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Maths-

General

Easy

Question

The area of a circle is A1 and the area of a regular pentagon inscribed in the circle is A2. Then A1 : A2 is -

$\frac{π}{5}$ cos $\frac{π}{10}$
$\frac{2 π}{5}$ sec $\frac{π}{10}$
$\frac{2 π}{5}$ cosec $\frac{π}{10}$
none of these

The correct answer is: $fraction numerator 2 pi over denominator 5 end fraction$ sec $fraction numerator pi over denominator 10 end fraction$

Related Questions to study

If A, A1, A2, A3 be the area of the in-circle and ex-circles, then $fraction numerator 1 over denominator square root of A subscript 1 end subscript end root end fraction plus fraction numerator 1 over denominator square root of A subscript 2 end subscript end root end fraction plus fraction numerator 1 over denominator square root of A subscript 3 end subscript end root end fraction$ is equal to-

If A, A1, A2, A3 be the area of the in-circle and ex-circles, then $fraction numerator 1 over denominator square root of A subscript 1 end subscript end root end fraction plus fraction numerator 1 over denominator square root of A subscript 2 end subscript end root end fraction plus fraction numerator 1 over denominator square root of A subscript 3 end subscript end root end fraction$ is equal to-

If $fraction numerator r over denominator r subscript 1 end subscript end fraction$ = $fraction numerator r subscript 2 end subscript over denominator r subscript 3 end subscript end fraction$ , then -

If $fraction numerator r over denominator r subscript 1 end subscript end fraction$ = $fraction numerator r subscript 2 end subscript over denominator r subscript 3 end subscript end fraction$ , then -

16R2 r r1 r2 r3 =

16R2 r r1 r2 r3 =

parallel

The Complete set of values of 'x' which satisfy the inequations: $5 x plus 2 less than 3 x plus 8 space a n d space fraction numerator x plus 2 over denominator x minus 1 end fraction less than 4 space i s$

The Complete set of values of 'x' which satisfy the inequations: $5 x plus 2 less than 3 x plus 8 space a n d space fraction numerator x plus 2 over denominator x minus 1 end fraction less than 4 space i s$

The interval in which $fraction numerator x squared plus 2 x plus 3 over denominator x squared minus 3 x plus 2 end fraction$ is positive is

The interval in which $fraction numerator x squared plus 2 x plus 3 over denominator x squared minus 3 x plus 2 end fraction$ is positive is

Rr (sin A + sin B + sin C) =

Rr (sin A + sin B + sin C) =

parallel

r1+ r2 =

r1+ r2 =

$fraction numerator r subscript 1 end subscript over denominator b c end fraction$ + $fraction numerator r subscript 2 end subscript over denominator c a end fraction$ + $fraction numerator r subscript 3 end subscript over denominator a b end fraction$ =

$fraction numerator r subscript 1 end subscript over denominator b c end fraction$ + $fraction numerator r subscript 2 end subscript over denominator c a end fraction$ + $fraction numerator r subscript 3 end subscript over denominator a b end fraction$ =

If a , b, c are in A.P., then r1, r2, r3 are in

If a , b, c are in A.P., then r1, r2, r3 are in

parallel

If the sides be a, b, c then (r1–r) (r2+ r3) =

If the sides be a, b, c then (r1–r) (r2+ r3) =

If the sides be a, b, c then $fraction numerator b minus c over denominator r subscript 1 end subscript end fraction$ + $fraction numerator c minus a over denominator r subscript 2 end subscript end fraction$ + $fraction numerator a minus b over denominator r subscript 3 end subscript end fraction$ =

If the sides be a, b, c then $fraction numerator b minus c over denominator r subscript 1 end subscript end fraction$ + $fraction numerator c minus a over denominator r subscript 2 end subscript end fraction$ + $fraction numerator a minus b over denominator r subscript 3 end subscript end fraction$ =

If the sides be a, b, c then (r + r1) tan $fraction numerator B minus C over denominator 2 end fraction$ +(r + r2) tan $fraction numerator C minus A over denominator 2 end fraction$ + (r+ r3) tan $fraction numerator A minus B over denominator 2 end fraction$ =

If the sides be a, b, c then (r + r1) tan $fraction numerator B minus C over denominator 2 end fraction$ +(r + r2) tan $fraction numerator C minus A over denominator 2 end fraction$ + (r+ r3) tan $fraction numerator A minus B over denominator 2 end fraction$ =

parallel

$open parentheses fraction numerator 1 over denominator r subscript 1 end subscript end fraction plus fraction numerator 1 over denominator r subscript 2 end subscript end fraction close parentheses$ $open parentheses fraction numerator 1 over denominator r subscript 3 end subscript end fraction plus fraction numerator 1 over denominator r subscript 1 end subscript end fraction close parentheses$ =

$open parentheses fraction numerator 1 over denominator r subscript 1 end subscript end fraction plus fraction numerator 1 over denominator r subscript 2 end subscript end fraction close parentheses$ $open parentheses fraction numerator 1 over denominator r subscript 3 end subscript end fraction plus fraction numerator 1 over denominator r subscript 1 end subscript end fraction close parentheses$ =

$I f space fraction numerator left parenthesis x minus 2 right parenthesis left parenthesis 1 minus x right parenthesis left parenthesis x minus 3 right parenthesis cubed left parenthesis x minus 4 right parenthesis squared over denominator left parenthesis x plus 1 right parenthesis end fraction less or equal than 0 space t h e n space x space l i e s space i n$

$I f space fraction numerator left parenthesis x minus 2 right parenthesis left parenthesis 1 minus x right parenthesis left parenthesis x minus 3 right parenthesis cubed left parenthesis x minus 4 right parenthesis squared over denominator left parenthesis x plus 1 right parenthesis end fraction less or equal than 0 space t h e n space x space l i e s space i n$

(r1 – r) (r2 – r) (r3 – r) =

(r1 – r) (r2 – r) (r3 – r) =

parallel

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