NDA 2017 Paper 1 | Matrices Question 18 | Mathematics

If $$A = \left[ {\matrix{ {\cos \alpha } & {\sin \alpha } \cr { - \sin \alpha } & {\cos \alpha } \cr } } \right]$$, then what is AA^T equal to (where, A^T is transpose of A)?

Null matrix

Identity matrix

$$-$$ A

NDA 2017 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

$$A = \left[ {\matrix{ {x + y} & y \cr x & {x - y} \cr } } \right]$$, $$B = \left[ {\matrix{ 3 \cr { - 2} \cr } } \right]$$ and $$C = \left[ {\matrix{ 4 \cr { - 2} \cr } } \right]$$. If AB = C, then what is A² equal to?

$$\left[ {\matrix{ 4 & 8 \cr { - 4} & { - 16} \cr } } \right]$$

$$\left[ {\matrix{ 4 & { - 4} \cr 8 & { - 16} \cr } } \right]$$

$$\left[ {\matrix{ { - 4} & { - 8} \cr 4 & {12} \cr } } \right]$$

$$\left[ {\matrix{ { - 4} & { - 8} \cr 8 & {12} \cr } } \right]$$

NDA 2017 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

Consider the set A of all matrices of order 3 $$\times$$ 3 with entries 0 or 1 only. Let B be the subset of A consisting of all matrices whose determinant is 1. Let C be the subset of A consisting of all matrices whose determinant is $$-$$1. Then which one of the following is correct?

C is empty

B has as many elements as C

A = B $$\cup$$ C

B has thrice as many elements as C

NDA 2017 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

If $$A = \left[ {\matrix{ {\cos \theta } & {\sin \theta } \cr { - \sin \theta } & {\cos \theta } \cr } } \right]$$, then what is A³ equal to?

$$\left[ {\matrix{ {\cos 3\theta } & {\sin 3\theta } \cr { - \sin 3\theta } & {\cos 3\theta } \cr } } \right]$$

$$\left[ {\matrix{ {{{\cos }^3}\theta } & {{{\sin }^3}\theta } \cr { - {{\sin }^3}\theta } & {{{\cos }^3}\theta } \cr } } \right]$$

$$\left[ {\matrix{ {\cos 3\theta } & { - \sin 3\theta } \cr {\sin 3\theta } & {\cos 3\theta } \cr } } \right]$$

$$\left[ {\matrix{ {{{\cos }^3}\theta } & { - {{\sin }^3}\theta } \cr {{{\sin }^3}\theta } & {{{\cos }^3}\theta } \cr } } \right]$$

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