NDA 2018 Paper 2 | Determinants Question 25 | Mathematics

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?

x $$-$$ 3

x $$-$$ y

y $$-$$ 3

x $$-$$ 3y

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

x = a

$$x = \sqrt {{{3({a^2} + {b^2} + {c^2})} \over 2}} $$

$$x = \sqrt {{{2({a^2} + {b^2} + {c^2})} \over 3}} $$

x = 0

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 $$5x - 3y - z = 16$$

is inconsistent

is consistent, with a unique solution

is consistent, with infinitely many solutions

has it solution lying along X-axis in three-dimensional space

NDA 2018 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

If u, v and w (all positive) are the pth, qth, and rth terms of a GP, then the determinant of the matrix $$\left( {\matrix{ {\ln \,u} & p & 1 \cr {\ln v} & q & 1 \cr {\ln w} & r & 1 \cr } } \right)$$ is

(p $$-$$ q) (q $$-$$ r) (r $$-$$ p)

$${\ln \,u}$$ $$\times$$ $${\ln \,v}$$ $$\times$$ $${\ln \,w}$$

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