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A student is allowed to select at most n-blocks from a collection of (2n + 1) books. If the total number of ways in which he can select a book is 63, find the value of n.Solution) Σ2n+1Cr,(from r=1 to r=n)=(22n+1/2)-1=22n-1=63,n=3.
Differentiate following functions. (a) f ( x ) = 2 x 5 cosh x (b) h (t ) = sinh t / t + 1 Solution (a) f ′ ( x ) = 10x 4 cosh x + 2x 5 sinh x (b) h′ (t ) = (t
Given A and B A = | 1 0 1 | B = | 1 1 0 | | 1 1 0 | | 0 1 1 | | 0
Determine if the following series converges or diverges by using limit comparison test. Solution To make use of the limit comparison test we require to find out a seco
Definition Assume that f(t) is a piecewise continuous function. The Laplace transform of f(t) is denoted L{ f (t )} and defined by, There is an optional notation for L
Define transportation problem
two numbers differ by 7 and have a product of 120.what are they ?
Position Vector There is one presentation of a vector that is unique in some way. The presentation of the ¯v = (a 1 ,a 2 ,a 3 ) that begins at the point A = (0,0,0) and ends
Definite integration It involve integration among specified limits, say a and b The integral is a definite integral whether the limits of integration are as: a and b
The base of a right cylinder is the circle in the xy -plane with centre O and radius 3 units. A wedge is obtained by cutting this cylinder with the plane through the y -axis in
Differentiate the following functions. (a) f (t ) = 4 cos -1 (t ) -10 tan -1 (t ) (b) y = √z sin -1 ( z ) Solution (a) Not much to carry out with this one other
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