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JEE MATHEMATICS MCQ: BINOMIAL THEOREM

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Assertion: Number of terms in the expansion of

(\sqrt{{x}}+\sqrt{{y}})^{10}+(\sqrt{{x}}-\sqrt{{y}})^{10} \text { is } 6 .

Reason: If

{n}

is even, then the expansion of

\left\{(x+a)^n+(x-a)^n\right\} \text { has }\left(\frac{n}{2}+1\right) \text { terms. }

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Correct option: A

Assertion is correct, reason is correct; reason is a correct explanation for assertion

Option A (Assertion is correct, reason is correct; reason is a correct explanation for assertion) is correct because the number of terms in the given expansion is indeed 6, and the reason provides the correct formula for the number of terms when n is even.

More Questions from BINOMIAL THEOREM

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\left({ }^{10} C_0\right)^2-\left({ }^{10} C_1\right)^2+\ldots-\left({ }^{10} C_9\right)^2+\left({ }^{10} C_{10}\right)^2

a

d

are two complex numbers, then the sum to

\left( {n + 1} \right)

terms of the following series

a{C_0} - \left( {a + d} \right){C_1} + \left( {a + 2d} \right){C_2} - ... + ...

is The number of different terms in the expansion of

(1-x)^{201}\left(1+x+x^2\right)^{200}

is The sum of the coefficient of the binomial expansion of

\left(\frac{1}{x}+2 x\right)^n

is equal to 6561 . The constant term in the expansion is The coefficient of

{x^5}

in the expansion of

\frac{{1 + {x^2}}}{{1 + x}},\left| x \right| < 1,

\left(\begin{array}{c}2 n+1 \\ 0\end{array}\right)+\left(\begin{array}{c}2 n+1 \\ 3\end{array}\right)+\left(\begin{array}{c}2 n+1 \\ 6\end{array}\right)+\ldots=170

n