1
TS EAMCET 2023 (Online) 13th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $y=m x+4(m>0)$ is a tangent to the hyperbola $\frac{x^2}{25}-\frac{y^2}{9}=1$, then the point of contact of this tangent is

A

$\left(-\frac{25}{4},-\frac{9}{4}\right)$

B

$\left(\frac{25}{4}, \frac{9}{4}\right)$

C

$(1,5)$

D

$\left(-\frac{1}{2}, \frac{7}{2}\right)$

2
TS EAMCET 2023 (Online) 13th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

Let $A(4,3,5), B(1,-2,1), C(3,2,1)$ be the vertices of a $\triangle A B C$. If the internal bisector of $\angle B A C$ meet the side $B C$ at $D$, then $C D=$

A

$\frac{\sqrt{5}}{4}$

B

$\frac{3 \sqrt{5}}{4}$

C

$2 \sqrt{5}$

D

$\frac{5 \sqrt{5}}{2}$

3
TS EAMCET 2023 (Online) 13th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

Let the direction cosines of two lines satisfy the equations $3 l+2 m+n=0$ and $2 m n-3 n l+5 l m=0$. If $\theta$ is the angle between these two lines, then $\cos \theta=$

A

$\sqrt{\frac{19}{28}}$

B

$\frac{3}{\sqrt{28}}$

C

$-\frac{25}{\sqrt{2991}}$

D

$\frac{1}{6}$

4
TS EAMCET 2023 (Online) 13th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$(1,-2,1)$ is a point on a plane $\pi$ and $\pi$ is parallel to the plane $x-y-z=0$. If the equation of $\pi$ is $a x+b y+c z-2=0$, then $b-2 c=$

A

$-a$

B

$2 a$

C

$-2 a$

D

$a$

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