1
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

An equilateral triangle is constructed between the lines $\sqrt{3} x+y-6=0$ and $\sqrt{3} x+y+9=0$ with base on one line and vertex on the other. The area (in sq units) of the triangle, so formed is

A
$\frac{175}{6 \sqrt{3}}$
B
$\frac{225}{2 \sqrt{3}}$
C
$\frac{225}{4 \sqrt{3}}$
D
$\frac{245}{4 \sqrt{2}}$
2
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $\theta$ is the acute angle between the lines joining the origin to the points of intersection of the curve $x^2+x y+y^2+x+3 y+1=0$ and the straight line $x+y+2=0$, then $\cos \theta=$

A
$\frac{1}{\sqrt{3}}$
B
$\frac{1}{\sqrt{5}}$
C
$\frac{3}{5}$
D
$\frac{4}{5}$
3
TS EAMCET 2023 (Online) 12th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The angle, by which the coordinate axes are to be rotated about the origin so that the transformed equation of $\sqrt{3} x^2+(\sqrt{3}-1) x y-y^2=0$ would be free from $x y$-term is
A
$45^{\circ}$
B
$22.5^{\circ}$
C
$15^{\circ}$
D
$7.5^{\circ}$
4
TS EAMCET 2023 (Online) 12th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the slope of a straight line passing through $A(3,2)$ is $3 / 4$, then the coordinates of the two points on the same line that are 5 units away from $A$ are
A
$(-7,5),(1,-1)$
B
$(7,5),(-1,-1)$
C
$(6,9),(-2,3)$
D
$(6,3),(-2,-3)$
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