Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE MainMathematicsTrigonometric Equations

The number of real solutions of the equation | x| = 1 - x 4 in the interval [0, 4 ] is

Options

  1. A7
  2. B4
  3. C9
  4. D8

Correct answer

D. 8

Step-by-step solution

The given equation is | x| = 1 - x 4 . Let f(x) = | x| and g(x) = 1 - x 4 . We need to find the number of points of intersection of these two graphs in the interval [0, 4 ] . The graph of f(x) = | x| consists of 4 positive arches of a sine wave in the interval [0, 4 ] , each of width and maximum height 1 . The graph of g(x) = 1 - x 4 is a straight line passing through (0, 1) and (4 , 0) . Let us analyze the intersections in each interval of length : 1. In [0, ] : g(x) decreases from 1 to 0.75 . The maximum of f(x)

Practice Trigonometric Equations on Quantrex Academy →

More from Trigonometric Equations

Match each entry in List-I to the correct entry in List-II and choose the correct option. List-I List-II (P) The number of elements in the set x [- , ] : ^6 x + ^4 x = 1 (1) is 1 ( 2026Passage: Consider the curve C₁ given by y = e^ -x for x [0, 10 ] , and the curve C₂ given by y = e^ -x ( x + x) for x [0, 10 ] . Let n be the total number of points of intersection 2026Let S = (-2 , 2 ) : + 1 = 3 . Then _ S is equal to: 2026If S = [- , ] : 5 2 = 7 7 2 , then n(S) is equal to _______. 2026Let S = x [- , ] : x ( x + x) = a, a Z . Then n(S) is equal to : 2026The number of elements in the set x [0,180^ ]: (x+100^ )= (x+50^ ) x (x-50^ ) is _ _ _ _ . 2026Number of solutions of 3 2 +8 +3 3 =0, [-3 , 2 ] is: 2026The number of solutions of the equation 2 2 + 5 2 =2 ^3 5 2 in [- 2 , 2 ] is : 2025 Full Trigonometric Equations list All JEE Main PYQs