Correct Answer: B. -1

Explanation

P = x² + 4x - 2, Q = 2x - 1

Q - p = 2, (2x - 1) - (x² + 4x - 2) = 2

2x - 1 - x² - 4x + 2 = 2

-2x - x² + 1

-x² - 2x - 1 = 0

x² + 2x + 1 = 0

x² + x + x + 1 = 0

x(x + 1) + 1(x + 1) = 0

(x + 1)(x + 1) = 0

x + 1 = 0 or x + 1 = 0

x = -1 or x = -1

x = -1

Correct Answer: D. 17°

Explanation

\(\bigtriangleup\) ABC, A + 153 = 180 (angles on straight line)

< A = 180 - 153 = 27

< B = 2m(vertically opposite angles)

< C = 7m (corresponding ngles)

< A +< B +< C = 180 (sum of int. angles of \(\bigtriangleup\))

i.e. 27 + 2m + 7m = 180^o

9m = 180 - 27

9m = 153

m = \(\frac{153}{9}\)

= 17

Correct Answer: B. 448m³

Explanation

Volume of pyramid = \(\frac{1}{3}\) x base area x height

= \(\frac{1}{3} \times 12^4 \times 8 \times 14\)

= 4 x 8 x 14 = 448m³

Correct Answer: B. \(x< \frac{-1}{2}, x > 3\)

Correct Answer: A. 112cm

Correct Answer: D. 2

Explanation

\(\sqrt{50} - K\sqrt{8} = \frac{2}{\sqrt{2}}\)

\(\sqrt{50} - \frac{2}{\sqrt{2}}\) = K\(\sqrt{8}\)

= \(\sqrt{2} \times 25 - \frac{2}{\sqrt{2}}\)

= K \(\sqrt{4 \times 2}\)

\(\frac{5\sqrt{2}}{1} - \frac{2}{\sqrt{2}}\) = 2K\(\sqrt{2}\)

\(\frac{5\sqrt{4} - 2}{\sqrt{2}} = 2K\sqrt{2}\)

\(\frac{10 - 2}{\sqrt{2}} = 2K \sqrt{2}\)

\(\frac{8}{\sqrt{2}} = \frac{2K\sqrt{2}}{1}\)

= 2k\(\sqrt{2} \times \sqrt{2}\) = 8

2k \(\sqrt{4}\) = 8

2k x 2 = 8

4k = 8

k = \(\frac{8}{4}\)

k = 2

Correct Answer: C. 38cm³

Explanation

Volume of a cone = \(\frac{1}{3} \pi r^2h\)

h² = 5² = 3²

= 25 - 9 = 16

h = \(\sqrt{16}\)

h = 4cm

v = \(\frac{1}{3} \times \frac{22}{7} \times 3^2 \times 4\)

\(\frac{1}{3} \times \frac{22}{7} \times 9 \times 4\)

= \(\frac{22 \times 3 \times 4}{7}\)

= 37.7cm³

= 38cm³

Correct Answer: A. \(4(6 + 5\pi)\)

Explanation

The angle subtended by the minor arc = \(\frac{\pi}{3} radians\)

The angle subtended by the major arc = \(2\pi - \frac{\pi}{3} = \frac{5\pi}{3}\)

Perimeter of the major arc = \(r\theta + 2r\)

= \(12 \times \frac{5\pi}{3} + 2(12) = 20\pi + 24\)

= \(4(5\pi + 6)\)

Correct Answer: B. \(\frac{1}{45}\)

Explanation

P(winning) = \(\frac{2}{10}\)

P(both tickets winning) = \(\frac{2}{10} \times \frac{1}{9} = \frac{1}{45}\)

Explanation

Assumed mean, A = 19.

(a) \(\bar{x} = A + \frac{\sum fd}{\sum f}\)

= \(19 + \frac{-54}{22}\)

= \(19 - 2.455\)

= \(16.545 \approxeq 16.5\) years.

(b) Standard deviation , \(\sigma = \sqrt{\frac{\sum fd^{2}}{\sum f} - (\frac{\sum fd}{\sum f})}\)

= \(\sqrt{\frac{360}{22} - (\frac{-54}{22})}\)

= \(\sqrt{16.364 - (2.45)^{2}}\)

= \(\sqrt{16.364 - 6.025}\)

= \(\sqrt{10.339}\)

= 3.215 \(\approxeq\) 3.22 years.