The value of the integral $$\int\limits_{0}^{\frac{\pi}{2}} 60 \frac{\sin (6 x)}{\sin x} d x$$ is equal to _________.

Consider the efficiency of carnot's engine is given by $$\eta=\frac{\alpha \beta}{\sin \theta} \log_e \frac{\beta x}{k T}$$, where $$\alpha$$ and $$\beta$$ are constants. If T is temperature, k is Boltzmann constant, $$\theta$$ is angular displacement and x has the dimensions of length. Then, choose the incorrect option :

At time $$t=0$$ a particle starts travelling from a height $$7 \hat{z} \mathrm{~cm}$$ in a plane keeping z coordinate constant. At any instant of time it's position along the $$\hat{x}$$ and $$\hat{y}$$ directions are defined as $$3 \mathrm{t}$$ and $$5 \mathrm{t}^{3}$$ respectively. At t = 1s acceleration of the particle will be

A pressure-pump has a horizontal tube of cross sectional area $$10 \mathrm{~cm}^{2}$$ for the outflow of water at a speed of $$20 \mathrm{~m} / \mathrm{s}$$. The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is :

[given: density of water $$=1000 \mathrm{~kg} / \mathrm{m}^{3}$$]