JEE Main 2015 · 4 Apr · Shift 1 · Mathematics Q67

MathematicsSingle correct+4 / -1Question 67 of 90

The sum of coefficients of integral powers of $x$ in the binomial expansion of $\left(1-2\sqrt x\right)^{50}$ is :

\dfrac12\left(3^{50}+1\right)

\dfrac12\left(3^{50}\right)

\dfrac12\left(3^{50}-1\right)

\dfrac12\left(2^{50}+1\right)

Answer and worked solution

Official answer: A

Integral powers come from even powers of $\sqrt x$ . Setting $\sqrt x=1$ and $-1$ :
$\frac{(1-2)^{50}+(1+2)^{50}}2=\frac12\left(3^{50}+1\right).$

JEE Main 2015 · 4 Apr · Shift 1, Mathematics question 67