`a+i bltc+i d ` i s m e a n i n g f u l , i f

Let f: ZrarrZ be defined by f(n)=3n for all n in Z and g: ZrarrZ be defined by g(n)={(n/3,if n "is a m u l ti pl e of" 3),(0,if n "i s no t m u l t i p l e of" 3):} for all n in Z Show that gof=I_Z and fog!=I_Z

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

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

Let f: NvecN be defined by f(n)={(n+1)/2,\ "if"\ n\ "i s\ o d d"n/2,\ \ "if\ "n\ "i s\ e v e n"\ \ for\ a l l\ n\ \ N} Find whether the function f is bijective.

The empirical relation between mean, mode and median is Mod e = 3 M e d i a n -2 M e a n Mod e=2 M e d i a n-3 M e a n M e d i a n=3 Mod e-2 M e a n M e a n=3 M e d i a n-2 Mod e

The percentage of marks obtained by a student in the monthly unit tests are given below: U n i t\ t e s t : I I I I I I I V V P e r c e n t ag e\ of\ m a r k s\ ob t a i n e d : 58 74 76 62 85 Find the probability that the student gets: (i) a first class i.e. at least 60% marks (ii) marks between 70% and 80% (iii) a distinction i.e. 75% or above (iv) less than 65% marks.

Let f: NvecN be defined by f(n)={(n+1)/2, "if" n "i s o d d"n/2, "if "n "i s e v e n" for a l l n N} Find whether the function f is bijective.

Let f: Nuu{0}->Nuu{0} be defined by f={(n+1 ,, ifn \ i s \ e v e n),(n-1 ,, ifn \ i s \ od d):} Show that f is a bijection.

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