Q81.If f(x) and g(x) are two polynomials such that the polynomial P(x) = f(x3) + xg(x3) is divisible by x2 + x + 1, then P(1) is equal to ___ .
What This Question Tests
This question tests the knowledge of cube roots of unity and their properties, specifically how they relate to the divisibility of a polynomial by x^2 + x + 1.
Concepts Tested
Formulas Used
ω^3 = 1
1 + ω + ω^2 = 0
P(x) is divisible by (x-a) if P(a)=0
📚 NCERT Sections This Tests
1.18 — A Point Charge Of 2.0 Mc Is At The Centre Of A Cubic Gaussian
Physics Class 11 · Chapter 1
1.18 A point charge of 2.0 mC is at the centre of a cubic Gaussian surface 9.0 cm on edge. What is the net electric flux through the surface?
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.
1.19 — A Point Charge Causes An Electric Flux Of –1.0 × 103 Nm2/C To Pass
Physics Class 11 · Chapter 1
1.19 A point charge causes an electric flux of –1.0 × 103 Nm2/C to pass through a spherical Gaussian surface of 10.0 cm radius centred on the charge. (a) If the radius of the Gaussian surface were doubled, how much flux would pass through the surface? (b) What is the value of the point charge?
📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Polynomials and Roots of Unity
- Year
- 2021
- Shift
- 18 Mar Shift 2
- Q Number
- Q81
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
More from this Chapter
Q84.If |z + 4| ≤3 , then the maximum value of |z + 1| is (1) 4 (2) 10 (3) 6 (4) 0
Q73.The conjugate of a complex number is 1 . Then the complex number is i−1 (1) −1 (2) 1 i−1 i+1 (3) −1 (4) 1 i+1 i−1
Q62.If z −4z = 2, then the maximum value of |z| is equal to (1) √3 + 1 (2) √5 + 1 (3) 2 (4) 2 + √2
Q61.If α and β are the roots of the equation x2 −x + 1 = 0, then α2009 + β2009 = (1) −1 (2) 1 (3) 2 (4) −2