(English Medium) ICSE Class 9 - CISCE Question Bank Solutions for Mathematics

Solve the following equations graphically :
x+ 2y - 7 = 0
2x - y - 4 = 0

Find graphically the vertices of the triangle, whose sides have the equations 2y - x = 8, 5y -x = 14 and y = 2x - 1.

Find graphically the vertices of the triangle, whose sides are given by 3y = x + 18, x + 7y = 22 and y + 3x = 26.

Solve the following system of linear equations graphically :
4x - 5y - 20 = 0
3x + 3y - 15 = 0
Determine the vertices of the triangle formed by the lines, represented by the above equations and the y-axis.

Solve the following system of equations graphically
x - y + 1 = 0
4x + 3y = 24

Draw the graph of the following equations :
3x + 2y + 6 = 0
3x + 8y - 12 = 0
Also, determine the co-ordinates of the vertices of the triangle formed by these lines and x-axis.

Solve the following system of equations graphically:
2x = 23 - 3y
5x = 20 + 8y
Also, find the area of the triangle formed by these lines and x-axis in each graph.

Solve the following system of equations graphically:
6x - 3y + 2 = 7x + 1
5x + 1 = 4x - y + 2
Also, find the area of the triangle formed by these lines and x-axis in each graph.

The difference of two numbers is 3, and the sum of three times the larger one and twice the smaller one is 19. Find the two numbers.

If a number is thrice the other and their sum is 68, find the numbers.

The sum of four times the first number and three times the second number is 15. The difference of three times the first number and twice the second number is 7. Find the numbers.

The age of the father is seven times the age of the son. Ten years later, the age of the father will be thrice the age of the son. Find their present ages.

A father's age is three times the age of his child. After 12 years, twice the age of father will be 36 more than thrice the age of his child. Find his present age.
* Question modified

In a ABC, ∠A = x°, ∠B = (2x - 30)°, ∠C = y° and also, ∠A + ∠B = one right angle. Find the angles. Also, state the type of this triangle.

A two-digit number is such that the ten's digit exceeds thrice the unit's digit by 3 and the number obtained by interchanging the digits is 2 more than twice the sum of the digits. Find the number.

The ratio of passed and failed students in an examination was 3 : 1. Had 30 less appeared and 10 less failed, the ratio of passes to failures would have been 13 : 4. Find the number of students who appeared for the examination.

Samidha and Shreya have pocket money Rs.x and Rs.y respectively at the beginning of a week. They both spend money throughout the week. At the end of the week, Samidha spends Rs.500 and is left with as much money as Shreya had in the beginning of the week. Shreya spends Rs.500 and is left with `(3)/(5)` of what Samidha had in the beginning of the week. Find their pocket money.

Evaluate the following: `(2^3)^2`

Evaluate the following: `(3^2)^2`

State, true of false:
log 4 x log 1 = 0