1
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
2
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
3
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
4
NDA 2018 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
The system of equations

$$2x + y - 3z = 5$$

$$3x - 2y + 2z = 5$$

and $$5x - 3y - z = 16$$
A
is inconsistent
B
is consistent, with a unique solution
C
is consistent, with infinitely many solutions
D
has it solution lying along X-axis in three-dimensional space
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12