This page offers a step-by-step solution to the specific question **NCERT Class 12th Mathematics - Differential Equations | determine order and degree if defined of differen Answer ** from NCERT Class 12th Mathematics, Chapter Differential Equations.

Question 7

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

Answer

The highest order derivative present in the differential equation is y^{m}. Therefore, its order is three.

It is a polynomial equation in y^{m },^{ }y^{n }and y' . The highest power raised to y^{m} is 1. Hence, its degree is 1.

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

- Q:-
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}

- Q:-
Determine order and degree(if defined) of differential equation (y

^{m})^{2}+ (y^{n})^{3}+ (y')^{4}+ y^{5}=0 - Q:-
Determine order and degree(if defined) of differential equation y

^{n}+ 2y^{'}+ siny = 0 - Q:-
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 - Q:-
Determine order and degree(if defined) of differential y

^{'}+ y =e^{x} - Q:-
y = Ax : xy

^{'}= y (x ≠ 0) - Q:-
\begin{align} y = xsinx:xy{'}=y +x\sqrt{x^2 -y^2}(x\neq0\; and\; x>y\; or\; x<-y)\end{align}

- Q:-
Determine order and degree(if defined) of differential equation y

^{n}+ (y')^{2}+ 2y =0 - Q:-
y = cosx + C

**:**y^{'}+ sinx = 0

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

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

- Q:-
If a line makes angles 90°, 135°, 45° with

*x*,*y*and*z*-axes respectively, find its direction cosines. - Q:-
Maximise Z = 3

*x*+ 4*y*Subject to the constraints:

*x*+*y*≤ 4,*x*≥ 0,*y*≥ 0 - Q:-
Find the area of the region bounded by the curve

*y*^{2}=*x*and the lines*x*= 1,*x*= 4 and the*x*-axis. - Q:- Evaluate the determinants

\begin{vmatrix} \mathbf{2} & \mathbf{4} \\ \mathbf{-5} & \mathbf{-1} \end{vmatrix} - Q:- Determine whether each of the following relations are reflexive, symmetric and transitive:

(i) Relation R in the set A = {1, 2, 3,13, 14} defined as

R = {(x, y): 3x − y = 0}

(ii) Relation R in the set N of natural numbers defined as

R = {(x, y): y = x + 5 and x < 4}

(iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as

R = {(x, y): y is divisible by x}

(iv) Relation R in the set Z of all integers defined as

R = {(x, y): x − y is as integer}

(v) Relation R in the set A of human beings in a town at a particular time given by

(a) R = {(x, y): x and y work at the same place}

(b) R = {(x, y): x and y live in the same locality}

(c) R = {(x, y): x is exactly 7 cm taller than y}

(d) R = {(x, y): x is wife of y}

(e) R = {(x, y): x is father of y} - Q:- Find the rate of change of the area of a circle with respect to its radius r when

(a) r = 3 cm

(b) r = 4 cm - Q:-
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).

- Q:- Integrals sin 2x

- Q:- Find the principal value of \begin{align} cot^{-1}\left(\sqrt3\right)\end{align}
- Q:-
Consider

*f*: R → R given by*f(x)*= 4x + 3. Show that*f*is invertible. Find the inverse of*f*. - Q:- Show that the relation R in the set A of all the books in a library of a college, given by R = {(x, y): x and y have same number of pages} is an equivalence relation.
- Q:-
An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?

- Q:- Find the principal value of \begin{align} cosec^{-1}\left({-\sqrt2}\right)\end{align}
- Q:-
Let

*f*: {1, 3, 4} → {1, 2, 5} and*g*: {1, 2, 5} → {1, 3} be given by*f*= {(1, 2), (3, 5), (4, 1)} and*g*= {(1, 3), (2, 3), (5, 1)}. Write down gof. - Q:- Show that the relation R in the set A of points in a plane given by R = {(P, Q): distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further, show that the set of all point related to a point P ≠ (0, 0) is the circle passing through P with origin as centre.
- Q:-
Consider

*f*: R_{+}→ [– 5, ∞) given by*f(x)*= 9x^{2}+ 6x – 5. Show that*f*is invertible

with**.** - Q:- Show that the relation R in R defined as R = {(a, b): a ≤ b}, is reflexive and transitive but not symmetric.
- Q:- If a matrix has 24 elements, what are the possible order it can have? What, if it has 13 elements?

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