In how many ways can the word MATHEMATICS be arranged?

• A. \(\frac{11!}{9!2!}\)
• B. \(\frac{11!}{9!2!2!}\)
• C. \(\frac{11!}{2!2!2!}\)
• D. \(\frac{11!}{2!2!}\)

(a) Write down the binomial expansion of \((2 - x)^{5}\) in ascending powers of x.

(b) Use your expansion in (a) to evaluate \((1.98)^{5}\) correct to four decimal places.

Find the radius of a sphere whose surface area is 154 cm2?

• A. 7.00 cm
• B. 3.50 cm
• C. 3.00 cm
• D. 1.75 cm

Given that \(\sin x = \frac{5}{13}\) and \(\sin y = \frac{8}{17}\), where x and y are acute, find \(\cos(x+y)\).

• A. \(\frac{130}{221}\)
• B. \(\frac{140}{221}\)
• C. \(\frac{140}{204}\)
• D. \(\frac{220}{23}\)

A bicycle wheel of radius 42cm is rolled over a distance 66 meters. How many revolutions does it make?[Take π = 22/7]

• A. 2.5
• B. 5
• C. 25
• D. 50

The weights to the nearest kilogram, of a group of 50 students in a College of Technology are given below:

65, 70, 60, 46, 51, 55, 59, 63, 68, 53, 47, 53, 72, 53, 67, 62, 64, 70, 57, 56, 73, 56, 48, 51, 58, 63, 65, 62, 49, 64, 53, 59, 63, 50, 48, 72, 67, 56, 61, 64, 66, 52, 49, 62, 71, 58, 53, 69, 63, 59.

(a) Prepare a grouped fraquency table with class intervals 45 - 49, 50 - 54, 55 - 59 etc.

(b) Using an assumed mean of 62 or otherwise, calculate the mean and standard deviation of the grouped data, correct to one decimal place.

Express \(\frac{1}{1 - \sin 45°}\) in surd form.

• A. \(2 + \sqrt{2}\)
• B. \(2 + \sqrt{3}\)
• C. \(2 - \sqrt{2}\)
• D. \(1 + 2\sqrt{2}\)

Evaluate 1 - (\(\frac{1}{5}\) x \(\frac{2}{3}\)) + ( 5 + \(\frac{2}{3}\))

• A. 4
• B. 3
• C. 2\(\frac{2}{3}\)
• D. \(\frac{98}{15}\)

If \(\begin{vmatrix} x & 3 \\ 2 & 7 \end{vmatrix} = 15\), find the value of x

• A. 3
• B. 4
• C. 5
• D. 2

What is the product of \(\frac{27}{5^1}\)(3)-3 and \(\frac{(1)^{-1}}{5}\)?

• A. 5
• B. 3
• C. 1
• D. 1/25