Download App

Geometric Progressions — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSGeometric Progressions4 Marks
Question
If $\text{x}^{\text{a}}=\text{x}^{\frac{\text{b}}{2}}\text{z}^{\frac{\text{b}}{2}}=\text{z}^{\text{c}},$ then prove that $\frac{1}{\text{a}},\frac{1}{\text{b}},\frac{1}{\text{c}}$ are in A.P.
✓

Answer

$\text{x}^{\text{a}}=\text{x}^{\frac{\text{b}}{2}}\text{z}^{\frac{\text{b}}{2}}=\text{z}^{\text{c}}=\lambda(\text{ say})$ $\text{x}=\lambda^{\frac{1}{\text{a}}},\text{z}=\lambda^{\frac{1}{\text{c}}}$ $\text{x}^{\frac{\text{b}}{2}}\times\text{z}^{\frac{\text{b}}{2}}=\lambda$ $\lambda^{\frac{1}{\text{a}}\big(\frac{\text{b}}{2}\big)}\times\lambda^{\frac{\text{b}}{2}\times\frac{1}{\text{c}}}=\lambda$ $\lambda^{\frac{\text{b}}{2\text{a}}+\frac{\text{b}}{2\text{c}}}=\lambda^1$ $\frac{\text{b}}{2\text{a}}+\frac{\text{b}}{2\text{c}}=1$ $\frac{1}{\text{a}}+\frac{1}{\text{c}}=\frac{2}{\text{b}}$ $\Rightarrow\frac{1}{\text{a}},\frac{1}{\text{b}},\frac{1}{\text{c}}\text{ are in A.P.}$

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 "(Each question 4 marks)" from Geometric Progressions→Geometric Progressions — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\text{f(x)}=\log_\text{e}(1-\text{x})$ and $\text{g(x)}=[\text{x}],$ then determine the following functions: (f + g)(-1)
→
From the following data, state which group is more variable, A or B?
Marks 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Group A 9 17 32 33 40 10 9
Group B 10 20 30 25 43 15 7
→
If A and B are mutually exclusive events such that P(A) = 0.35 and P(B) = 0.45, find:
  1. $\text{P}(\text{A}\cup\text{B})$
  2. $\text{P}({\text{A}}\cap{\text{B}})$
  3. $\text{P}({\text{A}}\cap\overline{\text{B}})$
  4. $\text{P}(\overline{\text{A}}\cap\overline{\text{B}})$
→
If the points (O, 4) and(O, 2) are respectively the vertex and focus of a parabola, then find the equation of the parabola.
→
Prove the following by the principle of mathematical induction: $1 + 3 + 5 + ... + (2n - 1) = n^2$ i.e., the sum of first n odd natural numbers is $n^2​​​​​​​$.
→
Find the derivative of $x^2– 2$ at $x = 10$.
→
Find the derivative of x at x = 1.
→
Differentiate the following functions with respect to x:$\frac{\text{x}}{1+\tan\text{x}}$
→
calculate the mean deviation from the mean for the following data: $36, 72, 46, 42, 60, 45, 53, 46, 51, 49$
→
For the function$\text{f}(\text{x})=\frac{\text{x}^{100}}{100}+\frac{\text{x}^{99}}{99}+...+\frac{\text{x}^2}{2}+\text{x}+1.$
Prove that $\text{f}'(1)=100$$\text{f}'(0)$.
→