1. If the system of equations 3x+ y = 1 and (2k-1)x + (k-1) y = 2k + 1 is inconsistent, then k =

2. The value of k for which the pair of equations kx = y +2 and 6x = 2y +3 has infinitely many solutions,

3. The pair of equations ax + 2y = 9 and 3x + by = 18 represent parallel lines, where a, b are integers , if

4. 3 chairs and 1 table cost ₹ 900; whereas 5 chairs and 3 tables cost ₹2,100. If the cost of 1 chair is ₹x  and the cost of 1 table is ₹y, then situation can be represented algebraically as

5. The father's age is six times his son's age. Four years hence, the age of the father will be four times his son. The present ages (in years) of the son and the father are, respectively

6. The pair of linear equations y = 0 and y = - 6 has

7. What is the value of q if p/2 +3q = 6 and 2p -2q =10?

8. The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2, then the fraction is

9. If 2x - 3y  =7 and (a + b)x - (a + b -3)y = 4a + b represent coincident lines, then a and b satisfy the  equation

10. The sum of the digits of a two-digit number is 9. If 27 is subtracted from the number, its digits are interchanged. Which of these is the product of the digits of the number?

11.Harsh correctly solved a pair of linear equations in two variables and found their only point of intersection as (3, -2). One of the lines was x - y = 5.

Which of the following could have been the other line?

(i) 3x-3y = 15        (ii) 2x-3y = 12     (iii) 2x - 3y = 14

12. Consider the equations shown:

ax + by = ab and 2ax + 3by = 3b, which of these is the value of y in terms of a?

13. Gunjan has only ₹1 and ₹ 2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is ₹75, then the number of ₹ 1 and 2 coins are respectively

14. Shown below is a pair of linear equations mx+4y-6 =0   ny - 12x + 12 = 0

For which of the following values of m and n do the above equations have infinitely many solutions?

15. The pair of linear equation 2x = 5y + 6 and 15 y = 6x - 18 represents two lines which are

16. The point of intersection of the line represented by 3x - y = 3 and y - axis is given by

17. If the pair of equations 3x - y + 8 = 0 and 6x - ry +16 =0 represent coincident lines, then the value of 'r' is

18. The value of k, for which the pair of linear equations kx + y = k^2 and x + ky = 1 have infinitely many solution is

19. The value of k for which the system of equations 2x + ky = 12, x + 3y - 4 = 0 is inconsistent  is

20. The value of k for which the line (k+1)x + 3 ky + 15 =0 and 5 x + ky + 5 = 0 are coincident is