1
AP EAPCET 2025 - 23rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If the circles $x^2+y^2+5 k x+2 y+k=0$ and $2 x^2+2 y^2+2 k x+3 y-1=0, k \in R$ intersect at points $P$ and $Q$ then the line $4 x+5 y-k=0$ passes through $P$ and $Q$ for

A

exactly one value of $k$

B

exactly two values of $k$

C

no value of $k$

D

infinitely many value of $k$

2
AP EAPCET 2025 - 23rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

The slope of one of the direct common tangents drawn to the circles $x^2+y^2-2 x+4 y+1=0$ and $x^2+y^2-4 x-2 y+4=0$ is

A

0

B

$\frac{4}{3}$

C

$\frac{3}{4}$

D

1

3
AP EAPCET 2025 - 23rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $(1, a),(b, 2)$ are conjugate points with respect to the circle $x^2+y^2=25$, then $4 a+2 b=$
A

25

B

50

C

100

D

150

4
AP EAPCET 2025 - 23rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If the pole of the line $x+2 b y-5=0$ with respect to the circle $S \equiv x^2+y^2-4 x-6 y+4=0$ lies on the line $x+b y+1=0$, then the polar of the point $(b,-b)$ with respect to the circle $S=0$ is

A

$5 y-6=0$

B

$y-6=0$

C

$x+5 y-6=0$

D

$5 x+y-6=0$

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