If the term independent of $x$ in the expansion of $\left(\sqrt{\frac{x}{3}}+\frac{3}{2 x^2}\right)^{10}$ is $\frac{m}{n}$ ($m, \, {n}$ are relatively prime) then the length of the tangent from $(0,0)$ to a circle with centre $(m, 0)$ and radius '$n$' units is

JEE MATHEMATICS MCQ: CIRCLES

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Application +4 | -1

If the term independent of

x

in the expansion of

\left(\sqrt{\frac{x}{3}}+\frac{3}{2 x^2}\right)^{10}

\frac{m}{n}

(

m, \, {n}

are relatively prime) then the length of the tangent from

(0,0)

to a circle with centre

(m, 0)

and radius '

n

' units is

View answer and explanation

Correct option: D

The correct answer is 3 because it represents the length of the tangent from the origin to the circle, calculated after finding the term independent of x and determining the circle's equation.

More Questions from CIRCLES

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The sum of the coefficients in the expansion of

{\left( {{\alpha ^2}{x^2} - 2\alpha \mathrm{ }x + 1} \right)^{51}},

as a polynomial in

x

, vanishes. Position of the point

\left( {\alpha ,2{\alpha ^2}} \right)

with respect to the circle

{x^2} + {y^2} = 4,

is One of the diameter of the circle

{x^2} + {y^2} - 2x + 4y - 4 = 0

is The locus of the middle point of the chords of the circle

{x^2} + {y^2} = {a^2}

such that the chords pass through a given point

\left( {{x_1},{y_1}} \right)

, is

\quad \alpha, \beta

and

\gamma

are the parametric angles of three points

P, Q

, and R respectively, on the circle

x^2+y^2=1

, and

A

is the point

(-1,0)

. If the lengths of the chords

A P, A Q

and

A R

are in

G P

, then

\cos \alpha / 2, \cos \beta / 2

and

\cos \gamma / 2

are in The radius of the circle passing through the point (6,2), two of whose diameters are

x+y=6

and

x+2 y=4

is If a circle has two of its diameters along the lines

x+y=5

and

x-y=1

and has area

9 \pi

, then the equation of the circle is