Q65.The coefficient of x−6 , in the expansion of ( 4x5 + 2x25 ) 9 5 9 x 2 4 is −84 and the coefficient of x−3l is 2αβ where 2 − xl
What This Question Tests
This question requires applying the general term formula for binomial expansion to find the power of x and then setting it equal to the desired exponent to find the coefficient and an unknown parameter.
Concepts Tested
Formulas Used
Tr+1 = nCr * a^(n-r) * b^r
📚 NCERT Sections This Tests
1.27 — If The Solubility Product Of Cus Is 6 × 10–16, Calculate The Maximum Molarity Of
Chemistry Class 11 · Chapter 1
1.27 If the solubility product of CuS is 6 × 10–16, calculate the maximum molarity of CuS in aqueous solution.
12.5 — A Hydrogen Atom Initially In The Ground Level Absorbs A Photon,
Physics Class 12 · Chapter 12
12.5 A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.
5.28 — How Many Ions Are Produced From The Complex Co(Nh3)6Cl2 In Solution?
Chemistry Class 11 · Chapter 5
5.28 How many ions are produced from the complex Co(NH3)6Cl2 in solution? (i) 6 (ii) 4 (iii) 3 (iv) 2 139 Coordination Compounds Reprint 2025-26
📋 Question Details
- Chapter
- Binomial Theorem
- Topic
- Coefficient of a specific term in binomial expansion
- Year
- 2023
- Shift
- 31 Jan Shift 2
- Q Number
- Q65
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 8: Binomial Theorem
More from this Chapter
Q89.In the binomial expansion of (a −b)n, n ≥5 , the sum of 5th and 6th terms is zero, then ab equals (1) 5 (2) 6 n−4 n−5 (3) n−5 (4) n−4 6 5
Q90.The sum of the series 20C0 −20C1 + 20C2 −20C3 + … −… + 20C10 is (1) −20C10 (2) 12 20C10 (3) 0 (4) 20C10
Q77.Statement-1: ∑nr=0(r + 1)nCr = (n + 2)2n−1 Statement -2: ∑nr=0(r + 1)nCrxr = (1 + x)n + nx(1 + x)n−1 . JEE Main 2008 JEE Main Previous Year Paper (1) Statement −1 is false, Statement −2 is true (2) Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1 (3) Statement −1 is true, Statement −2 is true; (4) Statement −1 is true, Statement −2 is false. Statement −2 is not a correct explanation for Statement −1.
Q65.The remainder left out when 82n −(62)2n+1 is divided by 9 is (1) 0 (2) 2 (3) 7 (4) 8