find the number of combinations of choosing 2 cubes from 5 cubes shown.

Find the number of combinations of choosing 2 cubes from 5 cubes shown. => 10 or 72 or 56 or 25..

Some Applications of Binomial Theorem for Fractional Index - If x be numerically so small that its cube and higher powers may be x 3 , x 4 , x 5 , . are all approximately zero. If x be numerically so small that its square and higher powers may be neglected, then (1+x) n = 1+nx (..

1. To find the sum of first n natural numbers. 2. To find the sum to squares of first n natural numbers. 3. To find the sum to the cubes of first n natural numbers. 4. Method of finding su..

Question 1 - Question: Show that the sum of the cubes of any number of consecutive integers is divisible by the sum of those integers. Answer: Let the consecutive integers be (n + 1), (n + 2), (n + 3),....,(n + m) Sum of the cubes of integers = S 1 (n+m) and ..

of (a + b) n and is given by - If n is an odd natural number, then there are two middle terms in the expansion of (a + b)n and are given by i) The sum of all binomial coefficients in the expansion of (1+x) n is 2 n . ii) The sum of all even binomial coefficients in the..

The ratio obtained by taking the cube root of the given ratio a : b is called sub-triplicate ratio. is sub-triplicate ratio of a : b. For example the sub-triplicate ratio of 8a 3 : 27b 6 is or 2a : 3b 2 . Find the compounded ratio of the duplicate ..

Multiplication of Matrices - Let us consider the sales done by a school canteen for two successive days. Monday 25 cokes 12 cakes Tuesday 40 cokes 7 cakes Each coke costs $ 5 and cake costs $ 10. The sales can be expressed as a 2 x 2 matrix and the price as a..

radius = ..

If (x-2) and (x-3) are factors of x 3 +ax 2 +bx+12, find a and ..

Question: Find the first four terms of the sequence 4 + 5n. Which term of the sequence is 99? Answer: When n = 1, t 1 = 4+5(1) = 9. When n = 2, t 2 = 4+5(2) = 14 When n = 3, t 3 = 4+5(3) = 19. When n = 4, t 4 = ..