- olympiad@cscacademy.org

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

**Section-1-Mathematical Thinking:**

**Q.1****- 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.2**- **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.3**- **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.4- ****If cos ^{4}A-sin^{4}A = x, then value of x is**

(a) cos^{2}A-1

(b) 2cos^{2}A-1

(c) 2cos^{2}A+1

(d) cos^{2}A+1

**Q.5**- **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

** **

**Section-****2****-** **Application Mathematics:**

**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)

**Q.7- ****What is the equation of the line passing through the point (-1, -3) and having x-intercept of 4 units?**

(a) 3x-5y = 12

(b) 3x+5y = 12

(c) 3x+5y = -12

(d) 3x-5y = -12

**Q.8**- **P and Q are the centres of two circles whose radii are 5 cm and 11 cm, respectively. If the direct common tangent to the circles meets PQ in M . Then, M divides PQ in the ratio:**

(a) 5:11 internally

(b) 11:5 internally

(c) 5:11 externally

(d) 11:5 externally

**Q.9- ****If the circumference of two circles is same, then their area will be:**

(a) unequal

(b) equal

(c) not related

(d) Can’t be determined

**Q.10- ****A farmer has three silos. The largest silo has a diameter of 18 ft. The radius of the smallest silo is one-third as big as the diameter of the largest. If the middle-sized has a radius that is 1 ft greater than the radius of the smallest silo, then, the area of the mid-sized silo is:**

(a) 154 sq ft

(b) 132 sq ft

(c) 101 sq ft

(d) 99 sq ft

**Section-****3****- Logical Thinking: **

**Q.11****- Which one set of letters when sequentially placed at the gaps in the given letter series shall complete it?**

**h_ t_ l_ tt_ lht_ m_ htt_ l**

(a) mmhtltm

(b) hmmttlm

(c) tmhmtlm

(d) Imtmhmt

**Q.12**- **A and B are a married couple. C and D are brothers. C is the brother of A. How is D related to B?**

(a) Brother-in-law

(b) Brother

(c) Son-in-law

(d) Cousin

**Q.13- ****A girl leaves from her home. She first walks 30 m in North-West direction and then 30 m in South-West direction. Next, she walks 30 m in South-East direction. Finally, she turns towards her house. In which direction is she moving?**

(a) North-East

(b) North-West

(c) South-East

(d) South-West

**Section-****4****- High Order Thinking (HOT)**

**Instruction: Assertion (A): The graphical representation of x+3y-6 = 0 and 2x+6y-48 = 0 will have a pair of parallel lines.**

**Reason (R): Let x+bxy+cx = 0 and a2x+b2y+c2 = 0 be pair of lines which are parallel, then they do not have any solution.**

**Q.14- ****Which of the following is true?**

(a) Both (A) and (R) are true and (R) is the correct explanation of (A)

(b) Both (A) and (R) are true but (R) is not the correct explanation of (A)

(c) (A) is true and (R) is false

(d) (A) is false and (R) is true

**Q.15- ****Chord AB of a circle when extended meets the tangent to the circle at point P. PT is the tangent touching the circle at point T. If lengths of PT and PB are 6 cm and 4 cm respectively, what is the length of PA?**

(a) 12 cm

(b) 18 cm

(c) 27 cm

(d) 9 cm