11th Class (1st Year HSSC-I) Mathematics MCQs Practice Examination

Question 1

Which of the following is a proper rational fraction?

Accepted Answer

(x - 5) / (x^2 + 3x + 2)

Answer

x^2 / (x+1)

Answer

(x^3 + 2x) / (x^2 - 1)

Answer

(x^2 + 1) / (x^2 - 4)

Question 2

To decompose an improper rational fraction into partial fractions, what is the essential first step?

Accepted Answer

Perform polynomial long division to express it as a sum of a polynomial and a proper rational fraction.

Answer

Factorize the numerator polynomial.

Answer

Find the roots of the numerator.

Answer

Multiply the numerator and denominator by the conjugate of the denominator.

Question 3

What is the correct form of partial fraction decomposition for the expression (3x+1) / ((x-1)(x+2))?

Accepted Answer

A/(x-1) + B/(x+2)

Answer

A/(x-1) + Bx/(x+2)

Answer

A/(x-1) + B/(x+2) + C

Answer

Ax/(x-1) + B/(x+2)

Question 4

The partial fraction form for (x^2+1) / ((x-1)^2 (x+3)) is:

Accepted Answer

A/(x-1) + B/(x-1)^2 + C/(x+3)

Answer

A/(x-1) + B/(x+3)

Answer

A/(x-1)^2 + B/(x+3)

Answer

A/(x-1) + Bx/(x-1)^2 + C/(x+3)

Question 5

Which of the following is an irreducible quadratic factor over real numbers?

Accepted Answer

x^2 + 9

Answer

x^2 - 4

Answer

x^2 - 2x + 1

Answer

x^2 - x

Question 6

What is the correct partial fraction form for (2x+5) / ((x^2+4)(x-3))?

Accepted Answer

(Ax+B)/(x^2+4) + C/(x-3)

Answer

A/(x^2+4) + B/(x-3)

Answer

A/(x^2+4) + (Bx+C)/(x-3)

Answer

(Ax+B)/(x^2+4) + (Cx+D)/(x-3)

Question 7

If 1 / ((x-1)(x-2)) = A/(x-1) + B/(x-2), what is the value of A?

Accepted Answer

-1

Answer

1

Answer

2

Answer

-2

Question 8

A rational fraction P(x)/Q(x) is improper if:

Accepted Answer

Both deg(P(x)) = deg(Q(x)) or deg(P(x)) > deg(Q(x))

Answer

deg(P(x)) < deg(Q(x))

Answer

deg(P(x)) = deg(Q(x))

Answer

deg(P(x)) > deg(Q(x))

Question 9

The partial fraction form for (x+1) / ((x^2+1)^2 (x-2)) is:

Accepted Answer

(Ax+B)/(x^2+1) + (Cx+D)/(x^2+1)^2 + E/(x-2)

Answer

(Ax+B)/(x^2+1) + C/(x-2)

Answer

A/(x^2+1) + B/(x^2+1)^2 + C/(x-2)

Answer

(Ax+B)/(x^2+1)^2 + C/(x-2)

Question 10

When decomposing a proper rational fraction with a denominator containing only non-repeated linear factors, how many constants (A, B, C, etc.) will be involved?

Accepted Answer

Equal to the number of linear factors.

Answer

One less than the number of linear factors.

Answer

Always two.

Answer

Always three.

Chapter-wise MCQs Practice