The statement "all tax payers above 60 years in India" is an example of
(A) Sample
(B) Finite population
(C) Infinite population
(D) Statistical Interference

\(\int_1^2 \frac{1}{x(x+1)} d x, x>0\) equals

Let A be a non-singular square matrix of order 3 and |adj A| = 5 then |A| is equal to

If the matrix \(\left[\begin{array}{ccc}-1 & x-y & 4 \\ 2 & 0 & 5 \\ x+y & z & 6\end{array}\right]\) is symmetric, then \(x+3 y+2 z\) is equal to

Match List - I with List - II.

LIST-I (Equation of curves)	LIST-II (Slope of tangent at \(x=2\))
(A) \(y=x^3-x\)	(I) 8
(B) \(y=(x-2)^2\)	(II) \(frac{2}{3}\)
(C) \(y=2 x^2+3\)	(III) \(11\)
(D) \(y=\sqrt{4 x+1}-7\)	(IV) \(0\)

Choose the correct answer from the options given below :

The function \(f(x)=\frac{x}{3}+\frac{3}{x}\) is increasing in the interval:

A random sample of size 16 has 53 as mean. The sum of the squares of the deviations taken from mean is 150 . If the population mean is 56 then the value of \(t\)-test statistic is :

The feasible region represented by the constraints \(x+2 y \geq 100,2 x-y \leq 0.2 x+y \leq 200, x \geq 0, y \geq 0\) of an LPP is

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.
Select the correct statement.

Let \(A=\left[\begin{array}{cc}3 & -1 \\ 2 & 4\end{array}\right]\), then \(\operatorname{adjoint}(A)\) is:

Somaclones can be defined as:

The current in a resistive series circuit is 7.0 A. On adding a resistance of 1.6 \( \Omega \) in the same circuit in series, the current drops to 5.0 A. The original resistance of the circuit is :

In an unbiased p-n junction, holes diffuse from the p-region to n-region because