Question:medium

The function \( f(x) = [x]\cos\left( \frac{2x-1}{2}\pi \right) \), where \( [\,\cdot\,] \) denotes the greatest integer function, is discontinuous at

Show Hint

If a discontinuous function is multiplied by a non-zero continuous function, discontinuity remains.

Updated On: Apr 23, 2026

all \( x \)
no \( x \)
all integral points
\( x \) which is not an integer

Show Solution

The Correct Option is C

Solution and Explanation

Was this answer helpful?

0

Top Questions on Continuity

The function \(f(x) = x - |x - x^2|\), \(-1 \le x \le 1\) is continuous on
- BITSAT - 2017
- Mathematics
- Continuity
View Solution
Consider the following statements in respect of the function f(x)=x³-1, x∈[-1,1]: I. f(x) is continuous in [-1,1]. II. f(x) has no root in (-1,1). Which of the statements given above is/are correct?
- BITSAT - 2016
- Mathematics
- Continuity
View Solution
Let \[ f(x)= \begin{cases} \dfrac{1-\sin^3 x}{3\cos^2 x}, & x < \dfrac{\pi}{2} \\ [6pt] p, & x = \dfrac{\pi}{2} \\ [6pt] \dfrac{q(1-\sin x)}{(\pi-2x)^2}, & x > \dfrac{\pi}{2} \end{cases} \] If \(f(x)\) is continuous at \(x=\dfrac{\pi}{2}\), then \((p,q)=\)
- BITSAT - 2014
- Mathematics
- Continuity
View Solution
If the function \( f(x) = ax + b \), \( 2 < x < 4 \), is continuous at \( x = 2 \) and 4, then the values of \( a \) and \( b \) are:
- BITSAT - 2012
- Mathematics
- Continuity
View Solution
Want to practice more? Try solving extra ecology questions todayView All Questions

Questions Asked in MET exam

At great distances from an electric dipole, the electric field strength due to the dipole varies with the distance as

MET - 2018
Electrostatics

A charged particle travels along a straight line with a speed $\nu$ in a region where both electric field $\mathbf{E}$ and magnetic fields $\mathbf{B}$ are present. It follows that}

MET - 2018
Magnetic Effects of Current and Magnetism

A solenoid of length $50~\mathrm{cm}$ and a radius of cross-section $1\mathrm{cm}$ has 1000 turns of wire wound over it. If the current carried is 5A, the magnetic field on its axis, near the centre of the solenoid is approximately (permeability of free space $\mu_{0} = 4\pi \times 10^{-7}\mathrm{T}\cdot \mathrm{m / A}$)

MET - 2018
Magnetic Effects of Current and Magnetism

A transformer of $100%$ efficiency has 200 turns in the primary and 40000 turns in secondary. It is connected to a $220~\mathrm{V}$ main supply and secondary feeds to a $100\mathrm{k}\Omega$ resistance. The potential difference per turn is

MET - 2018
Electromagnetic induction