Download App

Geometric Progressions — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsGeometric Progressions1 Mark
MCQ
If $p, q$ be two $A.M.'s$ and $G$ be one $G.M.$ between two numbers, then $G^2 =$
  • ✓
    $(2\text{p}-\text{q})(\text{p}-2\text{q})$
  • B
    $(2\text{p}-\text{q})(2\text{q}-\text{p})$
  • C
    $(2\text{p}-\text{q})(\text{p}+2\text{q})$
  • D
    None of these.
✓

Answer

Correct option: A.
$(2\text{p}-\text{q})(\text{p}-2\text{q})$
Let the two numbers be $a$ and $b.$
$a, p, q$ and $b$ are in $A.P.$
$\therefore\text{ p}-\text{a}=\text{q}-\text{q}=\text{b}-\text{q}$
$\Rightarrow\text{ p}-\text{a}=\text{q}-\text{p}\text{ and}\text{ q}-\text{p}=\text{b}-\text{q}$
$\Rightarrow\text{ a}=2\text{p}-\text{q}\text{ and}\text{ b}=2\text{q}-\text{p}\cdots(\text{i})$
Also, $a, G$ and $b$ are in $G.P.$
$\therefore\text{G}^2=\text{ab}$
$\Rightarrow\text{G}^2=(2\text{p}-\text{q})(2\text{q}-\text{p})$

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 Geometric Progressions→Geometric Progressions — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

The sum of the solutions in $x \in (0,4\pi )$ of the equation $4\sin \frac{x}{3}\left( {\sin \left( {\frac{{\pi  + x}}{3}} \right)} \right)\sin \left( {\frac{{2\pi  + x}}{3}} \right) = 1$ is
→
Mark the correct answer for $(2-3 i)(-3+4 i)=$ ?
→
The range of $f(x) = \cos 2x - \sin 2x$ contains the set
→
Consider an experiment of tossing a coin repeatedly until the outcomes of two consecutive tosses are same. If the probability of a random toss resulting in head is $\frac{1}{3}$, then the probability that the experiment stops with head is.
→
How many numbers of $4 -$ digits can be formed by using the digits $1, 2, 3, 4, 5, 6, 7$ if atleast one digit is repeated:
→
Value of ${\sin ^2}\frac{\pi }{8} + {\sin ^2}\frac{{3\pi }}{8} + {\sin ^2}\frac{{5\pi }}{8} + {\sin ^2}\frac{{7\pi }}{8}$ is
→
The lines $2x - 3y = 5$ and $3x - 4y = 7$ are two diameters of a circel of area $154$ sq. units. Then the equation of circle is:
→
If $f(1) = 1$ and $f'(1) = 4,$ then the value of $\mathop {\lim }\limits_{x \to 1} \frac{{\sqrt {f(x)} - 1}}{{\sqrt x - 1}}$ is
→
If $f(x) = cos x, x =n \pi , n = 0, 1, 2, 3, ..... = 3$, otherwise and $\phi (x) =\left[ {\begin{array}{*{20}{c}}  {{x^2}\,\, + \,\,1}&{when\,\,\,\,x\, \ne \,3\,,\,\,x\, \ne \,0} \\    3&{when\,\,\,\,x\, = \,0\,\,\,\,\,\,\,\,\,\,\,\,\,} \\   5&{when\,\,\,\,x\, = \,3\,\,\,\,\,\,\,\,\,\,\,\,\,}  \end{array}} \right.$ then $\mathop {Limit}\limits_{x\,\, \to \,\,0}  f(\phi (x)) =$
→
The sum of the infinity of the series $1+2/3 + 6/32 + 10/33 +14/34$ is:
→