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PRACTICE QUESTIONS CLASS – X
Q 1 A train travels 18 km at a uniform speed. If the speed had been 9 km/hr more, it would have taken 1 hour less for the same journey. Find the speed of the train?
Q 2 Determine the ratio in which the line 3x + y = 9 divides the line segment joining the points (1,3) and (2,7) ?
Q 3 Show that the points (12,8) , (-2,6) and (6,0) are the vertices of right angled triangle and also show that the mid point of the hypotenuse is equidistant from the angular point?
Q 4 The angle of elevation of a jet fighter from a point A on the ground is 60°.After a flight of 10 sec , the angle of elevation changes to 30°. If the jet is flying at a speed of 432 km/hr, find the constant height at which the jet is flying. (use √3 = 1.732)
Q 5 In fig. 1 two circular flower beds have been shown on two sides of a square lawn ABCD of side 56 m . If the centre of each circular flower bed is the point of intersection O of two diagonals of square lawns . Find the sum of areas of the lawn and flower bed? Fig. 1 ↓ Q 6 In fig. 2 , two tangents PA & PB are drawn from an external point P to a circle with centre 0 . Prove that AOBP is a cyclic quadrilateral?
Q 7 For what value of ‘m’ will the equation 2mx2 – 2(1 + 2m)x + (3+2m) = 0 have real but distinct roots?
Q 8 Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday) . Each is equally likely to visit the shop on any day as another day. What is the probability that both will visit the shop on (i) the same day (ii) consecutive days (iii) different days
Q 9 In fig. 3 , ABCD is a field in the shape of a trapezium with AB ║CD and ABC=90° , DAB =60° . Four sectors are formed with centre A,B,C,D . The radius of each sector is 17.5m . Find the total area of four sectors? Q 10 In fig. 4 , OP is equal to the diameter of the circle . Prove That ∆ABP is an
Q 1 A train travels 18 km at a uniform speed. If the speed had been 9 km/hr more, it would have taken 1 hour less for the same journey. Find the speed of the train?
Q 2 Determine the ratio in which the line 3x + y = 9 divides the line segment joining the points (1,3) and (2,7) ?
Q 3 Show that the points (12,8) , (-2,6) and (6,0) are the vertices of right angled triangle and also show that the mid point of the hypotenuse is equidistant from the angular point?
Q 4 The angle of elevation of a jet fighter from a point A on the ground is 60°.After a flight of 10 sec , the angle of elevation changes to 30°. If the jet is flying at a speed of 432 km/hr, find the constant height at which the jet is flying. (use √3 = 1.732)
Q 5 In fig. 1 two circular flower beds have been shown on two sides of a square lawn ABCD of side 56 m . If the centre of each circular flower bed is the point of intersection O of two diagonals of square lawns . Find the sum of areas of the lawn and flower bed? Fig. 1 ↓ Q 6 In fig. 2 , two tangents PA & PB are drawn from an external point P to a circle with centre 0 . Prove that AOBP is a cyclic quadrilateral?
Q 7 For what value of ‘m’ will the equation 2mx2 – 2(1 + 2m)x + (3+2m) = 0 have real but distinct roots?
Q 8 Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday) . Each is equally likely to visit the shop on any day as another day. What is the probability that both will visit the shop on (i) the same day (ii) consecutive days (iii) different days
Q 9 In fig. 3 , ABCD is a field in the shape of a trapezium with AB ║CD and ABC=90° , DAB =60° . Four sectors are formed with centre A,B,C,D . The radius of each sector is 17.5m . Find the total area of four sectors? Q 10 In fig. 4 , OP is equal to the diameter of the circle . Prove That ∆ABP is an