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Question: From 12 books, in how many ways can 5 be chosen i. to surely include a particular book ii. never to include a particular book iii. to have no restrictions at all? Answer: i. To include a particular book, one particular book has already been chosen. We have to select 4 books fr..

Using determinants, find the area of triangle whose vertices are (2, -7), (1, 3), (10, 8). Solution: (x 1 , y 1 ) = (2, -7) (x 2 , y 2 ) = (1, 3) (x 3 , y 3 ) = (10, 8) Area of the triangle = -47.5 Since area has to be a positive quantity, it is given by 47.5 sq.uni..

Let A = [a ij ] be a square matrix. We can associate with the square matrix A, a determinant which is formed by exactly the same array of elements of the matrix A. A determinant formed by the same array of elements of the square matrix A is called the determinant of the square matrix A and is denot..

If A and B are 2 matrices of the same order, then A + B is the sum of the 2 matrices where each element is got by adding corresponding elements of A and B. ..

The matrices are identify matrices of order 2 and 3 respectivel..

1. O!= 1 2. When n is a negative or fraction, n! is not defined...

Let the n t h term of series be an 3 + bn 2 + cn + d t n = an 3 + bn 2 + cn + d where a, b, c, d are constants. ..

If a,b,c,d are in A.P., then (ii) ka, kc, kb, kd are also in A.P. A remark on finding a few members of an A.P. whose sum is given along with other conditions: i) If the sum of three numbers in A.P. is given, take the numbers as a-d, a, a+..

Question 1 - Question: Prove that the number of ways in which (m+n) dissimilar things can be divided into two groups containing m and n Answer: If we select m things out of (m+n) things, then n things are left out . Then, this gives (m+n) that can be divided into two groups containing m and n thing..

Arithmetic Mean (A.M.) - 1. If a, x, b are in A.P, then x is called the arithmetic mean (A.M.) between the extremes a and b. 2. a. To insert n arithmetic means between two given quantities. Let a and b be any two given quantities, and let A 1 ,A 2 ,A 3 ,-----A n be n arithmetic means to be inserted..