1
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

Consider the following statements:

Assertion (A) : The direction ratios of a line $L_1$ are 2,5, 7 and the direction ratios of another line $L_2$ are $\frac{4}{\sqrt{19}}$, $\frac{10}{\sqrt{19}}, \frac{14}{\sqrt{19}}$. Then, the lines $L_1, L_2$ are parallel.

Reason : ( $\mathbf{R}$ ) If the direction ratios of a line $L_1$ are $a_1, b_1, c_1$ the direction ratios of a line $L_2$ are $a_2, b_2, c_2$ and $a_1 a_2+b_1 b_2+c_1 c_2=0$, then the lines of $L_1, L_2$ are parallel.

A
(A) and (R) are true, (R) is the correct explanation of (A)
B
(A) and (R) are true, (R) is not the correct explanation of (A)
C
(A) is true, (R) is false
D
(A) is false, (R) is true
2
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

A line $L$ is parallel to both the planes $2 x+3 y+z=1$ and $x+3 y+2 z=2$. If line $L$ makes an angle $\alpha$ with the positive direction of $X$-axis, then $\cos \alpha=$

A
$1 / \sqrt{3}$
B
$1 / \sqrt{2}$
C
$1 / 2$
D
$\sqrt{3} / 2$
3
TS EAMCET 2023 (Online) 12th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the direction cosines $(l, m, n)$ of two lines are connected by the relations $l+m+n=0$ and $l m=0$, then the angle between those lines is
A
$\frac{\pi}{3}$
B
$\frac{\pi}{4}$
C
$\frac{\pi}{2}$
D
$\frac{\pi}{6}$
4
TS EAMCET 2023 (Online) 12th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The sum of the squares of the perpendicular distances of a point $(x, y, z)$ from the coordinate axes is $k$ times the square of the distance of the point from the origin Then, $k=$
A
2
B
3
C
1
D
4
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