NTA Abhyas JEE Main2020MathematicsMatricesPractice

Let X = 2 1 0 3 be a matrix. If X 6 = a b c d , then the number of divisors of a + b + 2020 c + d is equal to

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Correct answer

B. 14

Step-by-step solution

X 2 = 2 1 0 3 2 1 0 3 = 4 5 0 9 X 3 = X 2 X = 4 5 0 9 2 1 0 3 = 8 19 0 27 X 6 = X 3 ⋅ X 3 = 8 19 0 27 8 19 0 27 = 64 665 0 729 ⇒ a = 64 , b = 665, c = 0 , d = 729 ⇒ a + b + 2020 c + d = 1458 = 2 × 3 6 Number of divisors = 1 + 1 6 + 1 = 14

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