Q8) The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greatest number is: 1) 111 2) 185 3) 103 4) 222 The numbers are 37a, 37b 37a × 37b = 4107 ab = 3 a = 3, b = 1 or a = 1, b = 3 Greatest number is 111. Hence, option 1. Q9) H.C.F. of two polynomials P(y), Q(y) is (y - 2) and their L.C.M. is (y ^{3} + 5y^{2} - 2y - 24). If Q(y) is y^{2} + y - 6, find the P(y).1) y ^{2} - 2y - 82) y ^{2} - 5y + 63) y ^{2} + 2y - 84) None of these H.C.F. × L.C.M. = P(y) × Q(y) Hence, option 3. Q10) Find the least number which when divided by 12 and 16 leaves 0 as the remainder. 1) 96 2) 48 3) 144 4) 75 L.C.M.(12,16) Hence, option 2. Q11) There are 3 bells. They start tolling together. First bell tolls every 4 seconds, second bell tolls every 6 seconds and the third bell tolls every 8 seconds. How many times will the three bells toll together in 4 minutes ? 1) 11 2) 12 3) 10 4) 9 Time after which the bells will toll together is the L.C.M.of 4, 6, 8 i.e. 24 sec. Number of times these bells will toll together in 4 minutes = Hence, option 1. Q12) H.C.F. of two numbers is 7 and their sum is 210. How many such ordered pairs are possible? 1) 4 2) 16 3) 8 4) None of these Let the two numbers be 7x, 7y x + y = 30 such that x, y are co-primes. Total ordered pairs possible = 8 Hence, option 3. Q13) A general can draw up his soldiers in rows of 10, 15, or 18 soldiers and he can also draw them up in the form of a solid square. Find the least number of soldiers with the general. 1) 100 2) 3600 3) 900 4) 90 LCM of 10, 15 and 18 is 90 To make it a perfect square, we multiply it with 10. Required number of soldiers are 900. Hence, option 3. |