Algebra (Railway Maths) (Part – I)

Total Questions: 50

11. Which of the following equations is NOT a quadratic equation? [Group D 27/09/2022 (Afternoon) ]

Correct Answer: (c) x² + 2√x - 5 = 0
Solution:

x² + 2√x - 5 = 0 Clearly it’s not a quadratic equation .

12. If the sum and the product of the roots of an quadratic equation are q/p and r²/q, respectively, where p, q ≠ 0, then the quadratic equation and the discriminant of the quadratic equation are given respectively, as: [Group D 30/09/2022 (Afternoon) ]

Correct Answer: (b) pqx² - q²x + pr² = 0 and q⁴ - 4p²r²q
Solution:

13. The discriminant of the quadratic equation bx² + cx + a = 0; b ≠ 0, is given by the expression [Group D 07/10/2022 (Afternoon) ]

Correct Answer: (d) c² - 4ab
Solution:

The quadratic equation ax 2 + bx + c = 0, the expression b 2 – 4ac is called the discriminant. ATQ, comparing the quadratic equation
(bx² + cx + a = 0), a = b, b = c, c = a
Hence, ⇒ b² - 4ac = c² - 4ab

14. If 3x + 2y = 13 and y² - 4y + 4 = 0, then find (x,y) [NTPC CBT II Level 6 (09/05/2022) Shift 1 ]

Correct Answer: (d) (3, 2)
Solution:

15. If a + b = 15, and a² + b² = 113, then what is the value of a³ + b³? [NTPC CBT II Level 3 (17/06/2022) Shift 2 ]

Correct Answer: (c) 855
Solution:

16. If x/2 + 2/y = 1 and y/2 + 2/z = 1, then the value of z/2 + 2/x is [NTPC CBT - I 28/12/2020 (Morning) ]

Correct Answer: (d) 1
Solution:

17. If x + (1/x) = 12 and x² - 1/x² = 50, then the value of x⁴ - 1/x⁴ is [NTPC CBT - I 29/12/2020 (Evening) ]

Correct Answer: (c) 7100
Solution:

18. If the degree of polynomial 9x⁵y²zʳ is 15, then r = ? [NTPC CBT - I 19/01/2021 (Morning) ]

Correct Answer: (b) 8
Solution:

Degree of polynomial 9x⁵y²zʳ is 15 So, Sum of all indices
= 5 + 2 + r = 15
r = 8

19. The sum of two numbers is 25 and the product is 35. The sum of their reciprocals is: [NTPC CBT - I 27/01/2021 (Morning) ]

Correct Answer: (d) 5/7
Solution:

Sum of reciprocals
= a + b / ab = 25/35 = 5/7

20. If x - 1/x = 5, find the value of x⁴ + 1/x⁴. [NTPC CBT - I 28/01/2021 (Morning) ]

Correct Answer: (b) 727
Solution: