Mathematics
Grade10
Easy

Question

Statement 1: Let n be some integer greater than 1, then floor fraction numerator left parenthesis straight n space minus space 1 right parenthesis over denominator straight n end fraction is 1.
Statement 2: Let n be some integer greater than 1, then ceiling fraction numerator left parenthesis straight n space minus space 1 right parenthesis over denominator straight n end fraction is 1.

  1. Only statement 1 is correct
  2. Only statement 2 is correct 
  3. Both statements 1 & 2 are correct 
  4. Both statements 1 & 2 are not correct

Hint:

The ceil function returns the smallest integer value which is greater than or equal to the specified number, whereas the floor function returns the largest integer value which is less than or equal to the specified number. 

The correct answer is: Only statement 2 is correct


    We have to find which of the two given statements are true.
    Since fraction numerator left parenthesis straight n space minus space 1 right parenthesis over denominator straight n end fraction will always be less than one, thus, floor fraction numerator left parenthesis straight n space minus space 1 right parenthesis over denominator straight n end fraction is 0.
    Since  fraction numerator left parenthesis straight n space minus space 1 right parenthesis over denominator straight n end fraction will always be less than one, thus, ceiling fraction numerator left parenthesis straight n space minus space 1 right parenthesis over denominator straight n end fraction is 1.
    Hence, the correct option is A.

    The ceiling function is also known as the smallest integer function. The floor function is the greatest integer function.

    Related Questions to study

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.