1
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Let $$A = \left[ {\matrix{ {x + y} & y \cr {2x} & {x - y} \cr } } \right]$$, $$B = \left[ {\matrix{ 2 \cr { - 1} \cr } } \right]$$ and $$C = \left[ {\matrix{ 3 \cr 2 \cr } } \right]$$. If AB = C, then what is A2 equal to?
A
$$\left[ {\matrix{ 6 & { - 10} \cr 4 & {26} \cr } } \right]$$
B
$$\left[ {\matrix{ { - 10} & 5 \cr 4 & {24} \cr } } \right]$$
C
$$\left[ {\matrix{ { - 5} & { - 6} \cr { - 4} & { - 20} \cr } } \right]$$
D
$$\left[ {\matrix{ { - 5} & { - 7} \cr { - 5} & {20} \cr } } \right]$$
2
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
If $$E(\theta ) = \left[ {\matrix{ {\cos \theta } & {\sin \theta } \cr { - \sin \theta } & {\cos \theta } \cr } } \right]$$, then E($$\alpha$$) E($$\beta$$) is equal to
A
E ($$\alpha$$$$\beta$$)
B
E ($$\alpha$$ $$-$$ $$\beta$$)
C
E ($$\alpha$$ + $$\beta$$)
D
$$-$$ E ($$\alpha$$ + $$\beta$$)
3
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
If A is an orthogonal matrix of order 3 and $$B = \left[ {\matrix{ 1 & 2 & 3 \cr { - 3} & 0 & 2 \cr 2 & 5 & 0 \cr } } \right]$$, then which of the following is/are correct?

1. $$\left| {AB} \right| = \pm \,47$$ 2. AB = BA

Select the correct answer using the code given below.
A
Only 1
B
Only 2
C
Both 1 and 2
D
Neither 1 nor 2
4
NDA 2016 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
If $$A = \left[ {\matrix{ 1 & { - 1} \cr 2 & 3 \cr } } \right]$$ and $$B = \left[ {\matrix{ 2 & 3 \cr { - 1} & { - 2} \cr } } \right]$$, then which of the following is/are correct?

I. AB (A$$-$$1 B$$-$$1) is a unit matrix.

II. (AB)$$-$$1 = A$$-$$1 B$$-$$1.

Select the correct answer using the code given below.
A
Only I
B
Only II
C
Both I and II
D
Neither I nor II
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