Q68.The value of lim cos−1(x−[x]2)⋅sin−1(x−[x]2) , where [x] denotes the greatest integer ≤x is: x→0+ x−x3 (1) π (2) 0 (3) π (4) π 4 2
What This Question Tests
This question tests the understanding of limits involving the greatest integer function for x approaching 0 from the right, combined with standard limits for inverse trigonometric functions.
Concepts Tested
Formulas Used
lim_{x->0+} [x] = 0
lim_{u->0} sin^{-1}(u)/u = 1
lim_{u->0} cos^{-1}(u) = π/2
📚 NCERT Sections This Tests
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.
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.
1.27 — If The Solubility Product Of Cus Is 6 × 10–16, Calculate The Maximum Molarity Of
Chemistry Class 11 · Chapter 1
1.27 If the solubility product of CuS is 6 × 10–16, calculate the maximum molarity of CuS in aqueous solution.
📋 Question Details
- Chapter
- Limits & Continuity
- Topic
- Limits involving greatest integer function and inverse trigonometric functions
- Year
- 2021
- Shift
- 17 Mar Shift 1
- Q Number
- Q68
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 5: Continuity and Differentiability
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