AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
An atom has \( 2 K, 8 L \) and \( 5 M \) electrons.
Choose the correct statement(s)
regarding it.
A. Trivalent anion of this atom will have
12 protons in its nucleus.
B. Trivalent cation of this atom will have
six p-electrons in it.
C. This atom form an amphoteric oxide
of formula \( X_{2} O_{3} \)
D. One of its allotrope is tetra atomic
\( \left(X_{4}\right) \)
A. \( A \) and \( B \)
B. \( B \) only
c. \( B \) and \( C \)
D. \( B \) and \( D \)
Subject: Physics
Quality factor of series resonance circuit is given by
A \( \cdot \frac{f_{2}-f_{1}}{f_{0}} \)
в. \( f_{2}-f_{1} \)
c. \( \frac{f_{1}-f_{0}}{f_{2}} \)
D. \( \frac{f_{0}}{f_{2}-f_{1}} \)
Subject: Physics
Turn ratio in a setup transformer is \( 1: 2.1 \mathrm{f} \) a lechlanche cell of \( 1.5 \mathrm{V} \) is connected
across the input, what is the voltage across the output?
A . \( 1.5 v \)
B. 0.0
\( c \cdot 3 v \)
D. 0.75 \( v \)
Subject: Physics
Find the potentials of points \( A \) and \( B: \)
A \( \cdot V_{A}=+10 V ; V_{B}=0 V \)
B . \( V_{A}=+7.5 V ; V_{B}=-2.5 V \)
c. \( V_{A}=+2.5 V ; V_{B}=-7.5 V \)
D. \( V_{A}=+0 V ; V_{B}=-10 V \)
Subject: Chemistry
The preparation of ammonia by Haber's process is an exothermic reaction. If the
preparation follows the following
temperature pressure relationship for
its \% yield. Then the temperatures
\( T_{1}, T_{2} \) and \( T_{3}, \) the correct option is:
A \( \cdot T_{3}>T_{2}>T_{1} \)
В \( \cdot T_{1}>T_{2}>T_{3} \)
\( \mathbf{c} \cdot T_{1}=T_{2}=T_{3} \)
D. Nothing can be predicted
Subject: Maths
If the chord \( y=m x+1 \) of the circle
\( x^{2}+y^{2}=1 \) subtends an angle of
measure \( 45^{\circ} \) at the major segment of
the circle then the value of \( m \) is
A \( .2 \pm \sqrt{2} \)
B. \( -2 \pm \sqrt{2} \)
c. \( -1 \pm \sqrt{2} \)
D. none of these
Subject: Physics
Two long thin parallel conductor are
kept very close to each other without
touching. One carries a current \( i \) and
the other has charge \( \lambda \) per unit length. An electron moving parallel to the
conductor is undeflected. If \( c \) is the
velocity of light. then :
This question has multiple correct options
A \( \cdot v=\frac{\lambda c^{2}}{i} \)
B. \( v=\frac{i}{\lambda} \)
c. \( c=\frac{i}{\lambda} \)
D. the electron may be at any distance from the conductor
Subject: Chemistry
Consider the reaction:
\( \mathbf{4} N \boldsymbol{O}_{2(\boldsymbol{g})}+\boldsymbol{O}_{2(\boldsymbol{g})} \rightarrow \mathbf{2} \boldsymbol{N}_{\mathbf{2}} \boldsymbol{O}_{\boldsymbol{5}}(\boldsymbol{g}) ; \quad \boldsymbol{\Delta}_{\boldsymbol{r}} \boldsymbol{H}= \)
\( -111 k J \)
If \( N_{2} O_{5(s)} \) is formed instead of \( N_{2} O_{5}(g) \)
in the above reaction, then \( \Delta_{r} H \) value
will be:
[Given, \( \Delta \boldsymbol{H} \) of sublimation for \( \boldsymbol{N}_{\mathbf{2}} \boldsymbol{O}_{\mathbf{5}} \) is
\( \left.\mathbf{5 4} k J m o l^{-1}\right] \)
A \( .+54 k J \)
B . \( +219 k J \)
c. \( -219 k J \)
D. \( -165 k J \)
Subject: Chemistry
Ethanedioic acid has the formula
\( H O_{2} C C O_{2} H . \) What is the formula of
aluminium ethanedioate?
A \( . A l C_{2} O_{4} \)
в. \( A l\left(C_{2} O_{4}\right)_{3} \)
\( \mathbf{c} \cdot A l_{2} C_{2} O_{4} \)
D. \( A l_{2}\left(C_{2} O_{4}\right)_{3} \)
Subject: Maths
Some equations are solved on the basis
of a certain system. Find the correct
answer for the unsolved equation on that basis. If \( 324 \times 289=35,441 \times \)
\( \mathbf{4 8 4}=\mathbf{4 3}, \mathbf{6 2 5} \times \mathbf{4 0 0}=\mathbf{4 5}, \) find the
value of \( 256 \times 729 \)
A . 33
B . 35
c. 43
D. 34
Subject: Maths
For \( \mathbf{0} \leq \boldsymbol{x} \leq \mathbf{1}, \) the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( |\boldsymbol{x}|+|\boldsymbol{x}-\mathbf{1}| \) is
A. Monotonically increasing
B. Monotonically decreasing
c. constant function
D. Identity function
Subject: Physics
A solid sphere hung at the lower end of a wire is suspended from a fixed point so
as to give an elongation of \( 0.4 m m \) When the first solid sphere is replaced by another one made of same material
but twice the radius, the new
elongation is
A . \( 0.8 m m \)
в. \( 1.6 m m \)
\( \mathrm{c} .3 .2 \mathrm{mm} \)
D. \( 1.2 m m \)
Subject: Physics
Positive and negative point charges of equal magnitude are kept at \( \left(0,0, \frac{a}{2}\right) \) and \( \left(0,0, \frac{-a}{2}\right), \) respectively. The work done by the electric field when another
positive point charge is moved from \( (-a, 0,0) \) to \( (0, a, 0) \) is:
A. positive
B. negative
c. zero
D. depends on the path connecting the initial and final positions
Subject: Physics
The equation of the standing wave in a string clamped at both ends, vibrating in its third harmonic is given by : \( y= \) \( 0.4 \sin (0.314 x) \cos (600 \pi t) \) where, \( x \)
and \( y \) are in \( \mathrm{cm} \) and \( t \) in sec.
a) the frequency of vibration is \( 300 H z \)
b) the length of the string is \( 30 \mathrm{cm} \)
c) the nodes are located at \( x= \)
\( 0,10 c m, 30 c m \)
A. a,
в. а,
\( c \cdot b, c \)
D. a,b,
Subject: Physics
An electric dipole coincides on the zaxis and its centre coincides with the origin of the cartesian coordinate system. The electric field at an axial
point at a distance \( z \) from the origin is
\( E(z) \) and the electric field at an
equatorial point at a distance \( y \) from
the origin is \( E(y) \)

Given that \( y=z>>a \), the value of
\( \frac{E(z)}{E(y)} \) is
A . 1
B. 2
\( c .4 \)
D. 3
Subject: Chemistry
At what temperature liquid water will be in equilibrium with water vapour? \( \boldsymbol{\Delta} \boldsymbol{H}_{\boldsymbol{v a p}}=\mathbf{4 0 . 7 3} \boldsymbol{k J} \boldsymbol{m o l}^{-1}, \boldsymbol{\Delta} \boldsymbol{S}_{\boldsymbol{v a p}}= \)
\( \mathbf{0 . 1 0 9} \boldsymbol{k J} \boldsymbol{K}^{-\mathbf{1}} \boldsymbol{m o l}^{-1} \)
A. \( 282.4 \mathrm{k} \)
в. 373.6 к
\( c \cdot 100 k \)
D. 400
Subject: Maths
\( \boldsymbol{A}=(\mathbf{1}, \mathbf{2}, \mathbf{3}), \boldsymbol{B}=(\mathbf{4}, \mathbf{5}, \mathbf{7}), \boldsymbol{C}= \)
\( (-4,3,-6), D=(2, k, 2) \) are four
points. If the lines \( A B \) and \( C D \) are
parallel, then \( k= \)
\( A \cdot 0 \)
в. -9
\( c .9 \)
D. 2
Subject: Maths
If \( \vec{a}, \vec{b}, \vec{c} \) are unit vectors such that \( \vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}, \) then the value of
\( \vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a} \) is equal to
\( A \)
B. \( \frac{3}{2} \)
\( c \cdot 3 \)
D. \( -\frac{3}{2} \)
Subject: Chemistry
Assertion (A): In the synthesis of ammonia by Haber's process, mixture of potassium and aluminium oxides
can be used as promoter. Reason (R): Promoter enhances the
activity of catalyst.
A. Both (A) and (R) are true and
(R) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not the correct explanation of \( (A) \)
c. (A) is true and
(R) is false
D. (A) is false but (R) is true
Subject: Physics
Two identical mercury drops, each of
radius r are charged to the same
potential V.If the mercury drops coalesce to form a big drop, each of radius \( R \) then the potential of the combined drop will be
\( \mathbf{A} \cdot(3)^{1 / 2} V \)
B . \( (3)^{2 / 3} V \)
c. \( (2)^{2 / 3} V \)
D. \( (2)^{3 / 2} V \)
Subject: Maths
\( \cos ^{-1}\left\{\cos \left(\frac{5 \pi}{4}\right)\right\} \) is given by
\( ^{\text {A }} \cdot \frac{5 \pi}{4} \)
в. \( \frac{3 \pi}{4} \)
c. \( \frac{-\pi}{4} \)
D. none of these
Subject: Chemistry
The molar concentrations of \( A, B \) and \( C \) at equilibrium for the reaction \( \boldsymbol{A}+ \) \( 2 B \Leftrightarrow 3 C \) are 2,3 and 4 moles/lit
respectively. Its \( \boldsymbol{K}_{c} \) is:
\( A \cdot 2 \)
в. 3.56
\( c \cdot 0.2 \)
D. 0.026
Subject: Chemistry
The half life of a first order reaction is
69.35 seconds, the value of rate constant of the reaction is:
A \( \cdot 1.0 s^{-1} \)
B. \( 0.1 s^{-1} \)
\( c \cdot 0.01 s^{-1} \)
D. \( 0.001 s^{-1} \)
Subject: Maths
Use the graphical method to find the
value of \( k, \) if \( (5, k-2) \) lies on the
straight line \( \boldsymbol{x}-\mathbf{2} \boldsymbol{y}+\mathbf{1}=\mathbf{0} \)
A .2
B. 3
\( c \cdot 4 \)
D. 5
Subject: Maths
\( \lim _{x \rightarrow x_{1}} \frac{x}{x-x_{1}} \int_{x_{1}}^{x} f(t) d t \) is equal to
В \( \cdot x_{1} f\left(x_{1}\right) \)
\( \mathbf{c} \cdot f\left(x_{1}\right) \)
D. Does not exist
Subject: Maths
Area enclosed by the graph of the function \( y=\ln ^{2} x-1 \) lying in the \( 4 t h \)
quadrant is
\( A \cdot \frac{2}{e} \)
B. \( \frac{4}{e} \)
c. \( _{2}\left(e+\frac{1}{e}\right) \)
D. \( 4\left(e-\frac{1}{e}\right) \)
Subject: Maths
Evaluate: \( \int \sec ^{4} x \cdot \operatorname{cosec}^{2} x d x \)
A. \( \frac{1}{3} t^{3}+t \)
B \( \cdot \frac{1}{3} t^{3}+2 t-\frac{1}{t} \)
c. \( \frac{1}{2} t^{3}+2 t-\frac{1}{t} \)
D. \( \frac{1}{3} t^{3}-t-\frac{1}{t} \)
Subject: Physics
A nucleus \( X \) initially at rest, undergoes alpha decay according to the equation
\[
\mathbf{9 2}^{\boldsymbol{X}^{A}} \rightarrow \boldsymbol{Z}^{Y^{228}}+\boldsymbol{\alpha}
\]
Then, the values of \( A \) and \( Z \) are
A .94,230
в. 232,90
c. 190,32
D. 230,94
Subject: Physics
What quantity of heat would be given out by 200 gm of copper in cooling from
\( 80^{\circ} \mathrm{C} \) to \( 20^{\circ} \mathrm{C} \) (Specific heat of copper
\( \left.=\mathbf{0 . 0 9 c a l g}^{-1 o} \mathbf{C}^{-1}\right) ? \)
A. 1080 cal
B. 1000 cal
c. 1500 cal
D. 1100 cal
Subject: Maths
In solving a problem, one student makes a mistake in the coefficient of
the first degree term and obtains -9
and -1 for the roots. Another student
makes a mistake in the constant term
of the equation and obtains 8 and 2 for the roots. The correct equation was?
A. \( x^{2}+10 x+9=0 \)
B . \( x^{2}-10 x+16=0 \)
c. \( x^{2}-10 x+9=0 \)
D. None of the above
Subject: Chemistry
Carbon atoms in compound \( \left(C N_{4}\right) C_{2} \)
are:
A. sp hybridizes
B \( \cdot s p^{2} \) hybridized
c. \( s p \& s p^{2} \) hybridized
D. \( s p, s p^{2} \& s p^{3} \) hybridized
Subject: Chemistry
The final step for the extraction of
copper from copper pyrites in Bessemer converter the reaction involves is as:
A \( \cdot C u_{2} S+2 F e O \rightarrow 2 C u+2 F e+S O_{2} \)
в. \( C u_{2} S+2 C u O \rightarrow 6 C u+S O_{2} \)
c. \( 4 C u_{2} S+F e S \rightarrow 8 C u+2 F e S O_{4} \)
D. \( 2 C u_{2} O+F e S \rightarrow 4 C u+2 F e+S O_{2} \)
Subject: Chemistry
Hybridization and shape of \( \mathbf{X e F}_{4} \) is:
A \( \cdot \mathrm{sp}^{3} \mathrm{d} \), trigonal bipyramidal
B . sp \( ^{3} \), tetrahedral
c. \( s p^{3} d^{2}, \) square planar
D. \( \operatorname{sp}^{3} \mathrm{d}^{2} \), hexagonal
Subject: Maths
On comparing the ratios \( \frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}} \) and \( \frac{c_{1}}{c_{2}} \)
find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident.
\( \mathbf{6} \boldsymbol{x}-\mathbf{3} \boldsymbol{y}+\mathbf{1 0}=\mathbf{0} ; \mathbf{2} \boldsymbol{x}-\boldsymbol{y}+\mathbf{9}=\mathbf{0} \)
A. Intersect at a point
B. Parallel
c. coincident
D. Data insufficient
Subject: Physics
A current-carrying circular coil of magnetic moment \( M \) is situated in a
magnetic field \( B \). The work done in
deflecting it from an angle \( 0^{\circ} \) to \( \theta^{\circ} \) will
be :
\( A . M B \)
В. \( M B(1-\cos \theta) \)
\( \mathrm{c} \cdot-M B \)
D. \( M B(1-\sin \theta) \)
Subject: Maths
Find the general solution of \( \frac{d y}{d x}=\frac{2 y}{x} \)
A \( \cdot y=e^{5 \log x+c} \)
B . \( y=e^{3 \log x+c} \)
C \( \cdot y=e^{2 \log x+c} \)
D. None of these
Subject: Physics
A point source of light is placed at the
bottom of a water lake. If the area of the
illuminated circle on the surface is
equal to 3 times the square of the lake. The refractive index of water is
A. \( \sqrt{\pi+1} \)
B. \( \sqrt{\frac{\pi}{3}+1} \)
c. \( \frac{\pi}{3}+1 \)
D. \( \frac{\pi}{4}+1 \)
Subject: Chemistry
Which of the following is a true
statement:
A. The ionisation constant and ionic product of water are same.
B. Water is a strong electrolyte.
C. The value of ionic product of water is less than that of its ionisation constant
D. At \( 298 K \), the number of \( H^{+} \) ions in a litre of water is \( 6.023 \times 10^{16} \)
Subject: Physics
A lens produces an image of an object on a screen. If a slab of refractive index
n is placed in between lens and screen,
the screen has to be moved by distance
d behind. The thickness of slab is
A \( . n d \)
в. \( \frac{n-1}{n d} \)
c. \( \frac{(n-1) d}{n} \)
D. \( \frac{n d}{n-1} \)
Subject: Physics
A spring is stretched by \( 0.20 m \) when a
mass of \( 0.50 \mathrm{kg} \) is suspended. A mass of \( 0.25 \mathrm{kg} \) is suspended, then its period
of oscillation will be \( \left(g=10 m / s^{2}\right) \)
(approximately)
A \( .0 .628 s \)
B. \( 0.251 s \)
\( \mathbf{c} \cdot 6.28 s \)
D. 2.51s
Subject: Physics
In elastic collision, \( A \) is conserved while
in inelastic collision \( B \) is conserved.
I.Momentum
II.Kinetic Energy
III.Potential Energy
A. \( A= \) ।, ॥ \( B=1, \) II
в. \( A= \) ।, ॥ \( B=1 \)
c. \( A=\| \) \( B= \) ॥, ॥ ॥
D. \( A=\| \) \( B=1, \) II
Subject: Maths
If area bounded by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{\frac{1}{3}}(\boldsymbol{x}-\mathbf{1}) \)
\( x- \) axis is \( A \) then find the value of \( 28 A \)
A . 5
B. 6
\( c \cdot 7 \)
D. 9
Subject: Physics
The focal length of a thin biconvex lens
is \( 20 \mathrm{cm} \). When an object is moved from
a distance of \( 25 \mathrm{cm} \) in front of it to \( \mathbf{5 0} \mathrm{cm}, \) the magnification of its image
changes from \( \boldsymbol{m}_{25} \) to \( \boldsymbol{m}_{60} . \) The ratio
\( \boldsymbol{m}_{25} / \boldsymbol{m}_{50} \) is
Subject: Physics
If a force \( 10 \hat{i}+15 \hat{j}+25 \hat{k} \) acts on a
system and gives an acceleration \( 2 \hat{\mathbf{i}}+ \) \( 3 \hat{j}-5 \hat{k} \) to the centre of mass of the
system, the mass of the system is
A . 5 units
B. \( \sqrt{38} \)units
c. \( 5 \sqrt{38} \) units
D. Given data is not correct
Subject: Chemistry
\( 25.0 \mathrm{cm}^{3} \) of \( 0.0497 \mathrm{M} \) solution of
\( N H_{2} O H \) was boiled with excess of
ferric alum solutuion in \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \). The
\( \mathrm{Fe}(\|) \) formed rquired \( 24.7 \mathrm{cm}^{3} \) of 0.1007
\( \left.N K_{2} C r_{2}\right)_{7} \) solution. Identify the
product formed by oxidation of
\( N H_{2} O H \)
A \( \cdot N_{2} O_{4} \)
в. \( N_{2} \) О
\( \mathrm{c} \cdot \mathrm{N}_{2} \mathrm{O}_{2} \)
D. \( N O \)
Subject: Maths
If \( z_{0}=\frac{1-i}{2}, \) then
\( \left(\mathbf{1}+\boldsymbol{z}_{0}\right)\left(\mathbf{1}+\boldsymbol{z}_{\mathbf{0}}^{\mathbf{2}^{1}}\right)\left(\mathbf{1}+\boldsymbol{z}_{\mathbf{0}}^{\mathbf{2}^{2}}\right) \ldots \ldots \ldots(\mathbf{1}+ \)
must be
A \( \cdot(1-i)\left(1+\frac{1}{2^{2^{n}}}\right) \) for \( n>1 \)
B. \( (1-i)\left(1-\frac{1}{2^{2^{n}}}\right) \) for \( n> \)
c. \( \frac{1+i}{2} \) for \( n>1 \)
D. \( (1-i)\left(1-\frac{1}{2^{2 n+1}}\right) \) for \( n>1 \)
Subject: Chemistry
Which of the following will exhibit maximum ionic conductivity?
A \( \cdot K_{4}\left[\operatorname{Fe}(C N)_{6}\right] \)
B. \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{3} \)
\( \mathbf{c} \cdot\left[C u\left(N H_{3}\right)_{4}\right] C l_{2} \)
D. \( \left[N i(C O)_{4}\right] \)
Subject: Chemistry
When chlorine gas and hydrogen gas react to form hydrogen chloride, what will be the change of enthalpy of the reaction? (bond energies are at the end of this test)
A . \( +245 k J / m o l \)
в. +185 k \( J / \) mol
c. \( -185 k J / m o l \)
D. \( -1105 k J / m o l \)
E . \( +1105 ~ k J / m o l \)
Subject: Chemistry
From the following find out groups of isotopes, isobars and isotones:
\( _{8}^{16} \boldsymbol{O}_{, 19}^{39} \boldsymbol{K}_{, 6}^{14} \boldsymbol{C}_{, 92}^{239} \boldsymbol{U}_{, 7}^{14} \boldsymbol{N}_{, 20}^{40} \boldsymbol{C} \boldsymbol{a}_{, 92}^{238} \boldsymbol{U}_{, 32}^{77} \boldsymbol{G} \)
Subject: Physics
In a magnetic field of \( 0.05 T \) area of coil
changes from \( 101 \mathrm{cm}^{2} \) to \( 100 \mathrm{cm}^{2} \)
without changing the resistance which
is \( 2 \Omega . \) The amount of charge that flow during this period is
A \( .2 .5 \times 10^{-6} \mathrm{C} \)
В. \( 2 \times 10^{-6} C \)
\( \mathbf{c} \cdot 10^{-6} C \)
D. \( 8 \times 10^{-6} C \)
Subject: Chemistry
For the following reactions:
\( Z n \rightarrow Z n^{2+}+2 e^{-} ; E=+0.76 V \)
\( \boldsymbol{A u} \rightarrow \boldsymbol{A u}^{3+}+\mathbf{3} e^{-} ; \boldsymbol{E}=-\mathbf{1 . 4 2} \boldsymbol{V} \)
If gold foil is placed in a solution
containing \( Z n^{2+}, \) the reaction potential
would be:
A . \( -1.34 V \)
в. \( -2.18 V \)
c. \( -0.66 V \)
D. \( +2.18 V \)
E . \( +1.34 V \)
Subject: Physics
A solid copper sphere has a charge of \( +\mathrm{Q} \)
on it. Where on the sphere does the
charge reside?
A. \( +Q \) at the center of the sphere
B. \( \mathrm{Q} / 2 \) at the center of the sphere and \( \mathrm{Q} / 2 \) on the outer surface
c. \( \mathrm{Q} \) at the center of the sphere and \( +2 \mathrm{Q} \) on the outer surface
D. \( + \) Q on the outer surface
E. The charge is spread evenly throughout the sphere
Subject: Chemistry
Which of the following statements, about the advantage of roasting of sulphide ore before reduction is not
true?
A. The \( \Delta G_{f}^{0} \) of the sulphide is greater than those for \( C S_{2} \) and \( H_{2} S \)
B. The \( \triangle G_{f}^{0} \) is negative for roasting of sulphide ore to oxide
c. Roasting of the sulphide to the oxide is thermodynamically feasible
D. Carbon and hydrogen are suitable reducing agents for metal sulphides.
Subject: Chemistry
Calculate the oxidation number of the
underlined elements.
a. \( \underline{P H}_{3} \)
b. \( \underline{S} O_{2} \)
\( \boldsymbol{H} \underline{\boldsymbol{N}} \boldsymbol{O}_{3} \)
d. \( \boldsymbol{H}_{3} \underline{\boldsymbol{P}} \boldsymbol{O}_{\mathbf{4}} \)
\( \begin{array}{llll}\text { A. } \text { a. }-3 ; & \text { b. }+4 ; & \text { c. }+5 ;\end{array} \) +5
В. а. \( -3 ; \quad \) b. \( +2 ; \quad \) с. \( +5 ; \)
d. +5
c. a. \( -3 ; \) b. +4
c. +5 +4
D. None of these
Subject: Physics
A straight conductor of uniform cross section carries a time varying current, which varies at the rate \( \boldsymbol{d} \boldsymbol{I} / \boldsymbol{d} \boldsymbol{t}=\boldsymbol{I} \). If \( s \)
is the specific charge that is carried by each charge carrier of the conductor
and \( \ell \) is the length of the conductor, then the total force experienced by all the charge carriers per unit length of
the conductor due to their drift
velocities only is
A. \( F= \) Is
\( ^{\mathrm{B}} F=\frac{\dot{I}}{2 \sqrt{I_{S}}} \)
\( ^{\mathrm{c}} \cdot_{F}=\frac{\dot{I}}{s} \)
D. \( _{F}=\frac{2 I \dot{I}}{s} \)
Subject: Maths
Find the correct statement pertaining to the functions \( f(x)=(x-3)^{2}+2 \) and
\( g(x)=\frac{1}{2} x+1 \) graphed above
A \( \cdot f(x)=g(x) \) for exactly 2 values of \( x \)
B . \( f(x)=g(x) \) for exactly 1 values of \( x \)
c. \( f(x) \) is the inverse of \( g(x) \)
\( \mathbf{D} \cdot f(x)>g(x) \) for all \( x \)
Subject: Maths
If \( \boldsymbol{y}(\boldsymbol{t}) \) is a solution of \( (\boldsymbol{1}+\boldsymbol{t}) \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{t}}-\boldsymbol{t} \boldsymbol{y}= \)
1 and \( y(0)=-1, \) then \( y(1) \) equal to
A. \( -\frac{1}{2} \)
B. \( e+\frac{1}{2} \)
c. \( _{e-\frac{1}{2}} \)
D. \( \frac{1}{2} \)
Subject: Physics
Assertion
No net force acts on a rectangular coil
carrying a steady current when
suspended freely in a uniform magnetic
field.
Reason
Force on coil in magnetic field is always
non-zero.
A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
C. If Assertion is correct but Reason is incorrect.
D. If Assertion is incorrect but Reason is correct.
Subject: Physics
A centre tapped transformer is rated 12
0-12 V. The peak voltage obtained is
A . 12 v
B. \( \frac{12}{\sqrt{2}} V \)
\( \mathrm{c} \cdot 12 \sqrt{2} V \)
D. \( 24 V \)
E \( .24 \sqrt{2} V \)
Subject: Chemistry
In an equilibrium \( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{C}+\boldsymbol{D}, \boldsymbol{A} \)
and \( B \) are mixed in a vessel at
temperature \( \boldsymbol{T} \). The initial
concentration of \( A \) was twice the initial
concentration of \( B \). After the
equilibrium has reached, concentration
of \( C \) was thrice the equilibrium
concentration of \( B . \) Calculate \( \boldsymbol{K}_{\boldsymbol{C}} \)
A . 0.14
B. 65
\( c .3 .6 \)
D. 1.8
Subject: Chemistry
Match the column
1. Common salt
a. magnetic separation
2. lodine in chloroform
b. alcohol and water
3. Separating funnel \( \quad \) c. evaporation
4. Fractional
d. liquid-liquid distillation
A. \( 1-\mathrm{c}, 2-\mathrm{a}, 3-\mathrm{d}, 4-\mathrm{b} \)
B. 1-c, 2-d, 3-a, 4-b
c. \( 1-d, 2-c, 3-b, 4-a \)
D. \( 1-b, 2-c, 3-d, 4-a \)
Subject: Maths
\( A B C \) is an isosceles triangle with
\( A B=A C \) and \( A D \) is one of its altitude
A. State the three pairs of equal parts in \( \triangle A D B \) and \( \triangle A D C \)
B. Is \( \triangle A D B \cong A D C \) ? Why or why not?
c. Is \( \angle B=\angle C \) ? Why or why not?
D. Is \( B D=C D \) ? Why or why not?
Subject: Chemistry
For the equilibrium, \( N_{2} O_{4}(g) \rightleftharpoons \) \( 2 N O_{2}(g) ; \) if percentage dissociation of
\( N_{2} O_{4} \) are \( 25 \%, 50 \%, 75 \% \) and \( 100 \% \) then
the sequence of observed vapour densities will be:
A \( \cdot d_{1}>d_{2}>d_{3}>d_{4} \)
в. \( d_{4}>d_{3}>d_{2}>d_{1} \)
c. \( d_{1}=d_{2}=d_{3}=d_{4} \)
\( \mathbf{D} \cdot\left(d_{1}=d_{2}\right)>\left(d_{3}=d_{4}\right) \)
Subject: Physics
A cord is wound round the
circumference of a solid cylinder of
radius \( R \) and mass \( M . \) The axis of the
cylinder is horizontal. A weight \( m g \) is
attached to the end of the cord and falls
from rest. After falling through a
distance \( h \)
The angular velocity of the cylinder will
be :
A \( \cdot \frac{2 m g}{M+2 m} \)
в. \( \sqrt{\frac{2 g h}{R^{2}}} \)
c. \( \sqrt{\frac{4 m g h}{(M+2 m) R^{2}}} \)
Subject: Maths
If vectors \( i+2 j+2 k \) is rotated through
an angle of \( 90^{\circ} \) so as to cross positive
direction of \( y \) -axis, then the vector in the new positive is?
A \( \cdot-\frac{2}{\sqrt{5}} i+\sqrt{5} j-\frac{4}{\sqrt{5}} k \)
B. \( \frac{2}{\sqrt{5}} i-\sqrt{5} j+\frac{4}{\sqrt{5}} k \)
c. \( 4 i-j-k \)
D. None of these
Subject: Maths
The construction of \( 3 \times 4 \) matrix \( A \)
whose elements \( a_{i j} \) is given by \( \frac{(i+j)^{2}}{2} \) is
\( \mathbf{A} \cdot\left[\begin{array}{llll}2 & 9 / 2 & 8 & 25 \\ 9 & 4 & 5 & 18 \\ 8 & 25 & 18 & 49\end{array}\right] \)
\( \mathbf{B} \cdot\left[\begin{array}{cccc}2 & 9 / 2 & 25 / 2 & 9 \\ 9 / 2 & 5 / 2 & 5 & 45 / 2 \\ 25 & 18 & 25 & 9 / 2\end{array}\right] \)
\( \mathbf{C} \cdot\left[\begin{array}{cccc}2 & 9 / 2 & 8 & 25 / 2 \\ 9 / 2 & 8 & 25 / 2 & 18 \\ 8 & 25 / 2 & 18 & 49 / 2\end{array}\right] \)
D. None of these
Subject: Physics
Current sensitivity of a moving coil galvanometer is 5 div/mA and its voltage sensitivity (angular deflection per unit voltage applied) is 20 div/V. The resistance of the galvanometer is?
\( \mathbf{A} \cdot 250 \Omega \)
B. \( 40 \Omega \)
c. \( 500 \Omega \)
D. 25 \Omega
Subject: Physics
An arc lamp requires a direct current of \( 10 A \) at \( 80 \mathrm{V} \) to function. If it is connected to a \( 220 \mathrm{V}(\mathrm{rms}), 50 \mathrm{Hz} \) AC supply, the series inductor needed for it to work is
close to:
A . 80H
B. 0.08H
c. 0.0444
D. 0.065H
Subject: Physics
Density of water is
\( \mathbf{A} \cdot 1000 k g / m^{3} \)
B . \( 1 k g / m^{3} \)
\( \mathbf{c} \cdot 1000 g / \mathrm{cm}^{2} \)
D. \( 100 k g / m^{3} \)
Subject: Physics
The temperature of a one mole of diatomic gas changes from \( 4 \mathrm{T} \) to \( \mathrm{T} \) in adiabatic process. If \( R \) is universal gas constant. Then work done
A \( \cdot \frac{15 R T}{3} \)
в. \( \frac{15 R T}{2} \)
c. \( \frac{3 R T}{15} \)
D. \( \frac{12 R T}{5} \)