Algebra (Railway Maths) (Part – I)

Total Questions: 50

21. If x³ + 1/x³ = 18 then what will be the value value of + 1/x? [NTPC CBT - I 02/02/2021 (Morning) ]

Correct Answer: (c) 3
Solution:

22. If x⁴ + 1/x⁴ = 322 then, x³ - 1/x³ = ? [NTPC CBT - I 15/02/2021 (Morning) ]

Correct Answer: (b) 76
Solution:

23. Calculate the value of √80 + 4√5 if 2√5 + √125 = 7x [NTPC CBT - I 15/02/2021 (Evening) ]

Correct Answer: (c) 8x
Solution:

24. If (x + 1/x) = 7, then (x - 1/x) is equal to: [NTPC CBT - I 16/02/2021 (Evening) ]

Correct Answer: (c) 3 √5
Solution:

25. If the system of equation 3x - 2y = 8, 2ax + (a - b)y = 48 has infinitely many solutions then: [NTPC CBT - I 12/03/2021 (Evening) ]

Correct Answer: (a) a = 3b
Solution:

26. if x⁴ + 1/x⁴ = 47 then find x + 1/x? [RRB JE 01/06/2019 (Evening) ]

Correct Answer: (d) 3
Solution:

27. The two roots of an quadratic equation are given as x = 2/3 and x = -1/2 The equation can be written as: [ALP Tier - I 20/08/2018 (Afternoon) ]

Correct Answer: (c) (2x + 1) (3x - 2) = 0
Solution:

When two roots of the quadratic equation are given. Then, it can be written as:
x² - x(sum of roots) + product of roots = 0
x² - x(2/3 - 1/2) - 1/3 = 0
⇒ x² - 1/6x - 1/3 = 0                ⇒ 6x² - x - 2 = 0
⇒ 6x² - 4x + 3x - 2 = 0
⇒ 2x(3x - 2) + 1(3x - 2) = 0
⇒ (3x - 2) (2x + 1) = 0

28. If a² + 1/a² = 3, then a³ + 1/a³ = ? [ALP Tier - I 21/08/2018 (Evening) ]

Correct Answer: (c) 2√5
Solution:

29. If x + y + z = 11 and xy + yz + zx = 42, then the value of x² + y² + z² is: [Group D 17/08/2022 (Morning) ]

Correct Answer: (a) 37
Solution:

30. The expansion of (3a - 4b - 2c)² is: [Group D 17/08/2022 (Afternoon) ]

Correct Answer: (d) 9a² + 16b² + 4c² - 24ab + 16bc - 12ac
Solution: