The pattern and behavior of the data in any time series are based on which of the following components:
(A) Secular trend component
(B) Seasonal component
(C) Cyclical component
(D) Irregular component
Choose the correct answer from the options given below :

If \(2 P(A)=P(B)=\frac{5}{13}\) and \(P(A \mid B)=\frac{2}{5}\), then the value of \(P(A \cup B)\) is :

If z = 5x + 8y is the objective function of a LPP and (0,0), (3, 1), (2, 4), (0, 3), (5,0) are corner points of the bounded feasible region, then the maximum value of the objective function is

Match List-I with List-II

List-I (Integral)	List-II (Solution: C is an arbitrary constant)
(A) \(\int \frac{d x}{x^2+25}\)	(I) \(\frac{1}{10} \log \left|\frac{5+x}{5-x}\right|+C\)
(B) \(\int \frac{d x}{x^2-25}\)	(II) \(\log \left|x+\sqrt{x^2-25}\right|+C\)
(C) \(\int \frac{d x}{25-x^2}\)	(III) \(\frac{1}{5} \tan ^{-1}\left(\frac{x}{5}\right)+C\)
(D) \(\int \frac{d x}{\sqrt{x^2-25}}\)	(IV) \(\frac{1}{10} \log \left|\frac{x-5}{x+5}\right|+C\)

Choose the correct answer from the options given below:

\(\int \frac{d x}{2 \sin ^2 x+5 \cos ^2 x}\) is equal to

Let \(A=\left[\begin{array}{ccc}1 & -2 & 3 \\ 1 & 2 & 1 \\ \lambda & 2 & -3\end{array}\right]\). If \(A^{-1}\) does not exist, then \(\lambda=\)

The particular solution of the differential equation \(\frac{d y}{d x}+\frac{3 y}{x}=0, y(1)=1\) is

An inductor of reactance 100 \( \Omega \) and resistor of resistance 100 \( \Omega \) are joined in series and connected by AC source of emf 220 V. Power dissipated in the circuit is:

Scientific term for a situation where a single gene can exhibit multiple
phenotypic expressio is:

Carbonyl carbon in acetone is \(\mathrm{sp}^2\) hybridized. The C-O-C bond angle and the geometry of acetone is.......

If \(A=\left[\begin{array}{cc}a \cos \theta & b \sin \theta \\ -b \sin \theta & a \cos \theta\end{array}\right]\), then \(A^{-1}\) is equal to:

The angle between two vectors \(\vec{a}\) and \(\vec{b}\) with magnitudes \(\sqrt{3}\) and 4 respectively and \(\vec{a} \cdot \vec{b}=2 \sqrt{3}\) is :

Read the passage carefully and answer the questions
Biomolecules are the organic compounds present as an essential constituents of living organisms in different cells. molecules are generally termed as macromolecules, which are carbohydrates, enzymes, nucleic acids, amino acids and proteins The etc. Carbohydrates are classified as sugars and non-sugars include sucrose, glucose, fructose, starch and cellulose. Enzymes are coordinated with various chemical reactions in nucleic acid. Nucleic acids are found in living organisms made up of proteins and atural polymers. Two types that are generally found in biological systems are DNA and RNA nucleic acid. Amino acids bifunctional groups of carboxyl and amino groups. Proteins are a class of biologically important compounds. They are crucial are to virtually all processes in living systems. Some of them are hormones, which serve as chemical messengers that coordinate certain biochemical activities.
Starch is a polymer of saccharides known as