Functions and Relations MCQs with Answers

If $f(x) = x^3 - x^2 + x + 1$, then $f(2) =$ ?

• A.$5$
• B.$9$
• C.$11$
• D.$7$

For any non-empty set $A$, a function $f: A \to A$ is called a _ function if domain $=$ range.

• A.Injective
• B.Bijective
• C.Surjective
• D.Identity

If $A = \{1, 2, 3\}$, $B = \{a, b, c\}$ and $R = \{(1, a), (2, a), (3, b)\}$, then $R$ is a/an ?

• A.Bijective function
• B.Onto function
• C.One-one function
• D.Into function

What is the range of the cosecant function, $\csc \theta$?

• A.$y \leq -1$ or $y \geq 1$
• B.$-1 \leq y \leq 1$
• C.$y > 0$
• D.$-\infty < y < \infty$

Which function is not differentiable at $x = 0$?

• A.$f(x) = x^2$
• B.$f(x) = \sin x$
• C.$f(x) = |x|$
• D.$f(x) = x^3$

A subset of $A \times B$ is called a _?

• A.Function from $A$ to $B$
• B.Mapping from $A$ to $B$
• C.Relation from $A$ to $B$
• D.Cartesian product of $A$ and $B$

Which of the following represents $\tan\theta$?

• A.$\frac{|\mathbf{A} \times \mathbf{B}|}{|\mathbf{A}|\,|\mathbf{B}|}$
• B.$\frac{\mathbf{A} \cdot \mathbf{B}}{|\mathbf{A} \times \mathbf{B}|}$
• C.$\frac{|\mathbf{A} \times \mathbf{B}|}{\mathbf{A} \cdot \mathbf{B}}$
• D.$\frac{\mathbf{A} \cdot \mathbf{B}}{|\mathbf{A}|\,|\mathbf{B}|}$

The function $f(x)$ is said to be concave down in an interval $[a, b]$, if _?

• A.$f''(x) < 0$
• B.$f''(x) > 0$
• C.$f''(x) = 0$
• D.$f'(x) < 0$

If $f$ has a relative maximum at $x = c$, then which of the following is true?

• A.$f'(c) = 0$
• B.$f''(c) > 0$
• C.$f'(c)$ does not exist
• D.$f'(c) > 0$

A group $(G, *)$ is said to be abelian if $a * b =$ _?

• A.$b * b$
• B.$a * a$
• C.$b * a$
• D.$(a * b)^{-1}$