If \( \frac{(a^2b^{-3}c)^{\frac{3}{4}}}{a^{-1}b^4c^5}=a^pb^qc^r \) What is the value of p+2q?

Find the equation of the locus of a point P(x,y) such that PV = PW, where V = (1,1) and W = (3,5)

Find the area bounded by the curve y = x(2-x). The x-axis, x = 0 and x = 2.

Find the value of x for which the function y = x3 - x has a minimum value.

Find the volume of solid generated when the area enclosed by y = 0, y = 2x, and x = 3 is rotated about the x-axis.

What is the derivative of t2 sin (3t - 5) with respect to t?

Evaluate: \( \int_{0}^{z}(\sin x-\cos x)\,dx \) Where \( z=\frac{\pi}{4}.(\pi=pi) \)

Evaluate \( \int_{-2}^{1} (x - 1)^2 \, dx \)

The shaded portion in the graph is represented by