Exams › JEE Main › Maths

If the coefficients of rth, (r + 1)th, and (r + 2)th terms in the binomial expansion of (1 + y)^m are in A.P., then m and r satisfy the equation

1. m² - m(4r - 1) + 4r² - 2 = 0
2. m² - m(4r + 1) + 4r² + 2 = 0
3. m² - m(4r + 1) + 4r² - 2 = 0
4. m² - m(4r - 1) + 4r² + 2 = 0

Correct answer: m² - m(4r + 1) + 4r² - 2 = 0

Solution

Coefficients of the rth, (r+1)th, (r+2)th terms are C(m,r-1), C(m,r), C(m,r+1). The AP condition 2C(m,r)=C(m,r-1)+C(m,r+1) simplifies to m^2 - m(4r+1) + 4r^2 - 2 = 0.

Related JEE Main Maths questions

• Let Pn = cosⁿ θ + sinⁿ θ. If Pn - Pn-2 = k Pn-4, then the value of k is:
• For any natural number n, the expression x^(2n - 1) + y^(2n - 1) is divisible by which of the following?
• For a natural number n, which of the following always divides the expression x^(n+1) + (x + 1)^(2n−1)?
• For a positive integer n, the expression 5^(2n+2) − 24n − 25 is divisible by which of the following?
• For every natural number n, the expression 41ⁿ − 14ⁿ is divisible by which of the following?
• Let C0, C1, C2,..., C15 denote the binomial coefficients in the expansion of (1 + x)¹⁵. Then the value of C1/C0 + C2/C1 + C3/C2 +... + C15/C14 is:

⚔️ Practice JEE Main Maths free + battle 1v1 →