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# GATE 2022: Engineering Mathematics || Quiz -2 (App update required to attempt this test)

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Question 1

Consider the following system equations: The condition on value of , such that system has a unique solution:

Question 2

Let x and y be integers satisfying the following equations The value of (x+y) is ________.

Question 3

The system of algebraic equations x+2y+z=4 , 2x+y+2z=5 and x-y+z=1 has

Question 4

x + 2y – 3z = 8, 2x – 2y + 3z = –5, x + y + αz = β

Then for what value of α and β the system has a unique solution?

Question 5

The value of the constant for which the system of equations:   has a solution is _________.

Question 6

For the equation given below

x + 2y – z = 6 (i)

x + by – 6z = 11 (ii)

3x + cy – 18z = 33 (iii)

For what values of b and c the system has infinite number of solution.

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