SETS AND RELATIONS + FACTORIZATION AND ALGEBRAIC MANIPULATION

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1. Factorize: 6x² - 7x - 3

A (3x + 1)(2x - 3)

B (3x - 1)(2x + 3)

C (6x + 1)(x - 3)

D (2x + 1)(3x - 3)

2. Find the LCM of 4a²b and 6ab³.

A 12a²b³

B 24a²b³

C 2ab

D 12ab³

3. Factorize: x³ - 8

A (x - 2)(x² + 2x + 4)

B (x + 2)(x² - 2x + 4)

C (x - 2)(x² - 2x + 4)

D (x + 2)(x² + 2x + 4)

4. Simplify: (x + 3)/(x² + 5x + 6)

A 1/(x + 2)

B 1/(x + 3)

C (x + 3)/(x + 2)

D 1/(x - 2)

5. Which of the following is the identity element for union of sets?

A Universal set

B Empty set

C The set itself

D No identity exists

6. The commutative property for intersection of sets states that:

A A ∩ B = B ∩ A

B (A ∩ B) ∩ C = A ∩ (B ∩ C)

C A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

D A ∩ U = A

7. Factorize: x² - 10x + 25 - 4y²

A (x - 5 - 2y)(x - 5 + 2y)

B (x + 5 - 2y)(x + 5 + 2y)

C (x - 5 - 2y)²

D (x - 5)² - 4y²

8. If A = {a, b, c} and B = {c, d, e}, what is A ∩ B?

A {c}

B {a, b, c, d, e}

C {a, b}

D {d, e}

9. Simplify: (x² - 5x + 6)/(x - 2)

A x - 3

B x + 3

C x - 2

D x + 2

10. If A ⊆ B, then A ∪ B equals:

A A

B B

C A ∩ B

D ∅

SETS AND RELATIONS + FACTORIZATION AND ALGEBRAIC MANIPULATION

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