Q56.In the expansion of ( cosx θ + x sin1 θ )16, if l1 is the least value of the term independent of 8 ≤θ ≤π4 and l2 is the least value of the term independent of x when 16π ≤θ ≤π8 , then the ratio l2 : l1 is equal to: (1) 1 : 8 (2) 16 : 1 (3) 8 : 1 (4) 1 : 16
What This Question Tests
This question combines the binomial theorem to find the term independent of x with trigonometric minimization techniques, requiring careful calculation and range analysis.
Concepts Tested
Formulas Used
T_(r+1) = nCr * (a)^(n-r) * (b)^r
sin(2θ) = 2sinθcosθ
📚 NCERT Sections This Tests
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.
3.16 — The Rate Constant For A First Order Reaction Is 60 S–1. How Much Time Will
Chemistry Class 11 · Chapter 3
3.16 The rate constant for a first order reaction is 60 s–1. How much time will it take to reduce the initial concentration of the reactant to its 1/16th value?
📋 Question Details
- Chapter
- Binomial Theorem
- Topic
- General term, Term independent of x
- Year
- 2020
- Shift
- 09 Jan Shift 2
- Q Number
- Q56
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 8: Binomial Theorem
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