Let \(R\) be the relation in the set \(\{1,2,3\}\) given by \(R=\{(1,1),(2,2),(3,3),(1,2),(2,3)\}\). Choose the correct answer.

The mean of numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is:

A money lender charges Rs 10 for Rs 100 per month in advance then effective rate of interest per annum charged by money lender is : \(\left[\right.\) given \(\left.\left(\frac{10}{9}\right)^{12}=3.541\right]\)

The demand function (in Rs.) for a product is \(P=20-0.25 x\). where P is the price per unit and \(x\) is the number of units sold. Find the price of one unit when the revenue is maximized

If \(A\) is a square matrix such that \(A^2=A\), then \((I+A)^3-8 A\) is equal to:

The value of the determinant \(\left|\begin{array}{ccc}a+1 & b & c \\ a & b+1 & c \\ a & b & c+1\end{array}\right|\) is :

Unit vectors perpendicular to the plane of vectors \(\vec{a}=\hat{i}-\hat{j}-3 \hat{k}, \vec{b}=\hat{i}+3 \hat{j}-\hat{k}\) are:

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 ___________

Which of the following are not electromagnetic waves?
A. Gamma rays
B. Cathode rays
C. X-rays
D. \(\beta\)-rays
E. Radio waves
Choose the correct answer from the options given below:

The integral \(\int e^x\left(\frac{x-1}{2 x^2}\right) d x\) is equal to:

Which of the following can produce virtual image larger than the object?

The particular solution of the differential equation \(e^x \sqrt{1-y^2} d x+\frac{y}{x} d y=0\), given that \(y=1\), when \(x=0\), is:

A light with an energy flux of 25 \( W/cm^2 \) falls on a non-reflecting surface at normal incidence. If the surface has an area of 50 \( cm^2 \) and the total energy falling on the surface is \( 10 \times 10^5 \) J. The total duration of time of the incidence of light is