PAIR OF LINEAR EQUATION IN TWO VARIABLES

1 Buy hard book on amazon. For more details whatsapp at 8905629969. Chap 3 Pair of LINEAR EQUATION in Two VARIABLES Page 37. CHAPTER 3. PAIR OF LINEAR EQUATION IN TWO VARIABLES . 1. The value of k for which the system of LINEAR equations 5. In a number of two digits, unit's digit is twice the x + 2y = 3 , 5x + ky + 7 = 0 is inconsistent is tens digit. If 36 be added to the number, the digits are reversed. The number is (a) - 14. 3 (a) 36. (b) 2. 5 (b) 63. (c) 5 (c) 48. (d) 84. (d) 10. Sol : Sol : 6. If 3x + 4y : x + 2y = 9 : 4 , then 3x + 5y : 3x - y is 2. The value of k for which the system of equations equal to x + y - 4 = 0 and 2x + ky = 3 , has no solution, is (a) 4 : 1. (a) - 2. (b) 1 : 4. (b) ! 2. (c) 7 : 1. (c) 3. (d) 1 : 7. (d) 2. Sol : Sol : 7. A fraction becomes 4 when 1 is added to both 3. For which value(s ) of p , will the lines represented the numerator and denominator and it becomes 7.

2 By the following pair of LINEAR equations be parallel when 1 is subtracted from both the numerator and 3x - y - 5 = 0 denominator. The numerator of the given fraction is 6x - 2y - p = 0 (a) 2. (a) all real values except 10 (b) 3. (b) 10 (c) 5. (c) 5/2 (d) 15. (d) 1/2 Sol : Sol : 8. x and y are 2 different digits. If the sum of the two 4. 5. The 2 digit number which becomes th of itself when 6. digit numbers formed by using both the digits is a its digits are reversed. The difference in the digits of perfect square, then value of x + y is the number being 1, then the two digits number is (a) 10. (a) 45 (b) 11. (b) 54 (c) 12. (c) 36 (d) 13. (d) None of these Sol : Sol : This PDF is review version of hard book available on Amazon. In hard book all solutions are given with question. Page 38 Pair of LINEAR EQUATION in Two VARIABLES Chap 3.

3 9. The pair of equations 3x + y = 81, 81x - y = 3 has (b) intersecting at (b, a). (a) no solution (c) coincident (b) unique solution (d) intersecting at (a, b). (c) infinitely many solutions Sol : (d) x = 2 1 , y = 1 7. 8 8. Sol : 15. For what value of k , do the equations 3x - y + 8 = 0. and 6x - ky =- 16 represent coincident lines ? 10. The pair of LINEAR equations 2kx + 5y = 7 , (a) 1. 2. 6x - 5y = 11 has a unique solution, if (b) - 12. (a) k !- 3 (c) 2. (b) k ! 2 (d) - 2. 3. (c) k ! 5 Sol : (d) k ! 2. 9. 16. If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0. Sol : are parallel, then the value of k is (a) - 5. 4. 11. The pair of equations x + 2y + 5 = 0 and (b) 2. 5. - 3x - 6y + 1 = 0 has (c) 15. (a) a unique solution 4. (b) exactly two solutions (d) 3. 2. (c) infinitely many solutions Sol : (d) no solution Sol : 17. The value of c for which the pair of equations cx - y = 2 and 6x - 2y = 3 will have is 12.

4 If a pair of LINEAR equations is consistent, then the (a) 3. lines will be (b) - 3. (a) parallel (c) - 12. (b) always coincident (d) no value (c) intersecting or coincident Sol : (d) always intersecting Sol : 18. One EQUATION of a pair of dependent LINEAR equations - 5x + 7y = 2 The second EQUATION can be 13. The pair of equations y = 0 and y =- 7 has (a) 10x + 14y + 4 = 0. (a) one solution (b) - 10x - 14y + 4 = 0. (b) two solutions (c) - 10x + 14y + 4 = 0. (c) infinitely many solutions (d) 10x - 14y = - 4. (d) no solution Sol : Sol : 19. If x = a and y = b is the solution of the equations 14. The pair of equations x = a and y = b graphically x - y = 2 and x + y = 4 , then the values of a and b represents lines which are (a) parallel Buy hard book on amazon. For more details whatsapp at 8905629969. Chap 3 Pair of LINEAR EQUATION in Two VARIABLES Page 39.

5 Are, respectively solution if k = 2 . (a) 3 and 5 Reason : a1 x + b1 y + c1 = 0 and a2 x + b2 y + c2 = 0. (b) 5 and 3 are consistent if a1 ! k1 . a2 k2. (c) 3 and 1. (a) Both assertion (A) and reason (R) are true and (d) - 1 and - 3 reason (R) is the correct explanation of assertion Sol : (A). (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of 20. Aruna has only < 1 and < 2 coins with her. If the assertion (A). total number of coins that she has is 50 and the (c) Assertion (A) is true but reason (R) is false. amount of money with her is < 75, then the number (d) Assertion (A) is false but reason (R) is true. of < 1 and < 2 coins are, respectively (a) 35 and 15 Sol : (b) 35 and 20. (c) 15 and 35. 24. If the equations kx - 2y = 3 and 3x + y = 5 represent (d) 25 and 25 two intersecting lines at unique point, then the value Sol : of k is.

6 (a) k =- 6. (b) k !- 6. 21. The father's age is six times his son's age. Four years (c) k = 4. hence, the age of the father will be four times his (d) k ! 4. son's age. The present ages (in year) of the son and the father are, respectively. Sol : (a) 4 and 24. (b) 5 and 30. 25. What do you say about the solution of the pair of (c) 6 and 36. LINEAR equations y = 0 and y =- 5 ? (d) 3 and 24 (a) no solution Sol : (b) unique solution (c) infinitely solution (d) can't say anything 22. Assertion : Pair of LINEAR equations : 9x + 3y + 12 = 0, 8x + 6y + 24 = 0 have infinitely many solutions. Sol : Reason : Pair of LINEAR equations a1 x + b1 y + c1. = 0 and a2 x + b2 y + c2 = 0 have infinitely many solu- 26. If am = bl, then what do you say about the solution tions, if a1 = b1 = c1 of the pair of LINEAR equations ax + by = c and a2 b2 c2.

7 (a) Both assertion (A) and reason (R) are true and lx + my = n ? reason (R) is the correct explanation of assertion (a) no solution (A). (b) unique solution (b) Both assertion (A) and reason (R) are true but (c) infinitely solution reason (R) is not the correct explanation of (d) can't say anything assertion (A). (c) Assertion (A) is true but reason (R) is false. Sol : (d) Assertion (A) is false but reason (R) is true. Sol : 27. If ad ! bc, then what do you say about the solution of the pair of LINEAR equations ax + by = p and cx + dy = q ? 23. Assertion : x + y - 4 = 0 and 2x + ky - 3 = 0 has no (a) no solution This PDF is review version of hard book available on Amazon. In hard book all solutions are given with question. Page 40 Pair of LINEAR EQUATION in Two VARIABLES Chap 3. (b) unique solution (a) Lines are parallel (c) infinitely solution (b) pair of LINEAR EQUATION is consistent (d) can't say anything (c) pair of LINEAR EQUATION is inconsistent Sol : (d) Lines are coincident Sol : 28.

8 Two lines are given to be parallel. The EQUATION of one of the lines is 4x + 3y = 14 , then the EQUATION of 33. What do you say about the lines represented by ? the second line will be 2x + 3y - 9 = 0 and 4x + 6y - 18 = 0. (a) 12x + 9x = 42 (a) lines are parallel (b) 12x + 9y = 5 (b) lines are coincident (c) 12x + 9y = 15 (c) lines are intersecting (d) 12x + 9y = 32 (d) can't say anything Sol : Sol : 29. Which of the following value of k should be selected 34. Given the LINEAR EQUATION 3x + 4y = 9 . Select another so that the pair of equations x + 2y = 5 and LINEAR EQUATION in these two VARIABLES such that the 3x + ky + 15 = 0 has a unique solution ? geometrical representation of the pair so formed is (a) k ! 5 intersecting lines. (b) k ! 6 (a) 3x - 5y = 10. (c) k = 5 (b) 6x + 8y = 18. (d) k = 6 (c) 8x + 12y = 18. Sol : (d) above all Sol : 30.

9 If 2x + y = 23 and 4x - y = 19 , the value of (5y - 2x). and ^ yx - 2h will be 35. For what value of p does the pair of LINEAR equations (a) - 75 and 31 given below has unique solution ? (b) 31 and - 75 4x + py + 8 = 0 and 2x + 2y + 2 = 0 . 2. (c) 37 and 7 (a) p = 1. 2. (d) 7 and 37 (b) p = 2. Sol : (c) p ! 4. (d) p ! 2. 31. What do you say about the lines represented by Sol : 2x + y = 3 and 4x + 2y = 6 ? (a) lines are parallel 36. For what value of k , the pair of LINEAR equations (b) lines are coincident kx - 4y = 3, 6x - 12y = 9 has an infinite number of (c) lines are intersecting solutions ? (d) can't say anything (a) k = 2. (b) k ! 2. Sol : (c) k ! 3. (d) k = 4. 32. What do you say about the following pair of LINEAR EQUATION ? Sol : 3x + 2y = 8 , 6x - 4y = 9. Buy hard book on amazon. For more details whatsapp at 8905629969.

10 Chap 3 Pair of LINEAR EQUATION in Two VARIABLES Page 41. 37. For what value of k , the system of equations 41. What are the values of x and y for the following kx + 3y = 1, 12x + ky = 2 has no solution. system of LINEAR equations ? (a) k =- 6 2x - y = 2. (b) k !- 6. x + 3y = 15. (c) k = 4 (a) 4 and 5. (d) k =- 4 (b) 3 and 4. Sol : (c) 5 and 4. (d) 4 and 4. 38. What are the values of x and y for the following pair Sol : of LINEAR equations ? 3x + 2y - 7 = 0. 42. Select the value of k for which the pair of LINEAR 4x + y - 6 = 0 equations kx + y = d2 and x + ky = 1 have infinitely (a) 1 and 2 many solutions. (b) 2 and 2 (a) 1. (c) 1 and 1 (b) 2. (d) 1 and 1 (c) 3. (d) 4. Sol : Sol : 39. In the figure given below, ABCD is a rectangle. The values of x and y will be 43. What are the values of x and y for the following system of equations .