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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.51
A cylindrical pillar has a diameter of 50 cm and a height of 3.5 m. What is the cost of painting its curved surface at ₹ 12.50 per m²? (Take π = 22/7.)
- A ₹ 34.38
- B ₹ 68.75
- C ₹ 137.50
- D ₹ 6,875
Show answer
Correct answer: (B) ₹ 68.75
Radius = 0.25 m. Curved surface area = 2πrh = 2 × 22/7 × 0.25 × 3.5 = 5.5 m². Cost = 5.5 × ₹ 12.50 = ₹ 68.75.
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Q.52
A tailor has 1 km of cloth. Each shirt needs 2 m 15 cm of cloth. How many shirts can be made, and how much cloth is left over?
- A 465 shirts, 25 cm left
- B 466 shirts, nothing left
- C 46 shirts, 1 m 10 cm left
- D 465 shirts, 2 m 5 cm left
Show answer
Correct answer: (A) 465 shirts, 25 cm left
1 km = 1,00,000 cm and 2 m 15 cm = 215 cm. 1,00,000 ÷ 215 gives quotient 465 and remainder 25, since 465 × 215 = 99,975.
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Q.53
A school buys 578 chairs at ₹161 per chair. If each number is rounded to its greatest place, what is the estimated cost?
- A ₹92,800
- B ₹1,00,000
- C ₹60,000
- D ₹1,20,000
Show answer
Correct answer: (D) ₹1,20,000
578 rounds to 600 and 161 rounds to 200 (both to the nearest hundred), so the estimate is 600 × 200 = ₹1,20,000. Rounding 161 down to 100 or 578 down to 500 is a rounding error, and 580 × 160 rounds only to tens.
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Q.54
A saree with a marked price of ₹2,400 is sold at a discount of 15%. What is its selling price?
- A ₹2,040
- B ₹360
- C ₹2,385
- D ₹2,760
Show answer
Correct answer: (A) ₹2,040
Discount = 15% of 2400 = ₹360, so selling price = 2400 − 360 = ₹2,040. The discount is always calculated on the marked price.
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Q.55
A bag contains 5 red, 7 blue and 3 green balls of the same size. One ball is taken out without looking. What is the probability that it is NOT blue?
- A 8/15
- B 7/15
- C 1/3
- D 8/7
Show answer
Correct answer: (A) 8/15
There are 5 + 7 + 3 = 15 equally likely outcomes, and 5 + 3 = 8 balls are not blue. Probability = 8/15.
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Q.56
Which of the following can be the lengths of the sides of a right-angled triangle?
- A 9 cm, 40 cm, 41 cm
- B 6 cm, 8 cm, 12 cm
- C 5 cm, 11 cm, 13 cm
- D 7 cm, 23 cm, 25 cm
Show answer
Correct answer: (A) 9 cm, 40 cm, 41 cm
9² + 40² = 81 + 1600 = 1681 = 41², so these sides satisfy the Pythagoras property. The others fail: 36 + 64 = 100 ≠ 144, 25 + 121 = 146 ≠ 169 and 49 + 529 = 578 ≠ 625.
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Q.57
A pyramid has a base that is an octagon (8 sides). How many edges does the pyramid have?
- A 8 edges
- B 9 edges
- C 16 edges
- D 24 edges
Show answer
Correct answer: (C) 16 edges
There are 8 edges around the base and 8 slant edges from the base vertices to the top vertex, so 8 + 8 = 16. (It has 9 faces and 9 vertices; 9 + 9 − 16 = 2.)
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Q.58
What is the smallest number by which 2,925 must be multiplied to make it a perfect square?
- A 13
- B 3
- C 5
- D 39
Show answer
Correct answer: (A) 13
2,925 = 3² × 5² × 13. Only 13 is without a pair, so multiplying by 13 gives 3² × 5² × 13² = 38,025 = 195².
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Q.59
Consider the following statements about rays. 1. A ray has one end point and goes on endlessly in one direction. 2. Ray AB (starting at A) and ray BA (starting at B) are the same ray. Which of the statements is/are correct?
- A Only 1
- B Only 2
- C Both 1 and 2
- D Neither 1 nor 2
Show answer
Correct answer: (A) Only 1
A ray starts at its end point and extends without end in one direction, so 1 is correct. Ray AB starts at A and passes through B, while ray BA starts at B and goes the opposite way, so they are different rays and 2 is wrong.
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Q.60
How many lines of symmetry does a regular hexagon have, and what is its order of rotational symmetry?
- A 6 lines; order 6
- B 3 lines; order 3
- C 6 lines; order 3
- D 3 lines; order 6
Show answer
Correct answer: (A) 6 lines; order 6
A regular hexagon has 3 lines through opposite vertices and 3 through the midpoints of opposite sides, 6 in all. It looks the same after every turn of 360° ÷ 6 = 60°, so its order of rotational symmetry is 6.
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Q.61
The sum of three consecutive odd numbers is 147. The smallest of them is:
- A 45
- B 47
- C 48
- D 49
Show answer
Correct answer: (B) 47
Let the numbers be n, n + 2 and n + 4. Then 3n + 6 = 147, so n = 47; the numbers 47, 49 and 51 add to 147.
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Q.62
For all values of a and b, (a + b)² − (a − b)² is equal to:
- A 2b²
- B 2ab
- C 4ab
- D 2a² + 2b²
Show answer
Correct answer: (C) 4ab
(a² + 2ab + b²) − (a² − 2ab + b²) = 4ab. Check with a = 3 and b = 1: 16 − 4 = 12 = 4 × 3 × 1.
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Q.63
Which of the following conditions does NOT guarantee that two triangles are congruent?
- A Two sides and the angle included between them are equal
- B Two angles and the side included between them are equal
- C In right triangles, the hypotenuse and one side are equal
- D Two sides and an angle that is not between them are equal
Show answer
Correct answer: (D) Two sides and an angle that is not between them are equal
SAS, ASA and RHS are congruence criteria. Two sides with a non-included angle (SSA) can give two different triangles, so it does not guarantee congruence; RHS is the special case where that angle is a right angle.
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Q.64
Using the identity (x + a)(x + b) = x² + (a + b)x + ab with x = 100, the value of 104 × 97 is:
- A 9988
- B 10088
- C 10112
- D 10688
Show answer
Correct answer: (B) 10088
104 × 97 = (100 + 4)(100 − 3) = 10000 + (4 − 3) × 100 + 4 × (−3) = 10000 + 100 − 12 = 10088.
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Q.65
Factorise: x² + 9x + 20.
- A (x + 2)(x + 10)
- B (x + 1)(x + 20)
- C (x + 3)(x + 6)
- D (x + 4)(x + 5)
Show answer
Correct answer: (D) (x + 4)(x + 5)
Find two numbers whose product is 20 and whose sum is 9: they are 4 and 5. So x² + 9x + 20 = (x + 4)(x + 5).
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Q.66
Is it possible to have a regular polygon each of whose exterior angles measures 22°?
- A Yes, it would have 16 sides
- B Yes, it would have 18 sides
- C No, because an exterior angle cannot be less than 30°
- D No, because 360 is not exactly divisible by 22
Show answer
Correct answer: (D) No, because 360 is not exactly divisible by 22
The number of sides would be 360 ÷ 22 = 16.36..., which is not a whole number, so no such polygon exists. Exterior angles smaller than 30° are possible, for example 18° for 20 sides.
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Q.67
Consider the following statements. 1. Two angles that form a linear pair are supplementary. 2. Any two supplementary angles form a linear pair. 3. When two lines intersect, the vertically opposite angles are equal. Which of the statements are correct?
- A 1 and 2 only
- B 2 and 3 only
- C 1, 2 and 3
- D 1 and 3 only
Show answer
Correct answer: (D) 1 and 3 only
A linear pair is two adjacent angles whose non-common arms form a line, so they add up to 180°. Supplementary angles need not be adjacent (for example 110° and 70° drawn apart), so 2 is false; 3 is true.
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Q.68
A can holds 2 3/4 litres of milk. Then 1 5/6 litres more is poured in, and 2 1/3 litres is used to make tea. How much milk is left in the can?
- A 1 1/4 litres
- B 2 1/4 litres
- C 2 7/12 litres
- D 3 1/4 litres
Show answer
Correct answer: (B) 2 1/4 litres
With the common denominator 12: 2 9/12 + 1 10/12 − 2 4/12 = 1 15/12 = 2 3/12 = 2 1/4 litres. Forgetting to carry the extra whole from 15/12 gives 1 1/4.
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Q.69
Which of the following is NOT an identity (true for all values of the variables)?
- A (a + b)² = a² + 2ab + b²
- B (x + a)(x + b) = x² + (a + b)x + ab
- C a² − b² = (a + b)(a − b)
- D (a − b)² = a² − b²
Show answer
Correct answer: (D) (a − b)² = a² − b²
(a − b)² = a² − 2ab + b², not a² − b². For example, with a = 5 and b = 3, (5 − 3)² = 4 but 25 − 9 = 16.
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Q.70
Rohit has 126 red and 168 green marbles. He packs all of them into the greatest possible number of identical boxes, each box having the same number of red and the same number of green marbles. Which is correct?
- A 14 boxes, each with 9 red and 12 green
- B 21 boxes, each with 6 red and 8 green
- C 42 boxes, each with 3 red and 4 green
- D 42 boxes, each with 4 red and 3 green
Show answer
Correct answer: (C) 42 boxes, each with 3 red and 4 green
The greatest number of boxes is HCF(126, 168) = 42, since 126 = 2 × 3² × 7 and 168 = 2³ × 3 × 7. Each box then has 126 ÷ 42 = 3 red and 168 ÷ 42 = 4 green marbles.
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Q.71
(2x + 3)(x − 5) equals:
- A 2x² − 15
- B 2x² − 7x − 15
- C 2x² − 13x − 15
- D 2x² − 7x − 2
Show answer
Correct answer: (B) 2x² − 7x − 15
Multiply each term of the first bracket by each term of the second: 2x² − 10x + 3x − 15 = 2x² − 7x − 15.
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Q.72
A gardener has 1,500 plants. He wants to plant them in rows so that the number of rows equals the number of plants in each row, with no plant left over. What is the least number of extra plants he must buy?
- A 56 plants
- B 21 plants
- C 39 plants
- D 77 plants
Show answer
Correct answer: (B) 21 plants
38² = 1,444 < 1,500 < 1,521 = 39², so the next perfect square is 1,521 and he needs 1,521 − 1,500 = 21 more plants (39 rows of 39). 56 is the number he would have to remove to use 38 rows.
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Q.73
A machine bought for ₹50,000 depreciates (loses value) at 10% per annum. What will its value be after 2 years?
- A ₹40,000
- B ₹41,000
- C ₹45,000
- D ₹40,500
Show answer
Correct answer: (D) ₹40,500
Value after 1 year = 50000 × 0.9 = ₹45,000; after 2 years = 45000 × 0.9 = ₹40,500. Each year the 10% is taken on the reduced value, not on ₹50,000.
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Q.74
Which Roman numeral represents 1994?
- A MDCCCCXCIV
- B MCMXCIV
- C MCMLXLIV
- D MCMXCVI
Show answer
Correct answer: (B) MCMXCIV
1994 = 1000 + 900 + 90 + 4 = M + CM + XC + IV = MCMXCIV. A symbol is not repeated more than three times (so DCCCC is wrong), and MCMXCVI stands for 1996.
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Q.75
Each exterior angle of a regular polygon measures 24°. How many sides does the polygon have?
- A 13 sides
- B 15 sides
- C 17 sides
- D 30 sides
Show answer
Correct answer: (B) 15 sides
The exterior angles of any polygon add up to 360°, so n = 360° ÷ 24° = 15. Check: each interior angle is 180° − 24° = 156°, and 15 × 156° = 2340° = (15 − 2) × 180°.
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Q.76
The sum of two rational numbers is −5/8. If one of them is 7/12, what is the other?
- A −1/24
- B −29/24
- C 1/10
- D −12/20
Show answer
Correct answer: (B) −29/24
Other number = −5/8 − 7/12 = −15/24 − 14/24 = −29/24. Adding 7/12 instead of subtracting it gives −1/24, and adding numerators and denominators separately (as in 1/10) is never valid.
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Q.77
What is the value of 0.6 × 0.05 × 2.4?
- A 0.072
- B 0.72
- C 0.0072
- D 7.2
Show answer
Correct answer: (A) 0.072
6 × 5 × 24 = 720, and the factors have 1 + 2 + 1 = 4 decimal places in all, so the product is 0.0720 = 0.072.
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Q.78
If 15 notebooks cost ₹435, how much will 22 notebooks cost at the same rate?
- A ₹442
- B ₹580
- C ₹609
- D ₹638
Show answer
Correct answer: (D) ₹638
Unitary method: 1 notebook costs 435 ÷ 15 = ₹29, so 22 notebooks cost 22 × 29 = ₹638.
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Q.79
In an election between two candidates, the winner got 58% of the valid votes and won by 4,320 votes. How many valid votes were cast?
- A 7,448
- B 10,286
- C 54,000
- D 27,000
Show answer
Correct answer: (D) 27,000
The loser got 42%, so the winning margin is 58% − 42% = 16% of the valid votes. Since 16% = 4320, total = 4320 × 100 ÷ 16 = 27,000.
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Q.80
Three bells ring at intervals of 9, 12 and 15 minutes. If they ring together at 8:00 a.m., at what time will they next ring together?
- A 11:00 a.m.
- B 9:00 a.m.
- C 8:36 a.m.
- D 9:48 a.m.
Show answer
Correct answer: (A) 11:00 a.m.
They ring together again after LCM(9, 12, 15) minutes. 9 = 3², 12 = 2² × 3 and 15 = 3 × 5, so the LCM = 2² × 3² × 5 = 180 minutes = 3 hours, giving 11:00 a.m.
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Q.81
The ratio of boys to girls in a school is 7 : 5. There are 84 more boys than girls. How many students are there in the school?
- A 294
- B 588
- C 1008
- D 504
Show answer
Correct answer: (D) 504
The difference of 7 − 5 = 2 parts is 84, so one part is 42. Total = 12 parts = 12 × 42 = 504 (294 boys and 210 girls).
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Q.82
The floor of a room is 6.5 m long and 4 m wide. How many square tiles of side 25 cm are needed to cover it completely?
- A 42
- B 104
- C 208
- D 416
Show answer
Correct answer: (D) 416
Along the length 650 ÷ 25 = 26 tiles fit and along the width 400 ÷ 25 = 16, so 26 × 16 = 416 tiles. Check by area: 260000 cm² ÷ 625 cm² = 416 (104 comes from dividing 26 m² by 0.25 without squaring).
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Q.83
The 6-digit number 523x48, where x is a missing digit, is divisible by 9. What is the value of x?
- A x = 4
- B x = 2
- C x = 5
- D x = 8
Show answer
Correct answer: (C) x = 5
Digit sum = 5 + 2 + 3 + x + 4 + 8 = 22 + x, which must be a multiple of 9. Only x = 5 works (sum 27); x = 2, 4 and 8 give 24, 26 and 30, which are not multiples of 9.
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Q.84
The parallel sides of a trapezium are 20 cm and 14 cm, and the distance between them is 11 cm. What is its area?
- A 154 cm²
- B 187 cm²
- C 220 cm²
- D 374 cm²
Show answer
Correct answer: (B) 187 cm²
Area of a trapezium = 1/2 × (sum of parallel sides) × distance between them = 1/2 × (20 + 14) × 11 = 17 × 11 = 187 cm².
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Q.85
In an isosceles triangle, the angle between the two equal sides is three times each of the other two angles. What is the angle between the equal sides?
- A 36°
- B 108°
- C 120°
- D 135°
Show answer
Correct answer: (B) 108°
Let each base angle be x. Then x + x + 3x = 180°, so x = 36° and the angle between the equal sides is 3 × 36° = 108°. (135° comes from forgetting one base angle.)
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Q.86
A lift is 5 m below ground level. It goes up 9 m and then comes down 13 m. Where is the lift now?
- A 17 m above ground level
- B 1 m below ground level
- C 27 m below ground level
- D 9 m below ground level
Show answer
Correct answer: (D) 9 m below ground level
Taking upward movement as positive: −5 + 9 − 13 = −9, that is, 9 m below ground level.
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Q.87
Reena is facing east. She turns clockwise through three right angles. Which direction is she facing now?
- A North
- B South
- C West
- D East
Show answer
Correct answer: (A) North
Turning clockwise from east, one right angle brings her to south, two right angles to west and three right angles to north.
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Q.88
What is the median of the data 23, 17, 31, 12, 28, 19, 35, 26?
- A 20
- B 23
- C 24.5
- D 26
Show answer
Correct answer: (C) 24.5
Arranged in order: 12, 17, 19, 23, 26, 28, 31, 35. With 8 values, the median is the mean of the 4th and 5th values: (23 + 26) ÷ 2 = 24.5.
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Q.89
A square park has an area of 1764 m². What will it cost to fence it all around at ₹ 35 per metre?
- A ₹ 1,470
- B ₹ 2,940
- C ₹ 5,880
- D ₹ 61,740
Show answer
Correct answer: (C) ₹ 5,880
Side = √1764 = 42 m, so the perimeter is 4 × 42 = 168 m. Cost = 168 × ₹ 35 = ₹ 5,880.
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Q.90
Which of the following is a rational number between 2/5 and 3/5?
- A 3/4
- B 7/20
- C 13/20
- D 11/20
Show answer
Correct answer: (D) 11/20
2/5 = 8/20 and 3/5 = 12/20, so 9/20, 10/20 and 11/20 lie between them. 7/20 is less than 2/5, while 13/20 and 3/4 = 15/20 are greater than 3/5.
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Q.91
In a test of 40 questions, 4 marks are given for each correct answer and 1 mark is deducted for each wrong answer. Ravi attempted all 40 questions and scored 95. How many of his answers were correct?
- A 13
- B 23
- C 27
- D 45
Show answer
Correct answer: (C) 27
If x answers are correct, 40 − x are wrong, so 4x − (40 − x) = 95, giving 5x = 135 and x = 27. Check: 27 × 4 − 13 = 108 − 13 = 95.
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Q.92
₹2,070 is divided between Asha and Bina in the ratio 4 : 5. How much does Bina get?
- A ₹414
- B ₹920
- C ₹1,035
- D ₹1,150
Show answer
Correct answer: (D) ₹1,150
Total parts = 4 + 5 = 9, and one part = 2070 ÷ 9 = ₹230. Bina gets 5 × 230 = ₹1,150 (Asha gets ₹920, and 920 + 1150 = 2070).
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Q.93
Which of the following ratios is the greatest?
- A 2 : 3
- B 5 : 7
- C 7 : 10
- D 11 : 15
Show answer
Correct answer: (D) 11 : 15
Write each as a fraction with denominator 210: 2/3 = 140/210, 5/7 = 150/210, 7/10 = 147/210 and 11/15 = 154/210. So 11 : 15 is the greatest.
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Q.94
A circular flower bed of radius 14 m is surrounded by a path 7 m wide. What is the area of the path? (Take π = 22/7.)
- A 154 m²
- B 616 m²
- C 770 m²
- D 1386 m²
Show answer
Correct answer: (C) 770 m²
Outer radius = 14 + 7 = 21 m. Area of the path = 22/7 × (21² − 14²) = 22/7 × (441 − 196) = 22/7 × 245 = 770 m².
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Q.95
Solve: 5x − 7 = 3x + 15.
- A 4
- B 11
- C 22
- D 2.75
Show answer
Correct answer: (B) 11
Move the x terms to one side and the numbers to the other: 5x − 3x = 15 + 7, so 2x = 22 and x = 11. Check: 55 − 7 = 48 = 33 + 15.
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Q.96
Lines AB and CD are parallel, with AB above CD, and B and D lie to the right of A and C. A point E lies between the two lines, to the right of segment AC. If angle BAE = 42° and angle DCE = 37°, what is angle AEC?
- A 5°
- B 79°
- C 101°
- D 281°
Show answer
Correct answer: (B) 79°
Draw a line through E parallel to AB. It splits angle AEC into two parts that are alternate angles to 42° and 37°, so angle AEC = 42° + 37° = 79°.
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Q.97
Consider the following statements. 1. The volume of a cylinder of radius r and height h is 2πrh. 2. The total surface area of a cube of edge a is 4a². Which of the statements is/are correct?
- A Only 1
- B Only 2
- C Both 1 and 2
- D Neither 1 nor 2
Show answer
Correct answer: (D) Neither 1 nor 2
The volume of a cylinder is πr²h; 2πrh is its curved surface area. A cube has 6 square faces, so its total surface area is 6a²; 4a² is only its lateral surface area. Both statements are false.
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Q.98
The ratio of 75 cm to 2 m, in its simplest form, is:
- A 3 : 8
- B 75 : 2
- C 8 : 3
- D 3 : 80
Show answer
Correct answer: (A) 3 : 8
Use the same unit first: 2 m = 200 cm, so the ratio is 75 : 200 = 3 : 8 (dividing both terms by 25).
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Q.99
Including a sales tax of 8%, a mixer costs ₹3,510. What was its price before the tax was added?
- A ₹3,250
- B ₹3,229
- C ₹3,502
- D ₹3,791
Show answer
Correct answer: (A) ₹3,250
The bill is 108% of the price, so price = 3510 × 100 ÷ 108 = ₹3,250 (check: 3250 + 8% of 3250 = 3250 + 260 = 3510). Taking 8% off ₹3,510 is wrong because the tax was charged on the lower price.
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Q.100
What is the LCM of 16, 28 and 40?
- A 1,120
- B 280
- C 560
- D 17,920
Show answer
Correct answer: (C) 560
16 = 2⁴, 28 = 2² × 7 and 40 = 2³ × 5. The LCM takes every prime with its highest power: 2⁴ × 5 × 7 = 560. 17,920 is just the product of the three numbers.
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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.