Factorize m\(^3\) - m\(^2\) + 2m - 2
(m2 + 1)(m - 2)
(m - 1)(m + 1)(m + 2)
(m - 2)(m + 1)(m - 1)
(m2 + 2)(m - 1)
Correct answer is D
Using trial expansion of each option
(m\(^2\) + 2) (m - 1)
If g(x) = x\(^2\) + 3x find g(x + 1) - g(x)
(x + 2)
2(x + 2)
(2x + 1)
(x2 + 4)
Correct answer is B
g(x) = x2 + 3x
When g(x + 1) = (x + 1)^2 + 3(x + 1)
= x\(^2\) + 1 + 2x + 3x + 3
= x\(^2\) + 5x + 4
g(x + 1) - g(x) = x2 + 5x + 8 - (x\(^2\) + 3x)
= x\(^2\) + 5x + 4 - x2 -3x
= 2x + 4 or 2(x + 4)
= 2(x + 2)
uvw = 16(u + v)
16uv = 3w(u + v)
uvw = 12(u + v)
12uvw = u + v
Correct answer is C
W \(\alpha\) \(\frac{\frac{1}{uv}}{u + v}\)
∴ w = \(\frac{\frac{k}{uv}}{u + v}\)
= \(\frac{k(u + v)}{uv}\)
w = \(\frac{k(u + v)}{uv}\)
w = 8, u = 2 and v = 6
8 = \(\frac{k(2 + 6)}{2(6)}\)
= \(\frac{k(8)}{12}\)
k = 12
i.e 12 ( u + v) = uwv
Find the probability that a number selected at random from 41 to 56 is a multiple of 9
\(\frac{1}{8}\)
\(\frac{2}{15}\)
\(\frac{3}{16}\)
\(\frac{7}{8}\)
Correct answer is A
Given from 41 to 56
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56
The nos multiple of 9 are: 45, 54
P(multiple of 9) = \(\frac{2}{16}\)
= \(\frac{1}{8}\)
\(\frac{2}{3}\)
\(\frac{1}{2}\)
\(\frac{1}{3}\)
\(\frac{1}{4}\)
Correct answer is B
\(\begin{array}{c|c} 1 & 2 & 3 & 4\\\hline 1(1, 1) & (1, 2) & (1, 3) & (1, 4)\\ \hline 2(2, 1) & (2 , 2) & (2, 3) & (2, 4) \\ \hline 3(3, 1) & (3, 2) & (3, 3) & (3, 4)\\ \hline 4(4, 1) & (4, 2) & (4, 3) & (4, 4)\end{array}\)
sample space = 16
sum of nos. removed are (2), 3, (4), 5
3, (4), 5, (6)
(4), 5, (6), 7
(5), 6, 7, (8)
Even nos. = 8 of them
Pr(even sum) = \(\frac{8}{16}\)
= \(\frac{1}{2}\)