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
An organic compound with the molecular formula \( C_9H_{10}\)O forms \(2,4-DNP\) derivative,reduces Tollens’ reagent and undergoes Cannizzaro reaction.On vigorous oxidation,it gives \(1,2-benzenedicarboxylic\) acid.Identify the compound.
Give examples and suggest reasons for the following features of the transition metal chemistry:
Give one chemical test to distinguish between the following pairs of compounds. (i) Methylamine and dimethylamine (ii) Secondary and tertiary amines (iii) Ethylamine and aniline (iv) Aniline and benzylamine (v) Aniline and N-methylaniline