Which of the following functions from z to itself are bijections (one-one and onto)?

(a)

f(x) = x³

(b)

f(x) = x + 2

(c)

f(x) = 2x + 1

(d)

f(x) = x² + 1

The domain of the function \(f(x)=\sqrt{4-\sqrt{4-\sqrt{4-x^2}}}\)

(a)

(-∞, 4)

(b)

(-4, ∞)

(c)

(- 2,2)

(d)

[- 2,2]

The rationalising factor of \(\frac { 5 }{ \sqrt [ 3 ]{ 3 } } \) is

(a)

\(\sqrt [ 3 ]{ 6 } \)

(b)

\(\sqrt [ 3 ]{ 3 } \)

(c)

\(\sqrt [ 3 ]{ 9 } \)

(d)

\(\sqrt [ 3 ]{ 27 } \)

The condition that the equation ax² + bx + c = 0 may have one root is the double the other is ___________

(a)

2b² = 9ac

(b)

b² = ac

(c)

b² = 4ac

(d)

9b² = 2ac

Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is _________

(a)

24

(b)

30

(c)

125

(d)

100

Everybody in a room shakes hands with everybody else. The total number of handshakes is 91. The total number of persons in the room is _________

(a)

11

(b)

14

(c)

13

(d)

12

The larget coefficients in the expansion of (1 + X)²⁴ is ______________

(a)

24C₂₄

(b)

24C₁₃

(c)

24C₁₂

(d)

24C₁₁

The sum of 40 terms of an A.P whose first term is 2 and common difference 4 will be ______________

(a)

3200

(b)

1600

(c)

200

(d)

2800

Choose the incorrect pair:

(a)

\(\frac{d}{dx}(sin x)\) - cos x

(b)

\(\frac{d}{dx}(tanx)\) - sec²x

(c)

\(\frac{d}{dx}(cos x)\) - sin x

(d)

\(\frac{d}{dx}(logx)\) - \(\frac{1}{x}\)

The lines x cos \(\alpha\) + y sin \(\alpha\) = p and xcos\(\beta\) + y sin\(\beta\) = q will be perpendicular if ______________

(a)

\(\alpha =\beta\)

(b)

\(\alpha-\beta=\frac{\pi}{2}\)

(c)

\(|\alpha-\beta|=\frac{\pi}{2}\)

(d)

\(\alpha-\beta=0\)