All questions of Quadratic Equations for RRB NTPC/ASM/CA/TA Exam

Directions: In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer.
I. 7x + 12y = 13
II. 12x + 17y = 8
a)
if x > y
b)
if x ≤ y
c)
if x ≥ y
d)
if x < y
Correct answer is option 'D'. Can you explain this answer?

Ssc Cgl answered

I. 7x + 12y = 13
II. 12x + 17y = 8
→ I × 12 – II × 7
12y × 12 – 17y × 7 = 13 × 12 – 8 × 7
25y = 100
y = 4
7x + 12 × 4 = 13
x = – 5
Answer: x < y
Hence, Option D is correct.

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Directions: In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer.
I. 3x² – 21x + 36 = 0
II. 5y² – 25y + 30 = 0
a)
if x > y
b)
if x ≤ y
c)
if x ≥ y
d)
if x < y
Correct answer is option 'C'. Can you explain this answer?

Arnav Saini answered

Given Equations:
I. 3x^2 – 21x + 36 = 0
II. 5y^2 – 25y + 30 = 0

Solution:

Equation I:
Factorizing the equation 3x^2 – 21x + 36 = 0, we get:
3x^2 – 9x – 12x + 36 = 0
3x(x – 3) – 12(x – 3) = 0
(3x – 12)(x – 3) = 0
x = 4 or x = 3

Equation II:
Factorizing the equation 5y^2 – 25y + 30 = 0, we get:
5y^2 – 15y – 10y + 30 = 0
5y(y – 3) – 10(y – 3) = 0
(5y – 10)(y – 3) = 0
y = 2 or y = 3

Comparing x and y:
x = 4 or 3
y = 2 or 3
Since x can be greater than or equal to y, the correct answer is option 'C'.

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