Sujeet Kumar

Question 1.Choose the correct answers for the following questions. i. Which one is the quadratic equation?Answer:(B) ii. Out of the following equations which one is not a quadratic equation?(A) x2 + 4x = 11 + x2(B) x = 4x(C) 5×2 = 90(D) 2x – x2 = x2 + 5Answer:(A) iii. The roots of x2 + kx + k = 0 … Read more

Question 1.Product of Pragati’s age 2 years ago and years hence is 84. Find her present age.Solution:Let the present age of Pragati be x years.∴ 2 years ago,Age of Pragati = (x – 2) yearsAfter 3 years,Age of Pragati = (x + 3) yearsAccording to the given condition,(x – 2) (x + 3) = 84∴ … Read more

Question 1.Fill in the gaps and complete.Answer: Question 2.Find the value of discriminant.i. x2 + 7x – 1 = 0ii. 2y2 – 5y + 10 = 0iii. √2 x2 + 4x + 2√2 = 0Solution:i. x2 +7 x – 1 = 0Comparing the above equation withax2 + bx + c = 0, we geta = 1, b = 7, c … Read more

Question 1.Compare the given quadratic equations to the general form and write values of a, b, c.i. x2 – 7x + 5 = 0ii. 2m2 = 5m – 5iii. y2 = 7ySolution:i. x2 – 7x + 5 = 0Comparing the above equation withax2 + bx + c = 0, we geta = 1, b = -7, c = 5 ii. … Read more

Question 1.Solve the following quadratic equations by completing the square method.1. x2 + x – 20 = 02. x2 + 2x – 5 = 03. m2 – 5m = -34. 9y2 – 12y + 2 = 05. 2y2 + 9y + 10 = 06. 5×2 = 4x + 7Solution:1. x2 + x – 20 = 0If x2 + x + k = (x … Read more

Question 1.Solve the following quadratic equations by factorisation.i. x2 – 15x + 54 = 0ii. x2 + x – 20 = 0iii. 2y2 + 27y + 13 = 0iv. 5m2 = 22m + 15vii. √2×2 + 7x + 5√2 = 0 to solve this quadratic equation by factorisation complete the following activityviii. 3×2 – 2√6x + 2 = 0ix. 2m(m – … Read more

Question 1.Write any two quadratic equations.Solution:i. y2 – 7y + 12 = 0ii. x2 – 8 = 0 Question 2.Decide which of the following are quadratici. x2 – 7y + 2 = 0ii. y2 = 5y – 10v. (m + 2) (m – 5) = 03vi. m3 + 3m2 – 2 = 3m3Solution:i. The given equation is x2 + 5x – 2 … Read more

Choose correct alternative for each of the following questions. Question 1.To draw graph of 4x + 5y = 19, find y when x = 1.(a) 4(b) 3(c) 2(d) -3Answer:(b) Question 2.For simultaneous equations in variables x and y, Dx = 49, Dy = – 63, D = 7 then what is x?Answer:(a) Question 3.Find the value … Read more

Question 1.Two numbers differ by 3. The sum of twice the smaller number and thrice the greater number is 19. Find the numbers.Solution:Let the greater number be x and the smaller number be y.According to the first condition, x – y = 3 …(i)According to the second condition,3x + 2y = 19 …(ii)Multiplying equation (i) … Read more

Question 1.Solve the following simultaneous equations.Solution:i. The given simultaneous equations are ∴ Equations (i) and (ii) become2p – 3q = 15 …(iii)8p + 5q = 77 …(iv)Multiplying equation (iii) by 4, we get8p – 12q = 60 …(v)Subtracting equation (v) from (iv), we get ii. The given simultaneous equations areSubstituting x = 3 in equation … Read more