JEE Mains · Maths · STD 12 - 1. relation and function
A function \(f(x)\) is given by \(f(x)=\frac{5^{x}}{5^{x}+5}\), then the sum of the series \(f\left(\frac{1}{20}\right)+f\left(\frac{2}{20}\right)+f\left(\frac{3}{20}\right)+\ldots \ldots+f\left(\frac{39}{20}\right)\) is equal to ....... .
- A \(\frac{19}{2}\)
- B \(\frac{49}{2}\)
- C \(\frac{29}{2}\)
- D \(\frac{39}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{39}{2}\)
Step-by-step Solution
Detailed explanation
\(f(x)=\frac{5^{x}}{5^{x}+5} \quad f(2-x)=\frac{5}{5^{x}+5}\) \(f(x)+f(2-x)=1\) \(\Rightarrow f\left(\frac{1}{20}\right)+f\left(\frac{2}{20}\right)+\ldots+f\left(\frac{39}{20}\right)\)…
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
- The value of \(\int \limits_{\frac{\pi}{3}}^{\frac{\pi}{2}} \frac{(2+3 \sin x)}{\sin x(1+\cos x)} d x\) is equal toJEE Mains 2023 Hard
- If \((\vec{a}+3 \vec{b})\) is perpendicular to \((7 \vec{a}-5 \vec{b})\) and \((\vec{a}-4 \vec{b})\) is perpendicular to \((7 \vec{a}-2 \vec{b})\), then the angle between \(\vec{a}\) and \(\vec{b}\) (in degrees) is \(......\)JEE Mains 2021 Medium
- Let the equations of two ellipses be \({E_1}:\,\frac{{{x^2}}}{3} + \frac{{{y^2}}}{2} = 1\) and \({E_2}:\,\frac{{{x^2}}}{16} + \frac{{{y^2}}}{b^2} = 1,\) If the product of their eccentricities is \(\frac {1}{2},\) then the length of the minor axis of ellipse \(E_2\) isJEE Mains 2013 Hard
- If \(x, y, z\) are in arithmetic progression with common difference \(d , x \neq 3 d ,\) and the
determinant of the matrix \(\left[\begin{array}{ccc}3 & 4 \sqrt{2} & x \\ 4 & 5 \sqrt{2} & y \\ 5 & k & z\end{array}\right]\) is zero, then the value of \(k ^{2}\) is ..... .JEE Mains 2021 Hard - Consider three vectors \(\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}}, \overrightarrow{\mathrm{c}}\). Let \(|\overrightarrow{\mathrm{a}}|=2,|\overrightarrow{\mathrm{b}}|=3\) and \(\overrightarrow{\mathrm{a}}=\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}}\). If \(\alpha \in\left[0, \frac{\pi}{3}\right]\) is the angle between the vectors \(\vec{b}\) and \(\vec{c}\), then the minimum value of \(27|\overrightarrow{c}-\overrightarrow{a}|^2\) is equal to :JEE Mains 2024 Hard
- Three rotten apples are accidently mixed with fifteen good apples. Assuming the random variable \(x\) to be the number of rotten apples in a draw of two apples, the variance of \(x\) isJEE Mains 2024 Hard
More PYQs from JEE Mains
- Let the line passing through the points, \(P(2,-1,2)\) and \(Q(5,3,4)\) meet the plane \(x-y+z=4\) at the point \(R\). Then the distance of the point \(R\) from the plane \(x+2 y+3 z+2=0\) measured parallel to the line \(\frac{x-7}{2}=\frac{y+3}{2}=\frac{z-2}{1}\) is equal toJEE Mains 2023 Hard
- A survey shows that \(73 \%\) of the persons working in an office like coffee, whereas \(65 \%\) like tea. If \(x\) denotes the percentage of them, who like both coffee and tea, then \(x\) cannot beJEE Mains 2020 Medium
- If \(\sum_{ k =1}^{10} K ^{2}\left(10_{ C _{ K }}\right)^{2}=22000 L\), then \(L\) is equal to \(.....\)JEE Mains 2022 Hard
- The number of matrices \(A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]\), where a \(, b, c, d \in\{-1,0,1,2,3, \ldots \ldots, 10\}\), such that \(A=A^{-1}\), isJEE Mains 2022 Hard
- If \(f(x)=\left\{\begin{array}{cl}x^3 \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x=0\end{array}\right.\), thenJEE Mains 2024 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