HSC Science (Computer Science) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Find the polar co-ordinates of the point whose Cartesian co-ordinates are.

`(0, 1/2)`

Find the polar coordinates of the point whose Cartesian coordinates are `(1, - sqrt(3))`.

Find the polar co-ordinates of the point whose Cartesian co-ordinates are.

`(3/2, (3√3)/2)`.

In ΔABC, if cot A, cot B, cot C are in A.P. then show that a², b², c² are also in A.P.

Solve the following equation by the method of inversion:

2x - y = - 2, 3x + 4y = 3

Solve the following equations by the method of inversion:

x + y+ z = 1, 2x + 3y + 2z = 2,
ax + ay + 2az = 4, a ≠ 0.

Solve the following equation by the method of inversion:

5x − y + 4z = 5, 2x + 3y + 5z = 2 and 5x − 2y + 6z = −1

Solve the following equations by the method of inversion:

x + y + z = - 1, y + z = 2, x + y - z = 3

Express the following equations in matrix form and solve them by the method of reduction:

x − y + z = 1, 2x − y = 1, 3x + 3y − 4z = 2

Express the following equations in matrix form and solve them by the method of reduction:

`x + y = 1, y + z = 5/3, z + x 4/33`.

Express the following equations in matrix form and solve them by the method of reduction:

2x - y + z = 1, x + 2y + 3z = 8, 3x + y - 4z = 1.

Express the following equations in matrix form and solve them by the method of reduction:

x + 2y + z = 8, 2x + 3y - z = 11, 3x - y - 2z = 5.

The cost of 4 pencils, 3 pens, and 2 books is ₹ 150. The cost of 1 pencil, 2 pens, and 3 books is ₹ 125. The cost of 6 pencils, 2 pens, and 3 books is ₹ 175. Find the cost of each item by using matrices.

The sum of three numbers is 6. Thrice the third number when added to the first number, gives 7. On adding three times the first number to the sum of second and third numbers, we get 12. Find the three number by using matrices.

An amount of ₹ 5000 is invested in three types of investments, at interest rates 6%, 7%, 8% per annum respectively. The total annual income from these investments is ₹ 350. If the total annual income from the first two investments is ₹ 70 more than the income from the third, find the amount of each investment using matrix method.

Solve the following equations by the method of inversion:

2x + 3y = - 5, 3x + y = 3

Express the following equations in matrix form and solve them by the method of reduction:

x + 3y + 2z = 6,

3x − 2y + 5z = 5,

2x − 3y + 6z = 7

Find the feasible solution of the following inequation:

3x + 2y ≤ 18, 2x + y ≤ 10, x ≥ 0, y ≥ 0

Find the feasible solution of the following inequation:

2x + 3y ≤ 6, x + y ≥ 2, x ≥ 0, y ≥ 0

Find the feasible solution of the following inequation:

3x + 4y ≥ 12, 4x + 7y ≤ 28, y ≥ 1, x ≥ 0.