Class JEE Mathematics Sets, Relations, and Functions Q #1058
KNOWLEDGE BASED
APPLY
4 Marks 2020 JEE Main 2020 (Online) 2nd September Morning Slot MCQ SINGLE
If $R = {(x, y) : x, y \in Z, x^2 + 3y^2 \le 8}$ is a relation on the set of integers $Z$, then the domain of $R^{-1}$ is :
(A) {0, 1}
(B) {-2, –1, 1, 2}
(C) {-1, 0, 1}
(D) {-2, –1, 0, 1, 2}
Prev Next
Correct Answer: C
Explanation
Given $R = {(x, y) : x, y \in Z, x^2 + 3y^2 \le 8}$.
So $R = {(0,1), (0,-1), (1,0), (-1,0), (1,1), (1,-1), (-1,1), (-1,-1), (2,0), (-2,0), (2,1), (2,-1), (-2,1), (-2,-1)}$.
$\Rightarrow R : {-2, -1, 0, 1, 2} \rightarrow {-1, 0, 1}$.
$\therefore R^{-1} : {-1, 0, 1} \rightarrow {-2, -1, 0, 1, 2}$.
$\therefore$ Domain of $R^{-1} = {-1, 0, 1}$.

More from this Chapter

MCQ_SINGLE
Consider the sets $A = \{(x, y) \in R \times R : x^2 + y^2 = 25\}$, $B = \{(x, y) \in R \times R: x^2 + 9y^2 = 144\}$, $C = \{(x, y) \in Z \times Z: x^2 + y^2 \leq 4\}$ and $D = A \cap B$. The total number of one-one functions from the set $D$ to the set $C$ is:
NUMERICAL
Let A = {n $ \in $ N: n is a 3-digit number} B = {9k + 2: k $ \in $ N} and C = {9k + $l$: k $ \in $ N} for some $l ( 0 < l < 9)$ If the sum of all the elements of the set A $ \cap $ (B $ \cup $ C) is 274 $ \times $ 400, then $l$ is equal to ________.
MCQ_SINGLE
Let a relation $R$ on $N \times N$ be defined as: $(x_1, y_1) R (x_2, y_2)$ if and only if $x_1 \le x_2$ or $y_1 \le y_2$. Consider the two statements: (I) $R$ is reflexive but not symmetric. (II) $R$ is transitive Then which one of the following is true?
NUMERICAL
Let A = {n $ \in $ N: n is a 3-digit number} B = {9k + 2: k $ \in $ N} and C = {9k + $l$: k $ \in $ N} for some $l ( 0 < l < 9)$ If the sum of all the elements of the set A $ \cap $ (B $ \cup $ C) is 274 $ \times $ 400, then $l$ is equal to ________.
NUMERICAL
Let X = {n $ \in $ N : 1 $ \le $ n $ \le $ 50}. If A = {n $ \in $ X: n is a multiple of 2} and B = {n $ \in $ X: n is a multiple of 7}, then the number of elements in the smallest subset of X containing both A and B is ________.
View All Questions