Let Ajay will not appear in JEE exam with probability p = (2)/(7),...

The probability that Ajay will not appear in exam is, $P\left({A}^{'}\right) = p = \dfrac{2}{7}$.

$⇒ P\left(A\right) = \dfrac{5}{7}$

The probability that Ajay and Vijay will appear in exam is, $P\left(A \cap V\right) = q = \dfrac{1}{5}$.

$⇒ P\left(A\right) \times P\left(V\right) = \dfrac{1}{5}$

$⇒ P\left(V\right) = \dfrac{1}{5} \times \dfrac{7}{5}$

$⇒ P\left(V\right) = \dfrac{7}{25}$

The probability that Ajay will appear and Vijay will not appear in the exam is,

$⇒ P\left(A \cap {V}^{'}\right) = \dfrac{5}{7} \times \dfrac{18}{25}$

$⇒ P\left(A \cap {V}^{'}\right) = \dfrac{18}{35}$