$A$ 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 $D$)

The normal at the point $(1,1)$ on the curve $2y + x^{2} = 3$ is

The amplitude of a damped oscillator decreases to $0.9$ times its original magnitude in $5\,s$. In another $10\,s$ it will decrease to $\alpha$ times its original magnitude,where $\alpha$ equals

In non-cyclic photophosphorylation,the electron $(e^-)$ released by $PSI$ is accepted by.......

For the reversible reaction $N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$ at $500 \, ^\circ C$,the value of $K_p$ is $1.44 \times 10^{-5}$. When the partial pressure is measured in atmospheres,the value of $K_c$ in $\text{mol L}^{-1}$ is:

If $a>0$,then $\int_{-\pi}^\pi \frac{\sin ^2 x}{1+a^x} d x$ is equal to