WB JEE 2018 | Mathematical Induction and Binomial Theorem Question 28 | Mathematics

WB JEE 2018

MCQ (Single Correct Answer)

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

10⁴

10⁶

10⁸

10¹²

WB JEE 2018

MCQ (Single Correct Answer)

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If n is even positive integer, then the condition that the greatest term in the expansion of (1 + x)ⁿ may also have the greatest coefficient, is

$${n \over {n + 2}} < x < {{n + 2} \over n}$$

$${n \over {n + 1}} < x < {{n + 1} \over n}$$

$${{n + 1} \over {n + 2}} < x < {{n + 2} \over {n + 1}}$$

$${{n + 2} \over {n + 3}} < x < {{n + 3} \over {n + 2}}$$

WB JEE 2017

MCQ (Single Correct Answer)

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Let $${(1 + x + {x^2})^9} = {a_0} + {a_1}x + {a_2}{x^2} + ... + {a_{18}}{x^{18}}$$. Then,

$${a_0} + {a_2} + ... + {a_{18}} = {a_1} + {a_3} + ... + {a_{17}}$$

$${a_0} + {a_2} + ... + {a_{18}}$$ is even

$${a_0} + {a_2} + ... + {a_{18}}$$ is divisible by 9

$${a_0} + {a_2} + ... + {a_{18}}$$ is divisible by 3 but not by 9

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