\(\frac{13}{12}\)
\(\frac{5}{12}\)
-\(\frac{5}{12}\)
\(\frac{-1}{2}\)
Correct answer is C
P * q = \(\frac{q^2 - p^2}{2pq}\).
3 * 2 (where p = 3, q = 2)
i.e 3 *2 = \(\frac{3^2 - 2^2}{2 *3 * 2}\)
= \(\frac{4 - 9}{12}\)
= \(\frac{-5}{12}\)
For what value of k is 4x\(^2\) - 12x + k, a perfect square?
-9
\(\frac{-9}{4}\)
\(\frac{9}{4}\)
9
Correct answer is D
4x\(^2\) - 12x + k;
a = 4, b = -12, c = k.
For perfect square b\(^2\) = 4ac
(-12)\(^2\) = 4 * 4 * k;
144 = 16k
k = 144\16
k = 9
-7.0
-8.0
-9.6
9
Correct answer is B
f(x) = 4x\(^3\) + px\(^2\) + 7x - 23
If f(x) is divided by (2x -5), the remainder is f(\(\frac{5}{2}\))
f\(\frac{5}{2}\) = 4\(\frac{5}{2}\)\(^3\) + p\(\frac{5}{2}\)\(^2\) + 7\(\frac{5}{2}\) - 23
Hence;
= \(\frac{125}{8}\) + \(\frac{25}{4}\) p + \(\frac{35}{2}\) - 23
28 = 250 + 250p + 70 - 92
25p = -200; p = -8.0
If α and β are the roots of 3x\(^2\) - 7x + 6 = 0, find \(\frac{1}{α}\) + \(\frac{1}{β}\)
\(\frac{7}{6}\)
\(\frac{7}{3}\)
\(\frac{14}{5}\)
\(\frac{14}{3}\)
Correct answer is A
3x\(^2\) - 7x + 6 = 0
α + β = \(\frac{7}{3}\);
αβ = 2;
\(\frac{1}{α}\) + \(\frac{1}{β}\) = \(\frac{α +β}{αβ}\)
\(\frac{7}{3}\) ÷ 2
= \(\frac{7}{6}\)
In how many ways can 8 persons be seated on a bench if only three seats are available?
100
125
336
427
Correct answer is C
\(^3{P}_3\) = \(\frac{8!}{8-3}!\)
= \(\frac{(8 * 7 * 6 * 5)!}{5!}\)
= 336