JAMB Mathematics Past Questions & Answers - Page 54

266.

Score (x) 0 1 2 3 4 5 6
Freq (f) 5 7 3 7 11 6 7

Find the mean of the data.

A.

3.26

B.

4.91

C.

6.57

D.

3.0

Correct answer is A

Score (x) 0 1 2 3 4 5 6   Freq (f) 5 7 3 7 11 6 7 46 fx 0 7 6 21 44 30 42 150

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

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

= 3.26

267.

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

A.

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

B.

\(\begin{vmatrix} -6 & 0 & 13\\ 0 & -3 & 18 \\ 14 & 18 & 9 \end{vmatrix}\)

C.

\(\begin{vmatrix} 5 & 2 & 6 \\ 0 & 1 & 1\\ 3 & 4 & -7 \end{vmatrix}\)

D.

\(\begin{vmatrix} -4 & 0 & 8 \\ 0 & -2 & -16 \\ 10 & 12 & 6 \end{vmatrix}\)

Correct answer is B

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 = \(\begin{vmatrix} -6 & 0 & 13 \\ 0 & -3 & 18 \\ 14 & 18 & 9 \end{vmatrix}\)

268.

In how many ways can the word MATHEMATICIAN be arranged?

A.

6794800 ways

B.

2664910 ways

C.

6227020800 ways

D.

129729600 ways

Correct answer is D

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

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

= 129729600 ways

269.

If a fair coin is tossed 3 times, what is the probability of getting at least two heads?

A.

\(\frac{2}{3}\)

B.

\(\frac{4}{5}\)

C.

\(\frac{2}{5}\)

D.

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

Correct answer is D

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

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

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

270.

If \(6x^3 + 2x^2 - 5x + 1\) divides \(x^2 - x - 1\), find the remainder.

A.

9x + 9

B.

2x + 6

C.

6x + 8

D.

5x - 3

Correct answer is A

No explanation has been provided for this answer.