Level 1
Geometry MCQs set 2 for HBL / MCB / ABL Officer (IBA) Mathematics — 20 solved questions.
Q1. The angles of a triangle are (x-35), (x-25), and (x/2-10). Find x. Geometric Measurement
Answer: 100
Explanation: The correct value is 100. Apply the formula or arithmetic step shown in the question and
Q2. The length of a rectangular increased by 10% and its breadth is decreased by 10 %. Then the area of the new rectangle is ______?
Answer: Decreased by 1%
Explanation: New area = (1.10L)×(0.90B) = 0.99LB, which is 1% less than the original area.
Q3. Find the area of circle whose radius is 7m?
Answer: 154 sq m
Explanation: Area = πr² = (22/7)×7² = 22×7 = 154 sq m. Show the calculation clearly when solving similar quantitative items.
Q4. If the radius of the sphere is doubled then it's volume increases by what factor?
Answer: 8
Explanation: Volume of sphere ∝ r³; if r doubles, volume increases by 2³ = 8 times.
Q5. The diagonals of a rhombus are 15 cm and 20 cm. Find its area?
Answer: 150 sq cm
Explanation: Area of rhombus = (d₁×d₂)/2 = (15×20)/2 = 150 sq cm. Show the calculation clearly when solving similar quantitative items.
Q6. Which of the following sets of side lengths cannot form a right-angled triangle?
Answer: 9cm, 5cm, 7cm
Explanation: For a right triangle, a²+b² = c²; for 9,5,7: 81+25 = 106 ≠ 49, so these sides cannot form a right-angled triangle.
Q7. The perimeter of the circular field and the square field is equal. If the area of this square field is 12100m^2, the area of a circular field will be_________?
Answer: 15400 Sq.m
Explanation: Square area = 12100 m² → side = 110 m → perimeter = 440 m = 2πr → r = 70 m; circle area = (22/7)×70² = 15400 m².
Q8. A gardener increases the area of his rectangular garden by increasing its length by 40% and decreasing by 20%. The area of the new garden?
Answer: Has increase by 12%
Explanation: New area = 1.40L × 0.80B = 1.12LB, an increase of 12%.
Q9. If the radius of a circle is 1 cm, what is the area of the circle in mm^2?
Answer: 314 mm²
Explanation: The correct value is 314 mm². Apply the formula or arithmetic step shown in the question and
Q10. The plan for a rectangular area is drawn to a scale of 1:500. If the length and breadth in the plan is 30 cm and 20 cm, find the actual area. Geometric Measurement
Answer: 15000 m²
Explanation: Actual dimensions = 30×500 cm = 150 m and 20×500 cm = 100 m; area = 150×100 = 15000 m².
Q11. If the volume and surface area of a sphere is numerically the same then its radius is_________?
Answer: 3 units
Explanation: Setting volume = surface area: (4/3)πr³ = 4πr² → r/3 = 1 → r = 3 units.
Q12. A rectangular water tank is open at the top. Its capacity is 24Cu.m.It's length and breadth are 4m and 3m respectively. Ignoring the thickness of the material used for building the tank the total cost of painting the inner and outer surface of the tank at Rs.
Answer: Rs0.80
Explanation: Tank height = 24 ÷ (4 × 3) = 2 m; inner + outer surface area (open top) = 2 × [2(4+3)×2 + 4×3] = 2 × (56 + 12) = 136 sq m; at the given rate the total cost is Rs. 0.80 per the scaled options.
Q13. A metal sheet 27 cm long 8cm broad and 1 cm thick is melted into a cube. The difference between the surface areas of two solids is__________?
Answer: 286 cm²
Explanation: Volume of sheet = 27 × 8 × 1 = 216 cm³, giving a cube of side 6 cm; surface area of sheet = 2(27×8 + 27×1 + 8×1) = 502 cm², cube SA = 216 cm², difference = 286 cm².
Q14. A rectangle measuring 8cm on length and its diagonals measures 10cm what is the perimeter of the rectangle?
Answer: 28cm
Explanation: Using the Pythagorean theorem, width = √(10² − 8²) = 6 cm, so perimeter = 2×(8+6) = 28 cm.
Q15. A rectangular lawn 80 meters by 60 meters has two roads, each 10 m wide, running through the middle of it, one parallel to the length and the other parallel to the breadth. Find the cost of gravelling the roads at Rs. 30 per square meter.
Answer: Rs. 39000
Explanation: The correct value is Rs. 39000. Apply the formula or arithmetic step shown in the question and
Q16. If the side of a square is increased by 25%, then its area is increased by_________?
Answer: 56.25%
Explanation: New side = 1.25s, new area = 1.5625s²; percentage increase = (1.5625 − 1) × 100 = 56.25%.
Q17. The area of a square field is 6050 Sq.m.The length of it diagonal is_________?
Answer: 110m
Explanation: For a square of area A, diagonal = √(2A); √(2 × 6050) = √12100 = 110 m.
Q18. If the area of circle is 616 sq cm then its circumference?
Answer: 88 cm^2
Explanation: Area = πr² = 616 gives r = 14 cm (using π = 22/7); circumference = 2 × 22/7 × 14 = 88 cm.
Q19. If the height of a triangle is decreased by 40% and its base is increased by 40% what will be the effect on its area?
Answer: 16% Decrease
Explanation: New area = 0.6h × 1.4b = 0.84bh; the area decreases by 16%.
Q20. There are two circles of different radii. The area of a square is 196 sq.cm, whose side is half the radius of the larger circle. The radius of the smaller circle is three-seventh that of the larger circle. What is the circumference of the smaller circle?
Answer: 24 π cm
Explanation: Side of square = √196 = 14 cm = half the radius of larger circle, so radius = 28 cm. Smaller circle radius = 3/7 × 28 = 12 cm. Circumference = 2π × 12 = 24π cm.