The value of $k$ such that the lines $2x - 3y + k = 0$,$3x - 4y - 13 = 0$,and $8x - 11y - 33 = 0$ are concurrent,is

The product$(s)$ formed when $H_2O_2$ reacts with disodium hydrogen phosphate is

Two wires are made of the same material and have the same volume. Wire $1$ has cross-sectional area $A$ and wire $2$ has cross-sectional area $3A$. If the length of wire $1$ increases by $\Delta x$ on applying force $F$,how much force is needed to stretch wire $2$ by the same amount $\Delta x$?

Let $A(3-i)$ and $B(2+i)$ be two points in the Argand plane. If the point $P$ represents the complex number $z=x+iy$,which satisfies $|z-3+i|=|z-2-i|$,then the locus of the point $P$ is

The maximum possible number of real roots of the equation $x^5 - 6x^2 - 4x + 5 = 0$ is

The quadratic equation whose roots are $\sin ^2 18^{\circ}$ and $\cos ^2 36^{\circ}$ is :