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# Unicus Mathematics Olympiad (UMO) Sample Papers 2020-21 : unicusolympiads.com

Organisation : Unicus Olympiads
Exam Name : Unicus Mathematics Olympiad (UMO)
Document Type : Sample Papers
Year : 2020-21

Contents :

## Unicus Olympiads Sample Papers

The sample papers for all the subjects in Unicus Olympiads are designed by a team of experts.

Related / Similar Sample Paper : Unicus English Olympiad Sample Papers 2020-21

The aim of Unicus sample papers is to give the students a familiarity with the syllabus covered. Also, it will tell the pattern followed and the marking scheme which can help the students prepare nicely for the exam.

## UMO Sample Papers

1. The production of computers in a company increases uniformly by a fixed number every year, it produced 8000 computers in 6th year & 1300 in 9th year find the production in 8th year.
a) 11,500
b) 9,800
c) 8,520
d) 10,200

2. Consider the following points:
I (0, 5)
II. (2, -1)
III. (3, -4)

which of the above lie on the line 3x + y = 5 and at a distance of v10 from point (1, 2)?

a) Only I
b) Only II
c) I and II d) I, II and III

3. In the family of four members, 20 years ago the average age of them was 60 years. Two children were born in this span of 20 years. But the present average age of the family remains the same. Among the two children who were born during the 20 years, if the older child at present is 8 years older than the younger one, what is the ratio of the present age of the older child to the present age of the younger child?

a) 4: 3
b) 7: 3
c) 3: 2
d) 7: 4

4. There are two points A and B indicated on a wall. Point A is at a height of 2 m above the ground and point B is 4 m vertically above point A. At a certain instant, the angles of elevation of a kite from these points are observed to be 60 and 30, respectively. Find the height of the kite above the ground:
a) 2 m
b) 4 m
c) 8 m
d) 16 m

5. Look at the statements given below:
I. The quadrilateral formed by joining the mid-points of the sides of a quadrilateral, taken in order, is parallelogram.
II. The line drawn through the mid-point of one side of a triangle, parallel to another side, intersects the third side at its mid-points.
III. If two chords of a circle are equal, then their corresponding arcs are congruent and conversely, if two arcs are congruent, then their corresponding chords are equal.
IV. Sector is the region between the chord and its corresponding arc.

a) Only I and III
b) Only I and IV
c) I, II, III and IV
d) Only I, II and III

6.On the occasion of Holi, Anvi bought chocolates and gave one-third to her classmates and thrice the square root of the chocolates to her siblings. Still, she has 27 chocolates. Find the total number of chocolates purchased by Anvi:

a) 81
b) 98
c) 112
d) 144

7. In the beginning, A works at the rate such that he can finish a piece of work in 24 hours, but he only works at this rate for 16 hours. After that, he works at a rate such that he can do the whole work in 18 hours. If A is to finish the work at a stretch, how many hours will he take to finish this work?

a) 12 hours
b) 22 hours
c) 26 hours
d) 18 hours