The value of $\lambda$ such that $\lambda x^2-10 x y+12 y^2+5 x-16 y-3=0$ represents a pair of straight lines is:

If $A = \begin{bmatrix} 1 & 0 & 1 \\ 2 & 1 & 0 \\ 3 & 2 & 1 \end{bmatrix}$,then $\det(A)$ is equal to

An infinite number of identical capacitors each of capacitance $1 \mu F$ are connected as shown in the figure. Then,the equivalent capacitance between $A$ and $B$ is .......... $\mu F$.

If a complex number $z$ satisfies $|z^2-1|=|z|^2+1$,then $z$ lies on

$A$ particle is moving on a circular path of radius $r$ with uniform speed $v$. The change in velocity when the particle moves from $P$ to $Q$ is $(\angle POQ = 40^\circ)$.

The solution of $\frac{dy}{dx} + 1 = e^{x+y}$ is