Quadratic_Equation_Quiz-11

Quadratic Equation Quiz-11

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. The quadratic equation whose roots are sin218° and cos236° is

•  16x² -12x +1=0
•  16x² +12x +1=0
•  16x² -12x -1=0
•  16x² +10x +1=0

Solution

Q2.Consider the following statements:
1. If the ratio of roots of the quadratic equation ax²+bx+c=0 be p:q, then pqb²=(p+q)²ac.
2. If the roots of ax²+bx+c=0 are α and β, then the roots of cx²+bx+a=0 will be................,β.
3. The roots of the equation ax²+bx+c=0 are reciprocal to a′ x²+b′ x+c′=0, if (cc′-aa′)²=(ba′-cb′)(ab′-bc′).
Which of the statements given above are correct?

•  (1) and (2)
•  (2) and (3)
•  (1) and (3)
•  All (1), (2) and (3)

Solution
(b)

Q3.  If z₁,z₂,z₃ are vertices of an equilateral triangle with z₀ its centroid, then z₁²+z₂²+z₃²=

•   z₀²
•  9z₀²
•  3z₀²
•  2z₀²

Solution

Q4. The roots of the cubic equation (z+αβ)³= α³, α ≠ 0

•  Represent sides of an equilateral triangle
•  Represent the sides of an isosceles triangle
•  Represent the sides of a triangle whose one side is of length √3a
  
•  None of these

Solution

Q5. If b and c are odd integers, then the equation x²+bx+c=0 has

•  Two odd roots
•  Two integer roots, one odd and one even
•  No integer roots
•  None of these

Solution
(c)
Since a quadratic equation with coefficients as odd integers cannot have rational roots. Therefore, the given equation has no rational root

Q6. The number of non-zero integer solutions of the equation |1 - i|^x =2^x is

•  Infinite
•  1
•  2
•  None of these

Solution

Q7. If the roots of the equation ax²+bx+c=0 be α and β , then the roots of the equation cx²+bx+a=0 are

•  -α, -β
•  α,1/β
  
•  1/α , 1/β 
  
•  None of these

Solution

Q8.

•  2/√21
•  1/√21
  
•  √3
  
•  √21
  

Solution

Q9. If c and d are roots of the equation (x-a)(x-b)-k=0, then a,b are roots of the equation

•  (x-c)(x-d) - k= 0
•  (x-c)(x-d) + k= 0
•  (x-a)(x-c) + k= 0
•  (x-b)(x-d) - k= 0

Solution

Q10. POQ is a straight line through the origin O. P and Q represent the complex numbers a+ib and c+id respectively and OP=OQ. Then which one of the following is not true?

•  | a+ib| = |c+id|
•  a+b=c+d
•  arg(a+ib)=arg(c+id)
• None of these

Solution