QJEEM23Ma36f3: JEE Main 2023 Mathematics - Class 11 JEEM23Ma36f3 Solution: Let K be the sum of the coefficients of the odd powers of x in…

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QJEEM23Ma36f3: JEE Main 2023 Mathematics - Class 11 JEEM23Ma36f3 Solution: Let K be the sum of the coefficients of the odd powers of x in…

Let K be the sum of the coefficients of the odd powers of $x$ in the expansion of $(1 + x)^{99}$ . Let $a$ be the middle term in the expansion of ${(2 + \frac{1}{\sqrt{2}})}^{200}$ . If $\frac{^{200} C_{99} K}{a} = \frac{2^{l} m}{n}$ , where m and n are odd numbers, then the ordered pair $(l, n)$ is equal to

Multiple Choice Options

A (50, 101)
B (50, 51)
C (51, 101)
D (51, 99)

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Accepted Answer

$K = 2^{98}$

$a =^{200} C_{100} 2^{50}$

$∴$ $\frac{^{200} C_{99} . 2^{98}}{^{200} C_{100} . 2^{50}} = \frac{2^{l} m}{n}$

$\Rightarrow \frac{100}{101} . 2^{48} = \frac{2^{l} m}{n}$

$\Rightarrow \frac{25}{101} . 2^{50} = \frac{2^{l} m}{n}$

$∴$ $l = 50, m = 25, n = 101$

QJEEM23Ma36f3: JEE Main 2023 Mathematics - Class 11 JEEM23Ma36f3 Solution: Let K be the sum of the coefficients of the odd powers of x in…

Multiple Choice Options

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