Correct Answer: A. -1 and 5

Correct Answer: D. 96cm²

Explanation

Area of rhombus = \(\frac{pq}{2}\)

where p and q are the diagonals of the rhombus.

\(\therefore A = \frac{16 \times 12}{2}\)

= 96 cm\(^2\)

Correct Answer: C. N2,020.00

Explanation

Let a girl's share = x + 20

4x + 5(x + 20) = 18,100

4x + 5x + 100 = 18,100

9x + 100 = 18,100

9x = 18,000

x = \(\frac{18,000}{9}\)

x = 2,000

\(\therefore\) Each boy gets N(2,000 + 20)

= N2,020.

Correct Answer: B. 14

Explanation

(a) y =(\(\frac{pr}{m} - p^2r\))\(^{\frac{-3}{2}}\)

y\(^{\frac{-2}{3}}\) =(\(\frac{pr}{m} - p^r2\))

my\(^{\frac{-2}{3}}\) =(\(\frac{pr- p^r2m}{m}\))

my\(^{\frac{-2}{3}}\) = pr - p\(^2\)rm

my\(^{\frac{-2}{3}}\) = r(p - p\(^2\)m)

r = (\(\frac{my^{-2/3}}{m - p^2m}\))

(b) r = (\(\frac{1-8^{-2/3}}{3 - 3^2 * 1}\))

= \(\frac{1}{4}\) ÷ -6

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

= - \(\frac{1}{24}\)

Correct Answer: A. 1\(\frac{1}{2}\)

Explanation

(x - p)(2x + 1) = 0

2x² + x - 2px - p = 0

2x² + x (1 - 2p) - p = 0

2x² - (2p - 1)x - p = 0

divide through by 2

x² - \(\frac{(2p - 1)}{2}\)x - \(\frac{p}{2}\) = 0

compare to x² - (sum of roots)x + product of roots = 0

sum of roots = \(\frac{2p - 1}{2}\)

But sum of roots = 1

Given; \(\frac{2p - 1}{2}\) = 1

2p - 1 = 2 x 1

2p - 1 = 2

2p = 2 + 1 = 3

p = \(\frac{3}{2}\)

p = 1\(\frac{1}{2}\)

Correct Answer: D. \(62^0\)

Explanation

∠SOR = 2 × 28° = 56° (angle at the centre is twice the angle at the circumference)

From ?SOR

|OS| = |OR| (radii)

So, ?SOR is isosceles.

∠ORS = \(\frac{180^0 - 56^0}{2} = \frac{124^0}{2}\) ( base angles of isosceles triangle are equal)

∴ ∠ORS = 62°

Explanation

volume of rectangular block(cuboid) = l × b × h

V = 3x × 2x × y

72 = 6x\(^2\)y

y = \(\frac{72}{6x^2}\)

y = \(\frac{12}{x^2}\)

ii.

Area of cuboid = 2(lb + lh + bh)

l = 3x, b = 2x, h = y

A = 2(3x(2x) + 3x(y) + 2x(y))

A = 2(6x\(^2\) + 3xy + 2xy)

A = 12x\(^2\) + 6xy + 4xy

A = 12x\(^2\) + 10xy

where y = \(\frac{12}{x^2}\)

A = 12x\(^2\) + \(\frac{120}{x}\)

iii.

At stationary point \(\frac{dy}{dx}\) = 0

\(\frac{dA}{dx} = 2(12x^2-1) + -120x^{-1-1}\)

24x - 120x\(^{-2}\)

\(\frac{dA}{dx}\) = 0

24x- \(\frac{120}{x^2}\) = 0

multiply through by x\(^2\)

24x\(^3\) - 120 = 0

24x\(^3\) = 120

x\(^3\) = 5

x = ?5

x = 1.71

Correct Answer: B. -1, 5/3

Correct Answer: B. \(\frac{1}{6}\)

Explanation

When the die is rolled, occasion of getting 4

P(obtaining a 4) = \(\frac{1}{6}\)

= \(\frac{1}{6}\)