If `sum_(r=0)^2017 1/(7^r+7^(2017/2))=alpha/(sqrt7)^beta` where `alpha and beta` are coprime then `[beta/alpha]=` [Note: [k] denotes greatest integer function less than or equal to k.

If the value of the integral int_0^5 (x + [x])/(e^(x - [x])) dx = alphae^(-1) + beta ,where alpha, beta in R, 5alpha + 6beta = 0, and [x] denotes the greatest integer less than or equal to x, then the value of (alpha + beta )^2 is equal to :

sum_(k=0)^10 (2^k+3)^(10)C_(k)=alpha*2^10+beta*3^10 then value of alpha+beta

If the integral int_(0)^(10) ([sin2pi x])/(e^(x-[x]))dx=alpha e^(-1)+beta e^(-(1)/(2))+gamma , where alpha, beta, gamma are integers and [x] denotes the greatest integer less than or equal to x, then the value of alpha+beta+gamma is equal to :

If sum_(r=1)^9 ((r+3)/2^r)(.^9C_r)=alpha(3/2)^9+beta , then alpha+beta is equal to :

If complete solution set of e ^(-x) le 4- x is [alpha, beta] then [alpha] + [beta ] is equal to : (where [.] denotes greatest integer function )

If complete solution set of e ^(-x) le 4- x is [alpha, beta] then [alpha] + [beta ] is equal to : (where [.] denotes greatest integer function )

If cos alpha=13/14 and cos beta=1/7 where alpha and beta are acute angles,show that alpha-beta=pi/3 .

If alpha , beta are the zeroes of x^2+7x+10 , then alpha beta =