Which of the following statements is false ?

Below are two statements, one labeled as Assertion \((A)\) and the other as Reason \((R):\) Assertion \((A)\): Among group \(13\) elements, boron's melting point is unusually high \((2453 \mathrm{~K})\). Reason \((R):\) Solid boron has a strong crystalline lattice. In the context of the above statements, choose the correct answer from the following options:

The ionization energy of sodium in \(\mathrm{kJ} \mathrm{mol}^{-1}\). If electromagnetic radiation of wavelength \(242 \mathrm{~nm}\) is just sufficient to ionize sodium atom is _______.

Consider the following equilibrium, \(\mathrm{CO}(\mathrm{g})+2 \mathrm{H}_2(\mathrm{g}) \rightleftharpoons \mathrm{CH}_3 \mathrm{OH}(\mathrm{g})\) 0.1 mol of CO along with a catalyst is present in a \(2 \mathrm{dm}^3\) flask maintained at 500 K. Hydrogen is introduced into the flask until the pressure is 5 bar and 0.04 mol of \(\mathrm{CH}_3 \mathrm{OH}\) is formed. The \(\mathrm{K}_{\mathrm{p}}^0\) is ______ \(\times 10^{-3}\) (nearest integer).
Given : \(\mathrm{R}=0.08 \mathrm{dm}^3\) bar \(\mathrm{K}^{-1} \mathrm{~mol}^{-1}\)
Assume only methanol is formed as the product and the system follows ideal gas behaviour.

Sucrose hydrolyses in acid solution into glucose and fructose following first order rate law with a half-life of \(3.33\, h\) at \(25^{\circ} C\). After \(9 \,h ,\) the fraction of sucrose remaining is \(f\). The value of \(\log _{10}\left(\frac{1}{f}\right)\) is ..... \(\times 10^{-2} .\) (Rounded off to the nearest integer) [Assume : \(\ln 10=2.303, \ln 2=0.693\) ]

On reaction of Lead Sulphide with dilute nitric acid which of the following is not formed?

The successive 5 ionisation energies of an element are \(800,2427,3658,25024\) and \(32824 \mathrm{~kJ} / \mathrm{mol}\), respectively. By using the above values predict the group in which the above element is present :

During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of \(\frac{C_p}{C_V}\) for the gas is _______.

The perpendicular distance, of the line \(\frac{x-1}{2}=\frac{y+2}{-1}=\frac{z+3}{2}\) from the point \(\mathrm{P}(2,-10,1)\), is :

Planet \(A\) has mass \(\mathrm{M}\) and radius \(\mathrm{R}\). Planet \(\mathrm{B}\) has half the mass and half the radius of Planet \(A\). If the escape velocities from the Planets \(A\) and \(\mathrm{B}\) are \(v_{\mathrm{A}}\) and \(v_{\mathrm{B}},\) respectively, then \(\frac{v_{\mathrm{A}}}{v_{\mathrm{B}}}=\frac{\mathrm{n}}{4}\) The value of \(\mathrm{n}\) is

The number of the real roots of the equation \((x+1)^{2}+|x-5|=\frac{27}{4}\) is ....... .

Let \(\vec a = 2\hat i + \hat j - 2\hat k\) and \(\vec b = \hat i + \hat j\) . Let \(\vec c\) be vector such that \(\left| {\vec c - \vec a} \right| = 3,\;\left| {\left( {\vec a \times \vec b} \right) \times \vec c} \right| = 3\) and the angle between \(\vec c\) and \(\vec a \times \vec b\) be \(30^\circ \) . Then \(\vec a \cdot \vec c\) is equal to :

In a screw gauge, the zero of the circular scale lies 3 divisions above the horizontal pitch line when their metallic studs are brought in contact. Using this instrument thickness of a sheet is measured. If pitch scale reading is 1 mm and the circular scale reading is 51 then the correct thickness of the sheet is ___________ mm.
[Assume least count is 0.01 mm ]