Permutations an...

A group of 1200 persons consisting of captains and soldiers is travelling in a train. For every 15 soldiers there is one captain. The number of captains in the group is: 

Choose the correct statement(s):

A, B, C and D are four 4-digit numbers each having the digit 9 only once and in the place shown None of the other digits are known
What can be said about A, B, C and D?

Observe the following pattern for obtaining the sums then find the sum of numbers from 781 to 790?
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55
11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 = 155
21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 + 30 = 255
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
51 + 52 + 53 + 54 + 55 + 56 + 57 + 58 + 59 + 60 = 555
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
101 + 102 + 103 + 104 + 105 + 106 + 107 + 108 + 109 + 110 = 1055
251 + 252 + 253 + 254 + 255 + 256 + 257
258 + 259 + 260 = 2555

Given three vertices of a triangle whose coordinates are A (1, 1), B (3, -3) and (5, -3). Find the area of the triangle.

The area of triangle whose vertices are $$A (-3, -1), B(5, 3)$$ and $$C(2, -8)$$ is ____ $$\text{ sq. units}$$.

If there are five consecutive integer in a series and the first integer is $$1$$, what is the value of the last consecutive integer?

A sequence of numbers in which each term is related to its predecessor by same law is called

$$10,$$ __$$, 15, 15, 20, 20, 25, 25,...$$. What number should fill the blank?

________ can be defined as arrangement of terms in which sequence of terms follow some conditions.