Consider sets 
and 
. Now, match the following lists.
List I | List II | ||
(A) | Number of elements in which have negative imaginary part is | (P) | 18 |
(B) | Number of elements in which have positive real part is | (Q) | 17 |
(C) | Number of elements in is | (R) | 13 |
(D) | If number of elements in is then is divisible by | (S) | 9 |
Codes:
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
We have 
.
The roots of the equation are 
, 
.
This equation has one real root ' 1 '. The other 26 roots are in the form of 13 conjugate pairs.
Of these, 13 roots lie above real-axis and the other 13 are lie below real axis.
So, there are 13 roots having negative imaginary part.
The other equation is 
.
This equation has two real roots, 
and two purely imaginary roots, 
.
Of remaining 32 roots, 16 lie to the right of imaginary axis.
So, there are 17 roots having positive real part.
The roots of the equation are 
, 
.
Number of common roots 
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems