Let Z be the set of integers. If A = \ x Z:2^(x + 2)( x^2 - 5x + 6 ) = 1 \ and = \ x Z : - 3 < 2x - 1 < 9\, then the . number of subsets of the set A B is

(c) : Given, A = \ x Z:2^(x + 2)( x^2 - 5x + 6 ) = 1 \ \\ 2^(x + 2)( x^2 - 5x + 6 ) = 2^0 \\ (x + 2)( x^2 - 5x + 6 ) =

Let Z be the set of integers. If A = { x in Z:2^{(x + 2) ( x^{2} - 5x + 6 )} = 1 } and = { x in Z : - 3 < 2x - 1 < 9}, then the . number of subsets of the set A X B is: Relation (Mathematics)

JEE Mains (12$\ ^{th\ }$ Jan $2^{nd\ }$ Shift 2019) 12th January Shift 2

Mathematics

Let

Z

be the set of integers. If

A = \left\{ x \in Z:2^{(x + 2)\left( x^{2} - 5x + 6 \right)} = 1 \right\}

and

= \{ x \in Z

- 3 < 2x - 1 < 9\}

, then the . number of subsets of the set

A \times B

2^{18}

2^{12}

2^{15}

2^{10}

Prev Next

Correct Answer:

Explanation

(c) : Given, $A = \left\{ x \in Z:2^{(x + 2)\left( x^{2} - 5x + 6 \right)} = 1 \right\}$ $\\ \therefore 2^{(x + 2)\left( x^{2} - 5x + 6 \right)} = 2^{0} \\ \Rightarrow (x + 2)\left( x^{2} - 5x + 6 \right) = 0 \\ \Rightarrow (x + 2)(x - 2)(x - 3) = 0 \Rightarrow x = 2, - 2,3 \\ \therefore A = \{ - 2,2,3\}\\$ Also, $B = \{ x \in Z: - 3 < 2x - 1 < 9\}\\$ So, $- 3 < 2x - 1 < 9 \\ \Rightarrow - 2 < 2x < 10 \Rightarrow - 1 < x < 5$ $\\ \therefore B = \{ 0,1,2,3,4\}.\\$ Thus, $n(A \times B) = 15\\$ So, number of subsets of $A \times B$ is $2^{15}$ .

Select an option to instantly check whether it is correct or wrong.

Explanation

The minimum number of elements that must be added to the relation R = {(a,b),(b,c),(b,d)} on the set { a,b,c,d} so that it is an equivalence relation is

Let R be the set of real numbers. end{enumerate} Statement-1: A = {(x,y) in R X R:y - x is an integer } is an equivalence . relation on R. Statement-2: B = {(x,y) in R X R:x = alpha y for some rational number } is . an equivalence relation on R.

Let A = { 1,3,4,6,9} and B = { 2,4,5,8,10}. Let R be a relation defined on A X B such that R = {( ( a_{1},b_{1} ), ( a_{2},b_{2} )):a_{1} ? b_{2} and b_{1} ? a_{2}}. Then the number of elements in the set R is

Let R be a relation on Z X Z defined by (a,b)R(c,d) if and only if ad - bc is divisible by 5 . Then R is

Let A = { 1,2,3,4,...,10} and B = { 0,1,2,3,4}. The number of elements in the relation = {(a,b) in A X A : 2(a - b)^{2} + 3(a - b) in B} is .

The number of relations, on the set { 1,2,3} containing (1,2) and (2,3), which are reflexive and transitive but not symmetric, is .

Let A = { 0,3,4,6,7,8,9,10} and R be the relation defined on A such that R = {(x,y) in A X A:x - y is odd positive integer or x - y = 2}. The minimum number of elements that must be added to the relation R, so that it is a symmetric relation, is equal to .

If R is the smallest equivalence relation on the set { 1,2,3,4} such that {(1,2),(1,3)} subset R, then the number of elements in R is .

Let X = { 1,2,3,4,5}. The number of different ordered pairs ( Y,Z ) that can be formed such that Y subseteq X,Z subseteq X and Y cap Z. pty is

Download Divine JEE App

Quick Links

Exam Categories

Contact Info

Divine JEE