HSC Arts (English Medium) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

In a meeting, 70% of the members favour and 30% oppose a certain proposal. A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Find E(X) and Var(X).

Solve the following LPP by graphical method:

Maximize: z = 3x + 5y
Subject to: x + 4y ≤ 24
                  3x + y ≤ 21
                  x + y ≤ 9
                  x ≥ 0, y ≥ 0 

Also find the maximum value of z.

Evaluate : `∫(x+1)/((x+2)(x+3))dx`

Solve the following L. P. P. graphically:Linear Programming

Minimize Z = 6x + 2y

Subject to

5x + 9y ≤ 90

x + y ≥ 4

y ≤ 8

x ≥ 0, y ≥ 0

Solve the following LPP by graphical method:

Minimize Z = 7x + y subject to 5x + y ≥ 5, x + y ≥ 3, x ≥ 0, y ≥ 0

The point at which the maximum value of x + y subject to the constraints x + 2y ≤ 70, 2x + y ≤ 95, x ≥ 0, y ≥ 0 is obtained, is ______.

The value of objective function is maximum under linear constraints ______.

 Maximize: z = 3x + 5y  Subject to

x +4y ≤ 24                3x + y  ≤ 21 

x + y ≤ 9                     x ≥ 0 , y ≥0

Find the joint equation of the pair of the line through the point (2, -1) and parallel to the lines represented by 2x² + 3xy - 9y² = 0.

Find the joint equation of the pair of the line through the point (2, -3) and parallel to the lines represented by x² + xy - y² = 0.

Show that the equation x² + 2xy + 2y² + 2x + 2y + 1 = 0 does not represent a pair of lines.

Show that the equation 2x² − xy − 3y² − 6x + 19y − 20 = 0 represents a pair of lines.

Show that the equation 2x² + xy - y² + x + 4y - 3 = 0 represents a pair of lines. Also, find the acute angle between them.

Find the separate equation of the line represented by the following equation:

(x - 2)² - 3(x - 2)(y + 1) + 2(y + 1)² = 0

Find the value of k, if the following equations represent a pair of line:

3x² + 10xy + 3y² + 16y + k = 0

Find the value of k, if the following equations represent a pair of line:

kxy + 10x + 6y + 4 = 0

Find the value of k, if the following equations represent a pair of line:

x² + 3xy + 2y² + x - y + k = 0

Find p and q, if the equation 2x² + 8xy + py² + qx + 2y - 15 = 0 represents a pair of parallel lines.

Equations of pairs of opposite sides of a parallelogram are x² - 7x + 6 = 0 and y² − 14y + 40 = 0. Find the joint equation of its diagonals.

Find the separate equation of the line represented by the following equation:

10(x + 1)² + (x + 1)(y - 2) - 3(y - 2)² = 0