Algebra (Railway Maths) (Part – V)

Total Questions: 50

11. Which of the following represents a quadratic equation? [Group D 27/09/2022 (Evening)]

Correct Answer: (c) 5x² + 4x − 2 = 7x
Solution:

5x² + 4x – 2 = 7x
⇒ 5x² + 4x - 7x - 2 = 0
⇒ 5x² - 3x - 2 = 0

12. Simplify the given expression [Group D 27/09/2022 (Evening) ]

Correct Answer: (c) y²/x²
Solution:

13. If x = −2/3 is one of the solutions of the quadratic equation 7x² + kx − 3 = 0, then the value of k satisfies the equation [Group D 27/09/2022 (Evening)]

Correct Answer: (d) 12k² − 4k − 1 = 0
Solution:

14. Simplify the given expression x² + 3x + 12 − 2(x³ − x + 4) [Group D 28/09/2022 (Morning)]

Correct Answer: (d) 4 + 5x + x² − 2x³
Solution:

Given expression,
x² + 3x +12 – 2(x³ – x + 4)
= x² + 3x + 12 - 2x³ + 2x - 8
= 4 + 5x + x² - 2x³

15. If p and q are the roots of x² + 4x − 21 = 0 and p < q, then the quadratic equation in x whose roots are (p − 1) and (q + 1) is: [Group D 28/09/2022 (Morning)]

Correct Answer: (c) x² + 4x − 32 = 0
Solution:

16. If a and b are the roots of the equation x² − 5x − 6 = 0, then the value of (a − b)² is: [Group D 28/09/2022 (Morning)]

Correct Answer: (b) 49
Solution:

17. If the quadratic equation ax² − 4x + 1 = 0 has equal roots, then the value of a is: [Group D 28/09/2022 (Afternoon)]

Correct Answer: (d) 4
Solution:

For equal roots, D = 0 ;
D = b² - 4ac = ax² - 4x + 1 = 0
⇒ D = b² - 4ac ⇒ 16 - 4a = 0
⇒ a = 4

18. If x + y = 5 and xy = 4, find the value of x³ + y³. [Group D 28/09/2022 (Afternoon)]

Correct Answer: (b) 65
Solution:

19. The roots of the quadratic equation x + 20/x = 9 are: [Group D 28/09/2022 (Evening)]

Correct Answer: (a) 4, 5
Solution:

20. If α and β are the roots of the equation x² + 5x + 6 = 0, then the value of αβ − (1/α + 1/β) is: [Group D 28/09/2022 (Evening)]

Correct Answer: (c) 41/6
Solution: