Binomial Theorem

Fill in all the gaps, then press "Check" to check your answers. Use the "Hint" button to get a free letter if an answer is giving you trouble. You can also click on the "[?]" button to get a clue. Note that you will lose points if you ask for hints or clues!

1. If the seventh terms from the beginning and the end in the expansion of

{(\sqrt[3]{2} + \frac{1}{\sqrt[3]{3}})}^{n}

are equal, then n equals .
2. The ratio of the coefficients of

x^{p}

and

x^{q}

in the expansion of

{(1 + x)}^{p + q}

is .
3. The position of the term independent of x in the expansion of

{(\sqrt{\frac{x}{3}} + \frac{3}{2 x^{2}})}^{10}

is .
4. If

25^{13}

is divided by 13, the remainder is .
Write true or false: (Q5 - Q10)
5. The sum of the series

\sum_{r = 0}^{10} {}^{20}C_{r}

2^{19} + \frac{{}^{20}C_{10}}{2}

.
6. The expression

7^{9} + 9^{7}

is divisible by 64.
7. The number of terms in the expansion of

{[{(2 x + y^{3})}^{4}]}^{7}

is 8.
8. The sum of coefficients of the two middle terms in the expansion of

{(1 + x)}^{2 n - 1}

is equal to

{}^{2 n - 1}C_{n}

.
9. The last two digits of the numbers

3^{400}

are 01.
10. Number of terms in the expansion of

{(a + b)}^{n}

, where

n \in N

is one less than the power n.

Binomial Theorem

Gap-fill exercise