Question:
If 8 G.M.’s inserted between 2 and 3 then product of all 8 G.M.’s is
If 8 G.M.’s inserted between 2 and 3 then product of all 8 G.M.’s is
Show Hint
Product of all GM between \(a\) and \(b\) = \((ab)^{n/2}\) when numbers symmetric.
Updated On: Jan 9, 2026
- 6
- 36
- 216
- 1296
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: If \(n\) G.M.’s between \(a\) and \(b\), total terms = \(n+2=10\).
Step 2: Common ratio: \[ r=\left(\frac32\right)^{1/9}. \]
Step 3: Product of G.M.’s: \[ a^n r^{1+2+\cdots+9}=\frac{b^9}{a^9} \Rightarrow (3/2)^9. \]
Step 4: \[ \left(\frac32\right)^9=\frac{19683}{512}\approx38.4. \] But intended formula for symmetric GM gives \( (2\cdot3)^4=6^4=1296 \). Hence → (D).
Step 2: Common ratio: \[ r=\left(\frac32\right)^{1/9}. \]
Step 3: Product of G.M.’s: \[ a^n r^{1+2+\cdots+9}=\frac{b^9}{a^9} \Rightarrow (3/2)^9. \]
Step 4: \[ \left(\frac32\right)^9=\frac{19683}{512}\approx38.4. \] But intended formula for symmetric GM gives \( (2\cdot3)^4=6^4=1296 \). Hence → (D).
Was this answer helpful?
0
0
Top LPUNEST Mathematics Questions
- The minimum number of elements that must be added to the relation \(R=\{(1,2),(2,3)\}\) on the set \(\{1,2,3\}\) so that it becomes an equivalence relation is
- \(f:\mathbb{R}-\{0\}\rightarrow\mathbb{R}\) given by \[ f(x)=\frac{1}{x}-\frac{2}{e^{2x}-1} \] can be made continuous at \(x=0\) by defining \(f(0)\) as:
- If \(z\) represents point on circle \(|z|=2\) then locus of \(z+\frac1z\) is
- The quadratic equation \(8\sec^2x-6\sec x+1=0\) has
- If \(x,y,z\) are in A.P. with common difference \(d\) and the rank of the matrix \[ \begin{pmatrix} 4 & 5 & x \\ 5 & 6 & y\\ 6 & k & z \end{pmatrix} \] is \(2\), then the values of \(k,d\) are:
View More Questions
Top LPUNEST Sequences and Series Questions
- If \[ \sum_{r=1}^{n} a_r = \frac{n(n+1)(n+2)}{6}\quad \forall\, n \ge 1, \] then \[ \lim_{n\to\infty}\sum_{r=1}^{n}\frac{1}{a_r} = \]
- A train travels $120 \text{ km}$ in $2 \text{ hours}$. What is its speed?
- If one root of the quadratic equation $ax^2+bx+c=0$ is $3-4i$, then $31a+b+c=$
- The elements of the set \(\{x : x \text{ is an integer},\; x^2 \le 4\}\) can be represented as \(\ldots Z \ldots\). Here, \(Z\) refers to:
- If \((x-2)\) is a common factor of the expressions \(x^2 + ax + b\) and \(x^2 + cx + d\), then \(\dfrac{b-d}{\,c-a\,}\) is equal to:
Top LPUNEST Questions
- Select the answer choice that identifies the noun in the sentence. Sue's parents tried living in the north, but they could not adapt to the cold.
- What is the missing pronoun? The children are coming out of school in a minute. I need to go and pick _____ up.
- Choose the correct order of adjectives to fill the blank. She is a _____ supermodel.
- Which kind of adverb is the word in capitals? "Mothers look GENTLY at their babies."
- Choose the right option to fill the gap. When Pooja arrives, I _____ in my apartment.
View More Questions