Choose the correct number in place of '?'.
5 6 8 169
1 31 184
0 14 361
A)5
B)2
C)3
D)4
Formula also please
Answers
The correct answer is optionb) 2 .
Formula applied here is
TO DETERMINE
To Choose the correct number in place of ?
5 | 6 | 8 | 169 |
4 | 7 | 31 | 144 |
7 | ? | 14 | 361 |
EVALUATION
First we take a look that how the result is coming
For the first lines : 5 | 6 | 8 | 169 |
Now
\sf{ {(5)}^{3} + {(6)}^{2} + 8 }(5)
3
+(6)
2
+8
\sf{ = 125 + 36 + 8}=125+36+8
\sf{ = 169}=169
For the second lines : 4 | 7 | 31 | 144 |
\sf{ {(4)}^{3} + {(7)}^{2} + 31}(4)
3
+(7)
2
+31
= \sf{64 + 49 +31 }=64+49+31
\sf{ = 144}=144
Thus the pattern is of like below
\sf{ x \: | \: y \: | \: z \: | \: {x}^{3} + {y}^{2} + z\: | }x∣y∣z∣x
3
+y
2
+z∣
CONCLUSION
The third line is : 7 | ? | 14 | 361 |
Suppose the number in ? place is x
\sf{ {(7)}^{3} + {x}^{2} + 14 = 361 }(7)
3
+x
2
+14=361
\implies \sf{ 343 + {x}^{2} + 14 = 361 }⟹343+x
2
+14=361
\implies \sf{ {x}^{2} = 4 }⟹x
2
=4
\sf{ \implies x = 2 } \: \: \: ( \because \: all \: the \: numbers \: are \: natural \: numbers)⟹x=2(∵allthenumbersarenaturalnumbers)
FINAL ANSWER
Hence the correct number in place of ? is 2.
The correct answer is optionb) 2 .
Formula applied here is
{a}^{3} + {b}^{2} + ca
3
+b
2
+c
TO DETERMINE
To Choose the correct number in place of ?
5 | 6 | 8 | 169 |
4 | 7 | 31 | 144 |
7 | ? | 14 | 361 |
EVALUATION
First we take a look that how the result is coming
For the first lines : 5 | 6 | 8 | 169 |
Now
\sf{ {(5)}^{3} + {(6)}^{2} + 8 }(5)
3
+(6)
2
+8
\sf{ = 125 + 36 + 8}=125+36+8
\sf{ = 169}=169
For the second lines : 4 | 7 | 31 | 144 |
\sf{ {(4)}^{3} + {(7)}^{2} + 31}(4)
3
+(7)
2
+31
= \sf{64 + 49 +31 }=64+49+31
\sf{ = 144}=144
Thus the pattern is of like below
\sf{ x \: | \: y \: | \: z \: | \: {x}^{3} + {y}^{2} + z\: | }x∣y∣z∣x
3
+y
2
+z∣
CONCLUSION
The third line is : 7 | ? | 14 | 361 |
Suppose the number in ? place is x
\sf{ {(7)}^{3} + {x}^{2} + 14 = 361 }(7)
3
+x
2
+14=361
\implies \sf{ 343 + {x}^{2} + 14 = 361 }⟹343+x
2
+14=361
\implies \sf{ {x}^{2} = 4 }⟹x
2
=4
\sf{ \implies x = 2 } \: \: \: ( \because \: all \: the \: numbers \: are \: natural \: numbers)⟹x=2(∵allthenumbersarenaturalnumbers)
FINAL ANSWER
Hence the correct number in place of ? is 2.