The total number of stereoisomers for the complex \(\left[ Cr ( ox )_2 ClBr ^{3-}\right.\) (where ox = oxalate) is:

In 3, 3-dimethylhex-1-ene-4-yne, there are _______ \(\mathrm{sp}^3\), _______ \(\mathrm{sp}^2\) and _______ sp hybridised carbon atoms respectively :

The total number of \(Mn = O\) bonds in \(Mn _{2} O _{7}\) is

The \(K _{ sp }\) for bismuth sulphide \(\left( Bi _{2} S _{3}\right)\) is \(1.08 \times 10^{-73}\). The solubility of \(Bi _{2} S _{3}\) in \(mol \,L ^{-1}\) at \(298 \,K\) is ......

' X ' is the number of acidic oxides among \(\mathrm{VO}_2\), \(\mathrm{V}_2 \mathrm{O}_3, \mathrm{CrO}_3, \mathrm{~V}_2 \mathrm{O}_5\) and \(\mathrm{Mn}_2 \mathrm{O}_7\). The primary valency of cobalt in \(\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{NCH}_2 \mathrm{CH}_2 \mathrm{NH}_2\right)_3\right]_2\left(\mathrm{SO}_4\right)_3\) is Y. The value of \(\mathrm{X}+\mathrm{Y}\) is _______.

Total number of essential amino acid among the given list of amino acids is _______. Arginine, Phenylalanine, Aspartic acid, Cysteine, Histidine, Valine, Proline

\(X Y\) is the membrane / partition between two chambers 1 and 2 containing sugar solutions of concentration \(c_1\) and \(c_2\left(c_1 \gt c_2\right) \mathrm{mol} \mathrm{L}^{-1}\). For the reverse osmosis to take place identify the correct condition
(Here \(p_1\) and \(p_2\) are pressures applied on chamber 1 and 2)

(A) Membrane/Partition; Cellophane, \(\mathrm{p}_1 \gt \pi\)
(B) Membrane/Partition ; Porous. \(\mathrm{p}_2 \gt \pi\)
(C) Membrane/Partition ; Parchment paper, \(\mathrm{p}_1 \gt \pi\)
(D) Membrane/Partition : Cellophane, \(\mathrm{p}_2 \gt \pi\)
Choose the correct answer from the option given below :

Consider a binary star system of star \(A\) and star \(B\) with masses \(m_{A}\) and \(m_{B}\) revolving in a circular orbit of radii \(r_{A}\) and \(r_{B}\), respectively. If \(T_{A}\) and \(T_{B}\) are the time period of star \(A\) and star \(B\), respectively, then -

If \(P\) is a \(3 \times 3\) real matrix such that \(P ^{ T }=a P +( a -1) I\), where \(a > 1\), then \(..........\)

Suppose a, b, c are in A.P. and \( a^{2}, 2b^{2}, c^{2} \) are in G.P. If \( a < b < c \) and \( a+b+c=1, \) then \( 9(a^{2}+b^{2}+c^{2}) \) is equal to ___ .

The number of solutions of \(\tan^{-1}4x+\tan^{-1}6x=\frac{\pi}{6}\) where \(-\frac{1}{2\sqrt{6}}< x <\frac{1}{2\sqrt{6}}\) is equal to

Some distant star is to be observed by some telescope of diameter of objective lens \(a\), at an angular resolution of \(3.0\times 10^{-7}\) radian. If the wavelength of light from the star reaching the telescope is \(500\) nm, the minimum diameter of the objective lens of the telescope is ________ cm. (nearest integer)

An analyst wants to convert. \(1 L\,HCl\) of \(pH =1\) to a solution of \(HCl\) of \(pH 2\). The volume of water needed to do this dilution is \(......\,mL\). (Nearest Integer)