Binomial Theorem questions
776 published questions with worked solutions.
- ^ 15 C_0 ^5C_5+ ^ 15 C_1 ^5C_4+ ^ 15 C_2 ^5C_3+ ^ 15 C_3 ^5C_2+ ^ 15 C_4 ^5C_1 is equal to
- The value of the sum of the series 3 ^nC_0-8 ^nC_1+13 , ^nC_2-18 ^nC_3+ upto (n+1) terms is
- ^8C_0 6- ^8C_1+ ^8C_2 6- ^8C_3 6^2+ + ^8C_8 6^7 is equal to
- ^ 20 C_4+2 ^ 20 C_3+ ^ 20 C_2- ^ 22 C_ 18 is equal to
- In the expansion of (1+x)^ 30 , the sum of the coefficients of odd powers of x is
- For r=0, ,10 let A_r, B_r and C_r denote, respectively, the coefficient of x^r in (1+x)^ 10 , (1+x)^ 20 and (1+x)^ 30 . Then _...
- 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
Other chapters
Alcohols, Phenols and EthersAldehydes, Ketones and Carboxylic AcidsAlternating CurrentAminesAnatomy of Flowering PlantsAncient Indian HistoryAnimal KingdomApplication of DerivativesArea Under CurveAromatic Compounds and Aryl HalidesAtomsBasic Mathematics and LogarithmBiodiversity and ConservationBiological ClassificationBiomoleculesBiotechnology and Its ApplicationsBiotechnology: Principles and ProcessesBody Fluids and CirculationBreathing and Exchange of GasesCell Cycle and Cell DivisionCell: The Unit of LifeChemical Bonding and Molecular StructureChemical Coordination and IntegrationChemical Kinetics