NDA MATHEMATICS QUIZ-10

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Question 1:

If $\mathrm{D}, \mathrm{E}$ and $\mathrm{F}$ be the mid points of sides $\mathrm{AB}$, $\mathrm{BC}$ and $\mathrm{CA}$ respectively of a triangle $\mathrm{ABC}$ than $A \vec{D}+B E+C \vec{F}$ is equal to.

Question 2:

The function $f(x)=1-x-x^3$ is decreasing for

Question 3:

The function $y=\cos ^{-1}(\sin x)$ is not differentiable at:

Question 4:

The distance between the parallel planes $4 x-2 y+4 z+9=0$ and $8 x-4 y+8 z+21=0$ is

Question 5:

Vertex of the parabola $x^{2}+2 y=8 x-7$ will be.

Question 6:

Orthocentre of the triangle formed by the lines $x y=0$ and $x+y=3$ is

Question 7:

Two poles of equal height stand on either side of 60 meters wide roadway. At a point in the roadway between the pillars, the elevation of the top of poles are $30^{\circ}$ and $60^{\circ}$ what will be the height of the pillars ?

Question 8:

$\left(\frac{1-i}{1+i}\right)^{400}$ is equal to:

Question 9:

If roots of the equation $\lambda x^{2}+(2 \lambda-1) x+\lambda-2=0$ are rational then value of $\lambda$, where $\lambda \in \mathrm{I}$, is:

Question 10:

The given system of equations $2 x+y+3 z=$ $2, x+y+22=1,3 x+2 y+z=7$ are.