Class 12th

Two parallel plate capacitors of capacity C and 3C are connected in parallel combination and charged to a potential difference 18 F. The battery is then disconnected and the space between the plates of the capacitor of capacity C is completely filled with a material of dielectric constant 9. The final potential difference across the combination of capacitors will be ________V.

Two ideal diodes are connected in the network as shown is figure. The equivalent resistance between A and B is _______ $\Omega$ .

In a potentiometer arrangement, a cell of emf 1.20 V gives a balance point at 36cm length of wire. This cell is now replaced by another cell of emf 1.80 V. The difference in balancing length of potentiometer wire in above conditions will be ________cm.     

  $\frac{x}{x+4}$ is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its

(i) third permitted energy level to the second level and

(ii) the highest permitted energy level to the second permitted level.

The value of x will be ________.

The line of shortest distance between the lines $\frac{x-2}{0}=\frac{y-1}{1}=\frac{z}{1}$  and $\frac{x-3}{2}=\frac{y-5}{2}=\frac{z-5}{1}$  makes an angle of $co{s}^{-1}\left(\sqrt[]{\frac{2}{27}}\right)$  with the plane P : ax – y – z = 0, (a > 0). If the image of the point (1, 1, - 5) in the plane P is $(\alpha ,\beta ,\gamma ),$  then $\alpha +\beta -\gamma$  is equal to……….

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 __________.