WBJEE · Maths · Sequences and Series
Let \(a, b, c, p, q\) and \(r\) be positive real numbers such that \(a, b\) and \(c\) are in GP and \(a^{p}=b^{q}=c^{r}\). Then,
- A \(p, q, r\) are in G.P.
- B \(p, q, r\) are in A.P.
- C \(p, q, r\) are in H.P.
- D \(p^{2}, q^{2}, r^{2}\) are in A.P.
Answer & Solution
Correct Answer
(C) \(p, q, r\) are in H.P.
Step-by-step Solution
Detailed explanation
Let \(a^{p}=b^{4}=c^{r}=k\) \(\therefore \quad a=k^{1 / p}, b=k^{1 / q}, c=k^{1 / r}\) since, \(a, b, c\) are in \(\mathrm{GP} .\) \(\therefore\) \(\frac{b}{a}=\frac{c}{b}\) \(\frac{k^{1 / q}}{k^{1 / P}}=\frac{k^{1 / r}}{k^{1 / q}}\) \(k^{1 / q-1 / p}=k^{1 / r-1 / 4}\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The side \(A B\) of \(\triangle A B C\) is fixed and is of length \(2 a\) unit. The vertex moves in the plane such that the vertical angle is always constant and is \(\alpha\). Let \(x\)-axis be along \(A B\) and the origin be at \(A\). Then the locus of the vertex isWBJEE 2022 Hard
- Applying Lagrange's Mean Value Theorem for a suitable function \(f(x)\) in \([0, h],\) we have \(f(h)=f(0)+h f^{\prime}(\theta h), \quad 0 < \theta < 1 . \quad\) Then, for \(f(x)=\cos x,\) the value of \(\lim _{h \rightarrow 0^{*}} \theta\) isWBJEE 2014 Medium
- If the sum of the distances of a point from two perpendicular lines in a plane is 1 unit, then its locus isWBJEE 2022 Easy
- Given that \(\mathrm{f}: \mathrm{S} \rightarrow \mathrm{R}\) is said to have a fixed point at \(\mathrm{c}\) of \(\mathrm{S}\) if \(\mathrm{f}(\mathrm{c})=\mathrm{c}\).
Let \(f:[1, \infty) \rightarrow R\) be defined by \(f(x)=1+\sqrt{x}\). ThenWBJEE 2021 Easy - Let \(a_1, a_2, a_3, \ldots, a_n\) be positive real numbers. Then the minimum value of \(\frac{a_1}{a_2}+\frac{a_2}{a_3}+\ldots .+\frac{a_n}{a_1}\) isWBJEE 2023 Medium
- The greatest integer which divides \((p+1)(p+2)(p+3) \ldots(p+q)\) for all
\(p \in N\) and fixed \(q \in N\) isWBJEE 2017 Easy
More PYQs from WBJEE
- The value of \(\operatorname{Lt}_{x \rightarrow 0}\left(\frac{1+5 x^2}{1+3 x^2}\right)^{\frac{1}{x^2}}\) isWBJEE 2010 Easy
- If \(x=-1\) and \(x=2\) are extreme points of \(f(x)=\alpha \log |x|+\beta x^2+x,(x \neq 0)\), thenWBJEE 2025 Medium
- If the tangent to \(y^{2}=4 a x\) at the point \(\left(a t^{2}, 2 a t\right)\) where \(|t|>1\) is a normal to \(x^{2}-y^{2}=a^{2}\) at the point \((a \sec \theta, a \tan \theta),\) thenWBJEE 2017 Medium
- Amongst the following compounds, the one that will not respond to Cannizzaro reaction upon treatment with alkali isWBJEE 2016 Medium
- Ionic solids with Schottky defect may contain in their structureWBJEE 2016 Easy
- If \(n\) denotes a positive integer, \(h\) the Planck constant, \(q\) the charge and \(B\) the magnetic field, then the quantity \(\left[\frac{n h}{2 \pi q B}\right]\) has theWBJEE 2014 Easy