If in the expansion of (a + b)ⁿ and (a + b)^{n + 3}, the ratio of the coefficients of second and third terms and third and fourth terms respectively are equal then n is _____.

1

(a)

2

(b)

8

(c)

5

(d)

none of these

If in the expansion of (1 +x)ⁿ, the coefficients of fifth, sixth and seventh terms are inA.P. then n is equal to _____.

1

(a)

5,7

(b)

7,16

(c)

7,14

(d)

8,15

The middle term in the expansion of \(\left( \frac { { 2x }^{ 2 } }{ 3 } +\frac { 3 }{ { 2x }^{ 2 } } \right) ^{ 10 }\)is _____.

1

(a)

240

(b)

280

(c)

262

(d)

252

If in the expansion of (1 +x)¹⁵, the coefficient of (2x + 3)^th and (r - 1)^th terms are equal then r is equal to _____.

1

(a)

9

(b)

5

(c)

8

(d)

none of the these

The total number of terms in the expansion of (x + a)⁸⁰ + (x - a)⁸⁰ is _____.

1

(a)

41

(b)

31

(c)

51

(d)

161

The coefficient of x⁵y⁸ in the expansion of (x + y)¹³ is _____.

1

(a)

13C₅

(b)

13C₈

(c)

8C₅

(d)

None of the these

Constant term in the expansion of \(\left( x-\frac { 1 }{ x } \right) ^{ 14 }\) _____.

1

(a)

3032

(b)

3432

(c)

5042

(d)

-3442