JAMB Mathematics Past Questions & Answers - Page 259

1,291.

p = \(\begin{vmatrix} x & 3 & 0 \\ 2 & y & 3\\ 4 & 2 & 4 \end{vmatrix}\)

Q = \(\begin{vmatrix} x & 2 & z \\ 3 & y & 2\\ 0 & 3 & z \end{vmatrix}\)
PQ is equivalent to

A.

PPT

B.

pp-1

C.

qp

D.

pp

Correct answer is A

p = \(\begin{vmatrix} 0 & 3 & 0 \\ 2 & 1 & 3\\ 4 & 2 & 2 \end{vmatrix}\)

Q = \(\begin{vmatrix} 0 & 2 & 4 \\ 3 & 1 & 2\\ 0 & 3 & 2 \end{vmatrix}\) = pT

pq = ppT

1,292.

p = \(\begin{vmatrix} x & 3 & 0 \\ 2 & y & 3\\ 4 & 2 & 4 \end{vmatrix}\)

Q = \(\begin{vmatrix} x & 2 & z \\ 3 & y & 2\\ 0 & 3 & z \end{vmatrix}\) Where pT is the transpose P calculate /pT/ when x = 0, y = 1 and z = 2

A.

48

B.

24

C.

-24

D.

-48

Correct answer is B

p = \(\begin{vmatrix} 0 & 3 & 0 \\ 2 & 1 & 3\\ 4 & 2 & 2 \end{vmatrix}\)

PT = \(\begin{vmatrix}0 & 2 & 4 \\ 2 & 1 & 3\\ 0 & 3 & 2 \end{vmatrix}\)

/pT/ = \(\begin{vmatrix}0 & 2 & 4 \\ 3 & 1 & 3\\ 0 & 3 & 2 \end{vmatrix}\)

= 0[2 - 6] - 2[6 - 0] + 4[9 - 0]

= 0 - 12 + 36 = 24

1,293.

If the binary operation \(\ast\) is defined by m \(\ast\) n = mn + m + n for any real number m and n, find the identity of the elements under this operation

A.

e = 1

B.

e = -1

C.

e = -2

D.

e = 0

Correct answer is B

Identity(e) : a \(\ast\) e = a

m \(\ast\) e = m...(i)

m \(\ast\) e = me + m + e

Because m \(\ast\) e = m 

: m = me + m + e

m - m = e(m + 1)

e = \(\frac{0}{m + 1}\)

e = 0

1,294.

For an arithmetical sequence, the first term is 2 and the common difference is 3. Find the sum of the first 11 terms

A.

157

B.

187

C.

197

D.

200

Correct answer is B

a = 2, d = 3 and n = 11

To find Sn/sub> = \(\frac{n}{2}\) [2a + (n - 1) \(\delta\)]

= \(\frac{11}{2}\) [2(2) + (11 - 1) 3]

= \(\frac{11}{2}\)n [4 + 10(3)]

= \(\frac{11}{2}\)(34)

= 11 x 17

= 187

1,295.

What is the n-th term of the sequence 2, 6, 12, 20...?

A.

4n - 2

B.

2(3n - 1)

C.

n2 + n

D.

n2 + 3n + 2

Correct answer is C

Given that 2, 6, 12, 20...? the nth term = n\(^2\) + n

check: n = 1, u1 = 2

n = 2, u2 = 4 + 2 = 6

n = 3, u3 = 9 + 3 = 12

∴ n = 4, u4 = 16 + 4 = 20