In how many ways can 2 students be selected from a group of 5 students in a debating competition?
25 ways
10 ways
15 ways
20 ways
Correct answer is B
\(In\hspace{1mm} ^{5}C_{2}\hspace{1mm}ways\hspace{1mm}=\frac{5!}{(5-2)!2!}\\=\frac{5!}{3!2!}\\=\frac{5\times4\times3!}{3!\times2\times1}\\=10\hspace{1mm}ways\)
find the mean deviation of 1, 2, 3 and 4
2.5
2.0
1.0
1.5
Correct answer is C
X = 1, 2, 3, 4; ∑X = 10
x = ∑X/n = 10/4 = 2.5
X - x = -1.5, -0.5, 0.5, 1.5
lX - xl = 1.5, 0.5, 0.5, 1.5; ∑lX - xl = 4.0
mean deviation = (∑lX - xl)/n
= 4.0/4
= 1.0
12
21
28
32
Correct answer is B
Number of white balls = x
Number of red balls = 12
Number of black balls = 16
Total number of balls = 28 + x
P(white balls) = 3/7
But P(white balls) \(= \frac{x}{28+x}\\
= \frac{3}{7} = \frac{x}{28+x}\\
3(28 + x) = 7x\\
84 + 3x = 7x\\
7x - 3x = 84\\
4x = 84\\
x = 21\)
Evaluate \(\int_{1}^{3}(x^2 - 1)dx\)
\(\frac{2}{3}\)
\(-\frac{2}{3}\)
\(-6\frac{2}{3}\)
\(6\frac{2}{3}\)
Correct answer is D
\(\int_{1}^{3}(x^2 - 1)dx = \left[\frac{1}{3}x^2 - x\right] ^{3}_{1}\\ =(9-3)-(\frac{1}{3}-1)\\ =6-\left(-\frac{2}{3}\right)\\ =6+\frac{2}{3}=6\frac{2}{3}\)
Find the derivatives of the function y = 2x\(^2\)(2x - 1) at the point x = -1?
18
16
-4
-6
Correct answer is B
y = 2x\(^2\)(2x - 1)
expand the bracket
y = 4x\(^3\) - 2x\(^2\)
dy/dx = 12x\(^2\) - 4x
at x = -1
dy/dx = 12(-1)\(^2\) - 4(-1)
= 12 + 4
= 16