Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202319 May 2023Morning ShiftMathematicsContinuity and DifferentiabilityActual

Let [t] represents the greatest integer not exceeding t , Then the number of discontinuous points of [10^x ] in (0,10) is

Options

  1. A10¹⁰-1
  2. B10¹⁰
  3. C10¹⁰-2
  4. De ¹⁰

Correct answer

C. 10¹⁰-2

Step-by-step solution

(c) Given 0 < x < 10 1 < 10^x < 10¹⁰ Let 0 x 1 then [10^x ] will have to points of discontinuity But when 0 < x < 1 the [10 x] will have only (10^1-2 )=8 points of discontinuity because we are leaving point 0 & 1 . Similarly, when 0 < x < 10 then [10 x] will have (10¹⁰-2 ) points of discontinuity.

Practice Continuity and Differentiability on Quantrex Academy →

More from Continuity and Differentiability

The function f(x) = |x| + |x - 1| is: 2026If f(x) = cases 1+x - 1-x x , & x 0 k, & x = 0 cases is continuous at x = 0 , then k = 2026The function y = ||x| - 1| is differentiable for all values of ' x ' except 2026Let f : R R be the function given by f(x) = |x - 2| + 3|x - 1| + ||x - 2| - 1| . What is the number of points where f is NOT differentiable? 2026For real numbers a and b , consider the function f : R R given by f(x) = cases -ax - b & if x 1. cases How many pairs (a, b) are there for which f is continuous at every point of R 2026If f(x) = cases ax + 7 & if x 1 cases is continuous at x = 1 , then 2026If the function f(x) defined by f(x) = cases ax + 1 & if x 3 bx + 3 & if x > 3 cases is continuous at x = 3 , then (a - b) = .......... 2026Let [x] denotes the greatest integer less than or equal to x and f(x) = [ ^2 x] , then which of the following is true ? 2026 Full Continuity and Differentiability list All AP EAMCET PYQs