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Class X Mathematics

DELHI PUBLIC SCHOOL KATHUA
 SUMMER HOLIDAY HOMEWORK 
(2017-18)
 CLASS X 

Mathematics

Pair Linear Equations in Two Variables
  1. A boat goes 70km in 10 hours along the stream and returns back the same distance in 14 hours. Find the speed of the boat and the stream.     
  2. Five years hence, the age of Jacob will be three times that times that of his son. Five    years ago, Jacob’s was seven times that of his son. What are their present ages?  
  3. The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old an Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju  .
  4. A train covered a certain distance at a uniform speed. If the train would have been 10km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.    
  5. The sum of a two digit number and the number obtained by reversing the order of a digit is 99. If the digits differ by 3, find the number.  
  6. A boat goes 30km upstream and 44km downstream in 10 hours. In 13 hours, it can go 40km upstream and 55km down-stream Determine the speed of the stream and that of the boat in still water.
  7. The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digit. Find the number.
  8. The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.
  9. 2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.        
  10. Roohi travels 300km to her home partly by train and partly by bus. She takes 4 hours if she travels 60km by train and the remaining by bus. If she travels 100km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.
  11. A man has only 20 paisa coins and 25 paisa coins in his purse. If he has 50 coins in all totaling Rs 11.25. How many coins of each kind does he have?  
  12. A says to B “my present age is Five times your that age when I was an old as you are now. It the sum of their present ages is 48 years, find their present ages. 
  13. A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours it can go 40km upstream and 55 km down stream. Determined the speed of the stream and that of the boat in still water.

Real Numbers
  1. Express 140 as a product of its prime factors
  2. Find the LCM and HCF of 12, 15 and 21 by the prime factorization method.
  3. Find the LCM and HCF of 6 and 20 by the prime factorization method.
  4. State whether13/3125 will have a terminating decimal expansion or a non-terminating repeating decimal.
  5. State whether 17/8 will have a terminating decimal expansion or a non-terminating repeating decimal.
  6. Find the LCM and HCF of 26 and 91 and verify that LCM × HCF = product of the two numbers.
  7. Use Euclid’s division algorithm to find the HCF of 135 and 225
  8. Use Euclid’s division lemma to show that the square of any positive integer is either of the form
  9. 3m or 3m + 1 for some integer m
  10. Prove that √3 is irrational.
  11. Show that 5 – √3 is irrational
  12. Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some Integer.
  13. An army contingent of 616 members is to march behind an army band of 32 members in a parade. 
  14. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?
  15. Express 156 as a product of its prime factors.
  16. Find the LCM and HCF of 17, 23 and 29 by the prime factorization method.
  17. Find the HCF and LCM of 12, 36 and 160, using the prime factorization method.
  18. State whether 6/15 will have a terminating decimal expansion or a non-terminating repeating decimal.
  19. State whether35/50 will have a terminating decimal expansion or a non-terminating Repeating decimal.
  20. Find the LCM and HCF of 192 and 8 and verify that LCM × HCF = product of the two numbers.
  21. Use Euclid’s algorithm to find the HCF of 4052 and 12576.
  22. Show that any positive odd integer is of the form of 4q + 1 or 4q + 3, where q is some integer.
  23. Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.
  24. Prove that 3√2 5 is irrational.
  25. Prove that 1/√2 is irrational. 
  26. In a school there are tow sections- section A and Section B of class X. There are 32 students in section A and 36 students in section B. Determine the minimum number of books required for their class library so that they can be distributed equally among students of section A or section B.
  27. Express 3825 as a product of its prime factors.
  28. Find the LCM and HCF of 8, 9 and 25 by the prime factorization method.
  29. Find the HCF and LCM of 6, 72 and 120, using the prime factorization method.
  30. State whether 29/343 will have a terminating decimal expansion or a non-terminating repeating decimal.
  31. State whether 23/ 23 52 will have a terminating decimal expansion or a non-terminating repeating decimal
  32. Find the LCM and HCF of 336 and 54 and verify that LCM × HCF = product of the two numbers
  33. Use Euclid’s division algorithm to find the HCF of 867 and 255
  34. Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q + 1, where q is some integer.
  35. Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9lm + 1 or 9m + 8.
  36. Prove that 7 √5 is irrational. 
  37. Prove that √5 is irrational.
  38. There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?
  39. Express 5005 as a product of its prime factors.
  40. Find the LCM and HCF of 24, 36 and 72 by the prime factorization method.
  41. Find the LCM and HCF of 96 and 404 by the prime factorization method
  42. State whether 64/455 will have a terminating decimal expansion or a non-terminating repeating decimal
  43. State whether15/ 1600 will have a terminating decimal expansion or a non-terminating repeating decimal.
  44. Find the LCM and HCF of 510 and 92 and verify that LCM × HCF = product of the two numbers. 
  45. Use Euclid’s division algorithm to find the HCF of 196 and 38220 
  46. Show that 3√ 2 is irrational.
  47. Prove that 3 + 2 √5 is irrational.
  48. A sweet seller has 420 kaju barfis and 130 badam barfis. She wants to stack them in such a way that each stack has the same number, and they take up the least area of the tray. What is the maximum number of barfis that can be placed in each stack for this purpose?
  49. Use Euclid’s division algorithm to find the HCF of : (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255  




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