Mathematics questions
18011 published questions with worked solutions.
- 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...
- 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