MCQ Maths Questions and Quizzes

MCQ Maths Quiz – Sharpen Your Math Skills with Multiple-Choice Questions

Welcome to our MCQ Maths Quiz, where you can test and improve your math skills through a variety of engaging multiple-choice questions. This quiz is designed for students, learners, and math enthusiasts of all levels, whether you’re preparing for exams or just want to brush up on your problem-solving abilities.

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    Algebra — Class 10 · 50 MCQ Maths Quiz (with step-by-step solutions)

    Click Show solution for each question to see a simple step-by-step explanation on MCQ maths Quiz.

    1. Q1. Solve: x + 3 = 7
      1. 2
      2. 3
      3. 4
      4. 5
      Show solution
      1. Start: x + 3 = 7.
      2. Subtract 3 from both sides: x = 7 − 3.
      3. So x = 4.

      Answer: (c) 4

    2. Q2. Solve: 2x − 5 = 9
      1. 5
      2. 6
      3. 7
      4. 8
      Show solution
      1. 2x − 5 = 9 → add 5 both sides: 2x = 14.
      2. Divide by 2: x = 14 ÷ 2 = 7.

      Answer: (c) 7

    3. Q3. Solve: 3x = 12
      1. 2
      2. 3
      3. 4
      4. 6
      Show solution
      1. 3x = 12 → divide both sides by 3: x = 12 ÷ 3 = 4.

      Answer: (c) 4

    4. Q4. Solve: x / 2 = 6
      1. 8
      2. 10
      3. 12
      4. 14
      Show solution
      1. x/2 = 6 → multiply both sides by 2: x = 6 × 2 = 12.

      Answer: (c) 12

    5. Q5. Solve: 5x + 2 = 17
      1. 1
      2. 2
      3. 3
      4. 4
      Show solution
      1. 5x + 2 = 17 → subtract 2: 5x = 15.
      2. Divide by 5: x = 15 ÷ 5 = 3.

      Answer: (c) 3

    6. Q6. Roots of x² − 4 = 0 are:
      1. 2
      2. −2
      3. ±2
      4. 0
      Show solution
      1. x² − 4 = 0 → x² = 4.
      2. Take square root: x = ±√4 = ±2.

      Answer: (c) ±2

    7. Q7. Expand: (x − 1)(x + 1) = ?
      1. x² + 1
      2. x² − 1
      3. x² − 2x
      4. x² + 2
      Show solution
      1. Multiply: (x − 1)(x + 1) = x² + x − x − 1 = x² − 1.

      Answer: (b) x² − 1

    8. Q8. If x² = 25, then x = ?
      1. 5
      2. −5
      3. ±5
      4. 0
      Show solution
      1. x² = 25 → x = ±√25 = ±5.

      Answer: (c) ±5

    9. Q9. Expand: (x + y)² = ?
      1. x² + y²
      2. x² + 2xy + y²
      3. x² − y²
      4. x² − 2xy + y²
      Show solution
      1. (x + y)² = (x + y)(x + y) = x² + xy + yx + y² = x² + 2xy + y².

      Answer: (b) x² + 2xy + y²

    10. Q10. If (x + 2)(x + 3) = 0, then x = ?
      1. −2 only
      2. −3 only
      3. −2 or −3
      4. 2 or 3
      Show solution
      1. Product zero → at least one factor is 0: x + 2 = 0 or x + 3 = 0.
      2. So x = −2 or x = −3.

      Answer: (c) −2 or −3

    11. Q11. Factorize: x² + 5x + 6
      1. (x + 1)(x + 6)
      2. (x + 2)(x + 3)
      3. (x − 2)(x − 3)
      4. (x + 3)(x − 2)
      Show solution
      1. Find two numbers multiply 6 and add 5 → 2 and 3.
      2. So factorization: (x + 2)(x + 3).

      Answer: (b) (x + 2)(x + 3)

    12. Q12. Solve: x² − 5x + 6 = 0
      1. 1 & 6
      2. 2 & 3
      3. −2 & −3
      4. −2 & 3
      Show solution
      1. Factor: x² − 5x + 6 = (x − 2)(x − 3) = 0.
      2. So x = 2 or x = 3.

      Answer: (b) 2 & 3

    13. Q13. Solve: 2x² − 8 = 0
      1. 2
      2. −2
      3. ±2
      4. 0
      Show solution
      1. 2x² − 8 = 0 → 2x² = 8 → x² = 4.
      2. x = ±2.

      Answer: (c) ±2

    14. Q14. Simplify: (x² − y²) / (x − y) (x ≠ y) = ?
      1. x + y
      2. x − y
      3. xy
      4. x² − y²
      Show solution
      1. Use identity x² − y² = (x − y)(x + y).
      2. Divide by (x − y) → result x + y.

      Answer: (a) x + y

    15. Q15. Solve: 3(x − 2) = 9
      1. 4
      2. 5
      3. 6
      4. 7
      Show solution
      1. 3(x − 2) = 9 → divide both sides by 3: x − 2 = 3.
      2. So x = 3 + 2 = 5.

      Answer: (b) 5

    16. Q16. Solve: 4x + 7 = 3x + 12
      1. 2
      2. 3
      3. 4
      4. 5
      Show solution
      1. 4x + 7 = 3x + 12 → subtract 3x: x + 7 = 12.
      2. x = 12 − 7 = 5.

      Answer: (d) 5

    17. Q17. Solve: x / 3 + 2 = 7
      1. 12
      2. 15
      3. 18
      4. 21
      Show solution
      1. x/3 + 2 = 7 → subtract 2: x/3 = 5.
      2. Multiply by 3: x = 15.

      Answer: (b) 15

    18. Q18. Evaluate at x = 2: 3x² + x − 4 = ?
      1. 8
      2. 9
      3. 10
      4. 11
      Show solution
      1. Compute x² = 4 → 3×4 = 12.
      2. Then 12 + x − 4 = 12 + 2 − 4 = 10.

      Answer: (c) 10

    19. Q19. If f(x) = 2x + 1, find f(3).
      1. 5
      2. 6
      3. 7
      4. 8
      Show solution
      1. f(3) = 2×3 + 1 = 6 + 1 = 7.

      Answer: (c) 7

    20. Q20. Sum of roots of x² − 7x + 10 = 0 is:
      1. 10
      2. 7
      3. −7
      4. −10
      Show solution
      1. For ax² + bx + c, sum = −b/a. Here a = 1, b = −7 → sum = −(−7)/1 = 7.

      Answer: (b) 7

    21. Q21. Product of roots of x² − 7x + 10 = 0 is:
      1. 7
      2. 10
      3. −10
      4. 1
      Show solution
      1. Product = c/a = 10/1 = 10.

      Answer: (b) 10

    22. Q22. Solve: x² + 4x + 4 = 0
      1. −2
      2. 2
      3. ±2
      4. No real root
      Show solution
      1. x² +4x +4 = (x + 2)² = 0 → x + 2 = 0.
      2. So x = −2 (double root).

      Answer: (a) −2

    23. Q23. Factorize: x² − 9
      1. (x − 9)
      2. (x − 3)(x + 3)
      3. (x + 9)
      4. (x − 1)(x + 9)
      Show solution
      1. x² − 9 = (x − 3)(x + 3) (difference of squares).

      Answer: (b) (x − 3)(x + 3)

    24. Q24. If a² − b² = 15 and a − b = 3, then a + b = ?
      1. 3
      2. 5
      3. 15
      4. 45
      Show solution
      1. a² − b² = (a − b)(a + b) = 15.
      2. Given a − b = 3 → (3)(a + b) = 15 → a + b = 15 ÷ 3 = 5.

      Answer: (b) 5

    25. Q25. Simplify: (2x³) / x (x ≠ 0) = ?
      1. 2x²
      2. x²
      3. 2x³
      4. x
      Show solution
      1. Divide powers: x³ / x = x^(3−1) = x². Multiply by 2 → 2x².

      Answer: (a) 2x²

    26. Q26. Solve: 2(x − 1) = x + 3
      1. 3
      2. 4
      3. 5
      4. 6
      Show solution
      1. 2x − 2 = x + 3 → subtract x: x − 2 = 3.
      2. x = 5.

      Answer: (c) 5

    27. Q27. Solve: x² − x − 6 = 0
      1. 3 & −2
      2. 2 & −3
      3. −3 & 2
      4. None
      Show solution
      1. Factor: (x − 3)(x + 2) = 0 → x = 3 or x = −2.

      Answer: (a) 3 & −2

    28. Q28. Solve: 5x − 2 = 3(x + 4)
      1. 5
      2. 6
      3. 7
      4. 8
      Show solution
      1. 5x − 2 = 3x + 12 → subtract 3x: 2x − 2 = 12.
      2. 2x = 14 → x = 7.

      Answer: (c) 7

    29. Q29. Simplify: (x² + 2x) / x (x ≠ 0) = ?
      1. x
      2. x + 2
      3. x² + 2x
      4. 2x
      Show solution
      1. Split: (x² + 2x)/x = x²/x + 2x/x = x + 2.

      Answer: (b) x + 2

    30. Q30. Expand: (x + 1)² = ?
      1. x² + 2x + 1
      2. x² − 2x + 1
      3. x² + 1
      4. x² + 2
      Show solution
      1. (x + 1)² = x² + 2x + 1 (standard formula).

      Answer: (a) x² + 2x + 1

    31. Q31. For AP with a₁ = 2 and d = 3, the 5th term = ?
      1. 11
      2. 12
      3. 14
      4. 16
      Show solution
      1. nth term: aₙ = a₁ + (n − 1)d. For n = 5 → a₅ = 2 + 4×3 = 2 + 12 = 14.

      Answer: (c) 14

    32. Q32. Solve: |x| = 3 → x = ?
      1. 3
      2. −3
      3. ±3
      4. 0
      Show solution
      1. |x| = 3 means distance from 0 is 3 → x = 3 or x = −3.

      Answer: (c) ±3

    33. Q33. Solve: x² − 16 = 0
      1. 4
      2. −4
      3. ±4
      4. 0
      Show solution
      1. x² = 16 → x = ±4.

      Answer: (c) ±4

    34. Q34. Solve: 2x² + 3x − 2 = 0
      1. ½ and −2
      2. −½ and 2
      3. 1 and −2
      4. None
      Show solution
      1. Use formula or factor: Discriminant Δ = 3² − 4×2×(−2) = 9 + 16 = 25.
      2. x = [−3 ± √25] / (2×2) = [−3 ± 5]/4 → x₁ = (2)/4 = 1/2, x₂ = (−8)/4 = −2.

      Answer: (a) ½ and −2

    35. Q35. Expand: (x − 2)² = ?
      1. x² − 4x + 4
      2. x² + 4x + 4
      3. x² − 2x + 4
      4. x² + 2x + 4
      Show solution
      1. (x − 2)² = x² − 4x + 4 (use formula).

      Answer: (a) x² − 4x + 4

    36. Q36. Simplify: (x³ − y³) / (x − y) (x ≠ y) = ?
      1. x² − xy + y²
      2. x² + xy + y²
      3. (x + y)²
      4. None
      Show solution
      1. Use identity x³ − y³ = (x − y)(x² + xy + y²).
      2. Divide by (x − y) → x² + xy + y².

      Answer: (b) x² + xy + y²

    37. Q37. Solve: x² + x = 6
      1. 2 and −3
      2. −2 and 3
      3. 1 and −6
      4. None
      Show solution
      1. Bring all terms: x² + x − 6 = 0 → factor (x + 3)(x − 2) = 0.
      2. So x = 2 or x = −3.

      Answer: (a) 2 and −3

    38. Q38. Solve: 3x² − 12x + 12 = 0
      1. 2
      2. −2
      3. ±2
      4. None
      Show solution
      1. Divide by 3: x² − 4x + 4 = 0 → (x − 2)² = 0.
      2. So x = 2 (double root).

      Answer: (a) 2

    39. Q39. Factorize: 4x² − 9
      1. (2x − 3)(2x + 3)
      2. (4x − 9)
      3. (2x − 9)(2x + 1)
      4. (x − 3)(4x + 3)
      Show solution
      1. 4x² − 9 = (2x)² − 3² → difference of squares = (2x − 3)(2x + 3).

      Answer: (a) (2x − 3)(2x + 3)

    40. Q40. If x + y = 10 and xy = 21, find x² + y².
      1. 58
      2. 50
      3. 42
      4. 100
      Show solution
      1. (x + y)² = x² + 2xy + y². So x² + y² = (x + y)² − 2xy.
      2. (x + y)² = 10² = 100. Then x² + y² = 100 − 2×21 = 100 − 42 = 58.

      Answer: (a) 58

    41. Q41. Expand: (2x + 3)² = ?
      1. 4x² + 12x + 9
      2. 4x² + 6x + 9
      3. 2x² + 9
      4. None
      Show solution
      1. (2x + 3)² = (2x)² + 2·2x·3 + 3² = 4x² + 12x + 9.

      Answer: (a) 4x² + 12x + 9

    42. Q42. Solve: 3(x + 1) = 2(2x + 5)
      1. −7
      2. 7
      3. −3
      4. 3
      Show solution
      1. 3x + 3 = 4x + 10 → subtract 3x: 3 = x + 10 → x = 3 − 10 = −7.

      Answer: (a) −7

    43. Q43. Solve: x² + 2x = 0
      1. 0 and −2
      2. 0 only
      3. −2 only
      4. None
      Show solution
      1. x² + 2x = x(x + 2) = 0 → x = 0 or x + 2 = 0 → x = −2.

      Answer: (a) 0 and −2

    44. Q44. For x² − kx + 16 = 0 to have equal roots, k = ?
      1. 8
      2. −8
      3. ±8
      4. 0
      Show solution
      1. Equal roots → discriminant Δ = b² − 4ac = k² − 4×1×16 = k² − 64 = 0.
      2. So k² = 64 → k = ±8.

      Answer: (c) ±8

    45. Q45. Remainder when x³ − 2x² + x − 2 is divided by (x − 1) = ?
      1. −2
      2. 2
      3. 0
      4. 1
      Show solution
      1. Remainder theorem: remainder = P(1).
      2. P(1) = 1 − 2 + 1 − 2 = −2.

      Answer: (a) −2

    46. Q46. If x + y = 5 and x − y = 3, find x.
      1. 4
      2. 3
      3. 1
      4. 2
      Show solution
      1. Add equations: (x + y) + (x − y) = 5 + 3 → 2x = 8 → x = 4.

      Answer: (a) 4

    47. Q47. Expand: (x + y)³ = ?
      1. x³ + 3x²y + 3xy² + y³
      2. x³ + y³
      3. (x + y)²
      4. None
      Show solution
      1. Use binomial formula: (x + y)³ = x³ + 3x²y + 3xy² + y³.

      Answer: (a) x³ + 3x²y + 3xy² + y³

    48. Q48. Solve: x² − 6x + 9 = 0
      1. 3
      2. −3
      3. ±3
      4. None
      Show solution
      1. x² − 6x + 9 = (x − 3)² = 0 → x = 3.

      Answer: (a) 3

    49. Q49. Solve: 7x + 5 = 3(2x + 1)
      1. −2
      2. 2
      3. −1
      4. 1
      Show solution
      1. 7x + 5 = 6x + 3 → subtract 6x: x + 5 = 3 → x = 3 − 5 = −2.

      Answer: (a) −2

    50. Q50. Solve: x/4 + x/2 = 30
      1. 20
      2. 30
      3. 40
      4. 60
      Show solution
      1. x/4 + x/2 = 30. Convert x/2 = 2x/4 → so (x + 2x)/4 = 30 → 3x/4 = 30.
      2. Multiply both sides by 4: 3x = 120 → x = 120 ÷ 3 = 40.

      Answer: (c) 40

    Tip: practice the steps slowly — isolate x, simplify step-by-step, and check your answer by substituting back.MCQ Maths Quiz

    50 Trigonometry MCQs — with step-by-step solutions (kid-friendly)

    How to use: For each question, read the choices (a–d). Click Show solution to see simple steps and the final answer. I explain like you’re learning from scratch.

    1. Q1. What is sin 30°?
      • a) 1/2
      • b) √3/2
      • c) √2/2
      • d) 1
      Show solution
      1. Remember the special angles: sin 30° = 1/2.
      2. Final answer: a) 1/2.
    2. Q2. What is cos 60°?
      • a) 1/2
      • b) √3/2
      • c) -1/2
      • d) √2/2
      Show solution
      1. From special angles: cos 60° = 1/2.
      2. Final answer: a) 1/2.
    3. Q3. What is tan 45°?
      • a) 0
      • b) 1
      • c) √3
      • d) -1
      Show solution
      1. tan θ = sin θ / cos θ. For 45°, both sin and cos = √2/2, so tan = (√2/2)/(√2/2) = 1.
      2. Final answer: b) 1.
    4. Q4. What is sin 45°?
      • a) 1/2
      • b) √3/2
      • c) √2/2
      • d) 1
      Show solution
      1. Special angle: sin 45° = √2/2.
      2. Final answer: c) √2/2.
    5. Q5. What is cos 30°?
      • a) 1/2
      • b) √2/2
      • c) √3/2
      • d) 0
      Show solution
      1. Special angle: cos 30° = √3/2.
      2. Final answer: c) √3/2.
    6. Q6. What is csc 30°? (csc = 1/sin)
      • a) 2
      • b) 1/2
      • c) √2
      • d) √3
      Show solution
      1. sin 30° = 1/2. So csc 30° = 1 / (1/2) = 2.
      2. Final answer: a) 2.
    7. Q7. What is sec 60°? (sec = 1/cos)
      • a) 1
      • b) 2
      • c) √3
      • d) 1/2
      Show solution
      1. cos 60° = 1/2. So sec 60° = 1 / (1/2) = 2.
      2. Final answer: b) 2.
    8. Q8. What is cot 45°? (cot = 1/tan)
      • a) 0
      • b) 1
      • c) -1
      • d) undefined
      Show solution
      1. tan 45° = 1. So cot 45° = 1 / 1 = 1.
      2. Final answer: b) 1.
    9. Q9. What is tan 30°?
      • a) √3
      • b) √2/2
      • c) √3/3
      • d) 1
      Show solution
      1. tan 30° = 1/√3 = √3/3 (we rationalize denominator: 1/√3 × √3/√3 = √3/3).
      2. Final answer: c) √3/3.
    10. Q10. What is sin 90°?
      • a) 0
      • b) 1
      • c) -1
      • d) undefined
      Show solution
      1. Special angle: sin 90° = 1.
      2. Final answer: b) 1.
    11. Q11. If sin θ = 3/5 and θ is in quadrant I, what is cos θ?
      • a) 4/5
      • b) -4/5
      • c) 3/5
      • d) -3/5
      Show solution
      1. Use identity sin²θ + cos²θ = 1.
      2. Compute cos²θ = 1 - sin²θ = 1 - (3/5)² = 1 - 9/25 = 16/25.
      3. So cos θ = ±√(16/25) = ±4/5. In quadrant I, cos is positive → 4/5.
      4. Final answer: a) 4/5.
    12. Q12. If cos θ = -√3/2, and 0° ≤ θ < 360°, which θ is correct?
      • a) 30°
      • b) 150°
      • c) 210°
      • d) 330°
      Show solution
      1. cos(30°) = √3/2 (positive). We need negative √3/2 → cos is negative in quadrant II and III.
      2. cos 150° = cos(180° – 30°) = -cos 30° = -√3/2. So θ = 150° fits.
      3. Final answer: b) 150°.
    13. Q13. Solve tan θ = -1 for 0° ≤ θ < 360°.
      • a) 45° and 225°
      • b) 135° and 315°
      • c) 90° and 270°
      • d) 0° and 180°
      Show solution
      1. tan 45° = 1. We want -1. Tangent is negative in quadrants II and IV.
      2. Angles with magnitude 45° in QII and QIV are 180° – 45° = 135° and 360° – 45° = 315°.
      3. Final answer: b) 135° and 315°.
    14. Q14. What is sin(π/6)?
      • a) 1/3
      • b) 1/2
      • c) √3/2
      • d) √2/2
      Show solution
      1. π/6 = 30°. So sin(π/6) = sin 30° = 1/2.
      2. Final answer: b) 1/2.
    15. Q15. What is cos(π/4)?
      • a) √3/2
      • b) √2/2
      • c) 1/2
      • d) 1
      Show solution
      1. π/4 = 45°, and cos 45° = √2/2.
      2. Final answer: b) √2/2.
    16. Q16. Evaluate sin 75° exactly.
      • a) (√6 + √2)/4
      • b) (√6 – √2)/4
      • c) √3/2
      • d) 1/2
      Show solution
      1. Use sum formula: sin(45°+30°) = sin45 cos30 + cos45 sin30.
      2. Compute: sin45 = √2/2, cos30 = √3/2, cos45 = √2/2, sin30 = 1/2.
      3. So sin75 = (√2/2)(√3/2) + (√2/2)(1/2) = √2/2 * ( (√3/2) + (1/2) ) = √2/2 * ( (√3+1)/2 ) = (√2(√3+1))/4.
      4. Rewrite: (√6 + √2)/4.
      5. Final answer: a) (√6 + √2)/4.
    17. Q17. Evaluate cos 15° exactly.
      • a) (√6 – √2)/4
      • b) (√6 + √2)/4
      • c) √3/2
      • d) 1/2
      Show solution
      1. Use formula: cos(45° - 30°) = cos45 cos30 + sin45 sin30.
      2. Plug values: (√2/2)(√3/2) + (√2/2)(1/2) = (√6 + √2)/4.
      3. Final answer: b) (√6 + √2)/4.
    18. Q18. What is tan 15° simplified?
      • a) √3 – 1
      • b) 2 – √3
      • c) √3/3
      • d) 1/2
      Show solution
      1. Use difference formula: tan(45°-30°) = (tan45 - tan30)/(1 + tan45 tan30).
      2. tan45=1, tan30=1/√3. So numerator = 1 - 1/√3, denominator = 1 + 1/√3.
      3. Multiply numerator and denominator by √3: numerator = √3 - 1, denominator = √3 + 1.
      4. So tan15 = (√3 - 1)/(√3 + 1). Rationalize by multiplying top and bottom by (√3 – 1):
      5. ((√3 - 1)²)/((√3 + 1)(√3 - 1)) = (3 - 2√3 +1)/(3 -1) = (4 - 2√3)/2 = 2 - √3.
      6. Final answer: b) 2 – √3.
    19. Q19. If sin θ = 3/5 and cos θ = 4/5, what is sin 2θ?
      • a) 7/25
      • b) 24/25
      • c) 6/25
      • d) 1
      Show solution
      1. Formula: sin 2θ = 2 sin θ cos θ.
      2. Compute: 2 × (3/5) × (4/5) = 2 × 12 /25 = 24/25.
      3. Final answer: b) 24/25.
    20. Q20. If sin θ = 3/5 and cos θ = 4/5, what is cos 2θ?
      • a) 7/25
      • b) -7/25
      • c) 24/25
      • d) 1
      Show solution
      1. Formula: cos 2θ = cos²θ - sin²θ.
      2. Compute: cos²θ = (4/5)² = 16/25, sin²θ = (3/5)² = 9/25.
      3. So cos 2θ = 16/25 - 9/25 = 7/25.
      4. Final answer: a) 7/25.
    21. Q21. Solve sin x = 1/2 for 0° ≤ x < 360°.
      • a) 30° only
      • b) 150° only
      • c) 30° and 150°
      • d) 210° and 330°
      Show solution
      1. sin x = 1/2 at reference angle 30°. Sine positive in QI and QII → x = 30°, 180° – 30° = 150°.
      2. Final answer: c) 30° and 150°.
    22. Q22. Solve cos x = -1 for 0° ≤ x < 360°.
      • a) 0°
      • b) 90°
      • c) 180°
      • d) 360°
      Show solution
      1. cos x = -1 at x = 180° (unit circle leftmost point).
      2. Final answer: c) 180°.
    23. Q23. Solve tan x = √3 for 0° ≤ x < 360°.
      • a) 60° and 240°
      • b) 30° and 210°
      • c) 120° and 300°
      • d) 150° and 330°
      Show solution
      1. tan 60° = √3. Tan has period 180°, so x = 60° + k·180° gives 60° and 240° in [0,360).
      2. Final answer: a) 60° and 240°.
    24. Q24. What is the value of sec²θ - tan²θ in terms of constants?
      • a) 0
      • b) 1
      • c) sec θ
      • d) tan θ
      Show solution
      1. Identity: 1 + tan²θ = sec²θ. Rearranged → sec²θ - tan²θ = 1.
      2. Final answer: b) 1.
    25. Q25. If sin θ = -√2/2, what are possible θ in [0°,360°)?
      • a) 45° and 135°
      • b) 225° and 315°
      • c) 135° and 225°
      • d) 30° and 330°
      Show solution
      1. sin = -√2/2 has reference angle 45°. Negative in QIII and QIV → angles 180° + 45° = 225°, and 360° – 45° = 315°.
      2. Final answer: b) 225° and 315°.
    26. Q26. What is arcsin(1) in degrees?
      • a) 0°
      • b) 45°
      • c) 90°
      • d) 180°
      Show solution
      1. sin 90° = 1, and arcsin returns principal value 90° (or π/2 radians).
      2. Final answer: c) 90°.
    27. Q27. What is arccos(0) in degrees?
      • a) 0°
      • b) 45°
      • c) 90°
      • d) 180°
      Show solution
      1. cos 90° = 0, so arccos(0) = 90° (principal value).
      2. Final answer: c) 90°.
    28. Q28. What is arctan(1/√3) in degrees?
      • a) 15°
      • b) 30°
      • c) 45°
      • d) 60°
      Show solution
      1. tan 30° = 1/√3, so arctan(1/√3) = 30°.
      2. Final answer: b) 30°.
    29. Q29. Convert 150° to radians.
      • a) 5π/6
      • b) 2π/3
      • c) π/3
      • d) 3π/4
      Show solution
      1. Radians = degrees × π/180 → 150 × π/180 = 15/18 π = 5/6 π.
      2. Final answer: a) 5π/6.
    30. Q30. Convert π/3 to degrees.
      • a) 30°
      • b) 45°
      • c) 60°
      • d) 90°
      Show solution
      1. Degrees = radians × 180/π → (π/3) × 180/π = 60°.
      2. Final answer: c) 60°.
    31. Q31. Solve 2 sin² x - 1 = 0 for 0° ≤ x < 360°.
      • a) 0°, 180°
      • b) 45°, 135°, 225°, 315°
      • c) 30°, 150°
      • d) 90°, 270°
      Show solution
      1. Equation → sin² x = 1/2. So |sin x| = 1/√2.
      2. Reference angle = 45°. Values where sin = ±1/√2 are x = 45°, 135°, 225°, 315°.
      3. Final answer: b) 45°, 135°, 225°, 315°.
    32. Q32. What is cos 210°?
      • a) √3/2
      • b) -√3/2
      • c) -1/2
      • d) 1/2
      Show solution
      1. 210° = 180° + 30°. cos(180° + α) = -cos α. So cos 210° = -cos30° = -√3/2.
      2. Final answer: b) -√3/2.
    33. Q33. What is sin(-30°)?
      • a) 1/2
      • b) -1/2
      • c) √3/2
      • d) -√3/2
      Show solution
      1. sin is odd: sin(-θ) = -sin θ. sin 30° = 1/2 → sin(-30°) = -1/2.
      2. Final answer: b) -1/2.
    34. Q34. What is tan 225°?
      • a) -1
      • b) 0
      • c) 1
      • d) undefined
      Show solution
      1. 225° = 180° + 45°. tan(180° + θ) = tan θ. So tan 225° = tan 45° = 1.
      2. Final answer: c) 1.
    35. Q35. If sin θ = -4/5 and θ is in quadrant III, what is cos θ?
      • a) 3/5
      • b) -3/5
      • c) 4/5
      • d) -4/5
      Show solution
      1. Use sin² + cos² = 1. sin² = (−4/5)² = 16/25. So cos² = 1 – 16/25 = 9/25 → cos = ±3/5.
      2. In quadrant III, cosine is negative → -3/5.
      3. Final answer: b) -3/5.
    36. Q36. Which identity is always true?
      • a) 1 + tan²θ = sec²θ
      • b) 1 + sin²θ = cos²θ
      • c) tan θ = cos θ / sin θ
      • d) sec θ = sin θ
      Show solution
      1. Known Pythagorean identity is 1 + tan²θ = sec²θ. Other options are false or reversed.
      2. Final answer: a) 1 + tan²θ = sec²θ.
    37. Q37. Evaluate sin 15° exactly.
      • a) (√6 + √2)/4
      • b) (√6 – √2)/4
      • c) √3/2
      • d) 1/2
      Show solution
      1. Use sin(45° - 30°) = sin45 cos30 - cos45 sin30.
      2. Compute: (√2/2)(√3/2) - (√2/2)(1/2) = √2/2 * ( (√3/2) - (1/2) ) = (√6 - √2)/4.
      3. Final answer: b) (√6 – √2)/4.
    38. Q38. What is cos 120°?
      • a) 1/2
      • b) -1/2
      • c) -√3/2
      • d) √3/2
      Show solution
      1. 120° = 180° – 60°. cos(180° – α) = -cos α → cos120° = -cos 60° = -1/2.
      2. Final answer: b) -1/2.
    39. Q39. What is sec 45°?
      • a) 1
      • b) √2
      • c) 2
      • d) √3
      Show solution
      1. sec = 1/cos. cos45° = √2/2 → sec45° = 1 / (√2/2) = 2/√2 = √2.
      2. Final answer: b) √2.
    40. Q40. What is csc 225°?
      • a) √2
      • b) -√2
      • c) 1/2
      • d) -1/2
      Show solution
      1. 225° = 180° + 45°. sin225° = -sin45° = -√2/2.
      2. csc = 1/sin → csc225° = 1 / (-√2/2) = -2/√2 = -√2.
      3. Final answer: b) -√2.
    41. Q41. In a right triangle, angle A = 30°, hypotenuse = 10. What is the length of the side opposite angle A?
      • a) 5
      • b) 10√3/2
      • c) 10/2
      • d) both a) and c)
      Show solution
      1. Opposite = hypotenuse × sin 30° = 10 × 1/2 = 5.
      2. Options a) and c) are same number; final answer: d) both a) and c) (but simplest: 5).
    42. Q42. In a right triangle, angle B = 60°, adjacent side to B = 8. What is the hypotenuse?
      • a) 8
      • b) 16
      • c) 8/2
      • d) 4
      Show solution
      1. cos 60° = 1/2 = adjacent/hypotenuse → hypotenuse = adjacent / cos60° = 8 / (1/2) = 16.
      2. Final answer: b) 16.
    43. Q43. In a right triangle, opposite = 3 and hypotenuse = 5. What is cos θ (θ is the angle opposite the 3)?
      • a) 3/5
      • b) 4/5
      • c) 5/3
      • d) 1/2
      Show solution
      1. Use Pythagoras: adjacent side = √(hyp² – opp²) = √(25 – 9) = √16 = 4.
      2. cos θ = adjacent/hypotenuse = 4/5.
      3. Final answer: b) 4/5.
    44. Q44. What is sin(90° - θ) equal to?
      • a) sin θ
      • b) cos θ
      • c) -sin θ
      • d) -cos θ
      Show solution
      1. Co-function identity: sin(90° - θ) = cos θ.
      2. Final answer: b) cos θ.
    45. Q45. What is the period (in degrees) of the function sin x?
      • a) 90°
      • b) 180°
      • c) 360°
      • d) 720°
      Show solution
      1. The sine function repeats every 360° (or 2π radians).
      2. Final answer: c) 360°.
    46. Q46. What is sin(2π/3)?
      • a) √3/2
      • b) -√3/2
      • c) 1/2
      • d) -1/2
      Show solution
      1. 2π/3 = 120°. sin 120° = sin(180° – 60°) = sin 60° = √3/2.
      2. Final answer: a) √3/2.
    47. Q47. What is cos(3π/4)?
      • a) √2/2
      • b) -√2/2
      • c) 0
      • d) -1
      Show solution
      1. 3π/4 = 135°. cos 135° = -cos 45° = -√2/2.
      2. Final answer: b) -√2/2.
    48. Q48. Simplify sin² x - cos² x in terms of double angle.
      • a) cos 2x
      • b) -cos 2x
      • c) sin 2x
      • d) -sin 2x
      Show solution
      1. We know cos 2x = cos² x - sin² x. So sin² x - cos² x = - (cos² x - sin² x) = -cos 2x.
      2. Final answer: b) -cos 2x.
    49. Q49. If tan θ = 3/4 and θ in quadrant I, what is sin θ?
      • a) 3/5
      • b) 4/5
      • c) 5/3
      • d) 3/4
      Show solution
      1. Think right triangle: tan = opp/adj = 3/4. Hypotenuse = √(3² + 4²) = √(9 + 16) = √25 = 5.
      2. So sin θ = opp/hyp = 3/5.
      3. Final answer: a) 3/5.
    50. Q50. Solve sin x = 0 for 0° ≤ x < 360°.
      • a) 0° and 180°
      • b) 90° and 270°
      • c) 45°, 135°, 225°, 315°
      • d) 30° and 150°
      Show solution
      1. sin x = 0 at x = 0°, 180°, 360°… For 0° ≤ x < 360°, the solutions are 0° and 180°.
      2. Final answer: a) 0° and 180°.

    ✅ Tips if you’re learning:

    • Memorize key values for 0°, 30°, 45°, 60°, 90° (sin, cos, tan).
    • Remember identities: sin²x + cos²x = 1, 1 + tan²x = sec²x, double-angle and sum formulas.
    • For solving equations, find reference angle then pick the correct quadrant based on sign.

    Number Theory

    Number theory focuses on properties and relationships of integers, including prime numbers, divisibility, and modular arithmetic.

    🧠 10 Essential MCQs on Elementary Number Theory

    Test your understanding of number theory concepts with these carefully selected questions.

    1. What is the smallest prime number?

    Options: A) 0 B) 1 C) 2 D) 3

    Answer: C) 2

    Explanation: The number 2 is the smallest prime number, as it is divisible only by 1 and itself. It’s also the only even prime number.

    2. Which of the following numbers is divisible by 3?

    Options: A) 123 B) 124 C) 125 D) 126

    Answer: A) 123

    Explanation: A number is divisible by 3 if the sum of its digits is divisible by 3. For 123, 1 + 2 + 3 = 6, which is divisible by 3.

    3. What is the greatest common divisor (GCD) of 56 and 98?

    Options: A) 14 B) 28 C) 7 D) 49

    Answer: A) 14

    Explanation: The prime factorizations are 56 = 2³ × 7 and 98 = 2 × 7². The GCD is the product of the lowest powers of common prime factors: 2¹ × 7¹ = 14.

    4. Which number is a perfect square?

    Options: A) 50 B) 64 C) 75 D) 80

    Answer: B) 64

    Explanation: A perfect square is an integer that is the square of another integer. 64 = 8², so it is a perfect square.

    5. What is the least common multiple (LCM) of 15 and 20?

    Options: A) 30 B) 60 C) 75 D) 90

    Answer: B) 60

    Explanation: The LCM is found by taking the highest powers of all prime factors. 15 = 3 × 5 and 20 = 2² × 5. LCM = 2² × 3 × 5 = 60.

    6. Which of the following is a prime number?

    Options: A) 49 B) 51 C) 53 D) 55

    Answer: C) 53

    Explanation: 53 is divisible only by 1 and itself, making it a prime number.

    7. What is the remainder when 12345 is divided by 9?

    Options: A) 0 B) 1 C) 2 D) 3

    Answer: A) 0

    Explanation: A number is divisible by 9 if the sum of its digits is divisible by 9. 1 + 2 + 3 + 4 + 5 = 15, and 15 ÷ 9 leaves a remainder of 6. Therefore, the remainder is 6.

    8. Which of the following numbers is a perfect cube?

    Options: A) 27 B) 64 C) 125 D) 216

    Answer: D) 216

    Explanation: A perfect cube is an integer that is the cube of another integer. 216 = 6³, so it is a perfect cube.

    9. What is the greatest common divisor (GCD) of 81 and 243?

    Options: A) 27 B) 54 C) 81 D) 243

    Answer: C) 81

    Explanation: The prime factorizations are 81 = 3⁴ and 243 = 3⁵. The GCD is the product of the lowest powers of common prime factors: 3⁴ = 81.

    10. Which number is a perfect square and a perfect cube?

    Options: A) 16 B) 64 C) 81 D) 100

    Answer: B) 64

    Explanation: 64 = 8² = 4³, so it is both a perfect square and a perfect cube.

    For more MCQs on Elementary Number Theory, visit Ground Mint’s Number Theory Section.

    Geometry

    Geometry MCQs with Shapes

    1. How many sides does this shape have?

    This is a triangle. It has 3 sides.

    2. What is the shape below?

    It is a circle. Circles have no sides or corners.

    3. Find the perimeter of this square (side = 5 cm).

    Perimeter = 4 × side = 20 cm.

    4. What is the sum of angles in a triangle?

    Sum of triangle’s angles = 180°.

    5. Identify this 5-sided figure.

    This has 5 sides → Pentagon.

    6. How many diagonals does a square have?

    A square has 2 diagonals.

    7. Find the area of a rectangle (length=8 cm, width=5 cm).

    Area = l × w = 8 × 5 = 40 cm².

    8. What is the radius if circle’s diameter = 10 cm?

    Radius = diameter ÷ 2 = 5 cm.

    9. A hexagon has how many sides?

    A hexagon has 6 sides.

    10. The sum of angles of a quadrilateral is?

    Sum of interior angles = 360°.

    More MCQ Maths questions with answers

    11. Find the perimeter of rectangle (l=10, w=6).

    Perimeter = 2(l+w) = 2(10+6) = 32.

    12. How many edges does a cube have?

    A cube has 12 edges.

    13. How many faces does a cube have?

    A cube has 6 square faces.

    14. How many vertices does a cube have?

    A cube has 8 vertices.

    15. Find the area of triangle (base=6, height=4).

    Area = ½ × b × h = ½ × 6 × 4 = 12.

    16. How many sides does an octagon have?

    Octagon = 8 sides.

    17. What is the diameter of a circle if radius = 7 cm?

    Diameter = 2 × radius = 14 cm.

    18. How many sides does a decagon have?

    A decagon has 10 sides.

    19. The interior angle of a regular hexagon is?

    The formula for interior angle of regular n-gon is \((n-2)×180°/n\). For n=6: \((6-2)×180/6 = 4×180/6 = 120°\). So the interior angle is 120°.

    20. Find the circumference of a circle (radius = 7 cm). (Use π ≈ 22/7)

    Circumference = 2πr = 2 × (22/7) × 7 = 2 × 22 = 44 cm.

    Practice more MCQs on geometry here MCQ Maths questions

    📊 Class 10 Statistics – 20 Interactive MCQs Maths questions with Graphs

    Solve 20 MCQ Maths questions with visual graphs and detailed solutions. Click Show Solution to learn step by step.

    Practice more MCQs on class 10 statistics

    Frequently Asked Questions

    Algebra is the branch of mathematics that uses symbols and rules to solve problems and equations.
    Trigonometry is important for understanding angles, triangles, and periodic functions, widely applied in physics and engineering.
    Prime numbers are natural numbers greater than 1 that have no divisors other than 1 and themselves.
    Geometry is used in architecture, engineering, art, and navigation to understand space and structure.
    Statistics helps collect, analyze, and interpret data for decision making and predictions.
    Quadratic equations are equations of the form ax² + bx + c = 0 with real or complex solutions.
    The Pythagorean theorem states that in a right-angled triangle, a² + b² = c², where c is the hypotenuse.
    A prime number can only be divided by 1 and itself without remainder.
    Triangles can be classified as equilateral, isosceles, or scalene based on side lengths.
    Probability measures the likelihood of an event occurring, ranging from 0 to 1.
    Polynomials are algebraic expressions consisting of variables and coefficients combined with addition, subtraction, and multiplication.
    Sine and cosine are trigonometric functions relating angles to ratios of sides in a right-angled triangle.
    Modular arithmetic is a system of arithmetic for integers where numbers wrap around upon reaching a certain value, called the modulus.
    A circle is a set of points equidistant from a center, with properties like radius, diameter, and circumference.
    Data sampling is the process of selecting a subset of data from a larger population for analysis.
    Linear algebra studies vectors, matrices, and linear transformations used widely in computer science and engineering.
    A radian is a unit of measuring angles, defined by the arc length divided by the radius.
    Fermat’s Last Theorem states that no three positive integers a, b, and c can satisfy aⁿ + bⁿ = cⁿ for n > 2.
    Volume is calculated using formulas depending on the shape, such as length × width × height for a cuboid.
    Measures of central tendency include mean, median, and mode, which summarize data sets.

    10th Maths Guide

    Master key concepts in Algebra, Geometry, Calculus, and Statistics.

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    Discover Calculus Bridges

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