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Mathematics MCQs

MCQs on Algebra, Calculus, Statistics and Geometry

86 Questions
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Prepare Mathematics with confidence

Develop speed and accuracy in arithmetic, algebra, geometry, percentages, ratios and other quantitative concepts.

ArithmeticAlgebraGeometryPercentages and Ratios
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41
Medium css fpsc ppsc nts

What is the discriminant of x² - 5x + 6 = 0?

  • A 1
  • B 4
  • C 5
  • D 6
Permalink
Correct Answer: Option A — 1
Explanation: Discriminant D = b²-4ac = (-5)²-4(1)(6) = 25-24 = 1. Since D > 0 there are two distinct real roots. The discriminant determines nature of roots: D>0 (two real roots) D=0 (one repeated root) D<0 (complex roots). This concept is fundamental in quadratic equations tested across all competitive exam levels.
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42
Medium css fpsc ppsc nts

The slope of a line through points (2 3) and (4 7) is?

  • A 1
  • B 2
  • C 3
  • D 4
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Correct Answer: Option B — 2
Explanation: Slope = (y₂-y₁)/(x₂-x₁) = (7-3)/(4-2) = 4/2 = 2. The slope formula measures the steepness and direction of a line. Positive slope rises left to right. Slope is fundamental in coordinate geometry forming the basis for line equations parallel lines perpendicular lines and linear modeling.
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43
Medium css fpsc ppsc

How many ways can 4 people be arranged in a line?

  • A 16
  • B 24
  • C 32
  • D 48
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Correct Answer: Option B — 24
Explanation: Arrangements of 4 distinct objects in a line = 4! = 4×3×2×1 = 24. Permutations apply when order matters while combinations apply when it does not. This fundamental counting principle appears in probability seating arrangement and scheduling problems throughout competitive exam quantitative aptitude sections.
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44
Medium css fpsc ppsc nts

What is the value of (1/2) raised to the power of negative 2?

  • A 1/4
  • B 1/2
  • C 2
  • D 4
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Correct Answer: Option D — 4
Explanation: (1/2)^(-2) = 2² = 4. A negative exponent means taking the reciprocal: (a/b)^(-n) = (b/a)^n. Negative and fractional exponents frequently appear in competitive exam algebra. Understanding this rule prevents errors and enables simplification of complex exponential expressions in higher-level mathematics questions.
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45
Medium css fpsc ppsc

If P(A)=0.4 and P(B)=0.3 and events are mutually exclusive what is P(A or B)?

  • A 0.12
  • B 0.58
  • C 0.70
  • D 0.82
Permalink
Correct Answer: Option C — 0.70
Explanation: For mutually exclusive events P(A or B) = P(A)+P(B) = 0.4+0.3 = 0.7. Mutually exclusive events cannot occur simultaneously. The addition rule for mutually exclusive events simply adds probabilities. For non-mutually exclusive events we must subtract P(A and B) to avoid double counting.
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46
Medium fpsc ppsc nts

A pipe fills a tank in 6 hours another empties it in 8 hours. Both open: how long to fill?

  • A 24 hours
  • B 20 hours
  • C 18 hours
  • D 16 hours
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Correct Answer: Option A — 24 hours
Explanation: Net fill rate = 1/6 - 1/8 = 4/24 - 3/24 = 1/24 per hour. Time = 24 hours. Pipes and cisterns problems use the same framework as work problems where filling pipes add rates and draining pipes subtract rates. Combining rates correctly is the key skill tested in these extremely common aptitude questions.
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47
Medium fpsc ppsc nts

The product of two numbers is 48 and their HCF is 4. What is their LCM?

  • A 12
  • B 16
  • C 24
  • D 48
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Correct Answer: Option A — 12
Explanation: LCM × HCF = Product of the two numbers. LCM = 48 ÷ 4 = 12. This important formula is frequently tested in competitive exams. It allows rapid calculation of LCM or HCF when the product and one factor are known making it a key shortcut for number theory problems in timed exam conditions.
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48
Medium fpsc ppsc nts

If 5 workers finish a job in 8 days how many days will 10 workers take?

  • A 2 days
  • B 4 days
  • C 6 days
  • D 8 days
Permalink
Correct Answer: Option B — 4 days
Explanation: Total work = 5×8 = 40 worker-days. With 10 workers: days = 40÷10 = 4 days. Work and time problems rely on the inverse relationship between number of workers and time. They are among the most common question types in competitive exams requiring understanding of work rate as a fundamental concept.
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49
Medium fpsc ppsc nts

A man walks 4 km North then 3 km East. How far is he from the start?

  • A 5 km
  • B 6 km
  • C 7 km
  • D 8 km
Permalink
Correct Answer: Option A — 5 km
Explanation: This forms a right triangle with legs 4 and 3. Distance = √(4²+3²) = √(16+9) = √25 = 5 km. The 3-4-5 Pythagorean triple is the most commonly used in competitive exams. The Pythagorean theorem a²+b²=c² is applied in distance navigation construction and coordinate geometry problems.
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50
Medium fpsc ppsc nts

In a right triangle if one angle is 30° what is the other acute angle?

  • A 45°
  • B 50°
  • C 60°
  • D 70°
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Correct Answer: Option C — 60°
Explanation: Sum of angles = 180°. With 90° and 30° the third angle = 180°-90°-30° = 60°. The 30-60-90 triangle has side ratios 1:√3:2 and is one of the most important special triangles in mathematics. It appears extensively in trigonometry geometry and physics problems in all levels of competitive examinations.
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51
Medium css fpsc ppsc

What is the value of log base 10 of 1000?

  • A 2
  • B 3
  • C 4
  • D 5
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Correct Answer: Option B — 3
Explanation: 3! = 3 × 2 × 1 = 6. Factorial of n is the product of all positive integers from 1 to n. Factorials are fundamental in permutations combinations probability calculations and the binomial theorem. Key values to memorize include 0!=1 1!=1 2!=2 3!=6 4!=24 5!=120 and 6!=720 for fast competitive exam solutions.
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52
Medium fpsc ppsc nts

If 3x - 7 = 2x + 5 what is x?

  • A 10
  • B 12
  • C 14
  • D 16
Permalink
Correct Answer: Option B — 12
Explanation: Subtract 2x: x - 7 = 5. Add 7: x = 12. Solving linear equations with variables on both sides is a core algebraic skill. Such equations frequently appear in word problems about ages work rates and number relationships in competitive exams. The key step is collecting like terms on each side methodically.
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53
Medium fpsc ppsc nts

What is the compound interest on Rs 1000 for 2 years at 10% per annum?

  • A Rs 200
  • B Rs 210
  • C Rs 220
  • D Rs 100
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Correct Answer: Option B — Rs 210
Explanation: CI = P(1+r/100)ⁿ - P = 1000(1.1)² - 1000 = 1210 - 1000 = Rs 210. Compound interest exceeds simple interest because interest is earned on previously accumulated interest. CI problems appear in banking and finance sections of competitive exams and require correct application of the compound interest formula.
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54
Medium fpsc ppsc nts

Two numbers are in ratio 5:3 and their sum is 40. What is the larger number?

  • A 20
  • B 25
  • C 30
  • D 35
Permalink
Correct Answer: Option B — 25
Explanation: Let numbers be 5x and 3x. Sum = 8x = 40 so x = 5. Larger = 5×5 = 25. Ratio problems requiring algebraic substitution are consistent in competitive exams. Using a common multiplier x to represent ratio parts then solving with the given total sum or difference is the most reliable standard method.
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55
Medium fpsc ppsc nts

If the simple interest on Rs 1000 for 2 years is Rs 100 what is the rate?

  • A 4%
  • B 5%
  • C 6%
  • D 8%
Permalink
Correct Answer: Option B — 5%
Explanation: SI = (P×R×T)/100 → 100 = (1000×R×2)/100 → 100 = 20R → R = 5%. Simple interest problems are standard in competitive exams. The ability to rearrange the SI formula to find principal rate or time is a key skill. Always identify which variable is unknown and rearrange accordingly before substituting values.
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56
Medium css fpsc ppsc nts

Simplify: (a² - b²) divided by (a - b)

  • A a + b
  • B a - b
  • C a² + b²
  • D ab
Permalink
Correct Answer: Option A — a + b
Explanation: a² - b² factors as (a+b)(a-b) using the difference of squares identity. Dividing by (a-b) cancels that factor leaving (a+b). Recognizing algebraic identities including difference of squares perfect square trinomials and sum or difference of cubes is essential for quickly simplifying expressions in competitive exam algebra sections.
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57
Easy fpsc ppsc nts

What is the value of 3 factorial?

  • A 3
  • B 6
  • C 9
  • D 12
Permalink
Correct Answer: Option B — 6
Explanation: 3! = 3 × 2 × 1 = 6. Factorial of n is the product of all positive integers from 1 to n. Factorials appear in permutations combinations probability and the binomial theorem. Key values to memorize are: 0!=1 1!=1 2!=2 3!=6 4!=24 5!=120 6!=720 for competitive exam speed and accuracy.
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58
Easy css fpsc ppsc nts

What is the expansion of (a + b)²?

  • A a² + b²
  • B a² - b²
  • C a² + 2ab + b²
  • D a² - 2ab + b²
Permalink
Correct Answer: Option C — a² + 2ab + b²
Explanation: (a+b)² = a² + 2ab + b². This is one of the most fundamental algebraic identities alongside (a-b)² = a²-2ab+b² and (a+b)(a-b) = a²-b². These three identities are the foundation of algebra and appear constantly in competitive exam questions. Memorizing and recognizing them is essential for quick problem solving.
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59
Easy fpsc ppsc nts

What is the value of (3² + 4²)?

  • A 5
  • B 25
  • C 7
  • D 49
Permalink
Correct Answer: Option B — 25
Explanation: 3² = 9 and 4² = 16. Sum = 9 + 16 = 25. Notably √25 = 5 illustrating the 3-4-5 Pythagorean triple where 3² + 4² = 5². Recognizing Pythagorean triples such as 3-4-5 and 5-12-13 saves significant calculation time in competitive exam geometry distance and right triangle problems.
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60
Easy fpsc ppsc nts

What is the perimeter of a square with side 9 cm?

  • A 27 cm
  • B 32 cm
  • C 36 cm
  • D 40 cm
Permalink
Correct Answer: Option C — 36 cm
Explanation: Perimeter of square = 4 × side = 4 × 9 = 36 cm. For a square all four sides are equal so perimeter is simply four times the side length. Knowing the relationship between side length perimeter area and diagonal of a square is a basic geometry requirement for all competitive exam mathematics sections.
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