Class 12th

If $\overrightarrow{a}=\widehat{i}+6\widehat{j}+3\widehat{k},$ $\overrightarrow{b}=3\widehat{i}+2\widehat{j}+\widehat{k}$ and $\overrightarrow{c}=\left(\alpha +1\right)\widehat{i}+\left(\beta -1\right)\widehat{j}+\widehat{k}$ are linearly dependent vectors and $\left|\overrightarrow{c}\right|=\sqrt[]{6}$ then sum of all possible value of (a + b) is $\left(\alpha ,\beta \in R\right)$  

If f(x) = $[\begin{array}{cc}\hfill \frac{1}{\left|x\right|}\hfill & \hfill a{x}^2+b\hfill \end{array}\begin{array}{cc}\hfill \left|x\right|\ge 1\hfill & \hfill \left|x\right|<1\hfill \end{array},$  is differentiable everywhere and K = a + b, then value of k is

Value of ${\displaystyle \underset{-\pi /2}{\overset{\pi /2}{\int }}\frac{dx}{\left(1+ta{n}^{2}x\right)\left(1+2^x\right)}}$  equals

How many hydrogen atom(s) is/are present in precipitate (P)?

A thin circular-disk earrings 10.0cm in diameter is plated with a coating of gold 0.20mm thick from an Au³⁺ bath. How many days (approx.) does it take to deposit the gold on one side of one earring if the current is 0.193 ampere.

A metal crystallises as simple cubic crystal. The distance between the nearest neighbours of each atom is $\frac{258.36}{\sqrt[]{2}}pm.$  The atomic radius of metal atoms (in pm) is

How many H-atome can be exchanged by D-atom when the following compound is kept in $\stackrel{\Theta }{O}D/D_{2}O$  solution for long time?

The decomposition of hydrogen peroxide follows first order kinetics.

2H₂O₂(aq) $\stackrel{}{\to }$ 2H₂O $\left(\mathcal{l}\right)$ + O₂(g)

If the volume of O₂ gas liberated at S TP in first 2- minutes of the start of decomposition is 25.00ml, what should be the total volume of O₂ gas (in ml) collected in time, t >> T_1/2. (t_1/2 for the decomposition of H₂O₂ is 10 min)

In “Al” and “Si”, if temperature is changed from normal temperature to 70 K then

Two balls of same mass and carrying equal charge are hung by threads of length $l$ from a fixed support. At electrostatic equilibrium, assuming that angles made by each thread is small, the separation, $x$  between the balls is proportional to: