Q63.The value of ∑𝑟=22 0 22𝐶𝑟· 23𝐶𝑟 is (1) 45𝐶23 (2) 44𝐶23 (3) 45𝐶24 (4) 44𝐶22
What This Question Tests
The problem requires using De Moivre's theorem to simplify a complex number raised to a power, then equating real and imaginary parts to find p and q, and finally forming a quadratic equation from the given roots.
Concepts Tested
Formulas Used
(cosθ + i sinθ)ⁿ = cos(nθ) + i sin(nθ)
x² - (sum of roots)x + (product of roots) = 0
📚 NCERT Sections This Tests
5.23 — Give The Oxidation State, D Orbital Occupation And Coordination Number Of
Chemistry Class 11 · Chapter 5
5.23 Give the oxidation state, d orbital occupation and coordination number of the central metal ion in the following complexes: (i) K3[Co(C2O4)3] (iii) (NH4)2[CoF4] (ii) cis-[CrCl2(en)2]Cl (iv) [Mn(H2O)6]SO4
2.2 — A Regular Hexagon Of Side 10 Cm Has A Charge 5 Mc At Each Of Its
Physics Class 11 · Chapter 2
2.2 A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.
3.23 — The Rate Constant For The Decomposition Of Hydrocarbons Is 2.418 × 10–5S–1
Chemistry Class 11 · Chapter 3
3.23 The rate constant for the decomposition of hydrocarbons is 2.418 × 10–5s–1 at 546 K. If the energy of activation is 179.9 kJ/mol, what will be the value of pre-exponential factor.
📋 Question Details
- Chapter
- Complex Numbers
- Topic
- De Moivre's Theorem
- Year
- 2023
- Shift
- 24 Jan Shift 1
- Q Number
- Q63
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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