Download App

STD 11 - 4.2 Quadratic equations and inequations — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 4.2 Quadratic equations and inequations1 Mark
MCQ
The solution set of the equation ${x^{{{\log }_x}{{(1 - x)}^2}}} = 9$ is
  • ✓
    $\{-2, 4\}$
  • B
    $\{4\}$
  • C
    $\{0, -2, 4\}$
  • D
    None of these
✓

Answer

Correct option: A.
$\{-2, 4\}$
a
(a) ${x^{{{\log }_x}(1 - x)}}^2 = 9$

==>${\log _x}(9) = {\log _x}{(1 - x)^2}({a^x} = N\,\,\, $

$\Rightarrow {\log _a}N = x)$

==> $9 = {(1 - x)^2}\,\,\,$

$ \Rightarrow 1 + {x^2} - 2x - 9 = 0$

==> ${x^2} - 2x - 8 = 0$

==> $(x + 2)(x - 4) = 0$ ==> $x = - 2\,,4$.

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 (1 Marks)" from STD 11 - 4.2 Quadratic equations and inequations→STD 11 - 4.2 Quadratic equations and inequations — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

The middle term in the expansion of $\Big(\frac{2\text{x}}{3}=\frac{3}{2\text{x}^{2}}\Big)^{2\text{n}}$ is:
→
Let $P$ be the point on the parabola $y^2=4 x$ which is at the shortest distance from the center $S$ of the circle $x^2+y^2-4 x-16 y+64=0$. Let $Q$ be the point on the circle dividing the line segment $S P$ internally. Then

($A$) $S P=2 \sqrt{5}$

($B$) $S Q: Q P=(\sqrt{5}+1): 2$

($C$) the $x$-intercept of the normal to the parabola at $P$ is $6$

($D$) the slope of the tangent to the circle at $Q$ is $\frac{1}{2}$

→
If $X = \{8n - 7n - 1 | n \in N\}$ and $Y = \{49n - 49 | n \in N\}$. Then
→
The equation of a circle touching the axes of coordinates and the line $x\cos \alpha + y\sin \alpha = 2$ can be
→
The equation of the common tangents to the two hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ and $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ are-
→
If $\text{S}_\text{n}=\sum\limits^{\text{n}}_{\text{r}=1}\frac{1+2+2^2+\ ...\text{ Sum to r terms}}{2^{\text{r}}},$ then $S_n$ is equal to:
→
The number of ways in which 3 men and 2 men can sit on a bus, while the number of men and women sitting each side in 3 , will be :
→
The latus$-$rectum of the conic $3\text{x}^2+4\text{y}^2-6\text{x}+8\text{y}-5=0$ is:
→
The equation of a line passing through the point of intersection of the lines $x + 5y + 7 = 0,\;\;3x + 2y - 5 = 0,$ and perpendicular to the line $7x + 2y - 5 = 0,$ is given by
→
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
→