JEE Main 2017 (Online) 8th April Morning Slot | Binomial Theorem Question 182 | Mathematics

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

$${2^{21}} - {2^{10}}$$

$${2^{20}} - {2^{9}}$$

$${2^{20}} - {2^{10}}$$

$${2^{21}} - {2^{11}}$$

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MCQ (Single Correct Answer)

-1

If the coefficients of x⁻² and x⁻⁴ in the expansion of $${\left( {{x^{{1 \over 3}}} + {1 \over {2{x^{{1 \over 3}}}}}} \right)^{18}},\left( {x > 0} \right),$$ are m and n respectively, then $${m \over n}$$ is equal to :

182

$${4 \over 5}$$

$${5 \over 4}$$

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MCQ (Single Correct Answer)

-1

For x $$ \in $$ R, x $$ \ne $$ -1,

if (1 + x)²⁰¹⁶ + x(1 + x)²⁰¹⁵ + x²(1 + x)²⁰¹⁴ + . . . . + x²⁰¹⁶ =

$$\sum\limits_{i = 0}^{2016} {{a_i}} \,{x^i},\,\,$$ then a₁₇ is equal to :

$${{2017!} \over {17!\,\,\,2000!}}$$

$${{2016!} \over {17!\,\,\,1999!}}$$

$${{2017!} \over {2000!}}$$

$${{2016!} \over {16!}}$$

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