If points (5, 5), (10, k) and (-5, 1) are collinear, then k = - Vidyadip

MCQ

If points $(5, 5)$, $(10, k)$ and $(-5, 1)$ are collinear, then $k =$

A
$3$
B
$5$
✓
$7$
D
$9$

✓

Answer

Correct option: C.

$7$

c
(c) According to the condition $\left| {\,\begin{array}{*{20}{c}}5&5&1\\{10}&k&1\\{ - 5}&1&1\end{array}\,} \right| = 0$

$ \Rightarrow \,\,$$\left| {\,\begin{array}{*{20}{c}}5&5&1\\5&{k - 5}&0\\{ - 10}&{1 - 5}&0\end{array}\,} \right| = 0\,\, $

$\Rightarrow \,\,k = 7$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The term independent of $' x '$ in the expansion of ${\left( {9\,x, - frac{1}{{3\,\sqrt x }}} \right)^{18}}, x > 0$ , is $\alpha$ times the corresponding binomial co$-$efficient . Then $' \alpha \ '$ is :

If the line $\frac{x}{a} + \frac{y}{b} = 1$ passes through the points $(2, -3)$ and $(4, -5)$, then $(a,\;b)$=

If the sum of the first $15$ terms of the series ${\left( {\frac{3}{4}} \right)^3} + {\left( {1\frac{1}{2}} \right)^3} + {\left( {2\frac{1}{4}} \right)^3} + {3^3} + {\left( {3\frac{3}{4}} \right)^3} + .....$ is equal to $225\,k,$ then $k$ is equal to

Let $P(4, -4)$ and $Q(9, 6)$ be two points on the parabola, $y^2 = 4x$ and let $X$ be any point on the arc $POQ$ of this parabola, where $O$ is the vertex of this parabola, such that the area of $\Delta PXQ$ is maximum. Then this maximum Area (in sq. units) is

If $\int \frac{\sin ^{\frac{3}{2}} x+\cos ^{\frac{3}{2}} x}{\sqrt{\sin ^3 x \cos ^3 x \sin (x-\theta)}} d x=A \sqrt{\cos \theta \tan x-\sin \theta}+B \sqrt{\cos \theta-\sin \theta \operatorname{coc} x}+C,$ where $C$ is the integration constant, then $A B$ is equal to

$\int_1^e {\frac{{{e^x}}}{x}(1 + x\log x)\,dx} = $

$1 + \frac{1}{4} + \frac{{1.3}}{{4.8}} + \frac{{1.3.5}}{{4.8.12}} + ........... = $

Let $p, q, r \in R$ and $r > p > 0.$ If the quadratic equation $px^2 + qx + r = 0$ has two complex roots $\alpha $ and $\beta ,$ then is $\left| \alpha \right| + \left| \beta \right|$

The equation of a circle passing through the point $(4, 5)$ and having the centre at $(2, 2)$ is

Let the system of linear equations $x+y+k z=2$ ; $2 x+3 y-z=1$ ; $3 x+4 y+2 z=k$ , have infinitely many solutions. Then the system $( k +1) x +(2 k -1) y =7$ ; $(2 k +1) x +( k +5) y =10 \text { has : }$