Shine Mathematics Olympiad is designed for grades 6th to 12th by Graposs Connect for Shine Olympiad. Mathematics as a discipline builds mental rigor in students and is also the foundation of academia. Mathematical literacy promotes understanding of other school subjects and also encourages quantitative reasoning and spatial ability.
SMO Shine Mathematics Olympiad Exam Sample Question Paper
SMO Class 6 Sample Questions
Q.1 Which of the following are not twin primes? a. 3, 5 b. 11,13 c. 5,7 d. 17,23
Q.2 If the HCF of two numbers is 16 and their product is 3072 then their LCM is: a. 182 b. 192 c. 12 d. None of these
Q.3 Choose the incorrect option: a. -8 < 8 b. 0 < – 12 c. -15 < – 5 d. -386 < 308
Q.4 The value of 0.008 × 0.01 × 0.072 ÷ (0.12 × 0.0004) is- a. 1.2 b. 0.12 c. 0.012 d. 1.02
Q.5 What is the largest 5-digit number with distinct digit? a. 99999 b. 90009 c. 98765 d. 98009
Q.6 On a particular day the temperature of Delhi at 10.00 am was 13° C but by the midnight, it fell down to 6° C. The temperature of Mumbai at 10 am the same day was 18° C but fell down to 10° C by mid night. Which fall is greater? a. Delhi b. both are same c. Mumbai d. None of the above
SMO Class 7 Sample Questions
Q.1 The literal coefficient of -9xyz2 is a. -9 b. xyz c. xyz2 d. -9xy
Q.2 a(b-c)+b(c-a)+c(a-b) is equal to a. ab+bc+ca b. 0 c. 2(ab+bc+ca) d. none of these
Q.3 Area of a triangle is 30 cm2. If its base is 10 cm, then its height is a. 5 cm b. 6 cm c. 7 cm d. 8 cm
Q.4 If P and Q are any two points on a circle, then the line segment PQ is called a a. radius of the circle b. diameter of the circle c. chord of the circle d. secant of the circle
Q.5 If each edge of a cube is increased by 40% the percentage increase in its surface area is__ a. 40 b. 60 c. 80 d. 96
Q.6 The sum of the squares of 3 consecutive positive numbers is 365. The sum of the numbers is a. 30 b. 33 c. 36 d. 45
SMO Class 8 Sample Questions
Q.1 A number when divided by 6 leaves remainder 3. When the square of the same number is divided by 6, the remainder is- a. 0 b. 2 c. 1 d. 3
Q.2 If 21 is added to a number, it becomes 7 less than thrice of the number. Then, the number is- a. 14 b. 16 c. 18 d. 19
Q.3 The sum of the squares of 3 consecutive positive numbers is 365. The sum of the numbers is: a. 30 b. 33 c. 36 d. 45
Q.4 The sum of a two digit number and the number obtained by reversing its digits is a square number. How many such numbers are there ? a. 5 b. 6 c. 7 d. 8
Q.5 If 5 is added to twice of a number it becomes 6, then the number is: a. 0.5 b. 5 c. 0.25 d. None of these
Q.6 Mohan gets 3 marks for each correct sum and loses 2 marks for each wrong sum. He attempts 30 sums and obtains 40 marks. The number of sums solved correctly is- a. 25 b. 10 c. 15 d. 20
SMO Class 9 Sample Questions
Q.1- The sum of the squares of 3 consecutive positive numbers is 365. The sum of the numbers is: a. 30 b. 33 c. 36 d. 45
Q.2- Which of the following numbers should be added to 11158 to make it exactly divisible by 77? a. 9 b. 8 c. 6 d. 7
Q.3- If the number formed by the last two digits of a three digit integer is an integral multiple of 6% the original integer itself will always be divisible by: a. 6 b. 3 c. 2 d. 12
Q.4- The sum of two numbers is 2490 and if 6.5% of one number is equal to 8.5% of the other, then numbers are- a. 1414, 1076 b. 1411, 1079 c. 1412, 1078 d. None of these
Q.5- If 45% of a number is added to the another number, the first number becomes 135 times of the another number. What is the ratio of these two numbers? a. 8:7 b. 3:2 c. 7:8 d. None of these
Q.6- The sum of all prime numbers between 30 and 42 is: a. 103 b. 109 c. 105 d. 104
SMO Class 10 Sample Questions
Q.1- Pick the odd one out. a. 22, 16, 10, 4, … b. -5, -3, -1, 1, … c. -3, 3, -3, 3, 3, … d. 3, 1, -1, -3, …
Q.2- If cos4A-sin4A = x, then value of x is a. cos2A-1 b. 2cos2A-1 c. 2cos2A+1 d. cos2A+1
Q.3- Two events A and B have probabilities 0.25 and 0.50, respectively. The probability that both A and B occur simultaneously is 0.12. Then, the probability that neither A nor B occurs is: a. 0.13 b. 0.38 c. 0.63 d. 0.37
Q.4- Three numbers which are co prime to each other are such that the product of the first two numbers is 42 and the product of the last two numbers is 78. Then, the sum of all the three numbers is: a. 25 b. 32 c. 26 d. 13
Q.5- The greatest number which on dividing 1659 and 2036 leaves remainders 8 and 4, respectively is: a. 124 b. 129 c. 127 d. 305
Q.6- Reflection of the point (2, -7) in the y-axis is: a. (2, 7) b. (-2, -7) c. (-7, 2) d. (7, -2)
SMO Class 11 Sample Questions
Q.1- Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second set. The values of m and n are, respectively, a. 4, 7 b. 7, 4 c. 4, 4 d. 7, 7
Q.2- Let F1 be the set of parallelograms, F2 the set of rectangles, F3 the set of rhombuses, F4 the set of squares and F5 the set of trapeziums in a plane. Then F1 may be equal to: a. F2 ∩ F3 b. F3 ∩ F4 c. F2 ∪ F5 d. F2 ∪ F3 ∪ F4 ∪ F1
Q.3- The domain and range of the function f given by f(x) = 2 – |x – 5| is: a. Domain = R+, Range = (-∞, 1] b. Domain = R, Range = (-∞, 2] c. Domain = R, Range = (-∞, 2) d. Domain = R+, Range = (-∞, 2]
Q.4- Let x, y ∈ R, then x + iy is a non real complex number if: a. x = 0 b. y = 0 c. x ≠ 0 d. x ≠ 0
Q.5- If the sum of n terms of an A.P. is given by S = 3n + 2n2, then the common difference of the A.P. is: a. 3 b. 2 c. 6 d. 4
Q.6- lf f(x) = ax + b, where a and b are integers, f(-1) = -5 and f(3) = 3, then a and b are equal to a. a = -3, b = -1 b. a = 2, b = -3 c. a = 0, b = 2 d. a = 2, b = 3
SMO Class 12 Sample Questions
Q.1- Consider the non-empty set consisting of children in a family and a relation R defined as aRb if a is brother of b. Then R is: a. symmetric but not transitive b. transitive but not symmetric c. neither symmetric nor transitive d. both symmetric and transitive
Q.2- The points at which the tangents to the curve y = x3 – I2x + 18 are parallel to X-axis are: a. (2, -2), (-2, -34) b. (2, 34), (-2, 0) c. (0, 34), (-2, 0) d. (2, 2), (-2, 34)
Q.3- The maximum number of equivalence relations on the set A = {1,2, 3} are: a. 1 b. 2 c. 3 d. 5
Q.4- Total number of possible matrices of order 3 × 3 with each entry 2 or 0 is: a. 9 b. 27 c. 81 d. 512
Q.5- If A and B are matrices of same order, then (AB’-BA’) is a: a. skew symmetric matrix b. null matrix c. symmetric matrix d. unit matrix
Q.6- The function f(x) = tanx –x a. always increases b. always decreases c. never increases d. sometimes increases and sometimes decreases.
