## Complex Numbers Quiz-15

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 one root of the equation x+ (l-3i)x-2(l+i)=0 is -l+i, then the other root is
•  -l-i
•  (-l-i)/2
•  i
•  2i
Solution

Q2. In the argand plane, if O, P and Q represent respectively the origin O and the complex numbers z and z + iz              respectively, then ∠OPQ is
•  Ï€/4
•  Ï€/3
•  Ï€/2
•  2Ï€/3
Solution

Q3. If z1,z2,z3,…,zn are n nth roots of unity, then for k = 1,2,…,n
•  |zk| = k|zn+1|
•  |zk+1| = k|zk|
•  |zk+1| = |zk|+|zk+1|
•  |zk| = |zk+1|
Solution

Q4. If both the roots of the equation ax2+bx+c=0 are zero, then
•  b = c = 0
•  b = 0, c ≠ 0
•  b ≠ 0, c = 0
•  b ≠ 0, c ≠ 0
Solution

Q5. If (x2-bx)/(ax-c)=(Î»-1)/(Î»+1) has roots equal in magnitude and opposite in sign then the value of Î» is
•  (a - b)/(a + b)
•  (a + b)/(a - b)
•  c
•  1/c
Solution

Q6. Let n=2006!. Then 1/log2 ⁡n + 1/log3⁡ n +...+ 1/log2006⁡ n is equal to
•  2006
•  2005
•  2005!
•  1
Solution

Q7. All the values of m for which both roots of the equation x2-2mx+m2-1=0 are greater than -2 but less than 4 lie
in the interval
•  m>3
•  -1
•   1
•  -2
Solution

Q8. If (5z2)/(11z1) is purely imaginary, then the value of |(2z1+3z2)/(2z1-3z2)| is
•  37/33
•  2
•  1
•  3
Solution

Q9. If f(x)=∑nk=2(x - 1/(k-1))(x - 1/k), then the product of roots of f(x)=0 as n→∞, is
•  -1
•  0
•  1
•  None of these
Solution

Q10. If Î±,Î² and Î³ are the roots of the equation x3-8x+8=0, then ∑Î±2 and ∑1/Î±Î² are respectively
•  0 and -16
•  16 and 18
• -16 and 0
•  16 and 0
• Solution

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