The variance of first 20 natural numbers is

• 133/4

• 279/12

• 133/2

• 399/4

A vehicle registration number consists of 2 letters of English alphabet followed by 4 digits, where the first digit is not zero. Then, the total number of vehicles with distinct registration numbers is

• ${26}^2 \times {10}^4$

• ${}^{26}\mathrm{P}_2 \times {}^{10}\mathrm{P}_4$

• ${}^{26}\mathrm{P}_2 \times 9 \times {}^{10}\mathrm{P}_3$

• ${}^{26}\mathrm{P}_2 \times 9 \times {10}^3$

The number of words that can be written using all the letters of the word 'IRRATIONAL' is

• $\frac{10!}{{\left(2!\right)}^3}$

• $\frac{10!}{{\left(2!\right)}^2}$

• $\frac{10!}{2!}$

• 10!

If the mean and variance of a binomial distribution are 4 and 2, respectively. Then, the probability of atleast 7 successes is

• $\frac{3}{214}$

• $\frac{4}{173}$

• $\frac{9}{256}$

• $\frac{7}{231}$

Mean and standard deviation from the following observations of marks of 5 students of a tutorial group (marks out of 25)

8,12,13,15,22 are

• 14, 4.604

• 15, 4.604

• 14, 5.604

• None of these

The relationship between the correlation coefficient r and the regression coefficients b_xy and b_yx, is

• $\mathrm{r} = \sqrt{{\mathrm{b}}_{\mathrm{xy}}{\mathrm{b}}_{\mathrm{yx}}}$

• $\mathrm{r} = \frac{2{\mathrm{b}}_{\mathrm{xy}}{\mathrm{b}}_{\mathrm{yx}}}{{\mathrm{b}}_{\mathrm{xy}} + {\mathrm{b}}_{\mathrm{yx}}}$

• $\mathrm{r} = \frac{1}{2}\left({\mathrm{b}}_{\mathrm{xy} }+ {\mathrm{b}}_{\mathrm{yx}}\right)$

• $\mathrm{r} = {\mathrm{b}}_{\mathrm{xy}} . {\mathrm{b}}_{\mathrm{yx}}$

If $\overline{\mathrm{x}} = \overline{\mathrm{y}} = 0, \sum \mathrm{xy} = 12, {\mathrm{\sigma }}_{\mathrm{x}} = 2, {\mathrm{\sigma }}_{\mathrm{y}} = 3, \mathrm{n} = 10$ then the coefficient of correlation is

• 0.4

• 0.3

• 0.2

• 0.1

If the coefficient of correlation between two variables is 0.32, covariance is 8 andvariance of x is 25, then variance of y is

• 36

• 25

• 64

• None of these

When b_yx = 0.03 and b_xy = 0.3, then r is equal to approximately

• 0.003

• 0.095

• 0.3

• - 0.3

Find the regression coefficient b_xy for the data $\sum \mathrm{x} = 32, \sum \mathrm{y} = 24, \sum \mathrm{xy} = 218, \sum {\mathrm{x}}^2 = 216, \sum {\mathrm{y}}^2 = 246$ and n = 8

• 0.3

• 0.7

• 0.8

• 0.6