- olympiad@cscacademy.org
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
