[" Let "S-={a in N,a<=100}." If the equation "[tan^(2)x]-tan x-a=0" has real roots.Find "],[" the number of elements of "S" ."]

Let S={n in N ,[(0,i),(i,0)]^n[(a,b),(c,d)]=[(a,b),(c,d)] forall a,b,c,d in R. Find the number of 2-digit numbers in S

Let S_(k)=lim_(n rarr oo)sum_(i=0)^(n)(1)/((1+k)^(i)). Then sum_(k=1)^(n)kS_(k) equals:

Let S_(n) be the sum of n terms of an A.P. Let us define a_(n)=(S_(3n))/(S_(2n)-S_(n)) then sum_(r=1)^(oo)(a_(r))/(2^(r-1)) is

Let S_n = cos ((n pi )/( 10)) , n = 1,2,3,…… then the value of ( s_1 s_2 ……s_(10))/( s_1 + s_2 +…….. +s_(10)) is equal to

Let S = N xx N and ast is a binary operation on S defined by (a,b)^**(c,d) = (a+c, b+d) for all a,b,c,d in N .Prove that ** is an associate binary operation on S.

Let S_(n)=1+2+3+...+n and P_(n)=(S_(2))/(S_(2)-1)*(S_(3))/(S_(3)-1)*(S_(4))/(S_(4)-1)...(S_(n))/(S_(n)-1) Where n in N,(n>=2). Then lim_(x rarr oo)P_(n)=

Let S_n=1+2+3++n and P_n=(S_2)/(S_2-1)*(S_3)/(S_3-1)*(S_4)/(S_4-1)* . . . *(S_n)/(S_n-1) Where n in N ,(ngeq2)dot Then lim_(n→oo)P_n=______

Let alpha,beta , be the roots of the equation x^2+x-1=0 . Let S_n=alpha^n+beta^n "for" n ge 1 . Evaluate the determinant |{:(3,1+s_1,1+s_2),(1+s_1,1+s_2,1+s_3),(1+s_2,1+s_3,1+s_4):}|