$A$ cup of tea cools from $80^{\circ}C$ to $60^{\circ}C$ in $1$ minute. The ambient temperature is $30^{\circ}C$. How many seconds will it take to cool from $60^{\circ}C$ to $50^{\circ}C$?

Three non-zero non-collinear vectors $\vec{a}, \vec{b}$ and $\vec{c}$ are such that $\vec{a}+3\vec{b}$ is collinear with $\vec{c}$,and $3\vec{b}+2\vec{c}$ is collinear with $\vec{a}$. Then $\vec{a}+3\vec{b}+2\vec{c}$ equals to

If the direction ratios of two lines are given by $3lm - 4ln + mn = 0$ and $l + 2m + 3n = 0$,then the angle between the lines is:

Which of the following products is formed when $SiF_4$ reacts with water?

If the point $P(\alpha, \beta, \gamma)$ lies on the plane $2x+y+z=1$ and $[\alpha \ \beta \ \gamma] \begin{bmatrix} 1 & 9 & 1 \\ 8 & 2 & 1 \\ 7 & 3 & 1 \end{bmatrix} = [0 \ 0 \ 0]$,then $\alpha^2+\beta^2+\gamma^2=$

Three blocks,$A, B$ and $C,$ of masses $4\,kg, 2\,kg$ and $1\,kg$ respectively,are in contact on a frictionless surface,as shown. If a force of $14\,N$ is applied on the $4\,kg$ block,then the contact force between $A$ and $B$ is ....... $N$.