Class 11 Maths Olympiad: 40 Questions with Answers (2026)

Class 11 Maths Olympiad: 40 Practice Questions with Answers

Build deeper mathematical reasoning with 40 free Class 11 Maths Olympiad practice questions. You will find multiple-choice questions and complete worked answers directly on this page, covering sets, functions, trigonometry, complex numbers, counting, sequences, coordinate geometry, calculus, statistics and probability.

All questions below are original practice exercises, not an official previous-year examination paper. For the subject’s current topic list and learning materials, visit School Connect Olympiad Class 11 Maths. Competition formats and syllabuses differ across organisers, so refer to the rules for the examination you intend to enter.

How to use these practice problems

Try to solve the question before reading the correct answer.
Write out your reasoning, not just the letter of an option.
Check each step against the worked explanation.
If you miss a problem, practise the concept with different numbers.
Use shorter topic-by-topic sessions when reviewing unfamiliar mathematics.

Sets and functions

Question 1. A = {1, 2, 3, 4} and B = {3, 4, 5}. How many elements are in A ∪ B?
A. 4 | B. 5 | C. 6 | D. 7
Answer: B. 5. The union contains 1, 2, 3, 4 and 5, counted only once: five elements.
Question 2. A has 28 elements, B has 19 and A ∩ B has 8. Find n(A ∪ B).
A. 37 | B. 39 | C. 47 | D. 55
Answer: B. 39. Apply inclusion–exclusion: 28 + 19 − 8 = 39.
Question 3. If f(x) = 2x − 5 and g(x) = x², find f(g(3)).
A. 4 | B. 11 | C. 13 | D. 31
Answer: C. 13. Calculate g(3) = 9, then f(9) = 2×9 − 5 = 13.
Question 4. What is the real domain of f(x) = (x + 2)/(x − 3)?
A. All real numbers except −2 | B. All real numbers except 0 | C. All real numbers except 3 | D. Only x greater than 3
Answer: C. All real numbers except 3. The denominator cannot be zero. Since x − 3 = 0 at x = 3, exclude 3.
Question 5. If f(x) = 3x + 2, what is f⁻¹(x)?
A. (x + 2)/3 | B. (x − 2)/3 | C. 3x − 2 | D. 1/(3x + 2)
Answer: B. (x − 2)/3. Write y = 3x + 2, exchange x and y, then solve x = 3y + 2 for y: (x − 2)/3.

Trigonometric functions

Question 6. Find sin 150°.
A. 1/2 | B. −1/2 | C. √3/2 | D. 1
Answer: A. 1/2. 150° is in quadrant II, where sine is positive; sin(180°−30°) = sin 30° = 1/2.
Question 7. Simplify 2 sin 60° cos 60°.
A. 1/2 | B. √3/2 | C. 1 | D. √3
Answer: B. √3/2. Use sin 2θ = 2 sin θ cos θ: the result is sin 120° = √3/2.
Question 8. If cos θ = 3/5, find cos 2θ.
A. −7/25 | B. 7/25 | C. −1/5 | D. 24/25
Answer: A. −7/25. Use cos 2θ = 2 cos²θ − 1 = 2(9/25) − 1 = −7/25.
Question 9. Express 225° in radians.
A. 3π/4 | B. 5π/4 | C. 7π/4 | D. 4π/5
Answer: B. 5π/4. Convert degrees to radians: 225 × π/180 = 5π/4.
Question 10. For an acute angle θ with tan θ = 3/4, find sin θ.
A. 4/5 | B. 3/5 | C. 5/3 | D. 3/4
Answer: B. 3/5. A right triangle with opposite side 3 and adjacent side 4 has hypotenuse 5, so sin θ = 3/5.

Complex numbers and quadratics

Question 11. Calculate (3 + 2i) + (1 − 5i).
A. 4 + 7i | B. 2 − 3i | C. 4 − 3i | D. 4 + 3i
Answer: C. 4 − 3i. Combine real terms (3+1) and imaginary terms (2−5)i to get 4 − 3i.
Question 12. Multiply (2 + i)(3 − 2i).
A. 8 − i | B. 4 − i | C. 8 + i | D. 6 − i
Answer: A. 8 − i. Expand: 6 − 4i + 3i − 2i² = 8 − i because i² = −1.
Question 13. Find |−5 + 12i|.
A. 7 | B. 11 | C. 13 | D. 17
Answer: C. 13. The modulus is √[(−5)² + 12²] = √169 = 13.
Question 14. Find the roots of x² + 4x + 13 = 0.
A. −2 ± 3i | B. 2 ± 3i | C. −4 ± 3i | D. −2 ± i
Answer: A. −2 ± 3i. By the quadratic formula, x = [−4 ± √(16−52)]/2 = [−4 ± 6i]/2 = −2 ± 3i.
Question 15. Find the discriminant of 2x² − 4x + 5 = 0.
A. −24 | B. 24 | C. −4 | D. 4
Answer: A. −24. For ax²+bx+c, discriminant = b²−4ac. Here 16 − 40 = −24.

Counting and binomial theorem

Question 16. How many different arrangements of the letters in MATH are possible?
A. 12 | B. 16 | C. 24 | D. 48
Answer: C. 24. All four letters differ, so the number of orders is 4! = 4×3×2×1 = 24.
Question 17. How many ways can you select three students from seven, if order does not matter?
A. 21 | B. 28 | C. 35 | D. 42
Answer: C. 35. Use combinations: C(7,3) = 7×6×5/(3×2×1) = 35.
Question 18. How many ways can five independent yes/no decisions be made?
A. 10 | B. 20 | C. 25 | D. 32
Answer: D. 32. Each of five decisions has two choices: 2⁵ = 32.
Question 19. What is the coefficient of x² in (1 + x)⁵?
A. 5 | B. 10 | C. 15 | D. 20
Answer: B. 10. The x² coefficient is the binomial coefficient C(5,2) = 10.
Question 20. A four-character numeric code may start with zero. How many codes use four different digits?
A. 4,536 | B. 5,040 | C. 3,024 | D. 6,561
Answer: B. 5,040. Ten choices for the first digit, then 9, 8 and 7 unused digits: 10×9×8×7 = 5,040.

Sequences and series

Question 21. In an arithmetic progression the first term is 4 and the common difference is 3. What is the 10th term?
A. 28 | B. 30 | C. 31 | D. 34
Answer: C. 31. The nth term is a+(n−1)d. For n=10: 4 + 9×3 = 31.
Question 22. Find the sum of the first ten positive even integers.
A. 90 | B. 100 | C. 110 | D. 120
Answer: C. 110. The numbers are 2,4,…,20. Their average is (2+20)/2 = 11; ten terms total 110.
Question 23. A geometric progression has first term 3 and common ratio 2. What is its fifth term?
A. 24 | B. 36 | C. 48 | D. 96
Answer: C. 48. The nth GP term is ar⁽ⁿ⁻¹⁾. So the fifth term is 3×2⁴ = 48.
Question 24. Calculate the sum 2 + 6 + 18 + 54.
A. 68 | B. 72 | C. 80 | D. 84
Answer: C. 80. Add the first four terms of a GP with ratio 3: 2+6+18+54 = 80.
Question 25. A sequence has nth term 4n + 3. Find the 18th term.
A. 67 | B. 71 | C. 75 | D. 79
Answer: C. 75. Substitute n=18: 4×18+3 = 72+3 = 75.

Straight lines and conic sections

Question 26. Find the slope of the line joining (1,2) and (5,10).
A. 1/2 | B. 1 | C. 2 | D. 4
Answer: C. 2. Slope = (10−2)/(5−1) = 8/4 = 2.
Question 27. Which line has slope −2 and y-intercept 3?
A. y = 2x + 3 | B. y = −2x + 3 | C. y = −2x − 3 | D. y = 3x − 2
Answer: B. y = −2x + 3. Slope-intercept form is y = mx+c, with m=−2 and c=3.
Question 28. Find the distance between points (1,2) and (4,6).
A. 3 | B. 4 | C. 5 | D. 7
Answer: C. 5. Distance = √[(4−1)²+(6−2)²] = √(9+16) = 5.
Question 29. A circle has centre (−1,2) and radius 3. Which equation represents it?
A. (x+1)²+(y−2)²=9 | B. (x−1)²+(y+2)²=9 | C. (x+1)²+(y+2)²=3 | D. (x−1)²+(y−2)²=9
Answer: A. (x+1)²+(y−2)²=9. The standard circle equation is (x−h)²+(y−k)²=r². Substitute h=−1,k=2,r=3.
Question 30. The parabola y² = 12x has which focus?
A. (3,0) | B. (0,3) | C. (6,0) | D. (−3,0)
Answer: A. (3,0). Compare with y²=4ax. Here 4a=12, so a=3 and the focus is (3,0).

Limits and derivatives

Question 31. Evaluate lim as x approaches 2 of (x²−4)/(x−2).
A. 2 | B. 4 | C. 0 | D. Undefined
Answer: B. 4. Factor x²−4=(x−2)(x+2). For x≠2, cancel x−2; the limit is 2+2=4.
Question 32. Differentiate 3x³ − 2x² + 5 with respect to x.
A. 9x²−2x | B. 9x²−4x | C. 3x²−4x | D. 9x³−4x
Answer: B. 9x²−4x. Use the power rule term by term: 9x²−4x+0.
Question 33. What is the derivative of sin x when x is in radians?
A. −cos x | B. sin x | C. cos x | D. −sin x
Answer: C. cos x. The derivative of sin x is cos x for radian measure.
Question 34. Find lim as x approaches 0 of sin(5x)/x, with angles in radians.
A. 0 | B. 1 | C. 5 | D. Undefined
Answer: C. 5. Rewrite as 5[sin(5x)/(5x)] and use the standard limit sin u/u→1, giving 5.
Question 35. Find the slope of the tangent to y=x² at x=3.
A. 3 | B. 6 | C. 9 | D. 12
Answer: B. 6. Differentiate to get dy/dx=2x; at x=3 the slope is 6.

Probability, statistics and reasoning

Question 36. Two fair six-sided dice are rolled. What is the probability that their sum is 7?
A. 1/12 | B. 1/6 | C. 1/4 | D. 1/3
Answer: B. 1/6. Six of the 36 equally likely ordered pairs sum to 7: 6/36 = 1/6.
Question 37. A group has five boys and four girls. How many ways can a three-member team contain exactly two girls?
A. 20 | B. 30 | C. 36 | D. 45
Answer: B. 30. Choose two of four girls in C(4,2)=6 ways and one of five boys in 5 ways, giving 6×5=30.
Question 38. Find the mean of the numbers 3, 5, 7, 9 and 11.
A. 6 | B. 6.5 | C. 7 | D. 8
Answer: C. 7. Sum = 35 and count = 5, so mean = 35/5 = 7.
Question 39. Find the population variance of 2, 4 and 6.
A. 2 | B. 8/3 | C. 4 | D. 8
Answer: B. 8/3. The mean is 4. Squared deviations are 4, 0 and 4; divide their sum 8 by population size 3 to get 8/3.
Question 40. Given P(A)=0.6, P(B)=0.5 and P(A∩B)=0.2, find P(A∪B).
A. 0.7 | B. 0.8 | C. 0.9 | D. 1.0
Answer: C. 0.9. Inclusion–exclusion: P(A∪B)=P(A)+P(B)−P(A∩B)=0.6+0.5−0.2=0.9.

Class 11 Maths revision map

Questions	What you practised	Try next
1–5	Sets and functions	Draw Venn diagrams and check which inputs make a function undefined
6–10	Trigonometric functions	Sketch the unit circle and explain signs in each quadrant
11–15	Complex numbers and quadratics	Use i²=−1 and the discriminant to verify answers
16–20	Counting and binomial coefficients	Decide whether order matters before choosing a formula
21–25	Arithmetic and geometric sequences	Find the nth term and verify it by listing initial terms
26–30	Lines and conic sections	Plot points and label slope, centre, radius or focus
31–35	Limits and derivatives	Simplify expressions before substituting into limits
36–40	Probability and statistics	Count outcomes carefully and distinguish population from sample variance

Four problem-solving techniques worth remembering

Check whether order matters

Choosing three students from seven is different from placing three students in three ranked positions. For an unordered group, use C(7,3) = 35. For ranked positions without repeats, there are 7×6×5 = 210 possible assignments.

Test the domain before simplifying a function

For (x+2)/(x−3), the denominator cannot be zero. That excludes x=3 even if a later algebra step makes the expression look simpler. Domain restrictions are part of the answer.

Distinguish a limit from the function value

Although (x²−4)/(x−2) is undefined at x=2, its limit as x approaches 2 is 4. Factoring and cancelling for values near 2 explains why the limit exists.

Use the correct denominator for variance

The population variance of 2, 4 and 6 is 8/3. If those numbers were instead a sample used to estimate a larger population variance, the usual sample formula divides by n−1 and gives 4. Always read the question’s wording.

A practical four-session revision plan

Session 1 — Foundations: Solve Questions 1–15. Rework one set-operation question, one trigonometric identity and one complex-number multiplication without looking at the answers.
Session 2 — Counting and progressions: Solve Questions 16–25. For each counting problem, decide whether order matters; for sequences, write the formula before substituting.
Session 3 — Graphs and calculus: Solve Questions 26–35. Draw the coordinate axes for line and circle questions; check derivatives by applying the power rule term by term.
Session 4 — Data and review: Solve Questions 36–40. Revisit problems you missed and explain the rule or formula that resolves each one.

Three extra checks that prevent common mistakes

Complex multiplication: In (2+i)(3−2i), the term −2i² becomes +2 because i²=−1. The full result is 8−i, not 4−i.

Binomial coefficient: In (1+x)⁵, the coefficient of x² is C(5,2)=10. The power on x and the coefficient are not the same quantity.

Probability of a union: When two events overlap, adding P(A) and P(B) counts the overlap twice. Subtract P(A∩B) once to correct it.

Frequently asked questions

Are all the Class 11 Maths practice questions free?

Yes. Every problem and worked answer can be read directly on this page without signing in or paying.

Do I need a PDF to find the answers?

No. You can work through all 40 questions and explanations here. Use the Print function in your browser if you prefer a paper study copy.

Are these actual questions from an earlier official examination?

No. These are independently written educational practice problems. For past official competition documents, use your chosen competition’s own verified resources.

Which Class 11 topics should I study first?

Review sets and functions, trigonometry and algebra first, then progress to sequences, coordinate geometry, introductory calculus and probability. Use the Class 11 Maths learning chapters to plan a broader revision programme.

Are SCO, SOF and the International Mathematical Olympiad the same?

No. School Connect Olympiad, Science Olympiad Foundation competitions and the senior International Mathematical Olympiad are separately organised and have different formats and eligibility requirements.