If $y=a \sin x+b \cos x \quad$ (where $\mathrm{a}$ and $\mathrm{b}$ are constants), then $y^2+\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)^2$ is

If Rolle's theorem holds for the function $\mathrm{f}(x)=x^3+\mathrm{bx}{ }^2+\mathrm{ax}+5$ on $[1,3]$ with $\mathrm{c}=2+\frac{1}{\sqrt{3}}$, then the values of $a$ and $b$ respectively are

Ten bulbs are drawn successively, with replacement, from a lot containing $10 \%$ defective bulbs, then the probability that there is at least one defective bulb, is

If statement I : If the work is not finished on time, the contractor is in trouble. statement II : Either the work is finished on time or the contractor is in trouble. then