For eR let [x] denote the greatest integer `le x.` Largest natural number `n` for which `E=[pi/2]+[1/100+pi/2]+[2/100+pi/2]+[n/100+pi/2]<43,` is

For eR let [x] denote the greatest integer <=x. Largest natural number n for which E=[(pi)/(2)]+[(1)/(100)+(pi)/(2)]+[(2)/(100)+(pi)/(2)]+[(n)/(100)+(pi)/(2)]<43

Let [a] denote the greatest integer which is less than or equal to a. Then the value of the integral int_(-pi/2)^(pi/2) [ sin x cos x] dx is

Let X_(n) denote the mean of first n natural numbers, then the mean of X_(1), X_(2), ………….., X_(100) is

Let X_(n) denote the mean of first n natural numbers, then the mean of X_(1), X_(2), ………….., X_(100) is

If [.] denotes the greatest integer function , then lim_(xrarr pi//2)[(x-(pi)/(2))/(cos x)] is equal to.

Let [x] denote the greatest integer less than or equal to x and g (x) be given by g(x)={{:(,[f(x)],x in (0","pi//2) uu (pi//2","pi)),(,3,x=(pi)/(2)):} "where", f(x)=(2(sin x-sin^(n)x)+|sinx-sin^(n)x|)/(2(sinx-sin^(n)x)-|sinx-sin^(n)x|),n in R^(+) then at x=(pi)/(2),g(x) , is

Let [x] denote the greatest integer less than or equal to x and g (x) be given by g(x)={{:(,[f(x)],x in (0","pi//2) uu (pi//2","pi)),(,3,x=(pi)/(2)):} "where", f(x)=(2(sin x-sin^(n)x)+|sinx-sin^(n)x|)/(2(sinx-sin^(n)x)-|sinx-sin^(n)x|),n in R^(+) then at x=(pi)/(2),g(x) , is