Mathematics MCQ Practice Set

Test your knowledge with these 40 multiple-choice questions

Number System (6 Questions)

1. Which of the following has a terminating decimal expansion?

1. \(\frac{21}{30}\)
2. \(\frac{13}{25}\)
3. \(\frac{27}{50}\)
4. Both (b) and (c)

Answer: d) Both (b) and (c)

A rational number has a terminating decimal expansion if its denominator (in simplest form) has prime factors only 2 and/or 5. \(\frac{13}{25}\) (denominator 5²) and \(\frac{27}{50}\) (denominator 2×5²) satisfy this condition.

2. If \(\sqrt{3} = 1.732...\), then \( \frac{1}{\sqrt{3}} \) is:

1. Rational
2. Irrational
3. Integer
4. Whole number

Answer: b) Irrational

\(\frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}\), which is irrational as it cannot be expressed as a ratio of integers and has a non-terminating, non-repeating decimal expansion.

3. Between any two rational numbers:

1. Only one rational exists
2. Infinitely many rationals exist
3. No rational number exists
4. Exactly two exist

Answer: b) Infinitely many rationals exist

The rational numbers are dense, meaning between any two distinct rational numbers, there exist infinitely many other rational numbers.

4. Which of the following is an irrational number?

1. \(\frac{3}{7}\)
2. \(\sqrt{5}\)
3. \(\sqrt{16}\)
4. -2

Answer: b) \(\sqrt{5}\)

\(\sqrt{5}\) is irrational because it cannot be expressed as a ratio of integers and its decimal expansion is non-terminating and non-repeating.

5. The prime factorization of 360 is:

1. \(2^3 \times 3^2 \times 5\)
2. \(2^4 \times 3 \times 5\)
3. \(2^2 \times 3^3 \times 5\)
4. None of these

Answer: a) \(2^3 \times 3^2 \times 5\)

360 = 36 × 10 = (6×6)×(2×5) = (2×3)×(2×3)×(2×5) = \(2^3 \times 3^2 \times 5\).

6. The decimal expansion of \(\frac{77}{300}\) will:

1. Terminate
2. Recurring non-terminating
3. Non-repeating, non-terminating
4. None of these

Answer: b) Recurring non-terminating

\(\frac{77}{300} = \frac{77}{3 \times 100} = 0.25666...\), which is a recurring (repeating) non-terminating decimal.

Polynomial (6 Questions)

7. If \(p(x) = x^2 - 3x + 2\), then zeros are:

1. 1, 2
2. -1, -2
3. 2, 3
4. -2, 3

Answer: a) 1, 2

Solving \(x^2 - 3x + 2 = 0\) gives (x-1)(x-2)=0, so the zeros are x=1 and x=2.

8. If polynomial \(x^2 + 5x + 6\) is divided by \((x+2)\), the remainder is:

1. 0
2. 2
3. -2
4. 6

Answer: a) 0

By the remainder theorem, remainder = p(-2) = (-2)² + 5(-2) + 6 = 4 - 10 + 6 = 0.

9. The degree of polynomial \(5x^4 - x^2 + 2\) is:

1. 2
2. 3
3. 4
4. 5

Answer: c) 4

The degree of a polynomial is the highest power of the variable. Here, the highest power is 4.

10. The coefficient of \(x^3\) in \(-2x^3 + 7x^2 - x + 4\) is:

1. -2
2. 2
3. 7
4. -7

Answer: a) -2

The coefficient is the numerical factor of the term. For \(x^3\), the coefficient is -2.

11. If sum and product of zeros of \(p(x) = x^2 - 7x + 12\) are \(S, P\), then (S,P) =

1. (7,12)
2. (-7,-12)
3. (12,7)
4. (6,7)

Answer: a) (7,12)

For a quadratic equation \(ax^2 + bx + c = 0\), sum of zeros = -b/a = 7, product of zeros = c/a = 12.

12. Which of the following is not a polynomial?

1. \(2x^3 - \sqrt{x} + 7\)
2. \(x^4 - 3x^2 + 5\)
3. \(3t^2 - 2t + 1\)
4. \(\sqrt{2}x^5\)

Answer: a) \(2x^3 - \sqrt{x} + 7\)

A polynomial must have non-negative integer exponents. \(\sqrt{x} = x^{1/2}\) has a fractional exponent, so it is not a polynomial.

Linear Equations in Two Variables (6 Questions)

13. The solution of \(2x + 3y = 12, x=0\) is:

1. (0,4)
2. (4,0)
3. (6,0)
4. (0,6)

Answer: a) (0,4)

Substitute x=0: 2(0) + 3y = 12 → 3y = 12 → y = 4. So the solution is (0,4).

14. If x = 2, y = 3 satisfy equation \(kx + y = 7\), then k =

1. 2
2. 1
3. -2
4. 3

Answer: a) 2

Substitute x=2, y=3: k(2) + 3 = 7 → 2k = 4 → k = 2.

15. The line parallel to x-axis is of form:

1. x = a
2. y = a
3. y = mx
4. x+y=0

Answer: b) y = a

A line parallel to the x-axis has a constant y-value and is of the form y = a, where a is a constant.

16. The number of solutions of a pair of inconsistent linear equations is:

1. One
2. Two
3. Infinite
4. None

Answer: d) None

Inconsistent equations have no solution as they represent parallel lines that never intersect.

17. Graph of \(2x + 0y = 6\) represents:

1. Vertical line
2. Horizontal line
3. Slanted line
4. Point only

Answer: a) Vertical line

\(2x + 0y = 6\) simplifies to x = 3, which is a vertical line parallel to the y-axis.

18. If the pair of equations \(2x+3y=7\) and \(4x+6y=14\) is given, then lines are:

1. Intersecting
2. Parallel
3. Coincident
4. None

Answer: c) Coincident

The second equation is exactly twice the first, so they represent the same line (coincident lines).

Lines and Angles (10 Questions)

19. If two angles are complementary, then their sum is:

1. 0°
2. 90°
3. 180°
4. 360°

Answer: b) 90°

Complementary angles are two angles whose measures add up to 90°.

20. If two lines intersect, then vertically opposite angles are:

1. Unequal
2. Equal
3. Complementary
4. Supplementary

Answer: b) Equal

When two lines intersect, the vertically opposite angles formed are always equal.

21. If a transversal cuts two parallel lines, then alternate interior angles are:

1. Equal
2. Not equal
3. 90°
4. Supplementary

Answer: a) Equal

When a transversal cuts two parallel lines, the alternate interior angles are equal.

22. Angles on the same side of transversal are also called:

1. Vertically opposite
2. Co-interior
3. Alternate interior
4. None

Answer: b) Co-interior

When a transversal cuts two lines, the angles on the same side of the transversal are called co-interior angles.

23. If two supplementary angles differ by 20°, then angles are:

1. 80°, 100°
2. 70°, 110°
3. 60°, 120°
4. 90°, 90°

Answer: a) 80°, 100°

Let one angle be x. Then the other is x+20. Since they are supplementary, x + (x+20) = 180 → 2x = 160 → x = 80. So the angles are 80° and 100°.

24. An exterior angle of a triangle is equal to:

1. Sum of interior opposite angles
2. Difference
3. Half of base angles
4. None

Answer: a) Sum of interior opposite angles

According to the exterior angle theorem, an exterior angle of a triangle is equal to the sum of the two interior opposite angles.

25. The measure of each angle of an equilateral triangle is:

1. 45°
2. 60°
3. 90°
4. 120°

Answer: b) 60°

In an equilateral triangle, all angles are equal. Sum of angles = 180°, so each angle = 180°/3 = 60°.

26. If one angle of a triangle is 90° and other is 45°, then the third is:

1. 30°
2. 35°
3. 45°
4. 60°

Answer: c) 45°

Sum of angles in a triangle = 180°. So third angle = 180° - (90° + 45°) = 45°.

27. The diagonals of a rhombus bisect each other at:

1. 45°
2. 60°
3. 90°
4. 120°

Answer: c) 90°

In a rhombus, the diagonals bisect each other at right angles (90°).

28. Sum of all angles of a quadrilateral is:

1. 90°
2. 180°
3. 270°
4. 360°

Answer: d) 360°

The sum of all interior angles of a quadrilateral is always 360°.

Practice these MCQs to test your understanding of key mathematical concepts.