examday

tmua.me papers

tmua.me Medium Set B Paper 2 · Q12

Paper 2Algebra

Let aa be a real number and let bb be a positive real number. Consider the conditions

P:a2+b2≤1,P:\quad a^2+b^2\leq 1,
Q:ax+b≤x2+1for every real number x.Q:\quad ax+b\leq\sqrt{x^2+1}\quad\text{for every real number }x.

Which of the following is correct?

APP is both necessary and sufficient for QQ.
BPP is neither necessary nor sufficient for QQ.
CPP is sufficient but not necessary for QQ.
DPP is necessary but not sufficient for QQ.

Read the questions freely. Sign in to check your answer, see the worked solution and save your progress.

Sign in to check your answerPractise the whole paper →