Binomial Theorem questions
776 published questions with worked solutions.
- If 1 (1-ax)(1-bx) =a_0+a_1x+a_2x^2+ then a_n equals
- If (1 + x + x^2 + x^3)^7 = _ r=0 ^ 21 a_r x^r then the value of a_0 + a_4 + a_8 + a_ 12 + a_ 16 + a_ 20 is _____.
- Let (1 + x)^ 36 = a_0 + a_1x + a_2x^2 + + a_ 36 x^ 36 . STATEMENT-1: a_0 + a_3 + a_6 + + a_ 36 = 2 3 (2^ 35 + 1) STATEMENT-2: a_0...
- The value of _ j=0 ^ n ( ^ 4n+1 C_ j + ^ 4n+1 C_ 2n-j ) is
- If (1 + x)^n = ^nC_0 + ^nC_1x + ^nC_2x^2 + + ^nC_nx^n then the value of _ i=0 ^ 8 _ j=1 ^ 8 ^8C_j , ^jC_i for all i j is
- The coefficient of x^ 2^ n+1 in 1 (1 + x)(1 + x^2)(1 + x^4) (1 + x^ 2^n ) , where |x| < 1, is
- Let (1 + x + x^2 + x^3 + x^4)^ 10 = a_0 + a_1x + a_2x^2 + + a_ 40 x^ 40 . Then
- The value of _ r=1 ^ n r^2 ^ n C_ r ^ n C_ r-1 is
- For 2 r n, n r + 2 n r-1 + n r-2 is equal to
- In the binomial expansion of (a-b)^n (n 5), the sum of the 5th and 6th terms is zero. Then a b is equal to
- The sum of coefficients of integral powers of x in the binomial expansion of (1 - 2 x )^ 50 is
- If the coefficient of the three successive terms in the binomial expansion of (1+x)^n are in the ratio 1:7:42, then the first of...
- The term independent of x in the binomial expansion of (1 - 1x + 3x^5 ) (2x^2 - 1x )^8 is
- The value of _ r=1 ^ 15 r^2 ( ^ 15 C_r ^ 15 C_ r-1 ) is equal to:
- For x R, x -1, if (1+x)^ 2016 + x(1+x)^ 2015 + x^2(1+x)^ 2014 + + x^ 2016 = _ i=0 ^ 2016 a_ix^i, then a_ 17 is equal to
- If the coefficients of x^ -2 and x^ -4 , in the expansion of (x^ 13 + 1 2x^ 13 )^ 18 , (x > 0), are m and n respectively, then mn...
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