Q52.If 3+isinθ , θ ∈[0 ,2 π], is a real number, then an argument of sinθ + icosθ is 4−icosθ (1) π −tan−1( 34 ) (2) π −tan−1( 43 ) (3) −tan−1( 43 ) (4) tan−1( 43 )
What This Question Tests
This question tests the understanding of properties of roots of a quadratic equation and the derivation and application of a recurrence relation for sums of powers of roots.
Concepts Tested
Formulas Used
α+β = -b/a
αβ = c/a
p_k = p_(k-1) + p_(k-2)
📚 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?
9.21 — At What Angle Should A Ray Of Light Be Incident On The Face Of A Prism
Physics Class 12 · Chapter 9
9.21 At what angle should a ray of light be incident on the face of a prism of refracting angle 60° so that it just suffers total internal reflection at the other face? The refractive index of the material of the prism is 1.524.
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.
📋 Question Details
- Chapter
- Quadratic Equations
- Topic
- Roots of quadratic equations
- Year
- 2020
- Shift
- 07 Jan Shift 2
- Q Number
- Q52
- Type
- MCQ
- NCERT Ref
- Class 10 Mathematics Ch 4: Quadratic Equations
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