$A$ vertical mass-spring system executes simple harmonic oscillations with a period of $2\,s$. $A$ quantity of this system which exhibits simple harmonic variation with a period of $1\,s$ is

The equation of the $x$-axis is .....

If $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}$ and $|\overrightarrow{a}|=3, |\overrightarrow{b}|=4$ and $|\overrightarrow{c}|=\sqrt{37}$,then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is:

$A$ person lives in a high-rise building at a height of $30 \, m$ on the bank of a river. Across the river is a well-lit tower of height $60 \, m$. When the person looks through a polarizer at an appropriate angle at the light from the top of the tower reflecting from the river surface,he finds the intensity of light is least. If the refractive index of water is $\frac{4}{3}$,the width of the river is......$m$.

For the reaction $A + B \rightarrow C$,experiments were performed in the presence of a large amount of $B$ to measure the initial reaction rate $(V_f)$ as a function of the initial concentration of $A ([A]_0)$. The data from the experiments are plotted as shown below. The order of the reaction with respect to $A$ is $.....$

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+4x+1=0$,then $(\alpha+\beta)^{-1}+(\beta+\gamma)^{-1}+(\gamma+\alpha)^{-1}$ is equal to