Algebra (Railway Maths) (Part – I)

Total Questions: 50

1. The roots of the equation ax² + x + b = 0 are equal if: [Group D 17/08/2022 (Morning) ]

Correct Answer: (a) ab = 1/4
Solution:

2. Which is a quadratic equation? [Group D 17/08/2022 (Morning) ]

Correct Answer: (b) D
Solution:

(x - 4x² + 5) + √3x + 8 = 0
Quadratic equation is an equation in which the highest degree is 2. This is only in equation B.

3. What is the nature of the roots of 3x² + 6x - 5 = 0 [Group D 17/08/2022 (Afternoon) ]

Correct Answer: (a) The roots are real and distinct.
Solution:

3x² + 6x - 5 = 0
⇒ D = b² - 4ac = 36 + 60 = 96 > 0
Here, D > 0, so the roots are real and distinct.

4. The product of the roots of 3x² - 13x + 6 = 0 is: [Group D 17/08/2022 (Afternoon) ]

Correct Answer: (c) 2
Solution:

3x² - 13x + 6 = 0
Product of the roots = c/a = 6/3 = 2

5. One of the roots of the equation x² - 12x + k = 0 is x = 3. The other root is________. [Group D 18/08/2022 (Morning) ]

Correct Answer: (b) x = 9
Solution:

On putting x = 3,
x² - 12x + k = 0
⇒ 9 - 36 + k = 0 ⇒ k = 27
Now, x² - 12x + 27 = 0
(x - 9) (x - 3) = 0 ⇒ x = 9, 3

6. If a and b are the roots of the equation x² - 7x + 12 = 0, then the value of a³ + b³ / a² + b² + 1 is: [Group D 23/08/2022 (Afternoon) ]

Correct Answer: (d) 3.5
Solution:

7. If x - 1/x = 8, then find the value of x³ - 1/x³. [Group D 26/08/2022 (Afternoon) ]

Correct Answer: (b) 536
Solution:

8. If x + 1/x = 42, then what is the value of x³ + 1/x³ ? [Group -D 30/08/2022 (Afternoon) ]

Correct Answer: (c) 73,962
Solution:

9. Which of the following is a quadratic equation whose roots are 7 and 12? [Group D 08/09/2022 (Morning) ]

Correct Answer: (d) x² - 19x + 84 = 0
Solution:

10. If x + 1/x = 3, then x⁶ + 1/x⁶ is: [Group D 18/09/2022 (Evening) ]

Correct Answer: (d) 322
Solution: