(Paper) IIT UCEED Previous Year Question Paper - 2016

: Section A: Numerical :

1. A pyramid with a base side 6 cm and height 7 cm is merged with a cube of length 5 cm such that the centroid of the cube matches with the centre of the base of the pyramid. The base of the pyramid is parallel to the base of the cube and the edges of the base of the pyramid are parallel to the sides of the cube. Count the number surfaces in the resulting solid.

2. How many different types of symbols appear in the figure given below?

3. The numbers in the hexagon groups are arranged in a particular order. Find the number which would replace the question mark.

4. What is the maximum number of equilateral triangles of side 3 cm that can be fitted in a large equilateral triangle with length 11.2 cm?

5. The figure given below is to be cloned twice. The first clone on the right is to be reflected across the OP axis. The second clone on the left is to be reflected across the MN axis. The resultant figure is then to be cloned and reflected across the QR axis. Count the number of triangles in the final figure.

6. A company account book reveals the following figures:

Calculate the Operating Profit Ratio of the company.

7. How many different ways are there to get from Tile A to Tile I without visiting a tile more than once, if only horizontal and vertical movements are allowed?

8. There are some men and some women in a group. Each person shakes hands with exactly one other person in the entire group. After this round of handshakes, eight men and four women find that they shook hands with someone of the same sex. The total number of handshakes exchanged in the entire group is 87. At most how many women can there possibly be in this group?

9. It is 12 o’clock, and the hour and minute hands are aligned exactly one over the other. Both hands move continuously. After how many minutes will they meet again?

10. At most how many spheres of the same size can be placed around a same size sphere at the centre so that they all simultaneously touch the sphere at the centre?