De Moivre's Theorem MCQ Quiz in தமிழ் - Objective Question with Answer for De Moivre's Theorem - இலவச PDF ஐப் பதிவிறக்கவும்

Last updated on Mar 11, 2025

பெறு De Moivre's Theorem பதில்கள் மற்றும் விரிவான தீர்வுகளுடன் கூடிய பல தேர்வு கேள்விகள் (MCQ வினாடிவினா). இவற்றை இலவசமாகப் பதிவிறக்கவும் De Moivre's Theorem MCQ வினாடி வினா Pdf மற்றும் வங்கி, SSC, ரயில்வே, UPSC, மாநில PSC போன்ற உங்களின் வரவிருக்கும் தேர்வுகளுக்குத் தயாராகுங்கள்.

Latest De Moivre's Theorem MCQ Objective Questions

Top De Moivre's Theorem MCQ Objective Questions

De Moivre's Theorem Question 1:

If  are respectively the least positive and greatest negative integer values of  such that  then 

  1. 4
  2. 0
  3. 6
  4. 2

Answer (Detailed Solution Below)

Option 1 : 4

De Moivre's Theorem Question 1 Detailed Solution

Calculation

Using De Moivre's Theorem:

Comparing with -i, we have:

This implies:

⇒ 

⇒ 

⇒ 

⇒ 

For the least positive integer value of k, let n = 0:

Let n = 1:

Let n = 2:

So, m = 3.

For the greatest negative integer value of k, we can analyze the values of k for negative n.

For n = -1:

So, n = -1.

Hence option 1 is correct

De Moivre's Theorem Question 2:

For z ∈ , if (1 + z)n = 1 + nc1z + nc2z2 + .... ncnzn and , then k =

  1. 25
  2. 100
  3. 50
  4. 75

Answer (Detailed Solution Below)

Option 3 : 50

De Moivre's Theorem Question 2 Detailed Solution

Concept:

Euler's theorem:

e = cosθ + isinθ 

De Moivre's Theorem:

(cosθ + isinθ)ncos(nθ) + isin(nθ) 

Calculation:

Given, 

Putting z = eir, we get:

...(i)

Now 

, where Img(z) represents the imaginary part of z

 =  (given)

Comparing both sides we get, k = 50

∴ The value of k is 50.

De Moivre's Theorem Question 3:

If z = e and  =  

then  =

  1. 0
  2. 1
  3. 2
  4. 3

Answer (Detailed Solution Below)

Option 2 : 1

De Moivre's Theorem Question 3 Detailed Solution

Concept:

  • If  then by componendo and dividendo rule  

Calculation:

Given z = e and   = 

⇒    = 

We know that if  then 

⇒  = 

⇒  =   [e = cos θ + i sin θ ]

⇒  =  

We know zr = eirθ and in the R.H.S the value of r are 2, 3 and 5

∴ a0 + b0 = a1 + b1 = a4 + b4 = a6 + b6 = a7 + b7 = a8 + b8 = a9 + b9 = a10 + b10 = 0

∴ a2 + b2 = 2 and a3 + b3 = 3 and a5 + b5 = 5 .

⇒  = 1

Required value of the expression is 1

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