Let {left( {1 + x} right)^{10}} = Σlimits_{r = 0}^{10} {{Cᵣ}{x^r}} and {left( {1 + x}

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7.Binomial Theorem

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Let ${\left( {1 + x} \right)^{10}} = \sum\limits_{r = 0}^{10} {{C_r}{x^r}} $ and ${\left( {1 + x} \right)^7} = \sum\limits_{r = 0}^7 {{d_r}{x^r}} $ . If $P = \sum\limits_{r = 0}^5 {{C_{2r}}} $ and $Q = \sum\limits_{r = 0}^3 {{d_{2r + 1}}} $ , then $\frac{P}{{2Q}}$ is equal to

A

$2$

B

$4$

C

$8$

D

$16$

Solution

$P = \sum\limits_{r = 0}^5 {{C_{2r}} = {C_0} + {C_2} + …… + {C_{10}} = {2^9}} $

$Q = \sum\limits_{r = 0}^3 {{d_{2r + 1}} = {d_1} + {d_3} + {d_5} + {d_7} = {2^6}} $

Standard 11

Mathematics

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