Published by:
CGP EDU Academic Team
Published on: August 13, 2026
For any positive integer 
, let 
be defined by 
where any 
and 
. Then which of the following statements is (are) TRUE ? (JEE Advanced 2021)
A
, for all 
B
, for all 
C
The equation 
has a root in 
has a root in D
, for all 
and 
Text Solution
Verified by ExpertsThe correct answer is:
B
(a, b)
So, is true.
So, is true.
This equation has non-real roots.
So, option is not true.
Now, consider 
, for all 
and 
.
, for all 
and 
Now, 
and vertex has abscissa 
.
Hence, both the roots are positive.
So, 
for some values of 
.
So, is false.
──────────────────────────────────────────────────────────────────────────────────────────
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
The value of is (JEE Advanced 2013)
If and , where the inverse trigonometric functions take only the principal values, then the corre…
For any positive integer , define as for all . (Here, the inverse trigonometric function assu…
For non-negative integer , let Assuming takes values in which of the following options is/are c…
Match the statements in List I with those in List II. (IIT-JEE 2010)
List IList II(A) A line from t…
The number of real solutions of the equation lying in the interval is . (Here, the inverse trigo…