The maximum number of equivalence relations on the set \(A=\{a, b, c\}\) is:

A and B are two sets such that n(A) = 5 and n(B) = 7. The number of one-one functions from A to B is

If \(\vec{a}+\vec{b}+\vec{c}=0,|\vec{a}|=3,|\vec{b}|=25,|\vec{c}|=7\), then the angle between \(\vec{a}\) and \(\vec{b}\) is:

The general solution of the differential equation \(\frac{d y}{d x}+\sqrt{\frac{1-y^2}{1-x^2}}=0\) is :

A stone is dropped into a lake and waves move in circles at a speed of \(8 cm / sec\). At the instant, when the radius of the circular wave is 10 cm , how fast is the enclosed area increasing?

The area enclosed by the curve \(x=8 \cos t, y=4 \sin t\) between the lines \(x=0\) and \(x=4 \sqrt{3}\) is:

The intervals in which the function \(f(x) = 2x^3 + 9x^2 + 12x + 20\) is increasing is given by:

What is the magnification of simple microscope having focal length 5 mm?

If the probability of two successes is 9 times the probability of 3 successes in 3 trials of a binomial distribution, then the probability of success in each trial is:

The phenomenon responsible for the blue colour of the sky

Match List-l with List-II

List-l (Complex)	List-II (Property)
(A) \(\left[ CoF _6\right]^{3-}\)	(I) \(d^5\), high spin
(B) \(\left[ Fe ( CN )_6\right]^{4-}\)	(II) \(d^6\), high spin
(C) \(\left[ FeF _6\right]^{3-}\)	(III) \(d^5\), low spin
(D) \(\left[ Mn ( CO )_6\right]^{2+}\)	(IV) \(d^6\), low spin

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Read the passage carefully and answer the questions
The resistance (\(R\) ) of an object is given by the expression \(R=\rho \frac{l}{A}\).
The inverse of \(R\) is called conductance and the inverse of \(\rho\) is called conductivity or specific conductance represented by \(\kappa\).
The conductivity depends upon the nature of the material (insulator, semiconductor or conductor) and the temperature of the substance.
Similarly, the conductance due to the ions present in the solution (ionic conductance) depends upon the nature of the electrolyte, size of ions, the nature of the solvent and the temperature.
Molar conductivity ( \(\Lambda_m\) ) of a solution at a given concentration is the conductance of volume \(V\) containing one mole of electrolyte kept between two electrodes of area \(A\) and unit distance apart.
It is given by the expression \(\Lambda_m=\kappa V\).
Molar conductivity increases with decrease in concentration and when concentration approaches zero, it is called limiting molar conductivity.
The decrease is linear for a strong electrolyte. However, for a weak electrolyte the change is gradual at higher concentrations and sharp near zero concentration.
Using limiting molar conductivity values of strong electrolytes we can calculate the limiting molar conductivity of weak electrolytes using Kohlrausch law of independent migration of ions.
From molar conductivity and limiting molar conductivity we can determine the degree of dissociation \(\left(\frac{\Lambda_m}{\Lambda_m^0}\right)\) and the ionization constant of a weak acid.
SI units of conductance and conductivity, respectively, are ___________

The amines which are soluble in water
(A) Methanamine
(B) Ethanamine
(C) Propanamine
(D) Benzylamine
Choose the correct answer from the options given below: