Algebra (Railway Maths) (Part – II)

Total Questions: 50

11. Solve: (a − b)³ + (b − 2c)³ + (−a + 2c)³. [Group D 25/08/2022 (Evening)]

Correct Answer: (c) 3((a − b)(b − 2c)(−a + 2c))
Solution:

12. The roots of quadratic equation that satisfies 12x² = 27x are: [Group D 25/08/2022 (Evening) ]

Correct Answer: (d) 0, 9/4
Solution:

13. Simplify (2z − 5y)² + (5z + 2y)² − 25z² [Group D 26/08/2022 (Morning)]

Correct Answer: (b) 29y² + 4z²
Solution:

After simplification,
4z² + 25y² - 20yz + 25z² + 4y² +20yz - 25z² = 29y² + 4z²

14. The equation 2x² + 7x + 6 = 0 can be written as: [Group D 26/08/2022 (Morning)]

Correct Answer: (b) (2x + 3)(x + 2) = 0
Solution:

2x² + 7x +6 = 0
⇒ 2x² + 4x + 3x + 6 = 0
⇒ 2x(x + 2) + 3(x + 2) = 0
So, (2x + 3)(x + 2) = 0

15. If a² + b² = 50 and a × b = 7, find (a - b) / (a + b), where a>b. [Group D 26/08/2022 (Morning)]

Correct Answer: (d) 3/4
Solution:

16. If one of the roots of a quadratic equation is 1/ 2 - √2 , then find the quadratic equation. [Group D 26/08/2022 (Morning)]

Correct Answer: (d) 2x² − 4x + 1 = 0
Solution:

17. x² − 2x + 3 = 0 is a ______. [Group D 26/08/2022 (Afternoon)]

Correct Answer: (b) quadratic equation
Solution:

A quadratic equation is a second order equation written as ax² + bx + c = 0 ,where a, b, and c are coefficients of real numbers and a ≠ 0. We can clearly see that x² -2x +3 =0 is a quadratic equation.

18. Find the quadratic equation whose roots are equal to the sum and product of the roots of the quadratic equation 2x² + 4x − 1 = 0. [Group D 26/08/2022 (Afternoon)]

Correct Answer: (d) 2x² + 5x + 2 = 0
Solution:

19. If x³ − 3x + 6 = 0 then it is ______. [Group D 26/08/2022 (Evening)]

Correct Answer: (c) not a quadratic equation
Solution:

x³ - 3x + 6 = 0
A quadratic equation is a second order equation written as
ax ² + bx + c = 0 where a, b, and c are coefficients of real numbers and a ≠ 0. we can clearly see that x³ - 3x + 6 = 0 is not a quadratic equation.

20. If x = 2 + √5 and y = 2 − √5, then find the value of x² + y². [Group D 26/08/2022 (Evening)]

Correct Answer: (a) 18
Solution: