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:\((1+x^2)\frac {dy}{dx}+2xy=\frac {1}{1+x^2}; \ y=0 \ when \ x=1\)
On which of the following intervals is the function f given by \(f(x)=x^{100}+sin\ x-1\) strictly decreasing?
Find \(\frac{dy}{dx}\),if y=12(1-cost),x=10(t-sint),\(-\frac{\pi}{2}\)<t<\(\frac{\pi}{2}\)
Assume that each child born is equally likely to be a boy or a girl. If a family has two children,what is the conditional probability that both are girls given that
Matrices A and B will be inverse of each other only if
\(\int \frac{10x^9+10^x \log_e 10}{x^{10}+10^x}dx\) equals
The numbers of arbitrary constants in the particular solution of a differential equation of third order are:
The value of \(\int_{0}^{\frac{\pi}{2}}\) log(\(\frac{4+3\,sin\,x}{4+3\,cos\,x}\))dx is