two numbers at equal distance from 0 are called

For n N, in the expansion of (a + b) n , we observe that: the number of terms is n+1 the exponent of 'a' decreases from n to 0 the exponent of 'b' increases from 0 to n the sum of exponents of 'a' and 'b' in any term is n. the coefficient of any term i..

:d, the compounded ratio is ac:bd. Reciprocal ratio: The reciprocal ratio of a:b is which is b:a. Duplicate ratio: It is the compounded ratio of two equal ratios. The duplicate ratio of a:b is a 2 :b 2 . Triplicate ratio: It is the compounded ratio of three h..

Summary - A matrix is defined as a rectangular array of elements. If the arrangement has m rows and n columns, then the matrix is of order mxn (read as m by n). A matrix is enclosed by a pair of parameters such as ( ) or [ ]. It is denoted by a capital letter. Two matrices are said to be ..

1 , A 2 ,.....,A n are called the n arithmetic means between a and b. (vii) The sum of n A.M.s between given numbers a and b is equal to n times the A.M. between a and b. (viii) If a, b, c are in A.P., then for any k: (a) a+k, b+k, c+k a..

If two matrices have their corresponding elements equal, then they are called equal matrices. Two equal matrices are exactly the same. If the given matrix A is of the order m x n, then its transpose will be of the order n x m...

If two matrices have their corresponding elements equal, then they are called equal matrices. If then a = p, b = q, c = r and d = s. a = 7, b = 9, c = 3. (i) Two equal matrices are exactly the same. (ii) If rows are changed into columns an..

n C 0 , n C 1 , ..... n C n are called binomial coefficients. n C 0 , n C 2 n C 4 , ..... are called even binomial coefficients. n C 1 , n C 3 , n C 5 .... are called odd binomial coefficient..

1. Ratio is the numerical relationship between two quantities of the same kind. The first quantity is called the antecedent and the second quantity is called the consequent. 2. If two ratios are equal, we get four quantities in..

If a and b are any two quantities of the same kind a and b are not equal to zero. then the quotient a/b is called the ratio of a and b. It is expressed as a : b. (read as a is to b..

Square root of a negative number is known as an imaginary number . If x and y are real numbers, then x + iy is called a complex number . x is called the real part and y is called the imaginary part . The fo..