| LIST I | LIST II | ||
| A. | No. of triangles formed using 5 points in a line and 3 points on parallel line is | I. | 20 |
| B. | No. of diagonals drawn using the vertices of an octagon | II. | 10 |
| C. | The no. of diagonals in a regular polygon of 100 sides is | III. | 45 |
| D. | A polygon with 35 diagonals has sides | IV. | 4850 |
In the adjoining figure, \( \triangle CAB \) is a right triangle, right angled at A and \( AD \perp BC \). Prove that \( \triangle ADB \sim \triangle CDA \). Further, if \( BC = 10 \text{ cm} \) and \( CD = 2 \text{ cm} \), find the length of } \( AD \).
If a line drawn parallel to one side of a triangle intersecting the other two sides in distinct points divides the two sides in the same ratio, then it is parallel to the third side. State and prove the converse of the above statement.
In the adjoining figure, \( AP = 1 \, \text{cm}, \ BP = 2 \, \text{cm}, \ AQ = 1.5 \, \text{cm}, \ AC = 4.5 \, \text{cm} \) Prove that \( \triangle APQ \sim \triangle ABC \).
Hence, find the length of \( PQ \), if \( BC = 3.6 \, \text{cm} \).
Find the next two terms of the series:
The given series is: \( A, C, F, J, ? \).
(A) O
(B) U
(C) R
(D) V
Choose the correct answer from the options given below: