MCQ
$n$ gentlemen can be made to sit on a round table in
- A$\frac{1}{2}(n + 1)\;!$ ways
- ✓$(n - 1)\;!$ ways
- C$\frac{1}{2}(n - 1)\;!$ ways
- D$(n + 1)\;!$ ways
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$f (\theta)=(\sin \theta+\cos \theta)^2+(\sin \theta-\cos \theta)^4$
Suppose the function $f$ has a local minimum at $\theta$ precisely when $\theta \in\left\{\lambda_1 \pi, \ldots, \lambda_{ T } \pi\right\}$, where $0<\lambda_1<\cdots<\lambda_r<1$. Then the value of $\lambda_1+\cdots+\lambda_r$ is. . . . .