The greatest integer function \(f: R \rightarrow R\) given by f(x) = [x] is:

Match List I with List II and choose the correct answer from the options given below:

List - I	List - II
(A) \(\sin ^{-1} x+\cos ^{-1} x, x \in[-1,1]\)	(I) \(-\frac{\pi}{2}\)
(B) \(\tan ^{-1} \sqrt{3}-\cot ^{-1}(-\sqrt{3})\)	(II) \(-\frac{\pi}{6}\)
(C) \(\cos ^{-1}\left(\cos \frac{13 \pi}{6}\right)\)	(III) \(\frac{\pi}{2}\)
(D) \(\sin ^{-1}\left(-\frac{1}{2}\right)\)	(IV) \(\frac{\pi}{6}\)

If \(A\) and \(B\) are invertible matrices then which of the following statement is NOT correct?

If the matrix \(\left[\begin{array}{ccc}-1 & x-y & 4 \\ 2 & 0 & 5 \\ x+y & z & 6\end{array}\right]\) is symmetric, then \(x+3 y+2 z\) is equal to

If \(e^y(x+2) = 10\), then \(\frac{d^2y}{dx^2}\) is equal to :

The projection of the vector \(5 \hat{i}+\hat{j}-3 \hat{k}\) on the vector \(\hat{i}+2 \hat{j}-3 \hat{k}\) is

For the principal value branch, the value of \(\sin \left(\frac{\pi}{2}-\sin ^{-1}\left(-\frac{\sqrt{3}}{2}\right)\right)\) is

Which of the following is not correct about the order of a reaction?

Read the passage carefully and answer
When a metal is placed in a solution of its ions, the metal can lose electron and can go in the solution as ion or the metal ion in the solution can take electron from the electrode and get deposited as metal. Thus, the electrode acquires either positive or negative charge with respect to the solution leading to the development of a potential difference between the metal electrode and the solution. This potential difference is called the electrode potential of the metal. The electrode potential of a metal is a measure of relative tendency to undergo oxidation (loss of electron) or reduction (gain of electron). When the concentration of the ions in the solution is unity, the electrode potential is called standard electrode potential. The magni of potential depends upon the nature of electrode, concentration of ions in solution and the temperature. In a galvanic cell, the electrode at which oxidation occurs is known as anodic half-cell and the electrode at which reduction occurs is known as cathodic half cell. The emf of the cell in terms of standard reduction potential is given by \(E_{\text {cell }}^{\circ}=E_{\text {cathode }}^{\circ}-E_{\text {anode. }}^{\circ}\).The standard free energy change of the redox reaction taking place in the cell is related to \(E_{\text {cell }}^{\circ}\) by \(\Delta G^{\circ}=-n F E^{\circ}\). A redox reaction would occur spontaneously if the free energy change is negative. The equilibrium constant of the reaction is related to the standard free energy change by \(\Delta G^{\circ}=-R T \ln K\).
The standard reduction potential of Zinc is represented by the reaction

The decomposition of hydrogen peroxide follows the equation:
\(K=\left(2.9 \times 10^{14} s^{-1}\right) e^{-2 \mu o p}\)
The value of Ea is:

Amoebic dysentery is caused by:

Match List-I with List-II (Symbols have their usual meanings)

List-I (Physical Quantity)	List-II (Expression)
(A) Current density	(I) \( \frac{e E \tau}{m} \)
(B) Drift velocity	(II) \( \frac{n e^2 \tau}{m} \)
(C) Conductivity	(III) \( \frac{e \tau}{m} \)
(D) Mobility	(IV) \( n e v_d \)

Choose the correct answer from the options given below:

p-Hydroxyazobenzene is also called as