Mathematics Past Questions and Answers

A die is thrown and a coin is tossed. Find the probability that the die shows an even number and the coin shows a head.

If two triangles are similar, then
I. the corresponding angles are equal
II. the corresponding sides are proportional
III. the areas of the triangles are in the same ratio as the lengths of the corresponding sides
IV. the triangles are congruent

Which of the above statements are CORRECT?

A binary operation \(*\) is defined over the set of real numbers such that \(m * n=m+n+2\) and \(m \odot\) \(n=m-n+1\). Which of the following equations is not true?

If \(2 \cos 2 \theta=-\cos \theta\) and \(0<\theta<180^{\circ}\), then \(\theta\) is ____________

The coordinates of the vertices \(P\) and \(Q\) of a square \(P Q R S\) are \(P=(1,3)\) and \(Q=(5,1)\). The coordinates of \(R\) could be ____________