Mathematics questions
18011 published questions with worked solutions.
- If (1-x+x^2 )^n=a_0+a_1x+a_2x^2+ +a_ 2n x^ 2n then the value of a_0+a_2+a_4+ +a_ 2n is
- If ^nC_0, ^nC_1, ^nC_2 ^nC_n denote the coefficient in the binomial expansion of (1+x)^n, then the value of C_1+3C_3+5C_5+ is
- The sum of the last eight coefficients in the expansion of (1+x)^ 15 is
- Let (1+x)^n=1+a_1x+a_2x^2+ +a_nx^n. If a_1,a_2 and a_3 are in AP, then the value of n is
- The value of 1^2 C_1+3^2 C_3+5^2 C_5+ is
- Sum of the last 30 coefficients in the expansion of (1+x)^ 59 , when expanded in ascending powers of x is
- For natural numbers m,n if (1-y)^m(1+y)^n=1+a_1y+a_2y^2+ and a_1=a_2=10, then (m,n) is
- What is the sum of the coefficient of (x^2-x-1 )^ 99 ?
- Let C_1,C_2,C_3 are the usual binomial coefficients. Let S=C_1+2C_2+3C_3+ +nC_n, then S equals
- If (1+x-3x^2 )^ 10 =1+a_1x+a_2x^2+ +a_ 20 x^ 20 , then a_2+a_4+a_6+ +a_ 20 is equal to
- The coefficient of a^5b^6c^7 in the expansion of (bc+ca+ab)^9 is
- If the coefficient of r^ th , (r+1)^ th and (r+2)^ th terms in the binomial expansion of (1+y)^m are in AP, then m and r satisfy...
- If the sum of the coefficient in the expansion of (a^2x^2-6ax+11 )^ 10 , where a is constant is 1024, then the value of a is
- If the sum of the coefficient in the expansion of (x+y)^n is 1024, then the value of the greatest coefficient in the expansion is
- If (1+x+x^2 )^n= _ r=0 ^ 2n a_rx^r then, a_1-2a_2+3a_3- -2na_ 2n is equal to
- The number of terms in the expansion of (a+b+c)^ 10 is
- The coefficient of x^3y^4z^5 in the expansion of (xy+yz+xz)^6 is
- If (1+2x+3x^2 )^ 10 =a_0+a_1x+a_2x^2+ +a_ 20 x^ 20 , then a_1 equals
- If a_k is the coefficient of x^k in the expansion of (1+x+x^2 )^n for k=0,1,2, ,2n then a_1+2a_2+3a_3+ +2na_ 2n is equal to
- The number of dissimilar terms in the expansion of (a+b)^n is n+1 therefore number of dissimilar terms of the expansion (a+b+c)^...