A man runs 20 meters towards east and turns right, runs for 15 meters and again turns right. New the man runs for 10 meters and again turns to his left. Now he again runs for 10 meters and turns to his left. From here the man runs for 20 meters and once more turns to his left and runs for 12 meters. Now which direction the man is facing?

For different sets of datasets X and Y. correlation coefficient between X and Y, that is R and standard deviation of X and Y, that is, S(X) and S(Y) are given in A-D below. Estimate the covariance between X and Y for each dataset and arrange in ascending order.
A. R= 0.5,     S(X)= 8,     S(Y)= 10
B. R= 4/7,     S(X)= 7,     S(Y)= 9
C. R= 0.7,     S(X)= 12,     S(Y)= 5
D. R= 19/42, S(X)= 14,     S(Y)= 6
Choose the correct answer from the options given below:

Arrange the following fractions in increasing order:
A. $$\frac{7}{11}$$​​

B. $$\frac{11}{7}$$​​

C. $$\frac{9}{13}$$​​

D. $$\frac{13}{21}$$​​

Choose the most appropriate answer from the options given below:

If $$\bar{X}$$ is the mean of $$x_1, x_2, x_3, \dots, x_n$$, then for $$a \neq 0$$,  the mean of $$(a x_1, a x_2, a x_3, \dots, a x_n$$, $$\frac{x_1}{a}$$, $$\frac{x_2}{a}$$, $$\frac{x_3}{a}$$,....$$\frac{x_n}{a}$$) is:

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Two successive discounts of 10% and 15% are equivalent to a single discount of:

A man gets an annual pay of Rs 9.0 lakh. His expenditure and savings are in the ratio 5:1. What is his average savings per month?

Suppose a man swims 12 km upstream and 20 km downstream in a river in 4 hours. If he swims 18 km upstream and 10 km downstream also in 4 hours, then the speed at which he swims in the still water is.

The liquids A and B are in the ratio 5 : 1 in container 1 and 1 : 3 in container 2. In what ratio should the contents of the two containers be mixed so as to obtain a mixture of A and B in the ratio 1 : 1?

Six numbers a, b, c, d, e, f are such that ab = 1, bc = 1/2, cd = 6, de = 2, and ef = 1/2. What is the value of (ad : be : cf)?