\(\frac{5}{8}\)
\(\frac{5}{16}\)
\(\frac{1}{2}\)
\(\frac{3}{8}\)
Correct answer is A
\(\begin{vmatrix}& \hline 1 & 2 & 3 & 4\\\hline 1 & 1 & 2& 3 & 4\\2 & 2& 4 & 6 & 8\\ 3& 3& 6& 9 & 12\\4 & 4 & 8 & 12& 16\end{vmatrix}\)
p (product of x, and y \(\leq\) 6) = \(\frac{10}{16}\)
= \(\frac{5}{8}\)
\(\frac{2}{15}\)
\(\frac{7}{15}\)
\(\frac{11}{15}\)
\(\frac{13}{15}\)
Correct answer is C
p(x) = \(\frac{2}{5}\) p(y) = \(\frac{1}{3}\)
p(x or y) = p(x ∪ y)
= p(x) + p(y)
= \(\frac{2}{5}\) + \(\frac{1}{3}\)
= \(\frac{11}{5}\)
4
20
24
40
Correct answer is A
Number of red balls = 16,
Number of blue balls = 20
Let x represent the No of white balls to be added
∴ Total number of balls = 36 + x
2(36 + x) = 80
= 2x + 80 - 72
= 8
x = \(\frac{8}{2}\)
= 4
Find the positive value of x if the standard deviation of the numbers 1, x + 1, 2x + 1 is 6
1
2
3
4
Correct answer is C
mean (x) = \(\frac{1 + x + 1 + 2x + 1}{3}\)
= \(\frac{3x + 3}{3}\)
= 1 + x
\(\begin{array}{c|c} X & (X -X) & (X -X)^2\\ \hline 1 & -x & x^2 \\ x + 1 & 0 & 0\\2x + 1 & x & x^2\\ \hline & & 2x^2\end{array}\)
S.D = \(\sqrt{\frac{\sum(x - 7)^2}{\sum f}}\)
= \(\sqrt{(6)}^2\)
= \(\frac{2x^2}{3}\)
= 2x2
= 18
x2 = 9
∴ x = \(\pm\) \(\sqrt{9}\)
= \(\pm\)3
Find the variance of the numbers k, k+1, k+2,
\(\frac{2}{3}\)
1
k + 1
(k + 1)2
Correct answer is A
mean (x) = \(\frac{\sum x}{N}\)
= k + k + 1 + k + 3
= \(\frac{3k + 3}{3}\)
= k + 1
\(\begin{array}{c|c} X & (X -X) & (X -X)^2\\ \hline k & -1 & 1 \\ k + 1 & 0 & 0\\ k + 2 & 1 \\ \hline & & 2\end{array}\)
Variance (52) = \(\frac{\sum (x - x)^2}{N}\)
= \(\frac{2}{3}\)