Arts (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

Find the domain of sin^–1 (x² – 4).

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.

Write the following function in the simplest form:

`tan^-1 ((cos x - sin x)/(cos x + sin x)), (-pi)/4 < x < (3 pi)/4`

`tan^-1 sqrt3 - cot^-1 (- sqrt3)` is equal to ______.

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

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`

Show that the differential  equation `2xydy/dx=x^2+3y^2`  is homogeneous and solve it.

Find the particular solution of the differential equation:

2y e^x/y dx + (y - 2x e^x/y) dy = 0 given that x = 0 when y = 1.

Find the absolute maximum and absolute minimum values of the function f given by f(x)=sin²x-cosx,x ∈ (0,π)

Find the local maxima and local minima, of the function f(x) = sin x − cos x, 0 < x < 2π.

Two tailors, A and B, earn Rs 300 and Rs 400 per day respectively. A can stitch 6 shirts and 4 pairs of trousers while B can stitch 10 shirts and 4 pairs of trousers per day. To find how many days should each of them work and if it is desired to produce at least 60 shirts and 32 pairs of trousers at a minimum labour cost, formulate this as an LPP

if `A = [(1,2,-3),(5,0,2),(1,-1,1)], B = [(3,-1,2),(4,2,5),(2,0,3)] and C = [(4,1,2),(0,3,2),(1,-2,3)]` then compute (A + B) and (B - C). Also verify that A + (B -C) = (A + B) - C.

If ` A = [(2/3, 1, 5/3), (1/3, 2/3, 4/3),(7/3, 2, 2/3)]` and `B = [(2/5, 3/5,1),(1/5, 2/5, 4/5), (7/5,6/5, 2/5)]` then compute 3A - 5B.