Class 10 Practice – Level 2 – Set 2 – Circles Leave a Comment / By anushka kumari / September 19, 2024 Class 10 Practice – Level 2 – Set 2 – Circles Total questions: 25 1. A path of 8 m width runs around the outsider of a circular park whose radius is 17 m. Find the area of the path. Topic: Area of a Circular Path $ \displaystyle 1189\text{ }{{\text{m}}^{2}}$ $ \displaystyle 1056\text{ }{{\text{m}}^{2}}$ $ \displaystyle 1044\text{ }{{\text{m}}^{2}}$ $ \displaystyle 1136\text{ }{{\text{m}}^{2}}$ None 2. The radius of the wheel of a vehicle is 42 cm. How many revolutions will it complete in a 19.8km long journey? Topic: Revolutions of a Circular Wheel 5400 4500 2600 7500 None 3. A rope by which cow is tethered is increased from 16 m to 23 m. How much additional ground does it have now to graze? Topic: Additional Grazing Area $ \displaystyle638\text{ }{{\text{m}}^{2}}$ $ \displaystyle 587\text{ }{{\text{m}}^{2}}$ $ \displaystyle 858\text{ }{{\text{m}}^{2}}$ $ \displaystyle 769\text{ }{{\text{m}}^{2}}$ None 4. The area of a circle is 98.56 $ \displaystyle \text{c}{{\text{m}}^{2}}$. Find its circumference. Topic: Circumference of a Circle 25.3 cm 54.2 cm 35.2 cm 66.4 cm None 5. The circumference of a circle is 39.6 cm. What is the area? Topic: Circumference of a Circle 124.74 sq.cm 145.36 sq.cm 136.25 sq.cm 134.25 sq.cm None 6. What should be the radius of a circle whose perimeter and area are numerically equal? Topic: Perimeter and Area 6 cm 8 cm 2 cm 4 cm None 7. Find the area of the sector of a circle having radius 6 cm and angle 30°. (Take π = 3.14) Topic: Area of a Sector of a Circle $ \displaystyle 8.96\text{ c}{{\text{m}}^{2}}$ $ \displaystyle 9.42\text{ c}{{\text{m}}^{2}}$ $ \displaystyle 7.38\text{ c}{{\text{m}}^{2}}$ $ \displaystyle 5.98\text{ c}{{\text{m}}^{2}}$ None 8. The radius of a circle is 17.5cm. Find the area of the sector enclosed by two radii and an arc 44cm in length. Topic: Area of a Sector of a Circle $ \displaystyle 147\text{ c}{{\text{m}}^{2}}$ $ \displaystyle 296\text{ c}{{\text{m}}^{2}}$ $ \displaystyle 385\text{ c}{{\text{m}}^{2}}$ $ \displaystyle 285\text{ c}{{\text{m}}^{2}}$ None 9. The radii of two circles are 8 cm and 6 cm. Find the radius of the circle having area equal to the sum of the areas of the two circles. Topic: Radius of a Circle 12 cm 10 cm 16 cm 18 cm None 10. Find the perimeter of a semicircular protractor whose diameter is 14 cm. Topic: Perimeter of a Semicircle 48 cm 56 cm 36 cm 24 cm None 11. The difference between the circumference and radius of a circle is 37 cm. Using π = $ \displaystyle \dfrac{{22}}{7}$, find the circumference of the circle. Topic: Circumference of a Circle 36 cm 22 cm 57 cm 44 cm None 12. The circumference of a circle is 22 cm. What the area of its quadrant. Topic: Area of a Quadrant $ \displaystyle \dfrac{{66}}{4}\text{ c}{{\text{m}}^{2}}$ $ \displaystyle \dfrac{{77}}{8}\text{ c}{{\text{m}}^{2}}$ $ \displaystyle \dfrac{{85}}{5}\text{ c}{{\text{m}}^{2}}$ $ \displaystyle \dfrac{{32}}{8}\text{ c}{{\text{m}}^{2}}$ None 13. A sheet of paper is in the from of rectangular ABCD in which AB = 40 cm and AD = 28 cm. A semi-circular portion with BC as diameter is cut off. Find the area of the remaining paper. Topic: Area of Remaining Shape $ \displaystyle 654\text{ c}{{\text{m}}^{2}}$ $ \displaystyle 812\text{ c}{{\text{m}}^{2}}$ $ \displaystyle 432\text{ c}{{\text{m}}^{2}}$ $ \displaystyle 549\text{ c}{{\text{m}}^{2}}$ None 14. What is the diameter of a circle whose area is equal to the sum of the areas of two circles of diameters 10 cm and 24 cm? Topic: Diameter of a Circle 13 cm 36 cm 44 cm 26 cm None 15. The circumference of a circle is 8cm. Find the area of the sector whose central angle is 72° Topic: Area of a Sector of a Circle $ \displaystyle 1.02\text{ c}{{\text{m}}^{2}}$ $ \displaystyle 3.05\text{ c}{{\text{m}}^{2}}$ $ \displaystyle 5.12\text{ c}{{\text{m}}^{2}}$ $ \displaystyle 2.10\text{ c}{{\text{m}}^{2}}$ None 16. The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles. Topic: Radius of a Circle 35 cm 12 cm 64 cm 28 cm None 17. In the given figure, if O is the centre of a circle, PQ is a chord and the tangent PR at P makes an angle of 50° with PQ, then ∠POQ will be: Topic: Angle Between Chord and Tangent 100° 80° 90° 75° None 18. In the given figure, if PA and PB are tangents to the circle with centre O such that ∠APB = 50°, then ∠OAB is equal to: Topic: Angle Between Radius and Tangent 25° 30° 40° 50° None 19. If two tangents inclined at an angle 60° are drawn to a circle of radius 3 cm, then the length of each tangent is Topic: Tangent to a Circle $ \displaystyle \dfrac{3}{2}\sqrt{3}$ cm 6 cm 3 cm $ \displaystyle 3\sqrt{3}$ cm None 20. If a, b, c are the sides of a right triangle where c is the hypotenuse. The radius r of the circle which touches the sides of the triangle is given by: Topic: Incircle Radius of a Right Triangle $ \displaystyle r=\dfrac{{a+b+c}}{2}$ $ \displaystyle r={{a+b+c}}$ $ \displaystyle r=\dfrac{{2a+2b+2c}}{2}$ $ \displaystyle r=\dfrac{{a+b+c}}{4}$ None 21. If a circle touches the side BC of a triangle ABC at P and extended sides AB and AC at Q and R, respectively, Then AQ is equal to: Topic: Tangents and Segments in a Triangle $ \displaystyle \dfrac{1}{2}$ (BC + CA + AB) $ \displaystyle \dfrac{1}{4}$ (BC + CA + AB) $ \displaystyle \dfrac{1}{8}$ (BC + CA + AB) $ \displaystyle \dfrac{2}{3}$ (BC + CA + AB) None 22. A circle touches all the four sides of a quadrilateral ABCD.Then the angles subtended at the centre of the circle by the opposite sides are ? Topic: Tangents and Quadrilateral Properties Equal Complementary Supplementary None of these None 23. A quadrilateral ABCD is drawn to circumscribe a circle, then Topic: Circumscribed Quadrilateral Properties AB − CD = AD − BC AB + CD = AD + BC AB + AD = CD + BC AC + BD = AD + BC None 24. From an external point P, tangents PA and PB are drawn to a circle with center O. If ∠PAB = 90°, then find ∠AOB. Topic: Angle Between Tangents 120° 80° 100° 130° None 25. A circle inscribed in triangle ABC touches its sides AB, BC and AC at points D, E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10 cm, then find the lengths of AD. Topic: Inradius and Lengths in a Triangle 4 cm 6 cm 7 cm 3 cm None 1 out of 25 Time's up
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