JEE Mains · Maths · STD 12 - 5. continuity and differentiation
\(f(x)=\left\{\begin{array}{cc}\frac{\sin (x-[x])}{x-[x]} & , \quad x \in(-2,-1) \\ \max \{2 x, 3[|x|]\} & , \quad|x|<1 \\ 1 & , \quad \text { otherwise }\end{array}\right.\) where \([t]\) denotes greatest integer \(\leq t\). If \(m\) is the number of points where \(f\) is not continuous and \(n\) is the number of points where \(f\) is not differentiable, then the ordered pair \(( m , n )\) is
- A \((3,3)\)
- B \((2,4)\)
- C \((2,3)\)
- D \((3,4)\)
Answer & Solution
Correct Answer
(C) \((2,3)\)
Step-by-step Solution
Detailed explanation
\(f(x)=\left\{\begin{array}{ccc}\frac{\sin (x+2)}{x+2} & , & x \in(-2,-1) \\ \max \{2 x , 0\} & , & x \in(-1,1) \\ 1 & , & \text { otherwise }\end{array}\right.\) \(f\left(-2^{+}\right)=\lim \limits_{{h \rightarrow 0}} f(-2+h)=\lim _{h \rightarrow 0} \frac{\sinh }{h}=1\) \(f\)…
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
- A bag contains 19 unbiased coins and one coin with head on both sides. One coin drawn at random is tossed and head turns up. If the probability that the drawn coin was unbiased, is \(\frac{\mathrm{m}}{\mathrm{n}}, \operatorname{gcd}(\mathrm{m}, \mathrm{n})=1\), then \(\mathrm{n}^2-\mathrm{m}^2\) is equal to :JEE Mains 2025 Easy
- Consider the lines \(\mathrm{x}(3 \lambda+1)+\mathrm{y}(7 \lambda+2)=17 \lambda+5\), \(\lambda\) being a parameter, all passing through a point P . One of these lines (say L) is farthest from the origin. If the distance of \(L\) from the point \((3,6)\) is \(d\), then the value of \(d^2\) isJEE Mains 2025 Easy
- If \(\left| {\begin{array}{*{20}{c}}{x - 4}&{2x}&{2x}\\{2x}&{x - 4}&{2x}\\{2x}&{2x}&{x - 4}\end{array}} \right| = \left( {A + Bx} \right){\left( {x - A} \right)^2},\) then the ordered pair \(\left( {A,B} \right) = \). . . . .JEE Mains 2018 Medium
- The urns \(A, B\) and \(C\) contain \(4\) red, \(6\) black;\(5\) red,\(5\) black and \(\lambda\) red,\(4\) black balls respectively. One of the urns is selected at random and a ball is drawn. If the ball drawn is red and the probability that it is drawn from urn \(C\) is \(0.4\) then the square of the length of the side of the largest equilateral triangle, inscribed in the parabola \(y^2=\lambda x\) with one vertex at the vertex of the parabola isJEE Mains 2023 Hard
- Let \(y=y(x)\) be the solution of the differential equation \(\frac{d y}{d x}+2 y \sec ^2 x=2 \sec ^2 x+3 \tan x \cdot \sec ^2 x\) such that \(\mathrm{y}(0)=\frac{5}{4}\). Then \(12\left(\mathrm{y}\left(\frac{\pi}{4}\right)-\mathrm{e}^{-2}\right)\) is equal to _______.JEE Mains 2025 Medium
- Let \(A=\{1,2,3,4\}\) and \(R\) be a relation on the set \(A \times A\) defined by \(R=\{((a, b),(c, d)): 2 a+3 b=4 c+5 d\}\). Then the number of elements in \(R\) is:JEE Mains 2023 Hard
More PYQs from JEE Mains
- Let \(f(x)=\left|(x-1)\left(x^{2}-2 x-3\right)\right|+x-3, x \in R\). If \(m\) and \(M\) are respectively the number of points of local minimum and local maximum of \(f\) in the interval \((0,4)\), then \(m + M\) is equal toJEE Mains 2022 Hard
- One die has two faces marked 1 , two faces marked 2 , one face marked 3 and one face marked 4 . Another die has one face marked 1 , two faces marked 2 , two faces marked 3 and one face marked 4. The probability of getting the sum of numbers to be 4 or 5 , when both the dice are thrown together, isJEE Mains 2025 Medium
- Let \(S_n=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\ldots\) upto \(n\) terms. If the sum of the first six terms of an A.P. with first term -p and common difference p is \(\sqrt{2026 \mathrm{~S}_{2025}}\), then the absolute difference betwen \(20^{\text {th }}\) and \(15^{\text {th }}\) terms of the A.P. isJEE Mains 2025 Hard
- The integral \(16 \int \limits_1^2 \frac{d x}{x^3\left(x^2+2\right)^2}\) is equal toJEE Mains 2023 Hard
- If the lines \(x\,=\,ay\,+\,b,\,\,z\,=\,cy\,+\,d\) and \(x\, = \,a\,'z + \,b\,',\,\,y = \,c\,'z\, + \,d\,'\) are perpendicular, thenJEE Mains 2019 Easy
- Let \(\vec{a}\) and \(\vec{b}\) be two vectors. Let \(|\vec{a}|=1,|\vec{b}|=4\) and \(\vec{a} \cdot \vec{b}=2\). If \(\vec{c}=(2 \vec{a} \times \vec{b})-3 \vec{b}\), then the value of \(\overrightarrow{ b } \cdot \overrightarrow{ c }\) isJEE Mains 2023 Medium