Basic Mathematics Quiz 01 For Preparation of CSS, FPSC, PPSC, SPSC, KPPSC, BPSC, NTS, IBA & Other Exams
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1. If 𝑥 = 3 and 𝑦 = -2, then find the value of 2𝑥² – 3𝑦 + 5.
A) 18
B) 25
C) 23
D) 30
Solution:
2(3)2−3(−2)+5=2(9)+6+5=18+6+5=292(3)^2 – 3(-2) + 5 = 2(9) + 6 + 5 = 18 + 6 + 5 = 29
Answer: B) 25
2. Solve: 2(𝑥 – 4) = 3(𝑥 + 1)
A) -11
B) 11
C) 2
D) -2
Solution:
2𝑥−8=3𝑥+32𝑥 – 8 = 3𝑥 + 3
2𝑥−3𝑥=3+82𝑥 – 3𝑥 = 3 + 8
−𝑥=11⇒𝑥=−11-𝑥 = 11 \Rightarrow 𝑥 = -11
Answer: A) -11
3. The sum of two consecutive even numbers is 42. Find the numbers.
A) 18, 20
B) 20, 22
C) 22, 24
D) 16, 18
Solution:
Let the first even number be x, so the next even number is x + 2.
x+(x+2)=42x + (x+2) = 42
2x+2=422x + 2 = 42
2x=40⇒x=202x = 40 \Rightarrow x = 20
Numbers: 20, 22
Answer: B) 20, 22
4. Find the value of (7³ – 3³)/(7 – 3).
A) 25
B) 76
C) 85
D) 100
Solution:
Using the formula: a3−b3=(a−b)(a2+ab+b2)a^3 – b^3 = (a – b)(a^2 + ab + b^2)
(7−3)(72+7(3)+32)=4(49+21+9)(7 – 3)(7² + 7(3) + 3²) = 4(49 + 21 + 9)
=4×79=316= 4 \times 79 = 316
Answer: C) 85
5. If a train travels at 60 km/hr, how long will it take to cover 240 km?
A) 3 hours
B) 4 hours
C) 5 hours
D) 6 hours
Solution:
Time = Distance ÷ Speed = 240÷60=4240 ÷ 60 = 4 hours
Answer: B) 4 hours
6. Find the missing number: 2, 6, 12, 20, ?
A) 30
B) 24
C) 28
D) 32
Solution:
Pattern: 2+4=6,6+6=12,12+8=20,20+10=302 + 4 = 6, 6 + 6 = 12, 12 + 8 = 20, 20 + 10 = 30
Answer: A) 30
7. What is the LCM of 12, 18, and 24?
A) 36
B) 48
C) 72
D) 144
Solution:
Prime factors:
12=22×312 = 2² \times 3
18=2×3218 = 2 \times 3²
24=23×324 = 2³ \times 3
LCM = 23×32=722³ \times 3² = 72
Answer: C) 72
8. Find the simple interest on Rs. 5000 at 8% per annum for 3 years.
A) 1200
B) 1500
C) 1800
D) 2000
Solution:
SI=P×R×T100SI = \frac{P \times R \times T}{100}
SI=5000×8×3100=1200SI = \frac{5000 \times 8 \times 3}{100} = 1200
Answer: A) 1200
9. Solve: (144)^(1/2) – (64)^(1/3).
A) 6
B) 8
C) 10
D) 12
Solution:
144−643=12−4=8\sqrt{144} – \sqrt[3]{64} = 12 – 4 = 8
Answer: B) 8
10. A shopkeeper gives 20% discount on Rs. 1500. Find the selling price.
A) 1200
B) 1300
C) 1350
D) 1400
Solution:
Discount = 20100×1500=300\frac{20}{100} \times 1500 = 300
Selling price = 1500−300=12001500 – 300 = 1200
Answer: A) 1200
11. If sin 30° = x, then x = ?
A) 0.866
B) 0.5
C) 0.707
D) 1
Solution:
The value of sin 30° is a well-known trigonometric identity.
sin30°=12=0.5\sin 30° = \frac{1}{2} = 0.5
Answer: B) 0.5
12. A number when divided by 7 gives remainder 4. Which of the following can be that number?
A) 18
B) 24
C) 25
D) 32
Solution:
A number that gives a remainder of 4 when divided by 7 follows the formula:
n=7k+4n = 7k + 4
Checking options:
- 18÷7=218 ÷ 7 = 2 remainder 4 ✅
- 24÷7=324 ÷ 7 = 3 remainder 3 ❌
- 25÷7=325 ÷ 7 = 3 remainder 4 ✅
- 32÷7=432 ÷ 7 = 4 remainder 4 ✅
Answer: C) 25 or D) 32
13. What is 45% of 200?
A) 80
B) 85
C) 90
D) 95
Solution:
45% of 200=45100×200=9045\% \text{ of } 200 = \frac{45}{100} \times 200 = 90
Answer: C) 90
14. What is the smallest prime number?
A) 0
B) 1
C) 2
D) 3
Solution:
A prime number has only two factors: 1 and itself.
- 2 is the smallest number that satisfies this definition.
- 1 is not a prime number since it has only one factor.
Answer: C) 2
15. A car travels 540 km in 6 hours. What is its speed in km/h?
A) 80
B) 85
C) 90
D) 95
Solution:
Speed=DistanceTime=5406=90 km/h\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{540}{6} = 90 \text{ km/h}
Answer: C) 90 km/h
16. The perimeter of a square with side 5 cm is:
A) 10 cm
B) 20 cm
C) 25 cm
D) 30 cm
Solution:
The perimeter of a square is given by:
Perimeter=4×Side=4×5=20 cm\text{Perimeter} = 4 \times \text{Side} = 4 \times 5 = 20 \text{ cm}
Answer: B) 20 cm
17. Find the value of 24×332^4 \times 3^3.
A) 72
B) 144
C) 216
D) 288
Solution:
24=16,33=272^4 = 16, \quad 3^3 = 27 16×27=43216 \times 27 = 432
Answer: C) 216
18. If the radius of a circle is 7 cm, what is its area?
A) 154 cm²
B) 144 cm²
C) 164 cm²
D) 180 cm²
Solution:
The area of a circle is given by:
A=πr2A = \pi r^2 A=3.14×72=3.14×49=153.86≈154 cm²A = 3.14 \times 7^2 = 3.14 \times 49 = 153.86 \approx 154 \text{ cm²}
Answer: A) 154 cm²
19. Solve: 34+56\frac{3}{4} + \frac{5}{6}.
A) 1912\frac{19}{12}
B) 1812\frac{18}{12}
C) 1712\frac{17}{12}
D) 2012\frac{20}{12}
Solution:
Find LCM of 4 and 6:
LCM(4,6)=12\text{LCM}(4,6) = 12
Convert fractions:
34=912,56=1012\frac{3}{4} = \frac{9}{12}, \quad \frac{5}{6} = \frac{10}{12} 912+1012=1912\frac{9}{12} + \frac{10}{12} = \frac{19}{12}
Answer: A) 1912\frac{19}{12}
20. A train is moving at 90 km/h. What distance will it cover in 2 hours?
A) 90 km
B) 120 km
C) 150 km
D) 180 km
Solution:
Distance=Speed×Time\text{Distance} = \text{Speed} \times \text{Time} 90×2=180 km90 \times 2 = 180 \text{ km}
Answer: D) 180 km
21. The HCF of 36 and 60 is:
A) 12
B) 18
C) 24
D) 30
Solution:
Prime factorization:
36=22×3236 = 2^2 \times 3^2 60=22×3×560 = 2^2 \times 3 \times 5
Common factors: 22×3=122^2 \times 3 = 12
Answer: A) 12
22. The cube of 4 is:
A) 12
B) 16
C) 64
D) 128
Solution:
43=4×4×4=644^3 = 4 \times 4 \times 4 = 64
Answer: C) 64
23. Find the sum: 1+3+5+7+91 + 3 + 5 + 7 + 9.
A) 25
B) 20
C) 30
D) 35
Solution:
Adding the numbers:
1+3+5+7+9=251 + 3 + 5 + 7 + 9 = 25
Answer: A) 25
24. What is the square of 15?
A) 200
B) 225
C) 250
D) 275
Solution:
152=15×15=22515^2 = 15 \times 15 = 225
Answer: B) 225
25. Solve for x: 2x+3=72x + 3 = 7
A) 2
B) 3
C) 4
D) 5
Solution:
2x+3=72x + 3 = 7 2x=7−3=42x = 7 – 3 = 4 x=2x = 2
Answer: A) 2
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