A man starts from a point A and travels 3 km towards east to reach B and then turns left and travels thrice the distance to reach another point C. From there he again turns left and travels five times the distance he covered between A and B and reaches his distination D. What is the shortest distance between the starting point and his destination?

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:

​

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)?