1

Simplify: (3\(\frac{1}{2} + 4\frac{1}{3}) \div (\frac{5}{6} - \frac{2}{3}\))

A

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

B

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

C

35

D

47

CORRECT OPTION:
d

(3\(\frac{1}{2} + 4\frac{1}{3}) \div (\frac{5}{6} - \frac{2}{3}\)) = (7\(\frac{3 + 2}{6}) \div \frac{(5 - 4)}{6}\)

7\(\frac{5}{6} \div \frac{1}{6} = \frac{47}{6} \times \frac{6}{1}\) = 47

7\(\frac{5}{6} \div \frac{1}{6} = \frac{47}{6} \times \frac{6}{1}\) = 47

2

In a particular year, the exchange rate of naira (N) varies directly with the Dollars{$}. If N1122 is equivalent to $8, find the Naira equivalent of $36

A

N8976

B

N5049

C

N140.25

D

N31.17

CORRECT OPTION:
b

N1122 = $8; x = $36

x x $8 = N1122 x $36

\(\frac{N1122 \times $36}{$8}\) = x

x = N5049

x x $8 = N1122 x $36

\(\frac{N1122 \times $36}{$8}\) = x

x = N5049

3

If log 2 = x, log 3 = y and log 7 = z, find, in terms of x, y and z, the value of log (\(\frac{28}{3}\))

A

2x + y - z

B

2x + x - y

C

x + y - 2x

D

x + x - y

CORRECT OPTION:
b

log (\(\frac{28}{3}) = \log (\frac{7 \times 4}{3})\)

= log 7 + log 4 - log 3

log 7 + log 2^{2} - log 3 = log 7 + 2 - log 3

= x + 2x - y

= 2x + x - y

= log 7 + log 4 - log 3

log 7 + log 2

= x + 2x - y

= 2x + x - y

4

Arrange the following numbers in descending orders of magnitude: 22_{three}, 34_{five}, 21_{six}

A

21_{six}, 22_{three}, 34_{five},

B

21_{six}, 34_{five}, 22_{three}

C

22_{three}, 34_{five}, 21_{six}

D

34_{five}, 21_{six}, 22_{three}

CORRECT OPTION:
d

22_{three}, 34_{five}, 21_{six} = (2 x 3)(2 x 3^{o}), (3 x 5^{1}) = (4 x 5^{0}), (2 x 6^{1}) + (1 x 6^{0})

= (6 + 2), (15 + 4), (12 + 1) = 8_{ten}, 29_{ten}, 13_{ten} in descending order

29_{ten}, 13_{ten}, 8_{ten} = 34_{five}, 21_{six}, 22_{three}

= (6 + 2), (15 + 4), (12 + 1) = 8

29

5

Find the value to which N3000.00 will amount in 5 years at 6% per annum simple interest

A

N3,900.00

B

N3,750.00

C

N3,600.00

D

N3,300

CORRECT OPTION:
a

A = P + I

p + \(\frac{PRT}{100}\)

A = N3000 (1 + \(\frac{6 \times 5}{100}\))

= N3000(1 + 0.3)

A = N3000 (1.3)

= N3,900.00

p + \(\frac{PRT}{100}\)

A = N3000 (1 + \(\frac{6 \times 5}{100}\))

= N3000(1 + 0.3)

A = N3000 (1.3)

= N3,900.00

6

Express the square root of 0.000144 in the standard form

A

1.2 x 10^{-4}

B

1.2 x 10^{-3}

C

1.2 x 10^{-2}

D

1.2 x 10^{-1}

CORRECT OPTION:
c

\(\sqrt{0.000144}\) = 0.012

= 1.2 x 10^{-2}

= 1.2 x 10

7

Two sets are disjoint if

A

they are both empty

B

their union is an empty set

C

their intersection is an empty set

D

one of them is a subset of the other

CORRECT OPTION:
c

8

If \(\frac{3}{2x} - \frac{2}{3x} = 4\), solve for x

A

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

B

\(\frac{4}{13}\)

C

\(\frac{5}{24}\)

D

\(\frac{13}{24}\)

CORRECT OPTION:
c

\(\frac{3}{2x} - \frac{2}{3x} = 4\)

\(\frac{9 - 4}{6x}\); \(\frac{5}{6x}\) = 4

5 = 24x ; x = \(\frac{5}{24}\)

\(\frac{9 - 4}{6x}\); \(\frac{5}{6x}\) = 4

5 = 24x ; x = \(\frac{5}{24}\)

9

If (2x + 3)^{3} = 125, find the value of x

A

1

B

2

C

3

D

4

CORRECT OPTION:
a

(2x + 3 )^{2} = 125

2n + 3 = 3\(\sqrt{125}\)

2x + 3 = 5

2x = 5 - 3

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

= 1

2n + 3 = 3\(\sqrt{125}\)

2x + 3 = 5

2x = 5 - 3

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

= 1

10

Factorize x^{2} - 2x - 3xy completely

A

(x - 2)(3x - y)

B

(x - 3y)(x - 2)

C

(x - 3y)(x - 3y)

D

(3x + y)(x - 2)

CORRECT OPTION:
b

x^{2} - 2x - 3xy + 6y = x(x - 2) -3y(x - 2)

= (x - 3y)(x - 2)

= (x - 3y)(x - 2)

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