1
NDA 2017 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
If $$\left| {\matrix{ x & y & 0 \cr 0 & x & y \cr y & 0 & x \cr } } \right| = 0$$, then which one of the following is correct?
A
$${x \over y}$$ is one of the cube roots of unity
B
x is one of the cube roots of untiy
C
y is one of the cube roots of unity
D
$${x \over y}$$ is one of the cube roots of $$-$$ 1
2
NDA 2018 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
For a square matrix A, which of the following properties hold?

1. $${({A^{ - 1}})^{ - 1}} = A$$

2. $$\det \,({A^{ - 1}}) = {1 \over {\det \,A}}$$

3. $${(\lambda A)^{ - 1}} = \lambda {A^{ - 1}}$$, where $$\lambda$$ is a scalar

Select the correct answer using the code given below.
A
1 and 2
B
2 and 3
C
1 and 3
D
1, 2 and 3
3
NDA 2018 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Which one of the following factors does the expansion of the determinant

$$\left| {\matrix{ x & y & 3 \cr {{x^2}} & {5{y^3}} & 9 \cr {{x^3}} & {10{y^5}} & {27} \cr } } \right|$$ contain?
A
x $$-$$ 3
B
x $$-$$ y
C
y $$-$$ 3
D
x $$-$$ 3y
4
NDA 2018 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
If a + b + c = 0, then one of the solutions of $$\left| {\matrix{ {a - x} & c & b \cr c & {b - x} & a \cr b & a & {c - x} \cr } } \right| = 0$$ is
A
x = a
B
$$x = \sqrt {{{3({a^2} + {b^2} + {c^2})} \over 2}} $$
C
$$x = \sqrt {{{2({a^2} + {b^2} + {c^2})} \over 3}} $$
D
x = 0
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