Q80.Let S be the set of all points in (−π, π) at which the function, f(x) = min{sin x, cos x} is not differentiable. Then S is a subset of which of the following? (1) {−3π4 , −π2 , π2 , 3π4 } (2) {−3π4 , −π4 , 3π4 , π4 } (3) {−π4 , 0, π4 } (4) {−π2 , −π4 , π4 , π2 }
What This Question Tests
This question assesses understanding of differentiability, particularly for functions defined as the minimum of two other functions. The points of non-differentiability occur where the two functions are equal and their derivatives are different.
Concepts Tested
Formulas Used
f(x) = min{g(x), h(x)} is not differentiable where g(x) = h(x) and g'(x) != h'(x)
📚 NCERT Sections This Tests
9.15 — Apply Mirror Equation And The Condition:
Physics Class 12 · Chapter 9
9.15 Apply mirror equation and the condition: (a) f < 0 (concave mirror); u < 0 (object on left) (b) f > 0; u < 0 (c) f > 0 (convex mirror) and u < 0 (d) f < 0 (concave mirror); f < u < 0 to deduce the desired result.
9.17 — (A) Sin I¢C = 1.44/1.68 Which Gives I¢C = 59°. Total Internal Reflection
Physics Class 12 · Chapter 9
9.17 (a) sin i¢c = 1.44/1.68 which gives i¢c = 59°. Total internal reflection takes place when i > 59° or when r < rmax = 31°. Now, (sin i /sin r max max ) = 1.68 , which gives imax ~ 60°. Thus, all incident rays of angles in the range 0 < i < 60° will suffer total internal reflections in the pipe. (If the length of the pipe is finite, which it is in practice, there will be a lower limit on i determined by the ratio of the diameter to the length of the pipe.) (b) If there is no outer coating, i¢c = sin–1(1/1.68) = 36.5°. Now, i = 90° will have r = 36.5° and i¢ = 53.5° which is greater than i¢c. Thus, all incident rays (in the range 53.5° < i < 90°) will suffer total internal reflections.
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Differentiability of functions
- Year
- 2019
- Shift
- 12 Jan Shift 1
- Q Number
- Q80
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 5: Continuity and Differentiability
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