the sum of 10 less than a number and the number itself is three times the number. find the number.

Question: Four numbers are in AP. Sum of the first three is 21 and sum of last three is 30. Find the numbers. Answer: Let the numbers a - 3d, a - d, a + d, a + 3d be in AP. ..

If the rows and columns of a determinant are inter-changed, the value remains unaltered. If any two rows (columns) of a determinant are identical, its value of the determinant is zero. If any two rows (columns) of a determinant are interchanged, the value of the determinant is (-1) tim..

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 are in A.P...

The following are the steps to solve a system of linear equations using Cramer's rule. Step 1: Find the value of the determinant Step 2: If D 0, then the system has unique solution, given by Where D 1 , D 2 and D 3 are the determinants obtained from D by replacing respectively t..

Let a=first term, d = common difference, l=t n =last term, s = required sum. Then, Writing the series in the reverse order, Adding together the two series, ..

Square root of a negative number is known as an imaginary number. a > 0 is an imaginary number. or A number whose square is negative is known as an imaginary number. . . . The symbol i, We writ..

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 ..

1. Find the sum to the series 1+2x+3x 2 +.... to n terms and to infinity when x < ..

In case of a polynomial of one variable the highest power of the variable is called the degree of the polynomial. 3y-7y 3 has degree 3 and..

Approximation - We know that the digits of a number, one by one in order from left to right decrease in value rapidly. Let us illustrate it by examples. Mass of a gold ornament is 23.473 g. Round off to (i) two decimal places, (ii) one decimal place. 23.473 g = (2 x 10) + (..