IUC AcademyHome801. A bus's driving wheel has a diameter of 140 cm. How many revolutions per minute must it make for the bus to travel at 66 km per hour?
- A. 200
- B. 250
- C. 300
- D. 350
Answer: 250
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802. A wheel of diameter 56 cm covers 1.1 km. How many revolutions does it make?
- A. 31.25
- B. 56.25
- C. 62.5
- D. 625
Answer: 625
803. A wheel has a diameter of 1.26 m. How far does it travel in 500 turns?
- A. 1492 m
- B. 1980 m
- C. 2530 m
- D. 2880 m
Answer: 1980 m
804. If the areas of a circle and a square are equal then the ratio of their perimetersis
- A. 1 : 1 / 1: 1
- B. 2 : p / 2: p
- C. p : 2 / p: 2
- D. π :2 / π:2
Answer: π :2 / π:2
Explanation: Proceeding as in Q.279, we have: Ratio of perimeters = 2 : 2. 4 x x π π =π
Explanation: Proceeding as in Q.279, we have: Ratio of perimeters = 2 : 2. 4 x x π π =π
805. A circle and a square have the same area. The ratio of the side of the square and the radius of the circle is
- A. 22 : 7 / 22: 7
- B. π :1 / π:1
- C. 1 : p / 1: p
- D. 7 : 22 / 7: 22
Answer: π :1 / π:1
Explanation: Let the area of each of the circle and the square be x sq.units. Let the radius of the circle be r units and the side of the square be a unit. Then, 2 . x π =⇒= r xr π And, 2a xa x =⇒= . ∴ Required ratio = : 1. x x =π π
Explanation: Let the area of each of the circle and the square be x sq.units. Let the radius of the circle be r units and the side of the square be a unit. Then, 2 . x π =⇒= r xr π And, 2a xa x =⇒= . ∴ Required ratio = : 1. x x =π π
806. The perimeter of a circle is equal to the perimeter of a square. Then, their areas are in the ratio
- A. 4 : 1 / 4: 1
- B. 11 : 7 / 11: 7
- C. 14 : 11 / 14: 11
- D. 22 : 7 / 22: 7
Answer: 14 : 11 / 14: 11
807. The ratio of the radii of two circles is 1 : 3. Then the ratio of their areas is
- A. 1 : 3 / 1: 3
- B. 1 : 6 / 1: 6
- C. 1 : 9 / 1: 9
- D. None of these
Answer: 1 : 9 / 1: 9
808. The ratio of the radii of two circles is 3 : 2. What is the ratio of their circumferences?
- A. 2 : 3 / 2: 3
- B. 3 : 2 / 3: 2
- C. 4 : 9 / 4: 9
- D. None of these
Answer: 3 : 2 / 3: 2
809. A circular field contains a rectangular tank 180 m long and 120 m wide. The land area of the field (excluding the tank) is 40000 m². Find the field's radius.
- A. 130 m
- B. 135 m
- C. 140 m
- D. 145 m
Answer: 140 m
810. A square lawn with side 100 m long has a circular flower bed in the centre. If the area of the lawn, excluding the flower bed, is 8614 m2, the radius of the circular flower bed is
- A. 21 m
- B. 31 m
- C. 41 m
- D. None of these
Answer: 21 m
811. A circular wire of 42 cm diameter is reshaped into a rectangle with sides in the ratio 6 : 5. What is the rectangle's area?
- A. 540 cm2
- B. 1080 cm2
- C. 2160 cm2
- D. 4320 cm2
Answer: 1080 cm2
812. A wire bent into a square encloses 484 sq. cm. What area will it enclose if it is bent into a circle?
- A. 462 sq. cm
- B. 539 sq. cm
- C. 616 sq. cm
- D. 693 sq. cm
Answer: 616 sq. cm
813. The circumference of a circle is equal to the side of a square whose area measures 407044 sq. cm. What is the area of the circle?
- A. 22583.2 sq. cm
- B. 32378.5 sq. cm
- C. 39483.4 sq. cm
- D. 41263.5 sq. cm
Answer: 32378.5 sq. cm
814. A wire can be bent in the form of a circle of radius 56 cm. If it is bent in the form of a square, then its area will be
- A. 3520 cm2
- B. 6400 cm2
- C. 7744 cm2
- D. 8800 cm2
Answer: 7744 cm2
815. If the perimeter of a square is equal to the radius of a circle whose area is 39424 sq. m. What is the are area of the square?
- A. 441 sq.m
- B. 784 sq.m
- C. 1225 sq.m
- D. Cannot be determined
Answer: 784 sq.m
816. The perimeter of a circular field and a square field are equal. If the area of the square field is 12100 m2, the area of the circular field will be
- A. 15200 m2
- B. 15300 m2
- C. 15400 m2
- D. 15500 m2
Answer: 15400 m2
817. Between a square of perimeter 44 cm and a circle of circumference 44 cm, which figure has larger area and by how much?
- A. Both have equal area
- B. Square, 33 cm2
- C. Circle, 33 cm2
- D. Square, 495 cm2
Answer: Circle, 33 cm2
818. A circular pond has area equal to 616 m2. A circular stage is made at the centre of the pond whose radius is equal to half the radius of the pond. What is the area where water is present?
- A. 454 sq. m
- B. 462 sq. m
- C. 532 sq. m
- D. 564 sq. m
Answer: 462 sq. m
819. The radius of a circle is 20% more than the height of a right-angled triangle. The base of the triangle is 36 cm. If the area of triangle and circle be equal, what will be the area of circle?
- A. 72 cm2
- B. 128 cm2
- C. 144 cm2
- D. 216 cm2
Answer: 72 cm2
820. The sum of radii of two circles is 140 cm and the difference of their circumferences is 88 cm. The diameters of the circles are
- A. 77 cm, 63 cm
- B. 150 cm, 120 cm
- C. 154 cm, 126 cm
- D. 160 cm, 120 cm
Answer: 154 cm, 126 cm
821. The sum of areas of two circles A and B is equal to the area of a third circle C whose diameter is 30 cm. If the diameter of circle A is 18 cm, then the radius of circle B is
- A. 10 cm
- B. 12 cm
- C. 15 cm
- D. 18 cm
Answer: 12 cm
822. Two small circular parks of diameters 16 m and 12 m are to be replaced by a Bigger circular park. What would be the radius of this new park, If the new park has to occupy the same space as the two small parks?
- A. 10 m
- B. 15 m
- C. 20 m
- D. 25 m
Answer: 10 m
823. The difference between the circumference and the radius of a circle is 37 cm. The area of the circle is
- A. 111 cm2
- B. 148 cm2
- C. 154 cm2
- D. 259 cm2
Answer: 154 cm2
824. The magnitude of the area of a circle is seven times that of its circumference. What is the circumference (in units) of the circle?
- A. 88
- B. 132
- C. 616
- D. Cannot be determined
Answer: 88
825. If the circumference and the area of a circle are numerically equal, then the diameter is equal to
- A. 2 π
- B. 2 p
- C. 2
- D. 4
Answer: 4
826. Cost of fencing a circular plot at the rate of ₹ 15 per metre is ₹ 3300. What will be the cost of flooring the plot at the rate of ₹ 100 per square metre?
- A. ₹ 2,20,000
- B. ₹ 3,50,000
- C. ₹ 3,85,000
- D. Cannot be determined
Answer: ₹ 3,85,000
827. The circumferences of two circles are 132 metres and 176 metres respectively. What is the difference between the area of the larger circle and the smaller circle?
- A. 1048 sq. m
- B. 1076 sq. m
- C. 1078 sq. m
- D. 1090 sq. m
Answer: 1078 sq. m
828. What is the area of a circle whose circumference is 1047.2 metres?
- A. 69843.23 sq. m
- B. 78621.47 sq. m
- C. 79943.82 sq. m
- D. 87231.76 sq. m
Answer: 87231.76 sq. m
829. The circumference of a circular plot is 396 metres. what is the area of the circular plot?
- A. 9446 sq. m
- B. 9856 sq. m
- C. 12474 sq. m
- D. 18634 sq. m
Answer: 12474 sq. m
830. What would it cost to fence a circular field of area 18634 sq. m at ₹ 365 per metre?
- A. ₹ 1,76,660
- B. ₹ 2,43,250
- C. ₹ 56,60,220
- D. ₹ 68,01,410
Answer: ₹ 1,76,660
831. The circumference of a circle, whose area is 24.64 m2, is
- A. 14.64 m
- B. 16.36 m
- C. 17.60 m
- D. 18.40 m
Answer: 17.60 m
832. A circular field has the same area as a rectangular field whose sides are in the ratio 14 : 11 and whose perimeter is 100 m. What is the diameter of the circular field?
- A. 14 m
- B. 22 m
- C. 24 m
- D. 28 m
Answer: 28 m
833. A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. What is the area of the circle?
- A. 88 cm2
- B. 154 cm2
- C. 1250 cm2
- D. None of these
Answer: None of these
834. A cow is tethered in the middle of a field with a 14 feet long rope. If the cow grazes 100 sq. ft. per day, then approximately what time will be taken by the cow to graze the whole field?
- A. 2 days
- B. 6 days
- C. 18 days
- D. 24 days
Answer: 6 days
835. From a circular sheet of paper with radius 20 cm, four circles of radius 5 cm each are cut out. What is the ratio of the uncut to the cut portion?
- A. 1 : 3 / 1: 3
- B. 3 : 1 / 3: 1
- C. 4 : 1 / 4: 1
- D. 4 : 3 / 4: 3
Answer: 3 : 1 / 3: 1
836. A man jogs around a circular field of radius 50 m at 12 km/hr. How long does he take to complete twenty rounds?
- A. 30 min.
- B. 32 min.
- C. 34 min.
- D. None of these
Answer: None of these
837. The area of a circle of radius 5 is numerically what percent of its circumference?
- A. 200
- B. 225
- C. 240
- D. 250
Answer: 250
Explanation: 2 (5) Required% 100 % 250%. 25 [] π× = ×= π×
Explanation: 2 (5) Required% 100 % 250%. 25 [] π× = ×= π×
838. Area of a rectangle is equal to the area of a circle whose radius is 14 cm. If the breadth of the rectangle is 22 cm, what is its length?
- A. 24 cm
- B. 26 cm
- C. 28 cm
- D. Cannot be determined (d) None of these
Answer: 28 cm
839. The diameter of a circle is 3.5 cm. What is the circumference of the circle?
- A. 11 cm
- B. 22 cm
- C. 38.5 cm
- D. 45.2 cm
Answer: 11 cm
840. Which one of the following has a greater perimeter than the rest?
- A. A square with an area of 36 sq. cm
- B. An equilateral triangle with a side of 9 cm
- C. A rectangle with 10 cm as length and 40 sq. cm as area
- D. A circle with a radius of 4 cm
Answer: A rectangle with 10 cm as length and 40 sq. cm as area
841. Which of the following figures has the longest perimeter?
- A. A square of side 10 cm
- B. A rectangle of sides 12 cm and 9 cm
- C. A circle of radius 7 cm
- D. A rhombus of side 9 cm
Answer: A circle of radius 7 cm
842. Which two figure have an equal area? 10 cm 12 cm 12 cm 12 cm 12 cm 14 cm 14 cm AB C D
- A. A and B
- B. B and D
- C. A and C
- D. A and D
Answer: A and D
843. The cross-section of a canal is trapezium in shape. The canal is 12 m wide at the top and 8 m wide at the bottom. If the area of the cross-section is 840 sq. m, the depth of the canal is
- A. 8.75 m
- B. 42 m
- C. 63 m
- D. 84 m
Answer: 84 m
Explanation: 1 2 (sum of parallel sides) × depth = Its area 1 (12 8) 840 84 m. 2 ⇔ + ×= ⇔= dd
Explanation: 1 2 (sum of parallel sides) × depth = Its area 1 (12 8) 840 84 m. 2 ⇔ + ×= ⇔= dd
844. A trapezium-shaped field has an area of 1440 m² and its parallel sides are 24 m apart. If the parallel sides are in the ratio 5 : 3, what is the length of the longer one?
- A. 45 m
- B. 60 m
- C. 75 m
- D. 120 m
Answer: 75 m
845. ABCD is a rectangle and E and F are the mid-points of AD and DC respectively. Then the ratio of the areas of EDF and AEFC would be
- A. 1 : 2 / 1: 2
- B. 1 : 3 / 1: 3
- C. 1 : 4 / 1: 4
- D. 2 : 3 / 2: 3
Answer: 1 : 3 / 1: 3
846. In a trapezium, the distance between the parallel sides equals the distance between the mid-points of the slant sides, which is 4 cm. Find its area.
- A. 4 cm2
- B. 8 cm2
- C. 16 cm2
- D. 20 cm2
Answer: 16 cm2
847. A trapezium with parallel sides of 6 cm and 10 cm has an area of 32 sq. cm. How far apart are the parallel sides?
- A. 2 cm
- B. 4 cm
- C. 5 cm
- D. 8 cm
Answer: 4 cm
848. A trapezium has parallel sides of 1.5 m and 2.5 m, and they are 6.5 m apart. What is its area?
- A. 10 m2
- B. 13 m2
- C. 20 m2
- D. 26 m2
Answer: 13 m2
849. If a square and a rhombus stand on the same base, then the ratio of the areas of the square and the rhombus is
- A. greater than 1
- B. equal to 1
- C. equal to 1 2
- D. equal to 14
Answer: equal to 1
Explanation: A square and a rhombus on the same base are equal in area.
Explanation: A square and a rhombus on the same base are equal in area.
850. The length of one diagonal of a rhombus is 80% of the other diagonal. The area of the rhombus is how many times the square of the length of the other diagonal?
- A. 4 5
- B. 25
- C. 3 4
- D. 14
Answer: 4 5
851. If each side of a rhombus is 20 metres and its shorter diagonal is three-fourths of its longer diagonal, then the area of this rhombus must be
- A. 375 sq. m
- B. 380 sq. m
- C. 384 sq. m
- D. 395 sq. m
Answer: 384 sq. m
852. A diagonal of a rhombus is 6 cm. If its area is 24 cm2 then the length of each side of the rhombus is
- A. 5 cm
- B. 6 cm
- C. 7 cm
- D. 8 cm
Answer: 5 cm
853. Each side of a rhombus is 26 cm and one of its diagonals is 48 cm long. The area of the rhombus is
- A. 2400 cm2
- B. 3000 cm2
- C. 3600 cm2
- D. 4800 cm2
Answer: 2400 cm2
854. If the diagonals of a rhombus are 24 cm and 10 cm, the area and the perimeter of the rhombus are respectively
- A. 120 cm2, 52 cm
- B. 120 cm2, 64 cm
- C. 240 cm2, 52 cm
- D. 240 cm2, 64 cm
Answer: 120 cm2, 52 cm
855. The perimeter of a rhombus is 56 m and its height is 5 m. Its area is
- A. 64 sq. m
- B. 70 sq. m
- C. 78 sq. m
- D. 84 sq. m
Answer: 70 sq. m
Explanation: Perimeter of the rhombus = 56 m. Each side of the rhom-bus = 56 m 14 m. 4 = Height of the rhombus = 5 m. ∴ Area = (14 × 5) m2 = 70 m2.
Explanation: Perimeter of the rhombus = 56 m. Each side of the rhom-bus = 56 m 14 m. 4 = Height of the rhombus = 5 m. ∴ Area = (14 × 5) m2 = 70 m2.
856. One of the diagonals of a rhombus is double the other diagonal. Its area is 25 sq. cm. The sum of the diagonals is
- A. 10 cm
- B. 12 cm
- C. 15 cm
- D. 16 cm
Answer: 15 cm
857. The area of a rhombus is 150 cm2. The length of one of its diagonals is 10 cm. The length of the other diagonal is
- A. 25 cm
- B. 30 cm
- C. 35 cm
- D. 40 cm
Answer: 30 cm
858. If a parallelogram with area P, a rectangle with area R and a triangle with area T are all constructed on the same base and all have the same altitude, then which of the following statements is false?
- A. P = R
- B. P + T = 2R
- C. P = 2T
- D. 1 2 TR =
Answer: P + T = 2R
859. Two equilateral triangles of side 23 cm are joined to form a quadrilateral. The altitude of the quadrilateral, thus formed, is equal to
- A. 3 cm
- B. 4 cm
- C. 6 cm
- D. 8 cm
Answer: 3 cm
860. A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 100 m, then the altitude of the triangle is
- A. 10 2 m
- B. 100 m
- C. 100 2 m
- D. 200 m
Answer: 200 m
861. One diagonal of a parallelogram measures 70 cm and each of the two remaining vertices is 27 cm from this diagonal. Find the area of the parallelogram in sq. cm.
- A. 1800
- B. 1836
- C. 1890
- D. 1980
Answer: 1890
862. A parallelogram has sides 30 m and 14 m and one of its diagonals is 40 m long. Then, its area is
- A. 168 m2
- B. 336 m2
- C. 372 m2
- D. 480 m2
Answer: 336 m2
863. A rectangle and a parallelogram are drawn between the same parallel lines on a common base of 10 cm. If the perimeter of the rectangle is 36 cm, then the area of the parallelogram is
- A. 60 cm2
- B. 80 cm2
- C. 81 cm2
- D. 100 cm2
Answer: 80 cm2
864. Let ABCD be a parallelogram and ABEF be a rectangle with EF lying along the line CD. If AB = 7 cm and BE = 6.5 cm, then the area of the parallelogram is
- A. 11.375 cm2
- B. 22.75 cm2
- C. 45 cm2
- D. 45.5 cm2
Answer: 45.5 cm2
865. A field in the form of a parallelogram has one side 150 metres and its distance from the opposite side is 80 metres. The cost of watering the field at the rate of 50 paise per square metre is
- A. ₹ 3500
- B. ₹ 5000
- C. ₹ 6000
- D. ₹ 7000
Answer: ₹ 6000
866. The readings in a field book are: It is subsequently realised that the distances to C and D had been interchanged by mistake. The are of the actual field would be
- A. 1300 sq. m
- B. 1500 sq. m
- C. 1800 sq. m
- D. 2000 sq. m
Answer: 1300 sq. m
867. Four equilateral triangles are described on the four sides of a rectangle with perimeter 12 cm. If the sum of the areas of the four triangles is 10 3 cm2, what is the area of the rectangle?
- A. 5 cm2
- B. 8 cm2
- C. 9 cm2
- D. 6.75 cm2
Answer: 8 cm2
868. If an angle of a triangle remains unchanged but each of its two including sides is doubled, then by what factor does the area get multiplied?
- A. 2
- B. 3
- C. 4
- D. 6
Answer: 4
869. Two isosceles triangles have equal vertical angles and their corresponding sides are in the ratio 3 : 5. What is the ratio of their areas?
- A. 3 : 5 / 3: 5
- B. 6 : 10 / 6: 10
- C. 9 : 25 / 9: 25
- D. None of these
Answer: 9 : 25 / 9: 25
870. If the height of a triangle is decreased by 40% and its base is increased by 40%, what will be the effect on its area?
- A. No change
- B. 8% decrease
- C. 16% increase
- D. 16 % decrease
Answer: 16 % decrease
871. If the side of an equilateral triangle is decreased by 20%, its area is decreased by
- A. 36%
- B. 40%
- C. 60%
- D. 64%
Answer: 36%
872. If the sides of a triangle be in the ratio 2 : 3 : 4, the ratio of the corresponding altitudes is
- A. 6 : 5 : 3 / 6: 5: 3
- B. 4 : 5 : 6 / 4: 5: 6
- C. 5 : 4 : 3 / 5: 4: 3
- D. 6 : 4 : 3 / 6: 4: 3
Answer: 6 : 4 : 3 / 6: 4: 3
873. The ratio of bases of two triangles is x : y and that of their areas is a : b. Then the ratio of their corresponding altitudes will be
- A. ax : by
- B. : ab xy
- C. ay : bx / ay: bx
- D. : xb a y
Answer: ay : bx / ay: bx
874. A square and an equilateral triangle have equal perimeters. If the diagonal of the square is 12 2 cm, then the area of the triangle is
- A. 2 24 2 cm
- B. 2 24 3 cm
- C. 2 48 3 cm
- D. 2 64 3 cm
Answer: 2 64 3 cm
875. If an equilateral triangle of area X and a square of area Y have the same perimeter, then X is
- A. equal to Y
- B. greater than Y
- C. less than Y
- D. less than or equal to Y
Answer: less than Y
876. What will be the ratio between the area of a rectangle and the area of a triangle with one of the sides of the rectangle as base and a vertex on the opposite side of the rectangle ?
- A. 1 : 2 / 1: 2
- B. 2 : 1 / 2: 1
- C. 3 : 1 / 3: 1
- D. Data inadequate
Answer: 2 : 1 / 2: 1
Explanation: Area of rectangle = lb sq. units. 1 Area of the triangle sq. units. 2 = lb ∴ 1 Required ratio : 2 : 1. 2 = = lb lb
Explanation: Area of rectangle = lb sq. units. 1 Area of the triangle sq. units. 2 = lb ∴ 1 Required ratio : 2 : 1. 2 = = lb lb
877. An equilateral triangle is described on the diagonal of a square. What is the ratio of the area of the triangle to that of the square?
- A. 2: 3
- B. 4: 3
- C. 3:2
- D. 3:4
Answer: 3:2
878. ABCD is a square. E is the mid-point of BC and F is the mid--point of CD. The ratio of the area of triangle AEF to the area of the square ABCD is
- A. 1 : 2 / 1: 2
- B. 1 : 3 / 1: 3
- C. 1 : 4 / 1: 4
- D. 3 : 8 / 3: 8
Answer: 3 : 8 / 3: 8
879. If x is the length of a median of an equilateral triangle, then its area is
- A. x2
- B. 1 2 2 x
- C. 3 2 2 x
- D. 3 2 3 x
Answer: 3 2 3 x
880. From a point within an equilateral triangle, perpendiculars drawn to the three sides are 6 cm, 7 cm, and 8 cm respectively. The length of the side of the triangle is
- A. 7 cm
- B. 10.5 cm
- C. 14 3 cm
- D. 14 3 cm 3
Answer: 14 3 cm