Binomial Theorem questions
776 published questions with worked solutions.
- Let >0, >0 be such that ^3+ ^2=4. If the maximum value of the term independent of x in the binomial expansion of ( x^ 19 + x^ -...
- If the number of integral terms in the expansion of (3^ 12 +5^ 18 )^n is exactly 33, then the least value of n is
- If the term independent of x in the expansion of ( 32x^2- 1 3x )^9 is k, then 18k is equal to
- The value of _ r=0 ^ 20 ^ 50-r C_6 is equal to
- If for some positive integer n, the coefficients of three consecutive terms in the binomial expansion of (1+x)^ n+5 are in the...
- If the constant term in the binomial expansion of ( x- k x^2 )^ 10 is 405, then |k| equals
- If a, b and c are the greatest values of ^ 19 C_p, ^ 20 C_q and ^ 21 C_r respectively, then
- The value of - ^ 15 C_1+2 ^ 15 C_2-3 ^ 15 C_3+ -15 ^ 15 C_ 15 + ^ 14 C_1+ ^ 14 C_3+ ^ 14 C_5+ + ^ 14 C_ 11 is
- If n 2 is a positive integer, then the sum of the series ^ n+1 C_2+2 ( ^2C_2+ ^3C_2+ ^4C_2+ + ^nC_2 ) is
- The maximum value of the term independent of 't' in the expansion of (tx^ 15 + (1-x)^ 1 10 t )^ 10 where x (0,1) is
- If n is the number of irrational terms in the expansion of (3^ 14 +5^ 18 )^ 60 , then (n-1) is divisible by
- Let [x] denote greatest integer less than or equal to x. If for n N, (1-x+x^3 )^n= _ j=0 ^ 3n a_jx^j, then _ j=0 ^ [ 3n 2 ] a_ 2j...
- If the fourth term in the expansion of (x+x^ _2x )^7 is 4480, then the value of x where x N is
- The value of _ t=0 ^6 ( ^6C_t ^6C_ 6-t ) is equal to
- Let (1+x+2x^2)^ 20 =a_0+a_1x+a_2x^2+ +a_ 40 x^ 40 . Then a_1+a_3+a_5+ +a_ 37 is equal to
- If b is very small as compared to the value of a, so that the cube and other higher powers of ba can be neglected in the identity...
- If the greatest value of the term independent of 'x' in the expansion of (x +a x )^ 10 is 10! (5!)^2 , then the value of 'a' is...
- The sum of all those terms which are rational numbers in the expansion of (2^ 1/3 +3^ 1/4 )^ 12 is
- If _ k=1 ^ 31 31 k 31 k-1 - _ k=1 ^ 30 30 k 30 k-1 = (60!) (30!)(31!) , where R, then the value of 16 is equal to
- The term independent of x in the expansion of (1-x^2+3x^3 ) ( 52x^3- 1 5x^2 )^ 11 , x 0 is
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