If the function `f(x)=2x^3-9ax^2+12a^2x+1,` where `a gt 0,` attains its maximum and minimum at `p and q,` respectively, such that `p^2=q,` then `a` equal to (a) `1` (b) `2` (c) `1/2` (d) `3`

If f(x)=x^5-5x^4+5x^3-10 has local maximum and minimum at x=p and x=q , respectively, then (p , q)= (a) (0,1) (b) (1,3) (c) (1,0) (d) none of these

Given the function f(x)=x^2e^-(2x) ,x>0. Then f(x) has the maximum value equal to a) e^-1 b) (2e)^-1 . c) e^-2 d) none of these

The function 'f' is defined by f(x)=x^p(1-x)^q for all x\ in R , where p ,\ q are positive integers, has a maximum value, for x equal to : (p q)/(p+q) (b) 1 (c) 0 (d) p/(p+q)

If p and q are the roots of the equation x^2-p x+q=0 , then (a) p=1,\ q=-2 (b) p=1,\ q=0 (c) p=-2,\ q=0 (d) p=-2,\ q=1

If f(x) = px +q, where p and q are integers f (-1) = 1 and f (2) = 13, then p and q are

If the roots of the equation 1/ (x+p) + 1/ (x+q) = 1/r are equal in magnitude but opposite in sign, show that p+q = 2r & that the product of roots is equal to (-1/2)(p^2+q^2) .

suppose x_1, and x_2 are the point of maximum and the point of minimum respectively of the function f(x)=2x^3-9ax^2 + 12a^2x + 1 respectively, (a> o) then for the equality x_1^2 = x_2 to be true the value of 'a' must be

f(x)={(sqrt(1+p x)-sqrt(1-p x))/x ,-1lt=x<0(2x+1)/(x-2),0geqxgeq1 is continuous in the interval [-1,1], then p is equal to -1 (b) -1/2 (c) 1/2 (d) 1

f(x)={(sqrt(1+p x)-sqrt(1-p x))/x ,-1lt=x<0(2x+1)/(x-2),0geqxgeq1 is continuous in the interval [-1,1], then p is equal to -1 (b) -1/2 (c) 1/2 (d) 1

If f : R->Q (Rational numbers), g : R ->Q (Rational numbers) are two continuous functions such that sqrt(3)f(x)+g(x)=4 then (1-f(x))^3+(g(x)-3)^3 is equal to (1) 1 (2) 2 (3) 3 (4) 4