A company manufactures two types of novelty souvenirs made of polywood.Souvenirs of type A require 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and building.3 hours 20 minutes are available for cutting and 4 hours of assembling. The profit is Rs 5 each for type A and Rs 6 each for type B souvenirs. How many types of souvenirs of each type should the company manufacture in order to maximize the profit?
Using the property of determinants and without expanding, prove that: \(\begin{vmatrix}a-b&b-c&c-a\\b-c&c-a&a-b\\c-a&a-b&b-c\end{vmatrix}\)=0
In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.
State whether the following statements are true or false. Justify. (i) For an arbitrary binary operation * on a set N, a * a=a ∀ a * N. (ii) If * is a commutative binary operation on N, then a * (b * c)= (a * b)* a
At what points in the interval [0, 2\(\pi\)], does the function sin 2x attain its maximum value?
The integrating factor of the differential equation \(x\frac{dy}{dx}-y=2x^{2}\) is
Which of the following functions are strictly decreasing on (0,π/2)?
If A=\(\begin{bmatrix}3&1\\-1&2\end{bmatrix}\),show that A2-5A+7I=0.Hence find A-1.
In the matrix A= \(\begin{bmatrix} 2 & 5 & 19&-7 \\ 35 & -2 & \frac{5}{2}&12 \\ \sqrt3 & 1 & -5&17 \end{bmatrix}\),write:
I. The order of the matrix II. The number of elements III. Write the elements a13, a21, a33, a24, a23
Find a particular solution satisfying the given condition:\((1+x^2)\frac {dy}{dx}+2xy=\frac {1}{1+x^2}; \ y=0 \ when \ x=1\)