Post Utme Mathematics Past Questions and Answers

Question 456:

If \(\frac{r^{2}}{a^{2}}-\frac{1^{2}}{h^{2}}=1\). then \(i\) is

A. \(\pm \frac{h}{a} \sqrt{x^{2}-a^{2}}\)
B. \(\frac{a}{h^{2}} \sqrt{x^{2}-a^{2}}\)
C. \(\pm \frac{a}{h} \sqrt{x^{2}-a}\)
D. \(\pm \frac{h}{a} \sqrt{x^{2}-a^{2}}\)

Question 457:

\(Z\) is partly constant and partly varies inversely as the square of \(d\). when \(d=1, z=11\) and when \(d=2 . z=5\). Find the value of \(=\) when \(d=4 .\)

A. 2
B. \(3.5\)
C. 5
D. 5.5

Question 458:

Expand the expression \(\left(x^{2}-2 x-3\right)\left(x^{2}+x+1\right)\).

A. \(x^{4}-4 x^{2}-5 x-3\)
B. \(-x^{3}-4 x^{2}+5 x-3\)
C. \(x^{4}-x^{3}-\) \(4 x^{2}-5 x-3\)
D. \(x^{4}-4 x^{2}-5 x-3\)

Question 459:

Suppose we have matrices \(A=\left[\begin{array}{cc}1 & -1 \\ 2 & 3\end{array}\right]\) and \(B=\left[\begin{array}{ll}0 & 2 \\ 4 & 3\end{array}\right]\). Find \(A^{2}+A B-2 A\)

A. \(\left(\begin{array}{cc}-5 & -9 \\ 12 & 14\end{array}\right)\)
B. \(\left(\begin{array}{cc}-1 & -4 \\ 8 & 7\end{array}\right)\)
C. \(\left(\begin{array}{ll}-4 & -4 \\ 12 & 13\end{array}\right)\)
D. \(\left(\begin{array}{cc}0 & -4 \\ -8 & -6\end{array}\right)\)

Question 460:

The inverse of matrix \(B\) is

A. \(\frac{1}{8}\left[\begin{array}{cc}-3 & 2 \\ 4 & 0\end{array}\right]\)
B. \(\left[\begin{array}{cc}-3 & 2 \\ 4 & 0\end{array}\right]\)
C. \(\frac{1}{8}\left[\begin{array}{cc}3 & -4 \\ -2 & 0\end{array}\right]\)
D. \(\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\)