Mathematics MCQs include a wide range of solved multiple-choice questions from basic arithmetic to advanced mathematics. These questions cover topics such as Algebra, Geometry, Trigonometry, Calculus, Probability, Statistics, and Arithmetic. They are especially designed for students and candidates preparing for PPSC, FPSC, CSS, PMS, NTS, KPPSC, SPSC, and other competitive exams. Practicing these MCQs helps improve problem-solving skills, numerical ability, and analytical reasoning, making them ideal for both academic learning and job test preparation.
Correct answer: 47. Powers first: 8 × 9 − 25 = 72 − 25 = 47.
Background: Follow BODMAS: brackets, orders (powers), division and multiplication, then addition and subtraction.
Did you know? Multiply before you subtract.
Memory trick: BODMAS.
Correct answer: 1. Any non-zero number raised to the power 0 equals 1, so 1 × 1 × 1 = 1.
Background: a⁰ = 1 for any a ≠ 0.
Did you know? 0⁰ is undefined.
Memory trick: Power zero = 1.
Correct answer: 24. Let C = c and D = d. Then c − 3 = 3(d − 3) and c + 4 = 2(d + 4). Solving gives d = 10 and c = 24.
Background: Check: 3 years ago C = 21 and D = 7 (21 = 3 × 7); in 4 years C = 28 and D = 14 (28 = 2 × 14).
Did you know? Make equations for “ago” and “later” separately.
Memory trick: Write ago and later equations.
Correct answer: 3/2. Factorising gives (2x − 3)(x + 4) = 0, so x = 3/2 or x = −4. Of the options, 3/2 is a solution.
Background: Split the middle term: 2x² + 8x − 3x − 12.
Did you know? The other root, −4, is not in the options.
Memory trick: Product ac = −24; sum = 5.
Correct answer: (4x + 3)². 16x² + 24x + 9 = (4x)² + 2(4x)(3) + 3² = (4x + 3)².
Background: It is a perfect square trinomial of the form a² + 2ab + b².
Did you know? The middle term 24x = 2 × 4x × 3 matches.
Memory trick: a² + 2ab + b² = (a + b)².
Correct answer: 5, −2. Factorising gives (x − 5)(x + 2) = 0, so x = 5 or x = −2.
Background: Find two numbers with product −10 and sum −3: that is −5 and +2.
Did you know? Check: 25 − 15 − 10 = 0.
Memory trick: Product −10, sum −3.
Correct answer: 5, 12, 19, 26. Adding 7 each time gives 5, 12, 19, 26.
Background: In an A.P., each term is the previous term plus the common difference.
Did you know? The terms are a, a + d, a + 2d, a + 3d.
Memory trick: Keep adding 7.
Correct answer: 224. In a proportion, 7 × x = 8 × 196, so x = 1568 ÷ 7 = 224.
Background: In a : b :: c : d, we have a × d = b × c.
Did you know? 196 ÷ 7 = 28, and 8 × 28 = 224.
Memory trick: Cross-multiply.
Correct answer: 39999. 201 × 199 = (200 + 1)(200 − 1) = 200² − 1 = 40000 − 1 = 39999.
Background: Use the identity (a + 1)(a − 1) = a² − 1.
Did you know? It is quicker than long multiplication.
Memory trick: 200² − 1².
Correct answer: 5 m. tan 45° = 1 = 5 ÷ height, so height = 5 m.
Background: At 45°, the triangle is isosceles, so base = height.
Did you know? tan 45° = 1.
Memory trick: 45° → equal sides.
Correct answer: 50. By the remainder theorem, put x = −1: (−1)⁵¹ + 51 = −1 + 51 = 50.
Background: To divide by (x − a), put x = a.
Did you know? (−1) raised to an odd power is −1.
Memory trick: Put x = −1.
Correct answer: 49. Sugar 35 = 5 × 7, so water = 7 × 7 = 49.
Background: Multiply both parts of the ratio by the same number.
Did you know? The multiplier is 35 ÷ 5 = 7.
Memory trick: Same multiplier on both parts.
Correct answer: 31. The differences are 6, 8, 10, 12, 14, so the missing term is 21 + 10 = 31.
Background: If the pattern is not clear, find the differences between terms.
Did you know? Check: 31 + 12 = 43 and 43 + 14 = 57.
Memory trick: Differences go up by 2.
Correct answer: 100√3 cm². Side = 60 ÷ 3 = 20 cm, and area = (√3/4) × 20² = 100√3 cm².
Background: The area of an equilateral triangle is (√3/4) × side².
Did you know? Perimeter = 3 × side.
Memory trick: Area = (√3/4) a².
Correct answer: 49 m². The side is ∛343 = 7 m, so the area of one face = 7² = 49 m².
Background: Volume of a cube = side³.
Did you know? 7 × 7 × 7 = 343.
Memory trick: Cube root, then square.
Correct answer: 64. The pattern alternates ×2 and +3: 2, 4, 7, 14, 17, 34, 37, 74. The last term should be 74, so 64 is incorrect.
Background: Look for alternate operations when the pattern is not simple.
Did you know? 37 × 2 = 74.
Memory trick: ×2, +3, ×2, +3 …
Correct answer: 144. Area of a square = side² = 12 × 12 = 144 cm².
Background: All sides of a square are equal.
Did you know? The perimeter would be 4 × 12 = 48 cm.
Memory trick: Square → side × side.
Correct answer: 6. Radius = diameter ÷ 2 = 12 ÷ 2 = 6 cm.
Background: The diameter is twice the radius.
Did you know? The circumference is 2πr = 12π cm.
Memory trick: Radius = half of diameter.
Correct answer: 10x² + xy + √x. Combine the like terms 3x² + 7x² = 10x². The terms xy and √x stay as they are.
Background: Only like terms (same variables and powers) can be combined.
Did you know? xy and √x are not like terms of x².
Memory trick: 3x² + 7x² = 10x².
Correct answer: Two different roots. The discriminant is b² − 4ac = 25 + 48 = 73, which is positive, so there are two different real roots.
Background: D > 0 gives two different real roots, D = 0 gives equal roots, and D < 0 gives no real roots.
Did you know? 73 is not a perfect square, so the roots are irrational.
Memory trick: D = 73 > 0 → two roots.
Correct answer: x = 4, x = −3/2. Factorise: 2x² − 8x + 3x − 12 = 2x(x − 4) + 3(x − 4) = (2x + 3)(x − 4), so x = 4 or x = −3/2.
Background: Split the middle term −5x into −8x + 3x.
Did you know? Check: 2(16) − 20 − 12 = 0.
Memory trick: Product ac = −24; sum = −5.
Correct answer: x² + 4x + 3 = 0. The equation is x² − (sum)x + (product) = 0, so x² − (−4)x + 3 = x² + 4x + 3 = 0.
Background: For ax² + bx + c = 0, the sum of roots = −b/a and the product = c/a.
Did you know? The roots here are −1 and −3.
Memory trick: x² − (sum)x + product.
Correct answer: 1. A negative one raised to an even power equals 1, and 300 is even.
Background: (−1)ⁿ = 1 if n is even and −1 if n is odd.
Did you know? Pairs of −1 multiply to give +1.
Memory trick: Even power → +1.
Correct answer: m^(1/5) n^(−6/5). Multiply each exponent by 3/5: m has (1/3)(3/5) = 1/5 and n has (−2)(3/5) = −6/5.
Background: The rule is (aᵐ)ⁿ = aᵐⁿ.
Did you know? Multiply the outside power with each exponent inside.
Memory trick: Power outside multiplies inside.
Correct answer: 18. Each term is multiplied by 3: 2, 6, 18, 54, 162, 486. The 4th from the last is 18.
Background: A series where each term is multiplied by the same number is a geometric progression.
Did you know? To count from the end, write all terms first.
Memory trick: × 3 each time.