JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(f ( x )= x \cdot\left[\frac{ x }{2}\right],\) for \(-10< x <10,\) where \([ t ]\) denotes the greatest integer function. Then the number of points of discontinuity of \(f\) is equal to
- A \(8\)
- B \(10\)
- C \(12\)
- D \(14\)
Answer & Solution
Correct Answer
(A) \(8\)
Step-by-step Solution
Detailed explanation
\(x \in(-10,10)\) \(\frac{ x }{2} \in(-5,5) \rightarrow 9\) integers check continuity at \(x =0\) \(\left.\begin{array}{l}f(0)=0 \\ f\left(0^{+}\right)=0\end{array}\right\} \quad\) continuous at \(x=0\) \(\left(0^{-}\right)=0\) function will be distcontinuous when…
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 a line pass through two distinct points \(P(-2,-1,3)\) and \(Q\), and be parallel to the vector \(3 \hat{i}+2 \hat{j}+2 \hat{k}\). If the distance of the point Q from the point \(\mathrm{R}(1,3,3)\) is 5 , then the square of the area of \(\triangle P Q R\) is equal to :JEE Mains 2025 Medium
- If \(3 x+4 y=12 \sqrt{2}\) is a tangent to the ellipse \(\frac{\mathrm{x}^{2}}{\mathrm{a}^{2}}+\frac{\mathrm{y}^{2}}{9}=1\) for some a \(\in \mathrm{R},\) then the distance between the foci of the ellipse isJEE Mains 2020 Hard
- \(\lim _{x \rightarrow \infty} \frac{\left(2 x^2-3 x+5\right)(3 x-1)^{\frac{x}{2}}}{\left(3 x^2+5 x+4\right) \sqrt{(3 x+2)^x}}\) is equal to :JEE Mains 2025 Medium
- Let \(P\) the point of intersection of the lines \(\frac{x-2}{1}=\frac{y-4}{5}=\frac{z-2}{1}\) and \(\frac{x-3}{2}=\frac{y-2}{3}=\frac{z-3}{2}\). Then, the shortest distance of \(\mathrm{P}\) from the line \(4 \mathrm{x}=2 \mathrm{y}=\mathrm{z}\) isJEE Mains 2024 Medium
- Let \(A\) be a \(3 \times 3\) real matrix such that \(A^2(A-2 I)-\) \(4(\mathrm{~A}-\mathrm{I})=\mathrm{O}\), where I and O are the identity and null matrices, respectively. If \(A^5=\alpha A^2+\beta A+\gamma I\), where \(\alpha, \beta\) and \(\gamma\) are real constants, then \(\alpha+\beta+\gamma\) is equal to:JEE Mains 2025 Medium
- If \(\mathrm{y}=\mathrm{y}(\mathrm{x})\) is the solution of the differential equation, \(\mathrm{e}^{\mathrm{y}}\left(\frac{\mathrm{dy}}{\mathrm{dx}}-1\right)=\mathrm{e}^{\mathrm{x}}\) such that \(\mathrm{y}(0)=0,\) then \(\mathrm{y}(1)\) is equal toJEE Mains 2020 Hard
More PYQs from JEE Mains
- If \(f\left( {\frac{{x - 4}}{{x + 2}}} \right) = 2x + 1,(x \in R = \left\{ {1, - 2} \right\}),\) then \(\int {f(x)} \,dx\) is equal to (where \(C\) is a constant of integration)JEE Mains 2018 Hard
- Let \(\mathrm{a}_{1}, \mathrm{a}_{2}, \mathrm{a}_{3}, \ldots\) be an \(A.P.\) If \(\frac{a_{1}+a_{2}+\ldots+a_{10}}{a_{1}+a_{2}+\ldots+a_{p}}=\frac{100}{p^{2}}, p \neq 10\), then \(\frac{a_{11}}{a_{10}}\) is equal to :JEE Mains 2021 Hard
- If \(\overrightarrow{ a }=\hat{ i }+2 \hat{ k }, \overrightarrow{ b }=\hat{ i }+\hat{ j }+\hat{ k }, \overrightarrow{ c }=7 \hat{ i }-3 \hat{ k }+4 \hat{ k }\) \(\overrightarrow{ r } \times \overrightarrow{ b }+\overrightarrow{ b } \times \overrightarrow{ c }=\overrightarrow{0}\) and \(\overrightarrow{ r } \cdot \overrightarrow{ a }=0\) then \(\overrightarrow{ r } \cdot \overrightarrow{ c }\) is equal to :JEE Mains 2023 Hard
- From a month of \(31\) days, \(3\) different dates are selected at random. If the probability that these dates are in an increasing A.P. is equal to \(\dfrac{a}{b}\), where \(a,b \in \mathbb{N}\) and \(\gcd(a,b)=1\), then \(a+b\) is equal to ______JEE Mains 2026 Hard
- If \(8=3+\frac{1}{4}(3+p)+\frac{1}{4^2}(3+2 p)+\frac{1}{4^3}(3+3 p)+\ldots \infty,\) then the value of \(p\) isJEE Mains 2024 Medium
- If \(S_1\) and \(S_2\) are respectively the sets of local minimum and local maximum points of the function. \(f(x) = 9{x^4} + 12{x^3} - 36{x^2} + 25,x \in R\), thenJEE Mains 2019 Hard