Algebra (Railway Maths) (Part – IV)

Total Questions: 50

11. If α, β are the roots of the quadratic equation 2x² − 3x − 35 = 0, then the value of α³ + β³ is: [Group D 16/09/2022 (Afternoon)]

Correct Answer: (b) 657/8
Solution:

12. If 25 − (x² − 9) = (81)¹ᐟ², then the positive value of x = ________. [Group D 16/09/2022 (Afternoon)]

Correct Answer: (a) 5
Solution:

13. Which of the following is the standard representation of quadratic equation (x² + 1)(x − 1) = (x² − 3)(x + 3)? [Group D 16/09/2022 (Evening)]

Correct Answer: (d) 4x² − 4x − 8 = 0
Solution:

(x² + 1) (x - 1) = (x² - 3) (x + 3)
⇒ (x³ - x² + x - 1) = (x³ + 3x² - 3x - 9)
⇒ 4x² - 4x - 8 = 0

14. The discriminant of a quadratic equation is 0. The quadratic equation has: [Group D 17/09/2022 (Morning) ]

Correct Answer: (a) two equal real roots
Solution:

If discriminant = 0 Then the quadratic equation has two equal roots.

15. The value of the discriminant of the quadratic equation 2x² - 4x - 3 = 0 is [Group D 17/09/2022 (Afternoon) ]

Correct Answer: (c) 40
Solution:

16. If α, β be the roots of the quadratic equation 3x² − 9x + 8 = 0, then the value of (α/β + β/α) + 4(1/α + 1/β) is: [Group D 17/09/2022 (Afternoon)]

Correct Answer: (d) 5.875
Solution:

17. The roots of the quadratic equation x + 10/x = 7 are: [Group D 17/09/2022 (Evening) ]

Correct Answer: (b) 5 , 2
Solution:

18. Find the answer of given question? [Group D 18/09/2022 (Morning) ]

Correct Answer: (d) 2
Solution:

19. The roots of quadratic equation 3x² − 2√6x + 2 = 0 [Group D 18/09/2022 (Morning)]

Correct Answer: (c) √2/√3 , √2/√3
Solution:

20. The quadratic equation whose roots are 1/√2 and 1/√2 is: [Group D 18/09/2022 (Morning)]

Correct Answer: (d) 2x² − 2√2x + 1 = 0
Solution: