JEE Mains · Maths · STD 12 - 1. relation and function
Let \(f: R \rightarrow R\) be a function defined by \(f(x)=\left(2\left(1-\frac{x^{25}}{2}\right)\left(2+x^{25}\right)\right)^{\frac{1}{50}}\). If the function \(g(x)=f(f(f(x)))+f(f(x))\), the the greatest integer less than or equal to \(g (1)\) is
- A \(3\)
- B \(7\)
- C \(2\)
- D \(8\)
Answer & Solution
Correct Answer
(C) \(2\)
Step-by-step Solution
Detailed explanation
\(f(x)=\left[2\left(1-\frac{x^{25}}{2}\right)\left(2+x^{25}\right)\right]^{\frac{1}{50}}\) \(f(x)=\left[\left(2-x^{25}\right)\left(2+x^{25}\right)\right]^{\frac{1}{50}}\) \(\quad=\left(4-x^{50}\right)^{1 / 50}\)…
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 area of the region enclosed by the parabola \((y-2)^2=x-1\), the line \(x-2 y+4=0\) and the positive coordinate axes isJEE Mains 2024 Hard
- Let \(A\) and \(B\) be any two \(3\times3\) matrices. If \(A\) is symmetric and \(B\) is skewsymmetric, then the matrix \(AB - BA\) isJEE Mains 2014 Hard
- If the coefficents of \({x^3}\) and \({x^4}\) in the expansion of \(\left( {1 + ax + b{x^2}} \right){\left( {1 - 2x} \right)^{18}}\) in powers of \(x\) are both zero, then \( (a,b) \) is equal toJEE Mains 2014 Hard
- If the mean and variance of eight numbers \(3,7,9,12,13,20, x\) and \(y\) be \(10\) and \(25\) respectively, then \(\mathrm{x} \cdot \mathrm{y}\) is equal toJEE Mains 2020 Hard
- A ray of light passing through the point \(P (2,3)\) reflects on the \(x-\)axis at point \(A\) and the reflected ray passes through the point \(Q(5,4)\). Let \(R\) be the point that divides the line segment \(AQ\) internally into the ratio \(2: 1\). Let the co-ordinates of the foot of the perpendicular \(M\) from \(R\) on the bisector of the angle \(PAQ\) be \((\alpha, \beta)\). Then, the value of \(7 \alpha+3 \beta\) is equal to.......JEE Mains 2022 Hard
- Let the product of the focal distances of the point \(\mathrm{P}(4,2 \sqrt{3})\) on the hyperbola \(\mathrm{H}: \frac{\mathrm{x}^2}{\mathrm{a}^2}-\frac{\mathrm{y}^2}{\mathrm{~b}^2}=1\) be 32 .
Let the length of the conjugate axis of \(H\) be \(p\) and the length of its latus rectum be q . Then \(\mathrm{p}^2+\mathrm{q}^2\) is equal to _______JEE Mains 2025 Hard
More PYQs from JEE Mains
- For the natural numbers \(m, n\), if \((1-y)^{m}(1+y)^{n}=1+a_{1} y+a_{2} y^{2}+\ldots .+a_{m+n} y^{m+n}\) and \(a_{1}=a_{2}\) \(=10\), then the value of \((m+n)\) is equal to:JEE Mains 2021 Hard
- The area (in sq. units) of the region \(\left\{(\mathrm{x}, \mathrm{y}) \in \mathrm{R}^{2}: \mathrm{x}^{2} \leq \mathrm{y} \leq 3-2 \mathrm{x}\right\},\) isJEE Mains 2020 Hard
- The integral \(\int {\frac{{3{x^{13}}\, + \,\,2{x^{11}}}}{{{{(2{x^4}\, + \,3{x^2}\, + \,1)}^4}}}dx} \) is equal to (where \(C\) is a constant of integration)JEE Mains 2019 Hard
- For the function \(f(x)=\sin x+3 x-\frac{2}{\pi}\left(x^2+x\right) \text {, where } x \in\left[0, \frac{\pi}{2}\right] \text {, }\) consider the following two statements : (\(I\)) \(\mathrm{f}\) is increasing in \(\left(0, \frac{\pi}{2}\right)\). (\(II\)) \(\mathrm{f}^{\prime}\) is decreasing in \(\left(0, \frac{\pi}{2}\right)\). Between the above two statements,JEE Mains 2024 Hard
- If \(\sum_{r=1}^{13}\left\{\frac{1}{\sin \left(\frac{\pi}{4}+(r-1) \frac{\pi}{6}\right) \sin \left(\frac{\pi}{4}+\frac{r \pi}{6}\right)}\right\}=a \sqrt{3}+b, a, b \in \mathbf{Z}\), then \(a^2+b^2\) is equal to :JEE Mains 2025 Hard
- Let \(f(x) = \begin{cases} \dfrac{1}{3}, & x \leq \pi/2 \\ \dfrac{b(1-\sin x)}{(\pi-2x)^2}, & x > \pi/2 \end{cases}\). If \(f\) is continuous at \(x=\pi/2\), then the value of \(\displaystyle\int_{0}^{3b-6} |x^2+2x-3|\,dx\) is:JEE Mains 2026 Hard