JEE Main 2015 · 10 Apr · Shift 1 · Mathematics Q68

← JEE Main 2015 · 10 Apr · Shift 1

MathematicsSingle correct+4 / -1Question 68 of 90

If the coefficients of the three successive terms in the binomial expansion of $(1+x)^n$ are in the ratio 1 : 7 : 42, then the first of these terms in the expansion is :

^{\text{th}}

^{\text{th}}

^{\text{th}}

^{\text{th}}

Answer and worked solution

Official answer: B

Let the terms be $\binom n{r-1},\binom nr,\binom n{r+1}$ . Then $\dfrac{n-r+1}r=7$ and $\dfrac{n-r}{r+1}=6$ , so $n=8r-1=7r+6$ , giving $r=7$ and $n=55$ .

The first term is $\binom{55}6x^6=T_7$ , the 7th term.

Topics:Properties of binomial coefficients General and middle terms

← Previous question Next question →

JEE Main 2015 · 10 Apr · Shift 1, Mathematics question 68