Sequences and series, the binomial theorem and permutations and combinations together give several easy-to-score questions in JEE Main. This set covers nth terms and sums of AP and GP, AM and GM, binomial coefficients and general terms, and the standard counting methods, with the working for every answer.
How to practise: read each question and tap the option you think is correct. You will see right away whether you got it, along with a short explanation, and your score is tracked at the bottom of the screen. This set has 15 questions.
Topics covered in this set
- nth term and sum of an AP
- GP and sum to infinity
- AM, GM and sums of squares
- General term and binomial coefficients
- Arrangements with repeated letters
- Selections, circular arrangements and integer solutions
JEE Mathematics MCQs with answers and explanations
Q1. What is the 10th term of the AP 3, 7, 11, 15, ...?
a) 35
b) 43
c) 39
d) 40
Q2. What is the sum of the first 20 terms of the AP 2, 5, 8, ...?
a) 600
b) 620
c) 610
d) 590
Q3. What is the sum to infinity of the GP 8 + 4 + 2 + 1 + ...?
a) 12
b) 15
c) 16
d) 32
Q4. The arithmetic mean of two positive numbers is 10 and their geometric mean is 8. What are the numbers?
a) 4 and 16
b) 2 and 18
c) 5 and 15
d) 8 and 12
Q5. What is 1² + 2² + 3² + ... + 10²?
a) 385
b) 355
c) 505
d) 285
Q6. What is the coefficient of x³ in the expansion of (1 + 2x)⁶?
a) 20
b) 80
c) 160
d) 120
Q7. What is the term independent of x in (x² + 1/x)⁶?
a) 30
b) 6
c) 15
d) 20
Q8. What is the sum of the coefficients in the expansion of (3x − 2)⁵?
a) 32
b) −1
c) 243
d) 1
Q9. What is ¹⁰C₀ + ¹⁰C₂ + ¹⁰C₄ + ... + ¹⁰C₁₀?
a) 512
b) 256
c) 1023
d) 1024
Q10. In how many distinct ways can the letters of the word BANANA be arranged?
a) 720
b) 30
c) 60
d) 120
Q11. A committee of 3 men and 2 women is to be formed from 6 men and 4 women. In how many ways can this be done?
a) 60
b) 252
c) 120
d) 210
Q12. How many 4-digit numbers have all distinct digits?
a) 3024
b) 4500
c) 4536
d) 5040
Q13. In how many ways can 5 people be seated around a round table?
a) 60
b) 24
c) 12
d) 120
Q14. How many diagonals does a decagon (10-sided polygon) have?
a) 45
b) 35
c) 40
d) 90
Q15. How many non-negative integer solutions does x + y + z = 10 have?
a) 55
b) 66
c) 45
d) 78
Quick revision notes
- AP: aₙ = a + (n − 1)d, Sₙ = n/2 [2a + (n − 1)d].
- GP with |r| < 1: S∞ = a/(1 − r); AM ≥ GM for positive numbers.
- General term of (a + b)ⁿ: Tᵣ₊₁ = ⁿCᵣ aⁿ⁻ʳ bʳ.
- Sum of coefficients = value at x = 1; even and odd binomial coefficients each sum to 2ⁿ⁻¹.
- Repeated letters: n!/(p! q! ...); circular: (n − 1)!; x₁ + ... + xᵣ = n has ⁿ⁺ʳ⁻¹Cᵣ₋₁ non-negative solutions.
Frequently asked questions
Are these JEE previous year questions?
No. They are original practice questions at the JEE Main level.
How do I find the term independent of x quickly?
Write the general term, collect the power of x as a function of r, set it to zero and solve for r. If r is not a whole number, no such term exists.
When do I use permutations and when combinations?
Use permutations when the order of the chosen items matters, such as arrangements and numbers. Use combinations when only the group matters, such as committees and selections.
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