Daily Practice Problems
JEE Maths
Complex Numbers and Quadratic Equations
JEE Maths
Complex Numbers and Quadratic Equations
Question1:
If 
respectively denote the moduli of the complex numbers 
and 
, then their increasing order is [Level: Easy]
(a)
(b) 
(c) 
(d) 
.
Question2:
Let 
and 
be two complex numbers with 
and 
as their principal arguments such that 
, then principal 
is given by [Level: Moderate]
(a) 
(b) 
(c) 
(d) 
.
Question3:
If 
are odd integers, then the roots of the equation 
are [Level: Easy]
(a) rational
(b) irrational
(c) non-real
(d) none of these.
Question4:
The product of all values of 
is [Level: Difficult]
(a) 
(b) 
(c) 
(d) 
.
Question5:
If the roots of the equation 
are equal, then 
are in [Level: Moderate]
(a) H.P.
(b) G.P.
(c) 
(d) none of these.
Question6:
In the argand plane, the complex number 
is turned in the clockwise sense through 
and stretched three times. The complex number represented by the new number is [Level: Moderate]
(a) 
(b) 
(c) 
(d) 
.
Question7:
The number of real solutions of the equation 
is [Level: Difficult]
(a) zero
(b) one
(c) two
(d) more than two.
Question8:
Let 
, 
be the roots of 
, then the equation whose roots are
, is [Level: Difficult]
(a) 
(b) 
(c)
(d) 
.
Question9:
The set of all real values of 
for which 
, is [Level: Easy]
(a) 
(b)
(c)
(d) none of these.
Question10:
Let 
is an imaginary cube root of unity. The value of 
is [Level: Easy]
(a) 
(b) 
(c) 
(d) 
.
Question11:
If 
is an imaginary cube root of unity, then 
equals [Level: Moderate]
(a) 
(b) 
(c)
(d) 
Question12.
The roots of 
are always [Level: Moderate]
(a) equal
(b) imaginary
(d) real and equal.
Question13.
The number of integral solutions of 
, is [Level: Moderate]
(a) 3
(b) 4
(c) 6
(d) none of these.
Question14.
If 
and 
are two complex numbers such that 
, then [Level: Moderate]
(a) 
(b) 
(c) 
(d) none of these.
Question15.
Number of positive integers for which 
is a prime number is __________. [Level: Difficult]
Question16.
The number of real roots of the equation 
is __________. [Level: Moderate]
Question17.
If 
and 
, then equals __________. [Level: Difficult]
Question18.
If the roots of the equation 
be two consecutive integers, then 
is equal to__________. [Level: Moderate]
Question19.
If 
is a complex number such that 
and 
where 
, then 
equal to__________. [Level: Difficult]
Question20.
Let 
where 
is non zero real and 
. If the imaginary part of 
and 
are equal, then 
is __________. [Level: Moderate]
Question21.
If 
and the equation 
has rational roots, then 
is of the form [Level: Difficult]
(a) 
(b) 
(c) 
(d) none of these.
Question22.
If 
and 
are the roots of the equation 
and 
respectively and system of equations 
and 
has a non-zero solution, then [Level: Difficult]
(a) 
(b) 
(c) 
(d) none of these.
Question23.
The locus of 
satisying the inequality 
where 
, is [Level: Moderate]
(a) 
(b) 
(c) 
(d) 
.
Question24.
If 
, then the value of is [Level: Moderate]
(a) 
(b) 
(c) 
(d) 
.
Question25.
The roots of 
are equal, then the value of 
is [Level: Easy]
(a) 
(b) 
(c) 
(d) 
.
Question26.
The number of solutions of the system of equations 
is [Level: Easy]
(a) 4
(b) 3
(c) 2
(d) 1.
Question27.
The greatest negative integer satisfying 
and 
, is [Level: Moderate]
(a) 
(b) 
(c) 
(d) none of these.
Question28.
If is a cube root of unit and is not real, then 
has the value [Level: Easy]
(a) 
(b) 
(c) 
(d) 3.
Question29.
If the complex numbers 
form the vertices of equilateral triangle ( are real numbers between 0 and 1), then [Level: Moderate]
(a) 
(b) 
(c) 
(d) none of these.
Question30.
If the product of the roots of the equation 
is 2, then the sum of roots is [Level: Moderate]
(a) 1
(b)
(c) 2
(d) 
.
**********
Problem-solving on JEE Maths Complex Numbers and Quadratic Equations NCERT Chapter 5 after learning a theoretical concept is crucial for several reasons:
- Application of Knowledge: Problem-solving allows you to apply the theoretical concepts of the topic JEE Maths Complex Numbers and Quadratic Equations you have learned to real-life situations. It helps you bridge the gap between abstract knowledge and practical scenarios, making the learning more relevant and meaningful.
- Understanding Deeper Concepts: When you encounter problems related to a theoretical concept that you learned in JEE Maths Complex Numbers and Quadratic Equations NCERT Chapter 5, you are forced to delve deeper into its intricacies. This deeper understanding enhances your comprehension of the subject and strengthens your grasp of the underlying principles.
- Critical Thinking: Problem-solving encourages critical thinking and analytical skills. It requires you to analyze the problem, identify relevant information, and devise a logical solution. This process sharpens your mind and improves your ability to approach complex challenges effectively.
- Retention and Recall: Actively engaging in problem-solving reinforces your memory and improves long-term retention. Applying the concepts learned in Complex Numbers and Quadratic Equations JEE Maths in practical scenarios helps you remember them better than passive reading or memorization.
- Identifying Knowledge Gaps: When you attempt to solve problems, you may encounter areas where your understanding is lacking. These knowledge gaps become evident during problem-solving, and you can then focus on filling those gaps through further study and practice. You can refer Complex Numbers and Quadratic Equations JEE Maths Notes on LearnoHub.com
- Boosting Confidence: Successfully solving problems after learning a theoretical concept boosts your confidence in your abilities to handle Complex Numbers and Quadratic Equations. This confidence motivates you to tackle more challenging tasks and improves your overall performance in the subject.
- Preparation for Exams and Challenges: Many exams, especially in science, mathematics, and engineering, involve problem-solving tasks. Regular practice in problem-solving prepares you to face these exams with confidence and perform well. It is also advised to take tests on Complex Numbers and Quadratic Equations JEE Maths Online Tests at LearnoHub.com.
- Enhancing Creativity: Problem-solving often requires thinking outside the box and exploring various approaches. This fosters creativity and innovation, enabling you to come up with novel solutions to different problems.
- Life Skills Development: Problem-solving is a valuable life skill that extends beyond academics. It equips you with the ability to tackle various challenges you may encounter in personal and professional life.
- Improving Decision Making: Problem-solving involves making decisions based on available information and logical reasoning. Practicing problem-solving enhances your decision-making skills, making you more effective in making informed choices.
In summary, problem-solving after learning a theoretical concept on CBSE Complex Numbers and Quadratic Equations JEE Maths is an essential part of the learning process. It enhances your understanding, critical thinking abilities, and retention of knowledge. Moreover, it equips you with valuable skills that are applicable in academic, personal, and professional contexts.
You must have heard of the phrase “Practice makes a man perfect”. Well, not just a man, practice indeed enhances perfection of every individual.
Practicing questions plays a pivotal role in achieving excellence in exams. Just as the adage goes, "Practice makes perfect," dedicating time to solve a diverse range of exam-related questions yields manifold benefits. Firstly, practicing questions allows students to familiarize themselves with the exam format and types of problems they might encounter. This familiarity instills confidence, reducing anxiety and improving performance on the actual exam day. Secondly, continuous practice sharpens problem-solving skills and enhances critical thinking, enabling students to approach complex problems with clarity and efficiency. Thirdly, it aids in identifying weak areas, allowing students to focus their efforts on improving specific topics. Moreover, practice aids in memory retention, as active engagement with the material reinforces learning. Regular practice also hones time management skills, ensuring that students can allocate appropriate time to each question during the exam. Overall, practicing questions not only boosts exam performance but also instills a deeper understanding of the subject matter, fostering a holistic and effective learning experience.
All About Daily Practice Problems on JEE Maths Complex Numbers and Quadratic Equations NCERT Chapter 5
Our Daily Practice Problems (DPPs) offer a diverse range of question types, including Multiple Choice Questions (MCQs) as well as short and long answer types. These questions are categorized into Easy, Moderate, and Difficult levels, allowing students to gradually progress and challenge themselves accordingly. Additionally, comprehensive solutions are provided for each question, available for download in PDF format - Download pdf solutions as well as Download pdf Questions. This approach fosters a holistic learning experience, catering to different learning styles, promoting self-assessment, and improving problem-solving skills. With our well-structured DPPs, students can excel in exams while gaining a deeper understanding of the subject matter. Hope you found the content on JEE Maths Complex Numbers and Quadratic Equations NCERT Chapter 5 useful.
Last but not least, to get the best hold on JEE Maths Complex Numbers and Quadratic Equations NCERT Chapter 5, do not forget to check out:
- Complex Numbers and Quadratic Equations JEE Maths Best videos
- Complex Numbers and Quadratic Equations JEE Maths NCERT Solutions
- JEE Maths Complex Numbers and Quadratic Equations Revision notes
- Complex Numbers and Quadratic Equations JEE Maths DPPs, Download PDF of solutions
- JEE Maths Complex Numbers and Quadratic Equations Online Tests
- JEE Maths Sample papers