Unicus Non-Routine Mathematics Olympiad (UNRMO) Class 8 Sample Paper

Sample Paper
(2020-21)

Class 7 & 8
Unicus Non-Routine Mathematics Olympiad

Section – Class* Total Marks per
Total Marks
*Syllabus covered Questions Question
Classic Section – Class 7 & 8 10 3 30

Scholar Section – Class 7 & 8 10 6 60

Grand Total 20 90
Note: There will be negative marking of 1/3rd of the marks allotted for that question if the answer is incorrect.

1. Find the square root of x4 - 4x3 + 10x2 - 12x + 9
a) x2 + 2x + 3
b) x2 - 2x – 3
c) x2 - 2x + 3
d) x2 + 2x – 3

Correct Answer: c 3 Marks

2. When a number is divided by 25, its cube root is x. When it is multiplied with 5, then its
cube root is y. It x + y = 36 and the number is 5395 + a then a = _________.
a) 5400
b) 5100
c) 2100
d) 2400

Correct Answer: a 3 Marks

3. A beam of light shines from point S, reflects off a reflector at point P, and reaches point
T. Such that point is perpendicular to RS. Then x = ______

a) 32o
b) 37o
c) 45o
d) 38o

Correct Answer: a 3 Marks

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4. The ratio of the exterior angle of two regular polygons is 3 : 2 and the ratio of their
interior angle is 3 : 4 then the total no. of sides of both the polygons is
a) 8
b) 10
c) 12
d) 13

Correct Answer: b 3 Marks

5. Three carom board strikers of radius 3.5 cm are so arranged such that each strikers,
then the area of the empty space between the strikers is.
a) 10.5 m2
b) 38.5 m2
c) 1.967 cm2
d) 19.5 cm2

Correct Answer: c 3 Marks

6. In ∆ABC with an area (√3 – 1)/2; AB = √3 - 1, AC = 2, and ∠CAB is acute. What is the
measure of ∠ACB.
a) 15o
b) 18o
c) 20o
d) 225o

Correct Answer: a 3 Marks

7. If (a + b) : (a - b) is equal to the duplicate ratio of 3 : 1 then a : b is?
a) 17 : 11
b) 23 : 19
c) 5 :4
d) 2 : 5

Correct Answer: c 3 Marks

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8. If a commission of 10% is given on the written price of a article the gain is 20% . If the
commission is increased to 20% then the gain is.
a) 6 2⁄3 %
b) 7 1⁄4 %
c) 12 1⁄2 %
d) 13 1⁄3 %

Correct Answer: d 3 Marks

9. 2010√(2√7 - 3√3) . 4020√(55 + 12√21) =
a) -1
b) 1
c) 0
d) 2

Correct Answer: b 3 Marks

10. The simplest form of 1/(x + 1)2 (x + 2)2 - 1/(x + 1)2 + 2/(x + 1) - 2/(x + 2) is ______.
a) 1/(x + 2)2
b) 1/(x + 1)2
c) (x + 2)2
d) (x + 1)2

Correct Answer: a 3 Marks

11. The simplest form of
1 + a/(x - a) + bx/(x - a) (x - b) + cx2/(x - a) (x - b) (x - c) + dx3/(x - a) (x - b) (x - c) (x - d)
a) x4/(x - a) (x - b) (x - c) (x - d)
b) x4/(x - a) (x + b) (x + c) (x - d)
c) x4/(x - a) (x - b) (x + c) (x + d)
d) None of these

Correct Answer: a 6 Marks

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12. If 1/(21/3 + 2-1/3 )= c/d (22/3 + 2-2/3 -1) then the value of d/c = _______
a) 2/5
b) 5/2
c) 3/5
d) None of these

Correct Answer: b 6 Marks

13. A, B and C started the business with 6000/-, 8000/-, 4000/- respectively. After 4 months
A withdraws Rs. 1000/- where as B and C added 1000/- each to their investment. It the
end of the year they get a profit of 11,200/- then share of B is
a) 5,600/-
b) 5,000/-
c) 5,200/-
d) 5,800/-

Correct Answer: c 6 Marks

14. It the ratio of (1 + x + x2) : (1 - x + x2) is 13 (1 + x) : 14 (1 - x) then the value of x =
______
a) 1/3
b) 3
c) 2/3
d) 3/2

Correct Answer: a 6 Marks

5

15. In ∆ABC AB and AC are the equal sides of an isosceles triangle. ABC. In which an
equilateral triangle DEF is inscribed. Designate ∠BFD = a; ∠ADE = b, ∠FEC = c. then
the solution between a, b and c is

a) b = (a + c)/2
b) b = (a - c)/2
c) a = (b - c)/2
d) a = (b + c)/2

Correct Answer: d 6 Marks

16. It the number of square centimeters on the surface of a sphere is equal to the number
of cubic centimeters in its volume, what is the diameter of the sphere
a) 6 cm
b) 9 cm
c) 12 cm
d) 4cm

Correct Answer: a 6 Marks

6

17. AOB is a quarter circle of radius 10 and PQRO is a rectangle of perimeter 26. The
perimeter of the shaded region is

a) 7+5π
b) 17 + 5 π
c) 13 + 5 π
d) 19 + 5 π

Correct Answer: c 6 Marks

18. What is the sum of all the different solutions to the following equation
[(x2 + 1) (x4 + 1) (x6 + 1)/(x + 1)] + (x - 1) = 0
a) 4
b) 3
c) 2
d) 0

Correct Answer: d 6 Marks

19. The graphs of 2x + 3y - 6 = 0
4x - 3y - 6 = 0, x = 2, y = 2/3 intersect in:
a) 6 points
b) 1 point
c) 2 points
d) 0 points

Correct Answer: b 6 Marks

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20. The mean of n observations is 𝑥̅ . If the first term is increased by 1, second by 2 and so
on then the new mean is
a) 𝑥̅ + n
b) 𝑥̅ + n/2
c) 𝑥̅ + n + ½
d) None of these

Correct Answer: c 6 Marks

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