Related InterviewSolutions

• Find the sum of all integers between 84 and 719, which are multiples of 5
• Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers
• If x, y, z are in A.P. and A1is the A.M. of x and y, and A2 is the A.M. of y and z, then prove that the A.M. of A1 and A2 is y.
• A farmer buys a used tractor for ₹ 12000. He pays ₹ 6000 cash and agrees to pay the balance in annual instalments of ₹ 500 plus 12% interest on the unpaid amount. How much the tractor cost him?
• Find the sum of the following series:(i) 2 + 5 + 8 + … + 182(ii) 101 + 99 + 97 + … + 47(iii) (a – b)2 + (a2 + b2) + (a + b)2 + s…. + [(a + b)2 + 6ab]
• If a, b, c are in A.P., then show that:(i) a2(b + c), b2(c + a), c2(a + b) are also in A.P.(ii) b + c – a, c + a – b, a + b – c are in A.P.(iii) bc – a2, ca – b2, ab – c2 are in A.P.
• If (b + c)/a, (c + a)/b, (a + b)/c are in AP., prove that:(i) 1/a, 1/b, 1/c are in AP(ii) bc, ca, ab are in AP
• If a(1/b + 1/c), b(1/c + 1/a), c(1/a + 1/b) are in AP., prove that a, b, c are in AP.
• If a, b, c are in A.P., prove that:(i) (a – c)2 = 4 (a – b) (b – c)(ii) a2 + c2 + 4ac = 2 (ab + bc + ca)(iii) a3 + c3 + 6abc = 8b3