JAMB Mathematics Past Questions & Answers - Page 328

1,636.

The binary operation on the set of real numbers is defined by m*n = \(\frac{mn}{2}\) for all m, n \(\in\) R. If the identity element is 2, find the inverse of -5

A.

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

B.

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

C.

4

D.

5

Correct answer is A

m * n = \(\frac{mn}{2}\)

Identify, e = 2

Let a \(\in\) R, then

a * a\(^{-1}\) = e

a * a\(^{-1}\) = 2

-5 * a\(^{-1}\) = 2

\(\frac{-5 \times a^{-1}}{2} = 2\)

\(a^{-1} = \frac{2 \times 2}{-5}\)

\(a^{-1} = -\frac{4}{5}\)

1,637.

The binary operation * is defined on the set of integers such that p * q = pq + p - q. Find 2 * (3 * 4)

A.

11

B.

13

C.

15

D.

22

Correct answer is B

p * q = pq + p - q First execute for 3 * 4 ==> 3(4) + 3 - 4 = 12 + 3 - 4 = 11 Now we execute for 2 * 11 ==> 2(11) + 2 - 11 = 22 + 2 - 11 = 13

1,638.

The sum to infinity of a geometric progression is \(-\frac{1}{10}\) and the first term is \(-\frac{1}{8}\). Find the common ratio of the progression.

A.

\(-\frac{1}{5}\)

B.

\(-\frac{1}{4}\)

C.

\(-\frac{1}{3}\)

D.

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

Correct answer is B

Sr = \(\frac{a}{1 - r}\)

\(-\frac{1}{10}\) = \(\frac{1}{8} \times \frac{1}{1 - r}\)

\(-\frac{1}{10}\) = \(\frac{1}{8(1 - r)}\)

\(-\frac{1}{10}\) = \(\frac{1}{8 - 8r}\)

cross multiply...

-1(8 - 8r) = -10

-8 + 8r = -10

8r = -2

r = -1/4

1,639.

The nth term of a sequence is n2 - 6n - 4. Find the sum of the 3rd and 4th terms.

A.

24

B.

23

C.

-24

D.

-25

Correct answer is D

n2 - 6n - 4

For the 3rd term,
32 - 6(3) - 4

9 - 18 -4 = -13

For the 4th term,
42 - 6(4) - 4

16 - 24 - 4 = -12

Sum of both terms

-13 - 12 = -25

1,640.

Find the range of values of m which satisfy (m - 3)(m - 4) < 0

A.

2 < m < 5

B.

-3 < m < 4

C.

3 < m < 4

D.

-4 < m < 3

Correct answer is C

(m - 3)(m - 4) < 0

(m - 3) < 0 ; (m - 4) < 0

m < 3 ; m < 4

3 < m < 4