QBM021

Q1. If a and b are positive integers then 2 always lies between i. (a+b)/(a-b) and ab ii. a/b and (a+2b)/(a+b) iii. a and b iv. ab/(a+b) and (a-b)/ab Ans: ii Q2. X and Y are positive integers and it is given that X is less than Y. If X²+ Y² equals two times 5, the X/y= ? ANS: 1/3 Q3. The sides of triangle are in the ratio 1/3 : ¼ : 1/5 and its perimeter is 94 cm, the length of smallest side is: ANS: 31.3 cm Q4. An alloy of gold and silver is taken in the ratio 1 : 2, and another alloy of the same metals is taken in the ratio of 2 : 3. How many parts of the two alloys must be taken to obtain a new alloy consisting of gold and silver that are in the ratio 3 : 5? Ans: 3 and 5 Q5. The proportion of milk and water in 3 samples is 2:1, 3:2 and 5:3. A mixture comprising of equal quantities of all 3 samples is made. The proportion of milk and water in the mixture is ANS: 227:133 Q6. The weights of three heaps of gold are in the ratio 5: 6: 7. By what fractions of themselves must be the first two be increased so that the ratio of the weights may be changed to 7: 6: 5? Ans: 24/25, 2/5 Q7. A mixture contains milk and water in the ratio 5:1. On adding 5 lts of water the ratio of milk and water becomes 5:2. Find the quantity of milk in the original mixture ANS: 25lts Q8. The radius of the circum circle of an equilateral triangle of side 12 cm is. ANS: 4√3 cm Q9. Starting at 870 and counting backwards by 7’s, a student count 870, 863, 856, etc. A number that will be counted is: a. 116 b. 115 c. 114 d. 113 e. 112 Q10. Two numbers are such that their difference, their sum and their product are in the ratio of 1 : 7 : 24. The product of the numbers is ANS: 48 Q11. A second order recurrence relation is defined by un+1 = (un+un 1)/2; that is, each new term is the mean of the previous two terms.For example, when u1=2 and u2=5, we generate the following sequence: 2, 5, 3.5, 4.25, 3.875, Find the limit of the sequence for different starting values.