QUADRATIC-EQUATION-QUIZ-2

MATHEMATICS QUADRATIC EQUATION QUIZ-2

Dear Readers,

As per analysis for previous years, it has been observed that students preparing for JEE MAINS find Mathematics out of all the sections to be complex to handle and the majority of them are not able to comprehend the reason behind it. This problem arises especially because these aspirants appearing for the examination are more inclined to have a keen interest in Mathematics due to their ENGINEERING background. 

Furthermore, sections such as Mathematics are dominantly based on theories, laws, numerical in comparison to a section of Engineering which is more of fact-based, Physics, and includes substantial explanations. By using the table given below, you easily and directly access to the topics and respective links of MCQs. Moreover, to make learning smooth and efficient, all the questions come with their supportive solutions to make utilization of time even more productive. Students will be covered for all their studies as the topics are available from basics to even the most advanced. 

Q1. 

•  1
•  4
•  2+√3
•  5

Solution

Q2.Let z₁ and z₂ be the roots of the equation z²+pz+q=0 where p,q are real. The points represented by z₁,z₂ and the origin form an equilateral triangle, if

•  p²=3q
•  p²>3q
•  p² < 3q
•  p²=2q

Solution

Q3.  A point P which represents a complex number z moves such that |z-z₁ |=|z-z₂ |, then its locus is
        (i) Refletion about the line y=x
        (ii) Translation through a distance of 2 unit along the positive direction of x-axis
        (iii) Rotation through an angle of π/4 about the origin in the anti-clockwise direction
        The final position of the point is

•  A circle with centre z₁
•  A circle with centre z₂
•  A circle with centre z
•  Perpendicular bisector of line joining z₁ and z₂

Solution
Given, |z-z₁ |=|z-z₂ | It is perpendicular bisector of line joining z₁ and z₂

Q4. 

•  An ellipse
•  A straight line
•  A circle
•  A parabola

Solution

Q5.Let z₁ and z₂ be complex numbers, then |z₁+z₂ |²+|z₁-z₂ |² is equal to

•  |z₁ |²+|z₂ |²
•  2(|z₁ |²+|z₂ |²)
•  2(z₁²+z₂ ²)
•  4z₁ z₂

Solution

Q6. 

•  p and q respectively
•  r and t respectively
•  r and q respectively
•  q and p respectively

Solution

Q7.

•  α=1 and β=-1
•  α=1 and β=-2
•  α=2 and β=1
•  α=2 and β=-2

Solution

Q8.

•  z₃+i(z₁+z₃ )
•  z₃ - i(z₁ - z₃ )
•  z₃ + i(z₁ - z₃ )
•  None of these

Solution

Q9.

•  x²+y²+6x-8y=0
•  4x-3y+24=0
•  x²+y²-8=0
•  None of these

Solution

Q10. If a,b,c are real numbers in G.P. such that a and c are positive, then the roots of the equation ax²+bx+c=0

•  Are real and are in ratio b∶ac
•  Are real
•  Are imaginary and are in ratio 1∶ω, where ω is a complex cube root of unity
•  Are imaginary and are in ratio -1∶ω

Solution