Algebra (Railway Maths) (Part – IV)

Total Questions: 50

31. Which of the options given below correctly describes the nature of the roots of the quadratic equation x² + 4√3x + 3 = 0? [Group D 19/09/2022 (Evening) ]

Correct Answer: (b) irrational and unequal
Solution:

32. The roots of 2²ˣ - 10 × 2ˣ + 16 = 0 are : [Group D 19/09/2022 (Evening) ]

Correct Answer: (d) 1 , 3
Solution:

33. The positive root of 4x² − 1 = 0 is: [Group D 20/09/2022 (Morning)]

Correct Answer: (a) 1/2
Solution:

34. If one of the roots of a quadratic equation with rational coefficients is 2 + √3, then the quadratic equation is given as [Group D 20/09/2022 (Morning)]

Correct Answer: (b) x² − 4x + 1 = 0
Solution:

35. If (x + y + z) = 0 and x² + y² + z² = 36, then the value of xy + yz + zx is: [Group D 20/09/2022 (Morning)]

Correct Answer: (a) −18
Solution:

36. The value of [Group D 20/09/2022 (Morning) ]

Correct Answer: (d) x + y
Solution:

37. If the two roots of a quadratic equation are −3 and 3, then the quadratic equation is given as ________. [Group D 20/09/2022 (Afternoon)]

Correct Answer: (c) x² − 9 = 0
Solution:

38. If a, b are the roots of the equation x² − 5x + 6 = 0, then a² + b² − ab is: [Group D 20/09/2022 (Evening)]

Correct Answer: (c) 7
Solution:

39. The product of the roots of 6√3x² + 5x + 3√3 = 0 is [Group D 20/09/2022 (Evening)]

Correct Answer: (a) 1/2
Solution:

40. An equation, whose roots are the reciprocals of the roots of the equation 5x² − 3x − 4 = 0, is: [Group D 22/09/2022 (Morning)]

Correct Answer: (b) 4x² + 3x − 5 = 0
Solution: