DISTRICT COMMON EXAMINATION BOARD – KADAPA – YSR Dist.

Action Plan Model Question Paper 2019-2020

MATHEMATICS Paper – 1

(English Medium) Class: X (Max. Marks : 50) Time: 2.45 Hrs

Instructions: 1. Answer all the questions in a separate answer booklet. 2. The question paper consists of 4 sections and 33 questions. 3. There is internal choice in Section - IV. 4. Write answers neatly and legibly.

Section - Ⅰ

Note: 1. Answer all the Questions in one WORD or PHRASE. 2. Each Question carries ½ Mark. 12X ½ = 6

1. Solve 2𝑥 − (4 − 𝑥) = 5 − 𝑥.

2. 𝐼𝑛 𝟓𝑥 + 4𝑦 = 20, 𝑖𝑓 𝑥 = 2 𝑡ℎ𝑒𝑛 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝒚.

3. Find the length of the longest pole that can be kept in a room of dimensions 12𝑚X9𝑚X8𝑚 ?

4. 𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 ℎ𝑒𝑚𝑖𝑠𝑝ℎ𝑒𝑟𝑒 𝑜𝑓 𝑟𝑎𝑑𝑖𝑢𝑠 3.5𝑐𝑚. (𝜋 =22

7)

𝟓. 𝑊ℎ𝑖𝑐ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔 𝑖𝑠 𝑎 𝑙𝑖𝑛𝑒𝑎𝑟 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑖𝑛 𝑜𝑛𝑒 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒? A. 2𝑥 + 1 = 𝑦 − 3 B. 2𝑡 − 1 = 3𝑡 + 5 C. 2𝑥 − 1 = 𝑥2 D. 𝑥2 − 𝑥 + 1 = 0 6. Write the condition that 𝑎𝑥 + 𝑏𝑦 + 𝐶 = 0 represents a linear equation in two variables 𝑥 𝑎𝑛𝑑 𝑦.

7. Write the relation among speed, distance and time.

8. Which of the following statements is false A) The volume of cuboid = 𝑙𝑏ℎ B) The volume of cube=𝑎3

C) The volume of cylinder= 𝜋𝑟2 ℎ D) The volume of cone = 3𝜋𝑟2ℎ

9. Match the following.

Group – A Group – B

i) 𝑎1

𝑎2≠

𝑏1

𝑏2 a) No solution

ii) 𝑎1

𝑎2=

𝑏1

𝑏2≠

𝑐1

𝑐2 b) Infinitely many solutions

iii) 𝑎1

𝑎2=

𝑏1

𝑏2=

𝑐1

𝑐2 c) Unique solution

A. i-b, ii-c, iii-a B. i-c, ii-a, iii-b C. i-c, ii-b, iii-a D. None of these.

10. Write the formula to find volume of prism. 11. If the speed of the stream is 𝑥 kmph and speed of the boat in still water is 𝑦 kmph then write the speeds in down stream and upstream in terms of 𝑥 𝑎𝑛𝑑 𝑦.

12. Write the combinations of solids involved in a shuttle cock.

19-12-2029 . Day-15 Day

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15E

Section - Ⅱ

Note: 1. Answer all the Questions. 2. Each Question carries1 Mark. 8 X 1 =8

13. Solve the pair of Linear equations 𝑥 + 𝑦 = 10, 𝑥 − 𝑦 = 2 using elimination method. 14. For what value of ‘K’, the pair of equations 3𝑥 + 4𝑦 + 2 = 0 and 9𝑥 + 12𝑦 + 𝑘 = 0 represent coincident lines. 15. If the ratio between the volumes of two spheres is 8:27 then find ratio between their surface areas. 16. If the base radius and height of a cone are 7cm and 24cm then find slant heights.

17. Dependent pair of linear equations always consistent. Why?

18. Write the formula to find T.S.A of cylinder and explain the terms in it.

19.The perimeter of a floor of a room is 17cm. What is the area of four walls of the room, if its heights is 4m? 20. Draw the rough diagram of a toy in the form of a cone mounted on a hemisphere.

Section - Ⅲ

Note: 1. Answer all the Questions. 2. Each Question carries 2 Marks. 8 X 2= 16

21. Solve the following pair of equations using substitution method. 2𝑥 − 𝑦 = 5; 3𝑥 + 2𝑦 = 11

22. The larger of two supplementary angles exceeds by 180. Find the angles. 23. The curved surface area of a cone is 4070cm2 and its diameter is 70cm. What is its slant height?

24. A cylinder and a cone have bases of equal radii and are of equal heights. Show that their volumes are the ration 3:1 25. Lahari said that the pair of equations 2𝑥 + 3𝑦 = 1 𝑎𝑛𝑑 3𝑥 − 𝑦 = 7 represent parallel lines. Do you agree with Lahari? Justify your answer. 26. Write a pair of linear equations in two variables 𝑥 𝑎𝑛𝑑 𝑦 satisfying the following data.

In class X, if three students sit on each bench, one student will be left. If four students sit on each bench, one bench will be left. 27. The length, breadth and height of a cuboid are (log 500 + log 20), (log 800 − log 8) and log 10 respectively. Find the L.S.A of the cuboid. 28. Draw the graph of 2𝑥 + 3𝑦 = 12 𝑏𝑦 taking X and Y axes in plane paper.

Section - Ⅳ

Note: 1. Answer all the Questions. 5 X 4= 20 2. Each Question carries 4 Marks. 3.There is an internal choice for each question. 29. a) Solve the following pair of equations by reducing them to a pair of linear equations. 𝟐

√𝒙+

𝟑

√𝒚= 𝟐 ;

𝟒

√𝒙−

𝟗

√𝒚= −1

(Or)

b) The ratio of incomes of two persons is 9:7 and the ratio of their expenditures is 4:3. If each of them manages to save ₹2000 per months, find their monthly income.

30. a) An iron pillar consists of a cylindrical portion of 2.8m height and 20cm in diameter and a cone of 42cm height surmounting it. Find the weight of the pillar if 1cm3 of iron weight is 7.5grams.

(Or) b) Metallic spheres of radius 6cm, 8cm and 10cm respectively are melted to from a single solid sphere. Find the radius of the resulting sphere. 31. a) The taxi charges in Vijayawada are fixed, along with the charge for the distance covered. For a distance of 10km, the charge paid is ₹220. For a journey of 15km the charge paid is ₹ 310. Find the fixed charges and charge for 1 Km?

(Or) b) A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends.

The length of the capsule is 14mm and the width is 5mm. Find its surface area. 32. a) 2 women and 5 men can together finish an embroidery work in 4days while 3 women and 6 men can finish it in 3days. Find the time taken by 1 woman alone and 1 man alone to finish the work.

(Or) b) A well of diameter 14m is dug 15m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 7m. to form an embankment. Find the height of the embankment. 33. a) Solve the following pair of linear equations graphically. 𝟐𝒙 + 𝒚 − 𝟓 = 𝟎; 𝟑𝒙 − 𝟐𝒚 − 𝟒 = 𝟎

(Or) b) Solve the following system of linear equations graphically. 𝟐𝒙 − 𝟑𝒚 = 𝟖; 𝟒𝒙 − 𝟔𝒚 = 𝟗 .

Prepared by Sri D. VENKATA RAMANA, SA- Maths, ZPHS – Penagaluru- 7799339335