Let denote the greatest.. | Continuity and Differentiability

Competishun Header

JEE MAIN 2020

09-01-2020 S2

Question

Let $[t]$ denote the greatest integer $\leq t$ and $\lim _{x \rightarrow 0} x\left[\frac{4}{x}\right]=A$. Then the function, $f(x)=\left[x^2\right] \sin (\pi x)$ is discontinuous, when x is equal to

Select the correct option:

A

$\sqrt{A+21}$

B

$\sqrt{A}$

C

$\sqrt{A+1}$

D

$\sqrt{A+5}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Question Tags

JEE Main

Mathematics

Easy

Start Preparing for JEE with Competishun

Filters 0

Showing 18 questions

QJEE Advanced 20202020

Let $x, y$ and $z$ be positive real numbers. Suppose $x, y$ and $z$ are lengths of the sides of...

JEE AdvanceMathematicsEasy

View Solution→

QJEE Advanced 20202020

Let S be the set of all complex numbers z satisfying $\left|\mathrm{z}^2+\mathrm{z}+1\right|=1$. Then which of the following statements is/are TRUE...

JEE AdvanceMathematicsEasy

View Solution→

QJEE Advanced 20202020

Let M be a 3 X 3 invertible matrix with real entries and let I denote the $3 \times 3$...

JEE AdvanceMathematicsEasy

View Solution→

QJEE Advanced 20202020

Let the function $f: R \rightarrow R$ be defined by $f(x)=x^3-x^2+(x-1) \sin x$ and let $g: R \rightarrow R$ be...

JEE AdvanceMathematicsEasy

View Solution→

QJEE Advance 20202020

In an X-ray tube, electrons emitted from a filament (cathode) carrying current I hit a target (anode) at a distance...

JEE AdvancePhysicsEasy

View Solution→

QJEE Advance 20202020

A rod of mass $m$ and length $L$, pivoted at one of its ends, is hanging vertically. A bullet of...

JEE AdvancePhysicsEasy

View Solution→

QJEE Advanced 20202020

Consider all rectangles lying in the region $...

JEE AdvanceMathematicsEasy

View Solution→

QJEE Advanced 20202020

Let C1 and C2 be two biased coins such that the probabilities of getting head in a single toss are...

JEE AdvanceMathematicsEasy

View Solution→

QJEE Advance 20202020

A student skates up a ramp that makes an angle $30^{\circ}$ with the horizontal. $\mathrm{He} /$ she starts (as shown...

JEE AdvancePhysicsEasy

View Solution→

QJEE Advance 20202020

A beaker of radius $r$ is filled with water (refractive index $\frac{4}{3}$ ) up to a height $H$ as shown...

JEE AdvancePhysicsEasy

View Solution→

QJEE Advance 20202020

A thermally isolated cylindrical closed vessel of height 8 m is kept vertically. It is divided into two equal parts...

JEE AdvancePhysicsEasy

View Solution→

QJEE Advance 20202020

A point charge q of mass m is suspended vertically by a string of length $l$. A point dipole of...

JEE AdvancePhysicsEasy

View Solution→

QJEE Advanced 20202020

Let $\mathrm{a}, \mathrm{b}$ and $\lambda$ be positive real numbers. Suppose P is an end point of the latus rectum of...

JEE AdvanceMathematicsEasy

View Solution→

QJEE Advanced 20202020

Let the functions $f: \mathrm{R} \rightarrow \mathrm{R}$ and $\mathrm{g}: \mathrm{R} \rightarrow \mathrm{R}$ be defined by $...

JEE AdvanceMathematicsEasy

View Solution→

QJEE Advance 20202020

A hot air balloon is carrying some passengers, and a few sandbags of mass 1 kg each so that its...

JEE AdvancePhysicsEasy

View Solution→

QJEE Advance 20202020

Two large circular discs separated by a distance of 0.01 m are connected to a battery via a switch as...

JEE AdvancePhysicsEasy

View Solution→

QJEE Advanced 20202020

If the function $f: \mathrm{R} \rightarrow \mathrm{R}$ is defined by $\mathrm{f}(\mathrm{x})=|\mathrm{x}|(\mathrm{x}-\sin \mathrm{x})$, then which of the following statements is TRUE?

JEE AdvanceMathematicsEasy

View Solution→

QJEE Advance 20202020

A train with cross-sectional area $\mathrm{S}_{\mathrm{t}}$ is moving with speed $v_t$ inside a long tunnel of cross-sectional area $\mathrm{S}_0\left(\mathrm{~S}_0=4 \mathrm{~S}_{\mathrm{t}}\right)$....

JEE AdvancePhysicsEasy

View Solution→