Class JEE Mathematics Sets, Relations, and Functions Q #1062
KNOWLEDGE BASED
APPLY
4 Marks 2019 JEE Main 2019 (Online) 12th January Evening Slot MCQ SINGLE
Let $Z$ be the set of integers. If $A = {x \in Z : 2(x + 2) (x^2 - 5x + 6) = 1}$ and $B = {x \in Z : -3 < 2x - 1 < 9}$, then the number of subsets of the set $A \times B$, is
(A) $2^{12}$
(B) $2^{18}$
(C) $2^{10}$
(D) $2^{15}$
Correct Answer: D
Explanation
Given $A = {x \in Z : 2(x+2)(x^2 - 5x + 6) = 1}$.
Since $2(x+2)(x^2 - 5x + 6) = 1$, we can rewrite it as $2(x+2)(x^2 - 5x + 6) = 2^0$.
This implies that $x = -2, 2, 3$, so $A = {-2, 2, 3}$.
Also, $B = {x \in Z : -3 < 2x - 1 < 9}$.
Adding 1 to all sides, we get $-2 < 2x < 10$.
Dividing by 2, we get $-1 < x < 5$.
Thus, $B = {0, 1, 2, 3, 4}$.
Now, $A \times B$ has $3 \times 5 = 15$ elements.
The number of subsets of $A \times B$ is $2^{15}$.

More from this Chapter

MCQ_SINGLE
Two newspapers A and B are published in a city. It is known that $25$% of the city populations reads A and $20$% reads B while $8$% reads both A and B. Further, $30$% of those who read A but not B look into advertisements and $40$% of those who read B but not A also look into advertisements, while $50$% of those who read both A and B look into advertisements. Then the percentage of the population who look into advertisement is :-
NUMERICAL
Let $\mathrm{A}=\{-4,-3,-2,0,1,3,4\}$ and $\mathrm{R}=\left\{(a, b) \in \mathrm{A} \times \mathrm{A}: b=|a|\right.$ or $\left.b^{2}=a+1\right\}$ be a relation on $\mathrm{A}$. Then the minimum number of elements, that must be added to the relation $\mathrm{R}$ so that it becomes reflexive and symmetric, is __________
NUMERICAL
Let $A=\{1,2,3,4\}$ and $R=\{(1,2),(2,3),(1,4)\}$ be a relation on $\mathrm{A}$. Let $\mathrm{S}$ be the equivalence relation on $\mathrm{A}$ such that $R \subset S$ and the number of elements in $\mathrm{S}$ is $\mathrm{n}$. Then, the minimum value of $n$ is __________.
NUMERICAL
Let $S=\{4,6,9\}$ and $T=\{9,10,11, \ldots, 1000\}$. If $A=\left\{a_{1}+a_{2}+\ldots+a_{k}: k \in \mathbf{N}, a_{1}, a_{2}, a_{3}, \ldots, a_{k}\right.$ $\epsilon S\}$, then the sum of all the elements in the set $T-A$ is equal to __________.
MCQ_SINGLE
In a class of $140$ students numbered $1$ to $140$, all even numbered students opted Mathematics course, those whose number is divisible by $3$ opted Physics course and those whose number is divisible by $5$ opted Chemistry course. Then the number of students who did not opt for any of the three courses is
View All Questions