Download App

Functions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsFunctions2 Marks
MCQ
The range of function $f (x)=\log _{ e } \sqrt{4-x^2}$ is given by
  • A
    $(0, \infty)$
  • B
    $(-\infty, \infty)$
  • ✓
    $\left(-\infty, \log _e 2\right]$
  • D
    $\left(\log _e 2, \infty\right)$
✓

Answer

Correct option: C.
$\left(-\infty, \log _e 2\right]$
(C)
Let $y=\log _e \sqrt{4-x^2} \Rightarrow e ^y=\sqrt{4-x^2}$
$\Rightarrow e ^{2 y}=4-x^2 \Rightarrow x^2=4- e ^{2 y} \Rightarrow x=\sqrt{4- e ^{2 y}}$
$\therefore 4-e^{2 y} \geq 0$
$\Rightarrow e ^{2 y} \leq 4 \Rightarrow 2 y \leq \log _{ e } 4$
$\Rightarrow y \leq \frac{1}{2} \log _{ e } 4 \Rightarrow y \leq \log _{ e } 2$
$\therefore y \in\left(-\infty, \log _e 2\right]$

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 "MCQ" from Functions→Functions — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

The point (-4, 5) is the vertex of a square and one of its diagonals is 7x - y + 8 = 0 The equation of the other diagonal is
→
$\frac{\sin 3 \theta+\sin 5 \theta+\sin 7 \theta+\sin 9 \theta}{\cos 3 \theta+\cos 5 \theta+\cos 7 \theta+\cos 9 \theta}=$
→
The axis of the parabola $9 y^2-16 x-12 y-57=0$, is
→
The number of integral values of $\lambda$ for which the equation $\text{x}^2+\text{y}^2+\lambda+(1-\lambda)\text{y}+5=0$ is the equation of a circle whose radius cannot exceed $5,$ is :
→
$\lim _{x \rightarrow-\infty} \frac{3 x^3+2 x^3-7 x+9}{4 x^3+9 x-2}$ is equal to
→
If a function f(x) is given as $f(x)=x^2-3 x+2$ for all $x \in R$, then f(- 1) =
→
For an event, odds against is $6: 5$. The probability that event does not occur, is
→
The roots of equation $x^2-(5+i) x+18-i=0$ are
→
The intercept of a line between the coordinate axes is divided by the point (-5, 4) in the ratio 1: 2 . The equation of the line will be
→
$\lim _{x \rightarrow 4} \frac{3-\sqrt{5+x}}{1-\sqrt{5-x}}=$
→