\(\int_{\pi / 6}^{\pi / 3} \frac{1}{1+\sqrt{\cot x}} d x\) is :

If the matrix \(A=\left[\begin{array}{lll}0 & b & 1 \\ 2 & 0 & c \\ 3 & 4 & 0\end{array}\right]\) is a symmetric matrix, then the values of \(b\) and \(c\) are:

The Greatest Integer Function \(f: R \rightarrow R\) given by \(f(x)=[x], x \in R\) and \([x]\) denotes the greatest integer less than or equal to \(x\) is :

If \(x=a \sin ^2 \theta, y=a \cos ^2 \theta\) then \(\frac{d y}{d x}\) =

In the interval [-5, -3], the function f(x) = (x + 1)(x - 3) is:

If \(A\) and \(B\) are square matrices of the same order, then \((A+B)(A-B)\) is equal to

\(\int \sin x \sin 2 x \sin 3 x d x\) is equal to:

Let \(f: \mathbb{R} \rightarrow \mathbb{R}\) be defined as \(f(x) = 4x^2 - 16x + 5\).

The area (in sq. units) of the region bounded by the curve \(y=\cos x\) between \(x=-\frac{\pi}{2}, x=\frac{\pi}{2}\) and the \(x\)-axis is

Choose the correct statements from the following:
A. The minimum energy required to free the electron from the ground state of the hydrogen atom is 13.6 J
B. The principle quantum number n labels the stationary states in the ascending order of energy
C. Bohr gave the basic idea of discrete energy levels
D. de Broglie hypothesis provided an explanation for Bohr's second postulate for the quantization of angular momentum of the orbiting electron
E. line spectrum provides useful information about the atomic structure.
Choose the correct answer from the options given below:

Biopiracy refers to :

Light of uniform intensity shines perpendicularly on a totally absorbing surface, fully illuminating the surface. If the area of the surface is decreased, what is the effect on radiation pressure ?

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 biomass available for consumption by herbivores and decomposers is known as-