Engineer & Medical

Mathematical Induction question bank (Maths)

Practice 70 free Engineer & Medical Maths - Mathematical Induction questions with answers and step-by-step solutions.

Q1.

If $A=\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right]$ and $I=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$, then which one of the following holds for all $n \geq 1$, by the principle of mathematical indunction

(A)
$A^n=n A-(n-1) I$
(B)
$A^n=2^{n-1} A-(n-1) I$
(C)
$A^n=n A+(n-1) I$
(D)
$A^n=2^{n-1} A+(n-1) I$
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Q2.

$2^{3 n}-7 n-1 \text { is divisible by }$

(A)
64
(B)
36
(C)
49
(D)
25
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