Binomial Theorem questions
776 published questions with worked solutions.
- Let the coefficients of third, fourth and fifth terms in the expansion of (x+ a x^2 )^n, x 0 be in the ratio 12 : 8 : 3. Then the...
- If the fourth term in the expansion of (x+x^ _2x )^7 is 4480, then the value of x where x N is equal to
- Let ^nC_r denote the binomial coefficient of x^r in the expansion of (1+x)^n. If _ k=0 ^ 10 (2^2+3k) ^nC_k= .3^ 10 + .2^ 10 , ,...
- Let (1+x+2x^2)^ 20 =a_0+a_1x+a_2x^2+ +a_ 40 x^ 40 . Then a_1+a_3+a_5+ +a_ 37 is equal to :
- For the natural numbers m, n, if (1-y)^m(1+y)^n=1+a_1y+a_2y^2+ +a^ m+n y^ m+n and a_1=a_2=10, then the value of (m+n) is equal to...
- The number of rational terms in the binomial expansion of (4^ 1/4 +5^ 1/6 )^ 120 is _____.
- If the constant term, in binomial expansion of (2x^r+ 1 x^2 )^ 10 is 180, then r is equal to _____.
- If n 2 is a positive integer, then the sum of the series ^ n+1 C_2+2(^2C_2+^3C_2+^4C_2+ +^nC_2) is :
- For integers n and r, let n r = cases ^nC_r, & if n r 0 0, & otherwise cases The maximum value of k for which the sum _ i=0 ^k 10...
- The value of -^ 15 C_1+2.^ 15 C_2-3.^ 15 C_3+ -15.^ 15 C_ 15 +^ 14 C_1+^ 14 C_3+^ 14 C_5+ +^ 14 C_ 11 is :
- If S_n= _ r=0 ^n 1 ^nC_r and t_n= _ r=0 ^n r ^nC_r , then t_n s_n is equal to
- _ r=0 ^m ^ n+r C_n is equal to
- If ^nC_r denotes the number of combinations of n things takes r at a time, then the expression ^nC_ r+1 + ^nC_ r-1 +2 ^nC_r,...
- If a_n= _ r=0 ^n 1 ^nC_r , then _ r=0 ^n r ^nC_r equals
- ^nC_r+2 , ^nC_ r-1 + ^nC_ r-2 is equal to
- Let f(n)= _ r=0 ^n _ k=r ^n kr. Find the total number of divisors of f(9).
- If ^ n-1 C_6+ ^ n-1 C_7> ^nC_6, then
- The expression ^nC_r+4 ^nC_ r-1 +6 ^nC_ r-2 +4 ^nC_ r-3 + ^nC_ r-4 equals
- If ^nC_ n-r +3 ^nC_ n-r+1 +3 ^nC_ n-r+2 + ^nC_ n-r+3 = ^xC_r, then x=
- The value of _ r=1 ^n ^nP_r r! is
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