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

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

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

If ²⁰C_r = ²⁰C_r−10, then ¹⁸C_r is equal to

If ²⁰C_r = ²⁰C_{r + 4} , then ^rC₃ is equal to

If ¹⁵C_3r = ¹⁵C_{r + 3} , then r is equal to

If ²⁰C_{r + 1} = ²⁰C_{r − 1} , then r is equal to

If C (n, 12) = C (n, 8), then C (22, n) is equal to

If ^mC₁ = ⁿC₂ , then