Find the coefficient of x³ in the expansion of \(\left( 3x-\frac { 1 }{ x } \right) ^{ 7 }\)

2

(a)

If P and Q are the sum of odd and even terms in the expansion\(\left( y+b \right) ^{ n }\), then prove that\(\left( y+b \right) ^{ 2n }+\left( y-b \right) ^{ 2n }=2\left( { P }^{ 2 }+Q^{ 2 } \right) \).

2

(a)

Using binomial theorem, expand \( \left( { x+ }\frac { 1 }{ y }  \right) ^{ 6 }\)

2

(a)

using bionominal theorem compute (10.1)⁵.

2

(a)

Find the number of terms in the expansion of (1 + 2x + x²)¹⁴

2

(a)

Find the value of [x+\(\sqrt { x-1 } \)]⁶+[\(\sqrt { x-1 } \)]⁶ , using binomial theorem.

2

(a)

Find the middle term in the expansion of \(\left( \frac { x }{ a } -\frac { a }{ x } \right) ^{ 10 }\)

2

(a)

Find the term independent of x in the expansion of \(\left( 2x+\frac { 1 }{ { 3x }^{ 2 } } \right) ^{ 9 }\)

2

(a)

If the coefficients of x⁷ and x⁸in the expansion of \(\left( 3+\frac { x }{ { 2 } } \right) ^{ n }\)

2

(a)

Expand the following expressions by using binomial theorem:
(1- 3x)⁷

2

(a)

Find (a + b)⁵ - (a - b)⁵. Hence evaluate \(\left( \sqrt { 5 } +\sqrt { 3 } \right) ^{ 5 }+\left( \sqrt { 5 } -\sqrt { 3 } \right) ^{ 5 }\)

2

(a)

Find the co-efficient of \({ x }^{ 10 }\quad in\quad \left( 2x^{ 2 }-\frac { 3 }{ x } \right) ^{ 11 }\)

2

(a)

Find the co-efficient of x⁶y³ in (x + 2y)⁹

2

(a)

Find the value of a for which the co-efficient of the middle term in the expansions of (1 + ax)⁴ and (1 - ax)⁶ are equal.

2

(a)

In the binomial expansion of (1 + x)ⁿ, the coefficient of the 5^th, 6^th and 7^th terms are in A.P. Find all values of n for which this can happen.

2

(a)