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 the value of \(\tan\frac{1}{2}\bigg[\sin^{-1}\frac{2x}{1+x^2}+\cos^{-1}\frac{1-y^2}{1+y^2}\bigg],\mid x\mid<1,y>0\,and\:xy<1\)
Find the value of tan-1\((1)\)+cos-1\((-\frac{1}{2})\)+sin-1\((-\frac{1}{2})\)
Find the value of cos-1\((\frac{1}{2})\)+2 sin-1\((\frac{1}{2})\)
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
Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be: (i). f(x) = x2 (ii). g(x) = x3 − 3x (iii). h(x) = sinx + cos, 0 <x<\(\frac{\pi}{2}\) (iv). f(x) = sinx − cos x, 0 < x < 2π (v). f(x) = x3 − 6x2 + 9x + 15(vi) g(x)=\(\frac{x}{2}\)+\(\frac{2}{x}\)>0 (vii).g(x)=\(\frac{1}{x^2}\)+2(viii). f(x)=x√1-x,x>0
If a matrix has 24 elements, what are the possible order it can have? What, if it has 13 elements?
Classify the following measures as scalars and vectors. (i)10kg (ii)2metres north-west (iii)40° (iv)40watt (v)10-19coulomb (vi)20m/s2