1
NDA 2017 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
If a $$\ne$$ b $$\ne$$ c, then one value of x which satisfies the equation $$\left| {\matrix{ 0 & {x - a} & {x - b} \cr {x + a} & 0 & {x - c} \cr {x + b} & {x + c} & 0 \cr } } \right| = 0$$ is given by
A
a
B
b
C
c
D
0
2
NDA 2017 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
The equations $$x + 2y + 3z = 1$$, $$2x + y + 3z = 2$$, $$5x + 5y + 9z = 4$$
A
have the unique solution
B
have infinitely many solutions
C
are inconsistent
D
None of the above
3
NDA 2017 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
What is the value of the determinant

$$\left| {\matrix{ 1 & 1 & 1 \cr 1 & {1 + xyz} & 1 \cr 1 & 1 & {1 + xyz} \cr } } \right|$$ ?
A
1 + x + y + z
B
2 xyz
C
x2 y2 z2
D
2x2 y2 z2
4
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
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