JEE Advanced 2013 · Paper 1 · Mathematics Q56

MathematicsInteger+4 / -1Question 56 of 60

The coefficients of three consecutive terms of $(1+x)^{n+5}$ are in the ratio 5 : 10 : 14. Then $n=$

Your answer

Answer and worked solution

Official answer: 6

Ratios. With $N=n+5$ and terms $\binom N{r-1},\binom Nr,\binom N{r+1}$ :
$\frac{N-r+1}r=2,\qquad\frac{N-r}{r+1}=\frac75.$

Solve. $N=3r-1$ and $5N=12r+7$ give $r=4$ , $N=11$ , so $n=6$ .

Answer: 6

JEE Advanced 2013 · Paper 1, Mathematics question 56