Directions(1-5): Study the information given and answer the given below questions:
A group of 5 members needs to be formed from 4 doctors, 3 engineers and 5 teachers.
In how many ways the group can be formed if,
1. No teacher is included
A. 15
B. 18
C. 21
D. 24
E. None of these
Sol. Case-1 (4 doctors & 1 engineer) → 4c4 × 3c1 = 1×3 = 3
Case-2 (3 doctors & 2 engineer) → 4c3 × 3c2 = 4×3 = 12
Case-3 (2 doctors & 3 engineer) → 4c2 × 3c3 = 6×1 = 6
Total cases = 3+12+6 = 21.
2. Atleast 1 selected from each stream
A. 350
B. 400
C. 390
D. 380
E. None of these
Sol. Case-1 (2D , 2E & 1T) → 4C2×3C2×5C1 = 6×3×5 = 90
Case-2 (1D , 2E & 2T) → 4C1×3C2×5C2 = 4×3×10 = 120
Case-3 (2D , 1E & 2T) → 4C2×3C1×5C2 = 6×3×10 = 180
Total cases = 90+120+180 = 390.
3. Only teachers can be included
A. 5
B. 2
C. 3
D. 1
E. None of these
Sol. Total cases = 5c5 = 1.
4. Only engineers and teachers can be included
A. 56
B. 55
C. 54
D. 52
E. None of these
Sol. Case-1 (2 engineer & 3 teacher) → 3c2 × 5c3 = 3×10 = 30
Case-2 (3 engineer & 2 teacher) → 3c3 × 5c2 = 1×10 = 10
Case-3 (1 engineer & 4 teacher) → 3c1 × 5c4 = 3×5 = 15
Case-4 (5 teacher) → 5c5 = 1
Total cases = 30+10+15+1 = 56.
5. Total ways of forming the group
A. 756
B. 792
C. 764
D. 781
E. None of these
Sol. Total ways = 12c5 = 792.
Directions(6-10): What should come in place of (_) in the following series:
6. 16, 26, 42, 136, _
A. 534
B. 524
C. 494
D. 484
E. None of these
Sol. The series is ×1+10, ×2-10, ×3+10, ×4-10
7. 5, 6, 16, 57, 244, 1245, _
A. 7500
B. 7506
C. 7502
D. 7508
E. None of these
Sol. 5*1 + 1^2 = 6
6*2 + 2^2 = 16
16*3 + 3^2 = 57
57*4 + 4^2 = 244
244*5 + 5^2 = 1245
1245*6 + 6^2 = 7506
8. 95, 60, 36, 21, 13, _
A. 8
B. 9
C. 10
D. 11
E. 12
Sol. 95 - 60 = 35
60 - 36 = 24
36 - 21 = 15
21 - 13 = 8
13 - 10 = 3
35 - 24 = 11
24 - 15 = 9
15 - 8 = 7
8 - 3 = 5
Thus, C. 10
9. 25, 32, 53, 88, 137, _
A. 195
B. 200
C. 205
D. 210
E. None of these
Sol. 25 + (7*1) = 32
32 + (7*3) = 53
53 + (7*5) = 88
88 + (7*7) = 137
137 + (7*9) = 200
10. 3, 5, 13, 43, 177, _
A. 890
B. 889
C. 891
D. 892
E. None of these
Sol. 3*1 + 2 = 5
5*2 + 3 = 13
13*3 + 4 = 43
43*4 + 5 = 177
177*5 + 6 = 891.
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