Find the values of x for which the expression \(\frac{(x - 3)(x - 2)}{x^2 + x - 2}\)
1, -2
-1, 2
2, 3
-1. -2
-2, -3
Correct answer is A
to find the values of x for which the expression is underlined, let x2 + x - 2 = 0
By factorizing, we have (x + 2)(x - 1) = 0
when x + 2 = 0, when x - 1 = 0, x = -2 or x = 1
The two values are -2 and 1
Express 37.05 x 0.0042 in standard form
15.561 x 102
1.5561 x 10-4
1.556 x 10-1
1.5561 x 101
1.55 x 101
Correct answer is C
37.05 x 0.0042 in standard form
\(\begin{array}{c|c}No. & log \\\hline 37.05 & 1.5688\\ 0.0042 & 3.6232 \\ \hline & 1.1920\end{array}\)
= 0.1556
= 1.556 x 10-1
Solve for x, If \(\frac{\frac{2}{x}}{\frac{1}{p^2} + \frac{1}{p^2}}\) = m
\(\frac{4pq}{m(p + q)}\)
\(\frac{2p^2q^2}{m(q^2 + p^2)}\)
\(\frac{2pq}{m(q^2 + p^2)}\)
\(\frac{2p^2q^2}{m(p^2)}\)
Correct answer is B
\(\frac{1}{p^2}\) + \(\frac{1}{q^2}\) = \(\frac{q^2 + p^2}{p^2 + q^2}\)
\(\frac{\frac{2}{x}}{\frac{p^2 + q^2}{p^2 q^2}}\)
m = \(\frac{2p^2q^2}{x(p^2 + q^2)}\)
= m2p2q2 = m x (p2 + q2)
x = \(\frac{2p^2q^2}{m(q^2 + p^2)}\)
M2467
M2427
M2367
M3417
M3387
Correct answer is D
4 bags of rice - M 56 each
3 tins of milk - M 4 each
\(M 56 \times 4 = M 323\)
\(M 4 \times 3 = M 15\)
\(M (323 + 15) = M 341\)
If sin \(\theta\) = \(\frac{m - n}{m + n}\); Find the value of 1 + tan2\(\theta\)
\(\frac{(m^2 + n^2)}{m + n}\)
\(\frac{(m^2 + n^2 + 2mn)}{4mn}\)
\(\frac{2(m^2 + n^2 + mn)}{m + n}\)
\(\frac{(m^2 + n^2 + mn)}{m + n}\)
Correct answer is B
\((m + n)^{2} = (m - n)^{2} + x^{2}\)
\(m^{2} + 2mn + n^{2} = m^{2} - 2mn + n^{2} + x^{2}\)
\(x^{2} = 4mn\)
\(x = \sqrt{4mn} = 2\sqrt{mn}\)
1 + tan2\(\theta\) = sec2\(\theta\)
= \(\frac{1}{cos^2\theta}\)
\(\cos \theta = \frac{2\sqrt{mn}}{(m + n)}\)
\(\frac{1}{\cos \theta} = \frac{(m + n)}{2\sqrt{mn}}\)
\(\sec^{2} \theta = \frac{(m + n)^{2}}{4mn}\)
= \(\frac{(m^2 + n^2 + 2mn)}{4mn}\)