Complex Numbers Quiz-17

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. If the roots of the equation 1/(x+p)+1/(x+q) = 1/r are equal in magnitude but opposite in sign, then the product of the roots will be
•   (p2+q2)/2
•  -((p2+q2))/2
•   (p2-q2)/2
•  -((p2-q2))/2
Solution

Q2. If Î± and Î² are different complex numbers with |Î²|=1, then |(Î²-Î±)/( ̅Î±Î²)| is
•  0
•  3/2
•  1/2
•  1
Solution

Q3. If Ï‰ is a complex cube root of unity, then the value of sin⁡{(Ï‰10+Ï‰23)Ï€-Ï€/6} is
•  1/√2
•  √3/2
•  -1/√2
•  1/2
Solution

Q4. If x=3+i, then x3-3x2-8x+15 is equal to
•   45
•  -15
•   10
•   6
Solution

Q5. If cos⁡Î±+2 cos⁡Î²+3 cos⁡ Î³=sin⁡Î±+2 sin⁡Î²+3 sin⁡Î³=0 and Î±+Î²+Î³=n Ï€, then sin⁡3 Î± +
8 sin⁡3 Î² + 27 sin⁡ 3Î³ =
•   0
•   3
•   8
•  -18
Solution

Q6. If Ï‰ = (-1+√3i)/2, then (3 + Ï‰ + 3Ï‰2)4 is
•   16
•  -16
•   16Ï‰
•   16Ï‰2
Solution

Q7. For any complex number z, the minimum value of |z|+|z-2i|, is
•  0
•  1
•  2
•  4
Solution

Q8. If |z1| = |z2| = |z3| and z1+z2+z3=0, then z1,z2,z3 are vertices of
•  A right angled triangle
•  An equilateral triangle
•  Isosceles triangle
•  Scalene triangle
Solution

Q9. Consider the following statements: 1. If the quadratic equation is ax^2+bx+c=0 such that a + b + c = 0, then roots of the equation ax2+ bx+c=0 will be 1, c/a. 2. If ax2+bx+c=0 is quadratic equation such that a - b + c = 0, then roots of the equation will be, -1,c/a. Which of the statements given above are correct?
•  Only (1)
•  Only (2)
•  Both (1) and (2)
•  Neither (1) nor (2)
Solution
Q10. The number which exceeds its positive square roots by 12, is
•  9
•  16
•  25
• None of these
Solution

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Complex Numbers Quiz-17