1
COMEDK 2024 Evening Shift
+1
-0

Two finite sets have '$$m$$' and '$$n$$' number of elements respectively. The total number of subsets of the first set is 112 more than the total number of subsets of the second set. Then the values of $$\mathrm{m}$$ and $$\mathrm{n}$$ are respectively.

A
7, 4
B
7, 7
C
4, 4
D
4, 7
2
COMEDK 2024 Morning Shift
+1
-0

\begin{aligned} &\begin{aligned} & \text { A, B, C are subsets of the Universal set U } \\ & \text { If } \mathrm{A}=\{x: x \text { is even number, } x \leq 20\} \\ & \mathrm{B}=\{x: x \text { is multiple of } 3, x \leq 15\} \\ & \mathrm{C}=\{x: x \text { is multiple of } 5, x \leq 20\} \\ & \mathrm{U}=\text { Set of whole numbers } \end{aligned}\\ &\text { then the Venn diagram representing } \mathrm{U}, \mathrm{A}, \mathrm{B} \text { and } \mathrm{C} \text { is } \end{aligned}

A
B
C
D
3
COMEDK 2024 Morning Shift
+1
-0

$$\text { If } A=\{1,2,3,4,5\} \text { and } B=\{2,3,6,7\} \text { then number of elements in the set }(A \times B) \cap(B \times A) \text { is equal to }$$

A
20
B
10
C
4
D
5
4
COMEDK 2024 Morning Shift
+1
-0

Express the set $$A=\{1,7,17,31,49\}$$ in set builder form

A
$$\left\{x \mid x=2 n^2-1\right.$$, where $$n \in \mathcal{N}$$ and $$\left.n < 5\right\}$$
B
$$\left\{x \mid x=2 n^2-3\right.$$, where $$n \in \mathcal{N}$$ and $$\left.2 \leq n \leq 8\right\}$$
C
$$\left\{x \mid x=2 n^2+1\right.$$, where $$n \in \mathcal{N}$$ and $$\left.n \leq 7\right\}$$
D
$$\left\{x \mid x=2 n^2-1\right.$$, where $$n \in \mathcal{N}$$ and $$\left.n \leq 5\right\}$$
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