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 in the expansion of

{(1 + x)}^{15}

, the coefficients of

{(2 r + 3)}^{t h}

and

{(r - 1)}^{t h}

terms are equal, then the value of r is .
2. The total number of terms in the expansion of

{(x + a)}^{100} + {(x - a)}^{100}

after simplification is .
3. If

\frac{T_{2}}{T_{3}}

in the expansion of

{(a + b)}^{n}

and

\frac{T_{3}}{T_{4}}

in the expansion of

{(a + b)}^{n + 3}

are equal, then n = .
4. If the sum of binomial coefficients of the expansion

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

is equal to 256, then the term independent of x is .
5. If the fifth term of the expansion

{(a^{\frac{2}{3}} + a^{- 1})}^{n}

does not contain 'a'. Then n is equal to .
6. If the coefficients of the

{(n + 1)}^{t h}

term and the

{(n + 3)}^{t h}

term in the expansion of

{(1 + x)}^{20}

are equal, then the value of n is .
7. If the coefficients of 2nd, 3rd and 4th terms in the expansion of

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

are in A.P., then n = .
8. The number of terms with integral coefficients in the expansion of

{(17^{\frac{1}{3}} + 35^{\frac{1}{2}} x)}^{600}

is .
9. Constant term in the expansion of

{(x - \frac{1}{x})}^{10}

is - .
10. If a and b are coefficients of

x^{n}

in the expansions of

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

and

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

respectively, then a = b.

Binomial Theorem

Gap-fill exercise