NDA 2019 Paper 1 | Sets, Relations and Functions Question 32 | Mathematics

If $$A = \{ x \in Z:{x^3} - 1 = 0\} $$ and $$B = \{ x \in Z:{x^2} + x + 1 = 0\} $$, where, Z is set of complex numbers, then what is A $$\cap$$ B equal to?

Null set

$$\left[ {{{ - 1 + \sqrt 3 i} \over 2},{{ - 1 - \sqrt 3 i} \over 2}} \right]$$

$$\left[ {{{ - 1 + \sqrt 3 i} \over 4},{{ - 1 - \sqrt 3 i} \over 4}} \right]$$

$$\left[ {{{1 + \sqrt 3 i} \over 2},{{1 - \sqrt 3 i} \over 2}} \right]$$

NDA 2019 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

Consider the following statements for the two non-empty sets A and B.

1. $$(A \cap B) \cup (A \cap \overline B ) \cup (\overline A \cap B) = A \cup B$$

2. $$(A \cup (\overline A \cap \overline B )) = A \cup B$$

Which of the above statements is/are correct?

Only 1

Only 2

Both 1 and 2

Neither 1 nor 2

NDA 2019 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

Let X be a non-empty set and let A, B, C be subsets of X. Consider the following statements.

1. $$A \subset C \Rightarrow (A \cap B) \subset (C \cap B),\,(A \cup B) \subset (C \cup B)$$

2. $$(A \cap B) \subset (C \cap B)$$ for all sets $$B \Rightarrow A \subset C$$

3. $$(A \cup B) \subset (C \cup B)$$ for all sets $$B \Rightarrow A \subset C$$

Which of the above statements are correct?

Only 1 and 2

Only 2 and 3

Only 1 and 3

1, 2 and 3

NDA 2019 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

If A = {$$\lambda$$, {$$\lambda$$, $$\mu$$}}, then the power set of A is

{$$\phi$$, {$$\phi$$}, {$$\lambda$$}, {$$\lambda$$, $$\mu$$}}

{$$\phi$$, {$$\lambda$$}, {$$\lambda$$, $$\mu$$}, {$$\lambda$$, {$$\lambda$$, $$\mu$$}}}

{{$$\lambda$$}, {$$\lambda$$, $$\mu$$}, {$$\lambda$$, {$$\lambda$$, $$\mu$$}}}