Which one of the following is a finite set?

(a)

{x : x ∈ Z, x < 5}

(b)

{x : x ∈ W, x ≥ 5}

(c)

{x : x ∈ N, x > 10}

(d)

{x : x is an even prime number}

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

(a)

2

(b)

-2

(c)

4

(d)

-4

The value of sin²\(\frac { 5\pi }{ 12 } -sin^{ 2 }\frac { \pi }{ 12 } \) is ___________

(a)

\(\frac { 1 }{ 2 } \)

(b)

\(\frac { \sqrt { 3 } }{ 2 } \)

(c)

1

(d)

0

If ⁿC₁₀ = ⁿC₆, then ⁿC₂ =  _________

(a)

16

(b)

4

(c)

120

(d)

240

The value of \({ 9 }^{ \frac { 1 }{ 3 } }\) ,\({ 9 }^{ \frac { 1 }{ 9 } }\)\({ 9 }^{ \frac { 1 }{ 27}}\),\(\infty \) is ______________

(a)

1

(b)

3

(c)

9

(d)

none of these

The remainder when 52⁴⁰ is divided by 17 is ______________

(a)

1

(b)

3

(c)

5

(d)

6

Assertion (A): The inverse of \(\\ \\ \\ \begin{bmatrix} 2 & -1 \\ -4 & 2 \end{bmatrix}\) does not exist.
Reason (R): The matrix is non-singular

(a)

Both A and R are true and R is the correct explanation of A

(b)

Both A and R are true and R is not a correct explantion of A

(c)

A is true but R is false

(d)

A is false but R is true

Choose the correct statement ________

(a)

Derivative of odd functionis odd

(b)

Derivative of even function is even

(c)

Inverse of odd function is even

(d)

Inverse function of sin x is sin^-1 x

\(\int { \frac { 1 }{ 9x^{ 2 }-4 } } \) dx = ________+c.

(a)

log\(\left| \frac { 3x-2 }{ 3x+2 } \right| \)

(b)

\(\frac { 1 }{ 12 } \)log\(\left| \frac { 3x-2 }{ 3x+2 } \right| \)

(c)

12log\(\left| \frac { 3x-2 }{ 3x+2 } \right| \)

(d)

\(\frac { 1 }{ 12 } log\left| \frac { 3x+2 }{ 3x-2 } \right| \)

A speaks truth in 75% cases and B speaks truth in 80% cases. Probability that they contradict each other in a statement is

(a)

\(\frac { 7 }{ 20 } \)

(b)

\(\frac { 13 }{ 20 } \)

(c)

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

(d)

\(\frac { 2 }{ 5 } \)