1.A problem on mathematics is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the chance that the problem will be solved?
A.2/3
B.3/4
C.1/3
D.1/2
E.None of these
Sol. The chances of not solving the question would be subtracted from 1.
Therefore, 1 - ( 1/2 × 2/3 × 3/4 ) = 3/4
2. The sum of the second and the fifth term of an AP is 8 and that of the third and the seventh term is 14. Find the eleventh term.
A.19
B.17
C.15
D.16
E.None of these
Sol. From the given conditions we get the equations as
2a + 5d = 8 .................(1)
2a + 8d =14 .................(2)
Solving these equations, we get a = -1 and d = 2.
So, 11th term = (a +10d) = 19.
3. Two pipes can fill a cistern in 14 and 16 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom of the cistern, it takes 32 minutes extra for the cistern to be filled up. When the cistern is full, in what time will the leak empty it?
A.114 hrs
B.112 hrs
C.100 hrs
D.80 hrs
E.None of these
Sol. Work done by both pipes in a hour = (1 / 14) + (1 / 16) = 15 / 112 . So both pipes can fill the tank in 112 / 15 hours.
But because of the leak time taken by them is (112 / 15) + (32 /60)=8 hours
Considering the leak takes x hours to empty the tank, we get;
(1 / 14) + (1 / 16) – (1 / X) = 1 / 8.
On solving we get X = 112 hours.
4. The number of people in a boarding house increases at a fix annual percent rate. There were 216 people in the boarding house 6 years ago and 1728 people now. What will be the number of people 2 years later?
A.3956
B.3666
C.3456
D.3256
E.None of these
Sol. Since the no. of people increase at constant rate.
Therefore, 1728 = 216(1 + R/100)^6
1 + R/100 = (8)^1/6
Now, population after two years will be,
1728(1 + R/100)^2
1728(8)^1/3 = 1728*2 = 3456
Directions(5-10):Find the missing numbers in the given series
5. 12, 20, _, 57, -68
A. 2
B. 15
C. -7
D. -2
E. None of these
Sol. 12 + 2^3 = 20
20 - 3^3 = -7
-7 + 4^3 = 57
57 - 5^3 = -68
6. 68, 62, _, 54, 84
A. 76
B. 72
C. 74
D. 70
E. None of these
Sol. 68 - (2*3) = 62
62 + (3*4) = 74
74 - (4*5) = 54
54 + (5*6) = 84
7. 15, 3, _, 18/25, 72/125
A. 6
B. 3/5
C. 6/5
D. 8/5
E. None of these
Sol. 15 * 1/5 = 3
3 * 2/5 = 6/5
6/5 * 3/5 = 18/25
18/25* 4/5 = 72/125
8. 2, 0, _, -4, 12
A. 2
B. 4
C. 8
D. -2
E. None of these
Sol. 2 - 2 = 0
0 + 4 = 4
4 - 8 = -4
-4 + 16= 12
9. 1, 5, _, 57, 121
A. 25
B. 23
C. 21
D. 22
E. None of these
Sol. 1 + 2^2 = 5
5 + 4^2 = 21
21 + 6^2 = 57
57 + 8^2 = 121
10. 10, 15, 30, _, 225
A. 50
B. 65
C. 75
D. 60
E. None of these
Sol. 10 * 1.5 = 15
15 * 2 = 30
30 * 2.5 = 75
75 * 3 = 225
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