Question 1 :
What is the approximate length of the line segment joining the points N (7, 2) and J (2, 7)?
Question 2 :
Find the point on X-axis which is equidistant from $A\left( { - 3,4} \right)$ and $B\left( { 1,- 4} \right)$.
Question 3 :
If $A ( - 2, 5), B (3, 1)$ and $P,Q$ are the points of intersection of $AB$ then mid-point of $PQ$ is
Question 4 :
If point P divides the line joining the points $(5, 0)$ and $(0, 4)$ in the ratio $2 : 3$ internally, then the $x$-coordinate of $P$ is <br/>
Question 5 :
The point, which divides the line segment joining the points $(7, 6)$ and $(3, 4)$ in ratio $1 : 2$ internally, lies in the<br/>
Question 6 :
Mid point of $A(0,0)$ and $B(1024,2048)$ is ${A}_{1}$, midpoint of ${A}_{1}$ and $B$ is ${A}_{2}$ and so on. Coordinates of ${A}_{10}$ are
Question 7 :
The triangle formed by the points A (2a, 4a),B (2a, 6a) and C (2a+$\sqrt{3a}$,5a) is :
Question 8 :
<font><font>The distance of the origin from the point of intersection of $x + y = 11$ and $x - y -3=0$ is</font></font><br/>
Question 9 :
Let P be the point (1, 0) and Q a point on the curve ${ y }^{ 2 }=8x$. The locus of mid point of PQ is-
Question 10 :
A triangle has vertices at $(6,7),(2,-9)$ and $(-4,1)$. Find the slope of its sides.
Question 11 :
The line segment joining the points (-3, -4) and (1, -2) is divided by the y-axis in the ratio
Question 12 :
Find the points which divide the line segment joining $A(-4,0)$ and $B(0,6)$ into two equal parts.
Question 14 :
Find the ratio in which the line segment joining the points $(-3, 10)$ and $(6, -8)$ is divided by $(-1, 6)$<br>
Question 15 :
If $( 4, 3)$ and $(-4, 3)$ are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the interior of the triangle.<br/>
Question 16 :
If in a Δ ABC, CD is the angular bisector of the ∠ ACB, then CD is equal to
Question 17 :
The mid points of the sides of a triangle are D(6, 1), E(3, 5) and F( − 1, − 2), then the vertex opposite to D is
Question 18 :
In Δ ABC, if $\tan{\frac{A}{2}\tan\frac{C}{2}} = \frac{1}{2}$, then a, b, c are in
Question 19 :
The area of the region bounded by the lines y = |x−2|, x = 1, x = 3 and the x-axis is
Question 20 :
Each side of a square subtends an angle of 60<sup>∘</sup> at the top of a tower h metres high standing in the centre of the square. If a is the length of each side of the square, then
Question 21 :
The straight lines x = y, x − 2y= 3 and x + 2y = − 3 form a triangle, which is
Question 22 :
Orthocenter of the triangle formed by the lines x + y = 1 and xy = 0 is
Question 23 :
Two pillars of equal height stand on either side of a road-way which is 60 m wide. At a point in the road-way between the pillars, the elevation of the top of pillars are 60<sup>∘</sup>and 30<sup>∘</sup>.The height of the pillars is
Question 24 :
If a > 0, b > 0 the maximum area of the triangle formed by the points O(0, 0), A(acos θ, bsin θ) and B(acos θ, − bsin θ) is (in sq unit)
Question 25 :
From the top of a cliff of height a, the angle of depression of the foot of a certain tower is found to be double the angle of elevation of the top of the tower of height h. If θ be the angle of elevation, then its value is
