Download App

STD 11 - 8. sequence and series — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 8. sequence and series1 Mark
MCQ
If ${\log _a}x,\;{\log _b}x,\;{\log _c}x$ be in $H.P.$, then $a,\;b,\;c$ are in
  • A
    $A.P.$
  • B
    $H.P.$
  • ✓
    $G.P.$
  • D
    None of these
✓

Answer

Correct option: C.
$G.P.$
c
(c) Here $\frac{{\log x}}{{\log a}},\;\frac{{\log x}}{{\log b}},\;\frac{{\log x}}{{\log c}}$ are in $H.P.$

$ \Rightarrow $$\frac{{\log a}}{{\log x}},\;\frac{{\log b}}{{\log x}},\;\frac{{\log c}}{{\log x}}$ are in $A.P.$

$ \Rightarrow $${\log _x}a,\;{\log _x}b,\;{\log _x}c$ are in $A.P.$

$ \Rightarrow $$a,\;b,\;c$ are in $G.P.$

Note : Students should remember this question as a fact.

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 - 8. sequence and series→STD 11 - 8. sequence and series — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Which of the following is correct for any two complex numbers $z_1$ and $z_2$?
→
If $A$ and $B$ are two independent events such that $P\,(A) = 0.40,\,\,P\,(B) = 0.50.$ Find $P$ (neither $A$ nor $B$)
→
The sum of the cubes of all the roots of the equation $x^{4}-3 x^{3}-2 x^{2}+3 x+1=10$ is
→
For the ellipse $3{x^2} + 4{y^2} = 12$, the length of latus rectum is
→
If $\alpha $ and $\beta $ are roots of the equation $x^2 + px + \frac {3p}{4} = 0,$ such that $\left| {\alpha  - \beta } \right| = \sqrt {10} ,$ then $p$ belongs to the set
→
Area of a triangle whose vertices are $(a\cos \theta ,b\sin \theta ),$ $( - a\sin \theta ,b\cos \theta )$ and $( - a\cos \theta , - b\sin \theta )$ is
→
$\mathop {\lim }\limits_{x \to {a^ + }} \frac{{|x{|^3}}}{a} - {\left[ {\frac{x}{a}} \right]^3}\,(a\, > \,0);$ is equal to :- (where $[x]$ is greatest integer function and $|x|$ is modulus function)
→
If $\frac{{\sqrt 3 }}{a}x + \frac{1}{b}y = 2$ touches the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ then its, eccentric angle $\theta $ is equal to: ................ $^o$
→
A square is inscribed in the circle ${x^2} + {y^2} - 2x + 4y + 3 = 0$, whose sides are parallel to the coordinate axes. One vertex of the square is
→
Centre of the circle $x^2+y^2-10 x+16 y+6=0$ is at :
→