MODEL PAPER - 1 1 CONTINUOUS & COMPREHENSIVE EVALUATION SUMMATIVE ASSESSMENT MODEL PAPER - 1 MATHEMATICS - PAPER - II X CLASS Max Marks : 40] [Time : 2 : 45 hrs SECTION - I Note : 1. 2. 7×1=7M Answer all the following questions. Each question carries one mark . d a 1. Show that cos 32o . cos 58o – sin 32o . sin 58o = 0. 2. What is the probability of drawing a king from a deck of cards. 3. A vertical pole is 10 mt high. The length of it’s shadow is 10 3 . What is the angle of elevation of the sun. 4. ABC ~ DEF, BC = 3 cm, EF = 4 cm and area of ABC = 54 cm2. Determine the area of DEF. 5. Find the arithmetic mean of First Five prime numbers. 6. Express sec in terms of tan . 7. A cylinder and a cone have bases of equal radii and of equal heights. Show that their volumes are in the ratio 3 : 1. Note : 1. 2. 8. , B E C D b a r e d y H SECTION - II 6 × 2 = 12 M Answer the following questions. Each question carries two mark In a triangle ABC, AD is drawn perpendicular to BC prove that AB2 – BD2 = AC2 – CD2. A B D C 9. Write the formulae of median of a grouped data and explain the terms in it. 10. A box contains 5 red marbles, 9 white marbles and 6 green marbles, one marble is taken out the box at random. What is the probability that the marble taken out will be i) red ii) white iii) Non-green www.dcebhyderabad.webnode.in MATHEMATICS - PAPER - I 11. 2 Prove that 4(sin4 30o + cos4 60o) –3 (cos2 45o – sin2 90o) = 2 12. Calculate the mode for the following frequency distribution. C.I 0 4 4 8 8 12 12 16 f 13. 4 8 5 6 22 Find the surface area and volume of a sphere of radius 21 cm use = . 7 SECTION - III Note : 1. 2. 14. Internal choice is given in each question. Each question carries four mark . d a (a) Two boys are in opposite sides of a pole of 100 mts. height. They measure the angle of elevation of the top of the pole as 30o and 60o respectively. Find the distance through which the boys are separated. b a r e d y H (OR) (b) If sec + tan = a, show that sin = 15. 4 × 4 = 16 M a 2 1 a2 1 (a) The radius of a metallic sphere is 3 cm. It is melted and drawn into a wire having diameter of the cross section as 0.2 cm. Find the length of the wire. , B E C D (OR) (b) The frequency distribution of marks scored by 50 students in a test is given below. Find the arithmetic mean. Marks 0 19 20 39 40 59 60 79 80 99 No. of students 5 15 22 6 2 16. (a) (i) Show that the lengths of tangents drawn from an external point to a circle are equal. (ii) The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 15 minutes. (OR) (b) A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box. Find the probability that it bears (i) a two – digit number (ii) a perfect cube number (iii) a number divisible by 10. 17. (a) Draw 0 give curve for the following data. From the curve find out median. Marks 0 5 5 10 10 15 15 20 20 25 25 30 30 35 No. of students 3 7 13 25 40 14 10 (OR) www.dcebhyderabad.webnode.in MODEL PAPER - 1 3 (b) Construct an isosceles triangle whose base is 8 cm. and altitude is 4 cm. Then draw another triangle whose sides are 1 1 times. The corresponding sides of the isosceles triangle. 2 SECTION - IV Note : 1. Each question carries 24. o 2 sin 45 is (c) 3 (b) 1 (c) –1 ( ) ( ) (d) 1 . d a (d) none b a r e d y H (b) 4 : 5 (c) 16 : 25 (d) 25 : 16 The arithmetic mean of first n' natural number is n +1 2 (b) n 1 2 , B E C D (c) n 1 2 (d) ( ) n 2 If the diameter of the base of a right circular cylinder is 14 cm and it’s height is 20 cm. Then it’s curved surface area is ( ) (a) 594 cm2 23. =5M If one areas of two similar triangles are 16 cm2 and 25 cm2 respectively. Then the ratio their corresponding sides is ( ) (a) 22. 2 mark. sin 4 cos 4 sin 2 cos 2 (a) 5 : 4 21. 2 (b) 4 (a) 0 20. 1 The value of cos 00 + sin 90o + (a) 5 19. 1 Choose the correct answer. 2. 18. 10 × (b) 1188 cm2 (c) 440 cm2 (d) 1540 cm2 In ABC, if the sides are 5, 12, 13 then ABC is (a) Scalene triangle (b) Right angled triangle (c) an acute angled triangle (d) Obtuse angled triangle. Among the following a correct statement is (a) 0 P(I) 1 (b) 0 < P(I) < 2 (c) 0 P(I) ( ) ( ) (d) None 25. The angle between a tangent to a circle and the radius drawn at the end point of contact is _____ ( ) o o o o (a) 90 (b) 60 (c) 120 (d) 180 26. The probability of drawing out a face card from a deck of cards is _____ (a) 27. 1 52 (b) 1 26 (c) 3 13 (d) (b) 0 (c) 2 www.dcebhyderabad.webnode.in ) ( ) 2 13 cos 80o + cos 59o . cosec 31o is equal to _____ sin 10o (a) 1 ( (d) 3

© Copyright 2020