JEE Mains · Maths · STD 12 - 1. relation and function
Consider a function \(f : N \rightarrow R\), satisfying \(f(1)+2 f(2)+3 f(3)+\ldots+x f(x)=x(x+1) f(x) ; x \geq 2\) with \(f(1)=1\). Then \(\frac{1}{f(2022)}+\frac{1}{f(2028)}\) is equal to
- A \(8200\)
- B \(8000\)
- C \(8400\)
- D \(8100\)
Answer & Solution
Correct Answer
(D) \(8100\)
Step-by-step Solution
Detailed explanation
Given for \(x \geq 2\) \(f(1)+2 f(2)+\ldots \ldots+x f(x)=x(x+1) f(x)\) \(\text { replace } x \text { by } x +1\) \(\Rightarrow \quad x(x+1) f(x)+(x+1) f(x+1)\) \(=(x+1)(x+2) f(x+1)\) \(\Rightarrow \quad \frac{x}{f(x+1)}+\frac{1}{f(x)}=\frac{(x+2)}{f(x)}\)…
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
- In an examination, there are \(5\) multiple choice questions with \(3\) choices, out of which exactly one is correct There are \(3\) marks for each correct answer, \(-2\) marks for each wrong answer and \(0\) mark if the question is not attempted. Then, the number of ways a student appearing in the examination gets \(5\) marks is. . . . . ... . .JEE Mains 2022 Hard
- From a group of \(10\) men and \(5\) women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, isJEE Mains 2017 Hard
- The coefficient of \(t^4\) in the expansion of \({\left( {\frac{{1 - {t^6}}}{{1 - t}}} \right)^3}\) isJEE Mains 2019 Hard
- If the value of the integral \(\int \limits_{0}^{\frac{1}{2}} \frac{x^{2}}{\left(1-x^{2}\right)^{3 / 2}} d x\) is \(\frac{ k }{6},\) then \(k\) is equal toJEE Mains 2020 Medium
- Let \(\mathrm{n}\) be a non-negative integer. Then the number of divisors of the form " \(4 \mathrm{n}+1\) " of the number \((10)^{10} \cdot(11)^{11} \cdot(13)^{13}\) is equal to \(....\)JEE Mains 2021 Hard
- If \(\frac{{dy}}{{dx}} + y\tan x = \sin 2x\) and \(y(0)\,=1\) , then \(y(\pi)\) is equal toJEE Mains 2014 Hard
More PYQs from JEE Mains
- Let \(y = y\, (x)\) be the solution of the differential equation \(\frac{{dy}}{{dx}} + 2y = f\left( x \right) ,\) where \(f\left( x \right) = \left\{ \begin{array}{l}1,\,\,\,\,\,x \in \left[ {0,1} \right]\\0,\,\,\,\,\,otherwise\end{array} \right.\) If \(y\, (0)\) = \(0\), then \(y\left( {\frac{3}{2}} \right)\) isJEE Mains 2018 Hard
- Let m and \(\mathrm{n},(\mathrm{m} \lt \mathrm{n})\) be two 2-digit numbers. Then the total numbers of pairs \((m, n)\), such that \(\operatorname{gcd}(m, n)=6\), is ________JEE Mains 2025 Hard
- The number of triplets \((x, y, z)\). where \(x, y, z\) are distinct non negative integers satisfying \(x+y+z=15\), isJEE Mains 2023 Hard
- Let \(f: R \rightarrow R\) be such that for all \(\mathrm{x} \in \mathrm{R}\left(2^{1+\mathrm{x}}+2^{1-\mathrm{x}}\right), f(\mathrm{x})\) and \(\left(3 ^\mathrm{x}+3^{-\mathrm{x}}\right)\) are in \(A.P.\), then the minimum value of \(f(x)\) isJEE Mains 2020 Medium
- Let \(y = y ( x )\) be the solution of the differential equation \(x d y-y d x=\sqrt{\left(x^{2}-y^{2}\right)} d x, x \geq 1\), with \(y (1)=0 .\) If the area bounded by the line \(x =1, x = e ^{\pi}, y =0\) and \(y = y ( x )\) is \(\alpha e ^{2 \pi}+\beta\) then the value of \(10(\alpha+\beta)\) is equal to ....... .JEE Mains 2021 Medium
- Let the point \(P(\alpha, \beta)\) be at a unit distance from each of the two lines \(L_{1}: 3 x-4 y+12=0\), and \(L _{2}: 8 x+6 y+11=0\). If \(P\) lies below \(L _{1}\) and above \(L_{2}\), then \(100(\alpha+\beta)\) is equal toJEE Mains 2022 Hard