- olympiad@cscacademy.org

- 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 = x ^{3} - 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) a^{2} + c^{2} = 0

(b) b^{2} + c^{2} = 0

(c) b^{2} + d^{2} = 0

(d) a^{2} + b^{2} = c^{2} + d^{2}