The local minimum value of the function \(f(x)=|x|+2\), where \(x\) is a real number is :

\(\int_0^2(|x|+|x-2|) d x=\)

The rise in prices before festivals is an example of

If the curves \(x=y^2\) and \(x y=k\) meet at right angles, then the value of \(k\) is:

The random variable X can take only the values 0, 1, 2. Given that \(P(X = 0) = P(X = 1) = p\) and \(E(X^2) = E(X) + 1\), then the value of p is:

If the feasible region R for a linear programming problem is bounded, then the objective function \(Z=A x+B y\) has

If \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}\) and \(|\vec{a}|=5,|\vec{b}|=3,|\vec{c}|=7\), then the acute angle between \(\vec{a}\) and \(\vec{b}\) is

\(\text{t}_{99.9\%}\) with respect to \(\text{t}_{90\%}\) for a first order reaction is :

Resolving power of a telescope can be increased by increasing:

Read the passage carefully and give the answers to the question :
Does the number of species in a community really matter to the functioning of the ecosystem? This is a question for which ecologists have not been able to give a definitive answer. For many decades, ecologists believed that communities with more species, generally, tend to be more stable than those with less species. According to the International Union for Conservation of Nature and Natural Resources (IUCN) (2004), the total number of plant and animal species described so far is more than 1.5 million.
Among the vertebrates, which of the following is the most species-rich group ?

The probability of obtaining an even prime number on each die, when a pair of dice is rolled, is:

Match List - I with List - II.

List - I	List - II
A. Simple and face centred cubic	I. \(\text{a} = \text{b} = \text{c}\)
B. Cubic and rhombohedral	II. \(\alpha = \beta = \gamma = 90°\)
C. Cubic and tetragonal	III. have only two crystallographic angle of \(90°\)
D. Hexagonal and monoclinic	IV. belong to the same crystalline system

Choose the correct answer from the options given below :

Elements of group-15, 16 and 17 form compounds with hydrogen with general formula MH3, \(H 2 M\) and HX (called hydrogen halides). Stability of these hydrides, along with M-H bond strength and basic nature decreases down the group. Boiling point of these hydrides mainly depends on the strength of their inter molecular forces.
Bond angle (HMH) among hydrides of group-16 decreases down the group because: