Which of the following numbers is equal to $1$ billion?
(a) $10$ lakh
(b) $1$ crore
(c) $100$ lakh
(d) $100$ crore

The correct option is (d) ($100$ crore).
Given $1$ billion.
According to International system of numeration,
$1$billion $=1,000,000,000$
By arranging the commas according to Indian system of numeration,
we get, $1$ billion$=100,00,00,000$
$\Rightarrow 1$ billion $=100$ crores.
Hence, the correct option is (d) ($100$crore)