WB JEE 2010 | Mathematical Induction and Binomial Theorem Question 14 | Mathematics

WB JEE 2010

MCQ (Single Correct Answer)

-0.25

If $${(1 - x + {x^2})^n} = {a_0} + {a_1}x + {a_2}{x^2} + \,\,....\,\,{a_{2n}}{x^{2n}}$$, then the value of $${a_0} + {a_2} + {a_4} + \,\,....\,\,{a_{2n}}$$ is

$${3^n} + {1 \over 2}$$

$${3^n} - {1 \over 2}$$

$${{{3^n} - 1} \over 2}$$

$${{{3^n} + 1} \over 2}$$

WB JEE 2011

MCQ (Single Correct Answer)

-0.25

The coefficient of xⁿ om the expansion of $${{{e^{7x}} + {e^x}} \over {{e^{3x}}}}$$ is

$${{{4^{n - 1}} - {{( - 2)}^{n - 1}}} \over {\left| \!{\underline {\, n \,}} \right. }}$$

$${{{4^{n - 1}} - {2^{n - 1}}} \over {\left| \!{\underline {\, n \,}} \right. }}$$

$${{{4^n} - {2^n}} \over {\left| \!{\underline {\, n \,}} \right. }}$$

$${{{4^n} + {{( - 2)}^n}} \over {\left| \!{\underline {\, n \,}} \right. }}$$

WB JEE 2011

MCQ (Single Correct Answer)

-0.25

The number (101)¹⁰⁰ $$-$$ 1 is divisible by

10⁴

10⁶

10⁸

10¹²

WB JEE 2011

MCQ (Single Correct Answer)

-0.25

If A and B are coefficients of xⁿ in the expansions of (1 + x)²ⁿ and (1 + x)^{2n $$-$$ 1} respectively, then A/B is equal to

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