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

If s e ctheta+t a ntheta=5 . where theta in (0,pi//2) , then "tan"(theta//2) is equal to a. -2//3 b. 3//2 c. -3//2 d. none of these

If m ,n in Na n dm^2-n^2=13 ,t h e n(m+1)(n+1) is equal to a. 42 b. 56 c. 50 d. none of these

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

If x+i y=(1+i)(1+2i)(1+3i),\ t h e n\ x^2+y^2 is: (a) . 0 (b) . 1 (c) . 100 (d) . none of these

If b_(n+1)=1/(1-b_n)forngeq1a n db_1=b_3, t h e nsum_(r=1)^(2001)b r^ 2001 is equal to a. 2001 b. -2001 c. 0 d. none of these

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 cottheta-t a ntheta=s e ctheta , then theta is equal to 2npi+(3pi)/2, n Z b. npi+(-1)^npi/6,\ n Z c. npi+pi/2, n Z d. none of these

Comprehension 1 Let a^((log)_b x)=c\ w h e r e\ a ,\ b ,\ c\ &\ x\ are parameters. On the basis of above information, answer the following questions: If a=b=2xx3^sin^2theta+1/(1+tan^(2theta))\ &\ c=(4\ t a ntheta)/(sqrt(sec^2theta-1))(w h e r e\ theta lies in Ist Quadrant ) , then x is- a. 3 b. -3 c. \ 0 d. 4

If A+B+C=180^0 , then (t a n A+t a n B+t a n C)/(t a n A\ t a n B\ t a n C) is equal to a. t a n A t a n B t a n C b. 0 c. 1 d. none of these

(cos e c\ theta-sintheta)(sectheta-costheta)(tantheta+cottheta) is equal (a) 0 (b) 1 (c) -1 (d) None of these