JEE Mains · Maths · STD 11 - 13. statistics
If the mean deviation about the mean of the numbers \(1,2,3, \ldots ., n\), where \(n\) is odd, is \(\frac{5(n+1)}{n}\), then \(n\) is equal to
- A \(20\)
- B \(25\)
- C \(23\)
- D \(21\)
Answer & Solution
Correct Answer
(D) \(21\)
Step-by-step Solution
Detailed explanation
Mean deviation about mean of first \(n\) natural numbers is \(\frac{ n ^{2}-1}{4 n }\) \(\therefore n =21\)
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 \(\mathrm{f}(\mathrm{x})\) be a polynomial of degree \(3\) such that \(\mathrm{f}(\mathrm{k})=-\frac{2}{\mathrm{k}}\) for \(\mathrm{k}=2,3,4,5 .\) Then the value of \(52-10 \mathrm{f}(10)\) is equal to :JEE Mains 2021 Hard
- Let \(f(x)=3 \sin ^{4} x+10 \sin ^{3} x+6 \sin ^{2} x-3, x \in\left[-\frac{\pi}{6}, \frac{\pi}{2}\right] .\) Then, \(f\) is \(.....\)JEE Mains 2021 Hard
- The maximum area (in sq. units) of a rectangle having its base on the \(x-\) axis and its other two vertices on the parabola, \(y = 12 -x^2\) such that the rectangle lies inside the parabola, isJEE Mains 2019 Hard
- Let \(\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\mathrm{k}, \overrightarrow{\mathrm{b}}=3(\hat{\mathrm{i}}-\hat{\mathrm{j}}+\mathrm{k})\). Let \(\overrightarrow{\mathrm{c}}\) be the vector such that \(\vec{a} \times \vec{c}=\vec{b}\) and \(\vec{a} \cdot \vec{c}=3\). Then \(\overrightarrow{\mathrm{a}} \cdot((\overrightarrow{\mathrm{c}} \times \overrightarrow{\mathrm{b}})-\overrightarrow{\mathrm{b}}-\overrightarrow{\mathrm{c}})\) is equal to :JEE Mains 2024 Hard
- Let \(A\) and \(B\) be two independent events such that \(\mathrm{P}(\mathrm{A})=\frac{1}{3}\) and \(\mathrm{P}(\mathrm{B})=\frac{1}{6} .\) Then, which of the following is TRUE?JEE Mains 2020 Hard
- Let the area enclosed between the curves \(|y|=1-x^2\) and \(x^2+y^2=1\) be \(\alpha\). If \(9 \alpha=\beta \pi+\gamma ; \beta, \gamma\) are integers, then the value of \(|\beta-\gamma|\) equals.JEE Mains 2025 Medium
More PYQs from JEE Mains
- Let the image of the point \(P (1,2,3)\) in the line \(L : \frac{ x -6}{3}=\frac{ y -1}{2}=\frac{ z -2}{3}\) be \(Q .\) let \(R (\alpha, \beta, \gamma)\) be a point that divides internally the line segment \(PQ\) in the ratio \(1: 3\). Then the value of \(22(\alpha+\beta+\gamma)\) is equal toJEE Mains 2022 Hard
- If for \(n \geq 1\) , \({P_n} = \int\limits_1^e {{{\left( {\log \,x} \right)}^n}\,dx} \) , then \(P_{10} - 90P_8\) is equal toJEE Mains 2014 Hard
- Let \(R_{1}\) and \(R_{2}\) be relations on the set \(\{1,2, \ldots, 50\}\) such that \(R _{1}=\left\{\left( p , p ^{ n }\right)\right.\) : \(p\) is a prime and \(n \geq 0\) is an integer \(\}\) and \(R _{2}=\left\{\left( p , p ^{ n }\right)\right.\) : \(p\) is a prime and \(n =0\) or \(1\}\). Then, the number of elements in \(R _{1}- R _{2}\) is........JEE Mains 2022 Hard
- The relation \(R=\{(x, y): x, y \in \mathbb{Z}\) and \(x+y\) is even \(\}\) is:JEE Mains 2025 Medium
- Let \(a, b\) be two real numbers such that \(a b < 0\). If the complex number \(\frac{1+ ai }{ b + i }\) is of unit modulus and \(a+i b\) lies on the circle \(|z-1|=|2 z|\), then a possible value of \(\frac{1+[ a ]}{4 b }\), where \([ t ]\) is greatest integer function, is :JEE Mains 2023 Hard
- Let \(A=\{1,2,3,5,8,9\}\). Then the number of possible functions \(f : A \rightarrow A\) such that \(f(m \cdot n)=f(m) \cdot f(n)\) for every \(m, n \in A\) with \(m \cdot n \in A\) is equal to \(...............\).JEE Mains 2023 Medium