MCQs of Applications of Derivatives

Showing 201 to 210 out of 266 Questions

201.

If the curve y² = x and xy = c are orthogonal, then c = _____.(x, y ∈ R⁺, c ≠ 0)

202.

A tangent to the curve y = log_ex at point P is passing through the point (0, 0), then the co-ordinates of the points P are _____.

203.

The point on the parabola y² = 8x such that

\frac{d x}{d t} = \frac{d y}{d t}

is _____.

204.

The equation of the normal to the curve x² = 4y passing through the point (2, 1) is _____.

205.

Volume of a cube increases at a constant rate of 3 cm³/sec. The rate of increase of its surface area is _____, when its side is 10 cm.

206.

Find a point on the curve other than origin y = x³ where the slope of tangent is the same as the sum of both co-ordinates of that point _____

(a)	$(\frac{3 \pm \sqrt{5}}{2}, 9 \pm 4 \sqrt{5})$
(b)	$(\frac{3 \pm \sqrt{5}}{2}, 9 \mp 4 \sqrt{5})$
(c)	$(9 \pm \sqrt{5}, \frac{3 \pm \sqrt{5}}{2})$
(d)	point does not exist on the curve

207.

The approximate value of \log {}_{10}30 . 1 is

_____

where \log {}_{10}30 = 1.4771 and \log {}_{10}e = 0.4343 .

208.

The local maximum value for f(x) = x³ - 12x is _____.

209.

If p and q are positive real numbers such that p² + q² = 1, then maximum value of p + q is _____.

210.

The function f(x) = cot^-1x + x increases in the interval _____.

Showing 201 to 210 out of 266 Questions