MCQ
$\mathop {Lim}\limits_{n\, \to \,\infty } \,\int\limits_0^2 {{{\left( {1 + \frac{t}{{n + 1}}} \right)}^n}dt} $ is equal to
- A$0$
- B$e^2$
- ✓$e^2 - 1$
- Ddoes not exist
$=\mathop {Lim}\limits_{n\, \to \,\infty } \,\left[ {{{\left( {1 + \frac{t}{{n + 1}}} \right)}^{n + 1}}} \right]_{\,0}^{\,2}$
$=\mathop {Lim}\limits_{n\, \to \,\infty } \,{\left( {1 + \frac{2}{{n + 1}}} \right)^{n + 1}} - 1$
$= e^2 - 1$ $\left[ {\left( {1 + \frac{t}{{n + 1}}} \right){\rm{ is\, a\, linear\, function}}} \right]$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$\sin ^{-1}(a x)+\cos ^{-1}(y)+\cos ^{-1}(b x y)=\frac{\pi}{2} .$
Match the statements in Column $I$ with the statements in Column $II$ and indicate your answer by darkening the appropriate bubbles in the $4 \times 4$ matrix given in the $ORS$.
| Column $I$ | Column $II$ |
| $(A)$ If $a=1$ and $b=0$, then ( $x, y$ ) | $(p)$ lies on the circle $x^2+y^2=1$ |
| $(B)$ If $a=1$ and $b=1$, then $(x, y)$ | $(q)$ lies on $\left(x^2-1\right)\left(y^2-1\right)=0$ |
| $(C)$ If $a=1$ and $b=2$, then ( $x, y)$ | $(r)$ lies on $y=x$ |
| $(D)$ If $a=2$ and $b=2$, then $(x, y)$ | $(s)$ lies on $\left(4 x^2-1\right)\left(y^2-1\right)=0$ |