10th AYCD Maths Assignment, PDF

QTN1 Q UARTER N 102 E A YCD Time : 3.15 Hours] ASSIGNMENT X CLASS–MATHEMATICS [Max. Marks : 100...

QTN1 Q UARTER N 102 E A YCD Time : 3.15 Hours] ASSIGNMENT X CLASS–MATHEMATICS [Max. Marks : 100 1 Name :...................................................... Section :.......... Roll No.:........... Syllabus 1. REAL NUMBERS ; 2. POLYNOMIALS 3. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES; 4. QUADRATIC EQUATIONS ------------------------------------------------------------------------------------------------------------------------- Instructions :1. In the duration of 3 hours, 15 minutes, 15 minutes of time is allotted to read the question paper. 2. All answers shall be written in the answer booklet only. 3. Question paper consists of 4 Sections and 33 Questions. 4. Internal choice is available in Section IV only. 5. Answers shall be written neatly and legibly. ------------------------------------------------------------------------------------------------------------------------- SECTION - I Note : 1. Answer all the Questions in one word or phrase. 2. Each Question carries 1 mark. 12 × 1 = 12 1. Which of the following is a irrational number........................ (A) 3 (B) 4.1298 (C) 0.1011213..... (D) A, C 2. Find HCF of pq and pqr. 3. Express 475 as product of its prime factor. 4. If 3b2 = a2 then we can write a = (to get a and b have at least same number as a common factor) 5. Choose the correct matching. d (a) The zero of the linear polynomial cx + d...... ( ) (p) c (b) General formof a quadratic polynomial.......... ( ) (q) ax2 + bx + c (a 0) (c) (a – b) (a +b) =....... ( ) (r) a2 + b2 (s) a2 – b2 (A) a p; b q; c s (B) a p; b q; c r (C) a r; b q; c p (D) a r; b s; c p 6. If a are the aeroes of the cubic polynomial ax2 + bx + cx + d then the ratio of ++ and  is...... 7. If p(x) = 4x2 – 5x + 2 find the value of p 2. 1 102 E QUARTERN ASSIGNMENT -1 AYCD - 10EM - QTN 1 - 5  8. From the adjacent fig, find the number of zeroes of p(x) the graph of y = p(x). 9. The pair of lines represented by the equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 if they are consistent lines, the required condition is............ 10. The pair of linear equations are respectively 3x – y = 9 and 9x – 3y = 12 then they are consistent / in consistent. 11. Find the discriminent of the quadratic equation "x2 + 7x – 60 = 0". 12. Write the quadratic formula, to get roots of a quadratic equations ax2 + bx + c = 0 provided b2 – 4ac = > 0. SECTION - II Note : 1. Answer all the questions. 2. Each question carries 2 marks. 8 × 2 = 16 13. Given that HCF (306, 657) = 9, find LCM (306, 657). 14. Find the LCM of the given integers by applying the prime factorisation method. "6, 36 and 72". 15. Find the sum and produt of the zeroes of the polynmial 5x2 – 14x + 8 = 0. 16. Find the zeroes of the quadratic polynomial p2 – 15. a1 b1 c1 17. On comparing ratios a , b , c , find out whether the lines representing solutions 2 2 2 (a) 3x + 2y = 7; 2x – 4y = 8" (b) 2x – 2y = 9; 4x – 4y = 15". 18. From the pair of linear equations in the given proble : "The cost of 2 kg of aples and 1 kg of grapes on a day was found to be 260. After 1 month, the cost of 4 kgs of apples and 2 kgs of grapes is 580. Represent the situation algebraically.. 19. Find the discriminant of the quadratic equation 4x2 – 5x + 8 = 0, and hence find the nature of its roots. 1 20. Find the roots of quadratic equations by factorisation method "2x2 – x + = 0" 8 102 E 2 QUARTERN ASSIGNMENT -1 AYCD - 10EM - QTN 1 - 6  SECTION - III Note : 1. Answer all the questions. 2. Each question carries 4 marks. 8 × 4 = 32 21. Check whether 5n can end with the digit 0 for any natural number n. 22. Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers. 23. Find the zeroes of the quadratic polynomial x2 + 7x + 10, and verify the relationship between the zeroes and the coefficients. 24. If  are the zeroes of the cubic polynomial p(x) = 3x3 – 5x2 – 11x – 3 : find the values of ++, ++ and and sum of the squares of ++and . 25. Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden. 26. Given the linear equation 6x – 5y + 3 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is: (i) intersecting lines (ii) parallel lines (iii) coincident lines 27. Find two consecutive positive integers, sum of whose squares is 365. 28. A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was 90, find the number of articles produced and the cost of each article. SECTION - IV Note : 1. Answer all the questions. 2. Each question carries 8 marks. 3. There is internal choice for each question. 5 × 8 = 40 29. (A) Prove that 5 – 3 is irrational. (or) (B) Prove that 11 is irrational. 102 E 3 QUARTERN ASSIGNMENT -1 AYCD - 10EM - QTN 1 - 27  1 30. (A) Verify that 4, –2, are the zeroes ofthe cubic polynomial p(x) = 2x3 – 5x2 – 14x + 8, and 2 then verify the relationship between the zeroes and the coefficients. (or) (B) (a) Find a quadratic polynomial, the sum and product of whose zeroes are –3 and 2 respectively. (b) Find the zeroes of the quadratic polynomial "6x2 – 3 – 7x". 31. (A) Graphically, find whether the following pair of equations has no solution, unique solution or 24 3 infinitely many solutions: 5x – 8y + 1 = 0; 3x – y + = 0. 5 5 (or) (B) From the pair of equations for given situation and find their solutions. A fraction becomes 9 , if 2 is added to both the numerator and the denominator. If 3, is added to both the 11 5 numerator and the denominator it becomes. Find the fraction. 6 32. (A) Two rails are represented by the equations x + 2y – 4 = 0 and 2x + 4y – 12 = 0. Will the rails cross each other ? (or) (B) Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present age. Write the situation as form of pair of liner equation and their solution. 33. (A) A pole has to be erected at a point on the boundary of a circular park of diameter 13 metres in such a way that the differences of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. Is it possible to do so? If yes, at what distances from the two gates should the pole be erected ? (or) (B) A passenger train takes 3 h less for a journey of 360 km. if the speed is increased by 10 km/ h from its usual speed. Find its usual speed. 102 E 4 QUARTERN ASSIGNMENT -1 AYCD - 10EM - QTN 1 - 28