Class-12th (Mathematics) Olympiad - CANMO

Mock Instructions

  • 1. This is Model Question Paper.
  • 2. This is an Online Worksheet.
  • 3. Total Questions-50.
  • 4. Total Time-60 minutes.

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 maximum number of equivalence relations on the set A = {1,2, 3} are:

(a) 1

(b) 2

(c) 3

(d) 5

Q.3- 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.4- 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.5- 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.6- The function f(x) = tanx –x

(a) always increases

(b) always decreases

(c) never increases

(d) sometimes increases and sometimes decreases.

Q.7-  The area of the quadrilateral ABCD, where A(0,4,1), B (2, 3, -1), C(4, 5, 0) and D (2, 6,2), is equal to:

(a) 9 sq. units

(b) 18 sq. units

(c) 27 sq. units

(d) 81 sq. units

Q.8-  The locus represented by xy + yz = 0 is:

(a) A pair of perpendicular lines

(b) A pair of parallel lines

(c) A pair of parallel planes

(d) A pair of perpendicular planes

Q.9- Find the equation of a plane which bisects perpendicularly the line joining the points A (2, 3, 4) and B (4, 5, 8) at right angles.

(a) x + 2y + 2z = 15

(b) x + 3y + 2z = 17

(c) x + y + 2z = 19

(d) 3x + y + 4z = 20

Q.10- If the line drawn from the point (-2, -1, -3) meets a plane at right angle at the point (1, -3, 3), find the equation of the plane.

(a) x - 2y + 6z – 27 = 0

(b) 3x - 2y + 6z – 27 = 0

(c) 4x - 2y + 5z – 25 = 0

(d) 3x - 2y + 6z – 30 = 0

Q.11-   If two events are independent, then:

(a) they must be mutually exclusive

(b) the sum of their probabilities must be equal to 1

(c) (a) and (b) both are correct

(d) None of the above is correct

Q.12-  Three persons, A, B and C, fire at a target in turn, starting with A. Their probability of hitting the target are 0.4,0.3 and 0.2 respectively. The probability of two hits is:

(a) 0.024

(b) 0.188

(c) 0.336

(d) 0.452

Q.13-  If A and B are two matrices of the order 3 × m and 3 × n, respectively, and m = n, then the order of matrix (5A - 2B) is:

(a) m × 3

(b) 3 × 3

(c) m × n

(d) 3 × n

Q.14- A kite is moving horizontally at a height of 151.5 meters. If the speed of kite is 10 m/s, how fast is the string being let out; when the kite is 250 m away from the boy who is flying the kite? The height of boy is 1.5 m.

(a) 8m/s

(b) 6m/s

(c) 7m/s

(d) 9m/s

Q.15- If a + ib = c + id, then:

(a) a2 + c2 = 0

(b) b2 + c2 = 0

(c) b2 + d2 = 0

(d) a2 + b2 = c2 + d2