The vector sum of two forces is perpendicular to their vector difference. In that case,the forces

The coefficient of $x^5$ in the expansion of $\left(2 x^3-\frac{1}{3 x^2}\right)^5$ is

$A$ wire of length $l$ is bent into a circular coil of one turn of radius $R_1$. Another wire of the same material,same area of cross-section,and same length is bent into a circular coil of two turns of radius $R_2$. When the same current flows through the two coils,the ratio of magnetic induction at the centres of the two coils is

The maximum energy in the thermal radiation from a hot source occurs at a wavelength of $11 \times 10^{-5} \text{ cm}$. According to Wien's law,the temperature of the source (on Kelvin scale) will be $n$ times the temperature of another source (on Kelvin scale) for which the wavelength at maximum energy is $5.5 \times 10^{-5} \text{ cm}$. The value of $n$ is

Acidity of diprotic acids in aqueous solutions increases in the order

Which group of plants was the first to exist on Earth?