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Find the derivative of \(y = sin^2(5x)\) with respect to \(x.\)

A) \(10 \; \mathrm{sin} \; 5x \; \mathrm{cos} \; 5x\)

B) \(5 \; \mathrm{sin} \; 5x \; \mathrm{cos} \; 5x\)

C) \(2 \; \mathrm{sin} \; 5x \; \mathrm{cos} \; 5x\)

D) \(15 \; \mathrm{sin} \; 5x \; \mathrm{cos} \; 5x\)

The slope of the tangent to the curve \(y = 3x^2 - 2x + 5\) at the point \((1, 6)\) is

A) \(4\)

B) \(1\)

C) \(6\)

D) \(5\)

Evaluate \(\int \mathrm{sin} \; 3x dx\)

A) \(\frac{2}{3} \mathrm{cos} 3x + c\)

B) \(\frac{1}{3} \mathrm{cos} 3x + c\)

C) \(\frac{-1}{3} \mathrm{cos} 3x + c\)

D) \(\frac{-2}{3} \mathrm{cos} 3x + c\)

A circle with radius \(5\) cm has its radius increasing at the rate of \(0.2\) m/s. What will be the corresponding increase in the area?

A) \(2\pi\)

B) \(5\pi\)

C) \(\pi\)

D) \(4\pi\)

The sum of the interior angles of regular polygon is \(1800^{\circ}\). How many sides has the polygon?

A) 16

B) 12

C) 10

D) 8

Find the coefficient of m in the expression of \((\frac{m}{2} - 1\frac{1}{2})(m + \frac{2}{3})\)

A) \(-\frac{1}{6}\)

B) \(-\frac{1}{2}\)

C) \(-1\)

D) \(-1\frac{1}{6}\)

The volume of a cuboid is 54 cm^{3}. If the length, width and height of the cuboid are in the ratio 2:1:2 respectively, find its total surface area

A) 108 cm^{2}

B) 90 cm^{2}

C) 80 cm^{2}

D) 72 cm^{2}

A side and a diagonal of a rhombus are 10cm and 12cm respectively, Find its area

A) 20 cm^{2}

B) 24 cm^{2}

C) 48 cm^{2}

D) 96 cm^{2}

Factorise completely: 32x^{2}y - ^{3}y^{3}

A) 16x^{2}y(2 - 3xy^{2})

B) 8xy(4x - 6x^{2}y^{2})

C) 8x^{2}y(4 - 6xy^{2})

D) 16xy(2x - 3x^{2}y^{2})

If \(x\) and \(y\) are variables and \(k\) is a constant, which of the following describes an inverse relationship between \(x\) and \(y\)?

A) \(y = kx\)

B) \(y = \frac{k}{x}\)

C) \(y = k\sqrt{x}\)

D) \(y = x + k\)

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