Board Name: Odisha Public Service Commission (OPSC)
Post Name: Asst. Section Officer - 2012 - 13
Subject : Mathematics
Time: 1 Hours
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
|
|
|
100
|
|
2. Skill Test in
Computer (practical)
|
50
|
|
Total
|
600
|
OPSC Assistant Section Officer Previous Year Question Paper:
The decimal expansion of 23/ 23 x 52 will terminate after :
- One-decimal place
- Two-decimal place
- Three-decimal place
- Four-decimal place
3 + 2√5 is :
- An irrational number
- A rational number
- Neither rational nor irrational number
- Whole number
For a and b being co-prime, then a2 and b2 are :
- May or may not be co-prime
- Never co-prime
- Always co-prime
- None of the above
The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is :
- 10
- 252
- 504
- 2520
In Euclid's Division Lemma, a = bq + r, 0 ≤ r < b, the numbers 'a' and 'r' are the :
- Divisor and Dividend
- Dividend and Remainder
- Quotient and Divisor
- Remainder and Quotient
If 'a' and 'b' be two odd prime numbers, then (a2 - b2) is :
- An even prime
- An odd prime
- Prime
- Composite
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 :
- a3b3
- a2b2
- a3b2
- ab
A rational number (x = p / q) have a terminating decimal expansion if :
- The prime factorization of q is not of the form 2n . 5m, where n and m are non-negative integers
- The prime factorization of q is not of the form 2n . 5m, where n and m are integers
- The prime factorization of q is of the form 2n . 5m, where n and m are non-negative integers
- The prime factorization of q is of the form 2n . 5m, where n and m are integers
A rational number of 1.1666.. in the simplest form is :
- 10/9
- 100/99
- 115/99
- 116/99
The highest power of the variable in a polynomial is called its :
- Solution
- Zero
- Degree
- None of the above
If ∝ and β are zeroes of a quadratic polynomial ax2 + bx + c, then ∝ + β is equal to :
- b/a
- -b/a
- a/b
- -a/b
If a zero of the quadratic polynomial x2 + 3x + k is 2, then the value of k is :
- 5
- -5
- 10
- -10
If ∝, β and 𝛾 are the zeroes of a cubic polynomial ax3 +bx2 + cx + d, then ∝β𝛾 is equal to :
- -b/a
- -d/a
- -a/b
- -a/d
If one of the zeroes of the cubic polynomial x3 + ax2 + bx + c is -1, then the product of the other two zeroes is :
- a - b + 1
- a - b - 1
- b - a + 1
- b - a - 1
If one of the zeroes of the quadratic polynomial (k - 1) x2 + kx + 1 is -3, then the value of k is :
- 2/3
- -2/3
- -4/3
- 4/3
If an nth degree polynomial is divided by mth degree polynomial, then the possible degree of the quotient is :
- m - n
- m + n
- mn
- n - m
If ∝ and β are the zeroes of a quadratic polynomial x2 + x - 2 then the value of (1/∝ - 1/β) is :
- 2/3 or -2/3
- 3/2 or -3/2
- 5/3 or -5/3
- 3/5 or -3/5
The system of linear equations kx + y + 1 = 0 and x + ky + 2 = 0 has unique solution if :
- k = -1
- k = 1
- k = 2
- None of the above
- Which of the following will have no solution ?
- A system of consistent equations
- A system of inconsistent equations
- A system of dependent equations
- All of the above
The value of c, for which the pair of equations cx - y = 2 and 6x - 2y - 4= 0 will have infinitely many solution, is :
- 3
- -3
- -12
- 12
In a cyclic quadrilateral PQRS, ∠P = (2x + 4)o , ∠Q = (y + 3)o , ∠R = (2y + 10)o , ∠S = (4x + 5)o . Then :
- ∠P = 70o , ∠Q = 53o , ∠R = 110o , ∠S = 127o
- ∠P = 70o , ∠Q = 55o , ∠R = 110o , ∠S = 125o
- ∠P = 65o , ∠Q = 53o , ∠R = 115o , ∠S = 127o
- ∠P = 65o , ∠Q = 55o , ∠R = 113o , ∠S = 127o
The quadratic equation ax2 + bx + c = 0 will have real and distinct roots if :
- b2 - 4ac < 0
- b2 - 4ac > 0
- b2 - 4ac = 0
- All of the above
The 5th term of an A. P. is 1 and the 11th term is -17. Which term of the A. P. is -77 ?
- 22nd
- 31st
- 44th
- None of the above
Which of the following are in A. P. ?
- 2a - b, 2a, a + b, .....
- a - b, a, a + b, .....
- a - 2b, b, a + 2b, .....
- a - b, 2a, a + b, .....
For what value of n are the nth terms of two A. P.'s 63, 65, 67, ..... and 3, 10, 17, ....... equal ?
- 11
- 12
- 13
- 14
In an A. P., the first term is 22, nth term is -11 and sum of first n terms is 66. Then the common difference d is :
- -1
- -2
- -3
- -4
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 ?
- Area of the square = Area of the circle
- Area of the square is less than the area of the circle
- Area of the square is more than the area of the circle
- None of the above
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)
- 44 cm
- 11 cm
- 28 cm
- None of the above
The perimeter of semi-circle of radius r unit is :
- 𝜋r + r
- 𝜋r + 2r
- 2𝜋r + r
- 2𝜋r + 2r
If an arc of a circle makes an angle 𝛳 < 180o at the centre of a circle of radius r, then the length of the arc is :
- 2𝜋r𝛳 / 360o
- 𝜋r2𝛳 / 360o
- 1/2 r2 sin 𝛳
- None of the above
Area of the largest triangle that can be inscribed in a semi-circle of radius r unit is :
- 1/2 r2 sq. unit
- r2 sq. unit
- 2r2 sq. unit
- √2r2 sq. unit
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)
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A cylindrical pencil sharpened at one edge is a combination of :
- A hemisphere and a cylinder
- A cone and a cylinder
- A frustum of a cone and a cylinder
- Two cylinders
A shuttle cock used for playing badminton has the shape, the combination of :
- A sphere and a cone
- A cylinder and a sphere
- A frustum of a cone and a hemisphere
- A cylinder and a hemisphere
In a circular cone, the cross-section made by a plane parallel to the base is a :
- Frustum of a cone
- Sphere
- Circle
- Hemisphere
The length of the side of largest cube that can be inscribed in a sphere of diameter 'd' is :
- 3d
- d / √3
- d / √2
- 2d
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)
- 81
- 82
- 83
- 84
If the mean of the distribution is 2.6 then the value of p is :
Ans: (3)
Ans: (2)
Ans: (3)
Ans: (3)
Ans: (2)
Ans: (4)
- 1
- 3
- 7
- 6
Which of the following is not a measure of central tendency ?
- Standard deviation
- Median
- Mean
- Mode
The cumulative frequency test is useful in finding the :
- Mean
- Mode
- Median
- None of the above
Ans: (1)
Ans: (1)
Ans: (3)
- Mean
- Mode
- Median
- All of the above
Find the mode of the data :
Ans: (1)
- 24.25
- 25.25
- 26.25
- 27.25
Which of the following cannot be the probability of an event ?
- 2/3
- - 1.5
- 15%
- 0.7
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 ?
- p is always greater than q
- p + q = 1
- p is always less than q
- p + q = 0
When a die is thrown, the probability of getting an odd number less than 5 is :
- 1/2
- 1/3
- 2/3
- 1/6
A letter is chosen at random from English alphabet. Then the probability that the letter chosen precedes 'g' is :
- 1/26
- 3/13
- 5/26
- 7/26
What is the probability that two different friends have different birthdays ? (Ignoring leap year)
- 1/365
- 2/365
- 364/365
- 1
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 ?
- 2/9
- 7/9
- 3/9
- 4/9
Two dice are thrown at the same time. What is the probability of getting different numbers on the dice ?
- 1/36
- 1/6
- 5/6
- 35/36
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 :
- 1/5
- 3/5
- 7/10
- 3/10
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Below mentioned books are some of those (Last one is very practical)