Binomial Theorem questions
776 published questions with worked solutions.
- Let (x + 10)^ 50 + (x - 10)^ 50 = a_0 + a_1x + a_2x^2 + + a_ 50 x^ 50 , for all x ∈ R; then a_2 a_0 is equal to:
- Let S_n = 1 + q + q^2 + + q^n and T_n = 1 + ( q+1 2 ) + ( q+1 2 )^2 + + ( q+1 2 )^n where q is a real number and q ≠ 1. If ^ 101...
- The value of r for which ^ 20 C_r , ^ 20 C_0 + ^ 20 C_ r-1 , ^ 20 C_1 + ^ 20 C_ r-2 , ^ 20 C_2 + + ^ 20 C_0 , ^ 20 C_r is...
- The sum of the real values of x for which the middle term in the binomial expansion of ( x^3 3 + 3x )^8 equals 5670 is:
- If _ r=0 ^ 25 , ^ 50 C_r ^ 50-r C_ 25-r = K ( ^ 50 C_ 25 ), then K is equal to:
- The positive value of λ for which the co-efficient of x^2 in the expression x^2 ( x + x^2 )^ 10 is 720, is:
- If _ i=1 ^ 20 ( , ^ 20 C_ i-1 , ^ 20 C_i + ^ 20 C_ i-1 )^3 = k 21 , then k is equal to:
- If the third term in the binomial expansion of (1 + x^ _2x )^5 equals 2560, then a possible value of x is:
- If ^ 20 C_1 + (2^2) , ^ 20 C_2 + (3^2) , ^ 20 C_3 + + (20^2) , ^ 20 C_ 20 = A(2^ ), then the ordered pair (A, β) is equal to:
- The term independent of x in the expansion of ( 1 60 - x^8 81 ) (2x^2 - 3 x^2 )^6 is equal to:
- The coefficient of x^7 in the expression (1+x)^ 10 +x(1+x)^9+x^2(1+x)^8+ +x^ 10 is:
- If C_r= ^ 25 C_r and C_0+5 C_1+9 C_2+ +(101) C_ 25 =2^ 25 k, then k is equal to ___________.
- The coefficient of x^4 in the expansion of (1+x+x^2)^ 10 is _____
- If the term independent of x in the expansion of ( 3 2 x^2- 1 3x )^9 is k, then 18 k is equal to -
- Let m and n be the coefficients of seventh and thirteenth terms respectively in the expansion of ( 13x^ 13 + 1 2x^ 23 )^ 18 ....
- If the coefficient of x^ 30 in the expansion of (1 + 1x )^6(1 + x^2)^7(1 - x^3)^8; x ≠ 0 is α, then |α| equals_______.
- If the coefficients of x⁴, x⁵ and x⁶ in the expansion of (1 + x)^n are in the arithmetic progression, then the maximum value of n...
- The sum of all rational terms in the expansion of (2^ 15 + 5^ 13 )^ 15 is equal to-
- Let a = 1 + ^2C_2 3! + ^3C_2 4! + ^4C_2 5! + , b = 1 + ^1C_0 + ^1C_1 1! + ^2C_0 + ^2C_1 + ^2C_2 2! + ^3C_0 + ^3C_1 + ^3C_2 +...
- If the constant term in the expansion of (1 + 2x - 3x^3) ( 32x^2 - 1 3x )^9 is p, then 108p is equal to
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