$A$ presbyopic patient has a near point of $30 \, cm$ and a far point of $40 \, cm$. The dioptric power of the corrective lens required for seeing distant objects is: (in $D$)

In the adjoining circuit,the potential difference across $3\, \Omega$ is ............... $V$.

Which pair of the following belongs to Basidiomycetes?

If $\omega$ is a complex cube root of unity,then $\sin \left\{\left(\omega^{10}+\omega^{23}\right) \pi-\frac{\pi}{4}\right\}$ is equal to

Two charges $q_1$ and $q_2$ are placed $30\,cm$ apart,as shown in the figure. $A$ third charge $q_3$ is moved along the arc of a circle of radius $40\,cm$ from $C$ to $D$. The change in the potential energy of the system is $\frac{q_3}{4\pi \epsilon_0}k$,where $k$ is:

The equation of the hyperbola which passes through the point $(2,3)$ and has the asymptotes $4x+3y-7=0$ and $x-2y-1=0$ is