Page 1 5 SAMPLE PAPER CLASS-X General Instructions: 1. All questions are compulsory. 2. Section A consists of 10 questions of 1 mark each. Section B consists of 5 questions of 2 marks each. Section C consists of 10 questions of 3 marks each. Section D consists of 5 questions of 6 marks each. 3. There is no overall choice however internal choice has been provided. SECTION-A 1. State fundam ental theorem of arithmatic. 2. O ne card is draw n at random from a well shuffled deck of 52 cards. Find the probability of getting a king of red suit. 3. If kx+y=7 and 3x-2y=11 o represent inte rsecting lines then find the value of K. 4.Find the 18th term of A.P. 2 , 3 2,5 2,........ 5. If sec5A=cosec(A-36 ),where 5A is an acute angle. Find the value of A. 6. If m ode of the following data is 15. Find K . k 10,15,17,15, 6,17, 20 2 7. In the given fig DE is parallel to BC. AD 2 If and AC =18 cm. Find AE. BD 3 + = Page 2 5 SAMPLE PAPER CLASS-X General Instructions: 1. All questions are compulsory. 2. Section A consists of 10 questions of 1 mark each. Section B consists of 5 questions of 2 marks each. Section C consists of 10 questions of 3 marks each. Section D consists of 5 questions of 6 marks each. 3. There is no overall choice however internal choice has been provided. SECTION-A 1. State fundam ental theorem of arithmatic. 2. O ne card is draw n at random from a well shuffled deck of 52 cards. Find the probability of getting a king of red suit. 3. If kx+y=7 and 3x-2y=11 o represent inte rsecting lines then find the value of K. 4.Find the 18th term of A.P. 2 , 3 2,5 2,........ 5. If sec5A=cosec(A-36 ),where 5A is an acute angle. Find the value of A. 6. If m ode of the following data is 15. Find K . k 10,15,17,15, 6,17, 20 2 7. In the given fig DE is parallel to BC. AD 2 If and AC =18 cm. Find AE. BD 3 + = 6 8. Find X in the give n fig. if PT is tangent to the circle. 2 9. and are zeros of 2 5( 2), then find the product of and . 22 10. Find the perimeter of a quadrant of circle of radius 7cm( = ). 2 SECTION-B 11. Find 31 term If x x a ß a ß p + - of an AP whose 11 term is 38 and 16 term is 73. 12. Find the ratio in which the y-axis divides the join of (5,-6) and(-1,-4). Also find the point of intersection. 13. Evaluate without using trignometric table tan 50 sec 50 cos 40 cos 50 cot 40 cos 50 ec ec + + + OR sec 4 cos ( 20 ), where 4A is an acute angle, find the value of A. If A ec A = - 14. If AB,AC and PQ are tangents in the given fig. and AB=5 cm. Find the perimeter of APQ. ? Page 3 5 SAMPLE PAPER CLASS-X General Instructions: 1. All questions are compulsory. 2. Section A consists of 10 questions of 1 mark each. Section B consists of 5 questions of 2 marks each. Section C consists of 10 questions of 3 marks each. Section D consists of 5 questions of 6 marks each. 3. There is no overall choice however internal choice has been provided. SECTION-A 1. State fundam ental theorem of arithmatic. 2. O ne card is draw n at random from a well shuffled deck of 52 cards. Find the probability of getting a king of red suit. 3. If kx+y=7 and 3x-2y=11 o represent inte rsecting lines then find the value of K. 4.Find the 18th term of A.P. 2 , 3 2,5 2,........ 5. If sec5A=cosec(A-36 ),where 5A is an acute angle. Find the value of A. 6. If m ode of the following data is 15. Find K . k 10,15,17,15, 6,17, 20 2 7. In the given fig DE is parallel to BC. AD 2 If and AC =18 cm. Find AE. BD 3 + = 6 8. Find X in the give n fig. if PT is tangent to the circle. 2 9. and are zeros of 2 5( 2), then find the product of and . 22 10. Find the perimeter of a quadrant of circle of radius 7cm( = ). 2 SECTION-B 11. Find 31 term If x x a ß a ß p + - of an AP whose 11 term is 38 and 16 term is 73. 12. Find the ratio in which the y-axis divides the join of (5,-6) and(-1,-4). Also find the point of intersection. 13. Evaluate without using trignometric table tan 50 sec 50 cos 40 cos 50 cot 40 cos 50 ec ec + + + OR sec 4 cos ( 20 ), where 4A is an acute angle, find the value of A. If A ec A = - 14. If AB,AC and PQ are tangents in the given fig. and AB=5 cm. Find the perimeter of APQ. ? 7 15. If the mean of the following data is 18. find the missing frequency P. X i 10 15 20 25 f i 5 10 p 8 2 3 2 SECT IO N-C 16. Find the zeros of polynom ial p(x)= 2 3 2 2 and verify the relationship betw een the zeros and co-efficients. OR On dividing x -3x +x+2 by the x x - - polynomial g(x), the quotient and remainder w ere x-2 and -2x+4 respectively. Find g(x). 17. Find the value of K for which (k-3)x+3y=K, kx+ky=12 will have infinitely many solutions. 18. T he hypotenuse of a right triangle is 1 m less than tw ice the shortest side. If third side is 1 m m ore than the shortest side. Find the sides of the triangle. Page 4 5 SAMPLE PAPER CLASS-X General Instructions: 1. All questions are compulsory. 2. Section A consists of 10 questions of 1 mark each. Section B consists of 5 questions of 2 marks each. Section C consists of 10 questions of 3 marks each. Section D consists of 5 questions of 6 marks each. 3. There is no overall choice however internal choice has been provided. SECTION-A 1. State fundam ental theorem of arithmatic. 2. O ne card is draw n at random from a well shuffled deck of 52 cards. Find the probability of getting a king of red suit. 3. If kx+y=7 and 3x-2y=11 o represent inte rsecting lines then find the value of K. 4.Find the 18th term of A.P. 2 , 3 2,5 2,........ 5. If sec5A=cosec(A-36 ),where 5A is an acute angle. Find the value of A. 6. If m ode of the following data is 15. Find K . k 10,15,17,15, 6,17, 20 2 7. In the given fig DE is parallel to BC. AD 2 If and AC =18 cm. Find AE. BD 3 + = 6 8. Find X in the give n fig. if PT is tangent to the circle. 2 9. and are zeros of 2 5( 2), then find the product of and . 22 10. Find the perimeter of a quadrant of circle of radius 7cm( = ). 2 SECTION-B 11. Find 31 term If x x a ß a ß p + - of an AP whose 11 term is 38 and 16 term is 73. 12. Find the ratio in which the y-axis divides the join of (5,-6) and(-1,-4). Also find the point of intersection. 13. Evaluate without using trignometric table tan 50 sec 50 cos 40 cos 50 cot 40 cos 50 ec ec + + + OR sec 4 cos ( 20 ), where 4A is an acute angle, find the value of A. If A ec A = - 14. If AB,AC and PQ are tangents in the given fig. and AB=5 cm. Find the perimeter of APQ. ? 7 15. If the mean of the following data is 18. find the missing frequency P. X i 10 15 20 25 f i 5 10 p 8 2 3 2 SECT IO N-C 16. Find the zeros of polynom ial p(x)= 2 3 2 2 and verify the relationship betw een the zeros and co-efficients. OR On dividing x -3x +x+2 by the x x - - polynomial g(x), the quotient and remainder w ere x-2 and -2x+4 respectively. Find g(x). 17. Find the value of K for which (k-3)x+3y=K, kx+ky=12 will have infinitely many solutions. 18. T he hypotenuse of a right triangle is 1 m less than tw ice the shortest side. If third side is 1 m m ore than the shortest side. Find the sides of the triangle. 8 19.Construct a triangle of sides 4cm, 5cm & 6cm, and then a triangle 2 similar to it whose sides are of corresponding sides of first triangle. 3 20. Prove that: (1+cotA+tanA)(sinA-cosA)=sinAtanA-cotAcosA 2 or 1 cos (cosec -cot ) = 1 cos 21. he mid points of the sides of a triangle are (3,4), (4,6) and(5,7). Find the co-ordinates of the vertices of the triangle. 22. How many coin T ? ? ? ? - + s 1.75 cm in diameter and 2mm thick must be melted to form a cuboid 11cm X 10 cmX 7cm. 23.Prove that 5 -3 2 is an irrational number. 24. In a trapezium ABCD, AB CD and CD=2 AB Cuts AD in F and BC in E, s BC 3 uch that . EC 4 Diagonal BD intersect EF at G. Prove that 7EF=10AB. = 1 1 25. Prove that the points(a,0),(0,b) and (1,1) are collinear if 1. a SECTION-D 26.Prove that the ratio of areas of two similar triangles is equal to the b + = ratio of squares of their corresponding sides using the above theorem do the following: The area of two similar triangles ABC and PQR are in the ratio 9:16,. If BC=4.5 cm. Find the length of QR. OR State and prove Pythagoras theorem. Using the above theorem, Prove the following. In the given figure PQR is a right triangle right angled at Q. If QS=SR, show that PR 2 =4PS 2 -3PQ 2 . Page 5 5 SAMPLE PAPER CLASS-X General Instructions: 1. All questions are compulsory. 2. Section A consists of 10 questions of 1 mark each. Section B consists of 5 questions of 2 marks each. Section C consists of 10 questions of 3 marks each. Section D consists of 5 questions of 6 marks each. 3. There is no overall choice however internal choice has been provided. SECTION-A 1. State fundam ental theorem of arithmatic. 2. O ne card is draw n at random from a well shuffled deck of 52 cards. Find the probability of getting a king of red suit. 3. If kx+y=7 and 3x-2y=11 o represent inte rsecting lines then find the value of K. 4.Find the 18th term of A.P. 2 , 3 2,5 2,........ 5. If sec5A=cosec(A-36 ),where 5A is an acute angle. Find the value of A. 6. If m ode of the following data is 15. Find K . k 10,15,17,15, 6,17, 20 2 7. In the given fig DE is parallel to BC. AD 2 If and AC =18 cm. Find AE. BD 3 + = 6 8. Find X in the give n fig. if PT is tangent to the circle. 2 9. and are zeros of 2 5( 2), then find the product of and . 22 10. Find the perimeter of a quadrant of circle of radius 7cm( = ). 2 SECTION-B 11. Find 31 term If x x a ß a ß p + - of an AP whose 11 term is 38 and 16 term is 73. 12. Find the ratio in which the y-axis divides the join of (5,-6) and(-1,-4). Also find the point of intersection. 13. Evaluate without using trignometric table tan 50 sec 50 cos 40 cos 50 cot 40 cos 50 ec ec + + + OR sec 4 cos ( 20 ), where 4A is an acute angle, find the value of A. If A ec A = - 14. If AB,AC and PQ are tangents in the given fig. and AB=5 cm. Find the perimeter of APQ. ? 7 15. If the mean of the following data is 18. find the missing frequency P. X i 10 15 20 25 f i 5 10 p 8 2 3 2 SECT IO N-C 16. Find the zeros of polynom ial p(x)= 2 3 2 2 and verify the relationship betw een the zeros and co-efficients. OR On dividing x -3x +x+2 by the x x - - polynomial g(x), the quotient and remainder w ere x-2 and -2x+4 respectively. Find g(x). 17. Find the value of K for which (k-3)x+3y=K, kx+ky=12 will have infinitely many solutions. 18. T he hypotenuse of a right triangle is 1 m less than tw ice the shortest side. If third side is 1 m m ore than the shortest side. Find the sides of the triangle. 8 19.Construct a triangle of sides 4cm, 5cm & 6cm, and then a triangle 2 similar to it whose sides are of corresponding sides of first triangle. 3 20. Prove that: (1+cotA+tanA)(sinA-cosA)=sinAtanA-cotAcosA 2 or 1 cos (cosec -cot ) = 1 cos 21. he mid points of the sides of a triangle are (3,4), (4,6) and(5,7). Find the co-ordinates of the vertices of the triangle. 22. How many coin T ? ? ? ? - + s 1.75 cm in diameter and 2mm thick must be melted to form a cuboid 11cm X 10 cmX 7cm. 23.Prove that 5 -3 2 is an irrational number. 24. In a trapezium ABCD, AB CD and CD=2 AB Cuts AD in F and BC in E, s BC 3 uch that . EC 4 Diagonal BD intersect EF at G. Prove that 7EF=10AB. = 1 1 25. Prove that the points(a,0),(0,b) and (1,1) are collinear if 1. a SECTION-D 26.Prove that the ratio of areas of two similar triangles is equal to the b + = ratio of squares of their corresponding sides using the above theorem do the following: The area of two similar triangles ABC and PQR are in the ratio 9:16,. If BC=4.5 cm. Find the length of QR. OR State and prove Pythagoras theorem. Using the above theorem, Prove the following. In the given figure PQR is a right triangle right angled at Q. If QS=SR, show that PR 2 =4PS 2 -3PQ 2 . 9 27. A sailor can row a boat 8 km downstream and return back to the starting point in 1 hr. 40min. If speed of stream is 2 km/hr. Find the speed of boat in still water. 28. An aeroplane when 3000m high, passes vertically above another aeroplane at an instant when the angles of elevation of the two aeroplanes from the same point on the ground are 6 0 0 0 and 45 respectively. Find the vertical distance between two aeroplanes. 29. A solid in the form of right circular cylinder, with hemisphere at one end and a cone at other end. the radius of the common base is 3.5 cm and the heights of the cylindrical & conical portion are 10cm amd 6 cm respectively. 22 Find the total surface area of the (use = ) 7 p 30. Calculate Medians of the following data: Marks obtained No. of students Less than 20 0 Less than 30 4 Less than 40 16 Less than 50 30 Less than 60 46 Less than 70 66 Less than 80 82 Less than 90 92 Less than 100 100Read More

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