JEE Advanced2024MathematicsTrigonometric EquationsActual
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?
Options
- Af(x)=0 has infinitely many solutions in the interval [ 1 10¹⁰ , ) .
- Bf(x)=0 has no solutions in the interval [ 1 , ) .
- CThe set of solutions of f(x)=0 in the interval (0, 1 10¹⁰ ) is finite
- Df(x)=0 has more than 25 solutions in the interval ( 1 ^2 , 1 ) .
Correct 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 10¹⁰ 10¹⁰ n n 10²⁰ , finite number of solutions Option-2 : x = 1 n 1 n > 1 > n n 10¹⁰ n >10²⁰ , Infinite number of solutions Option-4 : 1 ^2 < 1 n < 1 n ( , ^2 ) n ( ^2, ^4 ) , Definitely more than 25 solutions