The vectors $\overrightarrow{AB} = 3\hat{i} + 4\hat{k}$ and $\overrightarrow{AC} = 5\hat{i} - 2\hat{j} + 4\hat{k}$ are the sides of a triangle $ABC$. The length of the median through $A$ is

Four light sources produce the following four waves:
$(i)$ $y_1 = a \sin(\omega t + \phi_1)$
(ii) $y_2 = a \sin(2\omega t)$
(iii) $y_3 = d' \sin(\omega t + \phi_2)$
(iv) $y_4 = d' \sin(3\omega t + \phi)$
Superposition of which two waves gives rise to interference?

$A$ codon has a sequence of $\underline{A}$,and specifies a particular $\underline{B}$ that is to be incorporated into a $\underline{C}$. What are $\underline{A}, \underline{B}, \underline{C}$ ?
$\underline{A} \quad \underline{B} \quad \underline{C}$

The length of the $x$-intercept made by the pair of lines $2x^2 + xy - 6y^2 - 2x + 17y - 12 = 0$ is

The magnetic induction and the intensity of the magnetic field inside an iron core of an electromagnet are $1 \ Wb \ m^{-2}$ and $150 \ A \ m^{-1}$,respectively. The relative permeability of iron is $\left(\mu_0 = 4 \pi \times 10^{-7} \ H \ m^{-1}\right)$.

What is the correct relationship between the $pH$ values of isomolar solutions of sodium oxide $(pH_1)$,sodium sulphide $(pH_2)$,sodium selenide $(pH_3)$,and sodium telluride $(pH_4)$?