Correct Answer: B. 250 m

Explanation

\(s = ut + \frac{1}{2} at^{2}\)

\(u = 0, t = 10 secs, a = 5 ms^{-2}\)

\(s = 0 + \frac{1}{2} 5 \times 10^{2}\)

\(s = 250 m\)

Correct Answer: C. 43cm

Explanation

Perimeter of a sector = \(2r + \frac{\theta}{360} \times 2\pi r\)

= \(2(10.5) + \frac{120}{360} \times 2 \times \frac{22}{7} \times 10.5\)

= \(21 + 22\)

= 43 cm

Correct Answer: D. \(x = \frac{y^2 + b}{a}\)

Explanation

\(y = \sqrt{ax-b}\)

\(y^2 = ax-b\)

\(y^2 +b = ax\)

\(x = \frac{y^2 + b}{a}\)

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

Explanation

\(\begin{array}{c|c}

& 1 & 2 & 3 & 4 & 5 & 6 \\

\hline

1 & 1,1 & 1,2 & 1,3 & 1,4 & 1,5 & 1,6 \\ \hline 2 & 2,1 & 2,2 & 2,3 & 2,4 & 2,5 & 2,6 \\ \hline 3 & 3,1 & 3,2 & 3,3 & 3,4 & 3,5 & 3,6 \\ \hline 4 & 4,1 & 4,2 & 4,3 & 4,4 & 4,5 & 4,6 \\ 5 & 5,1 & 5,2 & 5,3 & 5,4 & 5,5 & 5,6 \\ \hline 6 & 6,1 & 6,2 & 6,3 & 6,4 & 6,5 & 6,6\end{array}\)

From the table above, event space, n(E) = 6

sample space, n(S) = 36

Hence, probability sum of scores is at least 10, is;

\(\frac{n(E)}{n(S)}\)

= \(\frac{6}{36}\)

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

Correct Answer: A. 8.25

Explanation

Mean \(\bar{x}\) = \(\frac{3 + 7 + 6 + 2 + 8 + 5 + 9 + 1 + 4 + 10}{10} \)

= \(\frac{55}{10} = 5.50\)

Variance = \(\frac{\sum (x - \bar{x})^{2}}{n}\)

= \(\frac{82.5}{10}\)

= 8.25

Explanation

\(^{5y}{C}_2\) = 190

\(\frac{5y(5y-1) (5y-2)!}{(5y-2)!(2)!}\) = 190

\(\frac{5y(5y-1)}{2}\) = 190

25y\(^2\) - 5y = 380

5y\(^2\) - 5y - 76 = 0

= (y-4) (5y+ 19) = 0

Either y - 4 = 0 or 5y+ 19 = 0;

y = 4 or -19/5

: y= 4

Correct Answer: C. 192

Explanation

Using the sum of an AP, S\(_n\) = \(\fra{n}{2}\) [ 2a + (n - 1)d]

S\(_3\) = \(\fra{3}{2}\) [ 2a + (3 - 1)d]

18 = \(\fra{3}{2}\) [ 2a + 2d]

2a + 2d = 12

a = 4

2(4) + 2d = 18 --> 8 + 2d = 12

2d = 4; d = 2

a = 4: a + d

= 4 + 2 = 6

a + 2d = 4 + 2]2]

= 8

product of the terms = 4 * 6 * 8 = 192

Correct Answer: D. \(7\sqrt{2}cm\)

Explanation

\(A=\pi r^2 \Rightarrow 77 = \frac{22}{7} \times \frac{r^2}{1}\Rightarrow r^2 = \frac{77\times 7}{22} \Rightarrow r^2 = \frac{49}{2}\\

\Rightarrow r = \sqrt{\frac{49}{2}}=\frac{7}{\sqrt{2}}. Since D = 2r ? D = 2 \times \frac{7}{\sqrt{2}} = \frac{14}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = 7\sqrt{2}cm\)

Correct Answer: D. 30°

Explanation

4x + 3x + 2x + 90 =360° [angle at a point]

9x + 90 = 360°

9x = 360° - 90°

9x = 270

x = 270/9

x = 30°

Correct Answer: B. E' n F n G'

Explanation

The shaded/stripped portion in the diagram is set F only. This implies that sets E and G though present in the Universal set, are not included in the expression. Mathematically; we have E' n F n G'