An ideal transformer has $500$ and $5000$ turns in primary and secondary windings respectively. If the primary voltage is connected to a $6\,V$ battery, then the secondary voltage is.......$V$.

If the harmonic mean of the roots of the equation $\sqrt{2}x^2 - bx + (8 - 2\sqrt{5}) = 0$ is $4$,then the value of $b$ is:

$A$ body is sliding down a rough inclined plane. The coefficient of friction between the body and the plane is $0.5$. The ratio of the net force required for the body to slide down and the normal reaction on the body is $1:2$. Then the angle of the inclined plane is: (in $^{\circ}$)

The wavelength of the light used in Young's double slit experiment is $\lambda$. The intensity at a point on the screen is $I$,where the path difference is $\lambda/6$. If $I_0$ denotes the maximum intensity,then the ratio of $I$ and $I_0$ is

The lanthanide contraction is responsible for the fact that

Let $f$ be a differentiable function such that $f(1)=2$ and $f^{\prime}(x)=f(x)$,for all $x \in \mathbb{R}$. If $h(x)=f(f(x))$,then $h^{\prime}(1)$ is equal to