QJEEM20Mab493: JEE Main 2020 Mathematics - Class 11 JEEM20Mab493 Solution: If the number of integral terms in the expansion of (3 1/2 + 5…

General term of the expression,

${T_{r + 1}} = {}^n{C_r}{\left( {{3^{{1 \over 2}}}} \right)^{n - r}}{\left( {{5^{{1 \over 8}}}} \right)^r}$

$= {}^n{C_r}{\left( 3 \right)^{{{n - r} \over 2}}}{\left( 5 \right)^{{r \over 8}}}$

We will get integral term when ${{n - r} \over 2}$ and ${r \over 8}$ are integer

$\therefore$ (1) n $-$ r is multiple of 2

$\Rightarrow$ n $-$ r = 0, 2, 4, ......

(2) r is multiple of 8

$\Rightarrow$ r = 0, 8, 16, .......

From this two conditions common values are = 0, 8, 16, ....... which will becomes integral terms.

Given that there are 33 integral terms.

Here first integral term at 0^th position.

Second integral term at 8^th position.

$\therefore$ 33^th integral term will be at = 0 + (33 $-$ 1)8 = 256

So, there should be at least 256 terms.