Question
Let f: R R be a function defined by f(x)= \ array cc x^2 ( x^2 ), & if x 0 \\ 0, & if x=0 array . Then which of the following statements is TRUE?
JEE Advanced
Mathematics
Trigonometric Equations
2024
JEE Advanced 2024 (Paper 2)
JEE Advanced Mathematics Question (2024) — Solution
Options
- A. f(x)=0 has infinitely many solutions in the interval [ 1 10^ 10 , ).
- B. f(x)=0 has no solutions in the interval [ 1 , ).
- C. The set of solutions of f(x)=0 in the interval (0, 1 10^ 10 ) is finite
- D. f(x)=0 has more than 25 solutions in the interval ( 1 ^2 , 1 ).
Answer
D. f(x)=0 has more than 25 solutions in the interval ( 1 ^2 , 1 ).
Step-by-step solution
Option-1 : f ( x )= x ^2 x ^2 f(x)=0 x^2 =0 x^2 =n , n N x ^2= 1 n x = 1 n 1 n 1 10^ 10 10^ 10 n n 10^ 20 , finite number of solutions Option-2 : x = 1 n 1 n > 1 > n n 10^ 10 n >10^ 20 , Infinite number of solutions Option-4 : 1 ^2 < 1 n < 1 n ( , ^2 ) n ( ^2, ^4 ), Definitely more than 25 solutions
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