1
TG EAPCET 2024 (Online) 11th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$(a, b)$ is the point to which the origin has to be shifted by translation of axes so as to remove the first-degree terms from the equation $2 x^{2}-3 x y+4 y^{2}+5 y-6=0$. If the angle by which the axes are to be rotated in positive direction about the origin to remove the $x y$-term from the equation $a x^{2}+23 a b x y+b y^{2}=0$ is $\theta$, then $\tan 2 \theta=$
A
$\frac{\pi}{4}$
B
60
C
$\frac{\pi}{3}$
D
15
2
TG EAPCET 2024 (Online) 11th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$A(1,-2), B(-2,3), C(-1,-3)$ are the vertices of a $\triangle A B C . L_{1}$ is the perpendicular drawn from $A$ to $B C$ and $L_{2}$ is the perpendicular bisector of $A B$. If $(l, m)$ is the point of intersection of $L_{1}$ and $L_{2}$, then $26 m-3=$
A
261
B
$89 /$
C
$13 /$
D
431
3
TG EAPCET 2024 (Online) 11th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The area of the parallelogram formed by the lines $L_{1} \equiv \lambda x+4 y+2=0, L_{2} \equiv 3 x+4 y-3=0$, $L_{3} \equiv 2 x+\mu y+6=0, L_{4} \equiv 2 x+y+3=0$, where $L_{1}$ is parallel to $L_{2}$ and $L_{3}$ is parallel to $L_{4}$ is
A
9
B
7
C
5
D
3
4
TG EAPCET 2024 (Online) 11th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the angle between the pair of lines given by the equation $a x^{2}+4 x y+2 y^{2}=0$ is $45^{\circ}$, then the possible values of $a$
A
are -3 or 21
B
are $-6 \pm 4 \sqrt{3}$
C
are $-6 \pm 24 \sqrt{2}$
D
do not exist
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