Verify the theorem proved above for p= 2, p = 5 and for `a^2` = 1, 4, 9, 25, 36, 49, 64 and 81.

Verify the statement proved above for p=2, p=5 and for a^2=1,4,9,25,36,49,64 and 81.

Verify Rolle's theorem of the function log(x^2+2)-log 3 on (-1,1)

Verify mean value theorem for the function f(x)=x^(2) on [2,4]

Using binomial theorem prove that 50^n - 49n - 1 is divisible by 49^2, AA n in N

Verify that 3, -1, -1/3 are the zeroes of the cubic polynomial p(x) = 3x^(2)-5x^(2)-11x-3 , and then verify the relationship between the zeroes and the coefficients.

Verify proportion (or) not. a) 2:3 and 4:5, b) 8:9 and 9:8.

Explain why each of the lists above is a G.P. (i) 1, 4, 16, 64, 256,.......

If P(x) = X^2+ 5x + 4 , find p(1) and P(-1).

I : If the distances from P to the points ( 3,4), ( - 3, 4) are in the ratio 3 : 2 , then the locus of P is 5 x ^ 2 + 5y ^ 2 + 78 x - 40 y + 125 = 0 II : A ( -9, 0) , B( -1, 0) are two points. If P is a point such that P A : PB = 3 : 1 , then the locus of P is x ^ 2 + y^ 2 = 9