NDA 2015 Paper 2 | Determinants Question 4 | Mathematics

If a, b, c are real numbers, then the value of the determinant $$\left| {\matrix{ {1 - a} & {a - b - c} & {b + c} \cr {1 - b} & {b - c - a} & {c + a} \cr {1 - c} & {c - a - b} & {a + b} \cr } } \right|$$ is

(a $$-$$ b) (b $$-$$ c) (c $$-$$ a)

(a + b + c)²

(a + b + c)³

NDA 2016 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

For the system of linear equations 2x + 3y + 5z = 9, 7x + 3y $$-$$ 2z = 8 and 2x + 3y + $$\lambda$$z = $$\mu$$

Under what condition does the above system of equations have infinitely many solutions?

$$\lambda$$ = 5 and $$\mu$$ $$\ne$$ 9

$$\lambda$$ = 5 and $$\mu$$ = 9

$$\lambda$$ = 9 and $$\mu$$ = 5

$$\lambda$$ = 9 and $$\mu$$ $$\ne$$ 5

NDA 2016 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

For the system of linear equations 2x + 3y + 5z = 9, 7x + 3y $$-$$ 2z = 8 and 2x + 3y + $$\lambda$$z = $$\mu$$

Under what condition does the above system of equations have unique solutions?

$$\lambda$$ = 5 and $$\mu$$ = 9

$$\lambda$$ $$\ne$$ 5 and $$\mu$$ = 7 only

$$\lambda$$ $$\ne$$ 5 and $$\mu$$ has any real value

$$\lambda$$ has any real value and $$\mu$$ $$\ne$$ 9

NDA 2016 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

If A is a square matrix of order 3 and det A = 5, then what is det {2 (A)^$$-$$1} equal to?

$${1 \over {10}}$$

$${2 \over 5}$$

$${8 \over 5}$$

$${1 \over {40}}$$

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