymbol{2} \)
If \( \lim _{x \rightarrow 1} \frac{f(x)}{g(x)}=1 \) and \( \lim _{x \rightarrow 2} \frac{f(x)}{g(x)}=4, \) then
find the value of \( \frac{c^{2}+d^{2}}{a^{2}+b^{2}} \)