What is the rate of change of the volume V of a hemisphere with respect to its radius r when r = 2?
8π
16π
2π
4π
Correct answer is A
\(V = \frac{2}{3} \pi r^{3}\)
\(\frac{\mathrm d V}{\mathrm d r} = 2\pi r^{2}\)
\(\frac{\mathrm d V}{\mathrm d r} (r = 2) = 2\pi (2)^{2}\)
= \(8\pi\)
Find the derivatives of (2 + 3x)(1 - x) with respect to x
6
-3
1 - 6x
6x - 1
Correct answer is C
y = (2 + 3x)(1 - x)
y = 2 - 2x + 3x - 3x2
y = 2 + x - 3x2
dy/dx = 1 - 6x
If y = 3 cos(x/3), find dy/dx when x = (3π/2)
1
-3
2
-1
Correct answer is D
y = 3cos(x/3)
dy/dx = 3x(1/3)x - sin (x/3)
= - sin x/3
But x = 3π/2 ∴ -sin(x/3) = -sin(3π/6)
= -sin (3 * 180)/6
= - sin 90
= -1
The locus of a point which is 5 cm from the line LM is a
line distance 10 cm from LM and parallel to LM
pair of line on opposite sides of LM and parallel to it, each distance 5 cm from LM
line parallel to LM and 5 cm from LM
pair of parallel lines on one side of LM and parallel to LM
Correct answer is B
The locus of a point which is 5cm from the line LM is a pair of lines on opposite sides of LM and parallel to it, each distance 5cm from LM.
P, R and S lie on a circle center as shown above while Q lies outside the circle. Find ∠PSO
45o
55o
35o
40o
Correct answer is C
xo = 35 + 29 (Exterior angle = sum of two interior opposite angles)
x = 55o (∠ at the center twice ∠ at circumference) y = 110o
∠PSO = ∠SPO (base ∠S of 1sc Δ b/c PO = SO)
∴ ∠PSO = (180 - 110)/2
= 35o
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