Page 1 Summative Assessment1 20142015 Mathematics Class – X Time allowed: 3:00 hours Maximum Marks: 90 General Instructions: a) All questions are compulsory. b) Question paper contains 31 questions divide into 4 sections A, B, C and D. c) Question No. 1 to 4 are very short type questions, carrying 1 mark each. Question No. 5 to 10 are of short answer type questions, carrying 2 marks each. Question No. 11 to 20 carry 3 marks each. Question No. 21 to 31 carry 4 marks each. d) There are no overall choices in the question paper. e) Use of calculator is not permitted. Section A Question numbers 1 to 4 carry 1 mark each. 1. Find the angle of elevation of the top of the pole 75 3m high from a point at the distance of 75 m from the base of the pole in a horizontal plane. 2. Find the value(s) of the d if the distance between (d,2) and (3,4) is 8 units. 3. Two circular cylinders of equal volumes have their radii in the ration 2:1. Find the ratio of their heights. 4. What is the probability of having 53 Mondays in a nonleap year? Section B Question numbers 5 to 10 are two marks each. 5. Without finding the roots, comment upon the nature of roots of the equation 2 2 5 3 6 0 x x + + = . 6. A quadrilateral ABCD is drawn to circumscribe the circle with centre O. prove that AB+CD = AD+BC. OR PA and PB are tangents from an external point P to a circle with centre O and 80 APB ? = ° . Find POA ? . 7. Find the sum of first 20 terms of an AP whose nth term is given by 3 4 n t n =  8. If the difference between the circumference and the radius of a circle is 37 cm, then find the area of the circle. 9. Cards marked with numbers 5,6,7, …… 74 are placed in a bag and mixed thoroughly. A card is chosen at random. Find the probability that the number on the card is a cube number. 10. A coin is tossed twice. Find the probability of getting a) At most one head Page 2 Summative Assessment1 20142015 Mathematics Class – X Time allowed: 3:00 hours Maximum Marks: 90 General Instructions: a) All questions are compulsory. b) Question paper contains 31 questions divide into 4 sections A, B, C and D. c) Question No. 1 to 4 are very short type questions, carrying 1 mark each. Question No. 5 to 10 are of short answer type questions, carrying 2 marks each. Question No. 11 to 20 carry 3 marks each. Question No. 21 to 31 carry 4 marks each. d) There are no overall choices in the question paper. e) Use of calculator is not permitted. Section A Question numbers 1 to 4 carry 1 mark each. 1. Find the angle of elevation of the top of the pole 75 3m high from a point at the distance of 75 m from the base of the pole in a horizontal plane. 2. Find the value(s) of the d if the distance between (d,2) and (3,4) is 8 units. 3. Two circular cylinders of equal volumes have their radii in the ration 2:1. Find the ratio of their heights. 4. What is the probability of having 53 Mondays in a nonleap year? Section B Question numbers 5 to 10 are two marks each. 5. Without finding the roots, comment upon the nature of roots of the equation 2 2 5 3 6 0 x x + + = . 6. A quadrilateral ABCD is drawn to circumscribe the circle with centre O. prove that AB+CD = AD+BC. OR PA and PB are tangents from an external point P to a circle with centre O and 80 APB ? = ° . Find POA ? . 7. Find the sum of first 20 terms of an AP whose nth term is given by 3 4 n t n =  8. If the difference between the circumference and the radius of a circle is 37 cm, then find the area of the circle. 9. Cards marked with numbers 5,6,7, …… 74 are placed in a bag and mixed thoroughly. A card is chosen at random. Find the probability that the number on the card is a cube number. 10. A coin is tossed twice. Find the probability of getting a) At most one head b) No head Section C Question numbers 11 to 20 carry three marks each. 11. Find the middle term(s) of an AP 12, 15, 18, …… 99 12. In a circle of radius 21 cm, an arc subtends an angle of 90° at the centre. Find the a) Length of the arc b) Area of the sector formed by the arc 13. The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of a tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m. Or The angle of elevation of the tower from a point in a horizontal plane is 30° . After moving 30 metres towards the tower the angle of elevation changes to 60° . Find the height of the tower. 14. Find the value of k if A(7,2), B(5,1) and C(3,k) are collinear. 15. Three vertices of a parallelogram ABCD are A(3,4), B(1,3) and C(6,2). If E is the midpoint of AD, find the coordinates of E. 16. Draw a circle of radius 6 cm. Take a point P which is 10 cm away from its centre, construct a pair of tangents to the circle. Measure its lengths. 17. Solve for x: 2 3 2 2 2 3 0 x x   = 18. A company produced 600 smartphones in the third month. 700 in the seventh month. Assuming that production increases uniformly every month find a) The production in the first month b) The production in the 13 th month 19. Arav wants to colour wooden top which is in the form of a cone surmounted by a hemisphere. The total height of the top is 5 cm and the diameter of the top is 3.5 cm. Find the area he will have to colour. 20. “The lengths of tangents drawn from an external point to a circle are equal”:  Prove. Section D Question numbers 21 to 31 carry four marks each. 21. The line segment joining A(2,1) and B(5,8) is trisected at the point P and Q such that P is nearer to B. Find the coordinates of P and Q. Also if P also lies on the line given by 2x+y+k=0, find the value of k. 22. Construct a triangle ABC with BC=6 cm, AB=5cm and 60 ABC ? = ° . Then construct a triangle whose sides are 4 3 of the corresponding sides of ABC ? . 23. A container, opened from the top and made up of metal sheet, is in the form of a frustum of cone of height 16 cm with radii of its lower and upper ends are 8 cm and 20 cm, respectively. a) Find the cost of metal sheet used t make the container, if it costs Rs 8 per 100 sq.cm. b) Find the capacity of the container in liters (Use 3.14 p = ) Page 3 Summative Assessment1 20142015 Mathematics Class – X Time allowed: 3:00 hours Maximum Marks: 90 General Instructions: a) All questions are compulsory. b) Question paper contains 31 questions divide into 4 sections A, B, C and D. c) Question No. 1 to 4 are very short type questions, carrying 1 mark each. Question No. 5 to 10 are of short answer type questions, carrying 2 marks each. Question No. 11 to 20 carry 3 marks each. Question No. 21 to 31 carry 4 marks each. d) There are no overall choices in the question paper. e) Use of calculator is not permitted. Section A Question numbers 1 to 4 carry 1 mark each. 1. Find the angle of elevation of the top of the pole 75 3m high from a point at the distance of 75 m from the base of the pole in a horizontal plane. 2. Find the value(s) of the d if the distance between (d,2) and (3,4) is 8 units. 3. Two circular cylinders of equal volumes have their radii in the ration 2:1. Find the ratio of their heights. 4. What is the probability of having 53 Mondays in a nonleap year? Section B Question numbers 5 to 10 are two marks each. 5. Without finding the roots, comment upon the nature of roots of the equation 2 2 5 3 6 0 x x + + = . 6. A quadrilateral ABCD is drawn to circumscribe the circle with centre O. prove that AB+CD = AD+BC. OR PA and PB are tangents from an external point P to a circle with centre O and 80 APB ? = ° . Find POA ? . 7. Find the sum of first 20 terms of an AP whose nth term is given by 3 4 n t n =  8. If the difference between the circumference and the radius of a circle is 37 cm, then find the area of the circle. 9. Cards marked with numbers 5,6,7, …… 74 are placed in a bag and mixed thoroughly. A card is chosen at random. Find the probability that the number on the card is a cube number. 10. A coin is tossed twice. Find the probability of getting a) At most one head b) No head Section C Question numbers 11 to 20 carry three marks each. 11. Find the middle term(s) of an AP 12, 15, 18, …… 99 12. In a circle of radius 21 cm, an arc subtends an angle of 90° at the centre. Find the a) Length of the arc b) Area of the sector formed by the arc 13. The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of a tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m. Or The angle of elevation of the tower from a point in a horizontal plane is 30° . After moving 30 metres towards the tower the angle of elevation changes to 60° . Find the height of the tower. 14. Find the value of k if A(7,2), B(5,1) and C(3,k) are collinear. 15. Three vertices of a parallelogram ABCD are A(3,4), B(1,3) and C(6,2). If E is the midpoint of AD, find the coordinates of E. 16. Draw a circle of radius 6 cm. Take a point P which is 10 cm away from its centre, construct a pair of tangents to the circle. Measure its lengths. 17. Solve for x: 2 3 2 2 2 3 0 x x   = 18. A company produced 600 smartphones in the third month. 700 in the seventh month. Assuming that production increases uniformly every month find a) The production in the first month b) The production in the 13 th month 19. Arav wants to colour wooden top which is in the form of a cone surmounted by a hemisphere. The total height of the top is 5 cm and the diameter of the top is 3.5 cm. Find the area he will have to colour. 20. “The lengths of tangents drawn from an external point to a circle are equal”:  Prove. Section D Question numbers 21 to 31 carry four marks each. 21. The line segment joining A(2,1) and B(5,8) is trisected at the point P and Q such that P is nearer to B. Find the coordinates of P and Q. Also if P also lies on the line given by 2x+y+k=0, find the value of k. 22. Construct a triangle ABC with BC=6 cm, AB=5cm and 60 ABC ? = ° . Then construct a triangle whose sides are 4 3 of the corresponding sides of ABC ? . 23. A container, opened from the top and made up of metal sheet, is in the form of a frustum of cone of height 16 cm with radii of its lower and upper ends are 8 cm and 20 cm, respectively. a) Find the cost of metal sheet used t make the container, if it costs Rs 8 per 100 sq.cm. b) Find the capacity of the container in liters (Use 3.14 p = ) 24. How many terms of the series 54, 51, 48, …… be taken so that their sum is 513? Explain the double answer. 25. Some students planned to donate Rs 2,000 to help a child. But 5 students could not contribute due to some reason and thus contribution amount increased by Rs. 20 per student. How many students paid the amount and how much they contributed? 26. In the figure ABC is a right triangle with AB=6 cm, AC=8 cm and 90 A ? = ° . A circle with centre O is inscribed in it. Find r, the radius of the circle. Or Prove that the opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle. 27. A wooden toy was made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the surface area and volume of wood in the toy. 28. Solve for x: 24 24 1, 18,18 18 18 x x x  = ?   + 29. In the given figure, ABCD is a trapezium with AD BC , 90 DAB ? = ° , AD=10 cm and BC=4 cm. Area of trapezium is 24.5 sq. cm. If ABE is a quadrant of a circle, find the area of the shaded region. (use 22 7 p = ) 30. A hoarding on “SAVE YAMUNA”, 5 m high is fixed on the top of the tower. The angle of elevation of the top of the hoarding as observed from a point A on the ground is 60° and the angle of depression of point A from the top of the tower is 45° . Find the height of the tower. 3 1.73 = ). Why is necessary to spread awareness for saving Yamuna River? 31. A boys throws two dice at the same time. Find the probability of getting a) A doublet of odd number b) An even number as the sum c) The sum is not a prime number d) The product as a perfect cube number Page 4 Summative Assessment1 20142015 Mathematics Class – X Time allowed: 3:00 hours Maximum Marks: 90 General Instructions: a) All questions are compulsory. b) Question paper contains 31 questions divide into 4 sections A, B, C and D. c) Question No. 1 to 4 are very short type questions, carrying 1 mark each. Question No. 5 to 10 are of short answer type questions, carrying 2 marks each. Question No. 11 to 20 carry 3 marks each. Question No. 21 to 31 carry 4 marks each. d) There are no overall choices in the question paper. e) Use of calculator is not permitted. Section A Question numbers 1 to 4 carry 1 mark each. 1. Find the angle of elevation of the top of the pole 75 3m high from a point at the distance of 75 m from the base of the pole in a horizontal plane. 2. Find the value(s) of the d if the distance between (d,2) and (3,4) is 8 units. 3. Two circular cylinders of equal volumes have their radii in the ration 2:1. Find the ratio of their heights. 4. What is the probability of having 53 Mondays in a nonleap year? Section B Question numbers 5 to 10 are two marks each. 5. Without finding the roots, comment upon the nature of roots of the equation 2 2 5 3 6 0 x x + + = . 6. A quadrilateral ABCD is drawn to circumscribe the circle with centre O. prove that AB+CD = AD+BC. OR PA and PB are tangents from an external point P to a circle with centre O and 80 APB ? = ° . Find POA ? . 7. Find the sum of first 20 terms of an AP whose nth term is given by 3 4 n t n =  8. If the difference between the circumference and the radius of a circle is 37 cm, then find the area of the circle. 9. Cards marked with numbers 5,6,7, …… 74 are placed in a bag and mixed thoroughly. A card is chosen at random. Find the probability that the number on the card is a cube number. 10. A coin is tossed twice. Find the probability of getting a) At most one head b) No head Section C Question numbers 11 to 20 carry three marks each. 11. Find the middle term(s) of an AP 12, 15, 18, …… 99 12. In a circle of radius 21 cm, an arc subtends an angle of 90° at the centre. Find the a) Length of the arc b) Area of the sector formed by the arc 13. The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of a tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m. Or The angle of elevation of the tower from a point in a horizontal plane is 30° . After moving 30 metres towards the tower the angle of elevation changes to 60° . Find the height of the tower. 14. Find the value of k if A(7,2), B(5,1) and C(3,k) are collinear. 15. Three vertices of a parallelogram ABCD are A(3,4), B(1,3) and C(6,2). If E is the midpoint of AD, find the coordinates of E. 16. Draw a circle of radius 6 cm. Take a point P which is 10 cm away from its centre, construct a pair of tangents to the circle. Measure its lengths. 17. Solve for x: 2 3 2 2 2 3 0 x x   = 18. A company produced 600 smartphones in the third month. 700 in the seventh month. Assuming that production increases uniformly every month find a) The production in the first month b) The production in the 13 th month 19. Arav wants to colour wooden top which is in the form of a cone surmounted by a hemisphere. The total height of the top is 5 cm and the diameter of the top is 3.5 cm. Find the area he will have to colour. 20. “The lengths of tangents drawn from an external point to a circle are equal”:  Prove. Section D Question numbers 21 to 31 carry four marks each. 21. The line segment joining A(2,1) and B(5,8) is trisected at the point P and Q such that P is nearer to B. Find the coordinates of P and Q. Also if P also lies on the line given by 2x+y+k=0, find the value of k. 22. Construct a triangle ABC with BC=6 cm, AB=5cm and 60 ABC ? = ° . Then construct a triangle whose sides are 4 3 of the corresponding sides of ABC ? . 23. A container, opened from the top and made up of metal sheet, is in the form of a frustum of cone of height 16 cm with radii of its lower and upper ends are 8 cm and 20 cm, respectively. a) Find the cost of metal sheet used t make the container, if it costs Rs 8 per 100 sq.cm. b) Find the capacity of the container in liters (Use 3.14 p = ) 24. How many terms of the series 54, 51, 48, …… be taken so that their sum is 513? Explain the double answer. 25. Some students planned to donate Rs 2,000 to help a child. But 5 students could not contribute due to some reason and thus contribution amount increased by Rs. 20 per student. How many students paid the amount and how much they contributed? 26. In the figure ABC is a right triangle with AB=6 cm, AC=8 cm and 90 A ? = ° . A circle with centre O is inscribed in it. Find r, the radius of the circle. Or Prove that the opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle. 27. A wooden toy was made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the surface area and volume of wood in the toy. 28. Solve for x: 24 24 1, 18,18 18 18 x x x  = ?   + 29. In the given figure, ABCD is a trapezium with AD BC , 90 DAB ? = ° , AD=10 cm and BC=4 cm. Area of trapezium is 24.5 sq. cm. If ABE is a quadrant of a circle, find the area of the shaded region. (use 22 7 p = ) 30. A hoarding on “SAVE YAMUNA”, 5 m high is fixed on the top of the tower. The angle of elevation of the top of the hoarding as observed from a point A on the ground is 60° and the angle of depression of point A from the top of the tower is 45° . Find the height of the tower. 3 1.73 = ). Why is necessary to spread awareness for saving Yamuna River? 31. A boys throws two dice at the same time. Find the probability of getting a) A doublet of odd number b) An even number as the sum c) The sum is not a prime number d) The product as a perfect cube numberRead More
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