JEE Mains · Maths · STD 11 - 8. sequence and series
The sum of an infinite geometric series with positive terms is \(3\) and the sum of the cubes of its terms is \(\frac {27}{19}\). Then the common ratio of this series is
- A \(\frac {1}{3}\)
- B \(\frac {2}{3}\)
- C \(\frac {2}{9}\)
- D \(\frac {4}{9}\)
Answer & Solution
Correct Answer
(B) \(\frac {2}{3}\)
Step-by-step Solution
Detailed explanation
\(\frac{a}{{1 - r}} = 3\) Cube both sides \(\frac{{{a^3}}}{{{{(1 - r)}^3}}} = 27\,\,\,\,......\left( 1 \right)\) and \(\frac{{{a^3}}}{{1 - {r^3}}} = \frac{{27}}{{19}}\,\,\,\,......\left( 2 \right)\) \((1)/(2)\) given \(\frac{{1 - {r^3}}}{{{{(1 - r)}^3}}} = 19\)…
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
- Let \(\quad f(x)=x+\frac{a}{\pi^2-4} \sin x+\frac{b}{\pi^2-4} \cos x\) \(x \in R\) be a function which satisfies \(f(x)=x+\int \limits_0^{\pi / 2} \sin (x+y) f(y) d y\). Then \(( a + b )\) is equal to \(............\)JEE Mains 2023 Hard
- Let \(S =\{ z \in C :| z -2| \leq 1, z (1+ i )+\overline{ z }(1-\) i) \(\leq 2\}\). Let \(|z-4 i|\) attains minimum and maximum values, respectively, at \(z _{1} \in S\) and \(z _{2} \in S\). If \(5\left(\left|z_{1}\right|^{2}+\left|z_{2}\right|^{2}\right)=\alpha+\beta \sqrt{5}\), where \(\alpha\) and \(\beta\) are integers, then the value of \(\alpha+\beta\) is equal toJEE Mains 2022 Hard
- Given two independent events, if the probability that exactly one of them occurs is \(\frac {26}{49}\) and the probability that none of them occurs is \(\frac {15}{49}\) , then the probability of more probable of the two events isJEE Mains 2013 Hard
- Let \(P\) the point of intersection of the lines \(\frac{x-2}{1}=\frac{y-4}{5}=\frac{z-2}{1}\) and \(\frac{x-3}{2}=\frac{y-2}{3}=\frac{z-3}{2}\). Then, the shortest distance of \(\mathrm{P}\) from the line \(4 \mathrm{x}=2 \mathrm{y}=\mathrm{z}\) isJEE Mains 2024 Medium
- The number of bijective functions \(f :\{1,3,5, 7, \ldots \ldots . .99\} \rightarrow\{2,4,6,8, \ldots \ldots, 100\}\), such that \(f(3) \geq f(9) \geq f(15) \geq f(21) \geq \ldots \ldots f(99), \quad\) isJEE Mains 2022 Hard
- The general solution of the differential equation, \(\sin \,2x\,\left( {\frac{{dy}}{{dx}} - \sqrt {\tan \,x} } \right) - y = 0,\) isJEE Mains 2014 Hard
More PYQs from JEE Mains
- The area bounded by the curves \(y=|x-1|+|x-2|\) and \(y =3\) is equal toJEE Mains 2023 Hard
- The value of the integral \(\displaystyle\int_{0}^{2} \dfrac{\sqrt{x(x^2+x+1)}}{(\sqrt{x+1})(\sqrt{x^4+x^2+1})} \, dx\) is equal to:JEE Mains 2026 Hard
- Let \(f(x)=3 \sqrt{x-2}+\sqrt{4-x}\) be a real valued function. If \(\alpha\) and \(\beta\) are respectively the minimum and the maximum values of \(\mathrm{f}\), then \(\alpha^2+2 \beta^2\) is equal toJEE Mains 2024 Hard
- The number of values of \(z \in \mathbb{C}\), satisfying the equations \(|z-(4+8i)|=\sqrt{10}\) and \(|z-(3+5i)|+|z-(5+11i)|=4\sqrt{5}\), is:JEE Mains 2026 Hard
- Let \(\alpha, \beta, \gamma\) be the three roots of the equation \(x ^3+ bx + c =0\). If \(\beta \gamma=1=-\alpha\), then \(b^3+2 c^3-3 \alpha^3-6 \beta^3-8 \gamma^3\) is equal to \(......\).JEE Mains 2023 Hard
- The coefficients \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) in the quadratic equation \(a x^2+b x+c=0\) are chosen from the set \(\{1,2,3,4,5,6,7,8\}\). The probability of this equation having repeated roots is :JEE Mains 2024 Hard