Two positively charged particles \(m_{1}\) and \(m_{2}\) have been accelerated across the same potential difference of 200 keV as shown below.

[Given mass of \(m_{1} = 1 amu\) and \(m_{2} = 4 amu\)].
The deBroglie wavelength of \(m_{1}\) will be x times of \(m_{2}\). The value of x is __________ . (nearest integer)

Chemical nature of the nitrogen oxide compound obtained from a reaction of concentrated nitric acid and \(\mathrm{P}_{4} \mathrm{O}_{10}\) (in \(4: 1\) ratio \()\) is:

Rate law for a reaction between A and B is given by
\(\mathrm{R}=\mathrm{k}[\mathrm{~A}]^{\mathrm{n}}[\mathrm{~B}]^{\mathrm{m}}\)
If concentration of A is doubled and concentration of \(B\) is halved from their initial value, the ratio of new rate of reaction to the initial rate of reaction \(\left(\frac{r_2}{r_1}\right)\) is

The type of hybridisation and magnetic property of the complex \(\left[\mathrm{MnCl}_{6}\right]^{3-}\), respectively, are :

Given below are two statements: Statement \((I)\): A solution of \(\left[\mathrm{Ni}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}\) is green in colour. Statement \((II)\): A solution of \(\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}\) is colourless. In the light of the above statements, choose the most appropriate answer from the options given below:

The incorrect statement is

Choose the correct tests with respective observations.
(A) \(\mathrm{CuSO}_4\) (acidified with acetic acid) \(+ \mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right] \rightarrow\) Chocolate brown precipitate.
(B) \(\mathrm{FeCl}_3+\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right] \rightarrow\) Prussian blue precipitate.
(C) \(\mathrm{ZnCl}_2+\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]\), neutralised with \(\mathrm{NH}_4 \mathrm{OH}\) \(\rightarrow\) White or bluish white precipitate.
(D) \(\mathrm{MgCl}_2+\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right] \rightarrow\) Blue precipitate.
(E) \(\mathrm{BaCl}_2+\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]\), neutralised with NaOH \(\rightarrow\) White precipitate.
Choose the correct answer from the options given below :

Identify the correct truth table of the given logical circuit.

Let \(z_1, z_2\) and \(z_3\) be three complex numbers on the circle \(|z|=1\) with \(\arg \left(z_1\right)=\frac{-\pi}{4}, \arg \left(z_2\right)=0\) and \(\arg \left(z_3\right)=\frac{\pi}{4}\). If \(\left|z_1 \bar{z}_2+z_2 \bar{z}_3+z_3 \bar{z}_1\right|^2=\alpha+\beta \sqrt{2}, \alpha, \beta \in \mathbf{Z}\), then the value of \(\alpha^2+\beta^2\) is :

A force is applied to a steel wire ' \(A\) ', rigidly clamped at one end. As a result elongation in the wire is \(0.2\,mm\). If same force is applied to another steel wire ' \(B\) ' of double the length and a diameter \(2.4\) times that of the wire ' \(A\) ', the elongation in the wire ' \(B\) ' will be \(............\times 10^{-2}\,mm\) (wires having uniform circular cross sections)

\(\mathop {\lim }\limits_{x \to \pi /4} \frac{{{{\cot }^3}\,x - \tan \,x}}{{\cos \left( {x + \pi /4} \right)}}\) is

Let \(\mathrm{A}=\left[\mathrm{a}_{i j}\right]\) be a \(2 \times 2\) matrix such that \(\mathrm{a}_{i j} \in\{0,1\}\) for all \(i\) and \(j\). Let the random variable X denote the possible values of the determinant of the matrix \(A\). Then, the variance of \(X\) is :

Given below are two statements :
Statement I: The condensation reaction between \(CH_3-CH=O\) and \(H_2N-NH-C(=O)-NH_2\) under optimum pH will produce \(CH_3-CH=N-N(H)-C(=O)-NH_2\).
Statement II: The molecule, \(Ph-CH(O-H)(O-CH_3)\) will generate \(Ph-CH=O\) in the presence of dilute acid.
In the light of the above statements, choose the correct answer from the options given below :