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 the function f(x)= 2x^(3)-9ax^(2) +12a^(2)x +1 , where a gt 0 attains its maximum and minimum at x=p and x=q respectively, such that p^(2)=q , then the value of a is-

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

The function f(x)=sqrt(a x^3+b x^2+c x+d) has its non-zero local minimum and local maximum values at x=-2 and x = 2 , respectively. If a is a root of x^2-x-6=0 , then find a,b,c and d.

Find the maximum and minimum values, if any, of the functions given by f (x) = (2x – 1)^(2)+ 3

It is given that at x = 1, the function x^(4) – 62x^(2) + ax + 9 attains its maximum value, on the interval [0, 2]. Find the value of a.

For the equation 3x^2+p x+3=0,p >0, if one of the root is square of the other, then p is equal to (a) 1//3 b. 1 c. 3 d. 2//3

A straight line through the origin 'O' meets the parallel lines 4x +2y= 9 and 2x +y=-6 at points P and Q respectively. Then the point 'O' divides the segment PQ in the ratio : (A) 1:2 (B) 3:2 (C) 2:1 D) 4:3

If range of function f(x)=sin^(-1)x+2tan^(-1)x+x^2+4x+1 is [p , q], then the value of (p+q) is_______>

If sec alpha and alpha are the roots of x^2-p x+q=0, then (a) p^2=q(q-2) (b) p^2=q(q+2) (c) p^2q^2=2q (d) none of these

The circle C1 : x^2 + y^2 = 3 , with center at O, intersects the parabola x^2 = 2y at the point P in the first quadrant. Let the tangent to the circle C1 at P touches other two circles C2 and C3 at R2 and R3, respectively. Suppose C2 and C3 have equal radii 2sqrt(3) and centers Q2 and Q3, respectively.If Q_2 and Q_3 lies on the y-axis, then find Q_(2)Q_(3)=12 and R_(2)R_(3)=4sqrt(6)