OPSC ASO PREVIOUS YEAR QUESTION PAPER : MATHEMATICS

Board Name: Odisha Public Service Commission (OPSC)

Post Name: Asst. Section Officer - 2012 - 13 
Subject : Mathematics
Time: 1 Hours

Total Questions: 50

Full Marks: 100

Each Question Carries: 2 Mark

Exam Year: 2015

OPSC ASO Exam Syllabus:-

SL. No.	Subject	Marks
1.	English	100
2.	Mathematics	100
3	Essay
	1. English within 350 words	025
	2. Odia within 350 words	025
4.	General Awareness	100
5.	Test of Reasoning/ Mental Ability	100
6.	Computer Application
	Theory	100
	2. Skill Test in Computer (practical)	50
	Total	600

OPSC Assistant Section Officer Previous Year Question Paper:

1. The decimal expansion of 23/  2³ x 5²  will terminate after :

1. One-decimal place
2. Two-decimal place
3. Three-decimal place
4. Four-decimal place
Ans: (3)



2. 3 + 2√5 is :

1. An irrational number
2. A rational number
3. Neither rational nor irrational number
4. Whole number
Ans: (1)



3. For a and b being co-prime, then a² and b² are :

1. May or may not be co-prime
2. Never co-prime
3. Always co-prime
4. None of the above
Ans: (3)



4. The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is :

1. 10
2. 252
3. 504
4. 2520
Ans: (4)



5. In Euclid's Division Lemma, a = bq + r, 0 ≤  r < b, the numbers 'a' and 'r' are the :

1. Divisor and Dividend
2. Dividend and Remainder
3. Quotient and Divisor
4. Remainder and Quotient
Ans: (2)



6. If 'a' and 'b' be two odd prime numbers, then (a² - b²) is :

1. An even prime
2. An odd prime
3. Prime
4. Composite
Ans: (4)



7. If two positive integers p and q can be expressed as p = ab² and  q = a³b, (a and b being prime numbers), then LCM (p, q) is :

1. a³b³
2. a²b²
3. a³b²
4. ab
Ans: (3)



8. A rational number (x = p / q) have a terminating decimal expansion if :

1. The prime factorization of q is not of the form 2ⁿ . 5^m, where n and m are non-negative integers
2. The prime factorization of q is not of the form 2ⁿ . 5^m, where n and m are integers
3. The prime factorization of q is of the form 2ⁿ . 5^m, where n and m are non-negative integers
4. The prime factorization of q is of the form 2ⁿ . 5^m, where n and m are integers
Ans: (3)





9. A rational number of 1.1666.. in the simplest form is :

1. 10/9
2. 100/99
3. 115/99
4. 116/99
Ans: (3)



10. The highest power of the variable in a polynomial is called its :

1. Solution
2. Zero
3. Degree
4. None of the above
Ans: (3)



11. If ∝ and β are zeroes of a quadratic polynomial ax² + bx + c, then ∝ + β is equal to :

1. b/a
2. -b/a
3. a/b
4. -a/b
Ans: (2)



12. If a zero of the quadratic polynomial x² + 3x + k is 2, then the value of k is :

1. 5
2. -5
3. 10
4. -10
Ans: (4)



13. If ∝, β and 𝛾 are the zeroes of a cubic polynomial ax³ +bx² + cx + d, then  ∝β𝛾 is equal to :

1. -b/a
2. -d/a
3. -a/b
4. -a/d
Ans: (2)



14. If one of the zeroes of the cubic polynomial x³ + ax² + bx + c is -1, then the product of the other two zeroes is :

1. a - b + 1
2. a - b - 1
3. b - a + 1
4. b - a - 1
Ans: (3)



15. If one of the zeroes of the quadratic polynomial (k - 1) x² + kx + 1 is -3, then the value of k is :

1. 2/3
2. -2/3
3. -4/3
4. 4/3
Ans: (4)



16. If an n^th degree polynomial is divided by m^th  degree polynomial, then the possible degree of the quotient is :

1. m - n
2. m + n
3. mn
4. n - m
Ans: (4)



17. If ∝ and β are the zeroes of a quadratic polynomial x² + x - 2 then the value of (1/∝ - 1/β) is :

1. 2/3 or -2/3
2. 3/2 or -3/2
3. 5/3 or -5/3
4. 3/5 or -3/5
Ans: (2)



18. The system of linear equations kx + y + 1 = 0 and x + ky + 2 = 0 has unique solution if :

1. k = -1
2. k = 1
3. k = 2
4. None of the above
Ans: (3)





19. Which of the following will have no solution ?

1. A system of consistent equations
2. A system of inconsistent equations
3. A system of dependent equations
4. All of the above
Ans: (2)



20. The value of c, for which the pair of equations cx - y = 2 and 6x - 2y - 4= 0 will have infinitely many solution, is : 

1. 3
2. -3
3. -12
4. 12
Ans: (1)



21. In a cyclic quadrilateral PQRS, ∠P = (2x + 4)^o , ∠Q = (y + 3)^o , ∠R = (2y + 10)^o ,  ∠S = (4x + 5)^o . Then :

1. ∠P = 70o , ∠Q = 53o , ∠R = 110o , ∠S = 127o
2. ∠P = 70o , ∠Q = 55o , ∠R = 110o , ∠S = 125o
3. ∠P = 65o , ∠Q = 53o , ∠R = 115o , ∠S = 127o
4. ∠P = 65o , ∠Q = 55o , ∠R = 113o , ∠S = 127o
Ans: (1)



22. The quadratic equation ax² + bx + c = 0 will have real and distinct roots if :

1. b²  - 4ac < 0
2. b²  - 4ac > 0
3. b²  - 4ac = 0
4. All of the above
Ans: (2)



23. The 5th term of an A. P. is 1 and the 11th term is -17. Which term of the A. P. is -77 ?

1. 22^nd
2. 31^st
3. 44^th
4. None of the above
Ans: (2)



24. Which of the following are in A. P. ?

1. 2a - b, 2a, a + b, .....
2. a - b, a, a + b, .....
3. a - 2b, b, a + 2b, .....
4. a - b, 2a, a + b, .....
Ans: (2)



25. For what value of n are the n^th terms of two A. P.'s 63, 65, 67, ..... and 3, 10, 17, ....... equal ?

1. 11
2. 12
3. 13
4. 14
Ans: (3)



26. In an A. P., the first term is 22,  n^th term is -11 and sum of first n terms is 66. Then the common difference d is :

1. -1
2. -2
3. -3
4. -4
Ans: (3)



27. A steel wire is in the form of a square. The same wire is bent in the form of a circle. Which of the following is correct ?

1. Area of the square = Area of the circle
2. Area of the square is less than the area of the circle
3. Area of the square is more than the area of the circle
4. None of the above
Ans: (2)



28. A steel wire is in the form of a circle of radius 28 cm. It is bent in the form of a square. The length of the side of the square is :             (take 𝜋 = 22/7)

1. 44 cm
2. 11 cm
3. 28 cm
4. None of the above
Ans: (1)



29. The perimeter of semi-circle of radius r unit is :

1. 𝜋r + r
2. 𝜋r + 2r
3. 2𝜋r + r
4. 2𝜋r + 2r
Ans: (2)



30. If an arc of a circle makes an angle 𝛳 < 180^o at the centre of a circle of radius r, then the length of the arc is :

1. 2𝜋r𝛳 / 360^o  
2. 𝜋r²𝛳 / 360^o  
3. 1/2 r² sin 𝛳 
4. None of the above



Ans: (1)



31. Area of the largest triangle that can be inscribed in a semi-circle of radius r unit is :

1. 1/2 r² sq. unit
2. r² sq. unit
3. 2r² sq. unit
4. √2r² sq. unit
Ans: (2)



32. If r₁ and r₂ be radii of the two bases of a frustum of a cone of height 'h' and 'ℓ' be its slant height, then its volume is :

Ans: (3)



33. A cylindrical pencil sharpened at one edge is a combination of : 

1. A hemisphere and a cylinder
2. A cone and a cylinder
3. A frustum of a cone and a cylinder
4. Two cylinders
Ans: (2)



34. A shuttle cock used for playing badminton has the shape, the combination of :

1. A sphere and a cone
2. A cylinder and a sphere
3. A frustum of a cone and a hemisphere
4. A cylinder and a hemisphere
Ans: (3)



35. In a circular cone, the cross-section made by a plane parallel to the base is a :

1. Frustum of a cone
2. Sphere
3. Circle
4. Hemisphere
Ans: (3)



36. The length of the side of largest cube that can be inscribed in a sphere of diameter 'd' is :

1. 3d
2. d / √3
3. d / √2
4. 2d
Ans: (2)



37. How many spherical lead shots each having diameter 3 cm can be made from a cuboidal solid of dimensions 9 cm x 11 cm x 12 cm ?     (take 𝜋 = 22/7)

1. 81
2. 82
3. 83
4. 84
Ans: (4)



38. If the mean of the distribution is 2.6 then the value of p is :

1. 1
2. 3
3. 7
4. 6
Ans: (1)





39. Which of the following is not a measure of central tendency ?

1. Standard deviation
2. Median
3. Mean
4. Mode
Ans: (1)



40. The cumulative frequency test is useful in finding the :

1. Mean
2. Mode
3. Median
4. None of the above
Ans: (3)

1. Mean
2. Mode
3. Median
4. All of the above
Ans: (1)



42. Find the mode of the data :

1. 24.25
2. 25.25
3. 26.25
4. 27.25
Ans: (3)



43. Which of the following cannot be the probability of an event ?

1. 2/3
2. - 1.5
3. 15%
4. 0.7
Ans: (2)



44. For an event if 'p' be the probability of the happening of the event and 'q' be the probability of not happening the event, then which one of the following is true ?

1. p is always greater than q
2. p + q = 1
3. p is always less than q
4. p + q = 0
Ans: (2)



45. When a die is thrown, the probability of getting an odd number less than 5 is :

1. 1/2
2. 1/3
3. 2/3
4. 1/6
Ans: (2)



46. A letter is chosen at random from English alphabet. Then the probability that the letter chosen precedes 'g' is :

1. 1/26
2. 3/13
3. 5/26
4. 7/26
Ans: (2)



47. What is the probability that two different friends have different birthdays ? (Ignoring leap year)

1. 1/365
2. 2/365
3. 364/365
4. 1
Ans: (3)



48. A box contains 3 blue, 2 white and 4 red marbles. If a marble is drawn at random from the box, what is the probability that it will not be a white marble ?

1. 2/9
2. 7/9
3. 3/9
4. 4/9
Ans: (2)



49. Two dice are thrown at the same time. What is the probability of getting different numbers on the dice ?

1. 1/36
2. 1/6
3. 5/6
4. 35/36
Ans: (3)



50. From a group of 2 boys and 3 girls, two children are selected at random. Then the probability, such that at least one boy is selected, is :

1. 1/5
2. 3/5
3. 7/10
4. 3/10
Ans: (3)

For Mathematics it will be best practice if you starts preparation with specific Mathematics books rather than All in one Single books:-
Below mentioned books are some of those (Last one is very practical)