IUC AcademyHome721. Three circles of radius 3.5 cm are placed in such a way that each circle touches the other two. The area of the portion enclosed by the circles is
- A. 1.967 cm2
- B. 1.975 cm2
- C. 19.67 cm2
- D. 21.21 cm2
Answer: 1.967 cm2
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722. Three equal circles are described with vertices of the triangles as centres. If the radius of each circle is r, the sum of areas of the portions of the circles intercepted in a triangle is
- A. 2pr2
- B. 3 2 pr2
- C. pr2
- D. 1 2 pr2
Answer: 1 2 pr2
723. If the circumference of a circle is decreased by 50% then the percentage of decrease in its area is
- A. 25
- B. 50
- C. 60
- D. 75
Answer: 75
724. If the circumference of a circle is increased by 20%, what will be the effect on the circle?
- A. 40% increase
- B. 44% increase
- C. 48% increase
- D. Cannot be determined
Answer: 44% increase
725. If the circumference of a circle increases form 4p to 8p, what change occurs in its area?
- A. It is halved.
- B. It doubles.
- C. it triples.
- D. It quadruples.
Answer: It quadruples.
726. If the radius of a circle is increased to 3 times, then how many times will its circumference be increased?
- A. 1 times 3
- B. 2 times
- C. 3 times
- D. 9 times
Answer: 3 times
Explanation: Let the original radius be R. New radius = 3R. Original circumference = 2pR. New circumference = 2p(3R) = 6pR. ∴ Required ratio = 6 3. 2 R R π = π
Explanation: Let the original radius be R. New radius = 3R. Original circumference = 2pR. New circumference = 2p(3R) = 6pR. ∴ Required ratio = 6 3. 2 R R π = π
727. If the radius of a circle is doubled, its area is increased by
- A. 100%
- B. 200%
- C. 300%
- D. 400%
Answer: 300%
728. If the radius of a circle is diminished by 10%, then its area is diminished by
- A. 10%
- B. 19%
- C. 20%
- D. 36%
Answer: 19%
729. If the radius of a circle is increased by 200%, then its area will increase by
- A. 200%
- B. 400%
- C. 800%
- D. 900%
Answer: 800%
730. If the radius of a circle is increased by 6%, then the area is increased by
- A. 6%
- B. 12%
- C. 12.36%
- D. 16.64%
Answer: 12.36%
731. A runner can circle a circular track 8 times in 40 minutes. If the track's diameter becomes 10 times larger, how long does the runner take for a single round at the same speed?
- A. 20 min.
- B. 25 min.
- C. 50 min.
- D. 100 min.
Answer: 50 min.
732. If the radius of a circle is increased by 75%, then its circumference will increase by
- A. 25%
- B. 50%
- C. 75%
- D. 100%
Answer: 75%
733. ABC is a right-angled triangle with right angle at B. If the semi-circle on AB with AB as diameter encloses an area of 81 sq. cm and the semi-circle on BC with BC as diameter encloses an area of 36 sq. cm, then the area of the semi-circle on AC with AC as diameter will be
- A. 117 cm2
- B. 121 cm2
- C. 217 cm2
- D. 221 cm2
Answer: 117 cm2
734. The area of the largest triangle that can be inscribed in a semi-circle of radius r, is
- A. r2
- B. 2r2
- C. r3
- D. 2r3
Answer: r2
735. A circle, a square and an equilateral triangle have the same area. The correct increasing order of the perimeters will be
- A. triangle, square, circle
- B. triangle, circle, square
- C. circle, triangle, square
- D. circle, square, triangle
Answer: circle, square, triangle
736. An equilateral triangle, a square and a circle have equal perimeters. If T denotes the area of the triangle, S, the area of the square and C, the area of the circle, then
- A. S < T < C
- B. T < C < S
- C. T < S < C
- D. C < S < T
Answer: T < S < C
737. If in a triangle, the area is numerically equal to the perimeter, then the radius of the inscribed circle of the triangle is
- A. 1
- B. 1.5
- C. 2
- D. 3
Answer: 2
738. The perimeter of a triangle is 30 cm and the circumference of its incircle is 88 cm. The area of the triangle is
- A. 70 cm2
- B. 140 cm2
- C. 210 cm2
- D. 420 cm2
Answer: 210 cm2
739. A triangle with sides 13 cm, 14 cm and 15 cm is inscribed in a circle. The radius of the circle is
- A. 2 cm
- B. 3 cm
- C. 4 cm
- D. 8.125 cm
Answer: 8.125 cm
740. The product of the lengths of three sides of a triangle is 196 and the radius of its circumscribe is 2.5 cm. The area of the triangle is
- A. 19.6 cm2
- B. 39.2 cm2
- C. 61.25 cm2
- D. 122.5 cm2
Answer: 19.6 cm2
Explanation: Product of sides 4 r = ∆ Product of sides 196 2 19.6 cm . 4 4 2.5 r ⇒∆= = = ×
Explanation: Product of sides 4 r = ∆ Product of sides 196 2 19.6 cm . 4 4 2.5 r ⇒∆= = = ×
741. The sides of a triangle are 6 cm, 11 cm and 15 cm. The radius of its incircle is
- A. 3 2 cm
- B. 42 cm 5
- C. 52 cm 4
- D. 6 2 cm
Answer: 52 cm 4
742. What is the area of an equilateral triangle inscribed in a circle of unit radius?
- A. 3 3 sq. units
- B. 33 sq. units 2
- C. 33 sq. units 4
- D. 33 sq. units 16
Answer: 33 sq. units 4
743. Three boys are standing on a circular boundary of a fountain. They are at equal distance from each other. If the radius of the boundary is 5 m, the shortest distance between any two boys is
- A. 53 m 2
- B. 5 3m
- C. 15 3 m 2
- D. 10 m 3 π
Answer: 5 3m
Explanation: Let A, B and C denote the positions of the three boys. Then, AB = BC = AC. So, DABC is equilateral. Let the side of DABC be a. Then, =⇒ 5 =5 3. 3 a a ∴ Required shortest distance = 53 m.
Explanation: Let A, B and C denote the positions of the three boys. Then, AB = BC = AC. So, DABC is equilateral. Let the side of DABC be a. Then, =⇒ 5 =5 3. 3 a a ∴ Required shortest distance = 53 m.
744. A circle is inscribed in a square. An equilateral triangle of side 43 cm is inscribed in that circle. The length of the diagonal of the square is
- A. 42 cm
- B. 8 cm
- C. 82 cm
- D. 16 cm
Answer: 82 cm
745. The area of a circle inscribed in an equilateral triangle is 154 cm2. Find the perimeter of the triangle.
- A. 71.5 cm
- B. 71.7 cm
- C. 72.3 cm
- D. 72.7 cm
Answer: 72.7 cm
746. The area of the incircle of an equilateral triangle of side 42 cm is
- A. 2 22 3 cm
- B. 231 cm2
- C. 462 cm2
- D. 924 cm2
Answer: 462 cm2
747. The radius of the circumcircle of an equilateral triangle of side 12 cm is
- A. 42 cm 3
- B. 4 2 cm
- C. 43 cm 3
- D. 4 3 cm
Answer: 4 3 cm
748. The ratio of the areas of the incircle and circumcircle of an equilateral triangle is
- A. 1 : 2 / 1: 2
- B. 1 : 3 / 1: 3
- C. 1 : 4 / 1: 4
- D. 1 : 9 / 1: 9
Answer: 1 : 4 / 1: 4
749. The circumradius of an equilateral triangle is 8 cm. The inradius of the triangle
- A. 3.25 cm
- B. 4 cm
- C. 3.5 cm
- D. 4.25 cm
Answer: 4 cm
Explanation: = ⇒ = ×= 1 8 8 4 cm. 3 23 2 aa [] = ∵circum radius = , inradius 3 23 aa
Explanation: = ⇒ = ×= 1 8 8 4 cm. 3 23 2 aa [] = ∵circum radius = , inradius 3 23 aa
750. A square pond with 21 m sides has a semicircular garden on each of its four sides. What is the cost of fencing the whole outline at ₹ 12.50 per metre?
- A. ₹ 1560
- B. ₹ 1650
- C. ₹ 3120
- D. ₹ 3300
Answer: ₹ 1650
751. Four equal sized maximum circular plates are cut off from a square paper sheet of area 784 cm2. The circumference of each plate is
- A. 22 cm
- B. 44 cm
- C. 66 cm
- D. 88 cm
Answer: 44 cm
752. What is the area of the shaded region? 8 4
- A. 32 – 4 p sq. units
- B. 32 – 8 p sq. units
- C. 16 – 4 p sq. units
- D. 16 – 8 p sq. units
Answer: 32 – 8 p sq. units
Explanation: Radius of each circle = 2 units. Area of the shaded region = Area of the rectangle – Area of two circles = [(8 × 4) – 2 × p(2)2] sq. units = (32 – 8p) sq. units.
Explanation: Radius of each circle = 2 units. Area of the shaded region = Area of the rectangle – Area of two circles = [(8 × 4) – 2 × p(2)2] sq. units = (32 – 8p) sq. units.
753. A square circumscribes a circle and another square is inscribed in this circle with one vertex at the point of contact. The ratio of the areas of the circumscribed and the inscribed squares is
- A. 1
- B. 2 : 1 / 2: 1
- C. 3
- D. 4
Answer: 1
754. A circle is inscribed in a square of side 54 cms and another circle circumscribes the same square. Then the ratio of circumferences of the bigger circle to the smaller circle is
- A. 1 : 2 / 1: 2
- B. 2 :1 / 2:1
- C. 3 :1 / 3:1
- D. None of these
Answer: 2 :1 / 2:1
755. The circumference of a circle is 100 cm. The side of a square inscribed in the circle is
- A. 50 2 cm2
- B. 100 π cm2
- C. 50 2 cm π 2
- D. 100 2 π cm2
Answer: 50 2 cm π 2
756. A square is inscribed in a circle whose radius is 4 cm. The area of the portion between the circle and the square is :
- A. (8π – 16)
- B. (8π – 32)
- C. (16π – 16)
- D. (16π – 32)
Answer: (16π – 32)
757. The area of a circle is 220 sq. cm. The area of a square inscribed in this circle will be
- A. 49 cm2
- B. 70 cm2
- C. 140 cm2
- D. 150 cm2
Answer: 140 cm2
758. The area of the rectangle circumscribed by a circle is 32 cm2 and the length of one side of the rectangle is 8 cm. The length of the diameter of the circle is
- A. 16 cm
- B. 12 cm
- C. 5 2 cm
- D. 45 cm
Answer: 45 cm
759. The sides of a rectangle are 8 cm and 6 cm. The corners of the rectangle lie on a circle. Find the are a of the circle without the rectangle.
- A. 30.6 cm2
- B. 39 cm2
- C. 42.4 cm2
- D. 65.3 cm2
Answer: 30.6 cm2
760. The area of the largest circle, that can be drawn inside a rectangle with sides 18 cm by 14 cm, is
- A. 49 cm2
- B. 154 cm2
- C. 378 cm2
- D. 1078 cm2
Answer: 154 cm2
761. If the circumference of a circle is 100 units, then what will be the length of the arc described by an angle of 20 degrees?
- A. 5.55 units
- B. 4.86 units
- C. 5.85 units
- D. None of these
Answer: 5.55 units
762. If in a circle of radius 21 cm, an arc subtends an angle of 56º at the centre, the length of the arc is
- A. 15.53 cm
- B. 16.53 cm
- C. 18.53 cm
- D. 20.53 cm
Answer: 20.53 cm
763. Area of the segment of a circle is
- A. 1 2 lr
- B. 180º πθr
- C. 2 1 sin 360º 2 r () πθ −θ
- D. None of these
Answer: 2 1 sin 360º 2 r () πθ −θ
764. A horse is tied at the corner of a rectangular field whose length is 20 m and width is 16 m, with a rope whose length is 14 m. Find the area which the horse can graze:
- A. 144 sq. m
- B. 154 sq. m
- C. 156 sq. m
- D. 164 sq. m
Answer: 154 sq. m
765. The minute hand of a clock is 7 cm long. Find the area of the sector made by the minute hand between 7 a.m. and 7.05 a.m.
- A. 11.5 cm2
- B. 12.8 cm2
- C. 15.4 cm2
- D. None of these
Answer: 12.8 cm2
766. A sector of 56º has an area of 17.6 cm2. The its radius will be
- A. 1.5 cm
- B. 3 cm
- C. 4.2 cm
- D. 6 cm
Answer: 6 cm
767. In a circle of radius 7 cm, an arc subtends an angle of 108º at the centre. The area of the sector is
- A. 43.2 cm2
- B. 44.2 cm2
- C. 45.2 cm2
- D. 46.2 cm2
Answer: 46.2 cm2
768. The area of a sector of a circle of radius 5 cm, formed by an arc of length 3.5cm,is
- A. 7.5 cm2
- B. 7.75 cm2
- C. 8.5 cm2
- D. 8.75 cm2
Answer: 8.75 cm2
769. Semicircular lawns are attached to the edges of a 42 m × 35 m rectangular field. What is the total area of the field with lawns?
- A. 1358 m2
- B. 3818.5 m2
- C. 5813 m2
- D. 8318 m2
Answer: 3818.5 m2
770. A square is inscribed in a circle and another in a semi-circle of same radius. The ratio of the area of the first square to the area of the second square is
- A. 2 : 5 / 2: 5
- B. 5 : 2 / 5: 2
- C. 4 : 5 / 4: 5
- D. 5 : 4 / 5: 4
Answer: 5 : 2 / 5: 2
771. An athletic track 14 m wide consists of two straight sections 120 m long joining semi-circular ends whose inner radius is 35 m. The area of the track is
- A. 7026 m2
- B. 7036 m2
- C. 7046 m2
- D. 7056 m2
Answer: 7056 m2
772. In the given diagram, ABCD is a square and semi-circular regions have been added to it by drawing two semi-circles with AB and CD as diameters. If the total area of the three regions is 350 sq. cm, then the length of the side of the square is equal to
- A. 57 cm
- B. 7 cm
- C. 13 cm
- D. 14 cm
Answer: 14 cm
773. A wire bent into a square encloses 81 sq. cm. If the same wire is bent into a semicircle, what is the area enclosed?
- A. 22 cm2
- B. 44 cm2
- C. 77 cm2
- D. 154 cm2
Answer: 77 cm2
774. If the area of a semi-circular plot is 11088 m2, then its perimeter is
- A. 264 m
- B. 348 m
- C. 432 m
- D. 452 m
Answer: 432 m
775. What will be the area of a semi-circle whose perimeter is 36 cm?
- A. 154 cm2
- B. 168 cm2
- C. 308 cm2
- D. None of these
Answer: None of these
776. A vertical rod of height 33 metres is bent to form a semi-circular shape so that the top touches the ground. The distance between the top head and the base on the ground is
- A. 10.5 m
- B. 12 m
- C. 21 m
- D. 33 m
Answer: 21 m
777. What will be the area of a semi-circle of 14 m diameter?
- A. 22 m2
- B. 77 m2
- C. 154 m2
- D. 308 m2
Answer: 77 m2
778. The perimeter of a square is equal to twice the pe-rimeter of a rectangle of length 8 cm and breadth 7 cm. What is the circumference of a semi-circle whose diameter is equal to the side of the square? (rounded off to two decimal places)
- A. 23.57 cm
- B. 38.57 cm
- C. 42.46 cm
- D. 47.47 cm
Answer: 23.57 cm
779. The area of a circle is increased by 22 sq. cm if its radius is increased by 1 cm. The original radius of the circle is
- A. 3 cm
- B. 3.2 cm
- C. 3.5 cm
- D. 6 cm
Answer: 3 cm
780. The ratio of the outer and the inner perimeters of a circular path is 23 : 22. If the path is 5 metres wide, the diameter of the inner circle is
- A. 55 m
- B. 110 m
- C. 220 m
- D. 230 m
Answer: 220 m
781. A 4 ft wide concrete wall surrounds a circular pool, and its area is 11/25 of the pool's area. Find the pool's radius.
- A. 8 ft
- B. 16 ft
- C. 20 ft
- D. 30 ft
Answer: 20 ft
Explanation: Let the radius of the pool be R ft. Radius of the pool including the wall = (R + 4) ft. Area of the concrete wall 22 =π + − [( 4) ] sq. ft RR =π + + + − π [( 4 )( 4 ] sq. ft = 8 (R + 2) sq.ft. R RR R 11 2 8 ( 2) 25 π += π RR ⇔ 11R2 = 200 (R + 2 ⇔ 11R2 – 200R – 400 = 0 ⇔ 11R2 – 220R + 20R – 400 = 0 ⇔ 11R (R – 20) + 20 (R – 20) = 0 ⇔ (R – 20) (11R + 20) = 0 ⇔ R = 20. ⇔ Radius of the pool = 20 ft.
Explanation: Let the radius of the pool be R ft. Radius of the pool including the wall = (R + 4) ft. Area of the concrete wall 22 =π + − [( 4) ] sq. ft RR =π + + + − π [( 4 )( 4 ] sq. ft = 8 (R + 2) sq.ft. R RR R 11 2 8 ( 2) 25 π += π RR ⇔ 11R2 = 200 (R + 2 ⇔ 11R2 – 200R – 400 = 0 ⇔ 11R2 – 220R + 20R – 400 = 0 ⇔ 11R (R – 20) + 20 (R – 20) = 0 ⇔ (R – 20) (11R + 20) = 0 ⇔ R = 20. ⇔ Radius of the pool = 20 ft.
782. A small disc of radius r is cut out from a disc of radius R. The weight of the disc which now has a hole in it, is reduced to 24 25 of the original weight. If R = xr, what is the value of x?
- A. 4
- B. 4.5
- C. 24
- D. None of these
Answer: None of these
783. A circular road runs around a circular garden. If the difference between the circumference of the outer circle and the inner circle is 44 m, the width of the road is
- A. 3.5 m
- B. 4 m
- C. 7 m
- D. 7.5 m
Answer: 7 m
784. The areas of two concentric circles forming a ring are 154 sq. cm and 616 sq. cm. The breadth of the ring is
- A. 7 cm
- B. 14 cm
- C. 21 cm
- D. 28 cm
Answer: 7 cm
785. The circumference of a circular ground is 88 metres. A strip of land, 3 metres wide, inside and along the circumference of the ground is to be levelled. What is the budgeted expenditure if the levelling costs ₹ 7 per square metre?
- A. ₹ 1050
- B. ₹ 1125
- C. ₹ 1325
- D. ₹ 1650
Answer: ₹ 1650
786. A circle of radius 5 cm is drawn and another circle of 3 cm radius is cut out of this circle. What is the radius of a circle which has the same area as the area of the bigger circle excluding the cut one?
- A. 2 cm
- B. 3 cm
- C. 4 cm
- D. 4.5 cm
Answer: 4 cm
787. A circular grassy plot of land, 42 cm in diameter, has a path 3.5 m wide running around it outside. The cost of gravelling the path at ₹ 4 per square metre is
- A. ₹ 1002
- B. ₹ 1802
- C. ₹ 2002
- D. ₹ 3002
Answer: ₹ 2002
788. A circular ground of 35 m diameter has a 1.4 m wide garden running around it. What is the garden's area in square metres?
- A. 160.16
- B. 176.16
- C. 196.16
- D. None of these
Answer: None of these
789. Two boys are running on two different circular paths with same centre. If their radii are 5 m and 10 m, the maximum possible distance between them is
- A. 5 m
- B. 10 m
- C. 15 m
- D. 20 m
Answer: 15 m
Explanation: Since the diameter is the longest chord of a circle, so maximum possible distance = (10 + 5) m = 15 m.
Explanation: Since the diameter is the longest chord of a circle, so maximum possible distance = (10 + 5) m = 15 m.
790. The circumference of the back-sided wheel of a vehicle is 1 m greater than that of front side wheel. To travel 600 m, the front wheel rotates 30 times more than the back wheel. The circumference of the front wheel is
- A. 2 m
- B. 4 m
- C. 5 m
- D. None of these
Answer: 4 m
791. The circumferences of the front and rear wheels of a bicycle are 3.5 m and 3 m respectively. If the vehicle is moving at a speed of 15 m/sec, the shortest time in which both the wheels will make a whole number of turns is
- A. 1.4 seconds
- B. 2.1 seconds
- C. 4 seconds
- D. 6.4 seconds
Answer: 1.4 seconds
792. The radii of the front wheel and the rear wheel of a bike are 14 cm and 21 cm respectively. Rahul puts a red mark on the point of contact of each of the wheels with the ground when the bike is station-ary. Once the bike starts moving, then after what distance will the two red marks touch the ground again simultaneously?
- A. 42 cm
- B. 84 cm
- C. 264 cm
- D. 294 cm
Answer: 264 cm
793. The circumference of the front wheel of a cart is 40 ft long and that of the back wheel is 48 ft long. What is the distance travelled by the cart, when the front wheel has done five more revolutions than the rear wheel?
- A. 850 ft
- B. 950 ft
- C. 1200 ft
- D. 1450 ft
Answer: 1200 ft
Explanation: Let the rear wheel make x revolutions. Then, the front wheel makes (x + 5) revolutions. (x + 5) × 40 = 48x ⇒ 8x = 200 ⇒ x = 25. Distance travelled by the cart = (48 × 25) ft = 1200 ft.
Explanation: Let the rear wheel make x revolutions. Then, the front wheel makes (x + 5) revolutions. (x + 5) × 40 = 48x ⇒ 8x = 200 ⇒ x = 25. Distance travelled by the cart = (48 × 25) ft = 1200 ft.
794. Find the diameter of a wheel that makes 113 revolutions in covering 2 km 26 decametres.
- A. 4 4 13 m
- B. 4 6 11 m
- C. 4 12 11 m
- D. 8 12 11 m
Answer: 4 6 11 m
795. A small ring of negligible thickness and radius 2 cm moves on a bigger rung of radius 10 cm. How many rotations will the small ring take on the bigger ring to make a complete round?
- A. 5
- B. 6
- C. 7
- D. 10
Answer: 5
Explanation: Required number of rotations = Circumference of bigger ring Circumference of smaller ring = 2 10 5. 22 ×π× = ×π×
Explanation: Required number of rotations = Circumference of bigger ring Circumference of smaller ring = 2 10 5. 22 ×π× = ×π×
796. A toothed wheel of diameter 50 cm is attached to a smaller wheel of diameter 30 cm. How many revolutions will the smaller wheel make when the larger one makes 15 revolutions?
- A. 18
- B. 20
- C. 25
- D. 30
Answer: 25
797. Wheels of diameters 7 cm and 14 cm start rolling simultaneously from X and Y, which are 1980 cm apart, towards each other in opposite directions. Both of them make the same number of revolutions per second. If both of them meet after 10 seconds, the speed of the smaller wheel is
- A. 22 cm/sec
- B. 44 cm/sec
- C. 66 cm/sec
- D. 132 cm/sec
Answer: 22 cm/sec
798. A cycle wheel has a diameter of 70 cm. A cyclist rides at 22 km/hr for 30 hours. How many revolutions does the wheel make?
- A. 3 lakh
- B. 4 lakh
- C. 30 million
- D. None of these
Answer: 3 lakh
799. The radius of the wheel of a vehicle is 70 cm. The wheel makes 10 revolutions in 5 seconds. The speed of the vehicle is
- A. 29.46 km/hr
- B. 31.68 km/hr
- C. 32.72 km/hr
- D. 36.25 km/hr
Answer: 31.68 km/hr
800. If the wheel of the engine of a train 2 4 7 metres in circumference makes 7 revolutions in 4 seconds, then the speed (in km/hr) of the train is
- A. 27
- B. 28
- C. 29
- D. 30
Answer: 27