" If harmonic mean of "(1)/(2),(1)/(2^(2)),(1)/(2^(3)),....,(1)/(2^(10))" is "(lambda)/(2^(10)-1)" then "lambda=

If harmonic mean of numbers (1)/(2),(1)/(2^(2)),(1)/(2^(3)),............(1)/(2^(10)) is (lambda)/(2^(10)-1) then lambda is equal to

If (1)/(n+1)+(1)/(2(n+1)^(2))+(1)/(3(n+1)^(3))+….= lambda((1)/(n)-(1)/(2n^(2))+(1)/(3n^(3))-……) then lambda=

If (1)/(n+1)+(1)/(2(n+1)^(2))+(1)/(3(n+1)^(3))+….= lambda((1)/(n)-(1)/(2n^(2))+(1)/(3n^(3))-……) then lambda=

Let N=(2+1)(2^(2)+1)(2^(4)+1).........(2^(32)+1)+1 and N=2^(lambda) then the value of lambda is

Let alpha and beta be the values of x obtained form the equation lambda^(2) (x^(2)-x) + 2lambdax +3 =0 and if lambda_(1),lambda_(2) be the two values of lambda for which alpha and beta are connected by the relation alpha/beta + beta/alpha = 4/3 . then find the value of (lambda_(1)^(2))/(lambda_(2)) + (lambda_(2)^(2))/(lambda_(1)) and (lambda_(1)^(2))/lambda_(2)^(2) + (lambda_(2)^(2))/(lambda_(1)^(2))

The number of distinct real values of lambda for which the lines (x-1)/(1)=(y-2)/(2)=(z+3)/(lambda^(2)) and (x-3)/(1)=(y-2)/(lambda^(2))=(z-1)/(2) are coplanar is

Transition between three energy energy levels in a particular atom give rise to three Spectral line of wevelength , in increasing magnitudes. lambda_(1), lambda_(2) and lambda_(3) . Which one of the following equations correctly ralates lambda_(1), lambda_(2) and lambda_(3) ? lambda_(1)=lambda_(2)-lambda_(3) lambda_(1)=lambda_(3)-lambda_(2) (1)/(lambda_(1))=(1)/(lambda_(2))+(1)/(lambda_(3)) (1)/(lambda_(2))=(1)/(lambda_(3))+(1)/(lambda_(1))

int_(2)^(4) (3x^(2)+1)/((x^(2)-1)^(3))dx = (lambda)/(n^(2)) where lambda, n in N and gcd(lambda,n) = 1 , then find the value of lambda + n