Free Printable FYBSc Entry Level Competency Test 2021

1.

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

a)

$\log\left(2x\ +\ 1\right)\ +c$

b)

$\log\left(x^{2\ }+x\right)\ +c$

c)

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

d)

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

2.

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

a)

{2, 3, 6, 9}

b)

{6}

c)

{2, 3, 9}

d)

{3, 6, 9}

3.

Which of the following is an equation of circle?

a)

$4x^{2\ }-\ 3y^{2\ }=21$

b)

$x^{2\ }+\ 5y\ +\ 7x\ =\ 4$

c)

$x^{2\ }+\ y^{2\ }-4x\ -\ 6y\ =7$

d)

$y^{2\ }+\ 1\ =\ 5x^{2\ }$

4.

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

a)

b)

c)

d)

5.

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

a)

$xe^x$

b)

$xe^{x\ }+\ x$

c)

$x\ +\ e^{x\ }$

d)

$e^x\left(x\ +\ 1\right)$

6.

a)

does not exist

b)

0

c)

2

d)

3

7.

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

a)

$y\ =\ \log\ x$

b)

$y\ =\ \sin\ x\ +\ \cos\ x$

c)

$y\ =\ \cos\ x\ \sin\ x$

d)

$y\ \ =\ x^{2\ }-1$

8.

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

a)

f(p) must exist.

b)

f(p) may not exist.

c)

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

d)

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

9.

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

a)

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

b)

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

c)

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

d)

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

10.

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

a)

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

b)

A is a non-empty subset of B.

c)

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

d)

A is an empty set.

11.

a)

25

b)

120

c)

$5^5$

d)

only 5

12.

$What\ is\ the\ coefficient\ of\ x^{3\ }in\ \left(x\ +\ 1\right)\left(x\ +\ 2\right)\left(x\ +3\right)\left(x\ +4\right)\ ?$

a)

24

b)

35

c)

10

d)

4

13.

How many natural numbers between 1 and 100 are multiples of 2 or 3?

a)

67

b)

83

c)

50

d)

63

14.

What is the sum of first n natural numbers?

a)

$2n$

b)

$\frac{n\left(n-1\right)}{2}$

c)

$n^{2\ }+\ n$

d)

$\frac{n\left(n\ +\ 1\right)}{2}$

15.

$What\ are\ the\ roots\ of\ x^{3\ }-6x^{2\ }+\ 11x\ -6\ ?$

a)

1, -2, -3

b)

-1, 2, 3

c)

1, 2, 3

d)

-1, -2, -3

FYBSc Entry Level Competency Test 2021

Total questions: 15

Worksheet time: 30mins

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