Algebra (Railway Maths) (Part – III)

Total Questions: 50

31. If (a - b) = 8 and (a² + b²) = 160, then the value of ab is: [Group D 12/09/2022 (Morning) ]

Correct Answer: (d) 48
Solution:

32. Which of the following statements is true about the nature of roots for the equation 11x² + 19x + 8 = 0? [Group D 12/09/2022 (Morning) ]

Correct Answer: (a) Both roots are negative real
Solution:

33. The sum of two positive numbers is 34 and their product is 64. The positive difference between them is: [Group D 12/09/2022 (Morning)]

Correct Answer: (b) 30
Solution:

34. Roots of the equation x² + 2x - 6 = 0 are: [Group D 12/09/2022 (Afternoon) ]

Correct Answer: (a)
Solution:

35. Which of the following statements is true about the nature of roots for the equation x² + x + 12 = 0 ? [Group D 12/09/2022 (Evening) ]

Correct Answer: (d) Both roots are imaginary or non-real
Solution:

Here, Discrimination (D)
= b² - 4ac = (1)² - 4(1)(12) = - 47 < 0
So the roots are imaginary or non-real.

36. The quadratic equation for which, sum of the roots is (-3/5) and product of the roots is 2/5, is: [Group D 12/09/2022 (Evening) ]

Correct Answer: (c) 5x² - 3x + 2 = 0
Solution:

37. Which of the following represents the equation (x + 2)³ = x (x² - 1) in standard form? [Group D 13/09/2022 (Morning) ]

Correct Answer: (d) 6x² + 13x + 8 = 0
Solution:

(x + 2)³ = x (x² - 1)
⇒ x³ + 6x² + 12x + 8 = x³ - x
⇒ 6x² + 13x + 8 = 0

38. Which of the following describes the nature of the roots of the quadratic equation 4x² - 7√3x + 12 = 0 [Group D 13/09/2022 (Afternoon) ]

Correct Answer: (c) No real roots
Solution:

39. The discriminant of the equation 4x²- 5 x – 3 = 0 is: [Group D 13/09/2022 (Evening) ]

Correct Answer: (a) 73
Solution:

4x 2 - 5 x – 3 = 0
discriminant of the equation
= b² - 4ac = 25 + 48 = 73

40. 16x² + 4y² + 25z² - 16xy + 20yz - 40zx is equal to: [Group D 13/09/2022 (Evening) ]

Correct Answer: (d) (4x - 2y - 5z)²
Solution: