Problem 1
The line \(x=a y+b, z=c y+d\) and \(x=a^{\prime} y+b^{\prime}, z=c^{\prime} y+d^{\prime}\) are perpendicular if (a) \(a a^{\circ}+c c^{\prime}=1\) (b) \(a a^{\circ}+c c^{\prime}=-1\) (c) \(b b^{2}+d d^{\prime}=1\) (d) \(b b^{\prime}+d d^{\prime}=-1\).
Problem 2
The coordinates of the point of interseetion of the line \(\frac{x+1}{1}=\frac{y+3}{3}=\frac{z+2}{-2}\) with the plane \(3 x+4 y+5 z=5\) in \((a)(5,15,-14)\) (b) \((3,4,5)\) (c) \((1,3,-2)\) \((d)(8,12,-10)\)
Problem 3
The equation of a right eircular cylinder, whose axis in the \(z\)-axis and radius \(a\) is \((a) x^{2}+y^{2}+z^{2}=a^{2}\) (b) \(a^{2}+y^{2}=a^{2}\) (c) \(x^{2}+y^{2}=a^{2}\) \(\left(\right.\) d) \(2^{2}+x^{2}=a^{2}\)
Problem 4
The equation \(\sqrt{f x}+\sqrt{s y}+\sqrt{h z}=0\) represent a (\alpha) sphere (b) cylinder (c) cone (d) pair of planes.
Problem 8
The sum of the direction cosines of a straight line is (a) zero (b) one (c) constant (d) \(n\) one of the above.
Problem 9
The angle between the planes \(x-y+2 z-9=0\) and \(2 x+y+z=7\) is (a) \(30^{\circ}\) (b) \(90^{\circ}\) (c) \(6 \bar{B}\) (d) \(120^{\circ}\)
Problem 10
The equation of the right circular cone whone axin is \(x=y=z\), vertex is the origin and the eemi-vertical angle is \(45^{\circ}\) is given as (a) \(x^{2}+y^{2}+z^{2}=0\). (b) \(2\left(x^{2}+y^{2}+z^{2}\right)=3(x+y+z)^{2}\) (c) \(3\left(x^{2}+y^{2}+z^{2}\right)=2(x+y+z)^{2}\) \(\left(\right.\) d) \(x^{3}+y^{2}+z^{x}+x y+y z+2 x=0\)
Problem 11
The equation of a struight line parallel te the x-axis is given by (o) \(\frac{x-a}{1}=\frac{y-b}{1}=\frac{x-c}{1}\) (b) \(\frac{x-a}{0}=\frac{y-b}{1}=\frac{x-c}{1}\) (c) \(\frac{x-a}{0}=\frac{y-b}{0}=\frac{r-c}{1}\) (d) \(\frac{x-4}{1}=\frac{y-b}{0}=\frac{z-c}{0}\).
Problem 12
The equation of the plane pasning through \((4,-2,1)\) and perpendicular to the line with direction nation \(7,2,-3\) in (a) \(x+3 y-4 z-8=0\) (b) \(2 x+7 y-3 z-24=0\) \(\begin{array}{llll}\text { (c) } 7 x+2 y-3 z-21=0 . & \text { (d) } 7 x+3 y-2 z+21 & =0 . & \text { (V.T.t., } 2009 & S\end{array}\)
Problem 15
Section of a sphere by a plane is (a) parabola (b) ellipse (c) circle.
