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UCEED 2021

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Q5.The corners of the green and red triangles coincide with the centres of the circles. All the circles have equal diameters and adjacent circles touch each other. If the area of the green triangle is 3.14, what is the area of the red triangle?

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Q7.In the container given below of dimensions (40 cm X 20 cm X 20 cm), four objects are dipped in water. Objects P and Q are made of some light material while objects R and S are made of iron and copper, respectively. The object P is a cube of edge 4 cm with 1/10th floating above water; object Q displaces 50 cc of water while floating. The volumes of objects R and S are 295.4 cc and 397 cc, respectively. If all the objects are removed from the container, what would be the new water level inside the container measured from the bottom?

UCEED2021Q6·nat·Medium142 attempts

A Street has 13 houses in a row as shown in the figure. Some residents in the first house tested positive for COVID-19. The virus spreads in two ways: it can spread to the next house, or jump directly to the third house. Residents of house number 2 can get infection in only one way, the house number 3 in two ways, the house number 4 in 3 ways, the house number 5 in 5 ways and so on. If the virus only progresses from Left to Right direction, in how many ways can the residents of the house number 13 get infected?

Keyboards off — use the numpad, just like on exam day.