Arts (English Medium) कक्षा ११ - CBSE Question Bank Solutions

Solve the following systems of linear inequations graphically:

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

Find the number of ways in which : (a) a selection

Find the number of ways in which : (b) an arrangement, of four letters can be made from the letters of the word 'PROPORTION'.

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 

Write \[\sum^m_{r = 0} \ ^{n + r}{}{C}_r\] in the simplified form.

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