Download App

STD 11 - 9. straight line — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 9. straight line1 Mark
MCQ
A light ray emits from the origin making an angle $30^{\circ}$ with the positive $x$-axis. After getting reflected by the line $x + y =1$, if this ray intersects $x$-axis at $Q$, then the abscissa of $Q$ is
  • A
    $\frac{2}{(\sqrt{3}-1)}$
  • ✓
    $\frac{2}{3+\sqrt{3}}$
  • C
    $\frac{2}{3-\sqrt{3}}$
  • D
    $\frac{\sqrt{3}}{2(\sqrt{3}+1)}$
✓

Answer

Correct option: B.
$\frac{2}{3+\sqrt{3}}$
b
Slope of reflected ray $=\tan 60^{\circ}=\sqrt{3}$

Line $y=\frac{x}{\sqrt{3}}$ intersect $y+x=1$ at $\left(\frac{\sqrt{3}}{\sqrt{3}+1}, \frac{1}{\sqrt{3}+1}\right)$

Equation of reflected ray is

$y-\frac{1}{\sqrt{3}+1}=\sqrt{3}\left(x-\frac{\sqrt{3}}{\sqrt{3}+1}\right)$

Put $y=0 \Rightarrow x=\frac{2}{3+\sqrt{3}}$

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

More "M.C.Q (1 Marks)" from STD 11 - 9. straight line→STD 11 - 9. straight line — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

$\sqrt {[10 - \sqrt {(24)} - \sqrt {(40)} + \sqrt {(60)} ]} = $
→
The position of the point $(8,-9)$ with respect to the lines $2x + 3y - 4 = 0$ and $6x + 9y + 8 = 0$ is
→
Let $a, b, c, d$ be real numbers between $-5$ and $5$ such that  $|a|=\sqrt{4-\sqrt{5-a}},|b|=\sqrt{4+\sqrt{5-b}},|c|=\sqrt{4-\sqrt{5+c}}$ $|d|=\sqrt{4+\sqrt{5+d}}$ Then, the product $a b c d$ is
→
The number of numbers between $1$ and $10^{10}$ which contains digit $1$, is
→
$\frac{i^{4 R+1}-i^{4 R-1}}{2}( R \in N )$ is equal to :
→
If $A$ and $B$ are sets, then $A \cap (B -A)$ is
→
If $5\sin\alpha=3\sin(\alpha+2\beta)\not=0,$ then $\tan(\alpha+\beta)$ is equal to:
→
A straight line moves so that the sum of the reciprocals of its intercepts on two perpendicular lines is constant, then the line passes through
→
Let $y = f(x) = ax^2 + 2bx + c,$ (where $a, b, c \in  R$ and $a \neq 0)$ if $f(x) = 0$ has imaginary roots and $4a + 4b + c < 0$ then which of the following is true
→
A five digit number divisible by $3$ has to formed using the numerals $0, 1, 2, 3, 4$ and $5$ without repetition. The total number of ways in which this can be done is
→