Question:medium

The ceiling function of a real number \( x \), denoted by \( ce(x) \), is defined as the smallest integer that is greater than or equal to \( x \). Similarly, the floor function, denoted by \( fl(x) \), is defined as the largest integer that is smaller than or equal to \( x \). Which one of the following statements is NOT correct for all possible values of \( x \)?

Show Hint

Remember that the ceiling function always rounds up, while the floor function always rounds down. So, for non-integer values, \( fl(x) \) will always be less than \( ce(x) \).

Updated On: Nov 25, 2025

\( ce(x) \geq x \)
\( fl(x) \leq x \)
\( ce(x) \geq fl(x) \)
\( fl(x)<ce(x) \)

Questions Asked in GATE AR exam

Which one of the following options has the correct sequence of objects arranged in the increasing number of mirror lines (lines of symmetry)?

View Solution

The given figure is reflected about the horizontal dashed line and then rotated clockwise by 90° about an axis perpendicular to the plane of the figure.
Which one of the following options correctly shows the resultant figure?
Note: The figures shown are representative

View Solution

If HIDE and CAGE are coded as 19-23-7-11 and 5-2-17-11 respectively, then what is the code for HIGH?

View Solution

Identify the option that has the most appropriate sequence such that a coherent paragraph is formed:
Statement:
P. At once, without thinking much, people rushed towards the city in hordes with the sole aim of grabbing as much gold as they could.
Q. However, little did they realize about the impending hardships they would have to face on their way to the city: miles of mud, unfriendly forests, hungry beasts, and inimical local lords—all of which would reduce their chances of getting gold to almost zero.
R. All of them thought that easily they could lay their hands on gold and become wealthy overnight.
S. About a hundred years ago, the news that gold had been discovered in Kolar spread like wildfire and the whole State was in raptures.

View Solution