Quadratic_equation_Quiz-20

Quadratic equation Quiz-20

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 curve represented by Im(z²)=k, where k is a non-zero real number, is

•  A pair of straight lines
•  An ellipse
•  A parabola
•  A hyperbola

Solution

Q2. 

•  A straight line
  
•  A Circle
  
•  A parabola
  
•  An ellipse
  

Solution

Q3.The real root of the equation x³-6x+9=0 is

•  -6
•  -9
•   6
•  -3

Solution

Q4. Let z₁,z₂ be two complex numbers such that z₁+z₂ and z₁z₂ both are real, then

•  z₁= -z₂
• 
  
• 
•  z₁ = z₂

Solution

Q5.  

•  (0,3]
  
•  [-1,0)
  
•  (-1,0) U (0,3)
•  None of these

Solution

Q6.

•  2π/5
  
•  π/15
•  π/10
•  π/5

Solution

Q7.

•  < 0
  
•  > 0
•  ≤ 0
•  None of these

Solution 7

Q8. If α,β are the roots of x²+bx-c=0, then the equation whose roots are b and c is

• x²+ax-β=0
• x²-x(α+β+αβ)-α β(α+β)=0
  
•  x²+(α+β-αβ)x-αβ(α+β)=0
  
•  x²+(α+β+αβ)x+αβ(α+β)=0

Solution 

Q9. The number of values of a for which (a²-3a+2)x²+(a²-5a+6)x+a²-4=0 is an identity in x, is

•  0
•  1
•  2
•  3

Solution 

Q10. Given that ‘a’ is a fixed complex number, and λ′ is a scalar variable, the point z satisfying z=a(1+iλ) traces out

•  A straight line through the point ′a′
•  A circle with centre at the point ′a′
•  A straight line through the point ′a′ and perpendicular to the join 0 and that point ′a′
•  None of these

Solution

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QUESTIONS }, "encodingFormat": "text/markdown", "suggestedAnswer": [ //HERE PUT THE WRONG ANSWERS/OPTIONS { "@type": "Answer", "position": 2,//OPTION POSITION 0,1,2,3 "encodingFormat": "text/markdown", "text": " $$> 0$$",//ADD THE ANSWER "comment": { "@type": "Comment", "text": "This is a hint" //COMMENT FOR ANSWER } }, { "@type": "Answer", "position": 1, "encodingFormat": "text/markdown", "text": " $$ ≤ 0$$", //ADD THE ANSWER "comment": { "@type": "Comment", "text": "This is a hint"//COMMENT FOR ANSWER } }, { "@type": "Answer", "position": 3, "encodingFormat": "text/markdown", "text": "$$None of these$$ ",//ADD THE ANSWER "comment": { "@type": "Comment", "text": "This is a hint"//ADD COMMENT FOR ANSWER } } ], "acceptedAnswer": { //HERE PUT THE CORRECT ANSWER "@type": "Answer", "position": 0, "encodingFormat": "text/markdown", "text": "$$<0$$ ",//ADD THE ANSWER BETWEEN "comment": { "@type": "Comment", "text": "This is a hint"//ADD COMMENT FOR ANSWER } } }, { "@type": "Question", "eduQuestionType": "Multiple choice", //Question type "learningResourceType": "Practice problem", "name": "Average velocity from graphs",//ADD QUESTION NAME "text": " If α,β are the roots of x2+bx-c=0, then the equation whose roots are b and c is ",//ADD THE QUESTION TEXT "comment": { "@type": "Comment", "Text": "This is a hint of question"//ADD HINT FOR QUESTIONS }, "encodingFormat": "text/markdown", "suggestedAnswer": [ //HERE PUT THE WRONG ANSWERS/OPTIONS { "@type": "Answer", "position": 0,//OPTION POSITION 0,1,2,3 "encodingFormat": "text/markdown", "text": " $$x2+ax-β=0$$",//ADD THE ANSWER "comment": { "@type": "Comment", "text": "This is a hint" //COMMENT FOR ANSWER } }, { "@type": "Answer", "position": 1, "encodingFormat": "text/markdown", "text": " $$x2-x(α+β+αβ)-α β(α+β)=0$$", //ADD THE ANSWER "comment": { "@type": "Comment", "text": "This is a hint"//COMMENT FOR ANSWER } }, { "@type": "Answer", "position": 2, "encodingFormat": "text/markdown", "text": "$$ x2+(α+β-αβ)x-αβ(α+β)=0$$ ",//ADD THE ANSWER "comment": { "@type": "Comment", "text": "This is a hint"//ADD COMMENT FOR ANSWER } } ], "acceptedAnswer": { //HERE PUT THE CORRECT ANSWER "@type": "Answer", "position": 3, "encodingFormat": "text/markdown", "text:"$$x2+(α+β+αβ)x+αβ(α+β)=0$$ ",//ADD THE ANSWER BETWEEN “ “ "comment": { "@type": "Comment", "text": "This is a hint"//ADD COMMENT FOR ANSWER } } }, { "@type": "Question", "eduQuestionType": "Multiple choice", //Question type "learningResourceType": "Practice problem", "name": "graphical representation of the equation",//ADD QUESTION NAME "text": " The number of values of a for which (a2-3a+2)x2+(a2-5a+6)x+a2-4=0 is an identity in x, is ?",//ADD THE QUESTION TEXT "comment": { "@type": "Comment", "Text": "This is a hint of question"//ADD HINT FOR QUESTIONS }, "encodingFormat": "text/markdown", "suggestedAnswer": [ //HERE PUT THE WRONG ANSWERS/OPTIONS { "@type": "Answer", "position": 0,//OPTION POSITION 0,1,2,3 "encodingFormat": "text/markdown", "text": " $$ 0$$ ",//ADD THE ANSWER "comment": { "@type": "Comment", "text": "This is a hint" //COMMENT FOR ANSWER } }, { "@type": "Answer", "position": 1, "encodingFormat": "text/markdown", "text": " $$ 1$$", //ADD THE ANSWER "comment": { "@type": "Comment", "text": "This is a hint"//COMMENT FOR ANSWER } }, { "@type": "Answer", "position": 2, "encodingFormat": "text/markdown", "text": " $$ 3$$",//ADD THE ANSWER "comment": { "@type": "Comment", "text": "This is a hint"//ADD COMMENT FOR ANSWER } } ], "acceptedAnswer": { //HERE PUT THE CORRECT ANSWER "@type": "Answer", "position": 3, "encodingFormat": "text/markdown", "text": " $$2$$",//ADD THE ANSWER BETWEEN “ “ "comment": { "@type": "Comment", "text": "This is a hint"//ADD COMMENT FOR ANSWER } } }, { "@type": "Question", "eduQuestionType": "Multiple choice", //Question type "learningResourceType": "Practice problem", "name": "graphical representation of the equation",//ADD QUESTION NAME "text": " Given that ‘a’ is a fixed complex number, and λ′ is a scalar variable, the point z satisfying z=a(1+iλ) traces out ?",//ADD THE QUESTION TEXT "comment": { "@type": "Comment", "Text": "This is a hint of question"//ADD HINT FOR QUESTIONS }, "encodingFormat": "text/markdown", "suggestedAnswer": [ //HERE PUT THE WRONG ANSWERS/OPTIONS { "@type": "Answer", "position": 0,//OPTION POSITION 0,1,2,3 "encodingFormat": "text/markdown", "text": " $$ A straight line through the point ′a′$$",//ADD THE ANSWER "comment": { "@type": "Comment", "text": "This is a hint" //COMMENT FOR ANSWER } }, { "@type": "Answer", "position": 1, "encodingFormat": "text/markdown", "text": " $$ A circle with centre at the point ′a′$$", //ADD THE ANSWER "comment": { "@type": "Comment", "text": "This is a hint"//COMMENT FOR ANSWER } }, { "@type": "Answer", "position": 2, "encodingFormat": "text/markdown", "text": " $$ A straight line through the point ′a′ and perpendicular to the join 0 and that point ′a′$$",//ADD THE ANSWER "comment": { "@type": "Comment", "text": "This is a hint"//ADD COMMENT FOR ANSWER } } ], "acceptedAnswer": { //HERE PUT THE CORRECT ANSWER "@type": "Answer", "position": 3, "encodingFormat": "text/markdown", "text": " $$ None of these$$,",//ADD THE ANSWER BETWEEN “ “ "comment": { "@type": "Comment", "text": "This is a hint"//ADD COMMENT FOR ANSWER } } },