NDA 2017 Paper 1 | Matrices Question 20 | Mathematics

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?

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

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

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

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

NDA 2017 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

What is the order of $$\left[ {\matrix{ x & y & z \cr } } \right]\left[ {\matrix{ a & h & g \cr h & b & f \cr g & f & c \cr } } \right]\left[ {\matrix{ x \cr y \cr z \cr } } \right]$$ ?

3 $$\times$$ 1

1 $$\times$$ 1

1 $$\times$$ 3

3 $$\times$$ 3

NDA 2017 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

If $$A = \left[ {\matrix{ 0 & 1 \cr 1 & 0 \cr } } \right]$$, then the value of A⁴ is

$$\left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right]$$

$$\left[ {\matrix{ 1 & 1 \cr 0 & 0 \cr } } \right]$$

$$\left[ {\matrix{ 0 & 0 \cr 1 & 1 \cr } } \right]$$