NDA MATHEMATICS QUIZ-10

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.

0.0

3.0

1.0

$\quad A \vec{B}+B \vec{C}+C \vec{A}$

Question 2:

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

$x \geq \frac{-1}{3}$

$x<\frac{-1}{3}$

$x>1$

all values of $ x $

Question 3:

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

$x=\pi$

$x=\pi / 2$

$x =2 \pi$

$x=-2 \pi$

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

$\frac{1}{4}$

$\frac{1}{2}$

$\frac{3}{2}$

$\frac{7}{4}$

Question 5:

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

$(1,0)$

$\left(4, \frac{9}{2}\right)$

$\left(0,-\frac{7}{2}\right)$

$\left(2,-\frac{9}{2}\right)$

Question 6:

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

$(1,2)$

$(0,0)$

$\left(\frac{1}{3}, \frac{2}{3}\right)$

$\left(\frac{1}{4}, \frac{3}{4}\right)$

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 ?

$15 \sqrt{3} \mathrm{~m}$

$30 \mathrm{~m}$

$90 \mathrm{~m}$

$45 \sqrt{3} \mathrm{~m}$

Question 8:

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

–1

$i$

0.0

1.0

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:

$\mathrm{n}(\mathrm{n}+1)$

$n(n-1)$

$\mathrm{n}^{2}(\mathrm{~n}+1)$

$\frac{n(n+1)}{2}$

Question 10:

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

Non-consistent

Having trivial solution

Consistent and unique solution

Infinite Number of solution