Binomial Theorem questions
776 published questions with worked solutions.
- If the coefficients of three consecutive terms in the expansion of (1+x)^n are in the ratio 1 : 5 : 20, then the coefficient of...
- Let [t] denote the greatest integer . If the constant term in the expansion of (3x^2- 1 2x^5 )^7 is , then [ ] is equal to...
- If the coefficients of x and x^2 in (1+x)^p(1-x)^q are 4 and –5 respectively, then 2p + 3q is equal to -
- If the coefficient of x^7 in (ax- 1 bx^2 )^ 13 and the coefficient of x^ -5 in (ax+ 1 bx^2 )^ 13 are equal, then a^4b^4 is equal...
- The coefficient of x^7 in (1-x+2x^3)^ 10 is _________
- If the 1011^ th term from the end in the binomial expansion of ( 4x 5 - 5 2x )^ 2022 is 1024 times 1011^ th term from the...
- The sum of the coefficients of three consecutive terms in the binomial expansion of (1+x)^ n+2 , which are in the ratio 1 : 3 :...
- The number of integral terms in the expansion of (3^ 1/2 +5^ 1/4 )^ 680 is equal to
- The mean of the coefficients of x, x^2, …., x^7 in the binomial expression of (2+x)^9 is _____________.
- If 1 n+1 ^nC_n+ 1 n ^nC_ n-1 + + 1 2 ^nC_1+ ^nC_0= 1023 10 then n is equal to
- The coefficient of x^5 in the expansion of (2x^3- 1 3x^2 )^5 is :
- Let be the constant term in the binomial expansion of ( x- 6 x^ 3/2 )^n, n 15. If the sum of the coefficients of the remaining...
- Let (a+bx+cx^2)^ 10 = _ i=10 ^ 20 p_ix^i, a, b, c N. If p_1 = 20 and p_2 = 210, then 2(a + b + c) is equal to-
- If (^ 30 C_1)^2+2(^ 30 C_2)^2+3(^ 30 C_3)^2+ +30(^ 30 C_ 30 )^2= 60! (30!)^2 = then is equal to :
- Let the sum of the coefficients of the first three terms in the expansion of (x- 3 x^2 )^n, x 0. n N, be 376. Then the...
- Suppose _ r=0 ^ 2023 r2^ 2023 C_r=2023 2^ 2022 , the value of is ____________
- _ k=0 ^6 ^ 51-k C_3 is equal to
- If a_r is the coefficient of x^ 10-r in the Binomial expansion of (1+x)^ 10 , then _ r=1 ^ 10 r^3 ( a_r a_ r-1 )^2 is equal to
- The constant term in the expansion of (2x+ 1 x^7 +3x^2 )^5 is ___________.
- Let K be the sum of the coefficients of the odd powers of x in the expansion of (1+x)^ 99 . Let a be the middle term in the...
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