Science (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

Solve the following Linear Programming Problem graphically:

Minimize: Z = 60x + 80y

Subject to constraints:

3x + 4y ≥ 8

5x + 2y ≥ 11

x, y ≥ 0

The feasible region corresponding to the linear constraints of a Linear Programming Problem is given below.

Which of the following is not a constraint to the given Linear Programming Problem?

Given that A is a square matrix of order 3 and |A| = –2, then |adj(2A)| is equal to ______.

If f(x) = `1/(4x^2 + 2x + 1); x ∈ R`, then find the maximum value of f(x).

Find the maximum profit that a company can make, if the profit function is given by P(x) = 72 + 42x – x², where x is the number of units and P is the profit in rupees.

Check whether the function f : R `rightarrow` R defined by f(x) = x³ + x, has any critical point/s or not ? If yes, then find the point/s.

Find : `int sqrt(x/(1 - x^3))dx; x ∈ (0, 1)`.

Solve the following Linear Programming Problem graphically:

Minimize: z = x + 2y,

Subject to the constraints: x + 2y ≥ 100, 2x – y ≤ 0, 2x + y ≤ 200, x, y ≥ 0.

Solve the following Linear Programming Problem graphically:

Maximize: z = – x + 2y,

Subject to the constraints: x ≥ 3, x + y ≥ 5, x + 2y ≥ 6, y ≥ 0.

Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:

f(x) `= x sqrt(1 - x), 0 < x < 1`

Solve the following matrix equation for x: `[x 1] [[1,0],[−2,0]]=0`

If `|[2x,5],[8,x]|=|[6,-2],[7,3]|`, write the value of x.

Evaluate :`int_(pi/6)^(pi/3) dx/(1+sqrtcotx)`

Write the principal value of `tan^(-1)+cos^(-1)(-1/2)`

Find the value of a if `[[a-b,2a+c],[2a-b,3c+d]]=[[-1,5],[0,13]]`

If `|[x+1,x-1],[x-3,x+2]|=|[4,-1],[1,3]|`, then write the value of x.

Evaluate : `intsin(x-a)/sin(x+a)dx`

Show that the differential equation 2y^x/y dx + (y − 2x e^x/y) dy = 0 is homogeneous. Find the particular solution of this differential equation, given that x = 0 when y = 1.

Solve the differential equation :

`y+x dy/dx=x−y dy/dx`

If A =  `([cos alpha, sin alpha],[-sinalpha, cos alpha])` , find α satisfying 0 < α < `pi/r`when `A+A^T=sqrt2I_2` where A^T is transpose of A.