Area (in sq. units) of the region bounded by curves \(y^2=x\) and \(x=4\) is

Which of the following functions from Z to Z are bijections ? (where Z is the set of integers)

Let \(f: R \rightarrow R\) be defined as \(f(x)=5 x^2\). Choose the correct answer :

The values of \(x\) which satisfy the inequality \(|x-3|<2\) lie in :

If \(\sin ^{-1} x+\sin ^{-1} y=\frac{2 \pi}{3}\), then the value of \(\cos ^{-1} x+\cos ^{-1} y\) is :

Match List-I with List-II
Consider the function \(f(x)=2 x^3-21 x^2+36 x+80, x \in[0,6]\).

List-I	List-II
(A) one of its critical points is at \(x=\)	(I) \(-28\)
(B) Its absolute maximum value is	(II) \(-42\)
(C) Its absolute minimum value is	(III) 97
(D) Its second derivative at \(x=0\)	(IV) 6

Choose the correct answer from the options given below :

The mean of the number of heads in a simultaneous toss of three coins is

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

Which of the following statements are INCORRECT regarding biodiversity:
A. Rauwolfia vomitoria possess the species diversity in terms of potency and concentration of the active chemical reserpine.
B. Western Ghats have a greater amphibian species diversity than the Eastern Ghats.
C. India has more than 60,000 genetically different strains of rice and 10,000 varieties of mango.
D. India has greater ecosystem diversity than Norway.
Choose the correct answer from the options given below:

In the following matrix equation, the value of \(x\) is :
\(\left[\begin{array}{cc}x+y & 4 \\ -5 & 3 y\end{array}\right]=\left[\begin{array}{cc}3 & 4 \\ -5 & 6\end{array}\right]\)

The enzyme used to release DNA from bacterial cell is :

Which of the following is NOT a cause of biodiversity loss due to human activities?

Answer the question on the basis of passage given below:
In the periodic table, the d-block contains the elements of group \(3\) to \(12\). The d-orbitals are progressively filled in each of the four long periods. The elements of d block referred as transition metals have partly filled d orbitals and exhibit certain characteristic properties such as variety of oxidation states, formation of coloured ions, act as catalyst and show paramagnetic behaviour.
The two inner transition metals series \(4f\) and \(5f\) are known as Lanthanoids and Actinoids respectively. The lanthanoids resemble one another more closely as compared to ordinary transition elements in any series.
Highest oxidation state of manganese in fluoride is \(+4\left( MnF _4\right)\) but highest oxidation state in oxides is \(+7\left( Mn _2 O _7\right)\) because: