AP EAMCET · Maths · Continuity and Differentiability
The function \(y=\sin ^{-1}(\cos x)\) is not differentiable at ____
- A \(\pi\) only
- B \(2 \pi\) only
- C \(-2 \pi\) only
- D All options are correct
Answer & Solution
Correct Answer
(D) All options are correct
Step-by-step Solution
Detailed explanation
Domain for \(\sin ^{-1} x\) is, \(x \in(-1,1)\) both values -1 and 1 are excluded Now, \(\cos \pi=-1\) and \(\cos 2 \pi=1\) Also, \(\cos -2 \pi=1\) Hence, \(\sin ^{-1}(\cos x)\) is non differentiable at \(\pi, 2 \pi\) and \(-2 \pi\).
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
- \(\int \frac{\sec ^2 x}{(\sec x+\tan x)^{5 / 2}} d x=\)AP EAMCET 2025 Medium
- A box contains 6 bottles of \(\mathrm{V}_1\) drink, 3 bottles of \(\mathrm{V}_2\) drink and 4 bottles of \(\mathrm{V}_3\) drink. If three bottles are drawn at random, then the probability that the three are not of the same variety isAP EAMCET 2022 Easy
- The area (in sq. units) of the triangle formed by the straight line and the angular bisectors of the pair of straight lines isAP EAMCET 2018 Medium
- The angle between the lines whose direction cosines are \(\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2}\right)\) and \(\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{-\sqrt{3}}{2}\right)\), isAP EAMCET 2008 Easy
- If two lines are parallel to each other, then which of the following is true? (if \(\left(l_1, m_1, n_1\right)\) and \(\left(l_2, m_2, n_2\right)\) are direction cosines of the two lines).AP EAMCET 2020 Medium
- If the mean of a data is and if all the observations are multiplied by , then the mean of new data isAP EAMCET 2021 Easy
More PYQs from AP EAMCET
- A compound absorbs light in the wavelength region \(490-500 \mathrm{~nm}\). Its complementary colour isAP EAMCET 2013 Easy
- Which of the following represents a parabola?AP EAMCET 2022 Easy
- If \(\mathbf{a}\) is a vector of magnitude \(7, \mathbf{b}\) is a vector of magnitude 8 , then the maximum value of \(\mathbf|{a} \cdot \mathbf{b}|\) isAP EAMCET 2021 Easy
- Identify the correct statements from the following
(i) Petrol and CNG operated automobiles cause less pollution
(ii) Alkanes having tertiary hydrogen can be oxidised to alcohols by \(\mathrm{KMnO}_4\)
(iii) Methane can be prepared by Kolbe's electrolytic method.
(iv) Alkyl chloride on reduction with zinc and dilute hydrochloric acid gives alkaneAP EAMCET 2018 Medium - A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the determinant chosen is non-zero is .........AP EAMCET 2020 Easy
- Difference between the corresponding roots of is same and
, then AP EAMCET 2022 Easy