NDA 2019 Paper 1 | Sets, Relations and Functions Question 30 | Mathematics

Suppose X = {1, 2, 3, 4} and R is a relation on X. If R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (2, 3), (3, 2)}, then which one of the following is correct?

R is reflexive and symmetric, but not transitive

R is symmetric and transitive, but not reflexive

R is reflexive and transitive, but not symmetric

R is neither reflexive nor transitive, but symmetric.

NDA 2019 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

A relation R is defined on the set N of natural numbers as xRy $$\Rightarrow$$ x² $$-$$ 4xy + 3y² = 0. Then, which one of the following is correct?

R is reflexive and symmetric, but not transitive

R is reflexive and transitive, but not symmetric

R is reflexive, symmetric and transitive

R is reflexive, but neither symmetric not transitive

NDA 2019 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

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

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