The sum of the first n positive integers is

• A. 1/2 n(n-1)
• B. n(n+1)
• C. n(n-1)
• D. 1/2 n(n+1)

express 62 ÷ 3 as a decimal correct to 3 significant figures

• A. 20.6
• B. 20.667
• C. 20.67
• D. 20.7

If \(\frac{5}{\sqrt{2}} - \frac{\sqrt{8}}{8} = m\sqrt{2}\), where m is a constant. Find m.

• A. \(1\frac{1}{2}\)
• B. \(1\frac{1}{4}\)
• C. \(2\frac{1}{4}\)
• D. \(2\frac{1}{2}\)

If sin x \(\frac{P - Q}{P + Q}\), where 0\(^o\) \(\leq\) x \(\leq\) 90\(^o\), find 1 - tan\(^2\)x

A committee of six is to be formed by a state governor from nine state commissioners and three members of the state house of assembly. In how many ways can the members of the committee be chosen so as to include one member of the house of assembly

• A. 378 ways
• B. 462 ways
• C. 840 ways
• D. 924 ways

Find the area of the circle whose equation is given as \(x^{2} + y^{2} - 4x + 8y + 11 = 0\).

• A. \(3\pi\)
• B. \(6\pi\)
• C. \(9\pi\)
• D. \(12\pi\)

A binary operation * is defined by a*b = ab+a+b for any real number a and b. if the identity element is zero, find the inverse of 2 under this operation.

• A. 2/3
• B. 1/2
• C. -1/2
• D. -2/3

Find the dimensions of a rectangle of greatest area which has a fixed perimeter p.

• A. square of sides p
• B. square of sides 2p
• C. square of sides (p/2)
• D. square of sides (p/4)

Three consecutive positive integers k, l and m are such that l² = 3(k+m). Find the value of m.

• A. 4
• B. 5
• C. 6
• D. 7

Given that x² + y² + z² = 194, calculate z if x = 7 and \(\sqrt{y}\) = 3

• A. \(\sqrt{10}\)
• B. 8
• C. 12.2
• D. 13.4