If the third term in the binomial expansion of $(1 + x)^{m} i s - x^{2}$ , then the rational value of m is

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Solution

The correct option is B

$(1 + x)^{m} = 1 + m x + \frac{m (m - 1)}{1.2} x^{2} + \dots ∴ \frac{m (m - 1)}{2} x^{2} = \frac{1}{2} x^{2}$

$\Rightarrow 4 m (m - 1) = - 1 \Rightarrow 4 m^{2} - 4 m + 1 = 0 \Rightarrow (2 m - 1)^{2} = 0 \Rightarrow m = \frac{1}{2}$

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If the third term in the binomial expansion of (1+x)m is−x2, then the rational value of m is

The correct option is B (1+x)m=1+mx+m(m−1)1.2x2+⋯ ∴m(m−1)2x2=12x2 ⇒4m(m−1)=−1⇒4m2−4m+1=0⇒(2m−1)2=0⇒m=12

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