The two events E and F are independent. If \(P(E)=0.3\) and \(P(E \cup F)=0.5\), then \(P(E / F)-P(F / E)\) is :

If the relation \(R: A \rightarrow B\), where \(A=\{2,3,4\}\) and \(B=\{3,4,5\}\) is defined by \(R=\{(x, y): x < y, x \in A, y \in B\}\), then

Arrange the principal values of the following functions in ascending order
(A) \(\operatorname{cosec}^{-1}(2)\)
(B) \(\tan ^{-1}(-\sqrt{3})\)
(C) \(\tan ^{-1}(1)\)
(D) \(\tan ^{-1}\left(\cos \frac{3 \pi}{2}\right)\)
Choose the correct answer from the options given below:

The area of the smaller region bounded by the ellipse \(\frac{x^2}{16}+\frac{y^2}{9}=1\) and the straight line \(3 x+4 y=12\) is :

Rolle's theorem holds for the function \(x^3+b x^2+c x, 1 \leq x \leq 2\) at the point \(\frac{4}{3}\), the respective values of \(b\) and \(c\) are :

A and B are two students. Their chances of solving a problem correctly are \(\frac{1}{3}\) and \(\frac{1}{4}\) respectively.
If the probability of their making a common error is \(\frac{1}{20}\) and they obtain the same answer, then the probability that their answer is correct is:

If \(A=\left[\begin{array}{ll}5 & 3 \\ 2 & 4\end{array}\right]\) then the matrix \(A^2-6 A+14 I\) (where \(I\) is an identity matrix of order 2 )

\(\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{d x}{1+\sqrt{\tan x}}\) is equal to:

When blood cells are placed in 1\(\%\) (w/v) \(\text{NaCl}\) aqueous solution :

On prolonged heating with HI , glucose forms

The stain commonly used to visualise DNA fragments separated by gel electrophoresis is:

Read the passage carefully and answer the Questions
Werner in 1898, propounded his theory of coordination compounds. In coordination compounds metals show two types of linkages (valences)-primary and secondary. The primary valences are normally ionisable and are satisfied by negative ions. The secondary valences are non-ionisable. These are satisfied by neutral molecules or negative ions. The secondary valence is equal to the coordination number and is fixed for a metal. The ions or group bound by the secondary linkages to the metal have characteristic spatial arrangements corresponding to the different coordination numbers. Both double salts as well as complexes are formed by the combination of two or more stable compounds in stoichiometric ratio. However, they differ in the fact that double salts such as carnallite, Mohr's salt, potash alum etc. dissociate into simple ions completely when dissolved in water. But complex ions do not dissociate completely into simple ions.
When \(1 mol CrCl _3 \cdot 6 H _2 O\) is treated with excess of \(AgNO _3, 3 mol\) of AgCl are obtained. The formula of the complex is:

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