If $y=y(x)$ satisfies $\left(\frac{2+\sin x}{1+y}\right) \frac{\mathrm{d} y}{\mathrm{~d} x}=-\cos x$ such that $y(0)=2$, then $y\left(\frac{\pi}{2}\right)$ is equal to

In a bank, the principal increases continuously at a rate of $x \%$ per year. Then the rate $x$, if ₹$100$ double itself in 10 years, is ( $\log 2=0.6931$)

If a random variable $X$ follows the Binomial distribution $\mathrm{B}(33, \mathrm{p})$ such that $3 \mathrm{P}(\mathrm{X}=0)=\mathrm{P}(\mathrm{X}=1)$, then the variance of X is

The number of common tangents that can be drawn to the circles $x^2+y^2-6 x=0$ and $x^2+y^2+6 x+2 y+1=0$ is __________