Binomial Inside Binomial

JEE Main Mathematics · Binomial Theorem · 9 questions, latest first

• If (1-x^3)^10=Σ_r=0^10 a_r x^r(1-x)^30-2 r, then (9 a_9)/(a_10) is equal to ____.20266 April, Shift 2 · Q22
• Let the smallest value of k ∈ N, for which the coefficient of x^3 in (1+x)^3+(1+x)^4+(1+x)^5+…+(1+x)^99+(1+k x)^100, x ≠ 0, is…20264 April, Shift 1 · Q9
• The sum of the coefficients of x^499 and x^500 in (1+x)^1000+x(1+x)^999+x^2(1+x)^998+…+x^1000 is:202628 January, Shift 2 · Q6
• The coefficient of x^48 in (1+x)+2(1+x)^2+3(1+x)^3+…+100(1+x)^100 is equal to202622 January, Shift 1 · Q6
• The coefficient of x^70 in x^2(1+x)^98+x^3(1+x)^97+x^4(1+x)^96+…+x^54(1+x)^46 is ^99 C_p-^46 C_q. Then a possible value of p+q is:20249 April, Shift 1 · Q4
• Let the coefficient of x^r in the expansion of (x+3)^n-1+(x+3)^n-2(x+2)+(x+3)^n-3(x+2)^2+… … …+(x+2)^n-1 be α_r. If Σ_r=0^n…202431 January, Shift 2 · Q23
• In the expansion of (1+x)(1-x^2)(1+3/x+3/x^2+1/x^3)^5, x ≠ 0, the sum of the coefficients of x^3 and x^-13 is equal to ____202431 January, Shift 1 · Q24
• The coefficient of x^2012 in the expansion of (1-x)^2008(1+x+x^2)^2007 is equal to ____.202427 January, Shift 2 · Q24
• The coefficient of x^301 in (1+x)^500+x(1+x)^499+x^2(1+x)^498+… ….+x^500 is:202330 January, Shift 1 · Q64