2019 - JAMB Mathematics Past Questions and Answers - page 2

The possible outcomes are {HHH, HHT, HTT, HTH, THH, THT, TTH, TTT}

Hence, 

P(at least two heads) = \(\frac{4}{8}\)

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

MATHEMATICIAN has 13 letters with 2M, 3A, 2T, 2I.

Hence, the word MATHEMATICIAN can be arranged in \(\frac{13!}{2! 3! 2! 2!}\)

= 129729600 ways

Let M represent the matrix. 

M = \(\begin{vmatrix} -2 & 0 & 4 \ 0 & -1 & 6 \ 5 & 6 & 3 \end{vmatrix}\)

M\(^{T}\) = \(\begin{vmatrix} -2 & 0 & 5 \ 0 & -1 & 6\ 4 & 6 & 3 \end{vmatrix}\)

2M = \(\begin{vmatrix} -4 & 0 & 8\ 0 & -2 & 12\ 10 & 12 & 6\end{vmatrix}\)

M\(^T\) + 2M = \(\begin{vmatrix} -6 & 0 & 13 \ 0 & -3 & 18 \ 14 & 18 & 9 \end{vmatrix}\)

Mean (x) = \(\frac{\sum fx}{\sum f}\)

x = \(\frac{150}{46}\)

x = 3.26

Variance = \(\frac{\sum f(x - \bar{x})}{\sum f}\)

= \(\frac{170.888}{46}\)

= 3.72

The sum of two opposite angles of a cyclic quadrilateral is equal  to 180°

\(\therefore\) (2x + 18)° + 84° = 180°

2x + 102° = 180° \(\implies\) 2x = 78°

x = 39°

\(4\sin^2 x - 3 = 0\)

\(4 \sin^2 x = 3 \implies \sin^2 x = \frac{3}{4}\)

\(\sin x = \frac{\sqrt{3}}{2}\)

\(\therefore x = \sin^{-1} (\frac{\sqrt{3}}{2})\)

x = 60°

Area of rectangle ABCD = length x breadth

= 7 x 4 

= 28 cm\(^2\)

Area of triangle CDE = \(\frac{1}{2}\) base x height

= \(\frac{1}{2} \times 3 \times 4\)

= 6 cm\(^2\)

Hence, area of the figure = 28 cm\(^2\) + 6 cm\(^2\)

= 34 cm\(^2\)

Ans. = 75