Algebra (Railway Maths) (Part – IV)

Total Questions: 50

21. The sum of roots of x² − px + q = 0 is ______. [Group D 18/09/2022 (Morning)]

Correct Answer: (c) p
Solution:

x² - px + q = 0
Sum of the roots = -b/a = p/1 = p

22. If 3 is root of the equation x² − px + 15 = 0 and the quadratic equation x² + px + q = 0 has equal roots, then the value of q is [Group D 18/09/2022 (Evening)]

Correct Answer: (a) 16
Solution:

23. Which of the following is a quadratic equation written in standard form? [Group D 18/09/2022 (Evening)]

Correct Answer: (a) 5x² + 3x − 1 = 0
Solution:

Standard form of a quadratic equation = ax² + bx + c = 0
Now, from option 5x² + 3x - 1 = 0 is a quadratic equation.

24. Factorise (64 x⁶ - y⁶). [Group D 19/09/2022 (Morning) ]

Correct Answer: (b)
Solution:

25. Which of the following is the standard representation of quadratic equation (x − 4)(x + 1) = 2? [Group D 19/09/2022 (Morning)]

Correct Answer: (a) x² − 3x − 6 = 0
Solution:

(x - 4) (x + 1) = 2
= x² - 3x - 4 - 2 = 0 ⇒ x² - 3x - 6 = 0

26. What kind of roots does the quadratic equation 5x² + 7x + 4 = 0 have? [Group D 19/09/2022 (Morning)]

Correct Answer: (a) No real roots
Solution:

27. The equation (x + 1)³ − (x − 1)³ = 0 is: [Group D 19/09/2022 (Afternoon)]

Correct Answer: (c) a quadratic equation with non-real roots
Solution:

28. If α, β are the roots of px² + qx + r = 0, then α² + β² = ______. [Group D 19/09/2022 (Afternoon)]

Correct Answer: (b) (q² − 2qr) / p²
Solution:

29. If a² − 4a + 1 = 0, find a² + 1/a². [Group D 19/09/2022 (Afternoon)]

Correct Answer: (a) 14
Solution:

30. Find the answer of given question? [Group D 19/09/2022 (Afternoon) ]

Correct Answer: (b) 1/4
Solution: