## Complex Numbers Quiz-18

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 ecos⁡x -e-cos⁡x =4, then the value of cos ⁡x is
•  loge⁡ (2+√5)
•  -loge⁡(2+√5)
•  loge⁡(-2+√5)
•  None of these
Solution

Q2. If the sum of the squares of the roots of the equation x- (sin⁡Î±-2) x - (1+sin⁡Î±)=0 is least, then Î±=
•  Ï€/4
•  Ï€/3
•  Ï€/2
•  Ï€/6
Solution

Q3. Number of real roots of the equation (6 - x)4 + (8 - x)4 = 16 is
•  4
•  2
•  0
•  None of these
Solution

Q4. If x2+ax+10 = 0 and x2+bx-10 = 0 have a common root, then a2- b2 is equal to
•   10
•   20
•   30
•   40
Solution

Q5. If a and b are the non-zero distinct roots of x2+ax+b=0, then the least value of x2+ax+b is
•   2/3
•   9/4
•  -9/4
•   1
Solution

Q6. For a ≠ b, if the equation x2+ax+b=0 and x2+bx+a=0 have a common root, then the value of a+b equals
•  -1
•   0
•   1
•   2
Solution

Q7. The expression tan⁡{i log⁡((a-ib)/(a+ib))} reduces to
•  ab/(a2+b2)
•  (2 ab)/(a2-b2)
•  ab/(a2-b2)
•  (2 ab)/(a2+b2)
Solution

Q8. 72 log7⁡5 is equal to
•  log7⁡35
•  5
•  25
•  log7⁡25
Solution

Q9. The value of expression 2(1+Ï‰)(1+Ï‰2)+3(2+Ï‰)(2+Ï‰2)+4(3+Ï‰)(3+Ï‰2)+⋯+(n+1)(n+Ï‰)(n+Ï‰2), where Ï‰ is an imaginary cube root of unity is
•  {n(n+1)/2}2
•  {n(n+1)/2}2
•  {n(n+1)/2}2+n
•  None of these
Solution

Q10. If cos⁡Î±+2 cos⁡Î²+3 cos⁡Î³=sin⁡Î±+2 sin⁡Î²+3 sin⁡Î³=0, then the value of sin⁡3 Î±+8 sin⁡3 Î²+27 sin⁡3 Î³is
•  sin⁡(Î±+Î²+Î³)
•  3 sin⁡(Î±+Î²+Î³)
•  18 sin⁡(Î±+Î²+Î³)
•  sin⁡(Î±+2Î²+3Î³)
Solution

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