1
JEE Main 2021 (Online) 20th July Evening Shift
Numerical
+4
-1
Consider a triangle having vertices A($$-$$2, 3), B(1, 9) and C(3, 8). If a line L passing through the circum-centre of triangle ABC, bisects line BC, and intersects y-axis at point $$\left( {0,{\alpha \over 2}} \right)$$, then the value of real number $$\alpha$$ is ________________.
2
JEE Main 2021 (Online) 18th March Morning Shift
Numerical
+4
-1
A square ABCD has all its vertices on the curve x2y2 = 1. The midpoints of its sides also lie on the same curve. Then, the square of area of ABCD is _________.
3
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 ____________.
4
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 __________.