The statement holds because 2 and 4 divide 8. However, checking 2 and 4 is not enough for 8; for instance, 12 is divisible by both 2 and 4, but not 8. Class 9 Maths Ganita Manjari Part 2 chapter 9 ...
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For (i), n = 11 is prime, but 2¹¹ − 1 = 2047 = 23 × 89 is composite. For (ii), n = 6 is even, but 2⁶ + 1 = 65 = 5 × 13 is composite. Class 9 Maths ...
Counterexamples disprove all three: for (i), n = 4 gives 4(16) + 1 = 65 = 5 × 13; for (ii), n = 10 gives 121 = 11²; for (iii), n = 3 gives 67? No, n = 2 gives ...
The cylinder fitting inside a cube of edge r has diameter r, so base radius is r/2 and height is r. Its volume is π × (r/2)² × r = (πr³)/4 cm³. Class 9 Chapter 14 Math of Space Surface Area ...
Given r₁ : r₂ = 2 : 3 and h₁ : h₂ = 3 : 2. The volume ratio is (r₁/r₂)²(h₁/h₂) = (4/9)(3/2) = 2 : 3. The curved surface area ratio is (r₁/r₂)(h₁/h₂) = (2/3)(3/2) = 1 : 1. Class ...