1. If the degree of numerator N(x) is equal or greater than the degree of denominator D(x), then the fraction is:
(A) Proper
(B) Improper
(C) Neither proper nor improper
(D) Both proper and improper
2. If the degree of numerator is less than the degree of denominator, then the fraction is:
(A) Proper
(B) Improper
(C) Neither proper nor improper
(D) Both proper and improper
3. The fraction (2x² + 5) / (x² + 5x + 6) is known as:
(A) Proper
(B) Improper
(C) Both proper and improper
(D) None of these
4. The number of partial fractions of (6x + 27) / (3x² – 9x) are:
(A) 2
(B) 3
(C) 4
(D) None of these
5. The number of partial fractions of (2x³ – 3x² + 1) / ((x–1)(x+1)(x–1)²) are:
(A) 2
(B) 3
(C) 4
(D) 5
6. The equivalent partial fraction of (2x + 11) / ((x + 1)(x – 3)) is:
(A) A / (x + 1) + B / (x – 3)
(B) A / (x + 1) – B / (x – 3)
(C) A / (x + 1) + B / (x – 3) + C / (x – 3)²
(D) (Ax + C) / (x + 1) + B / (x – 3)
7. The equivalent partial fraction of (2x² + 4) / ((x + 1)(x – 3)²) is:
(A) (2x + B) / (x + 1) + (Cx + D) / (x – 3)
(B) (2x + B) / (x + 1) + (Cx) / (x – 3)
(C) (Ax + B) / (x + 1) + (Cx + D) / (x – 3)²
(D) (Ax) / (x + 1) + (Bx) / (x – 3)
8. Partial fraction of (2x) / (x(x + 1)) is:
(A) 2 / x – 1 / (x + 1)
(B) 1 / x – 2 / (x + 1)
(C) 2 / x – 2 / (x + 1)
(D) 2 / x + 2 / (x + 1)
9. Partial fraction of (2x + 3) / ((x–2)(x + 5)) is called:
(A) 2 / (x–2) + 1 / (x + 5)
(B) 3 / (x–2) + 1 / (x + 5)
(C) 2 / (x–2) + 3 / (x + 5)
(D) 1 / (x–2) + 1 / (x + 5)
10. The fraction ((x–1)(x–2)(x–3)) / ((x–4)(x–5)(x–6)) is called:
(A) Proper
(B) Improper
(C) Both proper and Improper
(D) None of these