FYBSc Entry Level Competency Test 2021

 $\int\ \frac{2x\ +\ 1}{x^{2\ }+1}dx\ =\ ?$  

•  $\log\left(2x\ +\ 1\right)\ +c$  

•  $\log\left(x^{2\ }+x\right)\ +c$  

•  $\log\left(x^{2\ }+1\right)+\ \tan^{-1\ }x\ +\ c$  

•  $\log\left(x^{\ _{2\ }}+1\right)\ \sin^{-1\ }x\ +c$  

If  A = {3 , 6}  and B = {2, 6, 9} and C = {3, 9, 5}, then  $A\cup\left(B\ \cap\ C\right)$  is ?

• {2, 3, 6, 9}

• {6}

• {2, 3, 9}

• {3, 6, 9}

Which of the following is an equation of circle?

• $4x^{2\ }-\ 3y^{2\ }=21$

• $x^{2\ }+\ 5y\ +\ 7x\ =\ 4$

• $x^{2\ }+\ y^{2\ }-4x\ -\ 6y\ =7$

• $y^{2\ }+\ 1\ =\ 5x^{2\ }$

Which of the following is the graph of y = 3x - 5 ?

• 
• 
• 
• 

 $\frac{d}{dx}\left(xe^{x\ }\right)\ =\ ?$  

•  $xe^x$  

•  $xe^{x\ }+\ x$  

•  $x\ +\ e^{x\ }$  

•  $e^x\left(x\ +\ 1\right)$  

• does not exist

• 0

• 2

• 3

 $y''\ +\ y\ =\ 0$  Which of the following is a solution of this differential equation ?

•  $y\ =\ \log\ x$  

•  $y\ =\ \sin\ x\ +\ \cos\ x$  

•  $y\ =\ \cos\ x\ \sin\ x$  

•  $y\ \ =\ x^{2\ }-1$  

 $If\ \ \lim_{x\rightarrow p}\ f\left(x\right)\ \ exist,\ then\$  

• f(p) must exist.

• f(p) may not exist.

• f(p) exists and it is equal to the above limit.

• f(p) exists but it may not equal to the above limit.

Let Z be any complex number. Which of the following statement is not true?

• $\left|\overline{Z}\right|\ =\ \left|Z\right|$

• $\overline{\overline{Z}}\ \ =\ \ Z\$

• $\overline{Z}\ \ =\ Z$

• $Z\ \cdot\ \overline{Z}\ =\ \left|Z\right|^{2\ }$

If a set A is a proper subset of B, then

• there is an element of A which is not in B.

• A is a non-empty subset of B.

• there is an element of B which is not in A.

• A is an empty set.