1
TS EAMCET 2022 (Online) 18th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If a line $L$ is common to the planes $x-y+z+2=0$ and $2 x+y-2 z+5=0$ then the direction cosines of the line $L$ are

A

$\left(\frac{1}{\sqrt{26}}, \frac{4}{\sqrt{26}}, \frac{3}{\sqrt{26}}\right)$

B

$\left(\frac{1}{3}, \frac{2}{3}, \frac{2}{3}\right)$

C

$\left(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\right)$

D

$\left(\frac{-1}{6}, \frac{5}{6}, \frac{\sqrt{10}}{6}\right)$

2
TS EAMCET 2022 (Online) 18th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

Let the foot of the perpendicular drawn from the point $(1,2,3)$ to a plane be $(-1,3,-2)$. Then, the perpendicular distance from the origin to the plane is

A

$\frac{5}{\sqrt{30}}$

B

$\sqrt{\frac{15}{2}}$

C

$\frac{2}{\sqrt{15}}$

D

$\frac{1}{\sqrt{3}}$

3
TS EAMCET 2022 (Online) 18th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \lim _{x \rightarrow 3^{-}} \frac{x^3-3 x^2-4 x+12}{2 x^3-7 x^2+2 x+3}= $$

A

0

B

$\infty$

C

$\frac{5}{14}$

D

$\frac{6}{13}$

4
TS EAMCET 2022 (Online) 18th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \lim _{x \rightarrow 0} \frac{2^{2 x}-2^{x+1}+2-\cos 2 x}{x^2}= $$

A

$2+\log 2$

B

$2+(\log 2)^2$

C

$2+(\log 4)^2$

D

$2+\log 4$

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