English Medium कक्षा १० - CBSE Question Bank Solutions

A thief runs with a uniform speed of 100 m/minute. After one minute, a policeman runs after the thief to catch him. He goes with a speed of 100 m/minute in the first minute and increases his speed by 10 m/minute every succeeding minute. After how many minutes the policeman will catch the thief.

A thief, after committing a theft, runs at a uniform speed of 50 m/minute. After 2 minutes, a policeman runs to catch him. He goes 60 m in first minute and increases his speed by 5 m/minute every succeeding minute. After how many minutes, the policeman will catch the thief?

Solve the following system of equations by cross-multiplication method.

2x + 3y + 8 = 0

4x + 5y + 14 = 0

Solve the follownig system of equations by the method of cross-multiplication.

2x – 6y + 10 = 0

3x – 7y + 13 = 0

Solve the following system of equations by the method of cross-multiplication.

11x + 15y = – 23; 7x – 2y = 20

Solve the following system of equations by cross-multiplication method.

ax + by = a – b; bx – ay = a + b

Solve the following system of equations by cross-multiplication method x + y = a – b; ax – by = a² + b²

Solve the following system of equations by the method of cross-multiplication:

`\frac{x}{a} + \frac{y}{b} = a + b; \frac{x}{a^{2}} + \frac{y}{b^{2}} = 2`

Solve the following system of equations by cross-multiplication method ax + by = 1;  `bx + ay = \frac{(a+b)^{2}}{a^{2}+b^{2}-1`

Solve the following system of equations in x and y by cross-multiplication method

`(a – b) x + (a + b) y = a^2 – 2ab – b^2`

`(a + b) (x + y) = a^2 + b^2`

Solve the following system of equations by cross-multiplications method.

`a(x + y) + b (x – y) = a^2 – ab + b^2`

`a(x + y) – b (x – y) = a^2 + ab + b^2`

 Solve the following system of equations by the method of cross-multiplication. `\frac{a}{x}-\frac{b}{y}=0;\text{}\frac{ab^{2}}{x}+\frac{a^{2}b}{y}=a^{2}+b^{2};` Where x ≠ 0, y ≠ 0

Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method

x – 3y – 3 = 0

3x – 9y – 2 = 0

Which of the following pairs of linear equations has unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method

2x + y = 5

3x + 2y = 8

Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method

3x – 5y = 20

6x – 10y = 40

Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method.

x – 3y – 7 = 0

3x – 3y – 15 = 0

For which values of a and b does the following pair of linear equations have an infinite number of solutions?

2x + 3y = 7

(a – b) x + (a + b) y = 3a + b – 2

For which value of k will the following pair of linear equations have no solution?

3x + y = 1

(2k – 1)x + (k – 1)y = 2k + 1

Solve the following pair of linear equations by the substitution and cross-multiplication methods

8x + 5y = 9

3x + 2y = 4

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method :

A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay Rs 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs 1180 as hostel charges. Find the fixed charges and the cost of food per day.