The compound $CH_3-C(CH_3)=CH-CH_3$ on reaction with $NaIO_4$ in the presence of $KMnO_4$ gives :-

If $f: N \rightarrow Z$ is defined by $f(n)=\begin{cases} 2 & \text{if } n=3k, k \in Z \\ 10 & \text{if } n=3k+1, k \in Z \\ 0 & \text{if } n=3k+2, k \in Z \end{cases}$,then $\{n \in N: f(n)>2\}$ is equal to

The stress versus strain graphs for wires of two materials $A$ and $B$ are as shown in the figure. If ${Y_A}$ and ${Y_B}$ are the Young's moduli of the materials,then

It takes $10$ minutes to cool a liquid from $61^oC$ to $59^oC$. If room temperature is $30^oC$,then the time taken in cooling from $51^oC$ to $49^oC$ is ....... $\min$.

Two wooden blocks of masses $M$ and $m$ are placed on a smooth horizontal surface as shown in the figure. If a force $P$ is applied to the system as shown in the figure such that the mass $m$ remains stationary with respect to the block of mass $M$,then the magnitude of the force $P$ is

The acute angle between the two lines whose direction ratios $(l, m, n)$ satisfy the equations $l+m-n=0$ and $l^2+m^2-n^2=0$ is