General Term

JEE Main Mathematics · Binomial Theorem · 36 questions, latest first

• 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
• The number of integral terms in the expansion of (5^(1/2)+7^(1/8))^1016 is20258 April, Shift 2 · Q8
• In the expansion of (√[3]2+1/(√[3]3))^n, n ∈ N, if the ratio of 15^th term from the beginning to the 15^th term from the end is…20254 April, Shift 1 · Q6
• The sum of all rational terms in the expansion of (2+√3)^8 is20253 April, Shift 1 · Q9
• The term independent of x in the expansion of (((x+1))/((x^2 / 3+1-x^1 / 3))-((x-1))/((x-x^1 / 2)))^10, x>1, is:20252 April, Shift 1 · Q16
• The least value of n for which the number of integral terms in the Binomial expansion of (√[3]7+√[12]11)^n is 183, is:202529 January, Shift 1 · Q8
• Let the coefficients of three consecutive terms T_r, T_r+1 and T_r+2 in the binomial expansion of (a+b)^12 be in a G.P. and let p…202528 January, Shift 2 · Q7
• The sum of the coefficient of x^2 / 3 and x^-2 / 5 in the binomial expansion of (x^2 / 3+1/2 x^-2 / 5)^9 is20249 April, Shift 2 · Q6
• If the term independent of x in the expansion of (√a x^2+1/(2 x^3))^10 is 105, then a^2 is equal to:20248 April, Shift 2 · Q6
• If the second, third and fourth terms in the expansion of (x+y)^n are 135, 30 and 10/3, respectively, then 6(n^3+x^2+y) is equal…20246 April, Shift 1 · Q23
• If the constant term in the expansion of ((√[5]3)/x+(2 x)/(√[3]5))^12, x ≠ 0, is α × 2^8 × √[5]3, then 25 α is equal to:20245 April, Shift 2 · Q9
• If the constant term in the expansion of (1+2 x-3 x^3)(3/2 x^2-1/(3 x))^9 is p, then 108p is equal to ____.20245 April, Shift 1 · Q24
• The sum of all rational terms in the expansion of (2^(1/5)+5^(1/3))^15 is equal to:20244 April, Shift 1 · Q8
• Let m and n be the coefficients of seventh and thirteenth terms respectively in the expansion of (1/3 x^(1/3)+1/(2 x^(2/3)))^18.…20241 February, Shift 2 · Q6
• If the Coefficient of x^30 in the expansion of (1+1/x)^6(1+x^2)^7(1-x^3)^8; x ≠ 0 is α, then |α| equals ____.20241 February, Shift 1 · Q23
• Number of integral terms in the expansion of {7^(1/2)+11^(1/6)}^824 is equal to ____.202430 January, Shift 1 · Q23
• The coefficient of x^5 in the expansion of (2 x^3-1/(3 x^2))^5 is202313 April, Shift 2 · Q7
• Let α be the constant term in the binomial expansion of (√x-6/(x^(3/2)))^n, n ≤ 15. If the sum of the coefficients of the…202313 April, Shift 1 · Q23
• If the 1011^th term from the end in the binominal expansion of ((4 x)/5-5/(2 x))^2022 is 1024 times 1011^th term from the…202311 April, Shift 2 · Q7
• The number of integral terms in the expansion of (3^(1/2)+5^(1/4))^680 is equal to202311 April, Shift 1 · Q27
• If the coefficient of x^7 in (a x-1/(b x^2))^13 and the coefficient of x^-5 in (a x+1/(b x^2))^13 are equal, then a^4 b^4 is…202310 April, Shift 1 · Q5
• The absolute difference of the coefficients of x^10 and x^7 in the expansion of (2 x^2+1/(2 x))^11 is equal to20238 April, Shift 2 · Q7
• Let [t] denote the greatest integer ≤ t. If the constant term in the expansion of (3 x^2-1/(2 x^5))^7 is α, then [α] is equal to…20238 April, Shift 1 · Q22
• If the coefficients of x^7 in (a x^2+1/(2 b x))^11 and x^-7 in (a x-1/(3 b x^2))^11 are equal, then20236 April, Shift 2 · Q7
• If the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of (√[4]2+1/(√[4]3))^n is √6:…20236 April, Shift 1 · Q6
• The coefficient of x^18 in the expansion of (x^4-1/x^3)^15 is ____20236 April, Shift 1 · Q24
• Let the sixth term in the binomial expansion of (√(2^log_2(10-3^x))+√[5](2^(x-2) log_2 3))^m, in the increasing powers of 2^(x-2)…20231 February, Shift 2 · Q82
• If the term without x in the expansion of (x^(2/3)+(α)/x^3)^22 is 7315, then |α| is equal to ____.20231 February, Shift 2 · Q84
• If the constant term in the binomial expansion of ((x^(5/2))/2-4/x^l)^9 is -84 and the coefficient of x^-3 l is 2^α β, where β<0…202331 January, Shift 2 · Q83
• The coefficient of x^-6, in the expansion of ((4 x)/5+5/(2 x^2))^9, is ____.202331 January, Shift 2 · Q90
• Let α>0, be the smallest number such that the expansion of (x^(2/3)+2/x^3)^30 has a term β x^-α, β ∈ N. Then α is equal to ____.202331 January, Shift 1 · Q84
• If the coefficient of x^15 in the expansion of (a x^3+1/(b x^1 / 3))^15 is equal to the coefficient of x^-15 in the expansion of…202330 January, Shift 1 · Q71
• If the co-efficient of x^9 in (α x^3+1/(β x))^11 and the co-efficient of x^-9 in (α x-1/(β x^3))^11 are equal, then (α β)^2 is…202329 January, Shift 1 · Q88
• Let the sum of the coefficients of the first three terms in the expansion of (x-3/x^2)^n, x ≠ 0. n ∈ N, be 376. Then the…202324 January, Shift 2 · Q82