Mathematics Past Questions and Answers

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

Question 12:

Factorize completely \(x^{2} + 2xy + y^{2} + 3x + 3y - 18\).

A (x+y+6)(x+y-3)
B (x-y-6)(x-y+3)
C (x-y+6)(x-y-3)
D (x+y-6)(x+y+3)

Question 13:

Three consecutive positive integers k, l and m are such that l\(^2\) = 3(k+m). Find the value of m.

Question 14:

Express \(\frac{1}{x^{3}-1}\) in partial fractions

A \(\frac{1}{3}(\frac{1}{x - 1} - \frac{(x + 2)}{x^{2} + x + 1})\)
B \(\frac{1}{3}(\frac{1}{x - 1} - \frac{x - 2}{x^{2} + x + 1})\)
C \(\frac{1}{3}(\frac{1}{x - 1} - \frac{(x - 2)}{x^{2} + x + 1})\)
D \(\frac{1}{3}(\frac{1}{x - 1} - \frac{(x - 1)}{x^{2} - x - 1})\)

Question 15:

The first term of a geometric progression is twice its common ratio. Find the sum of the first two terms of the G.P if its sum to infinity is 8.

A 8/5
B 8/3
C 72/25
D 56/9