Binomial Theorem questions
776 published questions with worked solutions.
- The sum of the co-efficients of all odd degree terms in the expansion of (x+ x^3-1 )^5+ (x- x^3-1 )^5, (x>1) is
- The coefficient of t^4 in the expansion of ( 1-t^6 1-t )^3 is
- If _ i=1 ^ 20 ( ^ 20 C_ i-1 ^ 20 C_i+ ^ 20 C_ i-1 )^3= k 21 , then k equals
- If the third term in the binomial expansion of (1+x^ _2x )^5 equals 2560, then a possible value of x is
- The positive value of for which the co-efficient of x^2 in the expression x^2 ( x+ x^2 )^ 10 is 720, 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
- 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
- A ratio of the 5^ th term from the beginning to the 5^ th term from the end in the binomial expansion of (2^ 13 + 1 2(3)^ 13 )^...
- The total number of irrational terms in the binomial expansion of (7^ 1/5 -3^ 1/10 )^ 60 is
- The sum of the co-efficients of all even degree terms in x in the expansion of (x+ x^3-1 )^6+ (x- x^3-1 )^6, (x>1) is equal to
- If the fourth term in the Binomial expansion of ( 2x+x^ _8x )^6 (x>0) is 20 8^7, then a value of x is
- If some three consecutive coefficients in the binomial expansion of (x+1)^n in powers of x are in the ratio 2:15:70, then the...
- If the coefficients of x^2 and x^3 are both zero, in the expansion of the expression (1+ax+bx^2 )(1-3x)^ 15 in powers of x, then...
- The smallest natural number n, such that the coefficient of x in the expansion of (x^2+ 1 x^3 )^n is ^nC_ 23 , is
- The coefficient of x^ 18 in the product (1+x)(1-x)^ 10 (1+x+x^2 )^9 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, ) 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 and be the coefficients of x^4 and x^2 respectively in the expansion of (x+ x^2-1 )^6+ (x- x^2-1 )^6, then
- In the expansion of ( x + 1 x )^ 16 , if l_1 is the least value of the term independent of x when 8 4 and l_2 is the least value...
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