AP EAMCET · Maths · Sets and Relations
Let \(f(x)=|x-3|+|x+5|\) and
\(A=\left\{a \in \mathbb{R} / \lim _{x \rightarrow a} \frac{f(x)-f(a)}{x-a}\right.\) exists \(\}\)
Then the number of real numbers which are in \((-\infty,-3)\) \(\cup(5, \infty)\) but not in \(A\) is
- A 2
- B 0
- C 1
- D 3
Answer & Solution
Correct Answer
(C) 1
Step-by-step Solution
Detailed explanation
\(A=I R /\{3,-5\}\) Now, real numbers which are in \((-\infty,-3) \cup(5, \infty)\) but not in \(A\) is only 3 . \(\therefore\) No. of required real no. is 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
- If \(a>0\) and \(f(x)=\left(\frac{a+x}{1+x}\right)^{a+1+2 x}\), then \(f^{\prime}(0)=\)AP EAMCET 2018 Medium
- A value of \(b\) for which the rank of the matrix \(A=\left[\begin{array}{cccc}1 & 1 & -1 & 0 \\ 4 & 4 & -3 & 1 \\ b & 2 & 2 & 2 \\ 9 & 9 & b & 3\end{array}\right]\) is 3 , isAP EAMCET 2019 Easy
- The minimum value of \(f(x)=\frac{x^2-2 x+3}{x^2-4 x+7}\) isAP EAMCET 2023 Medium
- If \(\alpha, \beta, \gamma\) are the roots of \(x^3+4 x+1=0\), then the equation whose roots are \(\frac{\alpha^2}{\beta+\gamma}, \frac{\beta^2}{\gamma+\alpha}\), \(\frac{\gamma^2}{\alpha+\beta}\) isAP EAMCET 2009 Medium
- The locus of a point which moves such that the area of the triangle formed by it with the vertices \((1,2)\) and \((-2,5)\) is 8 sq. units is/areAP EAMCET 2020 Easy
- Consider the following statements :
I : If \(a\) and \(b\) are positive real numbers, then \(\sqrt{-a} \times \sqrt{-b}=\sqrt{a b}\)
II : The argument of \(\frac{1+i \sqrt{3}}{1-i \sqrt{3}}\) is \(120^{\circ}\)
ThenAP EAMCET 2017 Medium
More PYQs from AP EAMCET
- A constant voltage of \(25 \mathrm{~V}\) is applied to a series \(L-R\) circuit at \(t=0\), by closing a switch. What is the potential difference across the resistor and the inductor at time \(t=0\) ?AP EAMCET 2011 Medium
- If \(\mathbf{a} \cdot \hat{\mathbf{i}}=\mathbf{a} \cdot(\hat{\mathbf{i}}+\hat{\mathbf{j}})=\mathbf{a} \cdot(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})\), then \(\mathbf{a}\) is equal toAP EAMCET 2002 Easy
- Two identical cells gave the same current through an external resistance of \(2 \Omega\) regardless whether the cells are grouped in series or parallel. The internal resistance of the cells isAP EAMCET 2024 Medium
- A polygon has 54 diagonals. The number of sides of this polygon isAP EAMCET 2020 Medium
- In each of four separate beakers (I, II, III, IV), X mL of \(y \mathrm{M} \mathrm{Fe}_2 \mathrm{O}_3 x \mathrm{H}_2 \mathrm{O}\) colloidal solution is present. Equal volume and equal concentration of of KCl, \(\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right], \mathrm{K}_3 \mathrm{PO}_4\) and \(\mathrm{K}_2 \mathrm{SO}_4\) was added into I, II, III and IV respectively. The efficiency of precipitations in these beakers follows the orderAP EAMCET 2025 Medium
- The number of 5 card combinations out of a deck of 52 cards if there is exactly one are in each combination isAP EAMCET 2022 Medium