......\(L\) litres of water must be added to \(1\, litre\) an aqueous solution of \(HCl\) with a \(pH\) of \(1\) to create an aqueous solution with \(pH\) of \(2\) ?

Lanthanoid ions with \(4 f^7\) configuration are :
(A) \(\mathrm{Eu}^{2+}\)
(B) \(\mathrm{Gd}^{3+}\)
(C) \(\mathrm{Eu}^{3+}\)
(D) \(\mathrm{Tb}^{3+}\)
(E) \(\mathrm{Sm}^{2+}\)
Choose the correct answer from the options given below :

The comect order of melting points of hydrides of group \(16\) elements is \(...\)

Which of the following nitrogen containing compound does not give Lassaigne's test ?

The higher concentration of which gas in air can cause stiffness of flower buds?

The solubility product of \(BaSO _4\) is \(1 \times 10^{-10}\) at \(298\,K\). The solubility of \(BaSO _4\) in \(0.1\,M\,K _2 SO _4( aq )\) solution is \(.........\times 10^{-9}\,g\,L ^{-1}\) (nearest integer). Given : Molar mass of \(BaSO _4\) is \(233\,g\,mol ^{-1}\)

Consider the following species:
BrF\(_5\), XeF\(_5^-\), BF\(_4^-\), ICl\(_4^-\), XeF\(_4\), SF\(_4\), NH\(_4^+\), ClF\(_3\), XeF\(_2\), ICl\(_2^-\)
Number of species having sp\(^3\)d hybridized central atom is __________.

If the equation of the plane passing through the point \((1,1,2)\) and perpendicular to the line \(x-3 y+2 z-1=04 x-y+z\) is \(Ax + By + Cz =1\), then \(140( C - B + A )\) is equal to \(.........\).

If in a \(G.P.\) of \(64\) terms, the sum of all the terms is \(7\) times the sum of the odd terms of the \(G.P,\) then the common ratio of the \(G.P\). is equal to

Consider the following two statements : Statement \(I\) : For any two non-zero complex numbers \(\mathrm{z}_1, \mathrm{z}_2\) \(\left(\left|z_1\right|+\left|z_2\right|\right)\left|\frac{z_1}{\left|z_1\right|}+\frac{z_2}{\left|z_2\right|}\right| \leq 2\left(\left|z_1\right|+\left|z_2\right|\right)\) and Statement \(II\) : If \(\mathrm{x}, \mathrm{y}, \mathrm{z}\) are three distinct complex numbers and a, b, c are three positive real numbers such that \(\frac{a}{|y-z|}=\frac{b}{|z-x|}=\frac{c}{|x-y|}\), then \(\frac{\mathrm{a}^2}{\mathrm{y}-\mathrm{z}}+\frac{\mathrm{b}^2}{\mathrm{z}-\mathrm{x}}+\frac{\mathrm{c}^2}{\mathrm{x}-\mathrm{y}}=1\) Between the above two statements,

If \(y=y(x)\) is the solution of the differential equation \(x \frac{d y}{d x}+2 y=x e^{x}, y(1)=0\) then the local maximum value of the function \(z(x)=x^{2} y(x)-e^{x}\), \(x \in R\) is

Which of the following reactions will yield benzaldehyde as a product?

If \(x^2-y^2+2 h x y+2 g x+2 f y+c=0\) is the locus of a point, which moves such that it is always equidistant from the lines \(x+2 y+7=0\) and \(2 x-y\) \(+8=0\), then the value of \(\mathrm{g}+\mathrm{c}+\mathrm{h}-\mathrm{f}\) equals