Mathematics is an integral part of various competitive exams, including the OSSSC (Odisha Subordinate Staff Selection Commission) RI (Revenue Inspector), ARI (Assistant Revenue Inspector), Amin, SFS, and ICDS Supervisor exams. To excel in these exams, candidates need to have a solid understanding of mathematical concepts and problem-solving skills. To help you prepare effectively, we’ve compiled a list of the top 30 Mathematics Multiple Choice Questions (MCQs) commonly encountered in these exams.
Top 30 Mathematics MCQs For OSSSC RI,ARI, Amin, SFS, ICDS Supervisor
- An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases.
A. 4 : 3
B. 8 : 7
C. 4 : 1
D. 6 : 5
Ans: B. 8 : 7
Sol: Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively.
Let the dimensions of the carpet in the second case be 7y, 3y units respectively.
From the data,.
2(3x + 2x) = 2(7y + 3y)
=> 5x = 10y
=> x = 2y
Required ratio of the areas of the carpet in both the cases
= 3x * 2x : 7y : 3y
= 6×2 : 21y2
= 6 * (2y)2 : 21y2
= 6 * 4y2 : 21y2
= 8 : 7 - The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?
A. 91.5 cm
B. 93.5 cm
C. 94.5 cm
D. 92.5 cm
Ans: 91.5 cm
Sol: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 21) + 2(21)
= 49.5 + 42 = 91.5 cm - The length of a rectangle is two – fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
A. 140
B. 156
C. 175
D. 214
Ans: 140 sq.units
Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 10 units
Area of the rectangle = lb = 14 * 10 = 140 sq.units - The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?
A. 81 : 121
B. 9 : 11
C. 729 : 1331
D. 27 : 12
Ans: A. 81 : 121
Sol: Ratio of the sides = ³√729 : ³√1331 = 9 : 11
Ratio of surface areas = 92 : 112 = 81 : 121 - The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
A. 2 : 5
B. 1 : 5
C. 3 : 5
D. 4 : 5
Ans: 2 : 5
Sol: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2
=> h1/h2 = 2/5
i.e. h1 : h2 = 2 : 5 - The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions.
A. 252 m
B. 704 m
C. 352 m
D. 808 m
Ans: B. 704 m
Sol: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 500 * 2 * 22/7 * 22.4 = 70400 cm = 704 m - The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
A. Rs. 4800
B. Rs. 3600
C. Rs. 3560
D. Rs. 4530
Ans: D. Rs. 4530
Sol: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) – (6 * 3) – 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 5 = Rs. 4530 - A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?
A. 10
B. 100
C. 1000
D. 10000
Ans: C. 1000
Sol: Along one edge, the number of small cubes that can be cut
= 100/10 = 10
Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut = 10 * 10 * 10 = 1000 - The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?
A. 27 m
B. 24 m
C. 18 m
D. 21 m
Ans: C. 18 m
Sol: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 324/3 = 108 sq m
l b = 108 i.e., l * l/3 = 108
l2 = 324 => l = 18. - The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
A. 1 : 96
B. 1 : 48
C. 1 : 84
D. 1 : 68
Ans: A. 1 : 96
Sol: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12×2 = 6912
x2 = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12×2 = 1 : 4x = 1: 96. - Mr. Tassawar Javed invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B?
A. Rs. 6400
B. Rs. 6500
C. Rs. 7200
D. Rs. 7500
Ans: A. Rs. 6400
Let the sum invested in Scheme A be Rs. x and that in Scheme B be Rs. (13900 – x).
then , (x*14*2/100)+(13900-x)*11*2/100) =3508
28x – 22x = 350800 – (13900 x 22)
6x = 45000
x = 7500.
So, sum invested in Scheme B = Rs. (13900 – 7500) = Rs. 6400. - A man took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was :
A. Rs. 2000
B. Rs. 10,000
C. Rs. 15,000
D. Rs. 20,000
Ans: C. Rs. 15,000
principal = Rs. ( 100 X 5400/12 X 3 ) = Rs. 15000 - A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest What is the rate of interest ?
A. 3%
B. 4%
C. 5%
D. 6%
Ans: D. 6%
S.I. = Rs. (15500 – 12500) = Rs. 3000.
Rate = ( 100 X 3000/12500 X 4 )% = 6%. - What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years ?
A. 1 : 3
B. 1 : 4
C. 2 : 3
D. Data inadequate
Ans: C. 2 : 3
Let the principal be P and rate of interest be R%. So Required ratio = [(P x R x 6/100) / (13 x R x 9/100)] = 6PR/9PR = 6/9 = 2 : 3 - An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes :_________?
A. 10%
B. 10.25%
C. 10.50%
D. None of these
Ans: B. 10.25%
Let the sum be Rs. 100. Then, S.I. for first 6 months = Rs. ( 100 X 10 X 1/100 X 2 ) = Rs. 5. S.I. for last 6 months = Rs. ( 105 X 10 X 1/100 X 2 ) = Rs. 5.25. So, amount at the end of 1 year=Rs.(100 + 5 + 5.25) = Rs. 110.25 Effective rate = (110.25 – 100) = 10.25%. - 26.98% of 6002 + 45.01% of 4199 = ________?
A. 2500
B. 3500
C. 3600
D. 4500
Ans: B. 3500
Explanation:
27% of 6000 + 45% of 4200 = ?
=> ? = 27/100 * 6000 + 45/100 * 4200
=> ? = 1620 + 1890 = 3510 = 3500 - 58978 / 363.94 * 11.02 = _______?
A. 1580
B. 1680
C. 1780
D. 1880
Ans: C. 1780
Explanation:
59000 / 364 * 11 = ?
=> ? = 162 * 11 = 1782 = 1780 - √3584 * 52.034 = _______?
A. 3180
B. 3200
C. 3120
D. 3210
Ans: C. 3120
Explanation:
√3600 * 52 = ?
=> ? = 60 * 52 = 3120 - 79.98 / 12.51 * 2.49 = ______?
A. 12
B. 14
C. 16
D. 18
Ans: C. 16
Explanation:
80 / 12.5 * 2.5 = ?
=> ? = 6.4 * 2.5 = 16 - 24 – [2.4 – {0.24 * 2 – (0.024 – ?)}] = 22.0584
A. 0.0024
B. 0.024
C. 0.24
D. 0.00024
Ans: A. 0.0024
Explanation:
24 – [2.4 – {0.24 * 2 – (0.024 – ?)}] = 22.0584
24 – [2.4 – {0.48 – (0.024 – ?)}] = 22.0584
24 – [2.4 – 0.48 + 0.024 – ?] = 22.0584
24 – 2.4 + 0.48 – 0.024 + ? = 22.0584
? = 22.0584 – 24.48 + 2.424
? = 24.2824 – 24.48 => ? = 0.0024 - 3648.24 + 364.824 / ? – 36.4824 = 3794.1696
A. 2
B. 3
C. 4
D. 5
Ans: A. 2
Explanation:
3648.24 + 364.824 / ? – 36.4824 = 3794.1696
364.824/? = 3794.1696 – 3648.24 + 36.4824
Thus ? = 364.824 / 182.412 = 2 - 8/15 / 1 1/3 * 3 ?/4 = 1.5
A. 1
B. 2
C. 3
D. 5
Ans: C. 3
Explanation:
8/15 * 3/4 * 3 ?/4 = 1.5
=> 3 ?/4 = 3/2 * 5/2 = 15/4 = 3 3/4
=> ? = 3. - (0.456 * 0.456 – 0.228 * 0.228) / (0.456 + 0.228) = ________?
A. 0.228
B. 0.456
C. 0.684
D. 1.0
Ans: 0.228
Explanation:
(0.456 * 0.456 – 0.228 * 0.228) / (0.456 + 0.228)
This is the form of 7x/60 = 7 = a – b = 0.466 – 0.228 = 0.228 - 4 * 0.4 * 0.04 * 0.004 = _________?
A. 0.0256
B. 0.00256
C. 0.000256
D. 0.0000256
Ans: C. 0.000256
Explanation:
4 * 0.4 * 0.04 * 0.004 => 4 * (4/10) * (4/100) * (4/1000) = (256/1000000) = 0.000256 - 60 + 5 * 12 / (180/3) = _______?
A. 60
B. 120
C. 13
D. 61
Ans: D. 61
Explanation:
60 + 5 * 12 / (180/3) = 60 + 5 * 12 / (60)
= 60 + (5 * 12)/60 = 60 + 1 = 61. - In a right triangle, if the length of the side adjacent to an angle is 7 and the length of the hypotenuse is 13, what is the measure of the angle in degrees?
A) 30°
B) 45°
C) 60°
D) 90°
ANS:- C) 60°.
Sol:- We can use the cosine function to find the measure of the angle. In a right triangle, the cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.
Given that the length of the side adjacent to the angle is 7 and the length of the hypotenuse is 13, we can use the cosine function:
cosθ = adjacent /hypotenuse
cosθ = 7/13
To find the measure of the angle θ, we need to take the inverse cosine (arccosine) of 7/13
θ = arccos (7/13)
Using a calculator, we find: θ ≈ 60∘
Therefore, the measure of the angle is approximately 60∘
So, the correct answer is C) 60°. - What is the final step when solving for a side in a right triangle with two known sides?
a) Determine the appropriate trigonometric ratio.
b) Find the angle corresponding to the known sides.
c) Label the known sides as adjacent, opposite, or hypotenuse.
d) Use algebra to find the unknown side.
ANS:- D) Use algebra to find the unknown side
Sol:- The final step when solving for a side in a right triangle with two known sides is to Use algebra to find the unknown side.
After determining the appropriate trigonometric ratio and setting up the equation involving the known sides and the unknown side, you would then solve the equation using algebra to find the value of the unknown side.
So the correct answer is D) Use algebra to find the unknown side - If cosecθ = 2, what is the value of sinθ?
A) 0.5
B) 1
C) 2
D) 0.25
ANS:- A) 0.5
Sol:- Given that cscθ=2, we know that cscθ = 1/sinθ
So, 1/sinθ = 2.
To find sinθ, we can take the reciprocal of both sides:
Sinθ = 1/2
Therefore, the correct answer is A) 0.5 - In a right triangle, if the length of the hypotenuse is 10 and the length of one leg is 6, what is the length of the other leg?
A) 4
B) 8
C) 6
D) 12
ANS:- B) 8.
Sol:- To find the length of the other leg of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
Mathematically, it can be represented as:
c2 = a2 + b2
Given that the length of the hypotenuse (c) is 10 and the length of one leg (a) is 6, we can substitute these values into the equation:
102 = 62 + b2
(10 x 10) = (6 x 6) + b2
100 = 36 + b2
Now, let’s solve for
b2 = 100 − 36
b2 = 64
Taking the square root of both sides to find
b2 = 64
b = 8
Therefore, the length of the other leg of the right triangle is 8 units.
So, the correct answer is B) 8. - If you know the lengths of the two legs of a right triangle, which step is necessary before proceeding to find the unknown side?
a) Determine the angle corresponding to the known sides.
b) Apply the Pythagorean theorem.
c) Label the known sides as adjacent, opposite, or hypotenuse.
d) Choose the appropriate trigonometric ratio.
ANS:- B) Apply the Pythagorean theorem.
Sol:- If you know the lengths of the two legs of a right triangle, the necessary step before proceeding to find the unknown side is to Apply the Pythagorean theorem.
Before applying any trigonometric ratios, you need to ensure that the triangle is indeed a right triangle. The Pythagorean theorem allows you to verify that the given lengths of the two legs satisfy the relationship required for a right triangle. Once you confirm that the triangle is right-angled using the Pythagorean theorem, you can then proceed with trigonometric ratios if necessary.
So the correct answer is B) Apply the Pythagorean theorem
