`I fx+1/x=2,`t h e p r i n c i p a l v a l u e o f `sin^(-1)x` is

IfI_n=int_x^pix^nsinx dx ,t h e n fin d t h e v a l u eof I_5+20 I_3dot

IfI_n=int_0^pix^nsinx dx ,t h e n fin d t h e v a l u eof I_5+20 I_3dot

IfI_n=int_0^pix^nsinx dx ,t h e n fin d t h e v a l u eof I_5+20 I_3dot

f: Rvec[-1,oo)a n df(x)=1n([|s in2x|+|cos2x|]) (where [.] is the greatest integer function.) Then, f(x)h a sr a ngZ f(x)i sp e r iod i cw i t hfu n d a m e n t a lp e r iodpi/4 f(x)i sin v e r t i b l ein[0,pi/4] f(x)i sin tofu n c t iondot

f(x)=int_1^x(tan^(-1)(t))/t dtAAx in R^+,t h e nfin dt h ev a l u eof f(e^2)-f(1/(e^2))

A B C D is a cyclic quadrilateral in which B A\ a n d\ C D when produced meet in E\ a n d\ E A=E Ddot Prove that: (i) A D is p a r a l l e l t o B C (ii) E B=E C

f: Rvec[-1,oo)a n df(x)=1n([|s in2x|+|cos2x|]) (where [.] is the greatest integer function.) Then, (a) f(x)h a sr a ngZ (b) f(x)i sp e r iod i c function (c) f(x)i sin v e r t i b l ein[0,pi/4] (d) f(x) is into function

Each question is based on the following alphabet-series : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z In the following letter sequence, how many n's are followed by m but not preceded by h ? a g r h t n m b e n m l b u v n m h er h n m g f e h n m e c n m w q a n m h l b

The complex number which satisfies the condition |(i+z)/(i-z)|=1\ lies on a. c i r c l e\ x^2+y^2=1 b. t h e\ x-a xi s c. t h e\ y-a xi s d. t h e\ l in e\ x+y=1

The solution of the differential equation 2x(dy)/(dx)-y=3 represents (a) c i r c l e s b.straight lines c. e l l i p s e s d. p a r a bol a s