If \(f(x)=\frac{3 x+2}{5 x-3}, x \in R-\left\{\frac{3}{5}\right\}\), then

Match List - I with List - II

List - I (Time series component)	List - II (Example)
(A) Secular Variation	(I) Pandemic
(B) Seasonal Variation	(II) Recession in business
(C) Cyclic Variation	(III) Monthly sale of woolen clothes
(D) Irregular Variation	(IV) Data regarding National income

Choose the correct answer from the options given below:

The number of all possible matrices of order 2 × 2 with each entry 0, 1 or 2 are:

The mean number of heads in two tosses of a coin is:

The corner points of the feasible region determined by a system of linear constraints are (0,0), (0, 40), (20, 40), (60, 20), (60, 0). If the objective function is \(Z = 4x + 3y\) then which one of the following is true?

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

The image of the point \((3,-2,1)\) in the plane \(3 x-y+4 z=2\) is:

Read the passage carefully and answer the questions
Amines are considered as derivatives of ammonia obtained by replacement of hydrogen atoms with alkyl or aryl groups. In nature they occur among proteins, vitamins, alkaloids and hormones. These can be primary, secondary or tertiary depending on the number of hydrogen groups replaced. They can be prepared from nitro compounds, alkyl halides, nitriles, amides etc. Due to unshared pair of electrons they behave as Lewis bases. Influence of the number of hydrogen atoms at nitrogen atom is displayed in physical properties such as solubility, boiling point and chemical reactions including basicity. Basic character of amines is expressed in terms of their \(K_b\) and \(p K_b\) values. Three classes of amines can be distinguished with p-toluene sulphonyl chloride which reacts with primary and secondary ddu amines. Amino group when attached to benzene ring behaves as an activating and ortho para directing group.
Which amine will have highest \(p K _{ b }\) value?

A student got data showing productivity of three different ecosystems, but the unit was missing, Choose the correct unit.

DNA fragments can be separated by a technique known as:

If \(D_1=\left|\begin{array}{ccc}\frac{1}{2} & \frac{1}{\sqrt{2}} & 0 \\ -\frac{1}{\sqrt{2}} & \frac{1}{2} & 0 \\ 0 & 0 & 1\end{array}\right|\) and \(D_2=\left|\begin{array}{ccc}\frac{1}{\sqrt{2}} & \frac{1}{2} & 0 \\ -\frac{1}{2} & \frac{1}{\sqrt{2}} & 0 \\ 0 & 0 & 1\end{array}\right|\), then \(D_1 D_2\) is equal to :

Hardy - Weinberg principle states that:

The general solution of the differential equation \(x\left(\frac{d y}{d x}\right)=y+x \tan \left(\frac{y}{x}\right)\) is