Class 11th

The sum of all integral values of k $\left(k\ne 0\right)$  for which the equation $\frac{2}{x-1}-\frac{1}{x-2}=\frac{2}{k}$  in x has no real roots, is___________

A wire of length 36m is cut into two pieces, one of the pieces is bent to form a square and the other is bent to form a circle. If the sum of the areas of the two figures is minimum, and the circumference of the circle is k (meter), then $\left(\frac{4}{\pi }+1\right)k$ $\frac{}{}$ is equal to_________.

The OH^- concentration in a mixture of 5.0 mL of 0.0504 M NH₄Cl and 2 mL of 0.0210 M NH₃ solution is x * 10^-6 M. The value of x is________. (Nearest integer)

[Given K_w = 1 * 10^-14 and K_b = 1.8 * 10^-5]

The Born-Haber cycle for KCl is evaluated with the following data:

${\Delta }_f{H}^{\Theta }forKC=-436.7kJmo{l}^{-1};{\Delta }_{sub}{H}^{\Theta }forK=89.2kJmo{l}^{-1};$

${\Delta }_{ionization}{H}^{\Theta }forK=419.0kJmo{l}^{-1};{\Delta }_{electrongain}{H}^{\Theta }forC{l}_{\left(g\right)}=-348.6kJmo{l}^{-1};$

${\Delta }_{bond}{H}^{\Theta }forC{l}_2=243.0kJmo{l}^{-1}$  

The magnitude of lattice enthalpy of KCl in kJ mol^-1 is_________ (Nearest integer)

Consider the two statements:

(S1): (p -> q) $\vee \left(\sim q\to p\right)$  is a tautology.
(S2): $(p\wedge \sim q)\wedge (\sim p\vee q)$  is a fallacy.

Then:

Given below are two statements one is labeled as Assertion A and the other is labeled as Reason R:

           Assertion A: The amphoteric nature of water is explained by using Lewis acid/base concept

           Reason R: Water acts as an acid with NH₃ and as a base with H₂S

           In the light of the above statements choose the correct answer form the options given below: