The angle between the pair of straight lines formed by joining the points of intersection of $x^2+y^2=4$ and $y=3x+c$ to the origin is a right angle. Then $c^2$ is equal to

The statement $\sim (p \leftrightarrow \sim q)$ is

At $20^{\circ}C$,the concentration of $Ag^{+}$ ions in a saturated solution of $Ag_2CrO_4$ is $1.5 \times 10^{-4} \ mol/L$. The solubility product $(K_{sp})$ of $Ag_2CrO_4$ at $20^{\circ}C$ is:

$A$ galvanometer of resistance $50 \Omega$ is connected to a battery of $3 \text{ V}$ along with a resistance of $2950 \Omega$ in series. $A$ full-scale deflection of $30$ divisions is obtained in the galvanometer. In order to reduce this deflection to $20$ divisions,the total resistance in series should be: (in $\Omega$)

$A$ poster is to be printed on a rectangular sheet of paper of area $18 \ m^2$. The margins at the top and bottom of $75 \ cm$ each and at the sides $50 \ cm$ each are to be left. Then the dimensions i.e. height and breadth of the sheet so that the space available for printing is maximum,are . . . . . . respectively.

The mean and standard deviation of a binomial variate $X$ are $4$ and $\sqrt{3}$ respectively. Then $P(X \geq 1)$ is equal to