If (1 + x²)² (1 + x)ⁿ = a₀+ a₁x + a₂x² + ... + xⁿ⁺⁴ and if a₀, a₁, a₂ are in AP, then n is

(a)

1

(b)

5

(c)

2

(d)

4

With usual notation C₀ + C₂ + C₄ + ... is ______________

(a)

2^n-1

(b)

2ⁿ

(c)

2ⁿ⁺¹

(d)

2ⁿ⁺²

In the expansion of (2x + 3)⁵ the coefficient of x² is ______________

(a)

720

(b)

1080

(c)

810

(d)

5

In the expansion of (1 +x )²² which term is the middle term ______________

(a)

T₁₁ and T₁₂

(b)

T₁₁

(c)

T₁₂

(d)

T₁₃

AM, GM, HM denote the Arithmetic mean, Geometric mean and Harmonic mean respectively the relationship between this is ______________

(a)

AM < GM < HM

(b)

AM ≤ GM ≤ HM

(c)

AM>GM>HM

(d)

AM≥GM≥HM

In the series \(\frac{1}{1+\sqrt 2}+\frac{1}{\sqrt 2+\sqrt 3}+\frac{1}{\sqrt 3+\sqrt 4}+...\) some of first 24 number is ______________

(a)

4

(b)

\(\sqrt 24\)

(c)

\(\frac{1}{\sqrt 24}\)

(d)

\(\frac{1}{\sqrt 25-\sqrt 24}\)

1 - 2x + 3x² - 4x³ + ..., Ixl< 1 is ______________

(a)

(1-x)^-2

(b)

(1+x)^-2

(c)

(1-x)²

(d)

(1+x)²

\(\frac{1}{1!}+\frac{1}{3!}+\frac{1}{5!}+...\) is ______________

(a)

\(\frac{e^{-1}}{2}\)

(b)

\(\frac{e+e^{-1}}{2}\)

(c)

\(\frac{e-e^{-1}}{2}\)

(d)

none of these

Expansion of \(log(\sqrt \frac{1+x}{1-x})\) is ______________

(a)

\(x+\frac{x^3}{3}+\frac{x^5}{5}+...\)

(b)

\(1.\frac{x^2}{2}+\frac{x^4}{4}+...\)

(c)

\(1-x+\frac{x^2}{2}+\frac{x^3}{5}+...\)

(d)

\(x-\frac{x^2}{3}+\frac{x^3}{3}+...\)

The value of \(1-\frac{1}{2}(\frac{3}{4})+\frac{1}{3}(\frac{3}{4})^2-\frac{1}{4}(\frac{3}{4})^3+...\)is ______________

(a)

\(\frac{3}{4}log(\frac{7}{4})\)

(b)

\(\frac{4}{3}log(\frac{7}{4})\)

(c)

\(\frac{1}{3}log(\frac{7}{4})\)

(d)

\(\frac{4}{3}log(\frac{4}{7})\)