everyday math use

Question: Given 6 flags of different colours, how many different signals can be generated, if a signal requires the use of two flags one below the other? Answer: Number of signals obtained by 6 flags taking 2 flags at a time is P(6,2). P(6,2) = 6 x 5 = 30..

Question: How many three letter words (with or without meaning) can be formed out of the letters of the word LOGARITHMS if repetition of letters is not allowed? Answer: Number of letters in the word LOGARITHMS is 10. The three letter words formed by using these letters will be..

Question: Four alphabets T, A, L and K, one each were purchased from a plastic warehouse. How many ordered pairs of alphabets to be used as initials, can be formed from them? Answer: Four letters A, K, L, T are purchased. For an initial, two alphabets are required. Thus, the n..

Question: Use the Binomial Theorem to (expand) evaluate. Answer: ..

Matrices - Consider the arrangement In this arrangement, there are two rows and four columns. The number 3 lies in the 2 n d row and 4 t h column. Each number has a fixed position. Matrix A has 2 rows and 3 columns and is thus of order 2 x 3. Matrix B has 3 rows and 2 columns and is thus of order 3..

Question: How many three digit numbers are there, with distinct digits, with each digits odd? Answer: Here, we have to form three digit numbers with distinct digits, each digit odd. The digits used are 1, 3, 5, 7, 9. Number of odd digits is 5. From 5 odd digits, we have to ta..

Question: How many four digit numbers can be formed using the digits 3,4,6,7 and 8 without repetition? Answer: Unit's place can be filled in 5 ways (First Digit). Ten's place can be filled in 4 ways (Second Digit). Hundred's place can be filled in 3 ways (Third Digit). Thous..

Question: Find the sum of all four digit numbers formed by using 2, 3, 6, 9 in which no digit is repeated. Answer: If 2 occupies unit's place, the remaining 3 digits can be arranged in 3!= 6ways. Similarly, if 2 occupies ten's place, hundred's place, thousand's place, in each ..

Question: The sides AB, BC, CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. Find the number of triangles that can be drawn using these points as vertices. Answer: The points 3+4+5=12 points lie in a plane. To construct a triangle, we require three no..

Note that we can also evaluate the determinant D 1 , D 2 and D 3 directly without using the properties of determinant. The solution of the system is given by It is important to mention here the consistency and inconsistency of a system of linear equations with three unknown..