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Question

Statement 1:The coefficient of $x to the power of n end exponent$ in the binomial expansion of $left parenthesis 1 minus x right parenthesis to the power of negative 2 end exponent$ is $left parenthesis n plus 1 right parenthesis$
Statement 2:The coefficient of $x to the power of r end exponent$ in $left parenthesis 1 minus x right parenthesis to the power of negative n end exponent$ when $n element of N$ is $blank to the power of n plus r minus 1 end exponent C subscript r end subscript$

Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
Statement 1 is True, Statement 2 is False
Statement 1 is False, Statement 2 is True

The correct answer is: Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1

Since, coefficient of $x to the power of r end exponent$ in $left parenthesis 1 minus x right parenthesis to the power of negative n end exponent equals blank to the power of n plus r minus 1 end exponent C subscript r end subscript$
$therefore$ Coefficient of $x to the power of n end exponent$ in $left parenthesis 1 minus x right parenthesis to the power of negative 2 end exponent equals blank to the power of 2 plus n minus 1 end exponent C subscript n end subscript$
$equals blank to the power of n plus 1 end exponent C subscript n end subscript equals left parenthesis n plus 1 right parenthesis$
Hence, option (a) is correct

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