32
MCQ (Single Correct Answer)
The sine of the angle between the straight line $\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}$ and the plane $2 x-2 y+z=5$ is
A
$\frac{10}{6 \sqrt{5}}$
B
$\frac{4}{5 \sqrt{2}}$
C
$\frac{2 \sqrt{3}}{5}$
D
$\frac{\sqrt{2}}{10}$
33
MCQ (Single Correct Answer)
The reflection of the point $(\alpha, \beta, \gamma)$ in the $X Y$-plane is
A
$(\alpha, \beta, 0)$
B
$(0,0, \gamma)$
C
$(-\alpha,-\beta, \gamma)$
D
$(\alpha, \beta,-\gamma)$
34
MCQ (Single Correct Answer)
The area of the quadrilateral $A B C D$ where $A(0,4,1)$, $B(2,3,-1), C(4,5,0)$, and $D(2,6,2)$ is equal to
A
9 sq units
B
18 sq units
C
27 sq units
D
81 sq units
35
MCQ (Single Correct Answer)
The locus represented by $x y+y z=0$ is
A
a pair of perpendicular lines
B
a pair of parallel lines
C
a pair of parallel planes
D
a pair of perpendicular planes
36
MCQ (Single Correct Answer)
If the plane $2 x-3 y+6 z-11=0$ makes an angle $\sin ^{-1} \alpha$ with $X$-axis, then the value of $\alpha$ is
A
$\frac{\sqrt{3}}{2}$
B
$\frac{\sqrt{2}}{3}$
C
$\frac{2}{7}$
D
$\frac{3}{7}$