JEE Main2018MathematicsMatricesActual

Let A = 1 0 0 1 1 0 1 1 1 and B = A 20 . Then the sum of the elements of the first column of B is

Options

A210
B211
C251
D231

Correct answer

D. 231

Step-by-step solution

Given, A = 1 0 0 1 1 0 1 1 1 ⇒ A 2 = 1 0 0 2 1 0 3 2 1 ;   A 3 = 1 0 0 3 1 0 6 3 1 A 4 = 1 0 0 4 1 0 10 4 1 ;   , … ;   A 20 = 1 0 0 20 1 0 210 20 1   ∵ a 31 = 20 th   term   in   1 + 3 + 6 + 10 + . . . . Hence, sum of the elements of first column = 231 .

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