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Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Number of roots.

## Number of roots – B.Stat Objective Problem

The number of roots of the equation $xsinx=1$ in the interval $[0,{2\pi}]$ is

• 0
• 2
• 53361
• 5082

### Key Concepts

Equation

Roots

Algebra

But try the problem first…

Source

B.Stat Objective Problem 712

Challenges and Thrills of Pre-College Mathematics by University Press

## Try with Hints

First hint

$f(x)=xsinx-1=0$

which can be written as sinx=$\frac{1}{x}$ and f(x) has solution at those points where sinx and $\frac{1}{x}$ intersects

So let us draw the graph

here we see two graphs y=sin x and y=$\frac{1}{x}$

Second Hint

both graphs intersect at two points between $(0,2\pi]$

Final Step

or, number of roots is 2.