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Check the below NCERT MCQ Questions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations with Answers Pdf free download. They include both multiple-choice and student-produced response questions. Check the below NCERT MCQ Questions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations with Answers Pdf free download. i = - 1 1) A) True B) False Write the number as a product of a real number and i. Simplify the radical expression. � � : : N. � � � : : � : � : . 8 cis 45 Get Chapter Wise MCQ Questions for Class 11 Maths with Answers PDF Free Download prepared here according to the latest CBSE syllabus and NCERT curriculum. Answer: d Explaination: Reason: Total cards = 18 शिक्षण प्रक्रिया में शिक्षक को अनेक कार्य एक साथ करने पड़ते हैं जैसे लिखना, प्रश्न पूछना, स्पष्ट करना, प्रदर्शन करना आदि... शिक्षण कौशल ( Teaching Skill) EMBED Equation.3 a. EMBED Equation.3 b. EMBED Equation.3 c. EMBED Equation.3 d. EMBED Equation.3 6. Test your understanding of Complex numbers concepts with Study.com's quick multiple choice quizzes. All quizzes are paired with a … But first equality of complex numbers must be defined. If you send me questions using the forms in MCQ Sets d. Get the most authentic answers for your subjective questions 31. Complex Numbers MCQs Practice Sheet 1. EMBED Equation.3 34 5 7 -34 2. Find all complex numbers z such that z 2 = -1 + 2 sqrt(6) i. a. Probability Questions And Answers Pdf Question 11. Tags: ... How to Effectively Answer CBSE Board Examination Question Papers. � � s+ � � � �- : @ 0�v��� t ^ ?, . 1. Math 120 Final Review: Multiple Choice Version 1 Find the domain of the following functions: 1. a. b. c. d. Y, � ,2 � � ,2 4 �- ,2 � �- 8 : : � : : : : : 9. EMBED Equation.3 i -i 1 -1 Name the complex number represented on the complex plane: (3,2) 2 + 3i 3 + 2i 3 � 2i 0 1 2 3 E F Y Z [ \ a b u v w x y z � � � � � � � � � � � � � �����������Ÿ����������������qd���� j� h &� h &� EH��Uj�@yP Answer: (a) a circleHint:Let w = 2/zNow, |w| = |2/z|=> |w| = 2/|z|=> |w| = 2This shows that w lies on a circle with center at the origin and radius 2 units. bjbjLULU J .? . 9. This is termed the algebra of complex numbers. . These MCQ's are extremely critical for all CBSE students to score better marks. � �� �� �� � � � � � � � � � \$ � �. Complex Numbers Name_____ MULTIPLE CHOICE. The section contains questions on deMoivre’s theorem, trigonometric functions expansion, complex conjugates, complex plane regions, complex numbers logarithm, powers and roots. ��ࡱ� > �� ���� �������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� '` �� � questions first and the harder questions last within each group of multiple-choice questions and again within each group of student-produced response questions. Download JEE Mathematics Complex Numbers MCQs Set A in pdf, Complex Numbers chapter wise Multiple Choice Questions free. 2) - 9 2) A complex number is of the form i 2 =-1. C ell references but not values d. Value and cell references Q. EMBED Equation.3 8i -8i 6i -6i 9. � L � : : : : : : : . You can also have online access to Engineering Maths Multiple Choice Questions Answers EBook. Please note that, as on the actual test form, approximately one third of the multiple-choice questions in this test guide are more complex questions that require 2–3 minutes All Chapter-13 Exercise Questions with Solutions to help you to revise complete Syllabus and Score More marks. Answer: (d) a hyperbolaHint:Let z = x + iyNow, z² = (x + iy)²⇒ z² = x² – y² + 2xyGiven, Im(z²) = k⇒ 2xy = k⇒ xy = k/2 which is a hyperbola. &. If you searching to check on Complex Numbers Multiple Choice Pdf And Income Tax Multiple Choice Questions And Answers Pdf price. Question 1.The value of √(-16) is(a) -4i(b) 4i(c) -2i(d) 2i, Answer: (b) 4iHint:Given, √(-16) = √(16) × √(-1)= 4i {since i = √(-1) }, Question 2.The value of √(-144) is(a) 12i(b) -12i(c) ±12i(d) None of these, Answer: (a) 12iHint:Given, √(-144) = √{(-1) × 144}= √(-1) × √(144)= i × 12 {Since √(-1) = i}= 12iSo, √(-144) = 12i, Question 3:The value of √(-25) + 3√(-4) + 2√(-9) is(a) 13i(b) -13i(c) 17i(d) -17i, Answer: (c) 17iHint:Given, √(-25) + 3√(-4) + 2√(-9)= √{(-1) × (25)} + 3√{(-1) × 4} + 2√{(-1) × 9}= √(-1) × √(25) + 3{√(-1) × √4} + 2{√(-1) × √9}= 5i + 3×2i + 2×3i {since √(-1) = i}= 5i + 6i + 6i= 17iSo, √(-25) + 3√(-4) + 2√(-9) = 17i, Question 4.if z lies on |z| = 1, then 2/z lies on(a) a circle(b) an ellipse(c) a straight line(d) a parabola. If points corresponding to the complex numbers z 1, z 2 and z 3 in the Argand plane are A,B and C respectively and if D ABC is isosceles, and right angled at B then a possible value of is (a) 1 (b) 1 (c) i (d) None of these. Engineering Maths Multiple Choice questions Answers can help in interview preparation. Title: Complex Numbers Quiz 2 Author: cmitchell Last modified by: cmitchell Created Date: 11/1/2010 8:29:00 PM Company: mvusd Other titles: . (3i)(2i) 6i -6i 6 -6 8. Further assume that the origin, z1 and z1 form an equilateral triangle. 3 - (-2+3i) + (-5+i) = ? Provide an appropriate response. Where can you find best quality multiple choice questions? � : . 3 + 2i. Question 12.The value of x and y if (3y – 2) + i(7 – 2x) = 0(a) x = 7/2, y = 2/3(b) x = 2/7, y = 2/3(c) x = 7/2, y = 3/2(d) x = 2/7, y = 3/2, Answer: (a) x = 7/2, y = 2/3Hint:Given, (3y – 2) + i(7 – 2x) = 0Compare real and imaginary part, we get3y – 2 = 0⇒ y = 2/3and 7 – 2x = 0⇒ x = 7/2So, the value of x = 7/2 and y = 2/3, Question 13.Find real θ such that (3 + 2i × sin θ)/(1 – 2i × sin θ) is imaginary(a) θ = nπ ± π/2 where n is an integer(b) θ = nπ ± π/3 where n is an integer(c) θ = nπ ± π/4 where n is an integer(d) None of these, Answer: (b) θ = nπ ± π/3 where n is an integerHint:Given,(3 + 2i × sin θ)/(1 – 2i × sin θ) = {(3 + 2i × sin θ)×(1 – 2i × sin θ)}/(1 – 4i² × sin² θ)(3 + 2i × sin θ)/(1 – 2i × sin θ) = {(3 – 4sin² θ) + 8i × sin θ}/(1 + 4sin² θ) …………. : : : : � � � d � � � � � � � � � � � � � ���� Complex Numbers Quiz 2 1. Choose your answers to the questions and click 'Next' to see the next set of questions. � : : : �. 3-√-2 a. EMBED Equation.3 45 27 9 + 36i -27 - 36i 5. The complex number 2 + 4i is one of the root to the quadratic equation x 2 + bx + c = 0, where b and c are real numbers. Engineering Maths Objective type Questions Answers are also used at SSC and HSc level for Exam preparation. 2 - 2i c. -2i d. 2i 2. Answer/ Explanation. 9+40i 11. ... Free JEE Mathematics Complex Numbers Online Mock Test with important multiple choice questions as per JEE syllabus. h &� CJ UVaJ j h &� UhH h &� # 4 5 8 : @ A ] ^ a y � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � h &� CJ UVaJ jH h &� h &� EH��Uj�@yP A complex number is usually denoted by the letter ‘z’. ‘a’ is called the real part, and ‘b’ is called the imaginary part of the complex number. Read and attempt to answer every question … You can skip questions if … The notion of complex numbers increased the solutions to a lot of problems. शिक्षण प्रक्रिया में शिक्षक को अनेक कार्य एक साथ करने पड़ते हैं जैसे लिखना, प्रश्न पूछना, स्पष्ट करना, प्रदर्शन करना... MCQ Questions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic... MCQ Questions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations with Answers, Click here to join our FB Page and FB Group for Latest update and preparation tips and queries, https://www.facebook.com/groups/tetsuccesskey/, Child Development and Pedagogy (English Medium), Teaching of Social Studies (English Medium), Teaching of Social Studies (Hindi Medium), सी टी ई टी नोट्स: बाल विकास एवं शिक्षाशास्त्र, सामान्य ज्ञान – General Knowledge In Hindi, MCQ Questions for Class 11 Maths Chapter 4 Principle of Mathematical Induction with Answers, Maths GK Questions With Answers for Competitive Exams -Part 1, Class 12 History Important Questions Chapter 3 Kinship, Caste and Class: Early Societies, CBSE Class 6 Mathematics Worksheets/ Part 5, CBSE Important Extra Questions for Class 12 Geography Chapter Wise, Lesson 113 – Parts of the Sentence – Review, दृष्टांत कौशल (Skill of Illustration with Examples), उद्दीपन परिवर्तन कौशल (Skill of Stimulus Variation), मानचित्र अध्ययन कौशल (Skill of Map Reading). 1Now, equation 1 is imaginary if3 – 4sin² θ = 0⇒ 4sin² θ = 3⇒ sin² θ = 3/4⇒ sin θ = ±√3/2⇒ θ = nπ ± π/3 where n is an integer, Question 14.If {(1 + i)/(1 – i)}n = 1 then the least value of n is(a) 1(b) 2(c) 3(d) 4, Answer: (d) 4Hint:Given, {(1 + i)/(1 – i)}n = 1⇒ [{(1 + i) × (1 + i)}/{(1 – i) × (1 + i)}]n = 1⇒ [{(1 + i)²}/{(1 – i²)}]n = 1⇒ [(1 + i² + 2i)/{1 – (-1)}]n = 1⇒ [(1 – 1 + 2i)/{1 + 1}]n = 1⇒ [2i/2]n = 1⇒ in = 1Now, in is 1 when n = 4So, the least value of n is 4, Question 15.If arg (z) < 0, then arg (-z) – arg (z) =(a) π(b) -π(c) -π/2(d) π/2, Answer: (a) πHint:Given, arg (z) < 0Now, arg (-z) – arg (z) = arg(-z/z)⇒ arg (-z) – arg (z) = arg(-1)⇒ arg (-z) – arg (z) = π {since sin π + i cos π = -1, So arg(-1) = π}, Question 16.if x + 1/x = 1 find the value of x2000 + 1/x2000 is(a) 0(b) 1(c) -1(d) None of these, Answer: (c) -1Hint:Given x + 1/x = 1⇒ (x² + 1) = x⇒ x² – x + 1 = 0⇒ x = {-(-1) ± √(1² – 4 × 1 × 1)}/(2 × 1)⇒ x = {1 ± √(1 – 4)}/2⇒ x = {1 ± √(-3)}/2⇒ x = {1 ± √(-1)×√3}/2⇒ x = {1 ± i√3}/2 {since i = √(-1)}⇒ x = -w, -w²Now, put x = -w, we getx2000 + 1/x2000 = (-w)2000 + 1/(-w)2000= w2000 + 1/w2000= w2000 + 1/w2000= {(w³)666 × w²} + 1/{(w³)666 × w²}= w² + 1/w² {since w³ = 1}= w² + w³ /w²= w² + w= -1 {since 1 + w + w² = 0}So, x2000 + 1/x2000 = -1, Question 17.The value of √(-144) is(a) 12i(b) -12i(c) ±12i(d) None of these, Answer: (a) 12iHint:Given, √(-144) = √{(-1)×144}= √(-1) × √(144)= i × 12 {Since √(-1) = i}= 12iSo, √(-144) = 12i, Question 18.If the cube roots of unity are 1, ω, ω², then the roots of the equation (x – 1)³ + 8 = 0 are(a) -1, -1 + 2ω, – 1 – 2ω²(b) – 1, -1, – 1(c) – 1, 1 – 2ω, 1 – 2ω²(d) – 1, 1 + 2ω, 1 + 2ω², Answer: (c) – 1, 1 – 2ω, 1 – 2ω²Hint:Note that since 1, ω, and ω² are the cube roots of unity (the three cube roots of 1), they are the three solutions to x³ = 1 (note: ω and ω² are the two complex solutions to this)If we let u = x – 1, then the equation becomesu³ + 8 = (u + 2)(u² – 2u + 4) = 0.So, the solutions occur when u = -2 (giving -2 = x – 1 ⇒ x = -1), or when:u² – 2u + 4 = 0,which has roots, by the Quadratic Formula, to be u = 1 ± i√3So, x – 1 = 1 ± i√3⇒ x = 2 ± i√3Now, x³ = 1 when x³ – 1 = (x – 1)(x² + x + 1) = 0, giving x = 1 andx² + x + 1 = 0⇒ x = (-1 ± i√3)/2If we let ω = (-1 – i√3)/2 and ω₂ = (-1 + i√3)/2then 1 – 2ω and 1 – 2ω² yield the two complex solutions to (x – 1)³ + 8 = 0So, the roots of (x – 1)³ + 8 are -1, 1 – 2ω, and 1 – 2ω², Question 19. Values but not cell references b. h &� CJ UVaJ j� h &� h &� EH��Uj�@yP 1. Then(a) a² = b(b) a² = 2b(c) a² = 3b(d) a² = 4b, Answer: (c) a² = 3bHint:Given, z1 and z2 be two roots of the equation z² + az + b = 0Now, z1 + z2 = -a and z1 × z2 = bSince z1 and z2 and z3 from an equilateral triangle.⇒ z12 + z22 + z32 = z1 × z2 + z2 × z3 + z1 × z3⇒ z12+ z22 = z1 × z2 {since z3 = 0}⇒ (z1 + z2)² – 2z1 × z2 = z1 × z2⇒ (z1 + z2)² = 2z1 × z2 + z1 × z2⇒ (z1 + z2)² = 3z1 × z2⇒ (-a)² = 3b⇒ a² = 3b, Question 10:The complex numbers sin x + i cos 2x are conjugate to each other for(a) x = nπ(b) x = 0(c) x = (n + 1/2) π(d) no value of x, Answer: (d) no value of xHint:Given complex number = sin x + i cos 2xConjugate of this number = sin x – i cos 2xNow, sin x + i cos 2x = sin x – i cos 2x⇒ sin x = cos x and sin 2x = cos 2x {comparing real and imaginary part}⇒ tan x = 1 and tan 2x = 1Now both of them are not possible for the same value of x.So, there exist no value of x, Question 11.The curve represented by Im(z²) = k, where k is a non-zero real number, is(a) a pair of striaght line(b) an ellipse(c) a parabola(d) a hyperbola. 10. Some 5 cis 36.87 b. Start below. We have provided Complex Numbers and Quadratic Equations Class 11 Maths MCQs Questions with Answers to help students understand the concept very well. Click here to join our FB Page and FB Group for Latest update and preparation tips and queries. addition, multiplication, division etc., need to be defined. d. 0 �. Students can practice CBSE Class 11 Maths MCQs Multiple Choice Questions with Answers to score good marks in the examination. If you have any queries regarding CBSE Class 11 Maths Complex Numbers and Quadratic Equations MCQs Multiple Choice Questions with Answers, drop a comment below and we will get back to you soon. Find the absolute value of complex numbers outlined in the quiz. . This is a multiple choice question (MCQ) quiz. .? . Absolute Value, Complex Numbers. A card is taken out from the bag at random. You will see that, in general, you proceed as in real numbers, but using i 2 =−1 where appropriate. Practice the multiple choice questions to test understanding of important topics in the chapters. Multiple Choice Questions. h &� CJ UVaJ j� h &� h &� EH��Uj�@yP 3+4i b. Perform the operations and write the result in standard form. 1) True or false? Having introduced a complex number, the ways in which they can be combined, i.e. Convert into polar form (cis form) a. Convert into rectangular form a. Cards bearing numbers 3 to 20 are placed in a bag and mixed thoroughly. 3 – 2i. Perform the operation and write the result in standard form. Questions on Complex Numbers . Free PDF download of RD Sharma Solutions for Class 11 Maths Chapter 13 - Complex Numbers solved by Expert Mathematics Teachers on Vedantu.com. शिक्षण प्रक्रिया में शिक्षक को अनेक कार्य एक साथ करने पड़ते हैं जैसे लिखना, प्रश्न पूछना, स्पष्ट करना, प्रदर्शन करना... शिक्षण कौशल ( Teaching Skill) Complex Numbers Chapter Exam Instructions. 2+2i b. � : : : : : 9. b. MCQ Questions for Class 11 Maths with Answers were prepared based on the latest exam pattern. Multiple choice questions on number system quiz answers PDF covers MCQ questions on topics: Properties of real numbers, rational numbers, irrational numbers, complex numbers, basic function, binary operation, De Moivre’s theorem, groups, linear and quadratic function, sets, operation on three sets, and relation. . We have provided Complex Numbers and Quadratic Equations Class 11 Maths MCQs Questions with Answers to help … If you have any queries regarding CBSE Class 11 Maths Complex Numbers and Quadratic Equations MCQs Multiple Choice Questions with Answers, drop a comment below and we will get back to you … Find the product of 4 + i and 4 � i 15 17 EMBED Equation.3 16 4. a) Find b and c b) Write down the second root and check it. Missed a question here and there? \$ J/ h �1 z 9. ... Then multiply the number by its complex conjugate. 1 -1 Name the complex number represented on the complex plane: (3,2) 2 + 3i. Question 5.If ω is an imaginary cube root of unity, then (1 + ω – ω²)7 equals(a) 128 ω(b) -128 ω(c) 128 ω²(d) -128 ω², Answer: (d) -128 ω²Hint:Given ω is an imaginary cube root of unity.So 1 + ω + ω² = 0 and ω³ = 1Now, (1 + ω – ω²)7 = (-ω² – ω²)7⇒ (1 + ω – ω2)7 = (-2ω2)7⇒ (1 + ω – ω2)7 = -128 ω14⇒ (1 + ω – ω2)7 = -128 ω12 × ω2⇒ (1 + ω – ω2)7 = -128 (ω3)4 ω2⇒ (1 + ω – ω2)7 = -128 ω2, Question 6.The least value of n for which {(1 + i)/(1 – i)}n is real, is(a) 1(b) 2(c) 3(d) 4, Answer: (b) 2Hint:Given, {(1 + i)/(1 – i)}n= [{(1 + i) × (1 + i)}/{(1 – i) × (1 + i)}]n= [{(1 + i)²}/{(1 – i²)}]n= [(1 + i² + 2i)/{1 – (-1)}]n= [(1 – 1 + 2i)/{1 + 1}]n= [2i/2]n= inNow, in is real when n = 2 {since i2 = -1 }So, the least value of n is 2, Question 7.Let z be a complex number such that |z| = 4 and arg(z) = 5π/6, then z =(a) -2√3 + 2i(b) 2√3 + 2i(c) 2√3 – 2i(d) -√3 + i, Answer: (a) -2√3 + 2iHint:Let z = r(cos θ + i × sin θ)Then r = 4 and θ = 5π/6So, z = 4(cos 5π/6 + i × sin 5π/6)⇒ z = 4(-√3/2 + i/2)⇒ z = -2√3 + 2i, Question 8:The value of i-999 is(a) 1(b) -1(c) i(d) -i, Answer: (c) iHint:Given, i-999= 1/i999= 1/(i996 × i³)= 1/{(i4)249 × i3}= 1/{1249 × i3} {since i4 = 1}= 1/i3= i4/i3 {since i4 = 1}= iSo, i-999 = i, Question 9.Let z1 and z2 be two roots of the equation z² + az + b = 0, z being complex. Multiple choice questions on number system quiz answers PDF covers MCQ questions on topics: Properties of real numbers, rational numbers, irrational numbers, complex numbers, basic function, binary operation, De Moivre’s theorem, groups, linear and quadratic function, sets, operation on three sets, and relation. Download MCQs for JEE Mathematics Complex Numbers, Get MCQs for Complex Numbers Mathematics for important topics for all chapters based on 2021 syllabus and pattern. The probability that the number on the card taken out is an even number, is. Multiple Choice Questions (MCQ) for CBSE Class 11-science Mathematics chapters on Topperlearning. To create a formula, you can use: a. It is reflects Algebra 2 (algebra ii) level exercises. Register for online coaching for IIT JEE (Mains & Advanced), NEET, Engineering and Medical entrance exams. शिक्षण प्रक्रिया में शिक्षक को अनेक कार्य एक साथ करने पड़ते हैं जैसे लिखना, प्रश्न पूछना, स्पष्ट करना, प्रदर्शन करना... शिक्षण कौशल ( Teaching Skill) h &� CJ UVaJ j h &� h &� EH��UjQ@yP We hope the given NCERT MCQ Questions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations with Answers Pdf free download will help you. 2. Don’t let the question position or question type deter you from answering questions. EMBED Equation.3 29 EMBED Equation.3 EMBED Equation.3 21 3. MCQ Questions for Class 11 Maths with Answers were prepared based on the latest exam pattern. Download latest questions with answers for Mathematics Complex Numbers in pdf free or … We hope the given NCERT MCQ Questions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations with Answers Pdf free download will help you. 9i(3i) 27i -27i 27 -27 7. Below is a set of multiple-choice questions and constructed-response questions that are similar to the questions you will see on Subtest I of CSET: Mathematics. Select the correct answer and submit. (1 – w + w²)×(1 – w² + w4)×(1 – w4 + w8) × …………… to 2n factors is equal to(a) 2n(b) 22n(c) 23n(d) 24n, Answer: (b) 22nHint:Given, (1 – w + w²)×(1 – w² + w4)×(1 – w4 + w8) × …………… to 2n factors= (1 – w + w2)×(1 – w2 + w )×(1 – w + w2) × …………… to 2n factors{Since w4 = w, w8 = w2}= (-2w) × (-2w²) × (-2w) × (-2w²)× …………… to 2n factors= (2² w³)×(2² w³)×(2² w³) …………… to 2n factors= (2²)n {since w³ = 1}= 22n, Question 20.The modulus of 5 + 4i is(a) 41(b) -41(c) √41(d) -√41, Answer: (c) √41Hint:Let Z = 5 + 4iNow modulus of Z is calculated as|Z| = √(5² + 4²)⇒ |Z| = √(25 + 16)⇒ |Z| = √41So, the modulus of 5 + 4i is √41. More.. Choose the one alternative that best completes the statement or answers the question. शिक्षण कौशल (Teaching Skill) . 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