MCQ
The function $F(x) = \int_0^x {\log \left( {\frac{{1 - x}}{{1 + x}}} \right)} \,dx$ is
- ✓An even function
- BAn odd function
- CA periodic function
- DNone of these
since the function here $f(x) = \log \frac{{1 - x}}{{1 + x}}$ is an odd function,
therefore $F(x)$ is an even function.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
| X: | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| P(X): | 0.15 | 0.23 | 0.12 | 0.10 | 0.20 | 0.08 | 0.07 | 0.05 |
If $\int\limits_{\beta-\frac{8}{3}}^{2 a-1} \operatorname{Max}\left\{\frac{9- x ^{2}}{5- x }, x \right\} dx =\alpha_{1}+\alpha_{2} \log _{e}\left(\frac{8}{15}\right)$ then $\alpha_{1}+\alpha_{2}$ is equal to
Then which of the following options is/are correct?
$(1)$ For $x =1$, there exists a unit vector $\alpha \hat{ i }+\beta \hat{ j }+\gamma \hat{ k }$ for which $R \left[\begin{array}{l}\alpha \\ \beta \\ \gamma\end{array}\right]=\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right]$
$(2)$ There exists a real number $x$ such that $P Q=Q P$
$(3)$ $\operatorname{det} R=\operatorname{det}\left[\begin{array}{lll}2 & x & x \\ 0 & 4 & 0 \\ x & x & 5\end{array}\right]+8$, for all $x \in R$
$(4)$ For $x=0$, if $R\left[\begin{array}{l}1 \\ a \\ b\end{array}\right]=6\left[\begin{array}{l}1 \\ a \\ b\end{array}\right]$, then $a+b=5$