Let `S(k) = 1 + 3 + 5 +...+ (2k -1) = 3 + k^2`. Then which of the following is true ?

Let s_1 = {(i,j, k) ∶ i,j, k ∈ {1,2, … ,10}} , s_2 = {(i,j) ∶ 1 ≤ i s_3 = {(i,j, k, l) ∶ 1 ≤ i s_4 = {(i,j, k, l) ∶ i,j, k and l are distinct elements in {1,2, … ,10}} . If the total number of elements in the set s_r is n_r , r= 1,2,3,4, then which of the following statements is (are) TRUE ?

Let alpha,beta and gamma be the roots of the equation x^(3)-x-1=0 . If P_(k)=(alpha)^(k)+(beta)^(k)+(gamma)^(k),kge1 , then which one of the following statements is not true?

If (tan3A)/(tan A)=k(k!=1) then which of the following is not true? (a) (cos A)/(cos3A)=(k-1)/(2)(b)(sin3A)/(sin A)=(2k)/(k-1)(c)(cot3A)/(cot A)=(1)/(k)(d) none of these

Let alpha and beta be the roots of the equation x^(2)-x-1=0 .If p_(k)=(alpha)^(k)+(beta)^(k),k>=1 then which one of the following statements is not true?

Let S _(K) = sum _(r=1) ^(k) tan ^(-1) (( 6 ^r)/( 2 ^( 2 r + 1) + 3 ^( 2r +1))) . Then lim _( k to oo) S _(k) is equal to :