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1
TS EAMCET 2022 (Online) 20th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

4 different pairs of lines are given in List I and the cosine of the angle between every pair of lines is given in List II. Match the following :

                                  List-I                     List-II
(A) 
<mspace width="1em"></mspace>
5 
<mi>x</mi>

<mn>2</mn>
+ 2 
<mn>7</mn>
x y − 
<mi>y</mi>

<mn>2</mn>
= 0 
<mspace width="1em"></mspace>
5 
<mi>x</mi>

<mn>2</mn>
+ 2 
<mn>7</mn>
x y − 
<mi>y</mi>

<mn>2</mn>
= 0 quad5x^(2)+2sqrt7xy-y^(2)=0		 (I) 
<msqrt>

  <mn>3</mn>

</msqrt>

<mn>2</mn>

<msqrt>

  <mn>3</mn>

</msqrt>

<mn>2</mn>
(sqrt3)/(2)
(B) 
<mspace width="1em"></mspace>

<mi>x</mi>

<mn>2</mn>
+ 
<mn>11</mn>
x y + 2 
<mi>y</mi>

<mn>2</mn>
= 0 
<mspace width="1em"></mspace>

<mi>x</mi>

<mn>2</mn>
+ 
<mn>11</mn>
x y + 2 
<mi>y</mi>

<mn>2</mn>
= 0 quadx^(2)+sqrt11xy+2y^(2)=0		 (II) 
<mo data-mjx-texclass="OPEN">(</mo>

<mfrac>

  <mn>1</mn>

  <mrow>

    <mn>2</mn>

    <msqrt>

      <mn>3</mn>

    </msqrt>

  </mrow>

</mfrac>

<mo data-mjx-texclass="CLOSE">)</mo>

<mrow>

  <mfrac>

    <mn>1</mn>

    <mrow>

      <mn>2</mn>

      <msqrt>

        <mn>3</mn>

      </msqrt>

    </mrow>

  </mfrac>  

</mrow>
((1)/(2sqrt3))
(C) 
<mspace width="1em"></mspace>

<mi>x</mi>

<mn>2</mn>
+ 2 
<mn>2</mn>
x y + 
<mi>y</mi>

<mn>2</mn>
= 0 
<mspace width="1em"></mspace>

<mi>x</mi>

<mn>2</mn>
+ 2 
<mn>2</mn>
x y + 
<mi>y</mi>

<mn>2</mn>
= 0 quadx^(2)+2sqrt2xy+y^(2)=0		 (III) 
<mn>1</mn>

<mn>2</mn>

<mn>1</mn>

<mn>2</mn>
(1)/(2)
(D) 
<mspace width="1em"></mspace>
3 
<mi>x</mi>

<mn>2</mn>
+ 4 
<mn>2</mn>
x y + 
<mi>y</mi>

<mn>2</mn>
= 0 
<mspace width="1em"></mspace>
3 
<mi>x</mi>

<mn>2</mn>
+ 4 
<mn>2</mn>
x y + 
<mi>y</mi>

<mn>2</mn>
= 0 quad3x^(2)+4sqrt2xy+y^(2)=0		 (IV) 
<mo data-mjx-texclass="OPEN">(</mo>

<mfrac>

  <mn>2</mn>

  <mn>3</mn>

</mfrac>

<mo data-mjx-texclass="CLOSE">)</mo>

<mrow>

  <mfrac>

    <mn>2</mn>

    <mn>3</mn>

  </mfrac>  

</mrow>
((2)/(3))
(V) 
<mn>1</mn>

<msqrt>

  <mn>2</mn>

</msqrt>

<mn>1</mn>

<msqrt>

  <mn>2</mn>

</msqrt>
(1)/(sqrt2)
$$ \text { The correct match is } $$
A
A B C D
III I V II
B
A B C D
III I IV V
C
A B C D
III I V IV
D
A B C D
III V II IV
2
TS EAMCET 2022 (Online) 20th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $a x^2+6 x y-2 y^2=0$ represents a pair of perpendicular lines and $9 x^2+2 h x y+4 y^2=0(h>0)$ represents a pair of coincident lines, then $h=$

A

$3 a$

B

$2 a$

C

$a$

D

$4 a$

3
TS EAMCET 2022 (Online) 20th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

The line $x+2 y=k$ meets the curve $2 x^2-2 x y+3 y^2+2 x-y-1=0$ at two points $A$ and $B$. Let $O$ be the origin. If the line segments $O A$ and $O B$ are perpendicular to each other, then $k=$

A

$\pm 1$

B

$\pm 2$

C

$\pm 3$

D

4

4
TS EAMCET 2022 (Online) 19th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

If a straight line $L$ passing through the point $(5,-3)$ is inclined at an angle of $60^{\circ}$ to the line $\sqrt{3} x+y-9=0$ and $L$ intersects $X$-axis, then the equation of $L$ is

A

$x-\sqrt{3} y-3-5 \sqrt{3}=0$

B

$\sqrt{3} x-y-3-5 \sqrt{3}=0$

C

$\sqrt{3} x-y+3+5 \sqrt{3}=0$

D

$x-\sqrt{3} y+3+5 \sqrt{3}=0$

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