In a $\triangle ABC$,the expression $\frac{(a+b+c)(b+c-a)(c+a-b)(a+b-c)}{4b^2c^2}$ is equal to:

The blocks shown in the figure move with a constant velocity of $10 \, m/s$ towards the right. All surfaces in contact are rough. The friction force applied by block $B$ on block $A$ is ........... $N$.

$A$ thin uniform rod of length $l$ and mass $m$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega$. Its centre of mass rises to a maximum height of:

What is the role of limestone during the extraction of iron from haematite ore?

The most important method of preparation of hydrocarbons of lower carbon number is

The area (in sq. units) of the parallelogram whose diagonals are along the vectors $8 \hat{i}-6 \hat{j}$ and $3 \hat{i}+4 \hat{j}-12 \hat{k}$ is: