Page 1 1. Which of the following is a quadratic equation? (a) 3 3 2 0 x x (b) 2 1 x x x (c) 2 2 1 5 x x (d) 2 2 2 5 1 x x x Answer: (d) 2 2 2 5 1 x x x Sol: A quadratic equation is the equation with degree 2. 2 2 2 2 2 2 2 5 1 2 5 2 1 2 5 2 1 0 x x x x x x x x x x x 2 3 1 0, x x which is a quadratic equation 2. Which of the following is a quadratic equation? (a) 2 2 1 2 3 x x (b) 3 3 2 1 x x x (c) 2 2 3 5 2 3 x x x (d) None of these Answer: (b) 3 3 2 1 x x x Sol: 3 3 2 3 2 3 2 1 3 3 1 x x x x x x x x 2 2 3 1 0, x x which is a quadratic equation 3. Which of the following is not a quadratic equation? (a) 2 2 3 5 x x x (b) 2 2 2 2 5 x x (c) 2 2 2 3 2 6 x x (d) 2 2 1 3 2 x x x Answer: (c) 2 2 2 3 2 6 x x Sol: 2 2 2 2 3 2 6 2 9 6 2 2 6 x x x x x 6 2 3 0, x which is not a quadratic equation Page 2 1. Which of the following is a quadratic equation? (a) 3 3 2 0 x x (b) 2 1 x x x (c) 2 2 1 5 x x (d) 2 2 2 5 1 x x x Answer: (d) 2 2 2 5 1 x x x Sol: A quadratic equation is the equation with degree 2. 2 2 2 2 2 2 2 5 1 2 5 2 1 2 5 2 1 0 x x x x x x x x x x x 2 3 1 0, x x which is a quadratic equation 2. Which of the following is a quadratic equation? (a) 2 2 1 2 3 x x (b) 3 3 2 1 x x x (c) 2 2 3 5 2 3 x x x (d) None of these Answer: (b) 3 3 2 1 x x x Sol: 3 3 2 3 2 3 2 1 3 3 1 x x x x x x x x 2 2 3 1 0, x x which is a quadratic equation 3. Which of the following is not a quadratic equation? (a) 2 2 3 5 x x x (b) 2 2 2 2 5 x x (c) 2 2 2 3 2 6 x x (d) 2 2 1 3 2 x x x Answer: (c) 2 2 2 3 2 6 x x Sol: 2 2 2 2 3 2 6 2 9 6 2 2 6 x x x x x 6 2 3 0, x which is not a quadratic equation 4. If 3 x is a solution of the equation 2 3 1 9 0, x k x then ? k (a) 11 (b) 11 (c) 13 (d) 13 Answer: (b) 11 Sol: It is given that 3 x is a solution of 2 3 1 9 0; x k x therefore, we have: 2 3 3 1 3 9 0 27 3 1 9 0 3 1 36 1 12 11 k k k k k 5. If one root of the equation 2 2 6 0 x a x is 2 then a=? (a) 7 (b) -7 (c) 7 2 (d) 7 2 Answer: (b) -7 Sol: It is given that one root of the equation 2 2 6 0 x a x is 2. 2 2 2 2 6 0 2 14 0 7 a a a 6. The sum of the roots of the equation 2 6 2 0 x x is (a) 2 (b) -2 (c) 6 (d) -6 Answer: (b) -2 Sol: Sum of the roots of the equation 2 6 2 0 x x is 6 6, 1 b a where and are the roots of the equation. 7. If the product of the roots of the equation 2 3 10 x x k is -2 then the value of k is (a) -2 (b) -8 (c) 8 (d) 12 Answer: (c) 8 Sol: It is given that the product of the roots of the equation 2 3 10 x x k is . 2 The equation can be rewritten as: 2 3 10 0 x x k Page 3 1. Which of the following is a quadratic equation? (a) 3 3 2 0 x x (b) 2 1 x x x (c) 2 2 1 5 x x (d) 2 2 2 5 1 x x x Answer: (d) 2 2 2 5 1 x x x Sol: A quadratic equation is the equation with degree 2. 2 2 2 2 2 2 2 5 1 2 5 2 1 2 5 2 1 0 x x x x x x x x x x x 2 3 1 0, x x which is a quadratic equation 2. Which of the following is a quadratic equation? (a) 2 2 1 2 3 x x (b) 3 3 2 1 x x x (c) 2 2 3 5 2 3 x x x (d) None of these Answer: (b) 3 3 2 1 x x x Sol: 3 3 2 3 2 3 2 1 3 3 1 x x x x x x x x 2 2 3 1 0, x x which is a quadratic equation 3. Which of the following is not a quadratic equation? (a) 2 2 3 5 x x x (b) 2 2 2 2 5 x x (c) 2 2 2 3 2 6 x x (d) 2 2 1 3 2 x x x Answer: (c) 2 2 2 3 2 6 x x Sol: 2 2 2 2 3 2 6 2 9 6 2 2 6 x x x x x 6 2 3 0, x which is not a quadratic equation 4. If 3 x is a solution of the equation 2 3 1 9 0, x k x then ? k (a) 11 (b) 11 (c) 13 (d) 13 Answer: (b) 11 Sol: It is given that 3 x is a solution of 2 3 1 9 0; x k x therefore, we have: 2 3 3 1 3 9 0 27 3 1 9 0 3 1 36 1 12 11 k k k k k 5. If one root of the equation 2 2 6 0 x a x is 2 then a=? (a) 7 (b) -7 (c) 7 2 (d) 7 2 Answer: (b) -7 Sol: It is given that one root of the equation 2 2 6 0 x a x is 2. 2 2 2 2 6 0 2 14 0 7 a a a 6. The sum of the roots of the equation 2 6 2 0 x x is (a) 2 (b) -2 (c) 6 (d) -6 Answer: (b) -2 Sol: Sum of the roots of the equation 2 6 2 0 x x is 6 6, 1 b a where and are the roots of the equation. 7. If the product of the roots of the equation 2 3 10 x x k is -2 then the value of k is (a) -2 (b) -8 (c) 8 (d) 12 Answer: (c) 8 Sol: It is given that the product of the roots of the equation 2 3 10 x x k is . 2 The equation can be rewritten as: 2 3 10 0 x x k Product of the roots of a quadratic equation c a 2 c a 10 2 1 8 k k 8. The ratio of the sum and product of the roots of the equation 2 7 12 18 0 x x is (a) 7 :12 (b) 7 :18 (c) 3 : 2 (d) 2 : 3 Answer : (d) 2 : 3 Sol: Given: 2 7 12 18 0 x x 12 18 , 7 7 and where and are the roots of the equation Ratio of the sum and product of the roots 12 18 : 7 7 12:18 2:3 9. If one root of the equation 2 3 10 3 0 x x is 1 3 then the other root is (a) 1 3 (b) 1 3 (c) -3 (d)3 Answer: (d)3 Sol: Given: 2 3 10 3 0 x x One root of the equation is 1 . 3 Let the other root be . Product of the roots c a 1 3 3 3 3 10. If one root of 2 5 13 0 x x k be the reciprocal of the other root then the value of k is Page 4 1. Which of the following is a quadratic equation? (a) 3 3 2 0 x x (b) 2 1 x x x (c) 2 2 1 5 x x (d) 2 2 2 5 1 x x x Answer: (d) 2 2 2 5 1 x x x Sol: A quadratic equation is the equation with degree 2. 2 2 2 2 2 2 2 5 1 2 5 2 1 2 5 2 1 0 x x x x x x x x x x x 2 3 1 0, x x which is a quadratic equation 2. Which of the following is a quadratic equation? (a) 2 2 1 2 3 x x (b) 3 3 2 1 x x x (c) 2 2 3 5 2 3 x x x (d) None of these Answer: (b) 3 3 2 1 x x x Sol: 3 3 2 3 2 3 2 1 3 3 1 x x x x x x x x 2 2 3 1 0, x x which is a quadratic equation 3. Which of the following is not a quadratic equation? (a) 2 2 3 5 x x x (b) 2 2 2 2 5 x x (c) 2 2 2 3 2 6 x x (d) 2 2 1 3 2 x x x Answer: (c) 2 2 2 3 2 6 x x Sol: 2 2 2 2 3 2 6 2 9 6 2 2 6 x x x x x 6 2 3 0, x which is not a quadratic equation 4. If 3 x is a solution of the equation 2 3 1 9 0, x k x then ? k (a) 11 (b) 11 (c) 13 (d) 13 Answer: (b) 11 Sol: It is given that 3 x is a solution of 2 3 1 9 0; x k x therefore, we have: 2 3 3 1 3 9 0 27 3 1 9 0 3 1 36 1 12 11 k k k k k 5. If one root of the equation 2 2 6 0 x a x is 2 then a=? (a) 7 (b) -7 (c) 7 2 (d) 7 2 Answer: (b) -7 Sol: It is given that one root of the equation 2 2 6 0 x a x is 2. 2 2 2 2 6 0 2 14 0 7 a a a 6. The sum of the roots of the equation 2 6 2 0 x x is (a) 2 (b) -2 (c) 6 (d) -6 Answer: (b) -2 Sol: Sum of the roots of the equation 2 6 2 0 x x is 6 6, 1 b a where and are the roots of the equation. 7. If the product of the roots of the equation 2 3 10 x x k is -2 then the value of k is (a) -2 (b) -8 (c) 8 (d) 12 Answer: (c) 8 Sol: It is given that the product of the roots of the equation 2 3 10 x x k is . 2 The equation can be rewritten as: 2 3 10 0 x x k Product of the roots of a quadratic equation c a 2 c a 10 2 1 8 k k 8. The ratio of the sum and product of the roots of the equation 2 7 12 18 0 x x is (a) 7 :12 (b) 7 :18 (c) 3 : 2 (d) 2 : 3 Answer : (d) 2 : 3 Sol: Given: 2 7 12 18 0 x x 12 18 , 7 7 and where and are the roots of the equation Ratio of the sum and product of the roots 12 18 : 7 7 12:18 2:3 9. If one root of the equation 2 3 10 3 0 x x is 1 3 then the other root is (a) 1 3 (b) 1 3 (c) -3 (d)3 Answer: (d)3 Sol: Given: 2 3 10 3 0 x x One root of the equation is 1 . 3 Let the other root be . Product of the roots c a 1 3 3 3 3 10. If one root of 2 5 13 0 x x k be the reciprocal of the other root then the value of k is (a) 0 (b) 1 (c)2(d)5 Answer: (d)5 Sol: Let the roots of the equation 2 3 be and 1 . Product of the roots c a 1 5 5 5 k k a k 11. If the sum of the roots of the equation 2 2 3 0 k x x k is equal to their product then the value of k (a) 1 3 (b) 1 3 (c) 2 3 (d) 2 3 Answer: (d) 2 3 Sol: Given: 2 2 3 0 k x x k Sum of the roots = Product of the roots 2 3 3 2 2 3 k k k k k 12. The roots of a quadratic equation are 5 and -2. Then, the equation is (a) 2 3 10 0 x x (b) 2 3 10 0 x x (c) 2 3 10 0 x x (d) 2 3 10 0 x x Answer: (b) 2 3 10 0 x x Sol: It is given that the roots of the quadratic equation are 5 and . 2 Then, the equation is: 2 2 5 2 5 2 0 3 10 0 x x x x 13. If the sum of the roots of a quadratic equation is 6 and their product is 6, the equation is Page 5 1. Which of the following is a quadratic equation? (a) 3 3 2 0 x x (b) 2 1 x x x (c) 2 2 1 5 x x (d) 2 2 2 5 1 x x x Answer: (d) 2 2 2 5 1 x x x Sol: A quadratic equation is the equation with degree 2. 2 2 2 2 2 2 2 5 1 2 5 2 1 2 5 2 1 0 x x x x x x x x x x x 2 3 1 0, x x which is a quadratic equation 2. Which of the following is a quadratic equation? (a) 2 2 1 2 3 x x (b) 3 3 2 1 x x x (c) 2 2 3 5 2 3 x x x (d) None of these Answer: (b) 3 3 2 1 x x x Sol: 3 3 2 3 2 3 2 1 3 3 1 x x x x x x x x 2 2 3 1 0, x x which is a quadratic equation 3. Which of the following is not a quadratic equation? (a) 2 2 3 5 x x x (b) 2 2 2 2 5 x x (c) 2 2 2 3 2 6 x x (d) 2 2 1 3 2 x x x Answer: (c) 2 2 2 3 2 6 x x Sol: 2 2 2 2 3 2 6 2 9 6 2 2 6 x x x x x 6 2 3 0, x which is not a quadratic equation 4. If 3 x is a solution of the equation 2 3 1 9 0, x k x then ? k (a) 11 (b) 11 (c) 13 (d) 13 Answer: (b) 11 Sol: It is given that 3 x is a solution of 2 3 1 9 0; x k x therefore, we have: 2 3 3 1 3 9 0 27 3 1 9 0 3 1 36 1 12 11 k k k k k 5. If one root of the equation 2 2 6 0 x a x is 2 then a=? (a) 7 (b) -7 (c) 7 2 (d) 7 2 Answer: (b) -7 Sol: It is given that one root of the equation 2 2 6 0 x a x is 2. 2 2 2 2 6 0 2 14 0 7 a a a 6. The sum of the roots of the equation 2 6 2 0 x x is (a) 2 (b) -2 (c) 6 (d) -6 Answer: (b) -2 Sol: Sum of the roots of the equation 2 6 2 0 x x is 6 6, 1 b a where and are the roots of the equation. 7. If the product of the roots of the equation 2 3 10 x x k is -2 then the value of k is (a) -2 (b) -8 (c) 8 (d) 12 Answer: (c) 8 Sol: It is given that the product of the roots of the equation 2 3 10 x x k is . 2 The equation can be rewritten as: 2 3 10 0 x x k Product of the roots of a quadratic equation c a 2 c a 10 2 1 8 k k 8. The ratio of the sum and product of the roots of the equation 2 7 12 18 0 x x is (a) 7 :12 (b) 7 :18 (c) 3 : 2 (d) 2 : 3 Answer : (d) 2 : 3 Sol: Given: 2 7 12 18 0 x x 12 18 , 7 7 and where and are the roots of the equation Ratio of the sum and product of the roots 12 18 : 7 7 12:18 2:3 9. If one root of the equation 2 3 10 3 0 x x is 1 3 then the other root is (a) 1 3 (b) 1 3 (c) -3 (d)3 Answer: (d)3 Sol: Given: 2 3 10 3 0 x x One root of the equation is 1 . 3 Let the other root be . Product of the roots c a 1 3 3 3 3 10. If one root of 2 5 13 0 x x k be the reciprocal of the other root then the value of k is (a) 0 (b) 1 (c)2(d)5 Answer: (d)5 Sol: Let the roots of the equation 2 3 be and 1 . Product of the roots c a 1 5 5 5 k k a k 11. If the sum of the roots of the equation 2 2 3 0 k x x k is equal to their product then the value of k (a) 1 3 (b) 1 3 (c) 2 3 (d) 2 3 Answer: (d) 2 3 Sol: Given: 2 2 3 0 k x x k Sum of the roots = Product of the roots 2 3 3 2 2 3 k k k k k 12. The roots of a quadratic equation are 5 and -2. Then, the equation is (a) 2 3 10 0 x x (b) 2 3 10 0 x x (c) 2 3 10 0 x x (d) 2 3 10 0 x x Answer: (b) 2 3 10 0 x x Sol: It is given that the roots of the quadratic equation are 5 and . 2 Then, the equation is: 2 2 5 2 5 2 0 3 10 0 x x x x 13. If the sum of the roots of a quadratic equation is 6 and their product is 6, the equation is (a) 2 6 6 0 x x (b) 2 6 6 0 x x (c) 2 6 6 0 x x (d) 2 6 6 0 x x Answer: (a) 2 6 6 0 x x Sol: Given: Sum of roots = 6 Product of roots = 6 Thus, the equation is: 2 6 6 0 x x 14. If a n d are the roots of the equation 2 3 8 2 0 x x then 1 1 ? (a) 3 8 (b) 2 3 (c) -4 (d) 4 Answer: (c) -4 Sol: It is given that and are the roots of the equation 2 3 8 2 0 x x 8 2 3 3 and 8 1 1 3 4 2 3 15. The roots of the equation 2 0 a x b x c will be reciprocal each other if (a) a = b (b) b = c (c) c = a (d) none of these Answer: (c) c = a Sol: Let the roots of the equation 2 0 a x b x c be and 1 . Product of the roots 1 1 1 c a c a 16. If the roots of the equation 2 0 a x b x c are equal then c=?Read More

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- RD Sharma Solutions: Exercise 5.1 - Arithmetic Progressions
- RD Sharma Solutions: Exercise 5.2 - Arithmetic Progressions
- RD Sharma Solutions: Exercise 5.3 - Arithmetic Progressions
- RD Sharma Solutions: Exercise 5.4 - Arithmetic Progressions
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