If a set \(P\) contains 5 elements and the set \(Q\) contains 8 elements, then the number of one-one functions from \(P\) to \(Q\) is:

If \(A=\left[\begin{array}{ccc}1 & 2 & 3 \\ -4 & -5 & -6\end{array}\right], \quad B=\left[\begin{array}{cc}2 & -3 \\ 4 & -5 \\ 2 & -1\end{array}\right]\) and \(B A=\left[b_{i j}\right]\), then \(\left(b_{23}-b_{31}\right)\) is equal to

The area of the smaller region enclosed by the ellipse \(\frac{x^2}{16}+\frac{y^2}{9}=1\) and the ne straight straight line \(\frac{x}{4}+\frac{y}{3}=1\) is \(a \pi+b\). The value of a + b is:

The integrating factor of the differential equation \(x \frac{d y}{d x}-y=2 x^2\) is :

The value of the integral \(I=\int e^x\left(\tan ^{-1} x+\frac{1}{1+x^2}\right) d x\) is :

\(\int \frac{x+\sqrt{x}}{2 \sqrt{x}} d x=\)

The general solution of the differential equation \(x\left(1+y^2\right) d x+y\left(1+x^2\right) d y=0\) is

Read the Passage carefully and answer the questions
When a ligand is bound to a metal ion through a single donor atom, it is said to be a unidentate ligand but when it bind through two donor atoms, then it is said to be didentate ligand and when several donor atoms are present in a single ligand, it is said to be a polydentate ligand. When a di- or polydentate ligand uses its two or more donor atoms simultaneously to bind a single metal ion, it is said to be a chelate ligand. The number of such ligating groups is called the denticity of the ligand. ligand which has two different donor atoms and either of the two ligetes in the complex is called ambidentate ligands. The number of ligand donor atoms to which the metal is directly bonded, is called coordination number of the metal ion in the complex. Complexes in which a metal is bound to only one kind of donor groups are known as homoleptic and in which a metal is bound to more than one kind of donor groups are known as heteroleptic complexes.
To make an octahesral complex of \(Mg ^{2+}\) ion, how many molecules of \(EDTA\) are used?

The angle between thee curves \(x y=\sqrt{2}\) and \(x^2-y^2=1\) at \((\sqrt{2}, 1)\) is:

In a box containing 100 bulbs, 10 are defective.
The probability that out of a sample of 5 bulbs none is defective is:

Which of the following is the best reducing agent to convert RCOOH into \(RCH _2 OH\) ?

After 4 hours, \( \frac{1}{16} \) of the initial amount of a certain radioactive isotope remains undecayed. What is the half life of the isotope?

The frequency of a photon whose energy is 66.3 eV would be (Given \(h = 6.63 \times 10^{-34} \text{ Js}\))