Pedagogy

CTET Maths MCQ with Answers, Paper 1 (Classes I-V)

222 practice questions on Mathematics, Classes I-V (Paper I) for CTET Paper I, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.

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1. Q.151

   Under a ration scheme, a family gets 35 kg of wheat at ₹ 2 per kg and 15 kg of rice at ₹ 3 per kg. How much does the family pay in all?

   1. A ₹ 115
   2. B ₹ 135
   3. C ₹ 150
   4. D ₹ 105
   Show answer

   Correct answer: (A) ₹ 115

   Wheat costs 35 × 2 = ₹ 70 and rice costs 15 × 3 = ₹ 45, so the family pays 70 + 45 = ₹ 115.

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2. Q.152

   If 12 pencils cost ₹ 66, what is the cost of 7 such pencils?

   1. A ₹ 38.50
   2. B ₹ 42.00
   3. C ₹ 35.00
   4. D ₹ 27.50
   Show answer

   Correct answer: (A) ₹ 38.50

   One pencil costs 66 ÷ 12 = ₹ 5.50, so 7 pencils cost 7 × 5.50 = ₹ 38.50. (₹ 27.50 is the cost of the other 5 pencils.)

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3. Q.153

   Four families share the ₹ 1,346 cost of repairing their hand pump equally. How much does each family pay?

   1. A ₹ 336.20
   2. B ₹ 336.00
   3. C ₹ 336.50
   4. D ₹ 337.00
   Show answer

   Correct answer: (C) ₹ 336.50

   1,346 ÷ 4 = 336 remainder 2, and ₹ 2 ÷ 4 = 50 paise, so each family pays ₹ 336.50. Check: 4 × 336.50 = 1,346. (₹ 336.20 wrongly writes the remainder 2 as 20 paise.)

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4. Q.154

   Each of the numbers 5 to 13 is placed once in a 3 × 3 magic square, so that every row, column and diagonal has the same sum. What is this sum?

   1. A 27
   2. B 81
   3. C 15
   4. D 24
   Show answer

   Correct answer: (A) 27

   5 + 6 + ... + 13 = 81, and the three rows share this total equally, so each row adds up to 81 ÷ 3 = 27. (It is the 1-to-9 square with 4 added to every number: 15 + 12 = 27.)

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5. Q.155

   How many grams are there in 3 kg 45 g?

   1. A 3045 g
   2. B 345 g
   3. C 3450 g
   4. D 30045 g
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   Correct answer: (A) 3045 g

   1 kg = 1000 g, so 3 kg = 3000 g and 3 kg 45 g = 3000 + 45 = 3045 g. Writing 345 g or 3450 g ignores the place value of the grams.

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6. Q.156

   Consider these statements about four-sided shapes:

   1. A shape with four equal sides is always a square.

   2. A shape with four right-angled corners is always a square.

   3. A square has four equal sides and four right-angled corners.

   Which of them are correct?

   1. A 3 only
   2. B 1 and 3 only
   3. C 2 and 3 only
   4. D 1, 2 and 3
   Show answer

   Correct answer: (A) 3 only

   A rhombus (a square pushed over) has four equal sides but no right angles, and a rectangle that is not a square has four right angles but unequal sides, so 1 and 2 are wrong. A square has both properties together, so only 3 is correct.

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7. Q.157

   What is the smallest two-digit number that leaves a remainder of 2 when divided by each of 3, 4 and 5?

   1. A 32
   2. B 62
   3. C 60
   4. D 58
   Show answer

   Correct answer: (B) 62

   The smallest common multiple of 3, 4 and 5 is 60, so the number is 60 + 2 = 62. Check: 62 = 3 × 20 + 2 = 4 × 15 + 2 = 5 × 12 + 2.

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8. Q.158

   Which of the following numbers is a multiple of both 4 and 6?

   1. A 84
   2. B 54
   3. C 68
   4. D 90
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   Correct answer: (A) 84

   84 = 4 × 21 = 6 × 14. 54 and 90 are multiples of 6 but not of 4, and 68 is a multiple of 4 but not of 6.

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9. Q.159

   Which unit is the most suitable for measuring the capacity of a teaspoon?

   1. A Litre
   2. B Millilitre
   3. C Kilogram
   4. D Millimetre
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   Correct answer: (B) Millilitre

   A teaspoon holds only about 5 mL, far less than 1 litre, so the millilitre is suitable. Kilogram measures weight and millimetre measures length.

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10. Q.160

    How many times is the digit 1 written when all the numbers from 1 to 50 are written?

    1. A 14
    2. B 11
    3. C 10
    4. D 15
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    Correct answer: (D) 15

    In the ones place, 1 appears in 1, 11, 21, 31 and 41 (5 times); in the tens place, in 10 to 19 (10 times). Total = 5 + 10 = 15, since 11 has the digit twice.

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11. Q.161

    A rectangular garden is 25 m long and 15 m wide. Fencing costs ₹40 per metre. What is the cost of fencing it all around?

    1. A ₹1,600
    2. B ₹2,600
    3. C ₹3,200
    4. D ₹15,000
    Show answer

    Correct answer: (C) ₹3,200

    Perimeter = 2 × (25 + 15) = 80 m, so cost = 80 × ₹40 = ₹3,200. Using the area (375 sq m) instead gives the wrong ₹15,000.

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12. Q.162

    The ones digits of the multiples of 4 (4, 8, 12, 16, 20, 24, ...) repeat in a fixed cycle. Which is that cycle?

    1. A 4, 8, 2, 6
    2. B 2, 4, 6, 8, 0
    3. C 4, 8, 12, 16, 20
    4. D 4, 8, 2, 6, 0
    Show answer

    Correct answer: (D) 4, 8, 2, 6, 0

    The ones digits are 4, 8, 2, 6, 0 and then 4 (24), 8 (28), 2 (32), 6 (36), 0 (40) again, so the cycle 4, 8, 2, 6, 0 repeats every five multiples.

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13. Q.163

    In a cricket innings, a batter hits 9 fours and 3 sixes, and makes 27 more runs by running between the wickets. How many runs did the batter score?

    1. A 81 runs
    2. B 93 runs
    3. C 39 runs
    4. D 54 runs
    Show answer

    Correct answer: (A) 81 runs

    Fours give 9 × 4 = 36 runs and sixes give 3 × 6 = 18 runs; 36 + 18 + 27 = 81 runs. (39 just adds 9 + 3 + 27.)

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14. Q.164

    What is the next number in the pattern 1, 3, 7, 15, 31, ...?

    1. A 63
    2. B 47
    3. C 62
    4. D 61
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    Correct answer: (A) 63

    Each number is double the previous one plus 1 (3 = 2 × 1 + 1, 7 = 2 × 3 + 1, ...), so the next is 2 × 31 + 1 = 63. The differences 2, 4, 8, 16 also double, and 31 + 32 = 63.

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15. Q.165

    Identical tiles of which of these shapes can NOT cover a flat floor completely, without gaps or overlaps?

    1. A Square
    2. B Equilateral triangle
    3. C Regular hexagon
    4. D Regular pentagon
    Show answer

    Correct answer: (D) Regular pentagon

    Around a point the corners must make a full turn (360°): 4 squares (4 × 90°), 6 equilateral triangles (6 × 60°) or 3 regular hexagons (3 × 120°) fit exactly. A regular pentagon's corner is 108°, so 3 leave a gap (324°) and 4 overlap (432°).

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16. Q.166

    Two bells ring every 8 minutes and every 12 minutes respectively. If they ring together at 9:00 a.m., when will they next ring together?

    1. A 10:36 a.m.
    2. B 9:24 a.m.
    3. C 9:20 a.m.
    4. D 9:48 a.m.
    Show answer

    Correct answer: (B) 9:24 a.m.

    Multiples of 8: 8, 16, 24, ...; multiples of 12: 12, 24, ... The smallest common multiple is 24, so they ring together again 24 minutes later, at 9:24 a.m.

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17. Q.167

    On a calendar page, a 3 × 3 square of dates (3 rows of 3 dates) is marked. If the date in the centre of the square is 18, what is the sum of all nine dates?

    1. A 153
    2. B 171
    3. C 144
    4. D 162
    Show answer

    Correct answer: (D) 162

    The dates are 10, 11, 12; 17, 18, 19; 24, 25, 26. Each pair opposite the centre (such as 10 and 26, or 11 and 25) adds up to 36 = 2 × 18, so the total is 9 × 18 = 162.

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18. Q.168

    A few drops of ink are put on one half of a sheet of paper. The sheet is folded along a straight line, pressed and then opened. Which statement about the ink pattern on the opened sheet is true?

    1. A The fold is a line of symmetry of the pattern
    2. B The pattern has no line of symmetry at all
    3. C Its lines of symmetry lie only along the diagonals of the sheet
    4. D The pattern has exactly four lines of symmetry
    Show answer

    Correct answer: (A) The fold is a line of symmetry of the pattern

    Pressing prints each drop on the other half as its mirror image, at the same distance from the fold. So the two halves match exactly when folded, and the fold is a line of symmetry of the pattern.

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19. Q.169

    Sita has a ribbon 5 m long. She cuts 4 pieces from it, each 85 cm long. How much ribbon is left?

    1. A 4 m 15 cm
    2. B 3 m 40 cm
    3. C 1 m 60 cm
    4. D 1 m 40 cm
    Show answer

    Correct answer: (C) 1 m 60 cm

    4 × 85 cm = 340 cm = 3 m 40 cm is used. 5 m = 500 cm, so 500 - 340 = 160 cm = 1 m 60 cm (1.60 m) is left.

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20. Q.170

    A closed shape is made of exactly one straight line and one curved line. Which of these could it be?

    1. A A circle
    2. B A triangle
    3. C A rectangle
    4. D A semicircle
    Show answer

    Correct answer: (D) A semicircle

    A semicircle is closed by its diameter (one straight line) and the half-circle arc (one curved line). A circle has only a curved line, while a triangle and a rectangle have only straight lines.

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21. Q.171

    A rangoli border repeats the unit flower, leaf, leaf, dot, dot, dot again and again. How many leaves are there among the first 50 shapes of the border?

    1. A 16 leaves
    2. B 17 leaves
    3. C 18 leaves
    4. D 25 leaves
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    Correct answer: (B) 17 leaves

    One unit has 6 shapes with 2 leaves. 50 = 8 × 6 + 2, so 8 full units give 16 leaves, and the next 2 shapes (flower, leaf) add 1 more: 17 leaves.

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22. Q.172

    A family buys 2 litres of milk every day at ₹ 56 per litre. What is their milk bill for the month of June?

    1. A ₹ 1,680
    2. B ₹ 3,360
    3. C ₹ 3,472
    4. D ₹ 3,136
    Show answer

    Correct answer: (B) ₹ 3,360

    June has 30 days. Milk bought = 2 × 30 = 60 litres, and 60 × 56 = ₹ 3,360. (₹ 3,472 wrongly takes 31 days.)

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23. Q.173

    School starts at 7:50 a.m. There are 6 periods of 40 minutes each, with a 20-minute break after the 3rd period. At what time does the 6th period end?

    1. A 11:50 a.m.
    2. B 12:30 p.m.
    3. C 11:30 a.m.
    4. D 12:10 p.m.
    Show answer

    Correct answer: (D) 12:10 p.m.

    Time taken = 6 × 40 + 20 = 260 minutes = 4 h 20 min. 7:50 a.m. + 4 h 20 min = 12:10 p.m. (11:50 a.m. forgets the break.)

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24. Q.174

    Meena had 60 marbles. She gave 1/4 of them to Ravi and then 1/3 of the remaining marbles to Gita. How many marbles does Meena have now?

    1. A 30 marbles
    2. B 25 marbles
    3. C 35 marbles
    4. D 45 marbles
    Show answer

    Correct answer: (A) 30 marbles

    1/4 of 60 = 15 go to Ravi, leaving 45. 1/3 of 45 = 15 go to Gita, leaving 45 - 15 = 30. Taking 1/3 of 60 instead of 1/3 of the remainder gives the wrong answer 25.

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25. Q.175

    The hour hand of a clock is exactly halfway between 7 and 8, and the minute hand points at 6. What time is it?

    1. A 7:06
    2. B 7:30
    3. C 8:30
    4. D 6:35
    Show answer

    Correct answer: (B) 7:30

    The minute hand at 6 means 30 minutes past the hour. The hour hand halfway between 7 and 8 means it is half past 7, i.e. 7:30.

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26. Q.176

    In which of these years does February have 29 days?

    1. A 2026
    2. B 2027
    3. C 2028
    4. D 2030
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    Correct answer: (C) 2028

    February has 29 days in a leap year, which, apart from century years such as 1900, is a year exactly divisible by 4. 2028 ÷ 4 = 507, while 2026, 2027 and 2030 are not divisible by 4.

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27. Q.177

    Seema buys 20 kg of tomatoes at ₹ 30 per kg. 2 kg get spoilt, and she sells the rest at ₹ 36 per kg. What is the result?

    1. A A profit of ₹ 120
    2. B A loss of ₹ 48
    3. C A profit of ₹ 48
    4. D A profit of ₹ 108
    Show answer

    Correct answer: (C) A profit of ₹ 48

    Cost = 20 × 30 = ₹ 600. She sells 18 kg for 18 × 36 = ₹ 648. Profit = 648 − 600 = ₹ 48.

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28. Q.178

    A shopkeeper packs 18 kg 600 g of peanuts into packets of 300 g each and sells every packet for ₹ 27. How much money does he get for all the packets?

    1. A ₹ 1,620
    2. B ₹ 502.20
    3. C ₹ 167.40
    4. D ₹ 1,674
    Show answer

    Correct answer: (D) ₹ 1,674

    18 kg 600 g = 18,600 g, and 18,600 ÷ 300 = 62 packets. Money = 62 × 27 = 1,620 + 54 = ₹ 1,674. (₹ 1,620 ignores the 600 g.)

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29. Q.179

    Which of the following products is the greatest?

    1. A 49 × 81
    2. B 4 × 999
    3. C 40 × 99
    4. D 400 × 9
    Show answer

    Correct answer: (B) 4 × 999

    4 × 999 = 3,996, 40 × 99 = 3,960, 400 × 9 = 3,600 and 49 × 81 = 3,969. So 4 × 999 is the greatest.

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30. Q.180

    Which of the following arranges 5/9, 2/9, 7/9 and 4/9 in ascending order?

    1. A 7/9, 5/9, 4/9, 2/9
    2. B 2/9, 5/9, 4/9, 7/9
    3. C 4/9, 2/9, 5/9, 7/9
    4. D 2/9, 4/9, 5/9, 7/9
    Show answer

    Correct answer: (D) 2/9, 4/9, 5/9, 7/9

    All four are like fractions (same denominator 9), so the one with the smaller numerator is smaller: 2 < 4 < 5 < 7 gives 2/9, 4/9, 5/9, 7/9.

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31. Q.181

    A school orders 38 boxes of chalk with 62 sticks in each box. Rounding each number to the nearest ten, what is the estimated total number of sticks?

    1. A 2,800
    2. B 2,400
    3. C 2,356
    4. D 1,800
    Show answer

    Correct answer: (B) 2,400

    38 rounds to 40 and 62 rounds to 60, so the estimate is 40 × 60 = 2,400. The exact product 38 × 62 = 2,356 is close to it, but it is not the estimate asked for.

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32. Q.182

    Which of the following shows the distributive property of multiplication over addition?

    1. A 23 × 15 = 15 × 23
    2. B (23 × 5) × 3 = 23 × (5 × 3)
    3. C 23 × 15 × 1 = 23 × 15
    4. D 23 × 15 = 23 × 10 + 23 × 5
    Show answer

    Correct answer: (D) 23 × 15 = 23 × 10 + 23 × 5

    Splitting 15 into 10 + 5 and multiplying 23 by each part is the distributive property: 230 + 115 = 345 = 23 × 15. The others show the commutative, associative and identity properties.

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33. Q.183

    Which of the following statements is NOT true?

    1. A The sum of an odd number and an even number is always even
    2. B The sum of two odd numbers is always even
    3. C The product of an even number and an odd number is always even
    4. D The product of two odd numbers is always odd
    Show answer

    Correct answer: (A) The sum of an odd number and an even number is always even

    Odd + even is always odd, e.g. 7 + 4 = 11. The other three statements are true: 7 + 5 = 12, 4 × 7 = 28 and 3 × 7 = 21.

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34. Q.184

    Which of the following numbers is NOT a multiple of 9?

    1. A 171
    2. B 316
    3. C 243
    4. D 405
    Show answer

    Correct answer: (B) 316

    171 = 9 × 19, 243 = 9 × 27 and 405 = 9 × 45, but 316 ÷ 9 = 35 remainder 1. Digit sums agree: 1+7+1 = 9, 2+4+3 = 9, 4+0+5 = 9, but 3+1+6 = 10.

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35. Q.185

    In a Class 5 survey, 12 children like kabaddi, twice as many like cricket, and 7 fewer than the cricket group like football. Each child chose one game. How many children were surveyed?

    1. A 41 children
    2. B 60 children
    3. C 67 children
    4. D 53 children
    Show answer

    Correct answer: (D) 53 children

    Kabaddi 12, cricket 2 × 12 = 24, football 24 − 7 = 17; total = 12 + 24 + 17 = 53 children.

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36. Q.186

    Observe the pattern: 11 × 11 = 121 and 111 × 111 = 12321. What is 1111 × 1111?

    1. A 123321
    2. B 12344321
    3. C 1234421
    4. D 1234321
    Show answer

    Correct answer: (D) 1234321

    The digits rise from 1 up to the number of 1s in each factor and then fall back, so four 1s give 1234321. Check: 11,11,000 + 1,11,100 + 11,110 + 1,111 = 12,34,321.

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37. Q.187

    Which solid has no flat face, no edge and no corner?

    1. A Cone
    2. B Cylinder
    3. C Cube
    4. D Sphere
    Show answer

    Correct answer: (D) Sphere

    A sphere, like a ball, has only one curved surface, so it has no flat face, no edge and no corner. A cone and a cylinder have flat faces and edges, and a cube has 6 faces, 12 edges and 8 corners.

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38. Q.188

    Which of the following is NOT equal to ₹ 5?

    1. A Two ₹ 2 coins and three 50-paise coins
    2. B 500 paise
    3. C Ten 50-paise coins
    4. D One ₹ 2 coin, two ₹ 1 coins and two 50-paise coins
    Show answer

    Correct answer: (A) Two ₹ 2 coins and three 50-paise coins

    Two ₹ 2 coins and three 50-paise coins make ₹ 4 + ₹ 1.50 = ₹ 5.50. The others are 500 paise = ₹ 5, 10 × 50 paise = ₹ 5 and ₹ 2 + ₹ 2 + ₹ 1 = ₹ 5.

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39. Q.189

    Which of the following fractions is greater than 1/2?

    1. A 6/11
    2. B 3/7
    3. C 4/9
    4. D 5/11
    Show answer

    Correct answer: (A) 6/11

    A fraction is more than 1/2 when twice its numerator is more than its denominator. 2 × 6 = 12 > 11, but 2 × 3 = 6 < 7, 2 × 4 = 8 < 9 and 2 × 5 = 10 < 11.

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40. Q.190

    In a 3 × 3 magic square using the numbers 1 to 9, the top row is 4, 9, 2 and the middle row is 3, 5, 7. What is the bottom row, from left to right?

    1. A 1, 8, 6
    2. B 8, 1, 6
    3. C 6, 1, 8
    4. D 8, 6, 1
    Show answer

    Correct answer: (B) 8, 1, 6

    Every row, column and diagonal must add up to 15. Columns: 15 - (4 + 3) = 8, 15 - (9 + 5) = 1, 15 - (2 + 7) = 6. The diagonals check: 4 + 5 + 6 = 15 and 2 + 5 + 8 = 15.

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41. Q.191

    How many minutes are there from 9:35 a.m. to 11:10 a.m.?

    1. A 95 minutes
    2. B 85 minutes
    3. C 135 minutes
    4. D 175 minutes
    Show answer

    Correct answer: (A) 95 minutes

    9:35 to 10:35 is 60 minutes and 10:35 to 11:10 is 35 minutes, so 95 minutes in all. Working out 1110 − 935 = 175 wrongly treats an hour as 100 minutes.

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42. Q.192

    A square handkerchief has an area of 64 sq cm. What is its perimeter?

    1. A 16 cm
    2. B 32 cm
    3. C 64 cm
    4. D 256 cm
    Show answer

    Correct answer: (B) 32 cm

    8 × 8 = 64, so each side is 8 cm and the perimeter = 4 × 8 = 32 cm. Taking 64 ÷ 4 = 16 as the answer mixes up area and perimeter.

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43. Q.193

    Trees planted in a week: Monday 14, Tuesday 22, Wednesday 9, Thursday 17, Friday 26. Consider: 1. Friday's number equals Wednesday's and Thursday's together. 2. Twice as many trees were planted on Tuesday as on Monday. Which is correct?

    1. A Only 1
    2. B Only 2
    3. C Both 1 and 2
    4. D Neither 1 nor 2
    Show answer

    Correct answer: (A) Only 1

    9 + 17 = 26, so statement 1 is true. Twice Monday's number is 2 × 14 = 28, not 22, so statement 2 is false.

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44. Q.194

    Which of the following shows the numbers 45,909; 49,059; 45,099 and 45,990 in ascending order?

    1. A 45,909 < 45,099 < 45,990 < 49,059
    2. B 45,099 < 45,990 < 45,909 < 49,059
    3. C 45,099 < 45,909 < 49,059 < 45,990
    4. D 45,099 < 45,909 < 45,990 < 49,059
    Show answer

    Correct answer: (D) 45,099 < 45,909 < 45,990 < 49,059

    All four have 4 ten-thousands; 49,059 has 9 thousands, so it is the largest. Among the rest, 45,099 has 0 hundreds, so it is the smallest, and 45,909 < 45,990 because 0 tens < 9 tens.

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45. Q.195

    In a 10 × 10 multiplication chart (rows and columns 1 to 10), which of these numbers appears exactly once?

    1. A 36
    2. B 16
    3. C 49
    4. D 40
    Show answer

    Correct answer: (C) 49

    49 appears only as 7 × 7. 36 appears 3 times (4 × 9, 6 × 6, 9 × 4), 16 appears 3 times (2 × 8, 4 × 4, 8 × 2) and 40 appears 4 times (4 × 10, 5 × 8, 8 × 5, 10 × 4).

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46. Q.196

    In a standard seven-piece tangram, the two small triangles placed together can exactly make the shape of each of the following pieces EXCEPT:

    1. A The square piece
    2. B The medium triangle
    3. C The parallelogram
    4. D A large triangle
    Show answer

    Correct answer: (D) A large triangle

    Each small triangle is 1/16 of the tangram, so the two make 1/8, the same as the square, the medium triangle and the parallelogram, and they can be arranged into each of these. A large triangle is 1/4 of the tangram, twice as big, so two small triangles cannot make it.

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47. Q.197

    Asha ate half of one-quarter of a cake. What fraction of the whole cake did she eat?

    1. A 2/6
    2. B 1/8
    3. C 1/6
    4. D 3/4
    Show answer

    Correct answer: (B) 1/8

    One-quarter of the cake is 1/4; half of it is 1/4 ÷ 2 = 1/8, since 8 such pieces make the whole cake. 3/4 (1/2 + 1/4) and 2/6 come from adding instead of taking a part of a part.

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48. Q.198

    Seven friends share ₹ 2,856 equally. How much does each friend get?

    1. A ₹ 408
    2. B ₹ 48
    3. C ₹ 480
    4. D ₹ 418
    Show answer

    Correct answer: (A) ₹ 408

    28 hundreds ÷ 7 = 4 hundreds; 5 tens ÷ 7 = 0 tens, with 5 tens left; 56 ÷ 7 = 8. So each gets ₹ 408 (check: 408 × 7 = 2,856).

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49. Q.199

    A team needs a total of 240 runs to win a 50-over match. After 30 overs it has scored 150 runs. On average, how many runs per over must it score in the remaining overs?

    1. A 5 runs per over
    2. B 4.5 runs per over
    3. C 3 runs per over
    4. D 4.8 runs per over
    Show answer

    Correct answer: (B) 4.5 runs per over

    Runs still needed = 240 − 150 = 90 and overs left = 50 − 30 = 20, so 90 ÷ 20 = 4.5 runs per over. (5 is the rate so far, 150 ÷ 30.)

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50. Q.200

    Tiles are laid in a row in the pattern blue, white, white, blue, white, white, blue, ... The row begins and ends with a blue tile and has 22 blue tiles. How many white tiles are there?

    1. A 44 tiles
    2. B 40 tiles
    3. C 66 tiles
    4. D 42 tiles
    Show answer

    Correct answer: (D) 42 tiles

    There are 2 white tiles between each pair of neighbouring blue tiles. 22 blue tiles make 21 gaps, so there are 21 × 2 = 42 white tiles.

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