JEE Main 2024 (Online) 29th January Morning Shift | Straight Lines and Pair of Straight Lines Question 52 | Mathematics

In a $$\triangle A B C$$, suppose $$y=x$$ is the equation of the bisector of the angle $$B$$ and the equation of the side $$A C$$ is $$2 x-y=2$$. If $$2 A B=B C$$ and the points $$A$$ and $$B$$ are respectively $$(4,6)$$ and $$(\alpha, \beta)$$, then $$\alpha+2 \beta$$ is equal to

JEE Main 2024 (Online) 27th January Evening Shift

MCQ (Single Correct Answer)

-1

Let $$\mathrm{R}$$ be the interior region between the lines $$3 x-y+1=0$$ and $$x+2 y-5=0$$ containing the origin. The set of all values of $$a$$, for which the points $$\left(a^2, a+1\right)$$ lie in $$R$$, is :

$$(-3,0) \cup\left(\frac{2}{3}, 1\right)$$

$$(-3,0) \cup\left(\frac{1}{3}, 1\right)$$

$$(-3,-1) \cup\left(\frac{1}{3}, 1\right)$$

$$(-3,-1) \cup\left(-\frac{1}{3}, 1\right)$$

JEE Main 2024 (Online) 27th January Morning Shift

MCQ (Single Correct Answer)

-1

The portion of the line $4 x+5 y=20$ in the first quadrant is trisected by the lines $\mathrm{L}_1$ and $\mathrm{L}_2$ passing through the origin. The tangent of an angle between the lines $\mathrm{L}_1$ and $\mathrm{L}_2$ is :

$\frac{30}{41}$

$\frac{8}{5}$

$\frac{2}{5}$

$\frac{25}{41}$

JEE Main 2023 (Online) 15th April Morning Shift

MCQ (Single Correct Answer)

-1

If $(\alpha, \beta)$ is the orthocenter of the triangle $\mathrm{ABC}$ with vertices $A(3,-7), B(-1,2)$ and $C(4,5)$, then $9 \alpha-6 \beta+60$ is equal to :