Correct Answer: C. 624

Correct Answer: A. 12.00%

Correct Answer: D. -3, 9/2

Explanation

2a² - 3a - 27 = 0

2a² - 9a + 6a - 27 = 0

a(2a - 9) + 3(2a - 9) = 0

(a + 3)(2a - 9) = 0

a = -3 or a = 92

Correct Answer: D. 1

Explanation

P(white or red) = P(white) + P(red)

= \(\frac{3}{4} + \frac{1}{4}\)

= 1

Correct Answer: D. -\( \frac{7}{36}\)

Explanation

The general form of a quadratic equation is:

\(x^2\) -(sum of roots)\(x\) +(product of roots) = 0

\(7x^2+12x-4=0\)

Divide through by 7

=\(x^2+\frac{12}{7}x-\frac{4}{7}=0\)

=\(x^2-(-\frac{12}{7})x+(-\frac{4}{7})=0\)

\(\therefore\) sum of roots = \(-\frac{12}{7}\), and products of roots =\(-\frac{4}{7}\)

α + β = \(-\frac{12}{7}, αβ = -\frac{4}{7}\)

\(\frac{αβ}{(α + β)^2} = \frac{\frac{-4}{7}}{(\frac{-12}{7})^2}\)

=\(\frac{\frac{-4}{7}}{\frac{144}{49}}=-\frac{4}{7}\times\frac{49}{144}\)

\(\therefore - \frac{7}{36}\)

Correct Answer: D. x = -1/2 or 2

Explanation

2x\(^2\) - 3x - 2 = 0

2x\(^2\) - 4x + x - 2 = 0

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

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

x = \(\frac{-1}{2}\) or x = 2

Correct Answer: A. \(\frac{2}{11}\)

Explanation

Total number of balls = 5 + 3 + 4 = 12 balls

P(one ball is green and the other is blue) = P(first ball is green and second blue) + P(first ball is blue and the second green)

= \(\frac{3}{12} \times \frac{4}{11} + \frac{4}{12} \times \frac{3}{11}\)

= \(\frac{2}{11}\)

Correct Answer: A. 12

Correct Answer: D. 3.3

Explanation

Using Lami's theorem, \(\frac{150}{\sin 80} = \frac{T_{1}}{\sin 40} = \frac{T_{2}}{\sin 60}\)

\(T_{1} = \frac{150 \sin 40}{\sin 80} = \frac{150 \times 0.6428}{0.9848} = 97.41 N\)

\(T_{2} = \frac{150 \sin 60}{\sin 80} = \frac{150 \times 0.8660}{0.9848} = 131. 90 N\)

(b) \(h = 2 + 20t + kt^{2}\)

\(\frac{\mathrm d h}{\mathrm d t} = v = 20 + 2kt\)

At the highest point, \(v = 0 ms^{-1}; t = 2 secs\)

\(\implies 20 + 2k(2) = 0\)

\(20 = -4k \implies k = -5\)

(ii) Its highest point

\(h = 2 + 20t - 5t^{2}\)

At highest point, t = 2 secs

\(h(2) = 2 + 20(2) - 5(2^{2}) = 2 + 40 - 20 = 22 m\)