SolveForX

Binomial Theorem — Class 11 solved problems

17 problems from this chapter, each solved step by step.

  1. If 1² 151² + 2² 152² + 3² 153² + + 15² 1515² = 2^m 3^n 5^k, where m,n,k are positive integers, then m + n + k is equal to:

    12

  2. For some n ≠ 10, let the coefficients of the 5th, 6th and 7th terms in the binomial expansion of (1 + x)^(n+4) be in A.P. Then the largest coefficient in the ex

    189

  3. Expand (x²+(3)/(x))^4, x ≠ 0

    x^8 + 12x^5 + 54x² + (108)/(x) + (81)/(x^4)

  4. The least value of n for which the number of integral terms in the Binomial expansion of ( [3]7 + [3]11)^n is 183, is:

    546

  5. In the expansion of ((√2)/(3) + (1)/(√3))^n, n N if the ratio of the 15th term from the beginning to the 15th term from the end is (1)/(6) then the value of n3

    2600

  6. The sum of the series 2 × 1 × 204 - 3 × 2 × 205 + 4 × 3 × 206 - 5 × 4 × 207 + + 18 × 17 × 2020 is equal to:

    6460

  7. If α = 1 + Σ_r=1^6 (-3)^(r-1) ^(12)C_2r-1, then the distance of the point (12, √3) from the line α x - √3 y + 1 = 0 is

    5

  8. Using binomial theorem, prove that 6^n-5 n always leaves remainder 1 when divided by 25.

    The expression 6^n - 5n can be written as 1 + 25K, where K is an integer. Therefore, 6^n - 5n always leaves a remainder of 1 when divided by 25.

  9. The sum of all rational terms in the expansion of (2+√3)^8 is:

    18817

  10. If in the expansion of (1 + x)^p (1 - x)^q, the coefficients of x and x² are 1 and -2, respectively, then p² + q² is equal to:

    13

  11. If Σ_r=0^(10) ((10^(r+1) - 1)/(10^r)) · ^(11)C_r+1 = (α^(11) - 11^(11))/(10^(10)), then α is equal to:

    α = 20

  12. The sum of all rational terms in the expansion of (1 + 2^(1/2) + 3^(1/2))^6 is equal to

    1296

  13. Let α, β, and be the coefficients of x^7, x^5, x³ and x respectively in the expansion of (x+√(x³-1))^5+(x-√(x³-1))^5, x>1. If u and v satisfy the equations α u+

    5

  14. For an integer n ≥ 2 if the arithmetic mean of all coefficients in the binomial expansion of (x + y)^(2n-3) is 16, then the distance of the point P(2n-1, n²-4n)

    3√2

  15. Suppose A and B are the coefficients of 30^(th) and 12^(th) terms respectively in the binomial expansion of (1 + x)²n - 1. If 2A = 5B, then n is equal to:

    n = (41)/(2)

  16. The number of integral terms in the expansion of ( (1)/(5²) + (1)/(7^8))^(1016) is:

    0

  17. If Σ_r=1^(30) r³ (^(30)C_r)²^(30)C_r-1 = α × 2^(29), then α is equal to:

    α = 13080

More Class 11 chapters

Solve your own maths question free →