A house of cards or card …

A house of cards or card castle is a structure created by stacking playing cards on top of each other, often in shape of pyramid. To build a tower of cards 2 cards are placed against each other in an upside down position forming a triangular shape. Another triangle next to it and so on. Same process is repeated in next row and so on. A man formed such a house of cards with 41 such triangular shape as base, 39 in the next, 37 in next and so on. He made 16 such rows in this manner one above another. (a) Number of triangles in the top row is (i) 10 (ii) 11 (iii) 12 (iv) 9 (b) Difference of number of triangles in the 8th and 13th row from bottom is (i) 10 (ii) 12 (iii) 15 (iv) 20 (c) The number of triangles in the 11th row from the bottom is (i) 10 (ii) 20 (iii) 21 (iv) 25 (d) Number of deck of cards each having 52 playing cards used by him if total cards he used was 832 is (i) 5 (ii) 6 (iii) 8 (iv) 16 (e) The number of triangles in the 4th row from the top is (i) 15 (ii) 16 (iii) 17 (iv) 18

(A + B )²

sin60° cos 30°+ cos60° sin 30°

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Is it possible to design a rectangular mango Grove whose length is twice it's breadth, and the area is 800m²? If so, find it's length and breadth

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