Q62.Let A = {θ ∈(0, 2π) : 1+2i1−i sinsinθθ is purely imaginary} Then the sum of the elements is in A is (1) 4π (2) 3π (3) π (4) 2π
What This Question Tests
This question tests the understanding of complex number properties, specifically the condition for a complex number to be purely imaginary, and solving the resulting trigonometric equation.
Concepts Tested
Formulas Used
z = x + iy
If z is purely imaginary, x = 0
📚 NCERT Sections This Tests
5.12 — Write All The Geometrical Isomers Of [Pt(Nh3)(Br)(Cl)(Py)] And How Many Of
Chemistry Class 11 · Chapter 5
5.12 Write all the geometrical isomers of [Pt(NH3)(Br)(Cl)(py)] and how many of these will exhibit optical isomers?
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.
8.17 — Complete Each Synthesis By Giving Missing Starting Material, Reagent Or Products
Chemistry Class 12 · Chapter 8
8.17 Complete each synthesis by giving missing starting material, reagent or products
📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Purely imaginary complex numbers
- Year
- 2023
- Shift
- 08 Apr Shift 2
- Q Number
- Q62
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations; Class 11 Mathematics Ch 3: Trigonometric Functions
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