- 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**- **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- 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

**Q.4- 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.5- Let x, y ∈ R, then x + iy is a non real complex number if:**

(a) x = 0

(b) y = 0

(c) x ≠ 0

(d) y ≠ 0

**Q.6-** 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.7**- **Let S _{n} denote the sum of the first n terms of an A.P. If S_{2n} = 3S_{n} then S_{3n} : S_{n} is equal to:**

(a) 4

(b) 6

(c) 8

(d) 10

**Q.8- The equation of the straight line passing through the point (3,2) and perpendicular to the line y = x is:**

(a) x - y = 5

(b) x + y = 5

(c) x + y = 1

(d) x – y = 1

**Q.9-** If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes is (3, 2), then the equation of the line will be:

(a) 2x + 3y = 12

(b) 3x + 2y = 12

(c) 4x - 3y = 6

(d) 5x - 2y = 10

**Q.10- Equation of a circle which passes through (3, 6) and touches the axes is:**

(a) x^{2} + y^{2} + 6x + 6y + 3 = 0

(b) x^{2} + y^{2} - 6x - 6y - 9 = 0

(c) x^{2} + y^{2} - 6x - 6y + 9 = 0

(d) none of these

**Q.11- If the vertex of the parabola is the point (-3, 0) and the directrix is the line x + 5 = 0, then its equation is:**

(a) y^{2} = 8 (x + 3)

(b) y^{2} = 8 (y + 3)

(c) y^{2} = -8 (x + 3)

(d) y^{2} = 8 (x + 5)

**Q.12- The negation of the statement**

“72 is divisible by 2 and 3” is:

(a) 72 is not divisible by 2 or 72 is not divisible by 3.

(b) 72 is not divisible by 2 and 72 is not divisible by 3.

(c) 72 is divisible by 2 and 72 is not divisible by 3.

(d) 72 is not divisible by 2 and 72 is divisible by 3.

**Q.13- The converse of the statement:**

**“If x > y, then x + a > y + a” is:**

(a) If x < y, then x + a < y + a.

(b) If x + a > y + a, then x > y.

(c) If x < y, then x + a > y + a.

(d) If x > y, then x + a < y + a.

**Q.14- 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.15- The number of ways in which we can choose a committee from four men and six women so that the committee includes at least two men and exactly twice as many women as men is:**

(a) 94

(b) 126

(c) 128

(d) None