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What Are The Fundamental Units

The fundamental units are the base units defined by International System of Units. These units are not derived from any other unit, therefore... View Article

Is Fe2o3 A Covalent Or Ionic Bond

Iron oxide or ferric oxide has three oxygen atoms and two iron atoms. It is represented by Fe2O3. The oxidation state of iron oxide is +3 and +2.... View Article

1 I By 1 Plus I Is Equal To

Solution: (1-i)/(1+i) = (1-i)(1-i)/(1+i)(1-i) = (1-2i-1)/2 = -i = cos π/2 - i sin π/2 Hence option (2) is the answer.... View Article

Root 8 6i Equals

(1) 1±3i (2) ±(1-3i) (3) ±(1+3i) (4) ±(3-i) Solution: Let x+iy be the square root. x+iy = √(-8-6i) Squaring both sides (x+iy)2 =... View Article

If Z I Log2 Root 3 Then Cos Z Is Equal To

Solution: Let cos z = (eiz+e-iz)/2 cos z = (e-log (2-√3)+elog (2-√3))/2 cos z = [(1/(2-√3))+(2-√3)]/2 = (2+√3+2-√3)/2 = 2 Hence... View Article

If Z 4 Less Than Or Equal To 3 Then The Greatest And Least Value

Solution: |z+4| ≤ 3 |z+1| = |z+4+-3| = |(z+4)+(-3)| ≤ |(z+4)+|(-3)| ≤ 3+3 ≤ 6 Greatest value is 6. |z+4| ≤ 3 => -3 ≤ z+1 ≤ 3 -6 ≤... View Article

If The Complex Numbers Z1 Z2 Z3 Represent The Vertices Of An Equilateral Triangle Such That Z1 Z2 Z3 Then Z1 Z2 Z3 Equal

Solution: Let z1,z2,z3 denote the vertices A,B,C of an equilateral triangle ABC. If O is the origin, OA = z1, OB = z2, OC = z3 |z1| =|z2|... View Article

Let 1 Ix By 1 Ix A Ib And A B2 1 Where A And B Are Real Then X Equal To

Solution: Given (1-ix)/(1+ix) = (a-ib) Multiply numerator and denominator with (1-ix) (1-ix)(1+ix)/(1+ix)(1-ix) = (1-2xi-x2)/(1+x2) =... View Article

If Alpha Not Equal 1 Is Any Nth Root Of Unity Then S Equal 1 N Terms Equals

Solution: Given S = 1+3α+5α2 ..n Tr = (2r-1)αr-1 S = S = 2S1-S2 … (i) (denote the terms of the above equation by S1 and S2 S1 =... View Article

Common Roots Of The Equations Z 3 2z 2 2z 1 Are

Solution: Given z3+2z2+2z+1 = 0 ..(i) (i) can be written as (z+1)(z2+z+1) = 0 Roots are z = -1 or ω, ω2 Also given z1985+z100+1 = 0... View Article

The Value Of Sigma K 1 To 6 Sin 2 Pi K

Solution: (sin 2πk/7 - i cos 2πk/7) = -i( cos 2πk/7 + i sin 2πk/7) = -ie2πk/7 = -i( sum of roots of equation x6+x5+x4+x3+x2+1 = 0) =... View Article

The Complex Numbers Z1 Z2 And Z3 Satisfying The Vertices Of A Triangle Which Is

Solution: Given (z1-z3)/(z2-z3) = (1-i√3)/2 (z2-z3)/(z1-z3) = (1+i√3)/2 (z2-z3)/(z1-z3) = cos π/3 + i sin π/3 |(z2-z3)/(z1-z3) | = 1 arg... View Article

Let Z Equal X Iy Be A Complex Number Whose X Y Are Integers

Solution: Given Put z = x+iy (x+iy)(x-iy)((x-iy)2+(x+iy)2 )= 350 (x2+y2)(2x2-2y2) = 350 (x2+y2)(x2-y2) = 175 = 25(7) x2+y2 = 25... View Article

For Complex Numbers Z1 Z2 If Z1 Eq 12 And Z2 3 Then Minimum Value Is

Solution: Given |z1| = 12 and |z2-3-4i| = 5 |z1-z2| ≥|z1| -|z2| |z2-3-4i| ≥ |z2| -|3+4i| |z2-3-4i| ≥ |z2| -√(32+42) |z2| ≥ 10 Minimum... View Article

If Xn Cos Pi By 2n Then X1 X2 X3 Infinity Equal

Solution: xn = cos (π/2n )+ i sin (π/2n) eiθ = cos θ+i sin θ Here θ = π/2n x1 = cos (π/2 )+ i sin (π/2) = ei(π/2) Similarly x2 =... View Article

Let Z Equal Cos Theta I Sin Theta Then The Value Of Sigma N 1 To 15

Solution: Given z = cos θ + i sin θ = eiθ = sin θ+ sin 3θ+sin 5θ+.....+sin 29θ = sin ((θ+29θ)/2 )sin ((15×2θ)/2 )/ sin (2θ)/2 = sin... View Article

If X 1 X Equal Root 3 Then X Equals

Solution: x +1/x = √3 x2+1 = √3x x2 -√3x+1 = 0 Roots = √3±√(3-4)/2 = (√3±√1)/2 = (√3±i)/2 (√3+i)/2 = cos π/6 + i sin π/6 Hence option... View Article

04 Dec 2020: The Hindu Analysis

UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 4th December 2020. Important news and views to... View Article

UPSC 2020: Weekly GK and Current Affairs Quiz Dec 05 – Dec 11

UPSC 2020: Weekly GK and Current Affairs Quiz Dec 05 - Dec 11 with Multiple Choice Questions and answers for IAS Exam Preparation other... View Article

04 Dec 2020: UPSC Exam Comprehensive News Analysis

04 Dec 2020 CNA:- Download PDF Here TABLE OF CONTENTS A. GS 1 Related B. GS 2 Related HEALTH 1. ‘Indian vaccines after phase 3 trials’... View Article

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