Mathematics Questions & Answers - Free Online Practice

1,771.

If \(\sqrt{3^{\frac{1}{x}}}\) = \(\sqrt{9}\) then the value of x is:

\(\frac{3}{4}\)

\(\frac{4}{3}\)

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

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

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

View answer & explanation

Correct answer is E

\(\sqrt{3^{\frac{1}{x}}}\) = \(\sqrt{9}\)

3\(^{\frac{1}{2x}}\) = \(9^{\frac{1}{2}}\)

3\(^{\frac{1}{2x}}\) = 3\(^{2 \times \frac{1}{2}}\)

3\(\frac{1}{2x}\) = 3\(\frac{2}{2}\) = 3

\(3^{\frac{1}{2x}}\) = \(3^{1}\)

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

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

1,772.

A father is now three times as old as his son. Twelve years ago he was six times as old as his son. How old are the son and the father?

20 and 45

100 and 150

45 and 65

35 and 75

20 and 60

View answer & explanation

Correct answer is E

Son = x, Father = 3x, 12 yrs ago

son = x - 12, father = 3x - 12

3x - 12 = 6(x - 12)

3x - 12 = 6x - 72

3x = 60

x = 20

1,773.

If y = x² - 2x - 3, Find the least value of y and corresponding value of x

x = 3, y = 3

x = 1, y = -3

x = 4, y = 1

x = 1, y = -4

x = 2, y = -3

View answer & explanation

Correct answer is D

If the graph of eqn. y = x² - 2x - 3 is plot and drawn, the lease value of y = -4 while the corresponding value of x = 1

x = 1, y = -4

1,774.

The following table relates the number of objects f corresponding to a certain size x. What is the average size of an object?
\(\begin{array}{c|c} f & 1 & 2 & 3 & 4 & 5 \\ \hline x & 1 & 2 & 4 & 8 & 16\end{array}\)

\(\frac{31}{15}\)

\(\frac{31}{5}\)

\(\frac{129}{5}\)

\(\frac{43}{5}\)

\(\frac{16}{5}\)

View answer & explanation

Correct answer is D

F = 1, 2, 3, 4, 5

x = 1, 2, 4, 8, 16

fx = 1, 4, 12, 32, 80, 3f = 15

(average size) = \(\frac{\sum fx}{\sum f}\)

= \(\frac{129}{15}\)

= \(\frac{43}{5}\)