Correct Answer: A. 1.2

Explanation

\(\begin{matrix}

x & x-m & |x-m| \\

6 & -2 & 2 \\

7 & -1 & 1 \\

8 & 0 & 0 \\

9 & 1 & 1 \\

10 & 2 & 2 \\

& & 6

\end{matrix}

\)

Mean deviation\(=\frac{\sum|x-m|}{n}=\frac{6}{5} = 1.2\)

Correct Answer: A. 70 kg ms\(^{-1}\)

Explanation

Change in momentum

= F x t = 35N x 2

= 70kg ms\(^{-1}\)

Correct Answer: D. \(\frac {8}{33}\)

Explanation

Let the number of white balls be n

The number of red balls = 8

Now, the probability of drawing a white ball = \(\frac {n}{n + 8}\)

The probability of drawing a red ball = \(\frac {8}{n + 8}\)

Since Pr(White ball) = \(\frac{1}{2}\) x Pr(Red ball)

\(\therefore \frac {n}{n + 8} = \frac {1}{2}\times \frac {8}{n + 8}\)

= \(\frac {n}{n + 8} = \frac {4}{n + 8}\)

\(\therefore n = 4\)

Number of white balls = 4

The possible number of outcomes = n + 8 = 4 + 8 = 12

Pr(Red ball and White ball) = Pr(Red ball) x Pr(White ball)

Pr(Red ball) = \(\frac {8}{12}\)

Pr(Red ball) = \(\frac {4}{11}\)

Pr(Red ball and white ball) = \(\frac {8}{12} \times \frac {4}{11}\)

\(\therefore\)Pr(Red ball and white ball) = \(\frac {8}{33}\)

Correct Answer: A. 2

Explanation

(a)

\(\frac{r}{R} = \cos 50\)

\(r = 6400 \cos 50 = 4,113.84 km\)

\(\approxeq 4,114km\)

The distance PQ along the parallel of latitude = speed (km/h) \(\times\) time (h)

= 600km/h x 3h

= 1800km

\(\frac{\theta}{360} \times 2 \times \frac{22}{7} \times r = 1800\)

\(\theta = \frac{1800 \times 7 \times 360}{44 \times 4113.84}\)

\(\theta = 25.059° \approxeq 25.1°\)

\(\therefore\) The longitude of Q = \(60 + \theta\)

= \(60 + 25.1 = 85.1°W\)

(b) The distance (Q) along the meridian

\(\frac{\theta}{360} \times 2\pi R\)

\(500 = \frac{\theta}{360} \times 2 \times \frac{22}{7} \times 6400\)

\(\theta = \frac{500 \times 360 \times 7}{44 \times 6400}\)

\(\theta = 4.47°\)

\(\therefore \text{The latitude of Y} = 50° - 4.47° = 45.53°\)

\(\approxeq 45.5°N\)

Correct Answer: B. \(\frac{y^2}{x^2 - y^2}\)

Correct Answer: B. a = -5, b = 14

Explanation

The terms of the sequence can be written as : \(u_{r} = ar + b\) in this case, being that they have a regular common difference for each of the r terms.

We can rewrite the sequence as \(a + b, 2a + b, 3a + b,...\) where a is the common difference of the sequence and b is a given constant gotten by solving

\(a + b = 9\) or \(2a + b = 4\) or any other one.

The common difference here is 4 - 9 = -1 - 4 = -5.

\(-5 + b = 9 \implies b = 9 + 5 = 14\)

\(\therefore\) The equation can be written as \(u_{r} = -5r + 14\).

Correct Answer: B. \(\frac{9}{1000}\)

Explanation

Place value of 9 in 3.0492

= 0.009

= \(\frac{9}{1000}\)

Correct Answer: B. 13.5

Explanation

When rearranged: 10, 10, 13, 14, 17, 18

median = \(\frac{13+14}{2}\)

= \(\frac{27}{2}\) or 13.5

Correct Answer: D. 770cm³

Explanation

Volume = \(\pi r^2 h\)

= \(\frac{22}{7} \times 7^2 \times 5\)

= \(770 cm^3\)