`5^(@)=5` (T/F)

Let E and F be tow independent events.The probability that exactly one of them occurs is 11/25 and the probability if none of them occurring is 2/25. If P(T) deontes the probability of occurrence of the event T, then P(E)=(4)/(5),P(F)=(3)/(5)P(E)=(2)/(5),P(F)=(1)/(5)P(E)=(2)/(5),P(F)=(1)/(5)P(E)=(3)/(5),P(F)=(4)/(5)

If int_(0)^(x)f(t)dt=x^(2)+int_(x)^(1)(:t^(2)backslash f(t)dt, then f((1)/(2)) is equal to (a) (24)/(25) (b) (4)/(25) (c) (4)/(5) (d) (2)/(5)

Let f: R to R be defined by f(x) = 5^(2x)/(5^(2x) + 5) , then f(x) + f(1-x) is equal to

Let f(x) polynomial of degree 5 with leading coefficient unity such that f(1)=5 ,f(2)=4,f(3)=3,f(4)=2,f(5)=1, then f(6) is equal to

s=5t^(3)-3t^(5)

If f(x) is differentiable and int_(0)^(t^2)xf(x)dx=(2)/(5)t^5 ,then 5 f((4)/(25)) is equal to ....

If f(x) is differentiable and int_(0)^(t^(2))xf(x)dx=(2)/(5)t^(5), then f((4)/(25)) equals (a)(2)/(5)(b)-(5)/(2)(c)1(d)(5)/(2)

If f and g are real fucntions defined by f(x)=x^(2)+7 and g (x) 3x+5 Then , find each of the following . f(3)+g(-5) (ii) f((1)/(2)) xxg(14) (iii) f(-2)+g(-1) (iv) f(t)-f(-2) (v) (f(t)-f(5))/(t-5)if t ne5

If int _(0) ^(k) f (t) d t = x ^(2) + int _(x) ^(1) t ^(2) f (t) d t, if f '(1//2) is (24)/(5 ^(k)), then the vlaue of k is