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

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

Let a,b,c,d be the four consecutive coefficients of the binomial expansion (1+x)^n On the basis of above information answer the following question: a/(a+b), b/(b+c), c/(c+d) are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

Evaluate: int(a x^2+b x+c)/((x-a)(x-b)(x-c))\ dx ,\ \ w h e r e\ a ,\ b ,\ c are distinct.

(log)_(A E)((A C)/(C D)) is equal to a. sqrt(2) b. \ 1 c. \ 0 d. -1

If log_(b)5=a,log_(b)2.5=c,and5^(x)=2.5 , then x=

If x=(log)_k b=(log)_b c=1/2(log)_c d ,t h e n(log)_k d is equal to 6x b. (x^3)/2 c. 2x^3 d. 2x^8

Statement I: the equation (log)_(1/(2+|"x"|))(5+x^2)=(log)_()(15+sqrt(x)) has real solutions. Because Statement II: (log)_(1//"b")a=(log)_b a\ (w h e r e\ a ,\ b >0\ a n d\ b!=1) and if number and base both are greater than unity then the number is positive. a. A b. \ B c. \ C d. D

The minimum value of x\ (log)_e x is equal to e (b) 1//e (c) -1//e (d) 2e (e) e

Find the value of 49^A+5^B w h e r e\ A=1-(log)_7 2\ &\ B=-(log)_5 4.