If ${ }^{(n-1)} C_3+{ }^{(n-1)} C_4>{ }^n C_3$,then the minimum value of $n$ is

The resistance of a bulb filament is $100 \ \Omega$ at a temperature of $100 \ ^oC$. If its temperature coefficient of resistance is $0.005 \ ^oC^{-1}$,at what temperature $(^oC)$ will its resistance become $200 \ \Omega$?

If the area of an equilateral triangle inscribed in the circle $x^2+y^2+10x+12y+c=0$ is $27\sqrt{3}$ sq. units,then $c$ is equal to:

Let $f(x)$ be a polynomial of degree $3$ such that $f(-1) = 10$,$f(1) = -6$,$f(x)$ has a critical point at $x = -1$,and $f'(x)$ has a critical point at $x = 1$. Then $f(x)$ has a local minima at $x =$

Magnetic lines of force due to a bar magnet do not intersect because

Three concentric spherical shells have radii $a, b,$ and $c$ $(a < b < c)$ and have surface charge densities $\sigma, -\sigma,$ and $\sigma$ respectively. If the potentials on the surfaces of these shells are $V_A, V_B,$ and $V_C$ respectively,then for $c = a + b$,which of the following is true?