1
JEE Main 2021 (Online) 17th March Evening Shift
Numerical
+4
-1
Let tan$$\alpha$$, tan$$\beta$$ and tan$$\gamma$$; $$\alpha$$, $$\beta$$, $$\gamma$$ $$\ne$$ $${{(2n - 1)\pi } \over 2}$$, n$$\in$$N be the slopes of three line segments OA, OB and OC, respectively, where O is origin. If circumcentre of $$\Delta$$ABC coincides with origin and its orthocentre lies on y-axis, then the value of $${\left( {{{\cos 3\alpha + \cos 3\beta + \cos 3\gamma } \over {\cos \alpha \cos \beta \cos \gamma }}} \right)^2}$$ is equal to ____________.
2
JEE Main 2021 (Online) 17th March Morning Shift
Numerical
+4
-1
The maximum value of z in the following equation z = 6xy + y2, where 3x + 4y $$\le$$ 100 and 4x + 3y $$\le$$ 75 for x $$\ge$$ 0 and y $$\ge$$ 0 is __________.
3
JEE Main 2020 (Online) 5th September Morning Slot
Numerical
+4
-0
If the line, 2x - y + 3 = 0 is at a distance
$${1 \over {\sqrt 5 }}$$ and $${2 \over {\sqrt 5 }}$$ from the lines 4x - 2y + $$\alpha$$ = 0
and 6x - 3y + $$\beta$$ = 0, respectively, then the sum of all possible values of $$\alpha$$ and $$\beta$$ is :
4
JEE Main 2020 (Online) 7th January Morning Slot
Numerical
+4
-0
Let A(1, 0), B(6, 2) and C $$\left( {{3 \over 2},6} \right)$$ be the vertices of a triangle ABC. If P is a Point inside the triangle ABC such that the triangles APC, APB and BPC have equal areas, then the length of the line segment PQ, where Q is the point $$\left( { - {7 \over 6}, - {1 \over 3}} \right)$$, is ________.