Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 8 - Binomial Theorem>Exercises>Q 12

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IMPORTANT

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For the expansion ${(x \sin p + x^{- 1} \cos p)}^{10}, (p \in R),$

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Important Questions on Binomial Theorem

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JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 8 - Binomial Theorem>Exercises>Q 13

For which of the following values of

x, 5^{th}

term is numerically the greatest term in the expansion of

{(1 + \frac{x}{3})}^{10}

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JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 8 - Binomial Theorem>Exercises>Q 15

If

\sum_{r = 0}^{n} \frac{r}{{}^{n}C_{r}} = \sum_{r = 0}^{n} \frac{n^{2} - 3 n + 3}{2 \cdot {}^{n}C_{r}}

, then

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 8 - Binomial Theorem>Exercises>Q 16

The value of

{}^{n}C_{1} + {}^{n + 1}C_{2} + {}^{n + 2}C_{3} + . . . . + {}^{n + m - 1}C_{m}

is equal to

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 8 - Binomial Theorem>Exercises>Q 17

In the expansion of

{(x^{2} + 1 + \frac{1}{x^{2}})}^{n}, n \in N

,

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 8 - Binomial Theorem>Exercises>Q 18

In the expansion of

{(7^{\frac{1}{3}} + 11^{\frac{1}{9}})}^{6561}

,

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JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 8 - Binomial Theorem>Exercises>Q 19

If

{(1 + x)}^{n} = C_{0} + C_{1} x + C_{2} x^{2} + . . . . . + C_{n} x^{n}

, then

C_{0} - (C_{0} + C_{1}) + (C_{0} + C_{1} + C_{2}) - (C_{0} + C_{1} + C_{2} + C_{3}) + . . . . {(- 1)}^{n - 1} (C_{0} + C_{1} + . . . . + C_{n - 1})

is (where

n

is an even integer and

C_{r} = {}^{n}C_{r}

)

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JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 8 - Binomial Theorem>Exercises>Q 20

In the expansion of

{(a + b)}^{n}

, if two consecutive terms are equal, then which of the following is/are always integer?

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 8 - Binomial Theorem>Archives>Q 1

Which of the following is/are true?