10th class Mathematics, Chapter 5: Algebraic Fractions MCQs

1. The expression (2x − 1)/(x² + 4) is:

1. (A) a polynomial
2. (B) an algebraic fraction ✓
3. (C) a numerical fraction
4. (D) an equation

2. Lowest form of 18a²bc²/(12ac) is:

1. (A) 9abc/6
2. (B) 3abc/2 ✓
3. (C) 18b/12
4. (D) 3/2

3. Lowest form of 15xyz/10 is:

1. (A) 3xyz/2 ✓
2. (B) 3/2
3. (C) xyz
4. (D) xyz/2

4. Simplified form of (3x + 1)/5 + (2x + 3)/5 is:

1. (A) (5x + 4)/10
2. (B) (5x + 4)/5 ✓
3. (C) (5x + 4)/25
4. (D) 5x + 4

5. Simplified form of ((x² − y²)/(x + y))(x − y) is:

1. (A) (x + y)²
2. (B) x² + y²
3. (C) x − y
4. (D) (x − y)² ✓

6. (x³ − y³) ÷ (x − y) in simplified form is:

1. (A) x² − xy + y²
2. (B) x² + xy + y² ✓
3. (C) x² − y²
4. (D) x² + y²

7. An equation of the form 5/x + (1 − x)/3 = 1/(6x) is called:

1. (A) radical equation
2. (B) reciprocal equation
3. (C) fractional equation ✓
4. (D) exponential equation

8. An equation of the form 5ˣ + 64·5⁻ˣ − 20 = 0 is called:

1. (A) radical equation
2. (B) exponential equation ✓
3. (C) reciprocal equation
4. (D) fractional equation

9. Roots of y² − 24y + 128 = 0 are:

1. (A) 8, −16
2. (B) 8, 16 ✓
3. (C) −8, 16
4. (D) −8, −16

10. Linear factors of 3x² + 10x + 3 are:

1. (A) (x + 3), (3x + 1) ✓
2. (B) (x + 3), (3x − 1)
3. (C) (x − 3), (3x + 1)
4. (D) (x − 3), (3x − 1)

11. The denominator of an algebraic fraction can never be:

1. (A) a monomial
2. (B) zero ✓
3. (C) one
4. (D) negative

12. A rational expression is a quotient of two:

1. (A) polynomials ✓
2. (B) integers only
3. (C) equations
4. (D) sets

13. Which of the following is a rational expression?

1. (A) x^(1/2) + 1
2. (B) 2ˣ
3. (C) (x + 1)/(x + 2) ✓
4. (D) √x/2

14. To reduce a fraction to its lowest form, we cancel the:

1. (A) common terms of numerator and denominator
2. (B) numerator only
3. (C) denominator only
4. (D) common factors of numerator and denominator ✓

15. The lowest form of (x² − 9)/(x + 3) is:

1. (A) x² − 3
2. (B) 1
3. (C) x − 3 ✓
4. (D) x + 3

16. The lowest form of 6x²/(3x) is:

1. (A) 3x
2. (B) 2x²
3. (C) 18x³
4. (D) 2x ✓

17. The lowest form of (x² − 5x)/(x − 5) is:

1. (A) x + 5
2. (B) 5x
3. (C) x ✓
4. (D) x − 5

18. The lowest form of (a + b)²/(a² − b²) is:

1. (A) a + b
2. (B) (a + b)/(a − b) ✓
3. (C) (a − b)/(a + b)
4. (D) 1

19. The LCM of x and x² is:

1. (A) 1
2. (B) x² ✓
3. (C) x
4. (D) x³

20. 2/x + 3/x =

1. (A) 6/x²
2. (B) 5/x²
3. (C) 5/x ✓
4. (D) 5/(2x)