If the coefficients $a$ and $b$ of a quadratic expression $x^2+ax+b$ are chosen from the sets $A=\{3,4,5\}$ and $B=\{1,2,3,4\}$ respectively,then the probability that the equation $x^2+ax+b=0$ has real roots is

Let $\overline{a}=\hat{i}+\hat{j}+\hat{k}$,$\overline{b}=\hat{i}-\hat{j}+\hat{k}$ and $\overline{c}=\hat{i}-\hat{j}-\hat{k}$ be three vectors. $A$ vector $\overline{v}$ in the plane of $\overline{a}$ and $\overline{b}$,whose projection on $\overline{c}$ is $\frac{1}{\sqrt{3}}$,is given by

What is common between parrot,Platypus and kangaroo?

When an $AC$ source of $e.m.f. \ e = E_0 \sin(100t)$ is connected across a circuit,the phase difference between the $e.m.f. \ e$ and the current $i$ in the circuit is observed to be $\frac{\pi}{4}$ as shown in the diagram. If the circuit consists possibly only of $RC$,$RL$,or $LC$ in series,find the relationship between the two elements.

$A$ charge of $1 \mu C$ is divided into two parts such that their charges are in the ratio of $2: 3$. These two charges are kept at a distance $1 \ m$ apart in vacuum. Then,the electric force between them (in $N$) is

Which of the following anions cannot be tested by dilute $H_2SO_4$?