If R is a relation on a finite set having n elements, then the number of relations on A is:
- A$2^{\text{n}}$
- ✓$2^{\text{n}^2}$
- C$\text{n}^2$
- D$\text{n}^\text{n}$
Answer: B.
View full solution →Question types
RELATIONS AND FUNCTIONS question types
254 questions across 5 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
254
Questions
5
Question groups
5
Question types
01
MCQ
165 Q→02(Each question 1 marks)
56 Q→03(Each question 2 marks)
18 Q→04(Each question 3 marks)
8 Q→05(Each question 4 marks)
7 Q→Sample Questions
RELATIONS AND FUNCTIONS questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Let a relation R be defined by R = {(4, 5), (1, 4), (4, 6), (7, 6), (3, 7)}, then ROR is equal to:
- ✓{(1, 5), (1, 6), (3, 6)}
- B{(1, 4), (1, 5), (3, 6)}
- C{(1, 5), (1, 6), (3, 7)}
- D{(1, 4), (1, 5), (3, 7)}
Answer: A.
View full solution →Which function is shown in graph?
- ✓Constant
- BModulus
- CIdentity
- DSignum function
Answer: A.
View full solution →Which of the following is not a function?
- A{(1, 2), (2, 4), (3, 6)}
- B{(-1, 1), (-2, 4), (2, 4)}
- ✓{(1, 2), (1, 4), (2, 5), (3, 8)}
- D{(1, 1), (2, 2), (3, 3)}
Answer: C.
View full solution →If n is the smallest natural number such that n + 2n + 3n + …. + 99n is a perfect square, then the number of digits in square of n is:
- A1
- B2
- ✓3
- D4
Answer: C.
View full solution →Let R be a relation from N to N defined by R = {(a, b) : a, b $\in$ N and $a = b^2$}. Check whether, (a, b) $\in$ R, (b, c) $\in$ R implies $(a, c) \in R$ ? Justify your answer.
View full solution →Let R be a relation from N to N defined by R = {(a, b) : a, b $\in$ N and $a = b^2$}. Is the given statement true? (a, b) $\in$ R, implies $(b,a) \in R$ ? Justify your answer.
View full solution →Let R be a relation from N to N defined by R = {(a, b) : a, b $\in$ N and $a = b^2$}. Check whether $(a,a) \in R$ for all $a \in N$ ? Justify your answer.
View full solution →If A = {9, 10, 11, 12,13} and f : A $\rightarrow$ N be defined by f(n) = the highest prime factor of n, then find the range of f.
View full solution →Let f be a subset of Z $\times$ Z defined by f = {ab, a + b ) : a, b $ \in $ Z}. Is f a function from Z to Z? Justify your answer.
View full solution →Let f = {(1, 1), (2, 3), (0, - 1), - 1, - 3)} be a function from Z to Z defined by f (x) = ax + b for some integers a, b. Determine a,b.
Let $f= \left\{ \left(x , \frac { x ^ { 2 } } { 1 + x ^ { 2 } } \right) : x \in R \right\}$ be a function from R into R. Determine the range of f.
View full solution →Find the domain and the range of the real function f defined by f(x) = |x - 1|.
Find the domain and range of the real function f defined by $f(x) = \sqrt {x - 1} $
View full solution →Find the domain of the function $f(x) = \frac{{{x^2} + 2x + 1}}{{{x^2} - 8x + 12}}$.
View full solution →Let f, g: $R \to R$ be defined, respectively by f(x) = x + 1, g(x) = 2x – 3. Find f + g, f – g and $\frac{f}{g}$.
View full solution →The relation f is defined by $f ( x ) = \left\{ \begin{array} { l } { x ^ { 2 } , 0 \leq x \leq 3 } \\ { 3 x , 3 \leq x \leq 10 } \end{array} \right.$and the relation g is defined by $g ( x ) = \left\{ \begin{array} { l } { x ^ { 2 } , 0 \leq x \leq 2 } \\ { 3 x , 2 \leq x \leq 10 } \end{array} \right..$ Show that f is a function and g is not a function.
View full solution →Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by {(a, b): a, b $ \in $A, b is exactly divisible by a}.
View full solution →- Write R in roster form
- Find the domain of R
- Find the range of R.
The function f is defined by $\begin{equation} f(x)=\left\{\begin{array}{ll} {1-x,} & {x<0} \\ {1} & {, x=0} \\ {x+1,} & {x>0} \end{array}\right. \end{equation}$
Draw the graph of f(x).
View full solution →Draw the graph of f(x).
Let R be the set of real numbers. Define the real function f: R $\rightarrow$ R by f(x) = x + 10 and sketch the graph of this function.
View full solution →Let f = {(1, 1), (2, 3), (0, –1), (–1, –3)} be a function from Z to Z defined by f(x) = ax + b, for some integers a, b. Determine a, b.
The relation f is defined by $\text{f(x)}=\begin{cases}\text{x}^2,0\leq\text{x}\leq3\\3\text{x},3\leq\text{x}\leq10\end{cases}$ The relation g is defined by $\text{g(x)}=\begin{cases}\text{x}^2,0\leq\text{x}\leq2\\3\text{x},2\leq\text{x}\leq10\end{cases}$ Show that f is a function and g is not a function.
View full solution →Let A = {9, 10, 11, 12, 13} and let f : A → N be defined by f(n) = the highest prime factor of n. Find the range of f.
Let $A = {1, 2}$ and $B = {3, 4}$. Write $A × B$. How many subsets will $A × B$ have? List them.
View full solution →Let A ={1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)} Are the following true?
- f is a relation from A to B.
- f is a function from A to B.
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