From the analysis of Previous Years Papers, it has come to the notice that this chapter has got great importance, each year lot of questions are asked from this chapter alone.
In the year 2024, two questions and in other Previous Years approximately 4-5 questions were asked directly from this chapter every year.
From the exam point of view, it is very important to cover this chapter with through understanding.
Illustration: The music director of a film wants to select four persons to work on ‘different aspects of the composition of a piece of music. Seven persons are available for this work, they are Rohit, Tanya, Shobha, Kaushal, Kunal, Mukesh and Jaswant. Rohit and Tanya will not work together. Kunal and Shobha will not work together. Mukesh and Kunal want to work together.
Which of the following is the most acceptable group of people that can be selected by the music director? UPSC (CSAT)
(a) Rohit, Shobha, Kunal and Kaushal
(b) Tanya, Kaushal, Shobha and Rohit
(c) Tanya, Mukesh, Kunal and Jaswant
(d) Shobha, Tanya, Rohit and Mukesh
Sol: (c) Rohit and Tanya cannot work together means that options (b) and (d) are out. Kunal and Shobha will not work together and so option (a) is out. Hence, the right answer is (c), where no one has problem working with another person of the group and Mukesh and Kunal can also work together.
Example 1: Which number will replace the question mark ?
Solution:
From fig. a: 6 + 4 + 8 = 18
18 + 2 = 20
From fig. b: 7 + 9 + 8 = 24
24 + 2 = 26
From fig. c: 6 + 5 + 12 = 23
23 + 2 = 25
Hence the number 25 will replace the question mark.
Example 2: Which number will replace the question mark ?
Solution:
From fig. a: (3)2 + (2)2 = 13
From fig. b: (4)2 + (8)2 = 80
From fig. c: ? = (1)2 + (5)2
? = 1 + 25
? = 26
Hence the number 26 will replace the question mark.
Example 3: Which number will replace the question mark?
Solution:
From fig. a: 7 x 6 + 3 = 45
From fig. b: 5 x 4 + 6 = 26
From fig. c: 7 x 3 + 8 = 29
Hence the number 29 will replace the question mark.
Example 4: Which number will replace the question mark ?
Solution:
From column I: (9 x 5) % 5 = 9
From column II: (17 x 4) % 4 = 17
From column III: (16 x ?) % 8 = 8
16? = 64
? = 4
Hence the number 4 will replace the question mark.
Example 5: Which number will replace the question mark ?
Solution:
From fig. a: (8 x 5) - (4 x 3) = 28
From fig. b: (12 x 7) - (8 x 9) = 12
From fig. c: (5 x 3) - (6 x ?) = 21
15 - 6? = 21
6? = -6
? = -1
Hence the number -1 will replace the question mark.
Example 6: Which number will replace the question mark ?
Solution:
In each row there are 'A', 'B' and 'C'
In second row 'A' and 'C' are already there
Hence in place of ?, there will be 'B'.
From first row : 4A x 6C = 24B
From third row : 9B x 4C = 36A
From second row : 5A x ? = 45C
? = (45C/5A)
? = 9B
Hence the number 9B will replace the question mark.
Example 7: Which number will replace the question mark?
Solution:
(5)2 = 25
(6)2 = 36
(4)2 = 16
(7)2 = 49
Hence the number 49 will replace the question mark.
Example 8: Which one will replace the question mark?
Solution:
(15 x 2 - 3) = 27
(31 x 2 - 6) = 56
(45 x 2 - 9) = 81
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