Elementary Mathematics Past Papers 

By: Prof. Dr. Fazal Rehman Shamil | Last updated: February 3, 2024

OBJECTIVE]

Subject: Elementary Mathematics-I (Algebra)

Time Allowed: 15 Minutes

Max Marks: 10

NOTE: Attempt this Paper on this Question Sheet only. Please encircle the correct option. Division of marks is given in front of each question. This Paper will be collected back after expiry of time limit mentioned above.

 

Part-I  Answer the following Questions, cutting and overwriting are not allowed. (10)

Consider the sets A = {a, b, c, d, e}, B = {1,2,3,4,5} Then A — B is ___

a) Ø b) B

c) A d) None of these

 

The product of cube root of unity is

a) 1 b) 2

c) 3 d) 0

For any two non-singular matrices A and B, (AB)^-1 =?

a) A^-1B^-1 b) B^-1A^-1

c) AB d) BA

Every recurring non terminating decimal is a ____ number.

(a) Rational                                         (b) Irrational

(c) Real                                                 (d) None of these

The conjugate of -2 + 3i is

a) 2—3i b) 2 + 3i

¢) -2 + 3i                                               d) -2 – 3i

An infinite geometric series is convergent if

a) r > 1 b) r <i

c) r=l d) Both b and c

Which of the following cannot be the term of a harmonic progression?

a) 0 b) 1

c) 2 d) 3

The middie term of the expansion (1 + 2x)⁶

a) 3^rd term b) 4^th term

c) 5^th term d) 2^nd term

3. The product of cube root of unity is
4. a) 1 b) 2
5. c) 3 d) 0
6. For any two non-singular matrices A and B, (AB)^-1 =?
7. a) A^-1B^-1 b) B^-1A^-1
8. c) AB d) BA
9. Every recurring non terminating decimal is a ____ number.

(a) Rational                                         (b) Irrational

(c) Real                                                 (d) None of these

6. The conjugate of -2 + 3i is
7. a) 2—3i b) 2 + 3i

¢) -2 + 3i                                               d) -2 – 3i

7. An infinite geometric series is convergent if
8. a) r > 1 b) r <i
9. c) r=l d) Both b and c
10. Which of the following cannot be the term of a harmonic progression?
11. a) 0 b) 1
12. c) 2 d) 3
13. The middie term of the expansion (1 + 2x)⁶
14. a) 3^rd term b) 4^th term
15. c) 5^th term d) 2^nd term

 

[SUBJECTIVE]

Subject: Elementary Mathematics-I (Algebra)

Time Allowed: 2 Hours 45 Minutes

Max Marks: 50

NOTE: ATTEMPT THIS (SUBJECTIVE) ON SEPARATE ANSWER SHEET PROVIDED

 

Part-II  Give Short Answers, Each question carries equal marks. (20)

Q#1: Define complex number

Q#2: Factorize 9a² + 16b²

Q#3: Find the inverse of the relation and check whether it is a function of not by diagram

{(1,2),(2,5),(3,4),(2,1),(5,4)}

Q#4: Define function with example.

Q#5: If A= [ⁱ₁  ⁰_-i] show that A⁴ = J₂

Q#6: The sum of a positive number and its square is 380. Find the number.

Q#7: By remainder theorem find remainder when x² + 3x + 7 is divided by x + 1.

Q#8: If 5 and 8 are two arithmetic means between a and b. Find a & b.

Q#9: If 1/a,1/b,1/c are in G.P then show that common ratio = + √a/c

Q#10: Prove that sin2θ + cos2 θ = 1

 

Part-III  Give Long Answers, Each question carries equal marks. (30)

Q#1: Solve by Cramer rule

2x—3y+4z= -12, x-2y +z =-5, 3x+y+2z = 1

Q#2: a) Solve: 4^1+x + 4^1-x = 10

b) If 1/a,1/b,1/c are in A.P then show that common difference = (a-c)/2ac

Q#3: a) Expand the following up to 4 times, taking the values of x such that the expansion is valid (2 — 3x)^-2

b). Prove that__________.

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[OBJECTIVE]

Subject: Elementary Mathematics-I

Time Allowed: 10 Minutes

Maximum Marks: 10

NOTE: Attempt this Paper on this Question Sheet only. Please encircle the correct option. Division of marks is given in front of each question. This Paper will be collected back after expiry of time limit mentioned above.

 

Part-I Encircle the right answer, cutting and overwriting is not allowed. (10)

[SUBJECTIVE]

Subject: Elementary Mathematics-I

Time Allowed: 2 Hours 45 Minutes

Maximum Marks: 50

NOTE: ATTEMPT THIS (SUBJECTIVE) ON THE SEPARATE ANSWER SHEET PROVIDED.

 

Part-II Give short answers, Each answer carries equal marks. (20)