Algebra (Railway Maths) (Part – III)

Total Questions: 50

11. If the roots of the equation 2x² + kx + 3 = 0 are real and equal, where k > 0, then the value of k will satisfy which of the following equations? [Group D 06/09/2022 (Afternoon)]

Correct Answer: (d) k² − √6k − 12 = 0
Solution:

12. The roots of the equation x² − 5x + 6 = 0 are ______. [Group D 06/09/2022 (Afternoon)]

Correct Answer: (b) 2, 3
Solution:

13. If α and β are the roots of x² − 5x + 3 = 0, find the quadratic equation whose roots are α² and β². [Group D 06/09/2022 (Evening)]

Correct Answer: (c) x² − 19x + 9 = 0
Solution:

14. If 2 and -3 are the roots of a quadratic equation, then that equation is________. [Group D 06/09/2022 (Evening) ]

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

15. Find the answer of given question? [Group D 06/09/2022 (Evening) ]

Correct Answer: (d) 2y
Solution:

16. If one root of the equation 4x² - 2x + k − 4 = 0 is reciprocal of the other, the value of k is: [Group D 08/09/2022 (Morning) ]

Correct Answer: (d) 8
Solution:

17. If α, β (α > β) are the roots of the quadratic equation x² - 10x + 16 = 0, then the value α⁴ - β⁴ is: [Group D 08/09/2022 (Afternoon) ]

Correct Answer: (a) 4080
Solution:

18. Find the nature of the roots of 2x² + 4 - 10x = 0. [Group D 08/09/2022 (Afternoon) ]

Correct Answer: (a) Real and distinct roots
Solution:

19. Roots of the equation x² - 5x - 14= 0 are: [Group D 08/09/2022 (Evening) ]

Correct Answer: (a) 7 , - 2
Solution:

20. If x + y = 8, product of x and y is 15, then the value of x⁴ + y⁴ is: [Group D 08/09/2022 (Evening) ]

Correct Answer: (d) 706
Solution: