Let Tn denote the number of triangles which can equal to be forme

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

61.

The solution of the differential equation dydx = 1x + y2 is

  • y = - x2 - 2x - 2 + cex

  • y = x2 + 2x + 2 - cex

  • x = - y2 - 2y + 2 - cey

  • x = - y2 - 2y - 2 + cey


62.

The solution of the equation 3 + 22x2 - 8 + 3 + 228 - x2 = 6 are

  • 3 ± 22

  • ± 1

  • ± 33, ± 22

  • ± 3, ± 7


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63.

Let Tn denote the number of triangles which can equal to be formed by using the vertices of a regular polygon of n sides. If Tn + 1 - Tn = 28, then n equals

  • 4

  • 5

  • 6

  • 8


D.

8

Given, Tn + 1 - Tn = 28

 C3n + 1 - C3n = 28 n + 1!3!n - 2! - n!n - 3!3! = 28 16n + 1nn - 1 - nn - 1n - 2 = 28 nn2 - 1 - n2 - 3n + 2 = 168                        n2 - n - 56 = 0                     n - 8n + 7 = 0                                          n = 8              n  - 7


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