enEnglishguગુજરાતી
JEE Mains · Maths · STD 11 - 8. sequence and series
The sum of the series : \((2)^2 + 2(4)^2 + 3(6)^2 + ...\) upto \(10\) terms is
- A \(11300\)
- B \(11200\)
- C \(12100\)
- D \(12300\)
Answer & Solution
Correct Answer
(C) \(12100\)
Step-by-step Solution
Detailed explanation
\({2^2} + 2{\left( 4 \right)^2} + 3{\left( 6 \right)^2} + .......upto\,\,10\,terms\) \( = {2^2}\left[ {{1^3} + {2^3} + {3^3} + ........upto\,\,10\,terms} \right]\) \( = 4.{\left( {\frac{{10 \times 11}}{2}} \right)^2} = 12100\)
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 \(y = y(x)\) be the solution of the differential equation, \(x\frac{{dy}}{{dx}} + y = x\,{\log _e}\,x,\,\left( {x > 1} \right)\) If \(2y(2) = log_e\, 4 -1\), then \(y(e)\) is equal toJEE Mains 2019 Hard
- The number of relations on the set \(\mathrm{A}=\{1,2,3\}\) containing at most 6 elements including \((1,2)\), which are reflexive and transitive but not symmetric, is ________JEE Mains 2025 Medium
- Let \(\alpha=8-14 i , A=\left\{ z \in C : \frac{\alpha z -\bar{\alpha} \overline{ z }}{ z ^2-(\overline{ z })^2-112 i }=1\right\}\) and \(B =\{ z \in C :| z +3 i |=4\}\) Then \(\sum_{z \in A \cap B}(\operatorname{Re} z-\operatorname{Im} z)\) is equal to \(...............\).JEE Mains 2023 Hard
- Let \(\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}\) be a function defined by \(f(x)=\|x+2|-2| x\|\). If \(m\) is the number of points of local minima and \(n\) is the number of points of local maxima of \(f\), then \(m+n\) isJEE Mains 2025 Easy
- A set \(S\) contains \(7\) elements. A non-empty subset \(A\) of \(S\) and an element \(x\) of \(S\) are chosen at random. Then the probability that \(x \in A\) isJEE Mains 2014 Hard
- If the function \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}}
{\frac{{\sqrt {2 + \cos \,x} - 1}}{{\left( {\pi - {x^2}} \right)}},}&{x \ne \pi } \\
{k\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,}&{x = \pi }
\end{array}} \right.\) is continuous at \(x\, =\pi \) , then \(k\) equalsJEE Mains 2014 Hard
More PYQs from JEE Mains
- Let \(A =\{1,2,3, \ldots, 10\}\) and \(f: A \rightarrow A\) be defined as \(f( k )=\left\{\begin{array}{cl} k +1 & \text { if } k \text { is odd } \\ k & \text { if } k \text { is even }\end{array}\right.\) Then the number of possible functions \(g : A \rightarrow A\) such that \(gof=f\) is ...... .JEE Mains 2021 Medium
- \(\frac{6}{3^{26}}+\frac{10 \cdot 1}{3^{25}}+\frac{10 \cdot 2}{3^{24}}+\frac{10 \cdot 2^2}{3^{23}}+\ldots+\frac{10 \cdot 2^{24}}{3}\) is equal toJEE Mains 2026 Easy
- Let \(S\left( \alpha \right) = \left\{ {\left( {x,y} \right):{y^2} \leq x,0 \leq \alpha } \right\}\) and \(A(\alpha )\) is area of the regions \(S(\alpha )\). If for a \(\lambda ,0 < \lambda < 4,A (\lambda ) : A\left( 4 \right)\,=\,2:5\) then \(\lambda \) equalsJEE Mains 2019 Hard
- The number of real solutions of the equation \(\mathrm{x}|\mathrm{x}+5|+2|\mathrm{x}+7|-2=0\) is ...........JEE Mains 2024 Hard
- The area of the region enclosed by the curves \(y=\mathrm{e}^x, y=\left|\mathrm{e}^x-1\right|\) and \(y\)-axis is:JEE Mains 2025 Medium
- Area of the region \(\left\{(x, y): x^2+(y-2)^2 \leq 4\right.\), \(\left.x^2 \geq 2 y\right\}\) isJEE Mains 2023 Hard