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CBSE Notes Class 10 2020 : Mathematics (Vidhyalakshmi School, North Arcot) Quadratic Equations

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VIDHYALAKSHMI [CBSE CURRICULUM] Chennangkuppam MATHS - QUESTION BANK Chapter Name Quadratic Equations Grade: X Name of the Student: 1 MARK 1. Write the standard form of a quadratic equation. 2. Check whether quadratic equation or not: x(x + 1) + 8 = (x + 2)(x -2). 3. What constant number must be added and subtracted to 4x2+ 12x + 8 = 0 to solve it by method of completing the square? 4. If the equation x2 + 4x + k = 0 has real and distinct roots, then find the value of k? 5. Find the nature of the roots for the quadratic equation 2x2 - 5 x + 1 = 0 6. What is the degree of a quadratic equation? 7. Find the value of p for which x(x- 4) + p = 0 has equal roots? 8. Write as a quadratic equation: Product of two consecutive positive integers is 306 . 9. If (1- b) is a root of the quadratic equation x2 + bx + 1 b = 0, then find the value of b. 2 MARKs 3 1. Find the value of p, if the quadratic equation p2x2 12x + p + 7 = 0 has the root . 2. Solve : 10x - 1 2 = 3. Solve (2x 3)2 = 25 Find the value of k for which the quadratic equation 9x2 3kx + k = 0 has equal roots. Solve for x: x2 ( 3 + 1)x + 3 = 0. Find whether the quadratic equation x2 x + 2 = 0 has equal roots or not. If yes, find the roots. 7. Find the numerical difference of the roots of the equation x2 7x 18 = 0. 8. In a football match Messi kicked three goals less than twice the goals kicked by Ronaldo. The product of goals kicked by them is 20. Represent the above situation in the form of quadratic equation. 9. If 2 is root of the quadratic equation 3x2 + px 8 = 0 and the quadratic equation 4x2 2px + k = 0 has equal roots, find k. 10. State whether the following quadratic equation have distinct real roots. Justify your answer. x(1 x) 2 = 0. 11. The product of two consecutive positive integers is 306. Represent the situation in the form of equation. 12. Divide 32 into two parts such that their product is 175. 3. 4. 5. 6. 13. Divide 16 into two parts such that twice the square of the greater part exceeds the square of the smaller part by 164. 3 MARKs 1 1. Find the roots of the quadratic equation 12x2 8x + 1 = 0. 3 2. A two digit number is such that the product of the digits is 18. When 63 is subtracted from the number, the digit interchange their places. Find the number. 3. Solve for x: 16 1= 15 +1 ; x 0, -1 4. If (x2 + y2) (a2 + b2) = (ax + by)2. Prove that = . 5. For what value of k, does the quadratic equation (4 k)x2 + (2k + 4)x + 8k + 1 = 0 has equal roots? 6. Find the roots of the equation 5x2 6x 2 = 0 by the method of completing square. 7. The difference of two numbers is 5 and the difference of their reciprocals is 1 . Find the 10 numbers. 8. The difference of the square of two numbers is 45. The square of the smaller number is 4 times the lager number. Determine the numbers. 9. Find the positive root of 3 2 + 6 = 9. 10. Find the value of 6 + 6 + 6+. . . 11. There are three consecutive positive integers such that the sum of the square of the first and the product of the other two is 154. What are the integers? 12. Using factorization method to solve the equation: 4x2 4ax + (a2 b2) = 0. 13. Solve: a2b2x2 + b2x - a2x 1 = 0. 4 MARKs 1. Out of a few birds, one fourth the number are moving about in lotus plants; one ninth coupled with one fourth as well as 7 times the square root of the number move on a hill; 56 birds remain in vakula tree. What is the total number of birds? 2. Speed of a boat in still water is 11km/h. it can go 12km upstream and return to the original point in 2hrs 45min. find the speed of the stream. 3. A tourist has Rs.10000 with him. He calculated that he could spend Rs. x every day on his holidays. He spent Rs. (x 50) every day and extended his holidays by 10 days. Calculate x. which value is depicted by the tourist? 4. 300 apples are distributed equally among a certain no of students. Had there been 10 more students, each would have received one apple less. Find the no of students. 5. A cottage industry produces a certain no of pottery articles in a day. It was observed on a particular day that the cost of production of each article was 3 more than twice the no of articles produced on that day. If the total cost of production on that day was Rs. 90, find the no of articles produced and the cost of each article. 6. A train, travelling at a uniform speed for 360km, would have taken 48min less to travel the same distance if its speed were 5km/h more. Find the original speed of the train. 7. In the centre of a rectangular lawn of dimensions 50m x 40m, a rectangular pond has to be constructed so that the area of the grass surrounding of the pond would be 1184m2. Find the length and breadth of the pond. 8. A farmer wishes to grow a 100m2 rectangular vegetable garden. Sine he has with him only 30m o barbed wire, he fences three sides of the sides of the garden letting compound wall of his act as the fourth side fence. Find the dimensions of his garden. 9. The sum S of first n even natural numbers is given by the relation S = n(n + 1). Find n, if the sum is 420. 10. The hypotenuse of a right triangle is 3 10 cm. if the smaller leg is tripled and the longer leg doubled, new hypotenuse will be 9 5 cm. How long are the legs of the triangle? 11. A man can go by boat 8km and come back within 4 hours 16 minutes. If the river runs at the rate of 1km per hour, find the speed of boat in still water. 12. A train cover a distance of 90 km at a uniform speed. If the speed had been 15 km/hr more, it would have taken 30 min less for the same journey. We need to find the original speed of the train. Represent the situation in the form of a quadratic equation. 13. A two digit number is such that the product of its digit is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number. 14. One year ago, a man was 8 times as old as his son. Now, his age is equal to the square of his son s age. Find their present ages. 15. A two digit number is such that the product of its digits is 14. If 45 is added to the number, the digits interchange their places. Find the number. 16. A train travels a distance of 360 km at a uniform speed. If the speed of the train is increased by 5 km/hr, the journey would have taken 1 hr less. Find the original speed of the train. 17. A person on tour has Rs 360 for his expenses. If he extends his tour for 4 days, he has to cut down his daily expenses by Rs 3. Find the original duration of the tour. 18. A train covers a distances of 90 km at a uniform speed. If the speed had been 15 km/hr more, it would have taken 30 min less for the same journey. Find the original speed of the train. 19. A ladder 10 feet long leans against a wall. The bottom of the ladder is 6 feet from the wall. The bottom of the ladder is then pulled out 3 feet farther. How much does the top end move down the wall? 20. In a class test, the sum of Shefali s marks in Mathematics and English is 30. Had she got 2 marks more In Mathematics and 3 marks less in English, the product of their marks would have been 210. Find the marks in the two subjects. 21. The diagonal of a rectangular field is 60 m more than the shorter side. If the longer side is 30 m more than the shorter side, find the sides of the field. 22. A two digit number is such that the product of the digits is 20. If 9 is subtracted from the number, the digits interchange their places. Find the number. 23. Two pipes running together can fill a tank in 11 1 min. If one pipe takes 5 min more than 9 the other to fill the tank, find the time in which each pipe alone would fill the tank. 24. Find the values of k for the following quadratic equation, so that they have two equal roots 2x2+kx+3=0 25. If -4 is a root of the quadratic equation x2+px-4=0 and the quadratic equation x2+px+k=0 has equal roots, find the value of k. 26. Find the value of k for which the quadratic equation (k+4)x2 + (k+1)x + 1=0 has equal roots. 27. If the roots of the quadratic equation p(q-r)x2 + q(r-p)x + r(p-q) = 0 are equal, show that 2 1 1 + = . q p r 28. If the equation (1+m2)x2 + 2mcx + (c2-a2) = 0 has equal roots, prove that c2= a2(1+m2). 29. A plane left 30 min later than the scheduled time and in order to reach its destination 1500 km away in time it has to increase its speed by 250 km/hr from its usual speed. Find its usual speed. 30. Solve the following equation for x : 1 2 + +2 = 1 2 1 1 2 + + Prepared by S.VISHNUVARMAN M.Sc., M.Ed., H.O.D MATHEMATICS VIDHYALAKSHMI SCHOOL

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