HBL / MCB / ABL Officer (IBA) Mathematics Algebra — Set 2

1. Question 1

   Q1. Solve: (√2 - 1/√2)².

   • A) 1
   • B) 0.5
   • C) 0.25
   • D) 0.125

   Answer: 0.5

   Explanation: (√2 − 1/√2)² = (1/√2)² = 1/2 = 0.5, since √2 − 1/√2 = (2−1)/√2 = 1/√2.

2. Question 2

   Q2. If 2x + 7 = 19, what is the value of x?

   • A) 7
   • B) 6
   • C) 8
   • D) 10

   Answer: 6

   Explanation: Subtracting 7 from both sides gives 2x = 12, so x = 6.

3. Question 3

   Q3. Simplify the expression: (x²-4x+4) / (x-2) - (x²-6x+9) / (x-3). Algebra

   • A) 2x+5/x-3
   • B) 1
   • C) x-3
   • D) 2x+5

   Answer: 1

   Explanation: (x²−4x+4)/(x−2) = (x−2)²/(x−2) = x−2, and (x²−6x+9)/(x−3) = x−3. Their difference = (x−2)−(x−3) = 1.

4. Question 4

   Q4. I. x² + 5x + 6 = 0, II. y² + 9y +14 = 0 to solve both the equations to find the values of x and y?

   • A) If x < y
   • B) If x > y
   • C) If x ≤ y
   • D) If x = y or the relationship between x and y cannot be established.

   Answer: If x = y or the relationship between x and y cannot be established.

   Explanation: Equation I gives x = −2 or −3; Equation II gives y = −2 or −7; since x can be greater than, equal to, or less than y depending on which roots are chosen, the relationship cannot be established.

5. Question 5

   Q5. I. x² + 3x - 18 = 0, II. y² + y - 30 = 0 to solve both the equations to find the values of x and y?

   • A) If x < y
   • B) If x > y
   • C) If x ≤ y
   • D) If x = y or the relationship between x and y cannot be established.

   Answer: If x = y or the relationship between x and y cannot be established.

   Explanation: Equation I gives x = −6 or 3; equation II gives y = −6 or 5; depending on the values chosen, x can be less than, equal to, or greater than y, so no fixed relationship exists.

6. Question 6

   Q6. Find the roots of the quadratic equation: x² + 2x - 15 = 0?

   • A) -5, 3
   • B) 3, 5
   • C) -3, 5
   • D) -3, -5

   Answer: -5, 3

   Explanation: Factoring x² + 2x − 15 = (x+5)(x−3) = 0 gives roots x = −5 and x = 3.

7. Question 7

   Q7. Simplify the expression: 5 + 2 × 6 ÷ (3 × 2). BODMAS

   • A) 9
   • B) 13
   • C) 7
   • D) 5

   Answer: 7

   Explanation: Following BODMAS: division first gives 6÷(3×2) = 1; then 2×1 = 2; finally 5+2 = 7.

8. Question 8

   Q8. Find the value of X if 3889 + 12.952 - X = 3854.402.

   • A) 44.95
   • B) 47.55
   • C) 50.95
   • D) None of these

   Answer: 47.55

   Explanation: The correct value is 47.55. Apply the formula or arithmetic step shown in the question and

9. Question 9

   Q9. If 7x - 1 = 4x + 8, what is the value of x?

   • A) 3
   • B) 4
   • C) 1
   • D) None of these

   Answer: 3

   Explanation: The correct value is 3. Apply the formula or arithmetic step shown in the question and

10. Question 10

    Q10. Solve: √169

    • A) 520
    • B) 169
    • C) 28561
    • D) 13

    Answer: 13

    Explanation: √169 = 13, since 13² = 169. 13 is correct because it matches what the question requires. Show the calculation clearly when solving similar quantitative items.

11. Question 11

    Q11. If 4X + 13 = 7 - 2X, what is the value of X?

    • A) 1
    • B) -1
    • C) 3
    • D) -3

    Answer: -1

    Explanation: 4X + 13 = 7 − 2X → 6X = −6 → X = −1.

12. Question 12

    Q12. The equations of two perpendicular lines in the xy-plane are y = (a/b)x + c and y = (d/e)x + f, where a, b, c, d, e, and f are constants. If a/b > 1, which of the following must be true?

    • A) d/e < -1
    • B) #NAME?
    • C) 0 < d/e < 1
    • D) d/e > 1

    Answer: #NAME?

    Explanation: Perpendicular lines have slopes whose product is −1; if a/b > 1, then d/e = −b/a, which lies strictly between −1 and 0.

13. Question 13

    Q13. Given that 543 x 21 = 11403. Find the value of: 1140.3 ÷ 5.43

    • A) 210
    • B) 150
    • C) 120
    • D) 200

    Answer: 210

    Explanation: Since 543 × 21 = 11403, then 1140.3 ÷ 5.43 = (11403/10) ÷ (543/100) = 11403×100/(10×543) = 210.

14. Question 14

    Q14. The value of an article is Rs. 12,000. Each year it depreciates by 5%. What will the value of the article be after 4 years?

    • A) Rs. 10870
    • B) Rs. 9774
    • C) Rs. 8990
    • D) Rs. 9765

    Answer: Rs. 9774

    Explanation: Value after 4 years = 12000 × (0.95)⁴ = 12000 × 0.81451 ≈ Rs. 9774.

15. Question 15

    Q15. The value of a plant depreciates by 10 % annually. If the present value of the plant is Rs. 100000, then what will be its value after 2 years?

    • A) Rs. 8000
    • B) Rs10,000
    • C) Rs. 18000
    • D) Rs. 81000

    Answer: Rs. 81000

    Explanation: Annual depreciation of 10% means value multiplies by 0.9 each year; after 2 years: 100000 × 0.81 = Rs. 81000.

16. Question 16

    Q16. I. x² - x - 42 = 0, II. y² - 17y + 72 = 0 to solve both the equations to find the values of x and y?

    • A) If x < y
    • B) If x > y
    • C) If x ≤ y
    • D) If x ≥ y

    Answer: If x < y

    Explanation: Solving: x = 7 or x = −6; y = 8 or 9. In all cases x < y.

17. Question 17

    Q17. If x = 3 + √8, what is the value of x² + 1/x²?

    • A) 32
    • B) 34
    • C) 36
    • D) None of these

    Answer: 34

    Explanation: The correct value is 34. Apply the formula or arithmetic step shown in the question and

18. Question 18

    Q18. What is the value of x in the equation 3x - 15 - 6 = 0?

    • A) 6
    • B) 7
    • C) 8
    • D) 9

    Answer: 7

    Explanation: Solving 3x − 15 − 6 = 0: 3x = 21, so x = 7.

19. Question 19

    Q19. One root of the quadratic equation x² - 12x + a = 0, is thrice the other. Find the value of a?

    • A) 29
    • B) 27
    • C) 28
    • D) 7

    Answer: 27

    Explanation: If roots are r and 3r, sum = 4r = 12 so r = 3; product = 3r² = 3×9 = 27 = a.

20. Question 20

    Q20. The difference between three times a number and four more than two times the number can be represented by which algebraic expression?

    • A) x - 4
    • B) x - 5
    • C) x- 6
    • D) x - 7

    Answer: x - 4

    Explanation: Three times a number minus (two times the number plus 4) = 3x − 2x − 4 = x − 4.