# KENDRIYA VIDYALAYA BURHANPUR

7. Solve graphically the pair of equations: 2x + y = 6 2x – y + 2 = 0. 8. Solve the following system of equations graphically and from the graph, find...

KENDRIYA VIDYALAYA BURHANPUR HOLIDAY HOME WORK (SUMMER VACATION)-2018-19 CLASS:-X SUBJECT:- ENGLISH

1 2 3 4 5

Write daily news headlines with their photograph (paste photos). Write five stories with hints and moral Write fifty verbs with their three forms (V1, V2,V3). Write three formal letters and three informal letters. Write an article on the following topic: (1) Promotion of girls education (2) Saving every drop of water. (3) Tree plantation .

6

Write questions and answers of the lessons taught till today.(two times)

कक्षा- दसव ीं

ववषय- ह द ीं ी

१ – सरू दास के पद पाठ के शब्दार्थ पाांच बार लिखें | २ – शब्दार्थ के अतिररक्ि अन्य कठठन शब्दों कक सूची िैयार करें | ३ – स्वेच्छा से कोई िीन पद याद करें | ४ – सरू दास के पद पाठ से १ से १२ प्रश्नों को एक बार लिखें | ५ – नेिाजी का चश्मा पाठ के प्रश्नोत्तर याद करें | ६ – बािगोबबन भगि पाठ के प्रश्नोत्तर एक बार लिखें |

KENDRIYA VIDYALAYA BURHANPUR HOLIDAY HOME WORK (SUMMER VACATION)-2018-19 CLASS:-X SUBJECT:- MATHEMATICS CHAPTER 1: REAL NUMBERS LEVEL-1 1. Use Euclid’s division algorithm to find the HCF of 105 and 120 (Ans.15) 2. Find the prime factorization of 234. (𝐴𝑛𝑠. 2 × 32 × 13) 3. Find the LCM and HCF of the pair of integers 13,11 (Ans. 1, 143) 4. Find the LCM and HCF of the pair of integers 510, 92 using fundamental theorem of arithmetic. 5. Find the missing number in the following factorization.

2 2

2

17 7

6. If the LCM (91, 26) =182, then find the HCF (91, 26). (Ans. 13) 7. Find the LCM (96,408) if the HCF is 24. (Ans.1632) 8. Without actual division, state where the rational number expansion or non- terminating decimal expansion. 9.

543 225

is a terminating decimal

139

Show that 23 53 will have terminating decimal expression.

10. .State where (√6 + √9) is rational or not. 11. Find LCM of 72, 80, and 120. (Ans.720 ,) 12. Prove that √11 is irrational. 13. The decimal expansion of a real number is 23.123456. If it is expressed as a rational number 𝑝 in the form of 𝑞 , write the prime factors of q. (Ans:26 56) 14. Find the largest number which divides 245 and 1029 leaving remainder 5 in each case. (Ans.16)

15. Use Euclid’s division algorithm to find the HCF of196, 38220. (Ans.196)

LEVEL-2 16. LCM of two numbers is 2079and HCF is 27.If one number is 297, find the other number. (Ans: 189). 17. Explain why 3 × 11 × 17 + 17 × 7 a composite number. 18. Find the LCM and HCF of the pair of integers 120, 70. Also verify that LCM x HCF=product of numbers. 11 19. After how many decimal places the decimal expansion of the rational number 23 52will terminate.(Ans 3) 20. Check whether (15)𝑛 can end with the digit 0. 21. Prove that 𝑛2 − 𝑛 is divisible by 2 for every positive integer. 22. Show that any positive odd integer is of the form 4q+1or 4q+3, where q is an integer. 23. What is the smallest number which when divided by 35, 56, 91, leaves the remainder 7 in each case.(Ans: 3647). 24. If d is the HCF of 45 and 27 find x and y satisfying d=27x+45y. (Ans: x=2,y= -1) 25. Using prime factorization method, find HCF and LCM of 72,126and168.Also show that HCF×LCM≠product of the three numbers. 26. In a school there are two sections A and B of class X. There are 48, 60 students in two sections respectively. Determine the least number of books required for the library so that the books can be distributed equally among the students.(Ans: 240 ) 27. Prove that 5+7√3 is an irrational number

LEVEL- 3 28. For some integer m, what is the form of every even integer. ( Ans: 2m) 29. For some integer q, what is the form of every odd integer (Ans:2q+1) 30. If two positive integers p and q can be expressed as p = 𝑎𝑏 2 and q = 𝑎3 b; a, b being prime numbers, Find the LCM (p, q) .(Ans:𝑎3 𝑏 2) 31. Using Euclid’s division algorithm, find which of the following pairs of numbers are coprime: (i) 231, 396 (ii) 847, 2160 32. Show that the square of an odd positive integer is of the form 8m + 1, for some whole number m. 33. Show that the square of any positive integer cannot be of the form 5q + 2 or 5q + 3 for any integer q.=2 34. If n is an odd integer, then show that 𝑛2 – 1 is divisible by 8. 35. Using Euclid’s division algorithm, find the largest number that divides 1251, 9377 and 15628 leaving remainders 1, 2 and 3, respectively.

CHAPTER 2: POLYNOMIALS LEVEL – 1 1. If p(x) = 2𝑥 2 – 3x + 5, then find p (–1). (ans :10) 2. Find the zero of the polynomial 3x + 2.

3. The following figure shows the graphs of y = p(x), where p(x) is a polynomial. Find the zeroes of the polynomial.

4. Find the zeroes of the polynomial 2𝑥 2 − 25

(𝐴𝑛𝑠. ±

5 ) √2

5. Find the quadratic polynomial whose roots are 3 + √5 and 3 − √5 (𝐴𝑛𝑠. 𝑥 2 − 6𝑥 + 7) 6. If one zero of 2𝑥 2 – 3x + k is reciprocal to the other, then find the value of k (ans: k= 2) −3 7. Find a quadratic polynomial whose sum and product of roots are 2, . 5 2 ( Ans :(5𝑥 − 10𝑥 − 3) ) 8. If 𝛼, 𝛽 are the zeroes of the quadratic polynomial 𝑥 2 − 6𝑥 + 𝑎 , find the value of a If 3𝛼 + 2𝛽 = 20. (Ans: -16) 9. Divide the polynomial 𝑥 3 − 3𝑥 2 + 5𝑥 − 3 by 𝑥 2 − 2. 10. Is x+2 a factor of 2 𝑥 2 + 3𝑥 + 1.

LEVEL-2 1

11. If𝛼, are the zeroes of the polynomial 4 − 2𝑥 + (𝑘 − 4), find the value of k. (Ans: k=8) 𝛼 12. The graph of y = f(x), where f(x) is a polynomial in x is given below .Find the number of zeroes lying between –2 to 0.

13. Show that 1, –1 and 3 are the zeroes of the polynomial 𝑥 3 – 3𝑥 2 – x + 3. 14. If (x + a) is a factor of 2𝑥 2 + 2ax + 5x + 10, find a. (ans: a=2) 15. If the polynomial 6𝑥 4 + 8𝑥 3 + 17𝑥 2 + 21 + 7is divided by the polynomial l3𝑥 2 + 4𝑥 + 1 and the remainder is ax +b, find the value of a, b. (Ans: a=1 , b=2) 16. If α and β are the zeroes of the quadratic polynomial f(x) = 𝑥 2 – 5x +6 then find the value of 1 1 + −𝛼𝛽. 𝛼

𝛽

(Ans : -31)

LEVEL-3

17. Find all the zeroes of the polynomial 2𝑥 4 − 3𝑥 3 − 3𝑥 2 + 6𝑥 − 2,if two of its zeroes are 1 √2 ,-√2. (Ans. 1,2 ) 18. What must be added to 8𝑥 4 + 14𝑥 3 − 2𝑥 3 + 7𝑥 − 8 so that the resulting polynomial is exactly divisible by 4𝑥 2 + 3𝑥 − 2. (ans.10-14x.) 19. Find the values of a, b so that 𝑥 4 + 𝑥 3 + 8𝑥 2 + 𝑎𝑥 + 𝑏 is divisible by 𝑥 2 + 1. (Ans.a=1, b=7) 20. Divide 2𝑥 4 − 9𝑥 3 + 5𝑥 2 + 3𝑥 − 8 by 1 − 4𝑥 + 𝑥 2 and verify division algorthim. 21. Find the zeroes of 3√2𝑥 2 + 13𝑥 + 6√2 and verify the relation between the zeroes and coefficients of the polynomial. 22. If the zeroes of the polynomial 𝑥 3 − 3𝑥 2 + 𝑥 + 1 are a-b, a, a+ b, find a, b (a=1,b=±√2 )

CHAPTER 3: LINEAR EQUATION IN TWO VARIABLES

LEVEL-1 1. Show that the pair of equations 2x-3y=6, x + y=1. has a unique solution. 2. Show that the pair of equations 2y=4x-6, 2x=y+3, has infinite solutions. 3. For what value of k, 2x+3y=4, (k+2) x+6y=3k+2 will have infinitely many solutions. (Ans.k=2) 4. Is the pair of equations : x+2y-4=0, 2x+4y-2=0 consistent. 5. Solve algebraically the pair of equations: 2 x-y=5, 3x+2y=11 .(Ans .x=3 ,y=1) 6. Solve by the method of cross multiplication the pair of equations: 2 x +3y +8=0 4x +5y +14=0 ( Ans: (-1, -2) ) 7. Solve graphically the pair of equations: 2x + y = 6 2x – y + 2 = 0. 8. Solve the following system of equations graphically and from the graph, find the points where these lines intersect the y-axis: x– 2y = 2, 3x + 5y = 17. 9. Solve the following system of equations graphically and find the vertices of the triangle formed by these lines and the x-axis : 4x– 3y + 4 = 0, 4x + 3y – 20 = 0. 10. Solve graphically: x–y=1 2x + y = 8. Shade the region bounded by these lines and y-axis. Also find its area. 11. Draw the graph of the equations x = 5, y= − 4. Also find area of rectangle so formed by these lines x-axis and y-axis.

LEVEL-2

12. If 2x-3y=7 and (a +b)x - (a+b-3)y=4a+b have infinite solution, find a, b 13. Solve:

𝑥 𝑦 + = 𝑎 𝑏 2 2

Ans. (-5,1)

2

ax-by =𝑎 − 𝑏 . (Ans:x=a, y=b) 14. Solve: 23x+29y=98 29x+23y=110. ( Ans. x=3,y=1). 15. Solve: 152x -378y=-74 -378x+152y=-604 16. The sum of the digits of a two digit number is 12. The number obtained by interchanging the two digits exceeds the given number by 18. Find the number. ( Ans: 57) 17. The monthly incomes of A and B are in the ratio of 5 : 4 and their monthly expenditures are in the ratio of 7 : 5. If each saves Rs. 3000 per month, find the monthly income of each. (Ans: Rs.10000 ,Rs.8000) 18. A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student Atakes food for 20 days, she has to pay Rs. 1000 as hostel charges whereas a student B, who takes food 26days, pays Rs 1180 as hostel charges. Find the fixed charges and the cost of the food per day. ( Ans: .x=Rs.400,y=Rs 30.) 19. Father’s age is 3 times the sum of ages of his two children. After 5 years his age will be twice the sum of ages of the two children. Find the age of father ( Ans: 45) 20. Two numbers are in the ratio 5 : 6. If 8 is subtracted from each of the numbers, the ratio becomes 4 : 5. Find the numbers. (Ans: 40,48) 21. If 4 times the area of a smaller square is subtracted from the area of a larger square, the result is 144 m2. The sum of the areas of the two squares is 464 m2. Determine the sides of the two squares (Ans: Side=8m) LEVEL-3 22. Solve: 𝑥+1 2

+

𝑦−1 3

=8 𝑥−1 3

+

𝑦+1 2

= 9.( Ans:x=7 , y=13)

23. Solve: 2 𝑥−1

+

24. Solve:

3 𝑦+1

=2 7𝑥−2𝑦 𝑥𝑦

3 2 + 𝑥−1 𝑦+1

=5

=

13 6

8𝑥+7𝑦 𝑥𝑦

(Ans: x=3, y=2)

= 15

(Ans: x=1 , y=1)

25. In the figure, ABCD is a rectangle. Find the values of x and y.

(Ans:x=16,y=6) 26. In the figure, ABCD is a parallelogram. Find the values of x and y.

(Ans:x=7,y=2) 27. The taxi charges in a city consists of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs. 105 and for journey of 15 km the charge paid is Rs. 155. What are the fixed charges and the charges per km? (Ans:Fixed charge=Rs.5 ,Charge per km=Rs.10 ) 28. Nine times a two-digit number is the same as twice the number obtained by interchanging the digits of the number. If one digit of the number exceeds the other number by 7, find the number. (Ans: no.=18) 29. A man travels 370 km partly by train and partly by car. If he covers 250 km by train and rest by car, it takes him 4 hours. But if he travels 130 km by train and rest by car, he takes 18 minutes longer. Find the speed of the train and that of the car. ( Ans: speed of the train=100km/hr,speed of the car =80km/hr) 30. A boat goes 12 km upstream and 40 km downstream in 8 hours. It goes 16 km upstream and 32 km downstream in the same time. Find the speed of the boat in still water and the speed of the stream. (Ans: 6km/hr, 2km/hr)

Subject: Physics

ELECTRICITY

1. Define the term “electric current. 2. Define the term ‘resistivity’ of a material. 3. How is a Voltmeter connected in the circuit to measure the potential difference between two points . 4. You have two metallic wires of resistances 6 ohm and 3 ohm. How will you connect these wires to get the effective resistance of 2 ohm? 5. State Ohm’s law. “The resistance of a conductor is 1Ω.” What is meant by this statement? 6. Why are coils of electric toaster made of an alloy rather than a pure metal? 7. Why is the series arrangement not used for domestic circuits? 8. A wire of resistivity ‘r’ is stretched to double its length. How does it affect the (a) resistance (b) resistivity?

9. Derive the equation for resultant resistance of Resistors in series

10. How much work is done in moving a charge of 3 coulumb from a point at the volts 115 to a point at 125 volts?[ 30j]

11. Study the following data and write which set of value should be rejected so that ohm’s law holds good for the remaining set of values. Draw the graph and find out the mean resistance (3)

V(volts)

2.5 5.0 10.0 15.0 20.0 25.0

I(A)

0.1 0.2 0.3

0.6

0.8

1.0

12 A wire of resistance 20 ohm is bent in the form of a closed circle. What is the effective resistance between the two points at the end of any diameter of the circle? 13 Two wires A and B are of equal lengths, different cross-sectional areas and made of the same metal. (i) Name the property which is same for both the wires. (ii) Name the property which is different for both the wires. (iii) If the resistance of wire A is four times the resistance of wire B, calculate (a)the ratio of the cross-sectional areas of the wires. (b)the ratio of the radii of the wires.

14.. A resistor of 8ohm is connected in parallel with another resistor X. The resultant resistance of the combination is 4.8 ohm . What is the value of X?

15 How will you connect three resistors of 2 ohm , 3 ohm , 5 ohm respectively so as to obtain a resultant resistance of 2.5 ohm ? Draw the diagram to show arrangement.

16. A wire of resistance 5 ohm is bent in form of closed circle. What is the effective resistance between the two points at ends of any diameter of circle? 17 Why electrons flow in a wire when connected to a battery ?

Q2 Define

1. Electric current

2. Potential difference 18 Find new resistance of wire if it is stretched to twice its original length. Original resistance was 20 ohm. Also how its resistivity will change . 19 Which combination we prefer for domestic circuit, parallel or series? Give reason 20 Find the total resistance in the diagram below.

Class- X – Science Holiday Homework Q.1 a) What is photosynthesis? b) Write a chemical equation to show the process of photosynthesis in plants. c) Explain the mechanism of photosynthesis. Q.2 Draw a labelled diagram of human digestive system. With the help of this diagram, describe process of digestion of food in humans. Q.3 a) Which part of the body secretes bile? Where is the bile stored? What is the function of bile? b) What is trypsin? What is it function? Q.4 a) What criteria can be used to decide whether something is alive? b) What is the meant by life processes? Name the basic life processes common to all living organisms which are essential for maintaining life. Q.5 Name the type of respiration in which the end products are:a) C2H5OH and CO2 b) CO2 and H2O c) Lactic acid Give one example of each case where such a respiration can occur. Q.6 Describe the process of respiration in the following parts of plant a) Root b) Stem c) Leaves Q.7 a) Explain how, the air we breathe in gets cleaned while passing through the nasal passage. b) Why do wall of trachea no collapse when there is less air in it?

c) How are lungs designed in human beings to maximize the exchange of gases? Q.8 Describe the working of human blood circulatory system with the help of suitable diagram which shows all steps involved. Q.9 a) Why is transport of materials necessary in organism? b) What is the need of special tissue or organ for transport of substances in plant and animal? c) How are water and minerals transported in plants? d) How is food transported? Q.10 a) Name the various organs of human excretory system. b) Draw a neat labelled diagram of human excretory system. c) What is the function of excretory system in humans? Q.11 Make a chart to draw a well labelled diagram of digestive OR respiratory system in human.

HOLIDAY HOMEWORK Sub:- social science Class X 1. Draw the two type of land pattern & pawer sharing concept Indian prospective 2. Write the articles:a. Power sharing b. Indian civil movement 3. Draw the major soil type in Indian outline map. 4. Make a list of 10 developing and 10 non- developing country’s income and find what are the reason behind this variation of income.