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 `b=(log)_(sqrt(3))3,\ c=2(log)_bsqrt(b)` and `sintheta`=a (where x >1) then `theta` can be a.`pi/4` b. `\ (3pi)/2` c.`\ pi/2` d. `0`

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=2\ x=a^((log)_5 25)&\ c=sqrt(2) , then b is- a. 2 b. \ 16 c. \ 12 d. 2

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=2\ x=a^((log)_5 25)&\ c=sqrt(2) , then b is a. 2 b. \ 16 c. \ 12 d. 2

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 costheta+sqrt(3)sintheta=2, then theta= a. pi//3 b. 2pi//3 c. 4pi//3 d. 5pi//3

The number of roots of the equation (log)_(3sqrt("x"))x+(log)_(3x)sqrt(x)=0 is 1 (b) 2 (c) 3 (d) 0

The number of solutions of (log)_4(x-1)=(log)_2(x-3) is (a) 3 (b) 1 (c) 2 (d) 0

The smallest positive value of x (in radians) satisfying the equation (log)_(cosx)((sqrt(3))/2sinx)=2-(log)_(secx)(tanx), is pi/(12) (b) pi/6 (c) pi/4 (d) pi/3

The smallest positive value of x (in radians) satisfying the equation (log)_(cosx)((sqrt(3))/2sinx)=2-(log)_(secx)(tanx) is (a) pi/(12) (b) pi/6 (c) pi/4 (d) pi/3

For 0 cos^(-1)(sintheta) is true when theta belongs to (a) (pi/4,pi) (b) (pi,(3pi)/2) (c) (pi/4,(3pi)/4) (d) ((3pi)/4,2pi)

The domain of the function f(x)=(log)_e{(log)_(|sinx|)(x^2-8x+23)-{3/((log)_2|sinx|)} contains which of the following interval(s)? 3,pi) (b) (pi,(3pi)/2) (c) ((3pi)/2,5) (d) none of these