If `2tan^2x-5secx=1` for exactly seven distinct value of `x in [0,(npi)/2],n in N` then find the greatest value of `ndot`

If tan^(2)x-5sec x=1 is satisfied by exactly seven distinct values of x in[0,((2n+1)pi)/(2)],n in N, then the greatest value of n is

If tan^(2)theta-sec theta-5=0 for exactly 9 values of theta in[0,(n pi)/(2)];n in N, then the greatest value of n is

If "sin"^(2) theta -2"sin" theta-1 = 0 is to be satisfied for exactly 4 distinct values of theta in [0, n pi], n in Z , then the least values of n, is

2 cot^2 x - 5 cos e c x is equal to 1 for exactly 6 distinct values of x ∈ [ 0 , n π ] then the greatest value of n is __________________

"If " 2"tan"^(2) theta - 5 "sec" theta = 1 has exactly 7 solution in the interval [0, n pi//2], n in N , then the least and greatest values of n are

If the equation sin ^(2) x - k sin x - 3 = 0 has exactly two distinct real roots in [0, pi] , then find the values of k .

If lim_(x rarr 2) [(x^(n)-2^(n))/(x-2)]=32 , then find the value of n.

If 2tan^2theta-5sectheta=1 has exactly 7 solutions in [0,(npi)/2] for least value of ninN , then sum_(k=1)^nk/(2n) is equal to..................

If x^(4) + 2kx^(3) + x^(2) + 2kx + 1 = 0 has exactly tow distinct positive and two distinct negative roots, then find the possible real values of k.

If 25^n^(-1)+100=5^(2n)^(-1), find the value of ndot