question_answer

 

Directions:  Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below.

Assertion Area of the square inscribed in a circle of radius r is \[2{{r}^{2}}\] sq units.

Reason Area of the major segment of a circle = Area of the circle - Area of minor segment.

A) A is true, R is true; R is a correct explanation for A.

B) A is true, R is true; R is not a correct explanation for A.

C) A is true; R is false.

D) A is false; R is true.

Correct Answer: D

Solution :

Let r be the radius of circle and a be the side of square inscribed in a circle. In \[\Delta ABC,\,\angle B=90{}^\circ \,\] \[A{{C}^{2}}=A{{B}^{2}}+B{{C}^{2}}\] \[\Rightarrow \,\,{{\left( 2r \right)}^{2}}={{a}^{2}}+{{a}^{2}}\] \[\Rightarrow \,\,4{{r}^{2}}=2{{a}^{2}}\] \[\Rightarrow \,\,\,{{a}^{2}}=2{{r}^{2}}\]            \[\left[ \because \,{{a}^{2}}=area\,of\,square \right]\]