The potassium ferrocyanide solution gives Prussian blue colour, when added to :

For complete combustion of ethene. \(C _2 H _4( g )+3 O _2( g ) \rightarrow 2 CO _2( g )+2 H _2 O ( l )\) the amount of heat produced as measured in bomb calorimeter is \(1406\,kJ\,mol { }^{-1}\) at \(300\,K\). The minimum value of \(T \Delta S\) needed to reach equilibrium is \((-).......\,kJ\). (Nearest integer) Given : \(R =8.3\,JK ^{-1} mol ^{-1}\)

The plots of radial distribution functions for various orbitals of hydrogen atom against \('r ^{\prime}\) are given below \({image}\) The correct plot for \(3\, s\) orbital is

Given below are two statements:
Statement I: Among \(Zn, Mn, Sc\) and \(Cu\), the energy required to remove the third valence electron is highest for \(Zn\) and lowest for \(Sc\).
Statement II: The correct order of the following complexes in terms of CFSE is \([Co(H_2 O)_6]^{2+} < [Co(H_2 O)_6]^{3+} < [Co(en)_3]^{3+}\).
In the light of the above statements, choose the correct answer from the options given below:

The total number of hydrogen atoms in product \(\mathrm{A}\) and product \(B\) is _______.

Given below are two statements : Statement \(-I :\) The pentavalent oxide of group\(- 15\) element. \(E _{2} O _{5}\). is less acidic than trivalent oxide. \(E _{2} O _{3}\). of the same element. Statement \(-II :\) The acidic character of trivalent oxide of group \(15\) elements. \(E _{2} O _{3}\). decreases down the group. In light of the above statements. choose most appropriate answer from the options given below

Which of the following statements are correct, if the threshold frequency of caesium is \(5.16 \times 10^{14} \mathrm{~Hz}\) ?
A. When Cs is placed inside a vacuum chamber with an ammeter connected to it and yellow light is focused on Cs the ammeter shows the presence of current.
B. When the brightness of the yellow light is dimmed, the value of the current in the ammeter is reduced.
C. When a red light is used instead to the yellow light, the current produced is higher with respect to the yellow light.
D. When a blue light is used, the ammeter shows the formation of current.
E. When a white light is used, the ammeter shows formation of current.
Choose the correct answer from the options given below :

If \(g \) is the inverse of a function \(f \) and \(f'\left( x \right) = \frac{1}{{1 + {x^5}}}\) thne \(g'\left( x \right)\) is equal to :

Which one of the following substituents at para position is most effective in stabilizing the phenoxide ion ?

A \(dc\) source of \(emf \,E_1 = 100\,V\) and internal resistance \(r = 0.5\,\Omega ,\) a storage battery of emf \(E_2 = 90\,V\) and an external resistance \(R\) are connected as shown in figure. For what value of \(R\) no current will pass through the battery ? ................ \(\Omega\)

The sum of \(162^{\text {th }}\) power of the roots of the equation \(x^{3}-2 x^{2}+2 x-1=0\) is

Let \(q\) be the maximum integral value of \(p\) in \([0,10]\) for which the roots of the equation \(x ^2- px +\frac{5}{4} p =0\) are rational. Then the area of the region \(\{(x, y): 0 \leq y\) \(\left.\leq(x-q)^2, 0 \leq x \leq q\right\}\) is

A body of mass \(m_1\) moving with an unknown velocity of \(v_1 \hat i\) undergoes a collinear collision with a body of mass \(m_2\) moving with a velocity \(v_2 \hat i\) . After collision \(m_1\) and \(m_2\) move with velocities of \(v_3 \hat i\) and \(v_4 \hat i\) respectively. If \(m_2 = 0.5\, m_1\) and \(v_3 = 0.5\, v_1\) then \(v_1\) is: