math chapter 2 mid chapter quiz answers

Let H be the harmonic mean between the quantities a and b. ..

Let a and b be two given quantities. It is required to insert n harmonic means h 1 , h 2 , h 3 ,....h n between the quantities a and b. Let d = common difference of the A.P. Hence h 1 , h 2..

We recall from our earlier classes that a system of linear equation with two variables is given by This system of linear equation may have either one solution or infinitely many solutions or no solutio..

i) 1.2 + 2.4 + 3.8 +.... to n terms The n t h term of (1,2,3,....n) is n. The n t h term of (2,4,8,...) is The n t h term of the given series is n2 n Subtracting (ii) from (i), we have ..

2. Find the sum to n terms of the seri..

From (1) and (2) (A + B) + C = A + (B + C) verify the associative la..

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..

Let S n = 1+2+3+4+...+n This series is an A.P. Here a=1, d=1, l = t n = n 2. To find the sum to squares of first n natural numbers. or..

= (14 - 12) - (7 - 3) + (4 - 2) = 2 - 4 + 2 = 0 The system may have infinite number of solutions or no solution. Put x = k in (1) and (2) and solve y + z = 6 - k 2y + 3z = 14 - k. Solving the above two equations, we have z = k + ..

1. 2 and 3 are two digits and with these digits, the numbers 32 and 23 are formed. Although both numbers viz., 32 and 23 consist of the digits 2 and 3, the order of digits is different. Each of the above arrangements is called a 'permutation'. Thus, the number of arra..