JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Binomial Theorem

The ratio of the coefficient of the middle term in the expansion of

(1 + x)^{20}

and the sum of the coefficients of two middle terms in expansion of

(1 + x)^{19}

Answer: 1

Solution

(1 + x)^{20}

the one middle term is the eleventh, whose coefficient is

(10 20)

. In

(1 + x)^{19}

the two middle terms are the tenth and the eleventh, with coefficients

(9 19)

and

(10 19)

. Pascal's rule gives

(9 19) + (10 19) = (10 20)

so the two quantities being compared are equal and the required ratio is

1

JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Integer answer