Higher Math 1st Paper MCQ-Rajshahi Board-2021

1. What is the value of $\int e^{x}\left(\frac{1}{x}-\frac{1}{x^{2}}\right)$ dx?

2. If $f(x)=2 x$ then -

i. $\int \frac{d x}{f(x)}=\frac{1}{2} \ln x+c$

ii. $\int e^{f(x)} d x=\frac{1}{2} e^{2 x}+c$

iii. $\int_{0}^{1} f(x) d x=1$

Which one is correct?

3. $\int \frac{1}{\cos ^{2} p \sqrt{\operatorname{tan} p}} d p=?$

4. A=$\left[\begin{array}{lll}1 & 3 & 5 \\ 2 & 4 & 6 \\ 4 & 6 & 8\end{array}\right], B=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]$

According to the information -

i. $|A|=0$

ii. order of $A B$ is $3 \times 1$

iii. $\mathrm{BA}$ is determined

Which one is correct?

5. $\lim _{x \rightarrow 0}(1+2 x)^{\frac{1}{2 x}}=?$