If f is an even function, then prove that \(\overset{lim f(x)}{x\rightarrow 0^{-}}=\overset{lim f(x)}{x\rightarrow 0^{+}}\)

Two die are rolled. Find the probability of getting: (i)a total of 8 or a doublet (ii)an even number on the first die or a total of 7

Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.
3y²-2x²=1

Find two numbers whose A.M. is 34 and G.M. is 16

If A and B are two mutually exclusive events in a sample space such that P(A) = 0.3 and P(B)= 0.6 then find \(P(A\cup B)\)

Reduce the equation 5x - 3y + 11 = 0 to the slope-intercept form and find its slope and intercept.

In how many ways can 5 letters be posted in 4 letter boxes?

Find the intersection of each of the following pairs of sets:
A = {x : x ∊ N, 5 \(\le\) x \(\le\) 10}, B = {x : x ∊ N, 15 \(\le\) x \(\le\) 20}

Evaluate the following limits \(\overset{lim}{x\rightarrow 4}\) \(\frac{4x+3}{x-2}\)

Find the equation of a circle touching both the axis and passing through the point (6, 3).

A and B are two events, such that P(A)=0.42, P(B)=0.48 and P(A and B)=0.16. Determine P(not B)

If A = {3,{4,5},6}, then find the following statement are true? 
\(\phi \subset\) A

Consider the following sets  \(\phi\) , A = {2,5}, B = {1,2,3,4} and C = {1,2,3,4,5} Insert the correct symbol  \(\subset\)  or \(\nsubseteq\)  between the pair set 
A.......C

Find the union of each of the following pair of sets A = {1, 3, 5}, B = {1, 2, 3}

Let n(U) = 700, n(A) = 200, n(B) = 300 and \(n(A\cap B)\) = 100 .Find \(n({ A }^{ ' }\cap { B }^{ ' })\).