If `sintheta=-1/2a n d\ t a ntheta=1/(sqrt(3))t h e n\ theta` s equal to- `30^0` b.`150^0` c.`210^0` d.none of these

2(sin^6theta+cos^6theta)-3(sin^4theta+cos^4theta)+1 is equal to a. 0 b.1 c.-2 d. none of these

If z=(i)^(i)^(i) where i=sqrt(-1),t h e n|z| is equal to 1 b. e^(-pi//2) c. e^(-pi) d. none of these

If (sin3theta)/(sintheta)=(11)/(25)\ t h e ntan(theta/2) can have the value equal to- a. 2 b. 1/2 c. -2 d. -1/2

If D_p=|p 15 8p^2 35 9p^3 25 10|,\ t h e n\ D_1+D_2+D_3+D_5 is equal to- a. 0 b. 25 c. 625 d. none of these

If vec b is a vector whose initial point divides thejoin of 5 hat ia n d5 hat j in the ratio k :1 and whose terminal point is the origin and | vec b|lt=sqrt(37),t h e nk lies in the interval a. [-6,-1//6] b. (-oo,-6]uu[-1//6,oo) c. [0,6] d. none of these

The number of real solutions of the equation (9//10)^x=-3+x-x^2 is a. 2 b. 0 c. 1 d. none of these

The values of sintheta_(1), cos^(2)theta_(2) and tan theta_(3) are given as 0.5, -0.5 and 3 (not in order), for some angles theta_(1), theta_(2) and theta_(3) . Choose incorrect statement.

If theta_(1)=(25.5+-0.1)^(@)C and theta_(2)=(35.3+-0.1)^(C) , then find theta_(1)-theta_(2) .

If A+B+C=pi,\ t h e n\ |"sin"(A+B+C) sinB cosC -sinB 0 tanA "cos"(A+B) -tanA 0| is equal to a. 2sinB tanA cosC b. 1 c. 0 d. none of these

If x^2+y^2+z^2=r^2,t h e ntan^(-1)((z y)/(x r))+tan^(-1)((x z)/(y r))+tan^(-1)((x y)/(z r)) is equal to pi (b) pi/2 (c) 0 (d) none of these