JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(f: R \rightarrow R\) be defined as \(f(x)=\left\{\begin{array}{ccc}\frac{a-b \cos 2 x}{x^2} & ; & x<0 \\ x^2+c x+2 & ; & 0 \leq x \leq 1 \\ 2 x+1 & ; & x>1\end{array}\right.\) If \(f\) is continuous everywhere in \(R\) and \(\mathrm{m}\) is the number of points where \(f\) is \(NOT\) differential then \(\mathrm{m}+\mathrm{a}+\mathrm{b}+\mathrm{c}\) equals :
- A \(1\)
- B \(4\)
- C \(3\)
- D \(2\)
Answer & Solution
Correct Answer
(D) \(2\)
Step-by-step Solution
Detailed explanation
At \(\mathrm{x}=1, \mathrm{f}(\mathrm{x})\) is continuous therefore, \(\mathrm{f}\left(1^{-}\right)=\mathrm{f}(1)=\mathrm{f}\left(1^{+}\right)\) \(\mathrm{f}(1)=3+\mathrm{c}\) \(.....(1)\) \(\mathrm{f}\left(1^{+}\right)=\lim _{h \rightarrow 0} 2(1+\mathrm{h})+1\)…
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
- Remainder when \( 64^{32^{32}}\) is divided by \(9\) is equal to ...........JEE Mains 2024 Hard
- The value of \(b>3\) for which \(12 \int \limits_{3}^{b} \frac{1}{\left(x^{2}-1\right)\left(x^{2}-4\right)} d x=\log _{e}\left(\frac{49}{40}\right)\), is equal toJEE Mains 2022 Medium
- The locus of a point, which moves such that the sum of squares of its distances from the points \((0,0),(1,0),(0,1)(1,1)\) is \(18\) units, is a circle of diameter \(\mathrm{d}\). Then \(\mathrm{d}^{2}\) is equal to ...... .JEE Mains 2021 Medium
- If \(\overrightarrow x = 3\hat i - 6\hat j - \hat k\) , \(\overrightarrow y = \hat i + 4\hat j - 3\hat k\) and \(\,\,\overrightarrow z = 3\hat i - 4\hat j - 12\hat k\) , then the magnitude of the projection of \(\overrightarrow x \times \overrightarrow y \) on \(\overrightarrow z\) isJEE Mains 2014 Medium
- If the distance of the point \((1,-2,3)\) from the plane \(x+2 y-3 z+10=0\) measured parallel to the line, \(\frac{x-1}{3}=\frac{2-y}{m}=\frac{z+3}{1}\) is \(\sqrt{\frac{7}{2}},\) then the value of \(\mid m \mid\) is equal to ....... .JEE Mains 2021 Hard
- Let \(N\) be the set of natural numbers and a relation \(R\) on \(N\) be defined by \(R=\left\{(x, y) \in N \times N: x^{3}-3 x^{2} y-x y^{2}+3 y^{3}=0\right\} .\) Then the relation \(R\) is:JEE Mains 2021 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
- If the three lines \(x - 3y = p, ax + 2y = q\) and \(ax + y = r\) form a right-angled triangle thenJEE Mains 2013 Hard
- The equation of a normal to the curve \(\sin \,y = x\,\sin \,\left( {\frac{\pi }{3} + y} \right)\) at \(x\, = 0\), isJEE Mains 2015 Hard
- If \(a, b, c\) are non-zero real numbers and if the system of equations \((a - 1 )x = y + z,\) \((b - 1 )y = z + x ,\) \((c - 1 )z= x + y,\) has a non-trivial solution, then \(ab + bc + ca\) equalsJEE Mains 2014 Hard
- Let \(\vec{v}=\alpha \hat{i}+2 \hat{j}-3 \hat{k}, \vec{w}=2 \alpha \hat{i}+\hat{j}-\hat{k}\), and \(\overrightarrow{ u }\) be a vector such that \(|\vec{u}|=\alpha > 0\). If the minimum value of the scalar triple product \([\vec{u} \vec{v} \vec{w}]\) is \(-\alpha \sqrt{3401}\), and \(|\vec{u} . \hat{i}|^2=\frac{m}{n}\) where \(m\) and \(n\) are coprime natural numbers, then \(m + n\) is equal to \(.........\).JEE Mains 2023 Hard
- If the area (in sq. units) bounded by the parabola \(y^2 =4\lambda x\) and the line \(y = \lambda x\), \(\lambda > 0\), is \(\frac{1}{9}\), then \(\lambda \) is equal toJEE Mains 2019 Hard