AD/ADP/BS 1 Semester/Term University Of Sargodha (UOS) 2025

ADP/BS 1" Semester Examination 2025

Subject: IT/CS/SE Paper: Mathematics-1 (URCM-5107)

Time Allowed: 02:30 Hours Maximum Marks: 60

Note: Objective part is compulsory. Attempt any three questions from sabjective part.

Objective Part (Compulsory)

Q.1. Write short answers of the following in 2-3 lines each on your answer sheet. (2*12)

i. Solve the following system of linear equation:

3x—4y=85"', x+y=4 | |

ii. Find thé Inverse of the following matrix: A = i” 30 :

iik ‘A ‘Define a one-to-one function and also give one example of one-to-one function. .

iv. Solve the following quadratic equation: (xX iy 3 (x +

2) -4=0.

x =. a

- v3 | : ~ \ -

Vv, Simplify the term (= - =i) as a S-1b. ~0O

vi. Solve the equation: V2x + 8 + Vx +5 = 7,

vii. Find cube roots of 8 and 27

viii. Find the indicated term of following sequence: 1,-3,5,-7, Qy4.

iX. Find the general and 15" term of Arithmetic Progression whose first term and common difference

are 3 and -5 respectively.

X. Ha=2b=S5,c=9,then find Geometric Mean and Harmonic Mean.

xi Find the domain and range of function: f(x) = v2x —

1.

xii Define the scalar matrix

Time Allowed: 02:30 Hours

Note: Objective part is compulsory. Attempt any three questions from subjective part.

Cbhjective Part (Compulsory)

Q.1. Write short answers of the following in 2-3 lines each on your answer sheet. (2°12)

3x—-4y=8\ , Nx+y=4.

wel : |

ii. Find, the Inverse of the following matrix: A = [5 rR ; [i

iik

2) Define a one-to-one function and also give one example 'of one-to-one function.

Div. Solve the following quadratic equation: (AP =3 (x +

3) —-—4=0.

= . ALN N § x

v. Simplify the term (5 —

70) as ad. o®

vi. Solve the equation: V2X + 8+ Vx +5 = 7, LAW

vii. Find cube roots of 8 and

27. No~

viii. Find the indicated term of following sequence: 1,-3.5, —7, +, ay. D+

ix. Find the general and 15% term of Arithmetic Progression whose first term and common difference

are 3 and -3 respectively.

Ifa=2b=S5,c=9,then find Geometric Mean and Harmonic Mean.

Find the domain and range of function: f(x) = V2x —

1.

xii. Define the scalar matrix

Subjective Part (3*12)

Q.2. Using Cramer's rule solve the following two systems.

Ix+y—z=-4 2x+2y+2=3

X+y—2z=-4 Ix=2y—-2z=1

-x+2y—2z=1 Sx4y=3z=2

Q.3. Find the solution set of following equations:

a) sec 3x = secx,

Q4.

a) If,2 and - are in Arithmetic progression then show that, b = =

b) sin 2x + sin x.

b) Find next three terms of sequence: —2, 4, 10, --

a) Find A, G, H and verify that A>G>H, (G>0),if:a=3,b=9,c = 6,d =

12.

Q.5.

b) If 5 term of A.P. is 16 and 20" term is 46, what is 12" term?

Q.6. Ifa and p are the roots of equation ax? + bx + ¢ = 0, form the equations whose roots are:

2 p2 1 1

a) a*, p*

b) 57

LK-6176/25-04-23