The approximate value of \(f(5.001)\), where \(f(x)=x^3-7 x^2+10\)

If \(S=\dfrac{2^2-1}{2}+\dfrac{3^2-2}{6}+\dfrac{4^2-3}{12}+\ldots\) upto 10 terms, then \(S\) is equal to

The length of the latus rectum of a conic \(49 y^2-16 x^2=784\) is

Let R be a relation on natural numbers defined by \(x+2 y=8, x, y \in N\). The domain of R is

A line making angles \(45^{\circ}\) and \(60^{\circ}\) with the positive directions of the axis of \(X\) and \(Y\), makes with the positive direction of \(Z\)-axis, an angle of

\(\int_0^1 x(1-x)^{99} d x=\)

If \(\sin \theta, \cos \theta\) and \(\tan \theta\) are in \(\mathrm{GP}\), then \(\cot ^{6} \theta-\cot ^{2} \theta\) is

Choose the correct metal/ ion from the brackets which ..........
A. has chemical reactivity similar to that of the first few members of the Lanthanoids \((\mathrm{Zn}, \mathrm{Ca}, \mathrm{Fe}, \mathrm{Cu})\).
B. has stable \(4 \mathrm{f}^7\) electronic configuration, but acts as a strong reducing agent and converts to \(\mathrm{M}^{3+}\) state. \(\left(\mathrm{Eu}^{2+}, \mathrm{Ce}^{2+}, \mathrm{Pr}^{2+}, \mathrm{Dy}^{2+}\right)\)
C. is a colorless ion \(\left(\mathrm{Tm}^{3+}, \mathrm{Lu}^{3+}, \mathrm{Gd}^{3+}, \mathrm{Sm}^{3+}\right)\).
D. shows stable +2 oxidation state and is diamagnetic \((\mathrm{Ce}, \mathrm{Sm}, \mathrm{Ho}, \mathrm{Yb})\)

The oxidation state of iron in \(\mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) is,

The product and its colour when MnO\(_2\) is fused with KOH in presence of O\(_2\):

Formation of alkanes by action of Zn on alkyl halides is called

A tuning fork of unknown frequency produces 4 beats with tuning fork of frequency \(310 \mathrm{~Hz}\). It gives the same number of beats on filing. The initial frequency of a tuning fork is

The velocity of an electron so that its momentum is equal to that of a photon of wavelength \(660 \mathrm{~nm}\) is