Download App

Model Paper 4 — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsModel Paper 41 Mark
MCQ
If $x=\sqrt{5}+2$, then $x-\frac{1}{x}$ equals
  • A
    $2$
  • ✓
    $4$
  • C
    $2 \sqrt{5}$
  • D
    $\sqrt{5}$
✓

Answer

Correct option: B.
$4$
$x=\sqrt{5}+2$, then equals
$\frac{1}{x}=\frac{1}{\sqrt{5}+2}$
$=\frac{1}{\sqrt{5+2}} \times \frac{\sqrt{5-2}}{\sqrt{5-2}}$
$=\frac{\sqrt{5}-2}{5-4}$
$=\sqrt{5}-2$
now,
$x-\frac{1}{x}=\sqrt{5}+2-(\sqrt{5}-2)$
$=\sqrt{5}+2-\sqrt{5}+2$
$=4$

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" from Model Paper 4→Model Paper 4 — all question types→Maths STD 9 question papers→Gujarat Board STD 9 question papers→Gujarat Board question paper generator→

Similar questions

Two points having same abscissae but different ordinates lie on
→
One of the factors of $\left(25 x^2-1\right)+(1+5 x)^2$ is:
→
Zero of the polynomial $f(x)=3 x+7$ is
→
If a spherical balloon grows to twice its radius when inflated, then the ratio of the volume of the inflated balloon to the original balloon is:
→
A frequency polygon is constructed by plotting frequency of the class interval and the:
→
The number of dimensions, a line has:
→
Which of the following is a polynomial$?$
→
If the volume of a cuboid is $=3 x^2-27$, then its possible dimensions are:
→
The volume of a sphere is numerically equal to its surface area, then its diameter is:
→
If a sphere of radius $2r$ has the same volume as that of a cone with a circular base of radius $r,$ then the height of the cone is:
→