Register

TIFR Mathematics 2022 | Part A | Question: 15

• edited by
189 views
1 votes
1 votes

Let $S$ be the set of nonnegative continuous functions $f$ on $[0,1]$ satisfying
\[ \int_{0}^{1} \sin ^{2}(x) f(x) d x=\int_{0}^{1} \sin (x) \cos (x) f(x) d x=\int_{0}^{1} \cos ^{2}(x) f(x) d x=1 . \]
Then $S$ is:

  1. an uncountable set
  2. a countably infinite set
  3. a finite and nonempty set
  4. the empty set
• edited by
User Avatar

Please log in or register to answer this question.

Voting & Accepting an answer helps improve the community
Answer:
← PreviousNext →
← Previous in categoryNext in category →

Related questions

1 votes
1 votes
0 answers
1
admin asked Sep 9, 2022
259 views
TIFR Mathematics 2022 | Part B | Question: 15
Answer whether the following statements are True or False. There exists $f \in C([0,1], \mathbb{R})$ satisfying the following two conditions: $\displaystyle{}\int_{0}^{1} f(x) d x=1;$ and $\displaystyle{}\lim _{n \rightarrow \infty} \int_{0}^{1} f(x)^{n} d x=0$.
Answer whether the following statements are True or False.There exists $f \in C([0,1], \mathbb{R})$ satisfying the following two conditions:$\displaystyle{}\int_{0}^{1} f...
User Avatar
1 votes
1 votes
0 answers
4
admin asked Sep 9, 2022
188 views
TIFR Mathematics 2022 | Part A | Question: 3
What is the number of solutions of: \[ x=\frac{x^{2}}{50}-\cos \frac{x}{2}+2 \] in $[0,10]?$ $0$ $1$ $2$ $\infty$
What is the number of solutions of: \[ x=\frac{x^{2}}{50}-\cos \frac{x}{2}+2 \] in $[0,10]?$ $0$$1$$2$$\infty$
User Avatar
Link Copied!