Mathematics Past Questions and Answers

The solution set of the shaded area above is

A Y ≥ 0, y ≥ x and y + x ≤ 4
B Y ≤ x, y + x ≤ 4
C Y + x ≥ 4, y ≤ x
D Y ≤ x, y + x ≤ 4 and y ≥ 0

Question 37:

A binary operation \(\oplus\) defined on the set of real number is such that x\(\oplus\)y = xy/6 for all x, y ∈ R. Find the inverse of 20 under this operation when the identity element is 6

A ¹/₁₂
B ¹⁰/₃
C ¹/₂₀
D ⁹/₅

Question 38:

If p varies inversely as the cube of q and q varies directly as the square of r, what is the relationship between p and r?

A P varies directly as r³
B P varies inversely as r⁶
C P varies inversely as ⁶âˆšP
D P varies directly as r⁶

Question 39:

A binary operation * on the set of rational numbers is defined as \(x \ast y = \frac{x^2 - y^2}{2xy}\). Find \(-5 \ast 3\)

A \(\frac{-8}{15}\)
B \(\frac{8}{15}\)
C \(\frac{17}{15}\)
D \(\frac{-17}{15}\)

Question 40:

Find the value of k if the expression kx³ + x² - 5x - 2 leaves a remainder 2 when it is divided by 2x + 1

A 10
B 8
C -10
D -8