CBSE Guess > Papers > Important Questions > Class X > Maths > Mathematics By Mr. Sanjay Kumar

Chapter - 4

Q. 36. Check whether the equation (x – 3) (x² + 5) + 3x – 5 = (x² + 1) (x + 1) – (3x – 7), is quadratic or not, if yes, then solve it.

Q. 37. Solve the equation: pqx² + (q² - pr) x = qr.

Q. 38. Find the values of p for which the quadratic equation 2x² + px + 8 = 0 has real roots.

Q. 39. Solve the equation: (x + 3) / (x + 2) + (x – 3)/ (x – 2) = (2x – 3)/ (x – 1).

Q. 40. Solve the following quadratic equation by using quadratic formula: 9x² – 6a²x + (a4 – b4) = 0.

Q. 41. Solve the equations: (i) 4x² + 12x + 9 = 0, (ii) 5x²–17x + 35 = 0, (iii) x² - 7x - 5 = 0.

Q. 42. Solve the equation: 2 (x – 3)² + 3 (x – 2) (2x – 3) = 8 (x + 4) (x – 4) – 1.

Q. 43. Solve the following equations: (i) (x + 1)/(x - 1) + (x – 2)/(x + 2) = 3, (ii) (x + 3) / (x - 2) - (1 - x) / x = 17/4.

Q. 44. The sum of the squares of two consecutive positive integers is 545. Find the integers.

Q. 45. Determine two consecutive odd natural numbers, the sum of whose squares is 1154.

Q. 46. The difference of the squares of two numbers is 45. The square of the smaller number is 4 times the larger. Find them.

Q. 47. A fast train takes 2 hours less than a slow train for a journey of 600 km. If the speed of the slow train is 10 km/h less than that of the fast train, find the speeds of the two trains.

Q. 48. A motor-boat, whose speed is 15 km/h in still water, goes 30 km downstream and comes back in a total time of 4 hours and 30 minutes. Find the speed of the stream.

Q. 49. Two trains leave a railway station at the same time. The first train travels due west and the second train due north. The first train travels 5 km/h faster than the second train. If after two hours, they are 50 km apart, find their average speeds.

Q. 50. The sum of the squares of two numbers is 233. If one number is 3 less than twice the other number, find the numbers.