Mathematics - Permutation & Combination Question with Solution | TestHub

MathematicsPermutation & CombinationFundamental PrincipleMedium2 minQB

MathematicsMediuminteger

Consider $n \times n$ graph paper where $n$ is a natural number. Consider the right angled isosceles triangles whose vertices are integer points of this graph and whose sides forming right angle are parallel to x and y axes. If the no.of such triangles is $\frac{2}{K} n (n + 1) (2 n + 1)$ , then K is $____$ .

Answer:

Solution:

Required no.of triangles $= 4 [n^{2} + (n - 1)^{2} + \dots + 1^{2}] = \frac{2}{3} n (n + 1) (2 n + 1)$ $∴ K = 3$

Stream:JEESubject:MathematicsTopic:Permutation & CombinationSubtopic:Fundamental Principle

⏱ 2mℹ️ Source: QB

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