Download App

STD 11 - basic of algoritham — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - basic of algoritham4 Marks
MCQ
If ${1 \over 2} \le {\log _{0.1}}x \le 2$ then
  • A
    The maximum value of $x$ is $1/\sqrt {10} $
  • B
    $x$ lies between $1/100$ and $1/\sqrt {10} $
  • C
    The minimum value of $x$ is $1/100$
  • ✓
    All of These
✓

Answer

Correct option: D.
All of These
d
(d) ${1 \over 2} \le {\log _{0.1}}x \le 2$

${1 \over 2} \le {\log _{0.1}}\,x \Rightarrow {\log _{0.1}}{(0.1)^{1/2}} \le {\log _{0.1}}x$

$ \Rightarrow $${(0.1)^{1/2}} \ge x$ $ \Rightarrow $$x \le {1 \over {\sqrt {10} }}$

${\log _{0.1}}x \le 2 \Rightarrow {\log _{0.1}}x \le {\log _{0.1}}{(0.1)^2}$

$x \ge {(0.1)^2} \Rightarrow x \ge {1 \over {100}}$, ${1 \over {100}} \le x \le {1 \over {\sqrt {10} }}$.

Hence, ${x_{{\rm{max}}}} = {1 \over {\sqrt {10} }},{x_{{\rm{min}}{\rm{.}}}} = {1 \over {100}}$.

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

Given the family of lines, $a (2x + y + 4) + b (x - 2y - 3) = 0 $. Among the lines of the family, the number of lines situated at a distance of $\sqrt{10}$ from the point $M (2, - 3)$ is :
→
Let $A = \{ (x,\,y):y = {e^x},\,x \in R\} $, $B = \{ (x,\,y):y = {e^{ - x}},\,x \in R\} .$ Then
→
The radius of a circle which touches $y$-axis at $(0,3)$ and cuts intercept of $8$ units with $x$-axis, is
→
The number of words not starting and ending with vowels formed, using all the letters of the word $'UNIVERSITY'$ such that all vowels are in alphabetical order, is
→
$\mathop {{\rm{lim}}}\limits_{x \to 0} \frac{{{\rm{sin}}\left( {\pi {{\cos }^2}x} \right)}}{{{x^2}}} = $
→
If $x + iy = \frac{3}{{2 + \cos \theta + i\sin \theta }},$then ${x^2} + {y^2}$ is equal to
→
Let $a,b,c$ be non-zero real numbers such that

$\int_0^1 {(1 + {{\cos }^8}x)(a{x^2} + bx + c)\,dx} = \int_0^2 {(1 + {{\cos }^8}x)(a{x^2} + bx + c)\,dx} $

Then the quadratic equation $a{x^2} + bx + c = 0$ has

→
If $\sin y = x\sin (a + y),$ then ${{dy} \over {dx}} = $
→
Circles ${(x + a)^2} + {(y + b)^2} = {a^2}$ and ${(x + \alpha )^2}$ $ + {(y + \beta )^2} = $ ${\beta ^2}$ cut orthogonally, if
→
A straight line through the vertex $P$ of a triangle $P Q R$ intersects the side $Q R$ at the point $S$ and the circumcircle of the triangle $P Q R$ at the point $T$. If $S$ is not the centre of the circumcircle, then

$(A)$ $\frac{1}{\mathrm{PS}}+\frac{1}{\mathrm{ST}}<\frac{2}{\sqrt{\mathrm{QS} \times \mathrm{SR}}}$

$(B)$ $\frac{1}{\mathrm{PS}}+\frac{1}{\mathrm{ST}}>\frac{2}{\sqrt{\mathrm{QS} \times \mathrm{SR}}}$

$(C)$ $\frac{1}{\mathrm{PS}}+\frac{1}{\mathrm{ST}}<\frac{4}{\mathrm{QR}}$

$(D)$ $\frac{1}{\mathrm{PS}}+\frac{1}{\mathrm{ST}}>\frac{4}{\mathrm{QR}}$

→