Algebra (Railway Maths) (Part – V)

Total Questions: 50

1. Expand (1/2x + 3y - 1/3z)². [Group D 26/09/2022 (Morning) ]

Correct Answer: (c)
Solution:

2. If α and β are the roots of the equation 2x² − 3x − 5 = 0, then the quadratic equation whose roots are α/β and β/α is: [Group D 26/09/2022 (Afternoon)]

Correct Answer: (d) 10x² + 29x + 10 = 0
Solution:

3. Find the sum of the roots of the quadratic equation x² + 19x + 60 = 0. [Group D 26/09/2022 (Evening)]

Correct Answer: (a) −19
Solution:

x² + 19x + 60 = 0
Standard equation : a² + bx + c = 0
Sum of the roots = -b/a = -19

4. A quadratic equation whose roots are 5/3 and −3/4 is: [Group D 27/09/2022 (Morning)]

Correct Answer: (a) 12x² − 11x − 15 = 0
Solution:

5. If 2 is a root of the equation x² − px + 6 = 0 and the quadratic equation x² + 2px + q = 0 has equal roots, then the value of q is: [Group D 27/09/2022 (Morning)]

Correct Answer: (a) 25
Solution:

6. Simplify the given equation (x² + xy + y²)² − (x² − xy + y²)² [Group D 27/09/2022 (Morning)]

Correct Answer: (a) 4xy(x² + y²)
Solution:

7. Simplify (5p - q)³ - (3p - 2q)³ - (q + 2p)³ / 13pq - 15p² - 2q². [Group D 27/09/2022 (Afternoon) ]

Correct Answer: (c) -6p - 3q
Solution:

8. If r and s are the roots of x² - 3x + 2 = 0, then quadratic equation in x whose roots are r² + s² and (rs)² is: [Group D 27/09/2022 (Afternoon) ]

Correct Answer: (c) x² - 9x + 20 = 0
Solution:

9. Simplify the given expression (y − z)³ + (z − x)³ + (x − y)³ [Group D 27/09/2022 (Evening)]

Correct Answer: (d) 3(x − y)(y − z)(z − x)
Solution:

10. If x = b + c, y = c − a, z = a − b, then find the value of x² + y² + z² − 2xy − 2xz + 2yz [Group D 27/09/2022 (Evening)]

Correct Answer: (a) 4b²
Solution: