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

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.

I₂ is the matrix ____________.

Given that `"dy"/"dx"` = ye^x and x = 0, y = e. Find the value of y when x = 1.

Solve `x^2 "dy"/"dx" - xy = 1 + cos(y/x)`, x ≠ 0 and x = 1, y = `pi/2`

The integrating factor of the differential equation `"dy"/"dx" (x log x) + y` = 2logx is ______.

An appropriate substitution to solve the differential equation `"dx"/"dy" = (x^2 log(x/y) - x^2)/(xy log(x/y))` is ______.

Integrating factor of the differential equation `x "dy"/"dx" - y` = sinx is ______.

Integrating factor of the differential equation `"dy"/"dx" - y` = cos x is e^x.

One root of the equation `abs ((3"x" - 8, 3,3),(3, 3"x" - 8, 3),(3,3,3"x" - 8)) = 0` is ____________.