Math Class 11 JEE NEET Study Material pdf

Complex Numbers MCQs | JEE Previous Year Questions(PYQs) | Download PDF

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Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations MCQs are provided here for students to help them in their preparation for the exams. The MCQs of Class 11 Maths Chapter 5 given here contain the right answers and explanations. These objective type questions cover all the concepts of the NCERT curriculum, which are important from the examination point of view.

Students can solve the MCQs provided here for Chapter 5 of Class 11 Maths to improve their skills in identifying complex numbers and solving quadratic equations, whose roots are complex numbers.

MCQs for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations with Answers

1. The value of 1 + i2 + i4 + i6 + … + i2n is

(a) positive

(b) negative

(c) 0

(d) cannot be evaluated

Correct option: (d) cannot be evaluated

Solution:

1 + i2 + i4 + i6 + … + i2n = 1 – 1 + 1 – 1 + … (–1)n

This cannot be evaluated unless the value of n is known.

2. If a + ib = c + id, then

(a) a2 + c2 = 0

(b) b2 + c2 = 0

(c) b2 + d2 = 0

(d) a2 + b2 = c2 + d2

Correct option: (d) a2 + b2 = c2 + d2

Solution:

Given,

a + ib = c + id

⇒ |a + ib| = |c + id|

⇒ √(a2 + b2) = √(c2 + d2)

Squaring on both sides, we get;

a2 + b2 = c2 + d2

3. If a complex number z lies in the interior or on the boundary of a circle of radius 3 units and centre (– 4, 0), the greatest value of |z +1| is

(a) 4

(b) 6

(c) 3

(d) 10

Correct option: (b) 6

Solution:

The distance of the point representing z from the centre of the circle is |z – (-4 + i0)| = |z + 4|

According to the given,

|z + 4| ≤ 3

Now,

|z + 1| = |z + 4 – 3| ≤ |z + 4| + |-3| ≤ 3 + 3 ≤ 6

Hence, the greatest value of |z + 1| is 6.

4. The value of arg (x) when x < 0 is

(a) 0

(b) π/2

(c) π

(d) none of these

Correct option: (c) π

Solution:

Let z = x + 0i and x < 0

Since the point (-x, 0) lies on the negative side of the real axis,

|z| = |x + oi| = √[(-1)2 + 0)] = 1

∴ Principal argument (z) = π

Alternative method:

Let x = cos θ + i sin θ

For θ = π, x should be negative.

Thus, x < 0 for θ = π.

5. If 1 – i, is a root of the equation x2 + ax + b = 0, where a, b ∈ R, then the value of a – b is

(a) -4

(b) 0

(c) 2

(d) 1

Correct option: (a) -4

Solution:

Given that 1 – i is the root of x2 + ax + b = 0.

Thus, 1 + i is also the root of the given equation since non-real complex roots occur in conjugate pairs.

Sum of roots = −a/1 = (1 – i) + (1 + i)

⇒ a = – 2

Product of roots, b/1 = (1 – i)(1 + i)

b = 1 – i2

b = 1 + 1 {since i2 = -1}

⇒ b = 2

Now, a – b = -2 – 2 = -4

6. Number of solutions of the equation z2 + |z|2 = 0 is

(a) 1

(b) 2

(c) 3

(d) infinitely many

Correct option: (d) infinitely many

Solution:

Given,

z2 + |z|2 = 0, z ≠ 0

⇒ (x + iy)2 + [√(x2 + y2)]2 = 0

⇒ x2 – y2 + i2xy + x2 + y2 = 0

⇒ 2x2 + i2xy = 0

⇒2x (x + iy) = 0

⇒ x = 0 or x + iy = 0 (not possible)

Therefore, x = 0 and z ≠ 0.

Thus, y can have any real value.

Hence, there exist infinitely many solutions.

7. If [(1 + i)/(1 – i)]x = 1, then

(a) x = 2n + 1, where n ∈ N

(b) x = 4n, where n ∈ N

(c) x = 2n, where n ∈ N

(d) x = 4n + 1, where n ∈ N

Correct option: (b) x = 4n, where n ∈ N

Solution:

Given,

[(1 + i)/(1 – i)]x = 1

By rationalising the denominator,

[(1 + i)(1 + i)/ (1 – i)(1 + i)]x = 1
[(1 + i)2/ (1 – i + i – i2)]x = 1
[(1 + i2 + 2i)/(1 + 1)]x = 1
[(1 – 1 + 2i)/ 2]x = 1

ix = 1

Thus, ix = i4n, where n is any positive integer.

8. If the complex number z = x + iy satisfies the condition |z + 1| = 1, then z lies on

(a) x-axis

(b) circle with centre (1, 0) and radius 1

(c) circle with centre (–1, 0) and radius 1

(d) y-axis

Correct option: (c) circle with centre (–1, 0) and radius 1

Solution:

Given,

z = x + iy

and

|z + 1| = 1

|x + iy + 1| = 1

⇒ |(x + 1) + iy| = 1

⇒ √[(x +1)2 + y2] = 1

Squaring on both sides,

(x + 1)2 + y2 = 1

This is the equation of a circle with centre (–1, 0) and radius 1.

9. The simplified value of (1 – i)3/(1 – i3) is

(a) 1

(b) -2

(c) -i

(d) 2i

Correct option: (b) -2

Solution:

(1 – i)3/(1 – i3)

= (1 – i)3/(13 – i3)

= (1 – i)3/ [(1 – i)(1 + i + i2)]

= (1 – i)2/(1 + i – 1)

= (1 – i)2/i

= (1 + i2 – 2i)/i

= (1 – 1 – 2i)/i

= -2i/i

= -2

10. sin x + i cos 2x and cos x – i sin 2x are conjugate to each other for:

(a) x = nπ

(b) x = [n + (1/2)] (π/2)

(c) x = 0

(d) No value of x

Correct option: (d) No value of x

Solution:

Consider sin x + i cos 2x and cos x – i sin 2x are conjugate to each other.

So, sin x – i cos 2x = cos x – i sin 2x

On comparing real and imaginary parts of both sides, we get

⇒ sin x = cos x and cos 2x = sin 2x

⇒ sin x/cos x = 1 and (cos 2x/sin 2x) = 1

⇒ tan x = 1 and tan 2x = 1

Now, consider tan 2x = 1

Using the formula tan 2A = 2 tan A/(1 – tan2A),

(2 tan x)/(1 – tan2x) = 1

However, this is not possible for tan x = 1.

Therefore, for no value of x, sinx + i cos 2x and cos x – i sin 2x are conjugate to each other

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Er. Neeraj K.Anand is a freelance mentor and writer who specializes in Engineering & Science subjects. Neeraj Anand received a B.Tech degree in Electronics and Communication Engineering from N.I.T Warangal & M.Tech Post Graduation from IETE, New Delhi. He has over 30 years of teaching experience and serves as the Head of Department of ANAND CLASSES. He concentrated all his energy and experiences in academics and subsequently grew up as one of the best mentors in the country for students aspiring for success in competitive examinations. In parallel, he started a Technical Publication "ANAND TECHNICAL PUBLISHERS" in 2002 and Educational Newspaper "NATIONAL EDUCATION NEWS" in 2014 at Jalandhar. Now he is a Director of leading publication "ANAND TECHNICAL PUBLISHERS", "ANAND CLASSES" and "NATIONAL EDUCATION NEWS". He has published more than hundred books in the field of Physics, Mathematics, Computers and Information Technology. Besides this he has written many books to help students prepare for IIT-JEE and AIPMT entrance exams. He is an executive member of the IEEE (Institute of Electrical & Electronics Engineers. USA) and honorary member of many Indian scientific societies such as Institution of Electronics & Telecommunication Engineers, Aeronautical Society of India, Bioinformatics Institute of India, Institution of Engineers. He has got award from American Biographical Institute Board of International Research in the year 2005.

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CBSE Class 11 Maths Syllabus for 2023-24 with Marking Scheme

CBSE syllabus for class 11 Maths is divided into 5 units. The table below shows the units, number of periods and marks allocated for maths subject. The maths theory paper is of 80 marks and the internal assessment is of 20 marks.

No.UnitsMarks
I.Sets and Functions23
II.Algebra25
III.Coordinate Geometry12
IV.Calculus08
V.Statistics and Probability12
Total Theory80
Internal Assessment20
Grand Total100

2025-26 CBSE Class 11 Maths Syllabus

Below you will find the CBSE Class Maths Syllabus for students.

Unit-I: Sets and Functions

1. Sets

Sets and their representations, empty sets, finite and infinite sets, equal sets, subsets, and subsets of a set of real numbers, especially intervals (with notations), universal set, Venn diagrams, union and intersection of sets, difference of sets, complement of a set and properties of complement.

2. Relations & Functions

Ordered pairs, Cartesian product of sets, number of elements in the Cartesian product of two finite sets, Cartesian product of the set of reals with itself (upto R x R x R), definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Function as a special type of relation. Pictorial representation of a function, domain, co-domain and range of a function. Real valued functions, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic and greatest integer functions, with their graphs. Sum, difference, product and quotients of functions.

3. Trigonometric Functions

Positive and negative angles, measuring angles in radians and in degrees and conversion from one measure to another, definition of trigonometric functions with the help of unit circle, truth of the identity, signs of trigonometric functions, domain and range of trigonometric functions and their graphs, expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple applications.

Unit-II: Algebra

1. Complex Numbers and Quadratic Equations

Need for complex numbers, especially√−1, to be motivated by the inability to solve some of the quadratic equations. Algebraic properties of complex numbers, Argand plane.

2. Linear Inequalities

Linear inequalities, algebraic solutions of linear inequalities in one variable and their representation on the number line.

3. Permutations and Combinations

The fundamental principle of counting. Factorial n. (n!) Permutations and combinations, derivation of Formulae for nPr and nCr and their connections, simple applications.

4. Binomial Theorem

Historical perspective, statement and proof of the binomial theorem for positive integral indices, Pascal’s triangle, simple applications.

5. Sequence and Series

Sequence and series, arithmetic progression (A. P.), arithmetic mean (A.M.),  geometric progression (G.P.), general term of a G.P., sum of n terms of a G.P., infinite G.P. and its sum, geometric mean (G.M.), relation between A.M. and G.M.

Unit-III: Coordinate Geometry

1. Straight Lines

Brief recall of two-dimensional geometry from earlier classes. Slope of a line and angle between two lines. Various forms of equations of a line: parallel to axis, point-slope form, slope-intercept form, two-point form, intercept form and normal form. General equation of a line. Distance of a point from a line.

2. Conic Sections

Sections of a cone: circles, ellipse, parabola, hyperbola, a point, a straight line and a pair of intersecting lines as a degenerated case of a conic section. Standard equations and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle.

3. Introduction to Three-Dimensional Geometry

Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points.

Unit-IV: Calculus

1. Limits and Derivatives

Derivative introduced as rate of change both as that of distance function and geometrically, intuitive idea of limit, limits of polynomials and rational functions trigonometric, exponential and logarithmic functions, definition of derivative relate it to the slope of the tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.

Unit-V: Statistics and Probability

1. Statistics

Measures of Dispersion: Range, mean deviation, variance and standard deviation of ungrouped/grouped data.

2. Probability

Events; occurrence of events, ‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, Axiomatic (set theoretic) probability, connections with other theories of earlier classes. Probability of an event, probability of ‘not’, ‘and’ and ‘or’ events.

Students can also get the syllabus of all the subjects by visiting CBSE Class 11 Syllabus page. Learn Maths & Science in an interactive & fun-loving way with Anand Classes App/Tablet.

Frequently Asked Questions on CBSE Class 11 Maths Syllabus 2025-26

Q1

What is the marks distribution for internals and theory exams according to the CBSE Maths Syllabus for Class 11?

The marks distribution for internals is 20 marks and the theory exam is 80 marks based on the CBSE Class 11 Maths Syllabus.

Q2

Which is the most important chapter in the CBSE Class 11 Maths Syllabus?

The important chapter in the CBSE Class 11 Maths Syllabus is Algebra which is for 25 marks in the overall weightage.

Q3

What are the chapters covered in Unit III of the CBSE Class 11 Maths Syllabus?

The chapters covered in Unit III of the CBSE Class 11 Maths Syllabus are straight lines, conic sections and an introduction to three-dimensional geometry.

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