Class 12th

If   $\underset{n\to \infty }{lim}\frac{{\left(n+1\right)}^{k-1}}{n^{k+1}}\left[\left(nk+1\right)+\left(nk+2\right)+....+\left(nk+n\right)\right]$

$=33.\underset{n\to \infty }{lim}\frac{1}{n^{k+1}}.$ $\left[1^k+2^k+3^k+...+n^k\right]$ , then the integral value of k is equal to…………

Let f(x) = $\left\{\begin{array}{cc}\hfill \left|4x^2-8x+5\right|,if8x^2-6x+1\ge 0\hfill & \hfill \left[4x^2-8x+5\right],if8x^2-6x+1<0\hfill \end{array}\right\}$ , where [a] denotes the greatest integer less than or equal to a. Then the number of points in R where f is not differentiable is………….

If the maximum value of the term independent of t in the expansion of ${\left(t^2{x}^{\frac{1}{5}}+\frac{{\left(1-x\right)}^{\frac{1}{10}}}{t}\right)}^{15}$ , x $\ge$ , is K, then 8 K is equal to………….

Let A = $\begin{array}{c}\hfill \hfill \end{array}$ $\begin{array}{ccc}\hfill 2\hfill & \hfill -1\hfill & \hfill -1\hfill \\ \hfill 1\hfill & \hfill 0\hfill & \hfill -1\hfill \\ \hfill 1\hfill & \hfill -1\hfill & \hfill 0\hfill \end{array}$  and B = A – I. If $\frac{\text{exception 25:}}{}$ $\omega =\frac{\sqrt[]{3}i-1}{2}$ , then the number of elements in the set $\left\{n\in \left\{1,2,...,100\right\}:A^n+{\left(\omega B\right)}^n=A+B\right\}$ ${}^{}{}^{}$ is equal to……….

In the given reaction

(Where Et is -C₂H₅)

The number of chiral carbon/s in product A is __________.

Among Co³⁺, Ti²⁺, V²⁺ and Cr²⁺ ions, one if used as a reagent cannot liberate H₂ from dilute mineral acid solution, its spin-only magnetic moment in gaseous state is _________ B.M. (Nearest integer)

Consider the following metal complexes:

[Co(NH₃)₆]³⁺

[CoCl(NH₃)₅]²⁺

[Co(CN)₆]^3-

[Co(NH₃)₅(H₂O)]³⁺

The spin-only magnetic moment value of the complex that absorbes light with shortest wavelength is _____________. B.M (Nearest integer)

The half life for the decomposition of gaseous compound A is 240s when the gaseous pressure was 500 Torr initially, When the pressure was 250 Torr, the half life was found to be 4.0 min. The order of the reaction is _________. (Nearest integer)

The cell potential for $Zn|Z{n}^{2+}(aq)?S{n}^{*+}|Sn$  is 0.801 V at 298 K. The reaction quotient of the above reaction is 10^-2. The number of electrons involved in the given electrochemical cell reaction is _________.

(Given: $E_{Z{n}^{2+}|Zn}^o=-0.763V,E_{S{n}^{*+}|Sn}^o=+0.008Vand\frac{2.303RT}{F}=0.06V)$

The required height of a TV tower which can cover the population of 6.03 lakh is h. If the average population density is 100 per square km and the radius of earth is 6400 km, then the value of h will be ________ m.