JEE Main 2017 · 2 Apr · Shift 1 · Mathematics Q67

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MathematicsSingle correct+4 / -1Question 67 of 90

The value of
$\left({}^{21}C_1-{}^{10}C_1\right)+\left({}^{21}C_2-{}^{10}C_2\right)+\left({}^{21}C_3-{}^{10}C_3\right)+\left({}^{21}C_4-{}^{10}C_4\right)+\dots+\left({}^{21}C_{10}-{}^{10}C_{10}\right)$
is :

2^{21}-2^{10}

2^{20}-2^9

2^{20}-2^{10}

2^{21}-2^{11}

Answer and worked solution

Official answer: C

$\sum_{r=1}^{10}{}^{21}C_r=\frac{2^{21}}2-1=2^{20}-1$ (by symmetry of the 21st row) and $\sum_{r=1}^{10}{}^{10}C_r=2^{10}-1$ . The difference is $2^{20}-2^{10}$ .

Topics:Properties of binomial coefficients

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JEE Main 2017 · 2 Apr · Shift 1, Mathematics question 67