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?
Correct
Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x^{2} = 6912
x^{2} = 576 = 4 * 144 = 2^{2} * 12^{2} (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x^{2} = 1 : 4x = 1: 96.
Incorrect
Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x^{2} = 6912
x^{2} = 576 = 4 * 144 = 2^{2} * 12^{2} (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x^{2} = 1 : 4x = 1: 96.
Question 2 of 25
2. Question
1 points
Category: Mathematics
The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
Correct
Let the sides of the rectangle be l and b respectively.
From the given data,
(√l^{2} + b^{2}) = (1 + 108 1/3 %)lb
=> l^{2} + b^{2} = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l^{2} + b^{2})/lb = 25/12
12(l^{2} + b^{2}) = 25lb
Adding 24lb on both sides
12l^{2} + 12b^{2} + 24lb = 49lb
12(l^{2} + b^{2} + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)^{2} = 49lb
=> 12(14)^{2} = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l – b = 8 – 6 = 2m.
Incorrect
Let the sides of the rectangle be l and b respectively.
From the given data,
(√l^{2} + b^{2}) = (1 + 108 1/3 %)lb
=> l^{2} + b^{2} = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l^{2} + b^{2})/lb = 25/12
12(l^{2} + b^{2}) = 25lb
Adding 24lb on both sides
12l^{2} + 12b^{2} + 24lb = 49lb
12(l^{2} + b^{2} + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)^{2} = 49lb
=> 12(14)^{2} = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l – b = 8 – 6 = 2m.
Question 3 of 25
3. Question
1 points
Category: Mathematics
The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?
Correct
Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 867
3b^{2} = 867
b^{2} = 289 = 17^{2} (b > 0)
b = 17 m.
Incorrect
Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 867
3b^{2} = 867
b^{2} = 289 = 17^{2} (b > 0)
b = 17 m.
Question 4 of 25
4. Question
1 points
Category: Mathematics
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?
Correct
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
l^{2} = 324 => l = 18.
Incorrect
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
l^{2} = 324 => l = 18.
Question 5 of 25
5. Question
1 points
Category: Mathematics
An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?
Correct
Length of the first carpet = (1.44)(6) = 8.64 cm
Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)
= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m
Cost of the second carpet = (45)(12.96 * 7) = 315 (13 – 0.04) = 4095 – 12.6 = Rs. 4082.40
Incorrect
Length of the first carpet = (1.44)(6) = 8.64 cm
Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)
= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m
Cost of the second carpet = (45)(12.96 * 7) = 315 (13 – 0.04) = 4095 – 12.6 = Rs. 4082.40
Question 6 of 25
6. Question
1 points
Category: Mathematics
What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?
Correct
Let the side of the square plot be a ft.
a^{2} = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 58 = Rs. 3944.
Incorrect
Let the side of the square plot be a ft.
a^{2} = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 58 = Rs. 3944.
Question 7 of 25
7. Question
1 points
Category: Mathematics
The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?
Correct
Incorrect
Question 8 of 25
8. Question
1 points
Category: Mathematics
The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square.
Correct
Incorrect
Question 9 of 25
9. Question
1 points
Category: Mathematics
The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square.
Correct
Incorrect
Question 10 of 25
10. Question
1 points
Category: Mathematics
The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles.
Correct
Incorrect
Question 11 of 25
11. Question
1 points
Category: Mathematics
A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is
Correct
Incorrect
Question 12 of 25
12. Question
1 points
Category: Mathematics
The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)
Correct
Incorrect
Question 13 of 25
13. Question
1 points
Category: Mathematics
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?
Correct
Incorrect
Question 14 of 25
14. Question
1 points
Category: Mathematics
The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions.
Correct
Incorrect
Question 15 of 25
15. Question
1 points
Category: Mathematics
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?
Correct
Incorrect
Question 16 of 25
16. Question
1 points
Category: Mathematics
A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?
Correct
Incorrect
Question 17 of 25
17. Question
1 points
Category: Mathematics
The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?
Correct
Incorrect
Question 18 of 25
18. Question
1 points
Category: Mathematics
Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?
Correct
Incorrect
Question 19 of 25
19. Question
1 points
Category: Mathematics
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?
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Incorrect
Question 20 of 25
20. Question
1 points
Category: Mathematics
The sector of a circle has radius of 21 cm and central angle 135^{o}. Find its perimeter?
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Incorrect
Question 21 of 25
21. Question
1 points
Category: Mathematics
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.
Correct
Incorrect
Question 22 of 25
22. Question
1 points
Category: Mathematics
A bicycle wheel has a diameter (including the tyre) of 56 cm. The
number of times the wheel will rotate to cover a distance of 2.2
km is ———–
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Incorrect
Question 23 of 25
23. Question
1 points
Category: Mathematics
If one diagonal of a rhombus ofside 13 cm is 10 cm, then the
other diagonal is ———-
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Incorrect
Question 24 of 25
24. Question
1 points
Category: Mathematics
A brick 2″ thick is placed against a wheel to act for a stop. The
horizontal distance of the face of the brick from the point where
the wheel touches the ground is 6″. The radius of the wheel in
inches is —————
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Incorrect
Question 25 of 25
25. Question
1 points
Category: Mathematics
A solid has 12 vertices and 30 edges. How many faces does it
have?