1
JEE Main 2023 (Online) 1st February Morning Shift
+4
-1 For a triangle $$ABC$$, the value of $$\cos 2A + \cos 2B + \cos 2C$$ is least. If its inradius is 3 and incentre is M, then which of the following is NOT correct?

A
$$\overrightarrow {MA} \,.\,\overrightarrow {MB} = - 18$$
B
$$\sin 2A + \sin 2B + \sin 2C = \sin A + \sin B + \sin C$$
C
perimeter of $$\Delta ABC$$ is 18$$\sqrt3$$
D
area of $$\Delta ABC$$ is $${{27\sqrt 3 } \over 2}$$
2
JEE Main 2023 (Online) 30th January Morning Shift
+4
-1 A straight line cuts off the intercepts $$\mathrm{OA}=\mathrm{a}$$ and $$\mathrm{OB}=\mathrm{b}$$ on the positive directions of $$x$$-axis and $$y$$ axis respectively. If the perpendicular from origin $$O$$ to this line makes an angle of $$\frac{\pi}{6}$$ with positive direction of $$y$$-axis and the area of $$\triangle \mathrm{OAB}$$ is $$\frac{98}{3} \sqrt{3}$$, then $$\mathrm{a}^{2}-\mathrm{b}^{2}$$ is equal to :

A
$$\frac{392}{3}$$
B
98
C
196
D
$$\frac{196}{3}$$
3
JEE Main 2022 (Online) 27th June Morning Shift
+4
-1 The lengths of the sides of a triangle are 10 + x2, 10 + x2 and 20 $$-$$ 2x2. If for x = k, the area of the triangle is maximum, then 3k2 is equal to :

A
5
B
8
C
10
D
12
4
JEE Main 2022 (Online) 25th June Morning Shift
+4
-1 Let a, b and c be the length of sides of a triangle ABC such that $${{a + b} \over 7} = {{b + c} \over 8} = {{c + a} \over 9}$$. If r and R are the radius of incircle and radius of circumcircle of the triangle ABC, respectively, then the value of $${R \over r}$$ is equal to :

A
$${5 \over 2}$$
B
2
C
$${3 \over 2}$$
D
1
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