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

If bx + ay = a^{2}+b^{2} and ax – by = 0, then the value of (x – y)

If 2x – 3y = 7 and (a+b)x – (a+b–3)y = 4a+b have an infinite number of solutions, then

8 chairs and 5 tables cost ₹ 10,500, while 5 chairs and 3 tables cost ₹ 6,450. The cost of each chair will be

The pair of linear equation 3x + 5y = 3 and 6x + ky = 8 do not have a solution, if k is

19x – 17y = 55 and 17x – 19y = 53 then the value of (x – y) is

If (6, k) is a solution of equation 3x + y – 22 = 0 then the value of k is

The value of k for which the system of equations x + 2y = 3 and 5x + ky + 7 = 0 has no solution is

If 2x + 3y = 0 and 4x – 3y = 0 then the value of (x + y) is

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’s age. The present ages, in years, of the son and the father are, respectively.

The angles of cyclic quadrilaterals ABCD are: A = (6x+10)°, B = (5x)°, C = (x+y)° and D = (3y-10)°. The value of x and y is:

The perimeter of a rectangular garden is 180 metres. If the length of the garden is 10 metres more than its width, what will be the area of the garden ?

Sum of two numbers is 35 and their difference is 13, then the numbers are

The solution of the linear pair px + qy = p – q and qx – py = p + q is

The value of c for which the pair of equation cx – y = 2 and 6x – 2y = 3 will have no solution

Seven times a two-digit number is equal to four times the number obtained by reversing the order of its digit. If the difference between the digits is 3, then the number is

If one equation of a pair of dependent linear equations is –3x + 5y – 2 = 0. The second equation will be:

A fraction becomes \frac{1}{3} when 1 is subtracted from the numerator and it becomes \frac{1}{4} when 8 is added to its denominator. The fraction obtained is:

The value of k for which the system of equation kx – y = 2, and 6x – 2y = 3 has a unique solution is

Five years ago, A was thrice as old as B and ten years later A shall be twice as old as B, then the present age of A is

Aruna 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.

The pair of equation x = a and y = b graphically represents the lines which are

Two numbers are in the ratio 5:6 if 8 is subtracted from each of the numbers, the ratio becomes 4:5. The two numbers

The pair of equation 5x – 15y = 8 and 3x – 9y = \frac{24}{3} has

The sum of the digits of a two digit number is 9. If 27 is added to it, the digits of the numbers get
reversed. The number is

A two-digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted from the number, the digits are reversed, then the number is

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

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
are, respectively.

₹ 4900 were divided among 150 children. If each girl gets ₹ 50 and a boy gets ₹ 25, then the number of boys is:

If the system of equations kx – 5y = 2 and 4x + my = 10 has infinitely many solution then the value of k and m are