PUC Science इयत्ता ११ - Karnataka Board PUC Question Bank Solutions

Solve the following systems of linear inequation graphically:

 2x + 3y ≤ 6, 3x + 2y ≤ 6, x ≥ 0, y ≥ 0 

Solve the following systems of linear inequation graphically:

2x + 3y ≤ 6, x + 4y ≤ 4, x ≥ 0, y ≥ 0 

Solve the following systems of linear inequations graphically: 

x − y ≤ 1, x + 2y ≤ 8, 2x + y ≥ 2, x ≥ 0, y ≥ 0

Solve the following systems of linear inequations graphically: 

 x + y ≥ 1, 7x + 9y ≤ 63, x ≤ 6, y ≤ 5, x ≥ 0, y ≥ 0 

Solve the following systems of linear inequations graphically:

2x + 3y ≤ 35, y ≥ 3, x ≥ 2, x ≥ 0, y ≥ 0 

Show that the solution set of the following linear inequations is empty set: 

 x − 2y ≥ 0, 2x − y ≤ −2, x ≥ 0, y ≥ 0 

Show that the solution set of the following linear inequations is empty set: 

x + 2y ≤ 3, 3x + 4y ≥ 12, y ≥ 1, x ≥ 0, y ≥ 0 

Find the linear inequations for which the shaded area in Fig. 15.41 is the solution set. Draw the diagram of the solution set of the linear inequations: 

Find the linear inequations for which the solution set is the shaded region given in Fig. 15.42 

Show that the solution set of the following linear in equations is an unbounded set:
x + y ≥ 9
3x + y ≥ 12
x ≥ 0, y ≥ 0

Solve the following systems of inequations graphically:

2x + y ≥ 8, x + 2y ≥ 8, x + y ≤ 6 

Solve the following systems of inequations graphically: 

12x + 12y ≤ 840, 3x + 6y ≤ 300, 8x + 4y ≤ 480, x ≥ 0, y ≥ 0

Solve the following systems of inequations graphically: 

x + 2y ≤ 40, 3x + y ≥ 30, 4x + 3y ≥ 60, x ≥ 0, y ≥ 0 

Solve the following systems of inequations graphically: 

 5x + y ≥ 10, 2x + 2y ≥ 12, x + 4y ≥ 12, x ≥ 0, y ≥ 0

Show that the following system of linear equations has no solution:  

\[x + 2y \leq 3, 3x + 4y \geq 12, x \geq 0, y \geq 1\]

Show that the solution set of the following system of linear inequalities is an unbounded region:  

\[2x + y \geq 8, x + 2y \geq 10, x \geq 0, y \geq 0\] 

Mark the correct alternative in each of the following:

If x\[<\]7, then

Write the solution of the inequation\[\frac{x^2}{x - 2} > 0\]

A sequence is defined by a_n = n³ − 6n² + 11n − 6, n ϵ N. Show that the first three terms of the sequence are zero and all other terms are positive.