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Question Bank

International Mathematics Olympiad Class 10 Exam Level-1 - English

Duration: 60 · Questions: 50 · Max Marks: 60 · Language: 1

View International Mathematics Olympiad (IMO) Class 10 2026 Exam Page

Logical Reasoning

1
Find the next term: ○, △, □, ○, △, ?
  1. A.○
  2. B.△
  3. C.□
  4. D.◇
2
Find the next term: ▲, ▼, ▲, ▼, ▲, ?
  1. A.▲
  2. B.■
  3. C.▼
  4. D.●
3
Find the next figure: ■, □, ■, □, ■, ?
  1. A.■
  2. B.□
  3. C.△
  4. D.○
4
Complete the pattern: ○, ○○, ○○○, ○○○○, ?
  1. A.○○○○○
  2. B.○○○○
  3. C.○○○
  4. D.○○
5
Which comes next? △, □, pentagon, hexagon, ?
  1. A.Triangle
  2. B.Circle
  3. C.Heptagon
  4. D.Square
6
Find the odd one out.
  1. A.Triangle
  2. B.Square
  3. C.Rectangle
  4. D.Circle
7
Find the odd one out.
  1. A.■
  2. B.□
  3. C.●
  4. D.▲
8
Which shape has the greatest number of sides?
  1. A.Hexagon
  2. B.Pentagon
  3. C.Triangle
  4. D.Quadrilateral
9
If ▲ becomes ▼ after rotation, the figure has been rotated through:
  1. A.45°
  2. B.180°
  3. C.90°
  4. D.360°
10
If → is rotated 90° anticlockwise, it becomes:
  1. A.↓
  2. B.↑
  3. C.←
  4. D.→
11
If ↑ is rotated 90° clockwise, it becomes:
  1. A.→
  2. B.←
  3. C.↓
  4. D.↑
12
If ← is rotated through 180°, it becomes:
  1. A.→
  2. B.↓
  3. C.↑
  4. D.←
13
Find the next direction: ↑, →, ↓, ←, ↑, ?
  1. A.←
  2. B.→
  3. C.↓
  4. D.↑
14
Find the next direction: →, ↓, ←, ↑, →
  1. A.↑
  2. B.↓
  3. C.←
  4. D.→
15
Complete the sequence: ↑, ↓, ↑, ↓, ↑, ?
  1. A.←
  2. B.→
  3. C.↓
  4. D.↑

Mathematical Reasoning

1
The HCF of 96 and 404 is:
  1. A.4
  2. B.2
  3. C.8
  4. D.12
2
The LCM of 12, 15 and 20 is:
  1. A.30
  2. B.60
  3. C.45
  4. D.120
3
If HCF(a, b) = 6 and LCM(a, b) = 180, and a = 30, then b is:
  1. A.24
  2. B.36
  3. C.30
  4. D.42
4
Which of the following is irrational?
  1. A.√49
  2. B.0.25
  3. C.√5
  4. D.7/11
5
The decimal expansion of 13/40 terminates after:
  1. A.1 decimal place
  2. B.2 decimal places
  3. C.3 decimal places
  4. D.4 decimal places
6
Which fraction has a terminating decimal expansion?
  1. A.7/12
  2. B.11/15
  3. C.17/21
  4. D.13/40
7
According to Euclid's division lemma, for positive integers a and b, we can write:
  1. A.a = bq − r
  2. B.a = br + q
  3. C.a = bq + r, where 0 ≤ r < b
  4. D.a = q + r
8
The prime factorisation of 360 is:
  1. A.2² × 3² × 5
  2. B.2⁴ × 3 × 5
  3. C.2³ × 3 × 5²
  4. D.2³ × 3² × 5
9
The HCF of 144 and 180 is:
  1. A.12
  2. B.36
  3. C.24
  4. D.18
10
The LCM of 18 and 24 is:
  1. A.72
  2. B.48
  3. C.36
  4. D.96
11
If p is a prime number, then √p is:
  1. A.Always rational
  2. B.Always irrational
  3. C.Always an integer
  4. D.Sometimes zero
12
The product of HCF and LCM of two positive integers equals:
  1. A.Their product
  2. B.Their difference
  3. C.Their sum
  4. D.Their quotient
13
Which number has a non-terminating recurring decimal expansion?
  1. A.7/12
  2. B.5/16
  3. C.3/8
  4. D.9/25
14
The decimal representation of 1/8 is:
  1. A.0.375
  2. B.0.25
  3. C.0.125
  4. D.0.625
15
Which of the following is rational?
  1. A.√2
  2. B.√3
  3. C.√7
  4. D.√16
16
The smallest number divisible by 12, 18 and 30 is:
  1. A.90
  2. B.180
  3. C.120
  4. D.360
17
If two positive integers are coprime, their HCF is:
  1. A.0
  2. B.1
  3. C.2
  4. D.Their product
18
The HCF of two consecutive positive integers is always:
  1. A.1
  2. B.0
  3. C.2
  4. D.Their difference
19
Which denominator, in lowest form, gives a terminating decimal expansion?
  1. A.40
  2. B.30
  3. C.21
  4. D.42
20
The value of √2 × √8 is:
  1. A.2
  2. B.16
  3. C.8
  4. D.4

Everyday Mathematics

1
A shopkeeper has 240 notebooks. He sells 35% of them. How many notebooks are left?
  1. A.144
  2. B.156
  3. C.160
  4. D.168
2
One number is 18 more than the other. What is the smaller number?
  1. A.33
  2. B.32
  3. C.30
  4. D.34
3
A father is three times as old as his son. Their total age is 56 years. What is the son's age?
  1. A.12 years
  2. B.18 years
  3. C.16 years
  4. D.14 years
4
A school has 720 students. If 5/8 of them are boys, how many girls are there?
  1. A.250
  2. B.260
  3. C.280
  4. D.270
5
A tank contains 480 litres of water. If 3/8 of the water is used, how much water remains?
  1. A.300 L
  2. B.280 L
  3. C.320 L
  4. D.340 L
6
What was the original number?
  1. A.360
  2. B.350
  3. C.340
  4. D.375
7
A rectangular field is 45 m long and 30 m wide. What is the cost of fencing it at ₹12 per metre?
  1. A.₹1,500
  2. B.₹2,160
  3. C.₹2,000
  4. D.₹1,800
8
If four of them are 20, 24, 32 and 36, find the fifth number.
  1. A.26
  2. B.28
  3. C.30
  4. D.32
9
A man spends 40% of his salary on household expenses and 20% on education. If he saves ₹18,000, what is his salary?
  1. A.₹36,000
  2. B.₹40,000
  3. C.₹45,000
  4. D.₹50,000
10
There are 48 students in a class. If 5/8 are present, how many are absent?
  1. A.18
  2. B.16
  3. C.20
  4. D.22

Achievers Section

1
If HCF(306, 657) = 9, then LCM(306, 657) is:
  1. A.21,324
  2. B.22,338
  3. C.23,256
  4. D.24,318
2
If a = 2³ × 3² × 5 and b = 2² × 3³ × 7, then HCF(a, b) is:
  1. A.36
  2. B.18
  3. C.72
  4. D.108
3
The decimal expansion of 13/1600 terminates after how many decimal places?
  1. A.4
  2. B.5
  3. C.6
  4. D.7
4
If x = 3 + 2√2, then 1/x equals:
  1. A.3 + 2√2
  2. B.3 − 2√2
  3. C.2√2 − 3
  4. D.1/(3 − 2√2)
5
Which of the following is irrational?
  1. A.√81 − √49
  2. B.√50 − √8
  3. C.√121/11
  4. D.√0.25