Consider the parabola y2 = 4x. A = (4, –4) and B = (9, 6) be two fixed points on the parabola. Let ‘C’ be moving point on the parabola between A and B such that the area of triangle ABC is maximum, then coordinate of ‘C’ is
y2 = 4x
If f (x) is a polynomial of degree 5 with real coefficients such that has 8 real roots then f (x) = 0 has:
If the function f (x) = | x2 + a | x | +b| has exactly three points of non-differentiability, then which of the following can be true?
If f (x) = loge x and g(x) = x2 and c Ïµ (4, 5), then is equal to:
If the equation has four solution then be lies in:
If the function f (x) = x3 – 9x2 + 24x + c has three real and distinct roots α, β and γ then the value of [α] + [β] + [γ] is,:
If at each point of the curve y = x3 – ax2 + x + 1 the tangents is inclined at an acute angle with the positive direction of the x-axis, a lies in the interval.
Two variable curves C1 : y2 = 4a (x – b1) and C2 : x2 = 4a (y – b2) where ‘a’ is a given positive real no. and b1 and b2 are variable such that C1 and C2 are tangents to each other at point of contact then locus of point of contact is:
f : R âŸ¶ R be a differentiable function ∀ x Ïµ R. If tangent drawn to the curve at any point x Ïµ (a, b) always lie below the curve then
A lamp of negliligible height is placed on the ground ‘l1’ m away from a wall. A man ‘l2’ m tall is walking at a speed of m/sec from the lamp to the nearest point on the well. When he is midway between the lamp and the wall, the rate of change in the length of his shadow on the wall is
If the rate of change of volume of a sphere is the same as rate of change of its radius, then radius, is equal to