Commerce (English Medium) कक्षा १२ - CBSE Question Bank Solutions

The objective function Z = 4x + 3y can be maximised subjected to the constraints 3x + 4y ≤ 24, 8x + 6y ≤ 48, x ≤ 5, y ≤ 6; x, y ≥ 0

If the constraints in a linear programming problem are changed

Which of the following is not a convex set?

In Figure ABCD is a regular hexagon, which vectors are:
(i) Collinear
(ii) Equal
(iii) Coinitial
(iv) Collinear but not equal.

Show that y = ae^2x + be^−x is a solution of the differential equation \[\frac{d^2 y}{d x^2} - \frac{dy}{dx} - 2y = 0\]

y² dx + (x² − xy + y²) dy = 0

Verify that the function y = e^−3x is a solution of the differential equation \[\frac{d^2 y}{d x^2} + \frac{dy}{dx} - 6y = 0.\]

In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-

y = e^x + 1            y'' − y' = 0

In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-

`y=sqrt(a^2-x^2)`              `x+y(dy/dx)=0`

Form the differential equation representing the family of curves y = a sin (x + b), where a, b are arbitrary constant.

Form the differential equation representing the family of parabolas having vertex at origin and axis along positive direction of x-axis.

Form the differential equation of the family of circles having centre on y-axis and radius 3 unit.

Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.

Solve for x `tan^-1((1 - x)/(1 + x)) = 1/2 tan^-1x, x > 0`

The domain of the function y = sin^–1 (– x²) is ______.

The domain of y = cos^–1(x² – 4) is ______.

The domain of the function defined by f(x) = sin^–1x + cosx is ______.

The equation tan^–1x – cot^–1x = `(1/sqrt(3))` has ______.

Prove that `cot(pi/4 - 2cot^-1 3)` = 7

Show that `2tan^-1 (-3) = (-pi)/2 + tan^-1 ((-4)/3)`