1
JEE Main 2022 (Online) 29th July Evening Shift
+4
-1 Let $$m_{1}, m_{2}$$ be the slopes of two adjacent sides of a square of side a such that $$a^{2}+11 a+3\left(m_{1}^{2}+m_{2}^{2}\right)=220$$. If one vertex of the square is $$(10(\cos \alpha-\sin \alpha), 10(\sin \alpha+\cos \alpha))$$, where $$\alpha \in\left(0, \frac{\pi}{2}\right)$$ and the equation of one diagonal is $$(\cos \alpha-\sin \alpha) x+(\sin \alpha+\cos \alpha) y=10$$, then $$72\left(\sin ^{4} \alpha+\cos ^{4} \alpha\right)+a^{2}-3 a+13$$ is equal to :

A
119
B
128
C
145
D
155
2
JEE Main 2022 (Online) 29th July Evening Shift
+4
-1 Let $$\mathrm{A}(\alpha,-2), \mathrm{B}(\alpha, 6)$$ and $$\mathrm{C}\left(\frac{\alpha}{4},-2\right)$$ be vertices of a $$\triangle \mathrm{ABC}$$. If $$\left(5, \frac{\alpha}{4}\right)$$ is the circumcentre of $$\triangle \mathrm{ABC}$$, then which of the following is NOT correct about $$\triangle \mathrm{ABC}$$ ?

A
area is 24
B
perimeter is 25
C
D
3
JEE Main 2022 (Online) 29th July Morning Shift
+4
-1 Let the circumcentre of a triangle with vertices A(a, 3), B(b, 5) and C(a, b), ab > 0 be P(1,1). If the line AP intersects the line BC at the point Q$$\left(k_{1}, k_{2}\right)$$, then $$k_{1}+k_{2}$$ is equal to :

A
2
B
$$\frac{4}{7}$$
C
$$\frac{2}{7}$$
D
4
4
JEE Main 2022 (Online) 27th July Evening Shift
+4
-1 The equations of the sides $$\mathrm{AB}, \mathrm{BC}$$ and CA of a triangle ABC are $$2 x+y=0, x+\mathrm{p} y=39$$ and $$x-y=3$$ respectively and $$\mathrm{P}(2,3)$$ is its circumcentre. Then which of the following is NOT true?

A
$$(\mathrm{AC})^{2}=9 \mathrm{p}$$
B
$$(\mathrm{AC})^{2}+\mathrm{p}^{2}=136$$
C
$$32<\operatorname{area}\,(\Delta \mathrm{ABC})<36$$
D
$$34<\operatorname{area}\,(\triangle \mathrm{ABC})<38$$
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