What is the concentration of nitrate ions if equal volumes of $0.1 \ M$ $AgNO_3$ and $0.1 \ M$ $NaCl$ are mixed together (in $M$)?

Let $a, b, c$ be non-zero real numbers such that $\int_{0}^{1} (1 + \cos^8 x)(ax^2 + bx + c) dx = \int_{0}^{2} (1 + \cos^8 x)(ax^2 + bx + c) dx$. Then the quadratic equation $ax^2 + bx + c = 0$ has:

Which one of the following population interactions is widely used in medical science for the production of antibiotics?

The magnetic induction and the intensity of the magnetic field inside an iron core of an electromagnet are $1 \ Wb \ m^{-2}$ and $150 \ A \ m^{-1}$,respectively. The relative permeability of iron is $\left(\mu_0 = 4 \pi \times 10^{-7} \ H \ m^{-1}\right)$.

The value of $c$ in the Lagrange's mean value theorem for $f(x)=\sqrt{x-2}$ in the interval $[2,6]$ is

If the difference between the roots of the equations $x^2+ax+b=0$ and $x^2+bx+a=0$ is the same,and $a \neq b$,then: