Question
If the homogeneous system of equations x + y + z
= 0 2x + 3y + 4z = 0 has a non-trivial solution, then the value of k is: 3x + 5y + kz = 0Solution
We are given a homogeneous system of equations: x + y + z = 0 2x + 3y + 4z = 0 3x + 5y + kz = 0 We are told the system has a non-trivial solution , and we are to find the value of A homogeneous system has a non-trivial solution if and only if the determinant of the coefficient matrix is zero , i.e., the rows are linearly dependent . Write the coefficient matrix 
Solve the quadratic equations and determine the relation between x and y:
Equation 1: x² - 45x + 450 = 0
Equation 2: y² - 48y + 540 = 0�...
I. x2 + 28x + 96 = 0
II. y2 + 3y - 70 = 0
I. x2 + x – 42 = 0
II. y2 + 6y – 27 = 0
What is the average salary of 10 officers , if a clerk’s salary is Rs. 15,000?
Statement I: The total salary of 10 officers and 5 clerk is Rs....
I. 6x2 – 7x - 20 = 0
II. 3y2Â - y - 14 = 0
I. 2x² - 12x + 16 = 0  Â
II. 4y² - 8y - 12 = 0  Â
I. 5x + y = 37
II. 4y+ x = 15
Solve the quadratic equations and determine the relation between x and y:
Equation 1: x² - 54x + 704 = 0
Equation 2: y² - 44y + 448 = 0
I: x2Â + 31x + 228 = 0
II: y2 + 3y – 108 = 0
I. x2 - x - 56 = 0
II. y2 - 20y + 96 = 0
Relevant for Exams:
