JEE Main 2021 (Online) 25th July Evening Shift

Numerical

-1

If a rectangle is inscribed in an equilateral triangle of side length $$2\sqrt 2 $$ as shown in the figure, then the square of the largest area of such a rectangle is _____________.

JEE Main 2021 (Online) 25th July Evening Shift Mathematics - Properties of Triangle Question 17 English

JEE Main 2021 (Online) 25th July Evening Shift Mathematics - Properties of Triangle Question 17 English

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JEE Main 2021 (Online) 16th March Evening Shift

Numerical

-1

In $$\Delta$$ABC, the lengths of sides AC and AB are 12 cm and 5 cm, respectively. If the area of $$\Delta$$ABC is 30 cm² and R and r are respectively the radii of circumcircle and incircle of $$\Delta$$ABC, then the value of 2R + r (in cm) is equal to ___________.

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JEE Main 2021 (Online) 16th March Morning Shift

Numerical

-1

Let ABCD be a square of side of unit length. Let a circle C₁ centered at A with unit radius is drawn. Another circle C₂ which touches C₁ and the lines AD and AB are tangent to it, is also drawn. Let a tangent line from the point C to the circle C₂ meet the side AB at E. If the length of EB is $$\alpha$$ + $${\sqrt 3 }$$ $$\beta$$, where $$\alpha$$, $$\beta$$ are integers, then $$\alpha$$ + $$\beta$$ is equal to ____________.

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JEE Main 2020 (Online) 6th September Morning Slot

Numerical

-0

The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be 45^o. After walking a distance of 80 meters towards the top, up a slope inclined at an angle of 30^o to the horizontal plane, the angle of elevation of the top of the hill becomes 75^o. Then the height of the hill (in meters) is ______.

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