If `sin^2x-2sinx-1=0` has exactly four different solutions in `x in [0,npi]` , then value/values of `n` is/are `(n in N)` 5 (b) 3 (c) 4 (d) 6

If f(x)=sgn(sin^(2)x-sin x-1) has exactly four points of discontinuity for x in(0,n pi),n in N, then

If the equation x^(2)+12+3sin(a+bx)+6x=0 has atleast one real solution, where a, b in [0,2pi] , then the value of a - 3b is (n in Z)

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

f(x)=[2+3|n|sin x],n in N,x in(0,pi) has exactly 11 points of discontinuity Then the value of n is

The equation x^(3)+3x^(2)+6x+3-2cosx=0 has n solution(s) in (0, 1), then the value of (n+2) is equal to

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 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=1\ a n d\ y=6 is a solution of the equation 8x-a y+a^2=0 , find the value of a

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