Mathematics · 2024
JEE Main · 31 January 2024, Shift 2 · Q8
Consider the function f:(0, ∞) → R defined by f(x)=e^-| log_e x|. If m and n be respectively the number of points at which f is not continuous and f…
Consider the function $\displaystyle f:(0, \infty) \rightarrow \mathbb{R}$ defined by $\displaystyle f(x)=e^{-\left|\log _e x\right|}$. If $\displaystyle m$ and $\displaystyle n$ be respectively the number of points at which $\displaystyle f$ is not continuous and $\displaystyle f$ is not differentiable, then $\displaystyle m+n$ is
Official answer
From NTA’s final answer key for this paper.
(2)
$\displaystyle 1$
More from Continuity and Differentiability
- Let f(x)= {(1+a x)^1 / x, x<0; 1+b, x=0; ((x+4)^1 / 2-2)/((x+c)^1 / 3-2), x>0} be continuous at x=0. Then e^a b c is equal to:2025
- Let [x] denote the greatest integer function, and let m and n respectively be the numbers of the points, where the function f(x)=[x]+|x-2|,-2<x<3, is…2025
- If the function f(x)= {2/x{ sin (k_1+1) x+ sin (k_2-1) x}, x<0; 4, x=0; 2/x log_e((2+k_1 x)/(2+k_2 x)), x>0} is continuous at x=0, then k_1^2+k_2^2…2025
- If the function f(x)= {1/(|x|), |x| ≥ 2; a x^2+2 b, |x|<2} is differentiable on R, then 48(a+b) is equal to ____.2024
- Let f(x)= {3 x, x<0; min {1+x+[x], x+2[x]}, 0 ≤ x ≤ 2; 5, x>2,} where [.] denotes greatest integer function. If α and β are the number of points,…2025
- The number of points, at which the function f(x)= max {6 x, 2+3 x^2}+|x-1| cos |x^2-1/4|, x ∈(-π, π), is not differentiable, is ____.2026
- Let m and n be the number of points at which the function f(x)= max {x, x^3, x^5, …, x^21}, x ∈ R, is not differentiable and not continuous,…2025
- Let f: R → R be a function given by f(x)= {(1- cos 2 x)/x^2, x<0; α, x=0, (β √(1- cos x))/x, x>0} where α, β ∈ R. If f is continuous at x=0, then…2024
JEE Main 2024 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.