If \(\left|\begin{array}{cc}2 x & 2 \\ 4 & x\end{array}\right|=10\), then \(x\) is:

Suppose that A, B and C are matrices of order \(m \times n, n \times 5\) and \(5 \times q\) respectively. The restriction on m, n and q so that AB - BC is defined are

For what value of k, the following system have a unique solution? (where R is set of real numbers)
x + y + z = 1
2x + 3y + 4z = 3
x - y + kz = 5

Given \(A=\left[\begin{array}{ll}2 & 3 \\ 1 & 4\end{array}\right]\) and \(B=\left[\begin{array}{ll}x & y \\ 1 & 4\end{array}\right]\), If \(A=B\), then \(x\) and \(y\) are :

If \(P\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6\end{array}\right]=\left[\begin{array}{ccc}-7 & -8 & -9 \\ 2 & 4 & 6\end{array}\right]\), then matrix \(P\) is equal to :

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:

A. General solution of \(\frac{d y}{d x}=\frac{1+y^2}{1+x^2}\) is \(\tan ^{-1} y=\tan ^{-1} x+c\); Where c is a constant
B. General solution of \(\frac{d y}{d x}+\frac{\sqrt{1-y^2}}{\sqrt{1-x^2}}=0\) is \(\sin ^{-1} y-\sin ^{-1} x=c\); Where c is a constant
C. General solution of \(\frac{y d x-x d y}{y}=0\) is \(y=c x\); Where c is a constant
D. General solution of \(\frac{d y}{d x}=e^{x+y}\) is \(e^x+e^y=c\); Where c is a constant
E. \(\left(x^2+x y\right) d y=\left(x^2+y^2\right) d x\) is a homogeneous differential equation
Choose the correct answer:

The value of \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(x^3+x \cos x+\tan ^5 x\right) d x\) is:

Read the following passage carefully and answer the given questions.
Productivity in the Ecosystem
The flow of energy through a terrestrial ecosystem starts with the harnessing of sunlight by autotrophs. The radiant energy is converted by photosynthesis to organic compounds is known as productivity. The productivity is expressed in units of energy per unit of area per unit time. The amount of organic matter present at any given time is biomass. The productivity of any ecosystem is affected by many parameters like weather conditions, nutrient availability etc. The productivity of any ecosystem does vary seasonally and yearly.
The unit for expressing productivity is -

Choose the most appropriate option about the presence of nitrogenous bases; Cytosine, 5-methyl uracil and Uracil.

For a fixed volume of liquid solvent, the solubility of a gaseous solute depends upon......
(A) Nature of the gas.
(B) Pressure at constant temperature.
(C) Temperature at constant pressure.
(D) Nature of solvent.
Choose the correct answer from the options given below:

The solution set of the inequation \(4x + 3y > 5\) is

\(\tan \left[\frac{1}{2} \cos ^{-1}\left(\frac{4}{5}\right)\right]=\)