1. The number of solutions of the pair of linear equations x + 2y – 8 = 0 and 2x + 4y = 16 is :
(a) 0
(b) 1
(c) infinitely many
(d) none of these
2. The graphical representation of the pair of equations x + 2y – 4 = 0 and 2x + 4y – 12 = 0 represents :
(a) intersecting lines
(b) parallel lines
(c) coincident lines
(d) all of these
3. If a pair of linear equations is consistent, then the lines will be :
(a) parallel
(b) always coincident
(c) intersecting or coincident
(d) always intersecting
4. The condition so that the pair of linear equations kx + 3y + 1 = 0, 2x + y + 3 = 0 has exactly one solution is :
(a) k = 6
(b) k ≠ 6
(c) k = 3
(d) k ≠ 3
5. The lines representing the linear equations 2x – y = 3 and 4x – y = 5 :
(a) intersect at a point
(b) are parallel
(c) are coincident
(d) intersect at exactly two points
6. The pair of linear equations 2x + 5y = –11 and 5x + 15y = –44 has :
(a) many solutions
(b) no solution
(c) one solution
(d) two solutions
7. The pair of equations y = 0 and y = –7 has :
(a) one solution
(b) two solutions
(c) infinitely many solutions
(d) no solution
8. If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is :
(a) –5/4
(b) 2/5
(c) 15/4
(d) 3/2
9. The pair of linear equations 8x – 5y = 7 and 5x – 8y = –7 have :
(a) one solution
(b) two solutions
(c) no solution
(d) many solutions
10. The pair of linear equations x – 2y = 0 and 3x + 4y = 20 have :
(a) one solution
(b) two solutions
(c) many solutions
(d) no solution
11. The pair of linear equations kx + 2y = 5 and 3x + y = 1 has unique solution, if :
(a) k = 6
(b) k ≠ 6
(c) k = 0
(d) k has any value
12. One equation of a pair of dependent linear equations is –5x + 7y = 2, the second equation can be :
(a) 10x + 14y + 4 = 0
(b) –10x = 14y + 4 – 0
(c) –10x + 14y + 4 = 0
(d) 10x – 14y = –4
13. The value of k for which the pair of equations : kx – y = 2 and 6x – 2y = 3 has a unique solution is
(a) k = 3
(b) k ≠ 3
(c) k ≠ 0
(d) k = 0
14. The value of k for which the pair of linear equations 4x + 6y – 1 = 0 and 2x + ky – 7 = 0 represents parallel lines is :
(a) k = 3
(b) k = 2
(c) k = 4
(d) k = –2
15. If x = a, y = b is the solution of the equations x – y = 2 and x + y = 4, then the values of a and b respectively are
(a) 3 and 5
(b) 5 and 3
(c) 3 and 1
(d) –1 and –3