Question : Three numbers are in Arithmetic Progression (A.P.) whose sum is 30 and the product is 910. Then the greatest number in the A.P. is:
Option 1: 17
Option 2: 15
Option 3: 13
Option 4: 10
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Correct Answer: 13
Solution : Let three numbers in A.P. be a – d, a, and a + d, respectively. According to the question, a – d + a + a + d = 30 ⇒ 3a = 30 ⇒ a = $\frac{30}{3}$ = 10 Again, a×(a – d)×(a + d) = 910 ⇒ 10×(10 – d)×(10 + d) = 910 ⇒ 100 – d2 = 91 ⇒ d2 = 100 – 91 = 9 ⇒ d = $\sqrt{9}$ = 3 $\therefore$ Largest number = a + d = 10 + 3 = 13 Hence, the correct answer is 13.
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Question : The sum of three positive numbers is 18 and their product is 162. If the sum of two numbers is equal to the third number, then the sum of the squares of the numbers is:
Option 1: 120
Option 2: 126
Option 3: 132
Option 4: 138
Question : The sum of three positive numbers is 18 and their product is 162. If the sum of two numbers is equal to the third number, the sum of the squares of the numbers is:
Question : Three numbers are in the ratio $\frac{1}{2}: \frac{2}{3}: \frac{3}{4}$. If the difference between the greatest number and the smallest number is 33, then the HCF of the three numbers is:
Option 1: 9
Option 2: 5
Option 4: 11
Question : What is the sum of the first 13 terms of an arithmetic progression if the first term is –10 and the last term is 26?
Option 1: 104
Option 2: 140
Option 3: 84
Option 4: 98
Question : The greater of the two numbers whose product is 900 and whose sum exceeds their difference by 30 is:
Option 1: 60
Option 2: 75
Option 3: 90
Option 4: 100
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