Question : ABCD is a trapezium with AD and BC parallel sides and E is a point on BC. The ratio of the area of ABCD to that of AED is:

Option 1: $\mathrm{\frac{AD}{BC}}$

Option 2: $\mathrm{\frac{BE}{EC}}$

Option 3: $\mathrm{\frac{AD+BE}{AD+CE}}$

Option 4: $\mathrm{\frac{AD+BC}{AD }}$

Question : Diagonals of a trapezium $ABCD$ with $AB \parallel CD$ intersect each other at the point $O$. If $AB = 2CD$, then the ratio of the areas of $\triangle AOB$ and $\triangle COD$ is:

Option 1: $4:1$

Option 2: $1:16$

Option 3: $1:4$

Option 4: $16:1$

Question : ABCD is a quadrilateral in which BD and AC are diagonals. Then, which of the following is true:

Option 1: AB + BC + CD + DA < (AC + BD)

Option 2: AB + BC + CD + DA > (AC + BD)

Option 3: AB + BC + CD + DA = (AC + BD)

Option 4: AB + BC + CD + DA > 2(AC + BD)

Question : If $\frac {x^2+3x+1}{x^2–3x+1}=\frac{1}{2 }$, then the value of $(x+\frac{1}{x})$ is:

Option 1: 9

Option 2: –9

Option 3: 1

Option 4: 2

Question : In a square ABCD, diagonals AC and BD intersect at O. The angle bisector of $\angle CAB$ meets BD and BC at F and G, respectively. OF : CG is equal to:

Option 1: $1 : 2$

Option 2: $1 : 3$

Option 3: $1: \sqrt{2}$

Option 4: $1: \sqrt{3}$