If \(y=\tan ^{-1}\left(\frac{4 x}{1+5 x^2}\right)+\cot ^{-1}\left(\frac{3-2 x}{2+3 x}\right)\), then \(\frac{\mathrm{d} y}{\mathrm{~d} x}\) is equal to
The principal value of \(\cos ^{-1}\left[\frac{1}{\sqrt{2}}\left(\cos \frac{9 \pi}{10}-\sin \frac{9 \pi}{10}\right)\right]\) is
\(\int \mathrm{e}^x\left(\frac{x+5}{(x+6)^2}\right) \mathrm{d} x\) is
The differential equation \(x \frac{\mathrm{~d} y}{\mathrm{~d} x}=2 y\) represents ________
\[ \int_1^3 \frac{\log x^2}{\log \left(16 x^2-8 x^3+x^4\right)} d x= \]
If \(\frac{x^2}{\mathrm{a}^2}+\frac{y^2}{\mathrm{~b}^2}=1\), then \(\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}\) is
The lines \(\frac{x-0}{1}=\frac{y-2}{2}=\frac{z+3}{\lambda}\) and \(\frac{x-2}{2}=\frac{y-6}{3}=\frac{z-3}{\lambda}\) are coplanar and \(p\) is the plane containing these lines, then which of following point lie on the plane for all values of (\(\lambda\)).
If Rolle's theorem holds for the function \(x^3+\mathrm{a} x^2+\mathrm{b} x, 1 \leq x \leq 2\) at the point \(\frac{4}{3}\), then the values of \(a\) and \(b\) are respectively
\[ \int \frac{1}{\mathrm{e}^x+1} \mathrm{~d} x= \]
The rate at which the population of a city increases varies as the population. In a period of 20 years, the population increased from 4 lakhs to 6 lakhs. In another 20 years the population will be
If \(\bar{a}=\hat{i}+\hat{j}+\hat{k}, \bar{b}=\hat{j}-\hat{k}\) then a vector \(\bar{c}\) such that \(\overline{\mathrm{a}} \times \overline{\mathrm{c}}=\overline{\mathrm{b}}\) and \(\overline{\mathrm{a}} \cdot \overline{\mathrm{c}}=3\) is
Find out total number of electrons present in 1.6 g methane?
Which from following amines has lowest \(\mathrm{pK}_b\) value?
The eccentricity of the curve represented by \(x=3(\cos t+\sin t), y=4(\cos t-\sin t)\) is
Which among the following is NOT dicarboxylic acid?
Which of the following forms 2-Methylbut-2-ene on heating with concentrated sulphuric acid?
What is the oxidation number of phosphorus in calcium phosphate?
If \(\mathrm{E}^{\circ}\left(\mathrm{Zn}_{(\mathrm{aq})}^{+2} \mid \mathrm{Zn}_{(\mathrm{s})}\right)=-0.76 \mathrm{~V}\).
Calculate potential for \(\mathrm{Zn}_{(\mathrm{s})} \rightarrow \mathrm{Zn}^{+2}(0.01 \mathrm{M})+2 \mathrm{e}^{-}\)at 298 K .
Which from following transformations is endothermic in nature?
Which of the following dopant is used in silicon to produce p-type semiconductor?
Which from following polymers is used to obtain rubber belts?
Identify anionic ligand from following.