Number of colourless lanthanoid ions among the following is _______. \(\mathrm{Eu}^{3+}, \mathrm{Lu}^{3+}, \mathrm{Nd}^{3+}, \mathrm{La}^{3+}, \mathrm{Sm}^{3+}\)

Some \(\mathrm{CO}_2\) gas was kept in a sealed container at a pressure of 1 atm and at 273 K . This entire amount of \(\mathrm{CO}_2\) gas was later passed through an aqueous solution of \(\mathrm{Ca}(\mathrm{OH})_2\). The excess unreacted \(\mathrm{Ca}(\mathrm{OH})_2\) was later neutralized with 0.1 M of 40 mL HCl . If the volume of the sealed container of \(\mathrm{CO}_2\) was \(x\), then \(x\) is ________ \(\mathrm{cm}^3\) (nearest integer).
[Given : The entire amount of \(\mathrm{CO}_2(\mathrm{~g})\) reacted with exactly half the initial amount of \(\mathrm{Ca}(\mathrm{OH})_2\) present in the aqueous solution.]

The electronic configuration of \(\mathrm{Cu}\) (II) is \(3 \mathrm{d}^9\) whereas that of \(\mathrm{Cu}(\mathrm{I})\) is \(3 \mathrm{d}^{10}\). Which of the following is correct?

Among the following, the CORRECT combinations are :
A. \( IF_{3} \) → T-shaped \( (sp^{3}d) \)
B. \( IF_{5} \) → Square pyramidal \( (sp^{3}d^{2}) \)
C. \( IF_{7} \) → Pentagonal bipyramidal \( (sp^{3}d^{3}) \)
D. \( ClO_{4}^{-} \) → Square planar \( (sp^{3}d) \)
Choose the correct answer from the options given below :

The ascending order of acidity of \(-\mathrm{OH}\) group in the following compounds is : Choose the correct answer from the options given below :

The noble gas that does Not occur in the atmosphere is

The molecule/ion with square pyramidal shape is _______.

Let \(A\) be a \(n \times n\) matrix such that \(| A |=2\). If the determinant of the matrix \(\operatorname{Adj}\left(2 . \operatorname{Adj}\left(2 A ^{-1}\right)\right.\) ). is \(2^{84}\), then \(n\) is equal to \(................\)

Number of ways of arranging \(8\) identical books into \(4\) identical shelves where any number of shelves may remain empty is equal to

The variation of stopping potential \(\left(V_0\right)\) as a function of the frequency \(\nu \left(\times 10^{14} Hz\right).\) of the incident light for a metal is shown in figure. The work function of the surface is \(...........\,eV\)

If the line \(y =4+ kx , k >0\), is the tangent to the parabola \(y = x - x ^{2}\) at the point \(P\) and \(V\) is the vertex of the parabola, then the slope of the line through \(P\) and \(V\) is

The aperture diameter of a telescope is \(5\; \mathrm{m} .\) The separation between the moon and the earth is \(4 \times 10^{5} \;\mathrm{km} .\) With light of wavelength of \(5500\;\mathring A\), the minimum separation between objects on the surface of moon, so that they are just resolved, is close to......\(m\)

The square of the distance of the image of the point \((6,1,5)\) in the line \(\frac{x-1}{3}=\frac{y}{2}=\frac{z-2}{4}\), from the origin is .............