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CTET Maths MCQ with Answers, Paper 2 (Classes VI-VIII)
234 practice questions on Mathematics, Classes VI-VIII (Paper II) for CTET Paper II (Mathematics and Science), with answers; most also have an explanation or a worked solution. Try each one before you open its answer.
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Q.201
Which of the following is a perfect cube?
- A 1,125
- B 2,700
- C 3,375
- D 6,750
Show answer
Correct answer: (C) 3,375
3,375 = 3³ × 5³ = 15³. In 2,700 = 2² × 3³ × 5², 1,125 = 3² × 5³ and 6,750 = 2 × 3³ × 5³, some prime factor has a power that is not a multiple of 3.
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Q.202
Raju has q marbles. Ravi has 5 fewer than twice the number Raju has. How many marbles do they have together?
- A 2q − 5
- B q − 5
- C 3q − 5
- D 3q − 10
Show answer
Correct answer: (C) 3q − 5
Ravi has 2q − 5 marbles, so together they have q + (2q − 5) = 3q − 5. The answer 3q − 10 comes from wrongly reading Ravi's share as 2(q − 5).
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Q.203
If triangle ABC is congruent to triangle PQR, written ΔABC ≅ ΔPQR, which of the following must be true?
- A AB = QR
- B AC = PQ
- C Angle B = Angle R
- D BC = QR
Show answer
Correct answer: (D) BC = QR
The order of the letters gives the correspondence A ↔ P, B ↔ Q, C ↔ R. So side BC corresponds to QR, AB to PQ and AC to PR, and angle B equals angle Q.
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Q.204
Consider the statements: 1. The number 1 is neither prime nor composite. 2. The smallest composite number is 4. 3. The sum of any two prime numbers is even. Which of these are true?
- A 2 and 3 only
- B 1 and 2 only
- C 1 and 3 only
- D 1, 2 and 3
Show answer
Correct answer: (B) 1 and 2 only
1 has only one factor, so it is neither prime nor composite, and 4 is the smallest number with more than two factors. Statement 3 is false: 2 + 3 = 5 is odd.
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Q.205
Two villages have populations of 5,290 and 17,986. If each population is estimated to the nearest thousand, what is the estimated total population?
- A 24,000
- B 22,000
- C 23,300
- D 23,000
Show answer
Correct answer: (D) 23,000
5,290 rounds to 5,000 and 17,986 rounds to 18,000, so the estimate is 5,000 + 18,000 = 23,000. The exact total, 23,276, is close to it.
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Q.206
Seven points A, B, C, D, E, F and G are marked in that order on a straight line. How many different line segments have two of these points as their end points?
- A 6 segments
- B 7 segments
- C 20 segments
- D 21 segments
Show answer
Correct answer: (D) 21 segments
Each segment is fixed by choosing 2 of the 7 points, and AB is the same segment as BA. A has 6 partners, B has 5 new ones, and so on: 6 + 5 + 4 + 3 + 2 + 1 = 21.
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Q.207
The mean of 10 observations was found to be 32. Later it was noticed that one observation, 64, had been wrongly copied as 46. What is the correct mean?
- A 30.2
- B 32.18
- C 33.8
- D 50
Show answer
Correct answer: (C) 33.8
Wrong total = 10 × 32 = 320. Correct total = 320 − 46 + 64 = 338, so the correct mean = 338 ÷ 10 = 33.8.
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Q.208
The marks scored by six students in a test are 38, 45, 52, 47, 41 and 59. What is the mean of their marks?
- A 21
- B 46
- C 47
- D 56.4
Show answer
Correct answer: (C) 47
Sum = 38 + 45 + 52 + 47 + 41 + 59 = 282, and mean = 282 ÷ 6 = 47. (46 is the median and 21 is the range.)
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Q.209
How many faces, edges and vertices does a triangular prism have?
- A 5 faces, 9 edges, 6 vertices
- B 6 faces, 9 edges, 5 vertices
- C 5 faces, 6 edges, 9 vertices
- D 3 faces, 9 edges, 6 vertices
Show answer
Correct answer: (A) 5 faces, 9 edges, 6 vertices
It has 2 triangular and 3 rectangular faces (5 faces), 3 + 3 edges on the two triangles plus 3 joining edges (9 edges), and 3 + 3 = 6 vertices. Check: 5 + 6 − 9 = 2.
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Q.210
x and y are in direct proportion. When x = 14, y = 35. What is the value of y when x = 22?
- A 8.8
- B 22.3
- C 43
- D 55
Show answer
Correct answer: (D) 55
In direct proportion y/x stays the same: 35/14 = 2.5, so y = 2.5 × 22 = 55. (43 comes from wrongly adding 8 to both values.)
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Q.211
Factorise: xy + 3x + 2y + 6.
- A (x + 2)(y + 3)
- B (x + 3)(y + 2)
- C (x + 6)(y + 1)
- D (x + 1)(y + 6)
Show answer
Correct answer: (A) (x + 2)(y + 3)
Group the terms: x(y + 3) + 2(y + 3) = (x + 2)(y + 3). Check: (x + 2)(y + 3) = xy + 3x + 2y + 6.
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Q.212
A teacher has more than 24 pieces of chalk. Whether she makes bundles of 12, of 16 or of 24, exactly 7 pieces are left over each time. What is the least number of pieces she can have?
- A 31
- B 41
- C 48
- D 55
Show answer
Correct answer: (D) 55
The number minus 7 must be a common multiple of 12, 16 and 24, and the least one is their LCM, 48. So the number is 48 + 7 = 55; check: 55 = 4 × 12 + 7 = 3 × 16 + 7 = 2 × 24 + 7.
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Q.213
Which of the following pairs is NOT a pair of like terms?
- A −7pq and 3qp
- B 4x²y and −x²y
- C 5ab² and 5a²b
- D m and 9m
Show answer
Correct answer: (C) 5ab² and 5a²b
Like terms have the same variables with the same powers. In 5ab² the power of b is 2, while in 5a²b the power of a is 2, so they are unlike terms. pq and qp are the same product, so −7pq and 3qp are like terms.
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Q.214
An exterior angle of a triangle measures 118°, and one of its interior opposite angles measures 49°. What is the other interior opposite angle?
- A 49°
- B 62°
- C 69°
- D 167°
Show answer
Correct answer: (C) 69°
An exterior angle equals the sum of the two interior opposite angles, so the other angle is 118° − 49° = 69°. (The third angle of the triangle, next to the exterior angle, is 180° − 118° = 62°.)
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Q.215
In a parallelogram ABCD, angle A is three times angle B. What is the measure of angle C?
- A 45°
- B 60°
- C 120°
- D 135°
Show answer
Correct answer: (D) 135°
Adjacent angles of a parallelogram add up to 180°, so 3x + x = 180° and x = 45°. Angle A = 135°, and angle C, opposite to angle A, is also 135°.
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Q.216
What is the smaller angle between the hour hand and the minute hand of a clock at 3:30?
- A 60°
- B 75°
- C 90°
- D 105°
Show answer
Correct answer: (B) 75°
At 3:30 the minute hand points to 6, which is 180° from 12. The hour hand is halfway between 3 and 4, at 3.5 × 30° = 105° from 12, so the angle between the hands is 180° − 105° = 75°.
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Q.217
The greatest common factor of 12a²b and 18ab² is:
- A 3ab
- B 6ab
- C 6a²b²
- D 36a²b²
Show answer
Correct answer: (B) 6ab
The greatest common factor of 12 and 18 is 6, and the highest powers of a and b that divide both terms are a and b, so the answer is 6ab.
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Q.218
One number is 5 times another, and their difference is 132. What is the smaller number?
- A 22
- B 26.4
- C 165
- D 33
Show answer
Correct answer: (D) 33
If the smaller number is x, the larger is 5x and 5x − x = 4x = 132, so x = 33 (the larger is 165, and 165 − 33 = 132).
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Q.219
A cuboidal box open at the top is 40 cm long, 25 cm wide and 15 cm high. How much cardboard is needed to make it, ignoring overlaps?
- A 2950 cm²
- B 3950 cm²
- C 4950 cm²
- D 15000 cm²
Show answer
Correct answer: (A) 2950 cm²
Total surface area = 2(40 × 25 + 25 × 15 + 15 × 40) = 2(1000 + 375 + 600) = 3950 cm². Without the top of 40 × 25 = 1000 cm², the cardboard needed is 2950 cm².
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Q.220
Petrol costs ₹96.75 per litre. Sunita buys 12.4 litres. How much does she pay?
- A ₹1,189.70
- B ₹119.97
- C ₹11,997.00
- D ₹1,199.70
Show answer
Correct answer: (D) ₹1,199.70
9,675 × 124 = 11,99,700, and there are 2 + 1 = 3 decimal places, so 96.75 × 12.4 = 1,199.700, i.e. ₹1,199.70. Estimate check: about ₹100 × 12 = ₹1,200.
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Q.221
How many pieces, each 3/4 m long, can be cut from a ribbon 12 3/4 m long?
- A 9 pieces
- B 17 pieces
- C 16 pieces
- D 12 pieces
Show answer
Correct answer: (B) 17 pieces
12 3/4 ÷ 3/4 = 51/4 × 4/3 = 17 pieces. Multiplying instead of dividing gives 51/4 × 3/4 = 9 9/16, which is wrong.
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Q.222
A sum of ₹2.7 × 10¹² is to be shared equally among 1.5 × 10⁸ families. How much does each family get?
- A ₹1,80,000
- B ₹1,800
- C ₹18,000
- D ₹4.05 × 10²⁰
Show answer
Correct answer: (C) ₹18,000
(2.7 × 10¹²) ÷ (1.5 × 10⁸) = (2.7 ÷ 1.5) × 10¹²⁻⁸ = 1.8 × 10⁴ = ₹18,000. Multiplying the two numbers instead gives 4.05 × 10²⁰.
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Q.223
A rectangular lawn is 75 m long and 60 m wide. Two roads, each 4 m wide, run through the middle, one parallel to the length and the other parallel to the width. What is the cost of gravelling the roads at ₹ 12 per m²?
- A ₹ 6,288
- B ₹ 6,480
- C ₹ 6,672
- D ₹ 12,576
Show answer
Correct answer: (A) ₹ 6,288
Area of the roads = 75 × 4 + 60 × 4 − 4 × 4 = 300 + 240 − 16 = 524 m², since the 4 m × 4 m crossing is counted twice. Cost = 524 × ₹ 12 = ₹ 6,288.
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Q.224
A semicircular protractor has a diameter of 21 cm. What is its perimeter, that is, the curved edge plus the straight edge? (Take π = 22/7.)
- A 33 cm
- B 54 cm
- C 66 cm
- D 87 cm
Show answer
Correct answer: (B) 54 cm
Curved edge = half of π × d = 1/2 × 22/7 × 21 = 33 cm. Adding the straight edge, the perimeter = 33 + 21 = 54 cm.
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Q.225
What is the value of (−42) − (−17) − 8?
- A −17
- B −67
- C −33
- D 51
Show answer
Correct answer: (C) −33
Subtracting −17 means adding 17: −42 + 17 − 8 = −25 − 8 = −33. Treating − (−17) as −17 gives the wrong answer −67.
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Q.226
The product of two rational numbers is −35/72. If one of them is 7/18, what is the other?
- A −4/5
- B −5/4
- C −245/1296
- D −7/8
Show answer
Correct answer: (B) −5/4
Other number = (−35/72) ÷ (7/18) = (−35/72) × (18/7) = −5/4. Check: (−5/4) × (7/18) = −35/72. Multiplying instead of dividing gives −245/1296.
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Q.227
Simplify (2⁵ × 2⁻³) ÷ 2⁻⁴.
- A 1/4
- B 64
- C 4
- D 1/64
Show answer
Correct answer: (B) 64
2⁵ × 2⁻³ = 2⁵⁻³ = 2², and 2² ÷ 2⁻⁴ = 2²⁺⁴ = 2⁶ = 64. Subtracting 4 instead of −4 gives 2⁻² = 1/4.
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Q.228
A triangular plot of land has a base of 14 m and a corresponding height of 9 m. What is its area?
- A 23 m²
- B 46 m²
- C 63 m²
- D 126 m²
Show answer
Correct answer: (C) 63 m²
Area of a triangle = 1/2 × base × height = 1/2 × 14 × 9 = 63 m². (126 m² forgets the 1/2.)
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Q.229
Consider the following statements:
1. In 5x²y, the coefficient of x² is 5y.
2. 3x and 3x² are like terms.
3. An expression with only one term is called a monomial.
Which of these are correct?
- A 1 and 2 only
- B 1 and 3 only
- C 2 and 3 only
- D 1, 2 and 3
Show answer
Correct answer: (B) 1 and 3 only
Statement 1 is correct, since 5x²y = (5y) × x². Statement 2 is wrong because the powers of x differ, and statement 3 is the definition of a monomial.
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Q.230
The price of a scooter rose from ₹64,000 to ₹72,000. What is the percentage increase?
- A 8%
- B 11.1%
- C 12.5%
- D 112.5%
Show answer
Correct answer: (C) 12.5%
Increase = ₹8,000. Percentage increase = (8000 ÷ 64000) × 100 = 12.5%; it is always calculated on the original price (calculating on ₹72,000 gives 11.1%).
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Q.231
The wheel of a cart has a radius of 28 cm. How many revolutions will it make in covering 1.1 km? (Take π = 22/7.)
- A 62.5
- B 625
- C 1,250
- D 6,250
Show answer
Correct answer: (B) 625
Circumference = 2 × 22/7 × 28 = 176 cm, and 1.1 km = 110000 cm. Number of revolutions = 110000 ÷ 176 = 625.
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Q.232
Look at the pattern: 1 = 1, 1 + 3 = 4, 1 + 3 + 5 = 9, 1 + 3 + 5 + 7 = 16. If the pattern continues, the sum of the first n odd numbers is:
- A 2n − 1
- B 3n − 2
- C n(n + 1)
- D n²
Show answer
Correct answer: (D) n²
The sums 1, 4, 9, 16 are the square numbers 1², 2², 3², 4², so the sum of the first n odd numbers is n². (2n − 1 is only the nth odd number; 3n − 2 fits the first two sums but gives 7, not 9, for n = 3.)
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Q.233
Between which two consecutive integers does −13/5 lie on the number line?
- A −3 and −2
- B −2 and −1
- C 2 and 3
- D −4 and −3
Show answer
Correct answer: (A) −3 and −2
−13/5 = −2 3/5 = −2.6, which is to the left of −2 and to the right of −3. Ignoring the minus sign would wrongly place it between 2 and 3.
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Q.234
What is the compound interest on ₹12,000 for 2 years at 5% per annum, compounded annually?
- A ₹1,230
- B ₹1,200
- C ₹1,260
- D ₹13,230
Show answer
Correct answer: (A) ₹1,230
Interest for year 1 = 5% of 12000 = ₹600; for year 2 = 5% of 12600 = ₹630. CI = 600 + 630 = ₹1,230 (the amount is ₹13,230).
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How these questions were made
Authored by an AI assistant (Claude) from its own general knowledge of stable, well-established facts (no live lookup) - not reviewed by a subject-matter expert; verify against an official source before relying on any fact.