1
NDA 2016 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
Which of the following determinants have value 'zero'?

1. $$\left| {\matrix{ {41} & 1 & 5 \cr {79} & 7 & 9 \cr {29} & 5 & 3 \cr } } \right|$$

2. $$\left| {\matrix{ 1 & a & {b + c} \cr 1 & b & {c + a} \cr 1 & c & {a + b} \cr } } \right|$$

3. $$\left| {\matrix{ 0 & c & b \cr { - c} & 0 & a \cr { - b} & { - a} & 0 \cr } } \right|$$

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 2016 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
The system of linear equations $$kx + y + z = 1$$, $$x + ky + z = 1$$ and $$x + y + kz = 1$$ has a unique solution under which one of the following conditions?
A
k $$\ne$$ 1 and k $$\ne$$ $$-$$ 2
B
k $$\ne$$ 1 and k $$\ne$$ 2
C
k $$\ne$$$$-$$ 1 and k $$\ne$$ $$-$$ 2
D
k $$\ne$$ $$-$$ 1 and k $$\ne$$ 2
3
NDA 2017 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
The system of equations kx + y + z = 1, x + ky + z = k and x + y + kz = k2 has no solution if k equals.
A
0
B
1
C
$$-$$ 1
D
$$-$$ 2
4
NDA 2017 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
The value of the determinant $$\left| {\matrix{ {1 - \alpha } & {\alpha - {\alpha ^2}} & {{\alpha ^2}} \cr {1 - \beta } & {\beta - {\beta ^2}} & {{\beta ^2}} \cr {1 - \gamma } & {\gamma - {\gamma ^2}} & {{\gamma ^2}} \cr } } \right|$$ is equal to
A
($$\alpha$$ $$-$$ $$\beta$$) ($$\beta$$ $$-$$ $$\gamma$$) ($$\alpha$$ $$-$$ $$\gamma$$)
B
($$\alpha$$ $$-$$ $$\beta$$) ($$\beta$$ $$-$$ $$\gamma$$) ($$\gamma$$ $$-$$ $$\alpha$$)
C
($$\alpha$$ $$-$$ $$\beta$$) ($$\beta$$ $$-$$ $$\gamma$$) ($$\gamma$$ $$-$$ $$\alpha$$) ($$\alpha$$ + $$\beta$$ + $$\gamma$$)
D
0
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