If `a_(1),a_(2),a_(3), . . . .,a_(n+1)` be (n+1) different prime numbers, then the number of different factors (other than 1) of `a_(1)^(m),a_(2)*a_(3), . . ,a_(n+1)` is

If a_(1), a_(2),….,a_(n) are n(gt1) real numbers, then

If a_(1), a_(2), a_(3), a_(4), a_(5) are consecutive terms of an arithmetic progression with common difference 3, then the value of |(a_(3)^(2),a_(2),a_(1)),(a_(4)^(2),a_(3),a_(2)),(a_(5)^(2),a_(4),a_(3))| is

If a_(1),a_(2),a_(3), . . .,a_(n) are non-zero real numbers such that (a_(1)^(2)+a_(2)^(2)+ . .. +a_(n-1).^(2))(a_(2)^(2)+a_(3)^(2)+ . . .+a_(n)^(2))le(a_(1)a_(2)+a_(2)a_(3)+ . . . +a_(n-1)a_(n))^(2)" then", a_(1),a_(2), . . . .a_(n) are in

If a_(1), a_(2), …..,a_(n) are in A.P. with common difference d ne 0, then the sum of the series sin d[sec a_(1)sec a_(2) +..... sec a_(n-1) sec a_(n)] is

If a_(1), a_(2), a_(3),...., a_(n) is an A.P. with common difference d, then prove that tan[tan^(-1) ((d)/(1 + a_(1) a_(2))) + tan^(-1) ((d)/(1 + a_(2) a_(3))) + ...+ tan^(-1) ((d)/(1 + a_( - 1)a_(n)))] = ((n -1)d)/(1 + a_(1) a_(n))

The number of all three element subsets of the set {a_(1),a_(2),a_(3)......a_(n)} which contain a_(3) , is

If a_(1), a_(2), . . . , a_(n) is a sequence of non-zero number which are in A.P., show that (1)/(a_(1)a_(n))+(1)/(a_(2)a_(n-1))+. . . + (1)/(a_(n)a_(1))= (2)/(a_(1) + a_(n)) [(1)/(a_(1))+(1)/(a_(2))+. . . +(1)/(a_(n))]

If A_(1), A_(2),..,A_(n) are any n events, then

If A_(1), A_(2), A_(3),....A_(51) are arithmetic means inserted between the number a and b, then find the value of ((b + A_(51))/(b - A_(51))) - ((A_(1) + a)/(A_(1) - a))

If a_(1),a_(2),a_(3),a_(4),,……, a_(n-1),a_(n) " are distinct non-zero real numbers such that " (a_(1)^(2) + a_(2)^(2) + a_(3)^(2) + …..+ a_(n-1)^(2))x^2 + 2 (a_(1)a_(2) + a_(2)a_(3) + a_(3)a_(4) + ……+ a_(n-1) a_(n))x + (a_(2)^(2) +a_(3)^(2) + a_(4)^(2) +......+ a_(n)^(2)) le 0 " then " a_(1), a_(2), a_(3) ,....., a_(n-1), a_(n) are in