$A$ particle moves in a circle of radius $25 \, cm$ at two revolutions per second. The acceleration of the particle in $m/s^2$ is

$A$ man weighing $60\, kg$ stands on the horizontal platform of a spring balance. The platform starts executing simple harmonic motion of amplitude $0.1\, m$ and frequency $\frac{2}{\pi }\, Hz$. Which of the following statements is correct?

The solution of $x dx + y dy = x^2 y dy - x y^2 dx$ is

The keys are based on contrasting characters generally in a pair called . . . . . . .

If the line $y=2x+c$ is a tangent to the circle $x^2+y^2=5$,then a value of $c$ is

$\int \frac{dx}{\sqrt{x-x^2}}$ is equal to