PUC Science इयत्ता ११ - Karnataka Board PUC Question Bank Solutions for Mathematics

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.

Let < a_n > be a sequence defined by a₁ = 3 and, a_n = 3a_{n − 1} + 2, for all n > 1
Find the first four terms of the sequence.

Let < a_n > be a sequence. Write the first five term in the following:

a₁ = 1, a_n = a_{n − 1} + 2, n ≥ 2

Let < a_n > be a sequence. Write the first five term in the following:

a₁ = 1 = a₂, a_n = a_{n − 1} + a_{n − 2}, n > 2

Let < a_n > be a sequence. Write the first five term in the following:

a₁ = a₂ = 2, a_n = a_{n − 1} − 1, n > 2

The Fibonacci sequence is defined by a₁ = 1 = a₂, a_n = a_{n − 1} + a_{n − 2} for n > 2

Find `(""^an +1)/(""^an")` for n = 1, 2, 3, 4, 5.

Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.

 3, −1, −5, −9 ...

Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.

−1, 1/4, 3/2, 11/4, ...

Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.

\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2}, 7\sqrt{2}, . . .\]