`pi/2ltxltpiw r i t e t h e d e r i v a t i v e o fsqrt((1+cos2x)/2)w i t h r e s p e c t t ox`

Differentiate: (logx)^x+x^(logx)w i t hr e s p e c t to x :

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

In a bucket is 80% full, then it contains 2 litres more water than I is 66 2/3% full. What is the capacity of the bucket? 10 l i t r e s b. 15 l i t r e s c. 16 2/3l i t r e s d. 20 l i t r e s

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

Assuming full occupancy, a bogie of which class exhibits the highest profit margin? 3 t i e r b. A C-3 t i e r c. A C-t i e r d. A C-fi r s t c l a s s

If S_n=sum_(r=1)^n r !(n >6),"t h e nf i n dt h ev a l u eo f" [cot^(-1)(cot(s_n-7[(S_n)/7]))],"w h e r e"[dot]"d e n o t e sg r e a t e s t" integer function

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.

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: a first class i.e. at least 60% marks marks between 70% and 80% a distinction i.e. 75% or above less than 65% marks.

. Raj and Suraj bought a bottle of water together in which there was 2 litres of water. Raj drank 1/4 th part of it. The rest water was drunk by Suraj. Find the amount of water used by Suraj. 1. 5 l i t r e s b. 0. 5 l i t r e s c. 2. 5 l i t r e s d. 2 l i t r e s

The area bounded by the curves y=x e^x ,y=x e^(-x) and the line x=1 is 2/e s qdotu n i t s (b) 1-2/e s qdotu n i t s 1/e s qdotu n i t s (d) 1-1/e s qdotu n i t s