Q1 · medium · PYQ 2025
What is the number of rational terms in the expansion of (3^(1/2) + 5^(1/4))^12?
- 2
- 3
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- 6
Q2 · medium · PYQ 2026
Let u be a positive integer and f be a real number lying between 0 and 1. Further, (√2 + 1)^10 = u + f and (√2 − 1)^10 = v. Consider the following statements: I. (u + v + f) is an integer. II. (f + v) is an integer. Which of the statements given above is/are correct?
- I only
- II only
- Both I and II
- Neither I nor II
Q3 · medium · PYQ 2024
If the 4th term in the expansion of (mx + 1/x)ⁿ is 5/2, then what is the value of mn?
- –3
- 3
- 6
- 12
Q4 · medium · PYQ 2026
Consider the following statements: I. (u + v + f) is an integer. II. (f + v) is an integer. [Given: u is a positive integer, 0 < f < 1 is a real number, (√2 + 1)¹⁰ = u + f and (√2 - 1)¹⁰ = v]. Which of the above statements is/are correct?
- I only
- II only
- Both I and II
- Neither I nor II
Q5 · medium · PYQ 2024
In a binomial expansion of (x + y)^(2n+1) (x – y)^(2n+1), the sum of middle terms is zero. What is the value of (x²/y²)?
- 1
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- 8