JAMB Mathematics Past Questions & Answers - Page 282

1,406.
1,407.

If x = \(\begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}\) and y = \(\begin{pmatrix} 2 & 1 \\ 4 & 3 \end{pmatrix}\). Find xy.

A.

\(\begin{pmatrix} 10 & 7 \\ 12 & 9 \end{pmatrix}\)

B.

\(\begin{pmatrix} 2 & 7 \\ 4 & 17 \end{pmatrix}\)

C.

\(\begin{pmatrix} 10 & 4 \\ 4 & 6 \end{pmatrix}\)

D.

\(\begin{pmatrix} 4 & 3 \\ 10 & 9 \end{pmatrix}\)

Correct answer is A

\(\begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}\); y = \(\begin{pmatrix} 2 & 1 \\ 4 & 3 \end{pmatrix}\).

= \(\begin{pmatrix} 2 + 8 & 1 + 6 \\ 0 + 12 & 0 + 9 \end{pmatrix}\)

= \(\begin{pmatrix} 10 & 7 \\ 12 & 9 \end{pmatrix}\)

1,408.

\(\begin{vmatrix} -2 & 1 & 1 \\ 2 & 1 & k \\1 & 3 & -1 \end{vmatrix}\) = 23

A.

1

B.

2

C.

3

D.

4

Correct answer is B

-2(-1 - 3k) - 1(-2 -k) + 1(6 - 1) = 23

7k = 14

k = 2

1,409.

Find the sum to infinity of the following sequence \(1, \frac{9}{10}, (\frac{9}{10})^{2}, (\frac{9}{10})^{3}\)

A.

\(\frac{1}{10}\)

B.

\(\frac{9}{10}\)

C.

\(\frac{10}{9}\)

D.

10

Correct answer is D

\(S_{\infty} = \frac{a}{1 - r}\) (Sum to infinity of a G.P)

\(a = 1; r = \frac{9}{10}\)

\(S_{\infty} = \frac{1}{1 - \frac{9}{10}}\)

= \(\frac{1}{\frac{1}{10}} = 10\)

1,410.

If a \(\ast\) b = + \(\sqrt{ab}\), evaluate 2 \(\ast\)(12 \(\ast\) 27)

A.

12

B.

9

C.

6

D.

2

Correct answer is C

\(2 \ast (12 \ast 27)\)

\(12 \ast 27 = + \sqrt{12 \times 27}\)

= \(+ \sqrt{324} = 18\)

\(2 \ast 18 = + \sqrt{2 \times 18}\)

= \(+ \sqrt{36} = 6\)