Assertion :In the expansion of (x+x2)n the coefficient of eighth term and nineteenth term are equal, then n=25. Reason: Middle term in the expansion of (x+a)n has greatest binomial coefficient.
A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct
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Solution
The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion It is given that coefficients of 8th and 19th terms are equal.
Hence, T8=T19
nC7=nC18
nCn−7=nC18 Hence, n−7=18
n=25.
The reason is also correct since in the pascal's triangle the middle term has the maximum value. However it is not the correct explanation of the assertion.