Question 1 :
If the projections of a line segment on the x, y and z axes in $3$-dimensional space are $2, 3$ and $6$ respectively, then the length of line segment is

Question 2 :
Find the distance from the point (2, 3) to the line 3x + 4y + 9 = 0

Question 3 :
The orthocentre of the triangle $ABC$ is $B$ and the circumstances is $S(a,b)$. If $A$ is the origin, then the coordinates of $C$ are:

Question 4 :
The condition for the points (x,y), (-2,2) and (3,1) to be collinear is

Question 5 :
The centroid of the triangle with vertices (2,6), (-5,6) and (9,3) is

Question 6 :
The vertices of a $\triangle {ABC}$ are $A(-5,7),B(-4,-5)$ and $C(4,5)$. Find the slopes of the altitudes of the triangle.

Question 8 :
The angle of inclination of a straight line parallel to x-axis is equal to

Question 9 :
How far is the line 3x - 4y + 15 = 0 from the origin?

Question 10 :
The distance between the points $(a , b)$ and $(-1, -b)$ is 

Question 11 :
$A(0, 0), B(7, 2), C(7, 7)$ and $D(2, 7)$ are the vertices of a quadrilateral. The respective slopes of diagonals $AC$ and $BD$ are&#160;<br/>

Question 12 :
If $A= (1, 2, 3), B = (2, 3, 4)$ and $AB$ is produced&#160;upto $C$ such that $2AB = BC$, then $C =$<br/>

Question 13 :
What is the value of k, if the line $\displaystyle 2x-3y=k$ passes through the origin.

Question 14 :
The distance between the points (sin x, cos x) and (cos x -sin x) is

Question 16 :
Which of the following is perpendicular to the line x/3 + y/4 = 1?

Question 17 :
Find the distance between the following pair of points.<br/>$(5, 7)$ and the origin

Question 18 :
Find the valueof c if the point $(4,5) $ pases through $y=5x+c$

Question 19 :
Consider a triangle ABC, whose vertical are $A(-2,1), B(1, 3) and C(x,y)$ .If C is a moving point such that area of $\Delta ABC$ is constant,then locus of C is:

Question 22 :
The points (2, 5) and (5, 1) are the two opposite vertices of a rectangle. If the other two vertices are points on the straight line $y = 2x + k$, then the value of k is

Question 23 :
$A=\left(2,-1\right), B=\left(4,3\right)$. If $AB$ is extended to $C$ such that $AB=BC$, then $C=$

Question 24 :
Which of the following points are $10$ units from the origin?

Question 26 :
The area of the triangle formed by the points (a,b+c), (b,c+a) and (c,a+b) is

Question 27 :
The length of the segment of the straight line passing through $(3,3)$ and $(7,6)$ cut off by the coordinate axes is

Question 28 :
If $\left| \begin{array} { l l l } { x _ { 1 } } &amp; { y _ { 1 } } &amp; { 1 } \\ { x _ { 2 } } &amp; { y _ { 2 } } &amp; { 1 } \\ { x _ { 3 } } &amp; { y _ { 3 } } &amp; { 1 } \end{array} \right| = \left| \begin{array} { l l l } { a _ { 1 } } &amp; { b _ { 1 } } &amp; { 1 } \\ { a _ { 2 } } &amp; { b _ { 2 } } &amp; { 1 } \\ { a _ { 3 } } &amp; { b _ { 3 } } &amp; { 1 } \end{array} \right|$<br/>&#160;then two triangles with vertices $\left( x _ { 1 } , y _ { 1 } \right) , \left( x _ { 2 } , y _ { 2 } \right) , \left( x _ { 3 } , y _ { 3 } \right)$ and $\left( a _ { 1 } , b _ { 1 } \right) , \left( a _ { 2 } , b _ { 2 } \right) , \left( a _ { 3 } , b _ { 3 } \right)$ are

Question 30 :
The distance of the point $(x_1, y_1)$ from the origin ........