Flux $\phi$ (in weber) in a closed circuit of resistance $10\,\Omega$ varies with time $t$ (in sec) according to the equation $\phi = 6t^2 - 5t + 1$. What is the magnitude of the induced current at $t = 0.25\,s$ (in $,A$)?

In how many ways can $7$ men and $7$ women be seated around a round table such that no two women sit together?

The circumcentre of the triangle with vertices at $(-2, 3)$,$(1, -2)$ and $(2, 1)$ is

Which of the following statements are true regarding Bohr's model of the hydrogen atom?
$(I)$ Orbiting speed of the electron decreases as it shifts to discrete orbits away from the nucleus.
$(II)$ Radii of allowed orbits of the electron are proportional to the principal quantum number.
$(III)$ Frequency with which electrons orbit around the nucleus in discrete orbits is inversely proportional to the cube of the principal quantum number.
$(IV)$ Binding force with which the electron is bound to the nucleus increases as it shifts to outer orbits.
Select the correct answer using the codes given below.

Natural gas is a mixture of .......

The radiation emitted by a star $A$ is $10000$ times that of the sun. If the surface temperatures of the sun and the star $A$ are $6000 \ K$ and $2000 \ K$ respectively,the ratio of the radii of the star $A$ and the sun is : (in $: 1$)