MCQ
$\left| {\,\begin{array}{*{20}{c}}{11}&{12}&{13}\\{12}&{13}&{14}\\{13}&{14}&{15}\end{array}\,} \right| = $
- A$1$
- ✓$0$
- C$-1$
- D$67$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$(A)$ $\cos \beta > 0$ $(B)$ $\sin \beta < 0$ $(C)$ $\cos (\alpha+\beta) > 0$ $(D)$ $\cos \alpha < 0$
| List-$I$ | List-$II$ |
| ($I$) Probability of $\left(X_2 \geq Y_2\right)$ is | ($P$) $\frac{3}{8}$ |
| ($II$) Probability of $\left(X_2>Y_2\right)$ is | ($Q$) $\frac{11}{16}$ |
| ($III$) Probability of $\left(X_3=Y_3\right)$ is | ($R$) $\frac{5}{16}$ |
| ($IV$) Probability of $\left(X_3>Y_3\right)$ is | ($S$) $\frac{355}{864}$ |
| ($T$) $\frac{77}{432}$ |
The correct option is:
$f(x)=\sin x-e^{x} \,\,\,\, \text { if } x \leq 0$
$\quad\quad\quad a+[-x] \,\,\,\, \text { if } 0\,<\,x\,<\,1$
$\quad\quad\quad 2 x-b \,\,\,\,\,\,\,\, \text { if } \geq 1$
where $[\mathrm{x}]$ is the greatest integer less than or equal to $\mathrm{x}$. If $\mathrm{f}$ is continuous on $\mathrm{R}$, then $(\mathrm{a}+\mathrm{b})$ is equal to: