Properties of Binomial Coefficients

JEE Main Mathematics · Binomial Theorem · 18 questions, latest first

• 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
• Let S=1/(25!)+1/(3!23!)+1/(5!21!)+… up to 13 terms. If 13 S=2^k/(n!), k ∈ N, then n+k is equal to202624 January, Shift 1 · Q7
• If (1/(^15 C_0)+1/(^15 C_1))(1/(^15 C_1)+1/(^15 C_2)) ⋯(1/(^15 C_12)+1/(^15 C_13))=(α^13)/(^14 C_0^14 C_1 …^14 C_12), then 30 α…202621 January, Shift 2 · Q21
• For an integer n ≥ 2, if the arithmetic mean of all coefficients in the binomial expansion of (x+y)^2 n-3 is 16, then the…20254 April, Shift 1 · Q7
• Suppose A and B are the coefficients of 30^th and 12^th terms respectively in the binomial expansion of (1+x)^2 n-1. If 2 A=5 B,…202524 January, Shift 2 · Q9
• For some n ≠ 10, let the coefficients of the 5th, 6th and 7th terms in the binomial expansion of (1+x)^n+4 be in A.P. Then the…202524 January, Shift 1 · Q6
• Let 0 ≤ r ≤ n. If ^n+1 C_r+1:^n C_r:^n-1 C_r-1=55: 35: 21, then 2 n+5 r is equal to:20246 April, Shift 2 · Q6
• If the coefficients of x^4, x^5 and x^6 in the expansion of (1+x)^n are in the arithmetic progression, then the maximum value of…20244 April, Shift 2 · Q4
• Suppose 2-p, p, 2-α, α are the coefficients of four consecutive terms in the expansion of (1+x)^n. Then the value of p^2-α^2+6…202430 January, Shift 2 · Q5
• ^n-1 C_r=(k^2-8)^n C_r+1 if and only if:202427 January, Shift 1 · Q5
• The sum, of the coefficients of the first 50 terms in the binomial expansion of (1-x)^100, is equal to202312 April, Shift 1 · Q5
• 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: 5, is…202311 April, Shift 2 · Q8
• 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 the…20238 April, Shift 1 · Q8
• The value of 1/(1!50!)+1/(3!48!)+1/(5!46!)+….+1/(49!2!)+1/(51!1!) is:20231 February, Shift 1 · Q67
• Let the coefficients of three consecutive terms in the binomial expansion of (1+2 x)^n be in the ratio 2: 5: 8. Then the…202329 January, Shift 1 · Q89
• Σ_k=0^6^51-k C_3 is equal to202325 January, Shift 2 · Q67
• If a_r is the coefficient of x^10-r in the Binomial expansion of (1+x)^10, then Σ_r=1^10 r^3(a_r/(a_r-1))^2 is equal to202325 January, Shift 1 · Q64