| Column - I | Column - II |
| P. The smallest number that should be subtracted from 130 to make it perfect cube is | (i) 4 |
| Q. The smallest number that should be subtracted from 9268 to make it perfect cube is | (ii) 3 |
| R. The smallest number that should be added to 2194 to make it perfect cube is | (iii) 5 |
| S. The smallest number that should be added to 6855 to make it perfect cube is | (iv) 7 |
A) P\[\to \](iii); Q\[\to \](i); R\[\to \](iv); S\[\to \](ii)
B) P\[\to \](ii); Q\[\to \](iv); R\[\to \](i); S\[\to \](iii)
C) P\[\to \](iii); Q\[\to \](i); R\[\to \](ii); S\[\to \](iv)
D) P\[\to \](iii); Q\[\to \](iv); R\[\to \](ii); S\[\to \](i)
Correct Answer: D
Solution :
(P) \[{{5}^{3}}\le 130\le {{6}^{3}}\] As perfect cube less than 130 = 125 So, 130 - 125 = 5 \[\therefore \] The smallest number that should be subtracted from 130 to make it a perfect cube \[=\text{ }5\] (Q) \[{{21}^{3}}\le 9268\le {{22}^{3}}\] \[\therefore \] Perfect cube less than 9268 is 9261. So, smallest number that should be subtracted from 9268 to make it a perfect cube = 7 (R) \[{{12}^{3}}\le 2194\le {{13}^{3}}\] Perfect cube just greater than 2194 is 2197. So, smallest number that should be added to 2194 to make it perfect cube is 3. (S) \[{{18}^{3}}<6855<{{19}^{3}}\] Perfect cube greater than 6855 is 6859. So, 6859 - 6855 = 4 \[\therefore \] Smallest number that should be added to 6855 to make it a perfect cube = 4.
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