jee_main_2024_01_february_morning - Limits, Continuity and Differentiability Topics

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QUESTION #15 Continuity and Differentiability of Piecewise Functions
Let f:Rarrow R be defined as f(x)= cases(a-b 2x)/(x²) & , & x<0 x²+cx+2 & , & 0≤ x≤1 2x+1 & , & x>1 cases If f is continuous everywhere in R and m is the number of points where f is NOT differentiable, then m+a+b+c equals:
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QUESTION #25 One Sided Limits
Let {x} denote the fractional part of x and f(x)= ⁻¹(1-x²) ⁻¹(1-x)x-x³, x≠0. If L and R respectively denotes the left hand limit and the right hand limit of f(x) at x=0 then 32π²(L²+R²) is equal to
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JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%) | JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%)

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