Algebra (Railway Maths) (Part – IX)

Total Questions: 50

11. If √(5 + √3) / √(5 - √3) = a + b√15, then what is the value of a? [RRB NTPC 21/03/2021 (Morning)]

Correct Answer: (c) 4
Solution:

12. When x + y + z = 16 and xy + yz + zx = 78, find the value of x³ + y³ + z³ - 3xyz. [RRB NTPC 21/03/2021 (Evening)]

Correct Answer: (a) 352
Solution:

13. If x + y = 1, then find the value of x³ + y³ + 3xy. [RRB NTPC 21/03/2021 (Evening)]

Correct Answer: (c) 1
Solution:

14. What is the value of the following? (a + 1)(1 - a)(1 - a + a²)(1 + a + a²)(1 + a⁶) [RRB NTPC 27/03/2021 (Morning)]

Correct Answer: (d) 1 - a¹²
Solution:

15. If x = a(b - c), y = b(c - a), and z = c(a - b) then what will be the value of (x / a)³ + (y / b)³ + (z / c)³? [RRB NTPC 27/03/2021 (Morning)]

Correct Answer: (d) 3xyz / abc
Solution:

16. If x² = y + z, y² = z + x, z² = x + y, then the value of 1 / (x + 1) + 1 / (y + 1) + 1 / (z + 1) will be: [RRB NTPC 27/03/2021 (Morning)]

Correct Answer: (a) 1
Solution:

17. If α + β + γ = 0, then α² / βγ + β² / γα + γ² / αβ = ? [RRB NTPC 27/03/2021 (Evening)]

Correct Answer: (b) 3
Solution:

18. If x = 2 + √2, then what will be the value of x² - 4x + 4? [RRB NTPC 27/03/2021 (Evening)]

Correct Answer: (c) 2
Solution:

19. For a = -5 and b = 5, value of a² - b² is: [RRB NTPC 01/04/2021 (Morning)]

Correct Answer: (b) 0
Solution:

a = -5 and b = 5
a² - b² = (-5)² - 5² = 25 - 25 = 0

20. What is the value of 8x³ + 18xy + y³ - 27 when 2x + y - 3 = 0? [RRB NTPC 01/04/2021 (Morning)]

Correct Answer: (c) 0
Solution: