MHT-CET

Sets and Relations question bank (Mathematics)

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Q1.

Let $S$ be a non-empty subset of $\mathbb{R}$. Consider the following statement: p : There is a rational number $x \in \mathrm{~S}$ such that $x\gt0$. Which of the following statements is the negation of the statement p?

(A)

There is a rational number $x \in \mathrm{~S}$ such that $x \leq 0$.

(B)

There is no rational number $x \in \mathrm{~S}$ such that $x \leq 0$.

(C)

Every rational number $x \in \mathrm{~S}$ satisfies $x \leq 0$.

(D)

$x \in \mathrm{~S}$ and $x \leq 0 \Rightarrow x$ is not a rational number.

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Q2.

If $n(A)=4, n(B)=2$. Then the number of subsets of the set $\mathrm{A} \times \mathrm{B}$ each having at least 3 elements are

(A)

275

(B)

510

(C)

219

(D)

256

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