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Maths-

General

Easy

Question

Assertion : In any ABC, minimum value of $fraction numerator r subscript 1 end subscript plus r subscript 2 end subscript plus r subscript 3 end subscript over denominator r end fraction$ is 9.
Reason : A.M.  G.M.

If both (A) and (R) are true, and (R) is the correct explanation of (A).
If both (A) and (R) are true but (R) is not the correct explanation of (A).
If (A) is true but (R) is false.
If (A) is false but (R) is true.

The correct answer is: If both (A) and (R) are true but (R) is not the correct explanation of (A).

Both are correct but reason is not correct explanation
 r₁ = $fraction numerator capital delta over denominator s minus a end fraction$ , r₂ = $fraction numerator capital delta over denominator s minus b end fraction$ , r₃ = $fraction numerator capital delta over denominator s minus c end fraction$
 $fraction numerator 1 over denominator r subscript 1 end subscript end fraction$ + $fraction numerator 1 over denominator r subscript 2 end subscript end fraction$ + $fraction numerator 1 over denominator r subscript 3 end subscript end fraction$ = $fraction numerator 3 s minus left parenthesis a plus b plus c right parenthesis over denominator capital delta end fraction$ = $fraction numerator s over denominator capital delta end fraction$ = $fraction numerator 1 over denominator r end fraction$
 A.M.  H.M.
r₁ + r₂ + r₃  $fraction numerator 3 over denominator fraction numerator 1 over denominator r subscript 1 end subscript end fraction plus fraction numerator 1 over denominator r subscript 2 end subscript end fraction plus fraction numerator 1 over denominator r subscript 3 end subscript end fraction end fraction$
 $fraction numerator r subscript 1 end subscript plus r subscript 2 end subscript plus r subscript 3 end subscript over denominator r end fraction$  9

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Reason : Pedal triangle is the ex-central triangle of the given triangle.

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Reason : Pedal triangle is the ex-central triangle of the given triangle.

A large number of primary follicles degenerate during the phase from birth to puberty. Therefore at puberty each ovary has about

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Assertion : The side of regular hexagon is 5 cm whose radius of inscribed circle is 5cm.
Reason : The radius of inscribed circle of a regular polygon of side a is $fraction numerator a over denominator 2 end fraction cot invisible function application open parentheses fraction numerator pi over denominator n end fraction close parentheses$ .

parallel

Assertion : In a ABC, $fraction numerator a cos invisible function application A plus b cos invisible function application B plus c cos invisible function application C over denominator a plus b plus c end fraction$ is equal to $fraction numerator r over denominator R end fraction$
Reason : In equilateral triangle the ratio between In-radius and circum-radius is 1 : 2.

Assertion : In a ABC, $fraction numerator a cos invisible function application A plus b cos invisible function application B plus c cos invisible function application C over denominator a plus b plus c end fraction$ is equal to $fraction numerator r over denominator R end fraction$
Reason : In equilateral triangle the ratio between In-radius and circum-radius is 1 : 2.

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Reason : R  2r.

Assertion : In any triangle ABC, $fraction numerator 1 over denominator a b end fraction plus fraction numerator 1 over denominator b c end fraction plus fraction numerator 1 over denominator c a end fraction equals fraction numerator 1 over denominator 2 r R end fraction$ , where r is in radius and R is circum radius.
Reason : R  2r.

In any equilateral , three circles of radii one are touching to the sides given as in the figure then area of the 

In any equilateral , three circles of radii one are touching to the sides given as in the figure then area of the 
Maths-General

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If the sides a, b, c of a triangle are such that a : b : c : : 1 : $square root of 3$ : 2, then the A : B : C is -

If the sides a, b, c of a triangle are such that a : b : c : : 1 : $square root of 3$ : 2, then the A : B : C is -

If the angles of a triangle are in ratio 4 : 1: 1 then the ratio of the longest side and perimeter of triangle is -

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parallel

In a triangle ABC, let C = $fraction numerator pi over denominator 2 end fraction$ . If r is the in radius and R is the circumradius of the triangle, then 2(r + R) is equal to -

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