Complex Numbers & Quadratic Equations Test

Result

Complex Numbers & Quadratic Equations Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

Consider the system of linear equation:
x₁ + 2x₂ + x₃ = 3
2x₁ + 3x₂ + x₃ = 3
3x₁ + 5x₂ + 2x₃ = 1
The system has

A
infinite number of solutions

B
exactly 3 solutions

C
a unique solution

D
no solution

Solution

Find discriminant D of the above equation, D = 0,
But D₃ ≠ 0
Thus, the system of equation has no solution.
Question 2
1 / -0

A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after.

A
18 months

B
19 months

C
20 months

D
21 months

Solution

Let it happened after m months
2 × 300 + (2 × 240 + (m - 4) × 40))
= 11040
⇒ m² + 5m - 546 = 0
⇒ (m + 26) (m - 21) = 0
⇒ m = 21.
Hence, option D is correct.