The value of

is

is

Order of a differential equation is defined as the order of the highest order derivative of the dependent variable present in the differential equation.

we know that direction cosines is coefficient of i,j,k of unit vector along that line ,i.e those coefficient are l,m,n .the length of the line r is such that and magnitute of unit vector r is 1 and . on squaring both side we get

Required area =

∫0πasinxdx=a[−cosx]π0=a(−cosπ+cos0)=a(1+1)=2a

The number of elements in a 3 X 3 matrix is the product 3 X 3=9.

Each element can either be a 0 or a 1.

Given this, the total possible matrices that can be selected is 29=512

Since the graph cuts the lines y = -1 and y = 1 , therefore ,it must cut y = 0 atleast once as the graph is a continuous curve in this case.

because , row 1 and row 3 are identical.

Traffic signal control types of problems cannot be solved by linear programming methods, because there is no need for optimization in such problems.

Let A and B be two sets . Then a relation R from set A to set B is a subset of A×B.Thus , R is a relation from A to B ⇔R⊆A×B⇔R⊆A×B.