In order to shift a body of mass $m$ from a circular orbit of radius $3R$ to a higher radius $5R$ around the earth,the work done is

In a seconds pendulum,the mass of the bob is $30\, g$. If it is replaced by a $90\, g$ mass,then its time period will be ... $\sec$.

If $\log x : \log y : \log z = (y - z) : (z - x) : (x - y)$,then

If the angle $\theta$ between the vectors $\overrightarrow{a}=2 x^2 \hat{i}+4 x \hat{j}+\hat{k}$ and $\overrightarrow{b}=7 \hat{i}-2 \hat{j}+x \hat{k}$ is such that $90^{\circ} < \theta < 180^{\circ}$, then $x$ lies in the interval

If $f(x) = \begin{cases} \frac{1-\sqrt{2} \sin x}{\pi-4x} & \text{if } x \neq \frac{\pi}{4} \\ a & \text{if } x = \frac{\pi}{4} \end{cases}$ is continuous at $x = \frac{\pi}{4}$, then $a$ is equal to

Identify the blank spaces $A, B, C$ and $D$ given in the following table and select the correct answer.

Types of Microbes	Scientific Name	Commercial Product
Bacterium	$A$	Clot buster enzyme
$B$	Aspergillus niger	Citric acid
Fungus	Trichoderma polysporum	$C$
Bacterium	$D$	Butyric acid