CAT Exam Model Paper 6 with solutions for free online practice

Question : 9 of 60

Marks: +1, -0

\A _ { 1 } , \A _ { 2 } , \A _ { 3 } , \A _ { 4} , \A _ { 5 } , \A _ { 6 }

are 6 points in clockwise order on the circumference of a circle of radius 4 cm. The length of the arc

\A _ { 1 } \A _ { 1+1 }

is one-third the length of

\A _ { 1 +1} \A _ { 1+2 }

for all i = 1 to 4. If the sum of the lengths of the 5 arcs is one-eighth the circumference of the circle, what is the angle (in radians) subtended by A

_{2}

_{3}

at the center of the circle?

$\π/484$
${{3\π}/484}$
$\π/243$
${3\π}/243$

Validate

Solution:

Arc length =

\θ/360×2\πr

As the radius is fixed, the arc length is directly proportional to the angle subtended by the arc at the centre. So if the arc length is getting tripled the angle is also getting tripled.
Therefore (0 + 30 + 90 + 270 + 810) =

1/8

.2π

⇒1210 = π/4

⇒θ = π/484

Angle subtended byA

_{2}

_{3}

at the centre is30

3×π/484={3π}/484

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