Binomial Theorem

JEE Main Mathematics · 9 questions

All questions, latest first

• If 26(2^3/3(^12 C_2)+2^5/5(^12 C_4)+2^7/7(^12 C_6)+⋯+(2^13)/13(^12 C_12))=3^13-α, then α is equal to:20268 April, Shift 2 · Q8
• 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
• If the coefficients of the middle terms in the binomial expansions of (1+α x)^26 and (1-α x)^28, α ≠ 0, are equal, then the value…20266 April, Shift 1 · Q8
• The coefficient of x^2 in the expansion of (2 x^2+1/x)^10, x ≠ 0, is:20265 April, Shift 2 · Q7
• If the sum of the coefficients of x^7 and x^14 in the expansion of (1/x^3-x^4)^n, x ≠ 0, is zero, then the value of n is ____.20265 April, Shift 1 · Q23
• In the expansion of (9 x-1/(3 √x))^18, x>0, if the term independent of x is (221)k, then k is equal to:20264 April, Shift 2 · Q9
• 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
• If for 3 ≤ r ≤ 30,(^30 C_30-r)+3(^30 C_31-r)+3(^30 C_32-r)+(^30 C_33-r)=^m C_r, then m equals:20262 April, Shift 2 · Q6
• The number of elements in the set S={(r, k): k ∈ Z. and.^36 C_r+1=(6(^35 C_r))/((k^2-3))}, is:20262 April, Shift 1 · Q7