MCQ
$\int_1^2 {{e^x}\left( {\frac{1}{x} - \frac{1}{{{x^2}}}} \right)\,dx = } $
- A$\frac{{{e^2}}}{2} + e$
- B$e - \frac{{{e^2}}}{2}$
- ✓$\frac{{{e^2}}}{2} - e$
- DNone of these
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$f_1(x)=\left\{\begin{array}{lll}|x| & \text { if } & x<0, \\ e^x & \text { if } & x \geq 0 ;\end{array}\right.$
$f_2(x)=x^2$
$f_3(x)=\left\{\begin{array}{ccc}\sin x & \text { if } & x < 0, \\ x & \text { if } & x \geq 0\end{array}\right.$ and
$f_4(x)=\left\{\begin{array}{ccc}f_2\left(f_1(x)\right) & \text { if } & x < 0, \\ f_2\left(f_1(x)\right)-1 & \text { if } & x \geq 0\end{array}\right.$
| List $I$ | List $II$ |
| $P.$ $ f_4$ is | $1.$ onto but not one-one |
| $Q.$ $f_3$ is | $2.$ neither continuous nor one-one |
| $R.$ $f _2 \circ f _1$ is | $3.$ differentiable but not one-one |
| $S.$ $ f_2$ is | $4.$ continuous and one-one |
Codes: $ \quad P \quad Q \quad R \quad S $