Q18. a + sinx x 1 b For some a, b, let f(x) = a 1 + sinx x b , x ≠0, limx→0 f(x) = λ + μa + νb. Then a 1 b + sinx x (λ + μ + ν)2 is equal to : (1) 16 (2) 25 (3) 9 (4) 36
What This Question Tests
This question involves evaluating a limit of a complex function using standard limit formulas or series expansions, and then calculating an expression based on the limit's components.
Concepts Tested
Formulas Used
lim (x->0) sin(x)/x = 1
Expansion of e^x or (1+x)^1/x
📚 NCERT Sections This Tests
9.18 — For Fixed Distance S Between Object And Screen, The Lens Equation
Physics Class 12 · Chapter 9
9.18 For fixed distance s between object and screen, the lens equation does not give a real solution for u or v if f is greater than s/4. Therefore, fmax = 0.75 m.
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 of Functions
- Year
- 2025
- Shift
- 24 Jan Shift 2
- Q Number
- Q18
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 5: Continuity and Differentiability
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