$A$ square matrix $[a_{ij}]$ in which $a_{ij} = 0$ for $i \neq j$ and $a_{ij} = k$ (constant) for $i = j$ is called a

Energy is being emitted from the surface of a black body at $127^{\circ}C$ temperature at the rate of $1.0 \times 10^6 \ J/\text{s} \cdot \text{m}^2$. The temperature of the black body at which the rate of energy emission is $16.0 \times 10^6 \ J/\text{s} \cdot \text{m}^2$ will be ......... $^{\circ}C$.

Which of the following is responsible for the production of biogas?

$A$ particle of mass $5 \times 10^{-5} \ kg$ is placed at the lowest point of a smooth parabola $x^2 = 40y$ (where $x$ and $y$ are in $m$). If it is displaced slightly such that it is constrained to move along the parabola,the angular frequency of oscillation (in $rad/s$) will be approximately:

The electrons which take part in order to exhibit variable oxidation states by transition metals are

The quadratic equation whose roots are $\sin ^2 18^{\circ}$ and $\cos ^2 36^{\circ}$ is :