Given A = {5,6,7,8}. Which one of the following is incorrect?

(a)

Ø ⊆ A

(b)

A⊆A

(c)

{7,8,9}⊆A

(d)

{5}⊆A

The shaded region in the adjoining diagram represents.

(a)

A\B

(b)

A'

(c)

B'

(d)

B\A

If A = {1, 2, 3}, B = {1, 4, 6, 9} and R is a relation from A to B defined by "x is greater than y". The range of R is __________

(a)

{1, 4, 6, 9}

(b)

{4, 6, 9}

(c)

{1}

(d)

None of these

Let R be the relation over the set of all straight lines in a plane such that l₁Rl₂ ⇔ l₁丄l₂ . Then  R is __________

(a)

symmetric

(b)

reflexive

(c)

transitive

(d)

an equivalent relation

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

If f : R➝R is given by f(x) = 3x - 5, then f^-1(x) is __________

(a)

\(\frac{1}{3x-5}\)

(b)

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

(c)

does not exist since f is not one-one

(d)

does not exists since f is not onto

Let f : R➝R be given by f(x) = x + \(\sqrt { { x }^{ 2 } } \) is __________

(a)

injective

(b)

Surjective

(c)

bijective

(d)

none of these

If \(f:R\rightarrow R\) is defined by \(f(x)=2x-3\) __________

(a)

\({1\over 2x-3}\)

(b)

\({1\over 2x+3}\)

(c)

\({x+3\over 2}\)

(d)

\({x-3\over 2}\)

Let S = (1, 2, 3), R be (1, 1) (1, 2) (2, 2) (1, 3) (3, 1), what are the elements to-be included to make R reflexive ___________

(a)

(3, 3)

(b)

(2, 3)

(c)

(3, 2)

(d)

none of these

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 range of the function is \(f(x)=\sqrt{3x^2-4x+5}\) is ___________

(a)

\(\left( -\infty,\sqrt{11\over 3}\right)\)

(b)

\(\left( -\infty,-\sqrt{11\over 3}\right)\)

(c)

\(\left( \sqrt{11\over 3},-\infty\right)\)

(d)

none

Let f and g be two odd functions then the function of f o g is ___________

(a)

an even function

(b)

an odd function

(c)

neither even nor odd

(d)

a periodic function

If \(f(x)={1-x\over 1+x}, x≠0\) then \(f[f(x)]+f\left[f\left(1\over x\right)\right]\)

(a)

<2

(b)

> 2

(c)

> 2

(d)

None

Choose the correct statement.

(a)

One-to-one function have inverse

(b)

Onto function have inverse

(c)

bijection function have inverse

(d)

many - to - one function hae inverse

If x is a real number and |x| < 5 then ___________

(a)

x ≥ 5

(b)

-5 < x < 5

(c)

x ≤ -5

(d)

-5 ≤ x ≤ 5

\(\sqrt [ 4 ]{ 11 } \) is equal to ___________

(a)

\(\sqrt [ 8 ]{ 11^{ 2 } } \)

(b)

\(\sqrt [ 8 ]{ 11^{ 4 } } \)

(c)

\(\sqrt [ 8 ]{ 11^{ 8 } } \)

(d)

\(\sqrt [ 8 ]{ 11^{ 6 } } \)

The value of log₁₀⁸ + log₁₀⁵- log₁₀⁴ = ___________

(a)

\({ log }_{ 10 }^{ 9 }\)

(b)

\({ log }_{ 10 }^{ 36 }\)

(c)

1

(d)

-1

The factors of the polynomial \(6\sqrt { { 3x }^{ 2 } } -47x+5\sqrt { 3 } \) are ___________

(a)

\((2x-5\sqrt { 3 } )(3\sqrt { 3 } x-1)\)

(b)

\((2x-5\sqrt { 3 } )(3\sqrt { 3 } x+1)\)

(c)

\((2x+5\sqrt { 3 } )(3\sqrt { 3 } x+1)\)

(d)

\((2x+5\sqrt { 3 } )(3\sqrt { 3 } x-1)\)

The zero of the polynomial function f(x) = 9x²-16 are ____________

(a)

(9, 16)

(b)

(3, 4)

(c)

\((\frac{4}{3},-\frac{4}{3})\)

(d)

\((\frac{3}{4},-\frac{3}{4})\)

Logarithm of 144 to the base 2\(\sqrt{3}\) is ___________

(a)

2

(b)

3

(c)

4

(d)

5

The value of 2 log₁₀ 3 + log₁₀ 16 - 2 log₁₀ \(6\over 5\) is ___________

(a)

1

(b)

0

(c)

2

(d)

3

If (x + 1) and (x - 3) are factors of x³ - 4x² + x + 6 then other linear factor is ___________

(a)

x + 2

(b)

x - 2

(c)

x - 1

(d)

x + 3

The value of log_a^x + log_1/a^x is ___________

(a)

1

(b)

0

(c)

2 log_a^x

(d)

2 log_a^x

For the below figure of ax² + bx + c = 0

(a)

a < 0, D > 0

(b)

a > 0, D > 0

(c)

a < 0, D < 0

(d)

a > 0, D = 0

The value of \(\sqrt [ 4 ]{ { (-2) }^{ 4 } } =\) _______.

(a)

2

(b)

-2

(c)

4

(d)

-4