Question 2 :
The adjacent sides of a parallelogram are 15 cm and 10 cm. If length of one diagonal of this parallelogram is 20 cm, the length of other diagonal will be

Question 3 :
The four angles of a quadrilateral are as $3 : 5 : 7 :9$. Find the angles<br/>

Question 4 :
The adjacent angles of a parallelogram are as 2 : 3.Find the measures of all the angles

Question 6 :
State true or false:<br/>In triangle&#160;&#160;$&#160;ABC&#160;&#160;$,&#160;&#160;$&#160;P&#160;&#160;$&#160;is the mid-point of side&#160;&#160;$&#160;BC&#160;&#160;$.&#160;A line&#160;through&#160;$&#160;P&#160;&#160;$&#160;and Parallel to &#160;$&#160;CA&#160;&#160;$&#160;meets&#160;&#160;$&#160;AB&#160;&#160;$&#160;at point&#160;&#160;$&#160;Q&#160;&#160;$; and a line through&#160;&#160;$&#160;Q&#160;&#160;$&#160;and&#160;parallel to&#160;&#160;$&#160;BC $&#160;meets median&#160;&#160;$&#160;AP&#160;&#160;$&#160;at&#160;point&#160;&#160;$&#160;R&#160;&#160;$. Can it be concluded that,$ AP= 2AR $ ?<br/><br/>

Question 7 :
$&#160;P,Q, R&#160;$&#160;and&#160;$&#160;S&#160;$&#160;are the mid-points of sides&#160;$&#160;AB, BC, CD&#160;$&#160;and&#160;$&#160;DA&#160;$&#160;respectively&#160;of&#160;rhombus&#160;$&#160;ABCD&#160;$. Quadrilateral $&#160;PQRS&#160;$&#160;is a&#160;rectangle.&#160;Under what&#160;condition will&#160;$&#160;PQRS&#160;$&#160;be a square ?

Question 8 :
Two adjacent angles of a parallelogram are $2x+ 30$ and $5x + 30$. Then the value of $x$ is ___ .<br/>

Question 9 :
State true or falseIn a square $ABCD$, diagonals meet at $O$. $P$ is a point on $BC$ such that $OB= BP$, then<br/>$\angle BOP= 3\, \angle COP$<br/>

Question 10 :
Tangents <i>PA</i> and <i>PB</i> drawn to $ x^2+y^2=9 $ from any arbitrary point <i>'P</i>' on the line $ x+y=25 $. Locus of midpoint of chord <i>AB</i> is

Question 11 :
ABCD is a square with side a. With centres A, B, C and D four circles are drawn such that each circle touches externally two of the remaining three circles. Let $\delta$ be the area of the region in the interior of the square and exterior of the circles. Then the maximum value of $\delta$ is

Question 12 :
Let ABCD be a parallelogram such that AB = q , AB = p, and $\angle BAD $ be an acute angle. If r is the vector that coincides with the altitude directed from the vertex B to the side AD, then r is given by

Question 13 :
If $(3, -4)$ and $(-6, 5)$ are the extremities of a diagonal of a parallelogram and $(2, 1)$ is its third vertex , then its forth vertex is

Question 14 :
$T_{m} $denotes the number of Triangles that can be formed with the vertices of a regular polygon of $m$ sides. If $T_{m+1}-T_{m}=15, $then $m=$<br><br>

Question 15 :
If two sides of a parallelogram are $6$ and $8$ and one diagonal is $7$, what is the length of the other diagonal?