1
TS EAMCET 2023 (Online) 14th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $x+\sqrt{3} y=3$ is the tangent to the ellipse $2 x^2+3 y^2=k$ at a point $P$, then the equation of the normal to this ellipse at $P$ is

A

$5 x-2 \sqrt{3} y=1$

B

$x-\sqrt{3} y=2$

C

$x-\sqrt{3} y+1=0$

D

$3 x-\sqrt{3} y=1$

2
TS EAMCET 2023 (Online) 14th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If the angle between the asymptotes of a hyperbola is $30^{\circ}$, then its eccentricity is

A

$\sqrt{5}-\sqrt{2}$

B

$\sqrt{6}-\sqrt{3}$

C

$\sqrt{5}-\sqrt{3}$

D

$\sqrt{6}-\sqrt{2}$

3
TS EAMCET 2023 (Online) 14th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

In a $\triangle A B C$, if the mid-points of sides $A B, B C$ and $C A$ are $(3,0,0),(0,4,0)$ and $(0,0,5)$ respectively, then $A B^2+B C^2+C A^2=$

A

50

B

200

C

300

D

400

4
TS EAMCET 2023 (Online) 14th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $l, m, n$ and $a, b, c$ are direction cosines of two lines, then

A

they are parallel when $l a+m b+n c=0$

B

they are perpendicular when $\frac{1}{a}=\frac{m}{b}=\frac{n}{c}$

C

the direction ratios of the bisectors of the angles between the two lines are $l \pm a, m \pm b$ and $n \pm c$

D

the direction ratios of the bisectors of the angles between the two lines are la, $m b$ and $n c$

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