# Maths Quiz on System of Linear Equations for IIT JEE & Engineering Exam

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## JEE Maths Quiz on System of Linear Equations

JEE Maths Quiz on System of Linear Equations : In this article you will get to Online test for JEE Main, JEE Advanced, UPSEE, WBJEE and other engineering entrance examinations that will help the students in their preparation. These tests are free of cost and will useful in performance and inculcating knowledge. In this post we are proving you quiz on System of Linear Equations, based on previous year paper.

## Quiz on System of Linear Equations

Q1. If S is the set of distinct values of ‘b’ for which the following system of linear equations x + y + z = 1 x + ay + z = 1 ax + by + z = 0 has no solution, then S is :
a) an empty set
b) an infinite set
c) a singleton
d) a finite set containing two or more elements

c) a singleton

Q2. If system of linear equations

x + y + z = 6

x + 2y + 3z = 10 and

3x + 2y + λz = μ

has more than two solutions, then μ − λ2 is equal to ________.

a) 13
b) 17
c) 15
d) 11

a) 13

Q3. If x = a, y = b, z = c is a solution of the system of linear equations

x + 8y + 7z = 0

9x + 2y + 3z = 0

x + y + z = 0

such that the point (a, b, c) lies on the plane x + 2y + z = 6, then 2a + b + c equals :

a) 0
b) 1
c) -1
d) 2

b) 1

Q4. The number of real values of λ for which the system of linear equations

2x + 4y − λz = 0

4x + λy + 2z = 0

λx + 2y + 2z = 0

has infinitely many solutions, is :

a) 0
b) 1
c) 2
d) 3

b) 1

Q5. If the system of linear equations

x + ky + 3z = 0

3x + ky – 2z = 0 and

2x + 4y – 3z = 0

has a non zero solution (x, y, z) then xz/y2 is equal to

a) -10
b) 10
c) -30
d) 30

b) 10

Q6. The following system of linear equations

7x + 6y − 2z = 0 ,

3x + 4y + 2z = 0

x − 2y − 6z = 0, has

a) infinitely many solutions, (x, y, z) satisfying y = 2z
b) infinitely many solutions, (x, y, z) satisfying x = 2z
c) no solution
d) only the trivial solution

b) infinitely many solutions, (x, y, z) satisfying x = 2z

Q7. For which of the following ordered pairs (μ, δ), the system of linear equations

x + 2y + 3z = 1

3x + 4y + 5z = μ

4x + 4y + 4z = δ

is inconsistent?

a) (4, 6)
b) (3, 4)
c) (1, 0)
d) (4, 3)

d) (4, 3)

Q8. If the system of linear equations

2x + 2ay + az = 0

2x + 3by + bz = 0 and

2x + 4cy + cz = 0,

Where a, b, c Є R are non-zero and distinct; has non-zero solution, then

a) a + b + c = 0
b) a, b, c are in A.P.
c) 1/a, 1/b, 1/c are in A.P.
d) a, b, c are in G.P.

c) 1/a, 1/b, 1/c are in A.P.

Q9. The system of linear equations

λx + 2y + 2z = 5

2λx + 3y + 5z = 8

4x + λy + 6z = 10 has:

a) no solution when λ = 2
b) infinitely many solutions when λ = 2
c) no solution when λ = 8
d) a unique solution when λ = -8

a) no solution when λ = 2

Q10. Consider the system of equations x + y + z = 1, 2x + 3y + 2z = 1, 2x + 3y + (a2 – 1)z = a + 1 then
a) System has a unique solution for |a| = √3
b) System is inconsistence for |a| = √3
c) System is inconsistence for a = 4
d) System is inconsistence for a = 3

b) System is inconsistence for |a| = √3

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