Class 12 Mathematics - Chapter Differential Equations NCERT Solutions | Determine order and degree(if defined) o

Determine order and degree(if defined) of differential equation y' + 5y = 0

Determine order and degree(if defined) of differential equation

\begin{align}\left(\frac{d^2y}{dx^2}\right)^2\;+\;cos\left(\frac{dy}{dx}\right)\;=\;0\end{align}

Determine order and degree(if defined) of differential equation yⁿ + 2y^' + siny = 0

The order of the differential equation

\begin{align}2x^2\frac{d^2y}{dx^2}\;- \;3\frac{dy}{dx}\;+ y=\;0\end{align}

is (A) 2 (B) 1 (C) 0 (D) not defined

Determine order and degree(if defined) of differential y^' + y =e^x

y = Ax : xy^' = y (x ≠ 0)

Determine order and degree(if defined) of differential equation y^m + 2yⁿ + y' =0

\begin{align} y = xsinx:xy{'}=y +x\sqrt{x^2 -y^2}(x\neq0\; and\; x>y\; or\; x<-y)\end{align}

Determine order and degree(if defined) of differential equation \begin{align} \frac{d^4y}{dx^4}\;+\;\sin(y^m)\;=0\end{align}

y = e^x +1 : yⁿ -y^' = 0

Prove that the function f(x) = 5x – 3 is continuous at x = 0, at x = – 3 and at x = 5.

Represent graphically a displacement of 40 km, 30° east of north.

If a line makes angles 90°, 135°, 45° with x, y and z-axes respectively, find its direction cosines.

Maximise Z = 3x + 4y

Subject to the constraints:x + y ≤ 4, x ≥ 0, y ≥ 0

Find the area of the region bounded by the curve y² = x and the lines x = 1, x = 4 and the x-axis.

Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P (E|F) and P(F|E).

Show that the Signum Function f : R → R, given by

is neither one-one nor onto.

In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.

(i) f : R → R defined by f(x) = 3 – 4x

(ii) f : R → R defined by f(x) = 1 + x² 

Let f: X → Y be an invertible function. Show that the inverse of f ^–1 is f, i.e., (f^–1)^–1 = f.

Maximise Z = 3x + 4y

Subject to the constraints:x + y ≤ 4, x ≥ 0, y ≥ 0

A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate at which the radius of the balloon increases when the radius is 15 cm.

A balloon, which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is 10 cm.

The total revenue in Rupees received from the sale of x units of a product is given by

R (x) = 3x² + 36x + 5. The marginal revenue, when x = 15 is

(A) 116 (B) 96 (C) 90 (D) 126

The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference?

The rate of change of the area of a circle with respect to its radius r at r = 6 cm is

(A) 10π (B) 12π (C) 8π (D) 11π