Square numbers always end in 0, 1, 4, 5, 6 or 9. No square ends in 2, 3, 7 or 8. Also, squares are formed by adding consecutive odd numbers starting from 1. Only squares have odd number of factors. Class ...
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The five lockers that are toggled exactly twice are lockers numbered 2, 3, 5, 7 and 11. These are all prime numbers, which have only two factors—1 and the number itself—so they are touched just twice during the process. Class 8 ...
The locker numbers that remain open are the ones which are perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100. These numbers have an odd number of factors and remain open after all toggling. Class 8 Mathematics ...
Cytoplasm is the jelly-like fluid in cells where all life processes occur. It holds organelles in place, allows movement of materials and supports chemical reactions necessary for the cell’s survival and growth. Class 8 Science Grade 8 Chapter 2 The Invisible ...
The nucleus controls all activities of the cell. It contains DNA, which holds instructions for growth, reproduction and functioning. It is often called the control center or brain of the cell. Class 8 Science Curiosity Chapter 2 The Invisible Living World: ...