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: 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.
Correct answer: 7. x + y = 5 + 2 = 7.
Background: Substitute the given values and add.
Did you know? 5 + 2 = 7.
Memory trick: Replace and add.
Correct answer: 4W + 12. Length = W + 6, so the perimeter = 2(W + 6 + W) = 4W + 12.
Background: The perimeter of a rectangle is 2 × (length + width).
Did you know? Name the smaller side W and write the other in terms of W.
Memory trick: 2(2W + 6) = 4W + 12.
Correct answer: 5. The ladder is the hypotenuse: √(3² + 4²) = √25 = 5 m.
Background: Use the Pythagorean theorem: a² + b² = c².
Did you know? 3-4-5 is a common Pythagorean triple.
Memory trick: 3-4-5 triangle.
Correct answer: 12.9. The first 10 primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. Their sum is 129, so the average is 129 ÷ 10 = 12.9.
Background: A prime number has exactly two factors: 1 and itself.
Did you know? 2 is the only even prime number.
Memory trick: Sum 129 ÷ 10 = 12.9.
Correct answer: 0.00006. 3 × 2 = 6, and 0.003 and 0.02 have 3 + 2 = 5 decimal places, so the product is 0.00006.
Background: Multiply the digits as whole numbers, then count the total decimal places.
Did you know? 0.003 has 3 decimal places and 0.02 has 2.
Memory trick: 3 + 2 = 5 decimal places.
Correct answer: 9:7. Girls : Boys = 18 : 14, and dividing both by 2 gives 9 : 7.
Background: Order matters in a ratio: the first-named quantity comes first.
Did you know? Always divide both terms by their HCF.
Memory trick: Girls first, boys second.
Correct answer: 35/2. For direct proportion, x₁/y₁ = x₂/y₂, so 2/5 = 7/y₂ and y₂ = 35/2.
Background: In direct proportion, when one quantity increases, the other increases in the same ratio.
Did you know? The ratio x/y stays constant at 2/5.
Memory trick: x/y = constant.
Correct answer: √2. √2 = 1.41421… never ends or repeats, so it cannot be written as a fraction p/q.
Background: A rational number can be written as p/q with q ≠ 0.
Did you know? √3 and π are other famous irrational numbers.
Memory trick: Can be a fraction → rational.
Correct answer: 15:32. Cross-multiplying gives 4x × 8 = 3y × 5, so 32x = 15y and x : y = 15 : 32.
Background: If a/b = c/d, then a × d = b × c.
Did you know? For a ratio x : y, keep x on one side and y on the other.
Memory trick: 32x = 15y → x : y = 15 : 32.
Correct answer: p = 14000(0.94)^(t/4). A 6% decrease leaves 94% (0.94) every 4 years, and there are t/4 such periods in t years, so p = 14000(0.94)^(t/4).
Background: Exponential decay has the form: final = initial × (decay factor)^(number of periods).
Did you know? Here the decay factor is 1 − 0.06 = 0.94.
Memory trick: Decay factor = 1 − rate.
Correct answer: 2 hour. Their relative speed is 60 + 90 = 150 km/h, so time = 300 ÷ 150 = 2 hours.
Background: When objects move toward each other, their speeds add.
Did you know? If they moved in the same direction, you would subtract the speeds.
Memory trick: Opposite → add speeds.
Correct answer: 29.6% decrease. Volume depends on r² × h: new volume = 0.8² × 1.1 = 0.704 of the old, a 29.6% decrease.
Background: The volume of a cone is V = (1/3)πr²h.
Did you know? A 20% radius decrease cuts the base area by 36%.
Memory trick: Radius is squared: 0.8² = 0.64.
Correct answer: 15. Multiply the top and bottom by 1000: 0.03 ÷ 0.002 = 30 ÷ 2 = 15.
Background: Making both numbers whole removes the decimals.
Did you know? Dividing decimals: move the decimal point the same number of places in both.
Memory trick: Move 3 places: 30 ÷ 2 = 15.
Correct answer: 30000. Paid amount = 120,000 × 25/100 = 30,000.
Background: To find x% of a number, multiply the number by x/100.
Did you know? 25% is the same as one-fourth.
Memory trick: 25% = ¼ → 120,000 ÷ 4.
Correct answer: −3. Total = 5 × 5 = 25. The known numbers add up to 28, so x = 25 − 28 = −3.
Background: Average = sum of numbers ÷ how many numbers.
Did you know? A missing number can be negative.
Memory trick: Missing = (average × count) − known sum.
Correct answer: 13/4. Squaring both sides gives 4x + 3 = 16, so 4x = 13 and x = 13/4.
Background: Squaring removes the square root.
Did you know? Check: 4 × 13/4 + 3 = 16 and √16 = 4.
Memory trick: Square both sides first.