UPSC Exam > UPSC Questions > 4, 196, 16, 144, 36, 100, 64, x x ?a)48b)6...
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अनुक्रम 4, 196, 16, 144, 36, 100, 64, x में x क्या है?
- a)48
- b)64
- c)125
- d)256
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
4, 196, 16, 144, 36, 100, 64, x x ?a)48b)64c)125d)256Correct answer...
To find the missing number in the given series, let's analyze the pattern:
Pattern 1:
4, 16, 36, 64, ...
This is a series of perfect squares starting from 2² (4), 4² (16), 6² (36), 8² (64), ...
Pattern 2:
196, 144, 100, ...
This is a series of perfect squares in reverse order, starting from 14² (196), 12² (144), 10² (100), ...
Based on these patterns, we can conclude that the missing number should follow the pattern of perfect squares.
Now, let's look at the given options:
a) 48: This number does not fit the pattern of perfect squares, so it is not the missing number.
b) 64: This number is a perfect square and fits the pattern perfectly. It is the square of 8, so it is the missing number.
c) 125: This number does not fit the pattern of perfect squares, so it is not the missing number.
d) 256: This number does not fit the pattern of perfect squares, so it is not the missing number.
Hence, the correct answer is option 'B' - 64.
Pattern 1:
4, 16, 36, 64, ...
This is a series of perfect squares starting from 2² (4), 4² (16), 6² (36), 8² (64), ...
Pattern 2:
196, 144, 100, ...
This is a series of perfect squares in reverse order, starting from 14² (196), 12² (144), 10² (100), ...
Based on these patterns, we can conclude that the missing number should follow the pattern of perfect squares.
Now, let's look at the given options:
a) 48: This number does not fit the pattern of perfect squares, so it is not the missing number.
b) 64: This number is a perfect square and fits the pattern perfectly. It is the square of 8, so it is the missing number.
c) 125: This number does not fit the pattern of perfect squares, so it is not the missing number.
d) 256: This number does not fit the pattern of perfect squares, so it is not the missing number.
Hence, the correct answer is option 'B' - 64.
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Community Answer
4, 196, 16, 144, 36, 100, 64, x x ?a)48b)64c)125d)256Correct answer...
2×2=4
14×14=196
(2+2)4×4=16
(14-2)12×12=144
(4+2)6×6=36
(12-2)10×10=100
(6+2)8×8=64
(10-2)8×8=64
ans 64
14×14=196
(2+2)4×4=16
(14-2)12×12=144
(4+2)6×6=36
(12-2)10×10=100
(6+2)8×8=64
(10-2)8×8=64
ans 64
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4, 196, 16, 144, 36, 100, 64, x x ?a)48b)64c)125d)256Correct answer is option 'B'. Can you explain this answer?
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