Foundation PN-3 FBMS Quiz 9

1. From the following four year centered moving average against year 4 is

Year      1      2     3     4     5  6  7

Import

(` m)  229 231 206 191 195 184 193

2. How many ways can 5 books be arranged on a shelf if 2 specific books must not be together?

3. The number of ways to arrange the letters of the word “BALLOON” is:

4. If 3^2x × 9^x-1 = 729, find X.

5. If log5 X + log5 (X-4) = 1, find X.

6. If loga 36 = 2+ loga 6 = 1

7. If log2 8 + log2 4 = ?

8. If 3^x+1 = 81, find the value of x.

9. In a class, 60 students took exams in math or science. 40 passed math, 35 passed science, and 10 passed both. How many passed only science?

10. In a class of 50 students, 28 play basketball, 22 play volleyball, and 10 play both. How many play exactly one sport?

11. In a group of 60 students, 25 like cricket, 30 like football, and 10 like both. How many students like neither cricket nor football?

12. A train running at 54 km/h crosses a pole in 30 seconds. What is the length of the train in meters?

13. A boat goes 30 km upstream in 2 hours and returns downstream in 1.5 hours. Find the speed of the stream.

14. Two trains start from two stations 250 km apart and move towards each other at speeds of 60 km/h and 40 km/h respectively. They cross after how much time?

15. A person covers a certain distance at a speed of 40 km/h and returns at a speed of 60 km/h. What is his average speed for the entire journey?

16. If the sum of the first n terms of an AP is Sₙ = 3n² + 2n, what is the 10th term?

17. The 5th term of a GP is 64 and the 8th term is 512. Find the common ratio.

18. The 12th term of an AP is 45, and the 20th term is 77. What is the common difference?

19. If ₹12,000 is invested for 2 years at compound interest and the total amount is ₹13,824, what is the rate of interest per annum?

20. A person wants to have ₹20,000 in 3 years. If the bank offers 8% per annum  compound  interest,  what amount should he invest now?

21. If ₹5,000 is invested for 4 years at 10% per annum simple interest, what is the total interest earned?

22. A sum of ₹10,000 is invested at 8% per annum compound interest, compounded annually. What will be the amount after 3 years?

23. If the mean proportional between 9 and x is 15, find x.

24. A sum of ₹480 is divided among A, B, and C such that A’s share : B’s share = 3 : 5 and B’s share : C’s share = 10 : 12. Find C’s share.

25. If x : y = 5 : 7 and y : z = 14 : 15, find x : z.

26. If a : b = 3 : 4 and b : c = 8 : 9, then what is a : b : c ?