If $ax^2+6xy+by^2-10x+10y-6=0$ represents a pair of perpendicular lines,then the value of $|a|$ equals

$A$ three-digit number $n$ is such that the last two digits are equal and differ from the first digit. The number of such $n$'s is:

$A$ nichrome wire $50 \text{ cm}$ long and $1 \text{ mm}^2$ cross-section carries a current of $4 \text{ A}$ when connected to a $2 \text{ V}$ battery. The resistivity of the nichrome wire in $\Omega \cdot \text{m}$ is:

If the imaginary part of $\frac{2z+1}{iz+1}$ is $-2$,then the locus of the point representing $z$ in the Argand plane is

The electric potential $V$ at any point $(x, y, z)$ (all in $m$) in space is given by $V = 4x^2 \, V$. The electric field at the point $(1 \, m, 0, 2 \, m)$ in $V/m$ is:

$A$ body executes simple harmonic motion under the action of a force $F_1$ with a time period $T_1 = \frac{4}{5} \ s$. If the force is changed to $F_2$,it executes $SHM$ with a time period $T_2 = \frac{3}{5} \ s$. If both the forces $F_1$ and $F_2$ act simultaneously in the same direction on the body,what is its new time period in seconds?