The number of gram atoms of oxygen present in $0.3 \, mole$ of $(COOH)_2 \cdot 2H_2O$ is

If the system of linear equations $x + 2ay + az = 0$,$x + 3by + bz = 0$,and $x + 4cy + cz = 0$ has a non-zero solution,then $a, b, c$:

The diameter of the objective of a telescope is $1 \ m$. Its resolving limit for light of wavelength $4538 \ \mathring A$ will be:

If $f(x) = \begin{cases} \frac{\sin(1+[x])}{[x]}, & \text{for } [x] \neq 0 \\ 0, & \text{for } [x] = 0 \end{cases}$ where $[x]$ denotes the greatest integer not exceeding $x$,then $\lim_{x \rightarrow 0^{-}} f(x)$ is equal to

If $f(x) = \frac{1}{x^2} \int_3^x (2t - 3f'(t)) dt$,then $f'(3)$ is equal to

Which of the following statements is not true?